Stefan Wirtz Vom Fachbereich VI (Geographie/Geowissenschaften ...

Stefan Wirtz 

Vom Fachbereich VI 

(Geographie/Geowissenschaften) 

der Universität Trier 

zur Verleihung des akademischen Grades 

Doktor der Naturwissenschaften (Dr. rer. nat.) 

genehmigte Dissertation 

Experimentelle Rinnenerosionsforschung vs. 

Modellkonzepte – Quantifizierung der 

hydraulischen und erosiven Wirksamkeit von 

Rinnen 

Betreuende: 

Prof. Dr. Johannes B. Ries 

Prof. Dr. Jean F. Wagner 

Datum der wissenschaftlichen Aussprache: 

28. Januar 2013 

Trier, 2013

Stefan Wirtz 

Vom Fachbereich VI 

(Geographie/Geowissenschaften) 

der Universität Trier 

zur Verleihung des akademischen Grades 

Doktor der Naturwissenschaften (Dr. rer. nat.) 

genehmigte Dissertation 

Experimentelle Rinnenerosionsforschung 

vs. Modellkonzepte – Quantifizierung der 

hydraulischen und erosiven Wirksamkeit 

von Rinnen 

Betreuende: 

Prof. Dr. Johannes B. Ries 

Prof. Dr. Jean F. Wagner 

Datum der wissenschaftlichen Aussprache: 

28. Januar 2013 

Trier, 2013

Danksagung 

Danksagung 

Die vorliegende Arbeit wäre ohne die Unterstützung von vielen mehr oder weniger 

freiwilligen Helfern so nicht zustande gekommen. Daher möchte ich mich bei allen bedanken, 

die zum Erfolg (hoffentlich…) des Projektes „Dr. rer. nat.“ beigetragen haben. Das 

Endergebnis lag bei Redaktionsschluss noch nicht vor. 

Herr Prof. Dr. J.B. Ries: Er hat nicht nur die Betreuung der Arbeit übernommen, sondern 

das Interesse für das Thema „Bodenerosion“ bei mir überhaupt erst geweckt. Außerdem 

ermöglichte er mir die Teilnahme an vielen interessanten Geländeaufenthalten. Zusätzlich hat 

er alles Menschen(un)mögliche unternommen, um Geldtöpfe aufzutreiben, die es eigentlich 

gar nicht gab. Dies ermöglichte 1) die Anschaffung von Materialien und Geräten für die 

Versuche und 2) dem Autor dieser Arbeit die regelmäßige Nahrungsaufnahme. 

Herr Prof. Dr. J.F. Wagner: Er hat sich nach der Diplomarbeit sofort bereiterklärt, auch die 

Zweitbetreuung der Dissertation zu übernehmen, obwohl das Thema nicht direkt etwas mit 

seinem Arbeitsgebiet zu tun hat. Trotzdem verfolgte er die Fortschritte der Arbeit immer mit 

großem Interesse und war zudem an der Erstellung von mehreren Artikeln direkt beteiligt. 

Dr. M. Seeger: Er hat den „Rinnenerosions-Stein“ 2005 mit einem denkwürdigen Zitat ins 

Rollen gebracht und trotz seiner zwischenzeitlichen Versetzung nach Holland immer noch die 

Zeit gefunden, zu diskutieren, Artikel mitzuschreiben und mich auf seine diplomatische Art 

notfalls wieder in die richtige Bahn zu treten. Ach ja, das denkwürdige Zitat: „Wir schütten 

oben mal Wasser rein und schauen, was so passiert!“ Hier, das ist passiert! Ausgeartet in eine 

Doktorarbeit. 

Alex, Sabrina, René, Sarah, Thomas, Miriam, Verena, Gilles, Chrissi, Bastienne, Britta: 

Sie haben viel Zeit und Geld investiert, um bei einer, zwei, drei oder sogar allen vier 

Geländephasen dabei zu sein und den Versuchsaufbau immer besser, schneller und noch 

besser zu machen, die Verpflegung sicherzustellen und Poster und/oder Artikel mit zu 

verfassen. Leider war nie genug Geld da, um alle Ideen umzusetzen. Bis jetzt… 

Die Studentinnen und Studenten der Lehrforschungsprojekte: Es waren diese (nicht 

immer) freiwilligen Helfer, die die Versuche im Rahmen von Lehrforschungsprojekten 

ermöglicht haben. Ohne sie wären wahrscheinlich nur wenige Experimente gelaufen. Sie 

I

Danksagung 

mussten mich und meine diplomatische Art jeweils 14 Tage auf dem Campingplatz in Freila 

ertragen, manche sogar zweimal. Einige reden sogar noch mit mir. 

Herr Prof. Dr. C. Wagner und Dr. A. Zell von der Abteilung für Technische Physik an der 

Universität in Saarbrücken. Sie stellten mir die Laboreinrichtungen kostenfrei zur Verfügung 

und unterstützten mich bei den Versuchen. Als Belohnung gab es jeweils Co-Autorenschaften 

auf einem Artikel und mehreren Postern. 

Die Mitarbeiter der Physischen Geographie: Sie haben durch technische Unterstützung, 

Hilfe bei bürokratischen Problemen oder durch wichtige und gute Vorschläge und Ideen die 

Arbeit unterstützt. Grüße an Harry Willger. 

Alle Korrekturleser und Reviewer: Neben schon oben genannten Personen seien hier noch 

zusätzlich Olli Gronz, Dr. Christoph Müller, Dr. Marco Hümann, Christoph Paulußen, Dr. 

Birgit Kausch und Frank Wirtz erwähnt. Die Kommentare und Kritiken haben die Qualität der 

Arbeit deutlich verbessert. 

Meine Eltern: Sie unterstützten mich während des gesamten Studiums. Außerdem mussten 

sie immer wieder als „Probe-Auditorium“ für Vorträge herhalten. Jede Hausarbeit sowie die 

Diplomarbeit und diese Dissertation wurden auf das Sorgfältigste korrekturgelesen. 

Dr. A. Keller und Alexander Weber: Ohne die Trainingseinheiten wäre die Arbeit nie fertig 

geworden. Klingt komisch, ist aber so. Sportverrückte wissen, was ich meine. Ach ja, da 

waren auch noch die Bildungsreisen nach Namibia, Jordanien und in die DomRep (Ja, auch 

das war eine Bildungsreise!!), die den Motivations-Akku regelmäßig aufgeladen haben. 

Moncho aus Aisa: Er hat dafür gesorgt, dass die Gamaschengang im Arnástal nicht erfroren 

und/oder verhungert ist. Die ca. 100.000 Kalorien pro Person und Tag kredenzt in der 

praktischen „Rohrbombenform“ waren knapp aber ausreichend. 

Die Liste erhebt keinen Anspruch auf Vollständigkeit, eine Nicht-Erwähnung ist aber nicht 

böse gemeint! 

II

Inhaltsverzeichnis 


Kurzfassung 1 

1. Experimentelle Rinnenerosionsforschung vs. Modellkonzepte – 

Quantifizierung der hydraulischen und erosiven Wirksamkeit von Rinnen 

3 

1.1 Einleitung 3 

1.2 Experimente zur Rinnenerosion 8 

1.3 Rinnen als Abflusssammler 12 

1.4 Rinnen als Sedimentquelle 13 

1.5 Prozesse in der Rinne 15 

1.6 Messen oder Modellieren 19 

1.7 Weitere Anwendungen 24 

1.8 Zusammenfassung und Ausblick 26 

Quellenangaben 32 

2. Wirtz, S., Iserloh, T., Rock, G., Hansen, R., Marzen, M., Seeger, M., Betz, 

S., Remke, A., Wengel, R., Butzen, V., Ries, J.B. (2012b): Soil erosion on 

abandoned land in Andalusia – a comparison of interrill– and rill erosion 

rates. ISRN Soil Science, doi: 10.5402/2012/730870. 

38 

3. Wirtz, S., Seeger, M., Ries, J.B. (2010): The rill experiment as a method to 

approach a quantification of rill erosion process activity. Zeitschrift für 

Geomorphologie 54 (1), 47-64. 

70 

4. Wirtz, S., Seeger, M., Ries, J.B. (2012a): Field experiments for 

understanding and quantification of rill erosion processes. Catena 91, 21-34. 

96 

5. Wirtz, S., Seeger, M., Remke, A., Wengel, R., Wagner, J.-F., Ries, J.B. 

(2013): Do deterministic sediment detachment and transport equations 

adequately represent process-interactions in eroding rills? An experimental 

field study. Catena 101, 61-78 

131 

III


6. Wirtz, S., Seeger, M., Zell, A., Wagner, C., Wagner, J.-F., Ries, J.B. (subm. 

2012): Applicability of different hydraulic parameters to describe soil 

detachment in eroding rills. PLoSOne. 

178 

7. Ries, J.B., Andres, K., Wirtz, S., Tumbrink, J., Wilms, T., Peter, K.D., 

Burczyk, M., Butzen, V., Seeger, M. (subm. 2011): Sheep and goat erosion – 

experimental geomorphology as an approach for the quantification of 

underestimated processes. Zeitschrift für Geomorphologie. 

224 

Wissenschaftlicher Werdegang 257 

Lebenslauf 258 

IV


Abbildungsverzeichnis 

Abbildung 1: Zusammenhänge zwischen den einzelnen Artikeln 7 

Abbildung 2: Veränderungen in der Methode „Spülversuch“ 12 

Abbildung 3: Idealtypischer Verlauf der Sedimentkonzentration bei Transport von 17 

losem Material 

Abbildung 4: Idealtypischer Verlauf der Sedimentkonzentration bei Einschneiden in 17 

die Rinnensohle 

Abbildung 5: Idealtypischer Verlauf der Sedimentkonzentration bei 

18 

Massenbewegungen an Stufen und Seitenwänden 

Abbildung 6: Quotient aus transport rate und transport capacity 20 

Abbildung 7: Quotient aus transport rate und transport capacity 20 

Abbildung 8: Relativer Messfehler verschiedener Parameter 22 

Abbildung 9: Empirischer Variationskoeffizient verschiedener Parameter 22 

Abbildung 10: Runoff-Koeffizienten auf Waldwegen 25 

Abbildung 11: Abtragswerte auf Waldwegen 26 

Abbildung 12: Drehkrankonstruktion 29 

Tabellenverzeichnis 

Tabelle 1: Englische Begriffe im Text 8 

Tabelle 2: Entwicklung der Spülversuche 11 

V

Experimentelle Rinnenerosionsforschung vs. Modellkonzepte – Quantifizierung der hydraulischen und erosiven Wirksamkeit von Rinnen 

Kurzfassung 

In der Bodenerosion zählen Rinnen zu den wirksamsten Formen: Sie stellen bevorzugte 

Fließwege für den Oberflächenabfluss dar und werden dadurch zu den ergiebigsten 

Sedimentquellen innerhalb eines Einzugsgebietes. Allerdings ist umstritten, wie hoch ihr 

Anteil an der Abtragsdynamik eines Gebietes im Vergleich zu anderen 

Bodenerosionsprozessen tatsächlich ist. Voraussetzung für die Bearbeitung dieser Thematik 

ist eine Vereinheitlichung der Messmethodik zur Quantifizierung der Erosion in Rinnen. Nur 

mittels einer reproduzierbaren Messung können Ergebnisse aus verschiedenen Studien 

miteinander verglichen und zu einem Gesamtergebnis synthetisiert werden. Im Bereich der 

Rinnenerosion ist eine solche messmethodische Standardisierung bisher nicht gegeben. 

Aus diesem Grund besteht das erste Ziel der vorliegenden Arbeit darin, einen 

Versuchsaufbau zu entwerfen, der es ermöglicht, unter reproduzierbaren Bedingungen 

vergleichbare Daten zur Prozessdynamik in Rinnen zu gewinnen. Die schrittweise 

Weiterentwicklung der Methode „Spülversuch“ spiegelt sich in den verschiedenen Versionen 

wider. Dabei werden jeweils Fehler und Probleme der vorherigen Version beseitigt, sodass 

eine stetige Optimierung stattfindet. Mithilfe der Spülversuche sowie zusätzlicher 

Beregnungssimulationen und geomorphologischer Kartierungen wird als zweites Ziel 

überprüft, wie hoch die Abflusseffektivität der Rinnen in einem Einzugsgebiet und als drittes 

Ziel wie hoch der Anteil der Rinnenerosion an der Gesamt-Erosionsdynamik ist. Hierbei zeigt 

sich eine hohe Variabilität: So weisen in einem Kleineinzugsgebiet in den spanischen 

Pyrenäen die Proben aus den untersuchten Rinnen zwar nur geringe Sedimentkonzentrationen 

auf, verglichen mit dem gesamten Einzugsgebiet zeigt sich jedoch die hohe Effektivität, mit 

der trotz Mangel an erodierbarem Material das wenige in den Versuchen eingeleitete Wasser 

in den Rinnen wirkt. In einem Gully-Einzugsgebiet in Andalusien weisen Rinnen eine 20-60- 

fach höhere Abtragsrate als die interrill-Bereiche auf. Die 0,25 % Rinnenfläche entwässert 

20 % dieses Gebietes. Deutlich erkennbar ist, dass nicht ein einzelner Prozess das 

Sedimentmaterial bereitstellt, vielmehr laufen in der Rinne verschiedene Prozesse mit großer 

räumlicher und zeitlicher Variabilität ab. Die Identifizierung und Quantifizierung der 

verschiedenen Prozesse kann als viertes Ziel der vorliegenden Arbeit angesehen werden. Es 

ist zu erkennen, dass bis zu 60 % der Prozesse, die Sediment mobilisieren, nicht durch 

hydraulische Parameter bestimmt sondern eher gravitativ gesteuert sind. Neben der 

hydraulisch gesteuerten Einschneidung in die Rinnensohle wird Material durch den 

Zusammenbruch von Seitenwänden und durch die rückschreitende Erosion an Stufen 

1


bereitgestellt. Ebenso wird lose in der Rinne liegendes Material abtransportiert. Die im Zuge 

dieser Arbeit ermittelten Werte beruhen auf experimentell im Gelände erhobenen Daten. 

Viele Publikationen veröffentlichen dagegen Abtrags- und Abflusswerte, die mit Hilfe von 

Modellen erzeugt worden sind. Den Bearbeitern fehlt oftmals ein Hintergrundwissen zu den 

spezifischen Gebietseigenschaften, welches nur durch vor Ort erworbene Geländekenntnisse 

erreicht werden kann. Die Ergebnisse solcher Modellrechnungen weisen oftmals eine 

unbefriedigende Qualität auf. Vergleiche von Modellergebnissen mit experimentell erhobenen 

Daten zeigen, dass die berechneten Werte deutlich von den Messwerten abweichen. Die 

verwendeten Modelle basieren auf bestimmten physikalischen Grundannahmen. Aufgrund der 

oftmals schlechten Ergebnisqualität von Bodenerosionsmodellen werden als fünftes Ziel 

diese physikalischen Grundannahmen mithilfe der Spülversuche überprüft. Dabei zeigt sich 

deutlich, dass ganz grundlegende Probleme auftreten können. So weisen viele der während 

der Spülversuche entnommenen Proben eine höhere Materialmenge auf, als dies aufgrund der 

hydraulischen Gegebenheiten nach gängigen Modellannahmen möglich sein sollte. Auch der 

in Modellen angenommene lineare Zusammenhang zwischen hydraulischen Parametern und 

Abtragswerten ist in den Ergebnissen der Geländeexperimente nicht zu erkennen. Es stellt 

sich die Frage, woran dies liegen könnte. Durch die Interaktion verschiedener Prozesse ist es 

nicht möglich, diese mithilfe eines einzelnen Parameters sinnvoll zu beschreiben. Als 

problematisch erweist sich auch, dass die Berechnung einzelner hydraulischer Parameter sehr 

uneinheitlich gehandhabt wird: Je nach Literaturangabe werden unterschiedliche Faktoren zur 

Berechnung herangezogen. Grundlage der Herleitung vieler hydraulischer Parameter ist dabei 

die Navier-Stokes-Gleichung, deren Gültigkeit allerdings bis heute weder bewiesen noch 

widerlegt ist. Als Ziel Sechs der Arbeit wird geprüft, in wieweit die Methode „Spülversuch“ 

zur Bearbeitung weiterer Fragestellungen im Bereich der Bodenerosion eingesetzt werden 

kann. Insgesamt zeigen die Ergebnisse der Spülversuche, wie wichtig es ist, experimentelle 

Daten im Gelände, also unter möglichst natürlichen Bedingungen, zu erheben. Nur auf diese 

Weise kann das Grundlagenwissen so weit verbessert werden, dass die Erstellung eines in der 

Praxis anwendbaren Bodenerosionsmodells überhaupt in den Bereich des Möglichen rückt. 

Dabei müssen jedoch die räumliche und zeitliche Variabilität sowie die verschiedenen 

Kombinationen der einzelnen Prozesse berücksichtigt werden. Die Abbildung natürlicher 

Prozesse mittels einfacher statischer mathematischer Formeln erscheint nach den Ergebnissen 

der im Rahmen dieser Arbeit durchgeführten Messungen nicht möglich. 

2


Kapitel 1 

Experimentelle Rinnenerosionsforschung vs. Modellkonzepte – Quantifizierung der 

hydraulischen und erosiven Wirksamkeit von Rinnen 

Probleme kann man niemals mit derselben 

Denkweise lösen, durch die sie entstanden sind. 

Albert Einstein 

1.1 Einleitung 

Im Bereich der Bodenerosionsforschung wird im Allgemeinen zwischen flächenhafter 

Erosion (interrill erosion), Rillen- und Rinnenerosion (rill erosion) sowie Gully-Erosion 

unterschieden (z. B. Richter, 2001; Ries, 2011). Die Arbeitsgruppe der Physischen 

Geographie unter Leitung von Herrn Prof. Ries an der Universität Trier befasst sich seit vielen 

Jahren mit den Prozessen und Formen der Bodenerosion, insbesondere mit der Erforschung 

der räumlichen und zeitlichen Entwicklung von Gullys (z. B. Marzolff et al., 2011; Ries & 

Marzolff, 2003). Da diese Erosionsformen ein sehr großes Schadenspotential aufweisen 

(Avni, 2005), ist es nicht empfehlenswert, die zur Entwicklung der Formen notwendigen 

Prozesse experimentell zu aktivieren. Daher wird durch Monitoring mit Hilfe verschiedener 

Kameraträger wie Heißluftzeppelin, Starkwinddrachen und unbemannter Drohne das 

Wachstum über mehrere Jahre festgestellt und ein Abtragswert ermittelt. Neben der Erfassung 

des Gullywachstums wird mit experimentellen Methoden wie der Beregnungssimulation 

mittels mobiler Kleinberegnungsanlage das Abfluss- und Abtragsverhalten im Einzugsgebiet 

eines Gullys quantifiziert. Hierbei wird der flächenhafte Abfluss und Abtrag ermittelt. Bisher 

ist jedoch nicht berücksichtigt worden, dass in vielen Fällen das Wasser aus dem 

Einzugsgebiet nicht über den flächenhaften sheet flow dem Gully zugeführt wird, sondern in 

konzentrierter Form über Rinnensysteme. Dabei laufen deutlich andere Prozesse als in den 

Bereichen zwischen den Rinnen (interrill area) ab: Der Abtrag im Zuge der interrill erosion 

wird durch den Einschlag der Regentropfen ausgelöst und verstärkt (Beuselinck et al., 2002). 

Neben dem Einfluss der wesentlichen Bodeneigenschaften (Kuhn & Bryan, 2004; Kuhn et al., 

2003; Le Bissonnais et al., 2005) wird angenommen, dass die interrill erosion hauptsächlich 

von der Niederschlagsintensität abhängt (Brodie & Rosewell, 2007; Bryan, 2000). 

Rill erosion dagegen wird durch den konzentrierten Abfluss von Wasser ausgelöst (Bryan, 

2000; Govers et al., 2007; Knapen et al., 2007) und gilt als der wichtigste Prozess der 

Sedimentproduktion und damit des Bodenverlustes (Cerdan et al., 2002; Poesen, 1987). 

3


Allgemein wird Rinnenerosion als ein Prozess angesehen, der eintritt, wenn fließendes 

Wasser bestimmte, die Erodibilität betreffende Kennwerte übersteigt (Knapen et al., 2007). 

Die Sonderstellung linearer Erosionsprozesse gegenüber flächenhaftem Abtrag aus 

geomorphologischer, hydrologischer und ökonomischer Sicht ergibt sich aus der Tatsache, 

dass abfließendes Wasser seine maximale Wirkung sowohl als Erosions- als auch als 

Transportmedium erreicht, wenn es in Rinnen konzentriert wird (Merz, 1993). Abflusstiefe 

und Fließgeschwindigkeit erreichen hier höhere Werte als beim flächenhaften sheet flow, 

sodass die auf einen Bodenpartikel wirkenden Kräfte um ein Vielfaches höher sind als bei 

flächenhaftem Abfluss (Poesen, 1987). Dadurch steht mehr Energie für die Mobilisierung und 

den Transport von Bodenmaterial zur Verfügung (Merz, 1993), was zu einer deutlichen 

Erhöhung der Erosionsraten führt. 

Übergeordnetes Ziel der Bodenerosionsforschung ist es, Gegenmaßnahmen zu finden, um den 

Verlust von fruchtbarem Boden zu verhindern. Empfehlungen basieren häufig auf 

Ergebnissen von Modellberechnungen. Werden in diesen Modellen jedoch keine Rinnen 

berücksichtigt, führt dies zu falschen Ergebnissen und Schlussfolgerungen und endet 

schließlich in unwirksamen Maßnahmen zur Erosionsbekämpfung. Allerdings ist der 

Forschungsstand zur Rinnenerosion der Bereich der Bodenerosionsforschung, der - verglichen 

mit dem zum flächenhaften Abtrag - noch viele offene Fragen aufweist. Es ist noch wenig 

über die Unterschiede im Verhalten von Rinnen in verschiedenen Einzugsgebieten bekannt. 

Aus dem aktuellen Forschungsstand lassen sich verschiedene Fragestellungen ableiten, 

welche im Rahmen dieser Arbeit bearbeitet werden. 

1) Experimente zur Rinnenerosion 

Um Rinnenerosionsprozesse verstehen und in der Folge in Modellen auch nur annähernd 

korrekt abbilden zu können, sind reproduzierbare Messmethoden notwendig. Viele 

Untersuchungen zur Rinnenerosion haben bisher unter Laborbedingungen stattgefunden, 

wobei Böden verschiedener Texturen und natürliche oder künstliche Niederschläge verwendet 

worden sind (Brunton & Bryan, 2000; Bryan & Poesen, 1989; Gilley et al., 1990; Huang et 

al., 1996; Mancilla et al., 2005). Giménez & Govers (2002) zeigen jedoch, dass die meisten 

Daten, die aus Rinnenmodellen mit glatter Sohle und Gerinnewandung abgeleitet werden, 

nicht auf natürlich entwickelte Rinnen mit rauem Bett übertragen werden können. 

Prozessbasierte Untersuchungen müssen also in natürlichen Rinnen durchgeführt werden oder 

zumindest sollte eine Kombination aus prozessorientierten Laborversuchen und 

Geländeuntersuchungen angestrebt werden. Oftmals werden hydraulische Parameter mittels 

4


Formeln berechnet, die ursprünglich für die Beschreibung des Fließverhaltens in Flüssen 

entwickelt worden sind. Untersuchungen von Govers (1992) und Govers et al. (2007) zeigen 

jedoch, dass diese Parameter nicht ohne Weiteres auf das Fließverhalten in Rinnen übertragen 

werden können. Wie lassen sich also unter möglichst natürlichen Bedingungen experimentelle 

Daten zur Rinnenerosion gewinnen? 

2) Rinnen als Abflusssammler 

Durch Rinnensysteme wird das Wasser des Einzugsgebietes schneller einem Gully zugeführt 

als über den sheet flow der interrill-Bereiche. Dabei erreicht das Wasser den headcut in 

konzentrierter Form, sodass dort verstärkte Erosionsprozesse ablaufen können. Die Frage ist 

also: Welcher Flächenanteil eines Einzugsgebietes wird über Rinnennetzwerke entwässert? 

Siehe: Wirtz et al., 2010, 2012b 

3) Rinnen als Sedimentquelle 

Das Wasser, das am headcut wirkt, transportiert meist bereits eine gewisse Sedimentmenge. 

Dieses Sediment stammt aus dem Einzugsgebiet, d. h., zusätzlich zur Aufzehrung des 

Einzugsgebietes durch den Gully führt auch die Wirkung des Wassers auf der Fläche und in 

den Rinnen zu Bodenabtrag. Die Frage ist in diesem Fall: Wie groß ist der Anteil der 

Rinnenerosion an der Gesamt-Sedimentdynamik? Siehe: Wirtz et al., 2010, 2012b 

4) Prozesse in der Rinne 

Um Maßnahmen gegen Erosionsprozesse aufzeigen zu können, müssen zunächst die Prozesse 

identifiziert und verstanden werden, die für den Bodenverlust verantwortlich sind. Während 

die Erosionsprozesse, die auf den interrill-Flächen stattfinden, relativ bekannt sind, gibt es 

noch Defizite beim Prozessverständnis zur Rinnenerosion. Die zu beantwortenden Fragen 

sind demnach: Welche Prozesse laufen in der Rinne ab? Wie sind die unterschiedlichen 

Prozesse anteilig vertreten? Siehe: Wirtz et al., 2012a, 2013 

5) Messen oder Modellieren? 

Da es im Bereich der angewandten Erosionsforschung nicht immer möglich ist, vor der 

Beurteilung des Erosionsverhaltens eines konkreten Gebietes eine Vielzahl von Experimenten 

durchzuführen, wird auf bestehende Bodenerosionsmodelle zurückgegriffen. Die Ergebnisse 

dieser Modellrechnungen stimmen jedoch oftmals nicht mit tatsächlich gemessenen Werten 

überein. Die Modelle weisen bestimmte Grundannahmen auf, die sich anhand von 

5


Experimenten überprüfen lassen. Die Fragen sind: Stimmen diese Grundannahmen? Und, für 

den Fall, dass sie es nicht tun: Wo liegen die Probleme der Modellannahmen? Siehe: Wirtz et 

al., subm. 2012, 2013 

6) Weitere Anwendungen 

Im Zuge dieser Arbeit ist die Methode „Spülversuch“ entwickelt worden, um experimentelle 

Daten zu verschiedenen Bereichen der Rinnenerosionsforschung v. a. in semiariden Gebieten 

zu liefern. Auf dieses Ziel hin ist die Entwicklung des Versuchsaufbaus abgestimmt. Neben 

der eigentlichen Funktion im Rahmen der Rinnenerosionsforschung stellt sich jedoch immer 

die Frage: Kann eine bereits erprobte Methode auch in Bereichen anderer Fragestellungen 

sinnvoll eingesetzt werden? Siehe: Ries et al., subm. 2011 

Jede der sechs Fragestellungen wird in einem oder mehreren Artikeln behandelt. In diesem 

zusammenfassenden Kapitel 1 sollen die einzelnen Veröffentlichungen, die als nachfolgende 

Kapitel 2-7 vorliegen, in einen wissenschaftlichen Zusammenhang gebracht werden. 

Abbildung 1 zeigt eine grafische Darstellung der Struktur der Arbeit. Die Fragestellungen und 

ihre Antworten werden in den folgenden Unterkapiteln kurz vorgestellt und die 

Zusammenhänge zwischen den einzelnen Artikeln deutlich herausgestellt. In einem 

abschließenden Ausblick werden v.a. die weiterführenden Änderungen der Methoden 

erläutert, die sich aktuell in der Erprobungsphase befinden. 

Um Unklarheiten, Ungenauigkeiten oder sperrige Begriffe durch Übersetzung zu vermeiden, 

werden die in Tabelle 1 aufgelisteten Begriffe im englischen Originalterminus beibehalten. 

Sie sind im Text kursiv gedruckt. 

Die Schreibweise der physikalischen Einheiten erfolgt gemäß der PTB Mitteilungen (2007). 

6


Abbildung 1: Struktur der Arbeit 

7


Begriff 

Black box 

Bulldozer-effect 

Cloud 

Connectivity 

Critical shear stress 

Detachement capacity 

Detachment rate 

Event 

Feature points 

Goat erosion 

Headcut 

High flow experiment 

Interrill 

Knickpoint 

Low flow experiment 

Open source 

Plunge pool 

Probability density functions 

Rill erosion 

Runoff 

Shear stres 

Sheet flow 

Stream power 

Transport capacity 

Transport rate 

Unit length shear force 

Water repellency 

Tabelle1: Englische Begriffe im Text 

Erklärung 

System, von dem in geg. Kontext nur äußeres Verhalten betrachtet wird 

Prozess, bei dem Substrat vor der Wasserfront hergeschoben wird 

IT-Infrastruktur, die über ein Netzwerk zur Verfügung gestellt wird 

Hydraulische Verbindung zwischen z.B. Rinne und Gully 

Substratabhängiger Parameter, Gegenpart zum shear stress [Pa] 

Max. möglich aufzunehmende Materialmenge pro Zeit und Fläche 

Aktuell aufgenommene Materialmenge pro Zeit und Fläche 

Singuläres Erosionsereignis z.B. Zusammenbruch einer Seitenwand 

Punkte ähnlicher Eigenschaften 

Durch Ziegentritt ausgelöste Bodenerosion 

Oberes Ende eines Gullys oder einer Rinne 

Spülversuch mit hoher Einleitintensität (≥ 250 L/min) 

Fläche zwischen zwei Rinnen 

Stufe innerhalb eines Rinnenlängsprofils 

Spülversuch mit geringer Einleitintensität (9 L/min) 

Öffentlich zugängliche Softwareform 

Vertiefung unterhalb eines knickpoints oder headcuts 

Wahrscheinlichkeits-Dichtefunktion 

Zusammenfassung für Rillen- und Rinnenerosion 

Oberflächenabfluss 

Hydraulischer Parameter [Pa] 

Flächenhafter Abfluss, Gegenteil: konzentrierter Abfluss 

Hydraulischer Parameter, versch. Varianten mit versch. Einheiten 

Max. möglich zu transportierende Materialmenge pro Zeit 

Aktuell transportierte Materialmenge pro Zeit 

Hydraulischer Parameter [N] 

„Wasserabweisungsvermögen“ 

1.2 Experimente zur Rinnenerosion 

Es sind bei Weitem noch nicht alle Faktoren bekannt, die Entstehung und Verhalten von 

Rinnen beeinflussen, und auch das Wissen um die Wechselwirkungen zwischen den einzelnen 

Parametern weist noch deutliche Lücken auf. Knapen et al. (2007) führen dies auf den Mangel 

vergleichbarer Daten zurück, die nötig wären, um eine vergleichende Analyse von 

verschiedenen Studien zur Rinnenerosion durchzuführen. Das Fehlen einer einheitlichen 

Methode führt zu großen Problemen in der Quantifizierung von Bodenerosionsprozessen und 

8


macht Messungen schwer vergleichbar (Auerswald et al., 2009; Knapen et al., 2007; 

Stroosnijder, 2005). Die Wichtigkeit standardisierter Methoden wird auch von Casali et al. 

(2006) aufgezeigt. Sie testen drei häufig verwendete Methoden, um die Intensität von 

Rinnenerosionsprozessen quantifizieren zu können und zeigen dabei, dass verschiedene 

Methoden stark abweichende Ergebnisse liefern können. Abhängig von Methode, Form der 

untersuchten Rinne, Position und Distanz zwischen den aufgenommenen Querschnitten liegt 

der Messfehler bei ≤ 40 %. Daher ist ein wichtiges Ziel dieser Arbeit, eine reproduzierbare 

Methode zur Quantifizierung von Rinnenerosionsprozessen zu entwickeln. Im Verlauf der 

Arbeit wird die Methode des Spülversuches aufgrund von praktischen Geländeerfahrungen 

immer wieder verbessert und gezielt erweitert. Die verschiedenen Versionen des 

Versuchsaufbaus sind jeweils in den zugehörigen Artikeln, die in den Kapiteln 2 bis 7 

vorliegen, beschrieben. An dieser Stelle soll die Entwicklung in ihrer Gesamtheit dargestellt 

werden. 

Die konstanten methodischen Parameter betreffen die Aufteilung eines Spülversuches in zwei 

Durchgänge, um den Einfluss einer erhöhten Bodenfeuchte berücksichtigen zu können. Der 

Einfluss der Ausgangsbodenfeuchte auf den Sedimenttransport wird von Govers et al. (1990) 

und Govers (1991) beschrieben. In ihren Experimenten unter trockenen Bedingungen erreicht 

die Sedimentkonzentration nahezu die transport capacity des Abflusses, während unter 

höherer Ausgangsbodenfeuchte die Sedimentkonzentrationen geringer ausfallen: Höhere 

Bodenfeuchte reduziert die Infiltrationsrate, was zu einer höheren Wassermenge führt, die 

durch den zu untersuchenden Rinnenabschnitt fließt. Gleichzeitig wird jedoch nicht 

entscheidend mehr Material transportiert, die Sedimentkonzentration sinkt. Dabei ist zu 

differenzieren, ob eine Befeuchtung und damit eine erhöhte Kohäsion oder eine 

Wassersättigung und damit eine Verringerung des Zusammenhaltes zwischen den einzelnen 

Bodenteilchen vorliegt. Eine höhere Bodenfeuchte an der Oberfläche reduziert zudem die 

water repellency des Bodens. Dies kann für die Abflussdynamik wichtig sein, besonders unter 

sonst trockenen Bedingungen. 

Des Weiteren werden in allen Versionen der Spülversuche pro Rinne drei Messstellen 

gewählt, an denen jeweils vier Proben nach dem Zeitschema 0, 30, 90, 150 Sekunden nach 

Eintreffen der Wasserfront entnommen werden. Auch die Sohlenneigung wird in allen 

Versionen aufgenommen, die Länge der Segmente wechselt jedoch: Je nach verfügbarem 

Messinstrument weisen die Segmente entweder eine Länge von 1 m oder von 2,5 m auf. 

Stufen in der Rinne werden dabei nicht aufgenommen, ihre Lage und Höhe wird getrennt 

vermerkt. Die Scherfestigkeit des Substrates wird mit Hilfe eines Flügelschergerätes zwischen 

9


der letzten Probennahmestelle und dem Ende des untersuchten Rinnenabschnittes bestimmt. 

Unterschiede betreffen die verwendete Pumpe, die eingeleitete Wassermenge, die 

Einleitintensität, die Erfassung des Wasserstandes an den Messstellen, den Einleitzeitpunkt 

von Farbtracern (um Veränderungen in der Fließgeschwindigkeit festzustellen) und die 

Erfassung des Rinnenquerschnittes. 

In der ersten im Rahmen dieser Arbeit zum Einsatz gekommenen Version der 

Versuchsanordnung (V1) des Spülversuchs wird mithilfe einer benzingetriebenen 

Motorpumpe (Fitosa-Spritze mit Bertolini-Pumpe), wie sie auch in 

Kleinberegnungsversuchen Verwendung findet, eine konstante Einleitintensität von 9 L min -1 

über acht Minuten aufrechterhalten (insgesamt also 72 L). Eine Mobilisierung von Material an 

der Einleitstelle wird durch eine spezielle Abbremsplatte verhindert. Die Bewertung der 

Abflussintensität erfolgt durch Messung des Abflusses nach einer vorher festgelegten 

Fließstrecke mittels Drucksensoren. Die Veränderung der Fließgeschwindigkeit wird mittels 

Farbtracern bestimmt. Allerdings können mit der Versuchsanordnung dieser Version noch 

keine Informationen zu hydraulischen Parametern, also Werten, die sich aus 

Rinnenquerschnitt und Wasserstand ableiten ließen, aufgenommen werden. 

Mit Einführung von V2 erfolgt an den drei Messstellen nun auch eine Erfassung des 

Rinnenquerschnittes mit Hilfe von Metallstäben. Diese werden durch Löcher in einer mobilen 

Messbrücke bis zur Rinnensohle geführt. Der Abstand zwischen Messbrückenunterkante auf 

Bodenniveau und Stabende auf Sohlenniveau wird gemessen und dadurch ein Rinnenprofil 

am Messpunkt erstellt. Der Wasserstand kann aufgrund von problembehafteter Benutzung der 

verwendeten Zollstöcke zunächst nur geschätzt werden: Durch das Eintauchen des Zollstocks 

entsteht ein Wasserwirbel, der das Ablesen erschwert, des Weiteren ist es nicht möglich, 

immer an derselben Position in der Rinne zu messen. 

Dieses Problem kann jedoch durch Aufstellen einer Messbrücke in V3 gelöst werden. Diese 

dient als fester vertikaler Referenzpunkt. So ist sichergestellt, dass immer an derselben Stelle 

der Rinne der Abstand zwischen Messbrücke und Wasseroberfläche mit einem Zollstock 

gemessen wird. Bei bekanntem Abstand zwischen Rinnensohle und Brücke lässt sich der 

Wasserstand berechnen ohne dass Verwirbelungen durch das Eintauchen des Zollstocks 

entstehen. Die bis zu dieser Version verwendete Pumpe ist in ihrer Leistung begrenzt, sodass 

ein realistischer Abfluss in Rinnen mit einem größeren Einzugsgebiet damit nicht zu 

simulieren ist. 

Als wichtige Neuerung wird in V4 die Fitosa-Spritze durch eine weit leistungsfähigere GMP- 

150-Pumpe der Firma Güde ersetzt, sodass nun pro Durchgang eine Wassermenge von 

10


1000 L in die Rinnen eingeleitet werden kann. Die Intensität schwankt je nach Anordnung 

von Wassertank, Pumpe und Einleitstelle im Hang zwischen 250 und 330 L min -1 . Die 

Einführung der leistungsfähigeren Pumpe macht es zudem erforderlich, die Einleitzeiten der 

Farbtracer von 3 min und 6 min auf 1 min und 2 min vorzuziehen sowie den Durchmesser des 

Abflussmessrohrs zu vergrößern. Ebenso wird eine veränderte Version der Abbremsplatte bei 

der Wassereinleitung eingesetzt. Die jetzt verwendete Pumpe stellt eine höhere Wassermenge 

bei geringerem Wasserdruck bereit, die Abbremsplatte muss diesen neuen Anforderungen 

angepasst werden. Die Erfassung des Rinnenquerschnittes kann durch das Ersetzen der 

Metallstangen durch den digitalen Laser-Entfernungsmesser Bosch PLR 30 genauer und 

schneller gestaltet werden. Die Zollstöcke zur Wasserstandsmessung werden in dieser Version 

durch Ultraschallsensoren ersetzt. 

Die Entwicklung der Spülversuche von V1 bis V4 ist in Tabelle 2 zusammengefasst und in 

Abbildung 2 grafisch dargestellt. 

Tabelle 2: Entwicklung der Spülversuche: Nicht erfasste Werte sind durch „X“ gekennzeichnet. In der 

Zeile „Artikel“ gilt, soweit kein anderer Autor angegeben ist, der Vorsatz „Wirtz et al.“ 

Version V1 V2 V3 V4 

Pumpe Fitosa Fitosa Fitosa Güde 

Intensität [L min -1 ] 9 9 9 250-330 

Menge [L] 72 72 72 1000 

Strecke bis Abflussmessung [m] 15-25 15-25 15-25 15-25 

Wasserstand X X Zollstock Ultraschall 

Farbtracer [min] 3 und 6 3 und 6 3 und 6 1 und 2 

Querschnitt X Metallstäbe Metallstäbe Laser 

Artikel 2010 2012a 

2012b 

2013 subm. 2012 

2012b 

Ries et al., 

subm. 2011 

11


Abbildung 2: Veränderungen in der Methode „Spülversuch“. Zu beachten: Es sind nur maßgebliche 

Veränderungen dargestellt, die die verwendeten Gerätschaften betreffen. Veränderungen der 

Messmethodik (z.B. Veränderung der Einleitzeiten der Farbtracer) sind hier nicht abgebildet. 

1.3 Rinnen als Abflusssammler 

Ein wichtiger Punkt im Rahmen der Rinnenerosionsforschung ist die Frage nach der 

Effektivität linearer Erosionsformen bezüglich der Konzentration des Oberflächenabflusses. 

Über Rinnen kann Wasser schneller z. B. einem Gully zugeführt werden, dadurch gelangt 

12


mehr Wasser gleichzeitig an einen bestimmten Punkt des headcuts und kann dort konzentriert 

rückschreitende Erosion leisten. Allerdings ist ein Einzugsgebiet niemals vollständig mit 

Rinnen bedeckt, sondern die Rinnennetzwerke werden durch unterschiedlich große interrill- 

Bereiche getrennt. Die Frage ist also, wie effektiv das Wasser durch den geringen 

Rinnenanteil eines Gebietes ab- und dem Gully zugeführt werden kann. Dies wird im Rahmen 

dieser Arbeit in zwei Artikeln diskutiert. In dem Gully-Einzugsgebiet Freila in Andalusien 

vergleichen Wirtz et al. (2012b) die Anteile von Rinnenerosion und flächenhaftem Abtrag an 

der Gesamterosion. Das etwa 10 ha große Einzugsgebiet besteht zu 0,25 % aus Rinnen, die 

aber mit den an die Rinnen angeschlossenen Flächen 20 % dieses Gebietes entwässern. Die 

runoff-Intensitäten liegen in den interrill-Bereichen um den Faktor 5 höher als in den Rinnen. 

Dies ist jedoch auf die größere interrill-Gesamtfläche zurückzuführen. Wird die runoff- 

Intensität pro Quadratmeter betrachtet, liegen die Werte in den Rinnen um den Faktor 50-60 

höher als auf den interrill-Bereichen. Im Arnástal in den spanischen Pyrenäen vergleichen 

Wirtz et al. (2010) gemessene Abflusswerte aus Rinnen mit Abflusswerten, die Seeger et al. 

(2005) im Rio Arnás gemessen haben. Der Arnás erreicht Werte zwischen 48 und 708 L s -1 

mit Abflussspitzen von bis zu 2.347 L s -1 . Bezogen auf das Gesamteinzugsgebiet von 284 ha 

bedeutet dies einen spezifischen Abfluss zwischen 1,7x10 -5 und 2,5x10 -4 L s -1 m -2 . In den 

untersuchten Rinnen werden spezifische Abflüsse von 7x10 -5 und 8x10 -5 L s -1 m -2 erreicht. 

Die Werte in den Rinnen liegen somit innerhalb der Spanne der im Rio Arnás gemessenen 

Werte. Dabei ist zu beachten, dass die experimentell verwendete Wassermenge als sehr gering 

eingestuft werden muss. Beregnungsversuche in den Rinneneinzugsgebieten zeigen, dass bei 

realen Niederschlägen ein bis 30-fach höherer Abfluss in den Rinnen erwartet werden kann 

(Wirtz et al., 2010). Es würden also in den Rinnen deutlich höhere spezifische runoff- 

Intensitäten auftreten als im Vorfluter Arnás. Damit zeigt sich die hohe Effektivität der 

Rinnen als Abflusssammler. Allerdings muss bedacht werden, dass die Rinnennetzwerke 

nicht zwangsläufig den Gully oder den Vorfluter erreichen. Es ist durchaus möglich, dass die 

Rinne ausläuft und der Abfluss wieder flächenhaft weitergeleitet wird (connectivity). Neben 

der schnellen und effektiven Zuführung zu einem Gully oder einem Vorfluter bewirkt der 

konzentrierte Abfluss auch eine erhöhte Erosionsleistung. Das bedeutet, der zweite wichtige 

Punkt bezüglich der Rinneneffektivität bezieht sich auf die Wirksamkeit als Sedimentquelle. 

1.4 Rinnen als Sedimentquelle 

In einem Einzugsgebiet kann Abtrag sowohl auf den interrill-Bereichen als auch in den 

Rinnen stattfinden. Die Frage dabei ist: Welcher Bereich liefert in einem Einzugsgebiet mehr 

13


Sediment? Die wenigen Rinnen oder der große interrill-Bereich? Bezüglich der Effektivität 

von Rinnen finden sich in der Literatur verschiedene Größenordnungen, gemeinsam ist ihnen 

jedoch, dass es sich meist um sehr hohe Werte handelt. Die Spanne reicht von 

„Verdreifachung“ der Erosionsraten nach der Entwicklung von Rinnen (Meyer et al., 1975) 

über „9-21-mal mehr“ als flächenhafter Abtrag (Morgan et al., 1987) bis hin zu „90 %“ des 

Bodenverlustes nach einzelnen Niederschlägen (Cerdan et al., 2002). Gemessene 

Sedimentkonzentrationen reichen von 10-130 g L -1 (Polyakov & Nearing, 2003) bis 210 g L -1 

(Loch, 2000). Gullys als größere Erosionsform weisen eine noch höhere Kapazität als 

Sedimentquelle auf. Allerdings sehen Faust & Schmidt (2009) aufgrund der seltenen Aktivität 

der Gullys die geomorphologische Effektivität dieser Großformen als eher gering an. Sie 

weisen den Gullys eine Aktivitätsfrequenz von 1/20 a -1 , den Rinnen 4 a -1 zu. Die im Rahmen 

dieser Arbeit durchgeführten Spülversuche decken eine Sedimentkonzentrationsspanne von 

0 g L -1 (Wirtz et al., 2010) bis 438 g L -1 (Wirtz et al., 2012a) ab. Dabei ist zu beachten, dass 

immer unterschiedliche Ausgangssituationen gegeben sind. Bei der Einordnung dieser Werte 

ist zu berücksichtigen, dass in einem Einzugsgebiet in den Pyrenäen, in dem sich die Rinnen 

im anstehenden Gestein gebildet haben bzw. unter starker Mitwirkung anderer Prozesse (wie 

Frostsprengung), die Werte deutlich geringer ausfallen als in einem schluffig-lehmigen 

Substrat ohne Vegetationsbedeckung in Andalusien. Daher ist die wichtigere Frage: Wie 

verhält sich die Rinnenerosion im Vergleich zur flächenhaften Erosion in einem bestimmten 

Testgebiet? Die Daten bezüglich des flächenhaften Abtrags können mittels 

Kleinberegnungsanlagen ermittelt werden. Das größere Problem besteht darin, die gegebenen 

Punktdaten sinnvoll und wissenschaftlich korrekt auf eine Fläche wie z. B. ein ganzes 

Einzugsgebiet zu extrapolieren. In Wirtz et al. (2010) wird im Arnástal in den spanischen 

Pyrenäen eine maximale Sedimentkonzentration von 6,3 g L -1 gemessen. Am Gebietsauslass 

des Arnástals ermitteln Seeger et al. (2005) maximale Sedimentkonzentrationen von 4,8 g L -1 , 

ähnliche Werte zeigen auch Beregnungsversuche (Seeger, 2007). Dies deutet zunächst darauf 

hin, dass die Rinnen keine deutlich höheren Abtragswerte als andere Prozesse liefern und 

damit auch keinen auffallend hohen Anteil am Sedimentaustrag des Gebietes aufweisen. 

Dabei gilt es jedoch, folgende Punkte zu bedenken: Die Beregnungsversuche werden mit 

einer Intensität von 40 mm h -1 durchgeführt, die Abflussintensität in den Spülversuchen liegt 

bei 9 L min -1 . Wird die Größe der Rinneneinzugsgebiete und deren runoff-Koeffizienten 

berücksichtigt, so ist klar zu erkennen, dass der Abfluss in den Rinnen unter einem solchen 

Niederschlagsereignis bis zu 30-mal höher ausfällt als der simulierte. Daraus folgt, dass die 

Rinnen trotz der schlechten Voraussetzungen (anstehendes Gestein, bestenfalls grob 

14


verwittert, Pflanzenwachstum im wenigen feineren Material in den Rinnen, viel zu wenig 

Wasser) das wenige Wasser aus den Experimenten sehr effektiv für den Abtrag nutzen 

können. Vermutlich ist das Material, das am Gebietsauslass gemessen wird, nicht allein durch 

den Oberflächenabfluss unter Niederschlagsereignissen am Messpunkt angekommen, sondern 

auch durch Massenbewegungen und Erosion im Flussbett selbst. 

In dem Gully-Einzugsgebiet Freila in Andalusien (Wirtz et al., 2012b) werden verschiedene 

Methoden (Beregnungen, Spülversuche, Luftbildaufnahmen, Kartierung) kombiniert, um die 

Anteile des flächenhaften und des linienhaften Abtrages in diesem Gesamtgebiet zu 

vergleichen. Die Gesamtmenge des abgetragenen Materials ist auf den interrill-Bereichen 5- 

15-mal höher als in den Rinnen. Dies ist nicht verwunderlich, da der Flächenanteil der 

interrill-Fläche 99,75 %, der Anteil der Rinnen nur 0,25 % beträgt. Werden jedoch die 

abgetragenen Mengen auf die Flächenanteile bezogen, zeigen die Rinnen eine 20-60-fach 

höhere Rate als die interrill-Flächen. In anderen Testgebieten in Andalusien können noch 

deutlich höhere Werte in Rinnen gemessen werden, allerdings fehlen bisher die Daten, um 

auch für diese Gebiete eine Hochrechnung auf das Gesamtgebiet durchführen zu können. Die 

Versuche zeigen eindeutig, dass Rinnen effektive Sedimentquellen sind, selbst unter für 

Erosionsprozesse erschwerten Bedingungen. Während Abflussereignissen laufen in Rinnen 

andere Prozesse als auf den interrill-Flächen ab und/oder ähnliche Prozesse laufen mit einer 

völlig anderen Intensität ab. Im Rahmen dieser Arbeit wird geprüft, welche Prozesse in den 

Rinnen ablaufen. 

1.5 Prozesse in der Rinne 

Es ist also zu klären, welche Prozesse die Rinnen zu einer solch effektiven Sedimentquelle 

machen. In Andalusien und in den Bardenas Reales (Wirtz et al., 2012a, 2013) wird versucht, 

die Prozesse anhand der Werte der einzelnen Proben und deren zeitliche Anordnung an den 

Messstellen zu identifizieren. Insgesamt lassen sich anhand der Ergebnisse der Spülversuche 

und der Beobachtungen während der Experimente mehrere parallel ablaufende Prozesse 

ausweisen. Zunächst wird das lose in der Rinne liegende Material aufgenommen und 

abtransportiert. Dies ist an der oft hohen Sedimentkonzentration der relativ langsam 

fließenden Wasserfront zu erkennen. Je nach Materialmenge und Abflusswirksamkeit 

geschieht dies direkt an der Wasserfront, oder der Prozess zieht sich über einen gewissen 

Zeitraum von bis zu mehreren Minuten hin, sodass die Auswirkungen in mehreren Proben an 

hohen Sedimentkonzentrationen zu erkennen sind. Dieser Prozess wird als bulldozer-effect 

bezeichnet (Seeger et al., 2004; Regüés et al., 2000), da ein großer Teil des losen Materials 

15


vor der Wasserfront hergeschoben wird. Ist dies der einzige Prozess der abläuft, fällt die 

Sedimentkonzentration von der ersten zur letzten Probe kontinuierlich ab. Im zweiten 

Durchgang wiederholt sich der Vorgang auf einem etwas geringeren Niveau, da nach 

Beendigung des ersten Durchgangs wieder eine gewisse Menge Material in der Rinne 

verbleibt. Der idealtypische Verlauf dieses Prozesses ist in Abbildung 3 dargestellt. 

Neben dem Abtransport losen Materials kann sich das Wasser durch Tiefenerosion in die 

Rinnensohle einschneiden, d. h. die Rinnensohle wird eingetieft. Dieser Prozess wird 

hauptsächlich über die hydraulischen Parameter wie shear stress gesteuert. Allerdings scheint 

es, dass während der Experimente nur in Ausnahmefällen die verwendete Wassermenge und 

Einleitintensität ausreichen, diesen Prozess auf der gesamten Rinnenlänge zu aktivieren. Dies 

wäre an einer gleichbleibenden oder sogar ansteigenden Sedimentkonzentration an einzelnen 

Messstellen zu erkennen. Im zweiten Durchgang verliefe die Sedimentkonzentration auf 

einem höheren Niveau, da das bereits vollständig wassergesättigte Material leichter zu 

erodieren wäre. Der idealtypische Verlauf dieses Prozesses ist in Abbildung 4 dargestellt. 

Des Weiteren treten Prozesse auf, die nur indirekt durch den Einfluss des fließenden Wassers 

kontrolliert werden. Der Abfluss unterschneidet sowohl die Seitenwände der Rinne als auch in 

Form von rückschreitender Erosion die Stufen (knickpoints) innerhalb des Rinnenbettes. 

Dabei werden noch vergleichsweise geringe Sedimentmengen mobilisiert. Der höhere Anteil 

an Material gelangt erst durch das Nachbrechen der unterspülten Wand- und Stufenbereiche 

gravitativ in die Rinne und wird, wie das vor Beginn des Experimentes in der Rinne 

vorhandene lose Material, vom fließenden Wasser aufgenommen und abtransportiert. Auch 

die plunge pool-Dynamik kann innerhalb kurzer Zeit relativ große Sedimentmengen 

bereitstellen: Zunächst wird die Senke unterhalb einer Stufe mit Sediment angefüllt. Sobald 

der pool jedoch gefüllt ist, kann das darüber fließende Wasser diesen innerhalb kurzer Zeit 

wieder freispülen, sodass das über einen längeren Zeitraum dort gespeicherte Material sehr 

schnell abtransportiert wird. Erkennbar sind diese events an deutlich hervorstechenden 

Sedimentkonzentrationen im Probenverlauf einer Messstelle. Der idealtypische Verlauf dieses 

Prozesses ist in Abbildung 5 dargestellt. 

16


Abbildung 3: Idealtypischer Verlauf der Sedimentkonzentration bei Transport von losem Material: a = 

erster Durchgang, b = zweiter Durchgang 

Abbildung 4: Idealtypischer Verlauf der Sedimentkonzentration bei Einschneiden in die Rinnensohle: 

a = erster Durchgang, b = zweiter Durchgang 

17


Abbildung 5: Idealtypischer Verlauf der Sedimentkonzentration bei Massenbewegungen an Stufen und 

Seitenwänden (durch Oval markiert): a = erster Durchgang, b = zweiter Durchgang 

Der idealtypische Verlauf wird durch Überlappung verschiedener Prozesse verwischt, sodass 

die direkten Beobachtungen der ablaufenden Prozesse in der Rinne während des Versuches 

wichtige Hinweise für die Interpretation liefern. Die verschiedenen Prozesse weisen eine hohe 

räumliche und zeitliche Variabilität auf, sodass eine allgemeingültige Aussage bezüglich der 

relativen Anteile nur sehr schwer zu treffen ist. In Untersuchungen von Govers (1987) liegt 

der Anteil der „Massenbewegungen“ an den Seitenwänden bei 37 %, an den Stufen und 

knickpoints bei 12 %. Das Einschneiden in die Rinnensohle kann nur während dreier extremer 

Ereignisse mit Spitzenabflüssen zwischen 70 und 90 L s -1 beobachtet werden, liefert dann 

aber den höchsten Anteil am Gesamtaustrag (Govers, 1987). Meist ist der Abfluss jedoch zu 

gering, um den Prozess des Einschneidens zu aktivieren. In den vorliegenden Untersuchungen 

muss zur Bestimmung des Anteils der einzelnen Prozesse ein anderer Weg beschritten 

werden. Eine wichtige Annahme in verschiedenen Bodenerosionsmodellen ist, dass die 

transport rate die transport capacity nicht überschreiten kann, da in diesem Falle 

Sedimentation einsetzt (Scherer, 2008). Die Modelle berücksichtigen jedoch nur den durch 

die hydraulischen Parameter gesteuerten Prozess des Einschneidens in die Rinnensohle. Das 

bedeutet, dass zumindest die Differenz zwischen transport rate und transport capacity durch 

andere, nicht durch hydraulische Parameter gesteuerte Prozesse bereitgestellt wird. In Wirtz et 

al. (subm. 2012) liegt in 82 von 144 Proben die transport rate oberhalb der transport 

18


capacity. Im Mittel wird die transport capacity um 41,5 % überschritten, d. h. mindestens 

41,5 % des transportierten Materials wird von Prozessen bereitgestellt, die nicht hydraulisch 

kontrolliert sind, also Transport von losem Material, rückschreitende Erosion an Stufen, 

Überlaufen von plunge pools und Zusammenbrüche an Seitenwänden. In Wirklichkeit wird 

der Anteil höher sein, da meist die transport capacity nicht allein durch das Einschneiden 

ausgeschöpft wird, insbesondere bei den in den vorliegenden Versuchen verwendeten 

Wassermengen und Intensitäten. Der Anteil der nicht hydraulisch kontrollierten Prozesse ist 

jedoch nicht gleichmäßig über die Versuche verteilt. In den drei Versuchen mit den geringsten 

Sedimentkonzentrationen liegt der Mittelwert nur bei 24,3 % nicht hydraulisch kontrollierter 

Prozesse, während in den drei Versuchen mit den höchsten Sedimentkonzentrationen ein Wert 

von 58,7 % ermittelt wird. Das wiederum bedeutet, dass der effektivste Prozess eben nicht die 

hydraulisch kontrollierte Erosion in die Rinnensohle sein kann, sondern die gravitativ 

gesteuerten Prozesse. Diese werden jedoch in gegebenen Bodenerosionsmodellen nicht 

berücksichtigt, die Bodenerosion wird hier als rein von hydraulischen Parametern gesteuerter 

Prozess angesehen. Daher erscheint es sinnvoll, einige Grundannahmen aus gängigen 

Bodenerosionsmodellen genauer zu betrachten und zu bewerten. 

1.6 Messen oder Modellieren? 

Die erste Modellannahme, dass die transport rate die transport capacity nicht übersteigen 

kann, wird in drei Artikeln überprüft (Wirtz et al., 2012a, subm. 2012, 2013). Es zeigt sich, 

dass in 75 % der Fälle (Wirtz et al., 2013) bzw. in 59 % der Fälle (Wirtz et al., subm. 2012) 

die transport rate die transport capacity um einen Faktor > 500 übersteigen kann. In Wirtz et 

al. (2012a) ist zudem deutlich zu erkennen, dass besonders in den Fällen, in denen hohe 

Sedimentkonzentrationen gemessen werden, die transport rate die transport capacity 

übersteigt. In diesem Fall ist der Quotient aus transport rate und transport capacity > 1 (siehe 

Abbildung 6 und 7). 

19


Abbildung 6: Quotient aus transport rate und transport capacity (Wirtz et al., 2013) 

Abbildung 7: Quotient aus transport rate und transport capacity (Wirtz et al., subm. 2012) 

In deterministischen Bodenerosionsmodellen werden die Erosionsprozesse als rein 

hydraulisch kontrolliert angesehen. Sie gehen von einem linearen Zusammenhang zwischen 

einem Abtragswert und einem hydraulischen Parameter aus. Abtragswerte sind z. B. 

20


Sedimentkonzentration, transport rate oder detachment rate, hydraulische Parameter shear 

stress, unit length shear force oder verschiedene Varianten der stream power. Knapen et al. 

(2007) berechnen in ihrer Studie die Korrelationen zwischen verschiedenen hydraulischen 

Parametern und der detachment capacity verschiedener WEPP-Datensätze (Water Erosion 

Prediction Project). Die beste Korrelation zur detachment capacity weist die stream power mit 

einem mittleren Bestimmtheitsmaß von R² = 0,59 auf. Im WEPP-Modell wird der shear stress 

verwendet, der allerdings in keinem der getesteten Datensätze einen hohen R²-Wert aufweist. 

In Wirtz et al. (subm. 2012) werden an eigenen Daten die Korrelationen zwischen der 

detachment rate und verschiedenen hydraulischen Parametern überprüft. Dabei wird die 

gesamte Breite von 0 ≤ R² ≤ 0,99 abgedeckt, Trendlinien sind steigend, fallend oder auch 

nahezu konstant, es ist letztendlich nicht möglich, irgendeine Regelmäßigkeit zu 

identifizieren. Nur 40 von 252 Korrelationen (16 %) zeigen eine steigende Trendlinie mit 

einem Bestimmtheitsmaß von R² ≥ 0,7. Auch hier ist wieder deutlich zu erkennen, dass die 

Versuche mit geringen Sedimentkonzentrationen höhere R²-Werte aufweisen als die Versuche 

mit hohen Sedimentkonzentrationen, ganz gleich ob alle Korrelationen oder nur diejenigen 

mit steigender Trendlinie berücksichtigt werden. 

In Wirtz et al. (2013) werden auf einer homogenen Ackerfläche in vier Rinnen sowohl die 

Eingangsparameter für die Berechnung des shear stress als auch Erosionswerte direkt 

gemessen, d. h. es stehen sowohl die Eingangsdaten als auch die „korrekten“ Ergebnisse eines 

theoretischen Modelldurchlaufes zur Verfügung. Die Eingangsdaten für die Berechnung des 

shear stress und damit auch die daraus resultierenden shear stress Werte weisen für die vier 

beprobten Rinnen relativ geringe Schwankungen (relative Messfehler und empirische 

Variationskoeffizienten) auf. Träfe die Modellannahme „linearer Zusammenhang zwischen 

hydraulischem Parameter und Erosionsparameter“ zu, müssten auch die gemessenen 

Erosionswerte eine geringe Schwankung aufweisen, bei gleichen Eingangsdaten liefert ein 

deterministisches Modell auch immer dieselben Ergebnisse. Die Erosionsparameter weisen 

jedoch hohe relative Messfehler (Abbildung 8) und empirische Variationskoeffizienten 

(Abbildung 9) auf. 

21


Abbildung 8: Relativer Messfehler verschiedener Parameter. Shear stress 1 berücksichtigt in der 

Probendichte Sedimentkonzentration und Korndichte, shear stress 2 nimmt einen konstanten Wert von 

1 an (Wirtz et al. 2013) 

Abbildung 9: Empirischer Variationskoeffizient verschiedener Parameter. Shear stress 1 

berücksichtigt in der Probendichte Sedimentkonzentration und Korndichte, shear stress 2 nimmt einen 

konstanten Wert von 1 an (Wirtz et al. 2013) 

22


Für das Nicht-Zutreffen der Modellannahmen können mehrere Gründe aufgeführt werden: 

Zum einen stellt sich die Vielzahl unterschiedlicher Prozesse mit großer räumlicher und 

zeitlicher Variabilität als kaum zu überwindendes Problem heraus. Der Ansatz, diese Prozesse 

mithilfe eines einzelnen hydraulischen Parameters abzubilden, erweist sich als unbrauchbar. 

Zum anderen liegt ein weiteres Problem in der Verwendung des hydraulischen Parameter an 

sich: In den meisten Modellen wird der shear stress als hydraulischer Parameter verwendet, 

aus diesem lassen sich andere Parameter wie unit length shear force und verschiedene stream 

power-Varianten ableiten. In einem Review-Teil in Wirtz et al. (subm. 2012) und Wirtz et al. 

(2013) wird gezeigt, dass die Berechnung von shear stress nicht eindeutig ist. Je nach 

Literaturangabe werden ganz unterschiedliche Faktoren verwendet, um den shear stress zu 

berechnen. Zudem wird nicht deutlich zwischen shear stress - einem hydraulischen Parameter 

- und critical shear stress - einem Substratparameter - unterschieden. Auch die Berechnung 

der transport capacity ändert sich je nach Quelle. Als Folge dieser wechselnden 

Eingangsparameter ergibt sich, dass der shear stress nicht in allen Fällen in Pascal und die 

transport capacity nicht immer in Kilogramm pro Sekunde angegeben ist. 

Basis der shear stress-Formel in der Hydraulik ist die Navier-Stokes-Gleichung. Diese 

beschreibt die Bewegung von Flüssigkeiten, wobei Newtons zweites Gesetz, das 

Aktionsprinzip, auf Flüssigkeiten angewendet wird: Die Änderung der Bewegung einer Masse 

ist zur Einwirkung der bewegenden Kraft proportional und geschieht nach der Richtung 

derjenigen geraden Linie, nach welcher jene Kraft wirkt. Kombiniert wird dies mit der 

Annahme, dass die Flüssigkeitsspannung als Summe aus einem Viskositätsterm und einem 

Druckterm darzustellen ist. Durch Verwendung der Navier-Stokes-Gleichung kann ein 

inkompressibles Fluid komplett beschrieben werden, hydrodynamische Fragen werden auf ein 

mathematisches Problem reduziert. Dieses Problem besteht jedoch aus einem System von 

nichtlinearen partiellen Differentialgleichungen zweiter Ordnung. Nur die einfachsten Fälle 

können mit den leistungsfähigsten Computern numerisch gelöst werden. Für den allgemeinen 

drei-dimensionalen Fall sind Existenz, Eindeutigkeit und Richtigkeit noch nicht bewiesen. 

Die Dringlichkeit dieses Problems spiegelt sich in der Tatsache wider, dass der Beweis oder 

ein Gegenbeweis der Navier-Stokes-Gleichung als eines der sieben wichtigsten Probleme der 

Mathematik angesehen wird, auf dessen Lösung vom Clay Mathematics Insitute eine 

Belohnung von 1 Mio. $ ausgesetzt ist (Constantin, 2001; Fefferman, 2006; Schneider, 2008; 

Seiler, 2002; Temam, 2000; Wiegner, 1999). 

Ein weiteres Problem ist, dass der Einfluss von Turbulenzen in Modellen nicht berücksichtigt 

wird. Nearing & Parker (1994) untersuchen den Einfluss der Turbulenz auf den shear stress. 

23


Sie zeigen, dass unter turbulenten Fließbedingungen dieselben shear stress Werte deutlich 

höhere Abtragsraten verursachen. Die Unterschiede zwischen den Abtragsraten bei 

turbulentem und laminarem Fließen vergrößern sich mit ansteigenden shear stress-Werten. 

Das bedeutet, wenn die gegebenen hydraulischen Bedingungen hohe shear stress-Werte 

verursachen, ist der Einfluss der Turbulenz auf die Bodenerosion höher als in Bereichen mit 

niedrigeren shear stress-Werten. Dies kann auch der Grund sein, warum 

Bodenerosionsmodelle geringe Bodenabträge überschätzen und große Bodenverluste 

unterschätzen. Nearing (1998) erklärt dies durch das Vorhandensein von natürlichen 

Variationen in den Modell-Daten, also Variationen, die das Modell nicht abbilden kann. Der 

Einfluss von Turbulenzen auf den Bodenabtrag wird auch von Nearing et al. (1991) gezeigt. 

In einer Laboruntersuchung messen sie shear stress-Werte zwischen 0,5 Pa und 2 Pa, 

während die Scherfestigkeit des Substrates zwischen 1 kPa und 2 kPa liegt, ein 

Größenunterschied um den Faktor 1000. Trotz dieses Ungleichgewichtes werden deutliche 

Abtragsraten gemessen. Nearing et al. (1991) erklären dieses Ergebnis mit plötzlich 

auftretenden Turbulenzen, die viel stärker sind als der mittlere shear stress. Die 

beschriebenen Probleme und Lücken zeigen deutlich die Notwendigkeit, auf experimentelle 

Art Daten zu gewinnen. 

1.7 Weitere Anwendungen 

Im Rahmen dieser Arbeit werden die Spülversuche in einer Studie eingesetzt, die nur indirekt 

die Problematik der Rinnenerosion mit einschließt. Der Spülversuch findet Verwendung in 

einer Studie zur goat erosion, also Erosion, die durch Viehtritt von Ziegen auf einer 

vegetationsarmen Fläche entsteht (Ries et al., subm. 2011). In dieser Studie wird der Einfluss 

von Viehtritt auf den Bodenabtrag ermittelt. Dazu wird eine Rinne zunächst ohne Viehtritt 

„bespült“ und beprobt, danach in einem zweiten Versuch noch mal nach dem Queren von 600 

Tieren. Die Ergebnisse zeigen, dass die Ziegen eine relativ große Menge an Material lockern, 

welches jedoch sehr schnell aus der Rinne ausgespült wird (bulldozer-effect). Unterschiede 

zwischen den beiden Versuchen sind nur in den ersten Durchgängen zu erkennen, die 

Unterschiede sind zudem auf die Wasserfront und die 30-Sekunden-Probe beschränkt. Die 

Sedimentkonzentrationen erreichen in den Versuchen mit vorherigem Viehtritt hier deutlich 

höhere Werte, in den nachfolgenden Proben weisen die Werte mit und ohne 

Ziegentritteinfluss wieder ähnliche Werte auf (Ries et al., subm. 2011). 

24


Auch wenn die Spülversuche nicht auf diese Fragestellung zugeschnitten sind, können sie hier 

dennoch gewinnbringend eingesetzt werden. Diese Tatsache zeigt den Wert der Methode 

„Spülversuch“ im Rahmen einer übergeordneten Erosionsforschung. 

Weitere Anwendungsbereiche sind z. B. die Quantifizierung von Abfluss und Abtrag aus 

Fahrspuren auf Waldwegen und Rückegassen. Dazu liegen bereits erste Ergebnisse aus 

verschiedenen Testgebieten in Luxemburg und Deutschland vor, diese sind bisher jedoch 

nicht publiziert. Die Wirksamkeit linearer Strukturen wie Waldwege und Rückegassen als 

Abfluss- und Sedimentquelle in Wäldern ist allgemein bekannt und akzeptiert (z.B. Anderson 

& Macdonald, 1998; Appelboom et al., 2002; Eastaugh et al., 2008; Grayson et al., 1993; 

Motha et al., 2003). Auf diesen linearen Strukturen befinden sich jedoch oftmals zusätzlich 

mehr oder weniger deutlich ausgeprägte Fahrspuren. Die Frage ist also, welchen Einfluss 

diese kleineren linearen Formen haben. Um diese Frage zu beantworten, werden auf den 

Wegen Beregnungssimulationen, in den Fahrspuren Spülversuche durchgeführt. Die runoff- 

Koeffizienten auf den Wegen und in den Fahrspuren erweisen sich als ähnlich, sie liegen 

meist zwischen 60 und fast 100 % (siehe Abb. 10), d. h. die Wirksamkeit des Abflusses ist in 

beiden Formen als vergleichbar anzusehen. 

Abbildung 10: Runoff-Koeffizienten in Fahrspuren (Spülversuche) und auf Waldwegen 

(Beregnungsversuche). LFE = low flow experiment (Einleitintensität 9 L min -1 ), HFE = high flow 

experiment (Einleitintensität 250 L min -1 ) 

25


Die Erosions-Effizienz zeigt ein etwas komplexeres Bild. In den Fahrspuren sind sowohl sehr 

hohe als auch sehr niedrige Werte zu verzeichnen. Insgesamt verursacht der Abfluss in den 

Fahrspuren bis zu 100-mal höhere Abtragswerte als der Abfluss auf dem restlichen Teil der 

Wege und Rückegassen, 432 g m -2 min -1 in den Fahrspuren gegenüber 4 g m -2 min -1 (siehe 

Abbildung 11). 

Abbildung 11: Abtragswerte in Fahrspuren (Spülversuche) und auf Waldwegen 

(Beregnungsversuche). LFE = low flow experiment (Einleitintensität 9 L min -1 ), HFE = high flow 

experiment (Einleitintensität 250 L min -1 ) 

Des Weiteren wäre der Einsatz auf Ackerflächen möglich und besonders im Bereich des 

Vorgewendes am Ackerrand sinnvoll. In diesem Bereich entwickeln sich sehr schnell deutlich 

ausgebildete Rinnen in Gefällsrichtung, da die normale Bearbeitungsrichtung meist parallel zu 

den Höhenlinien verläuft, im Vorgewende im rechten Winkel dazu. 

1.8 Zusammenfassung und Ausblick 

Die vorliegende Arbeit setzt sich mit verschiedenen Fragen und Problemen bezüglich der 

Rinnenerosion auseinander. Dabei kann zunächst gezeigt werden, dass Rinnen sehr effektive 

Abflusssammler sind. Es wird ein vergleichsweise großer Anteil der Gesamtfläche eines 

Einzugsgebietes über vorhandene Rinnennetzwerke entwässert, selbst wenn nur ein kleiner 

Teil eines betrachteten Gebietes (z. B. Gully-Einzugsgebiet) tatsächlich von Rinnen bedeckt 

26


ist. Die Abflussintensitäten sind insgesamt in den interrill-Bereichen höher, da diese Bereiche 

einen weit größeren Teil einnehmen. Bezogen auf eine bestimmte Grundfläche weisen die 

Rinnen jedoch eine deutlich höhere Abflussintensität auf. Dadurch kann zum einen das 

Wasser eines Einzugsgebietes einem vorhandenen Gully schnell zugeführt werden, zum 

anderen kann durch den konzentrierten Abfluss bereits in der Rinne eine starke Erosionsarbeit 

geleistet werden. Durch ihre im Vergleich zu Gullys deutlich höhere Aktivitätsfrequenz 

können in bestimmten Einzugsgebieten die Rinnen die effektivsten Sedimentquellen sein. In 

den vorliegenden Untersuchungen liegen die Abtragsraten in den Rinnen bis um den Faktor 

60 über den Abtragsraten auf der Fläche. Die Frage ist nun, welche Prozesse für diese 

effektive Sedimentbereitstellung verantwortlich sind. Es können mehrere parallel ablaufende 

Prozesse identifiziert werden, die mit einer großen räumlichen und zeitlichen Variabilität 

ablaufen. Diese Prozesskombination besteht zunächst aus dem Transport des losen Materials, 

welches in der Rinne vorhanden ist, zusätzlich wird durch Einschneiden die Rinnensohle 

tiefergelegt. Die vermutlich wichtigsten Sedimentquellen sind jedoch die rückschreitende 

Erosion an Stufen und headcuts, das Nachbrechen von Seitenwänden als Folge der seitlichen 

Unterschneidung und das Überlaufen von plunge pools unterhalb von Stufen. Diese 

Überlagerung unterschiedlicher Prozesse bereiten aktuell verwendeten, physikalisch basierten 

Bodenerosionsmodellen große Probleme. Diese Modelle verwenden meist hydraulische 

Parameter, die theoretisch in einem linearen Verhältnis zur Abtragsrate stehen. Allerdings 

wird nur das Einschneiden in die Rinnensohle hydraulisch kontrolliert, die anderen Prozesse 

haben nur bedingt etwas mit dem fließenden Wasser zu tun. Daher ist auch die Annahme, dass 

die transport rate die transport capacity nicht übersteigen könne, nicht zu bestätigen, 

zumindest dann nicht, wenn die allgemein üblichen Gleichungen zur Berechnung der 

transport capacity verwendet werden. Als weitere Probleme der Bodenerosionsmodelle 

können Unklarheiten bei der Definition und der Herleitung bestimmter Parameter ausgemacht 

werden. Da die gegebenen Modelle keine zufriedenstellenden Ergebnisse liefern, ist es 

wichtig, weiterhin experimentelle Daten zu erheben. Dazu ist eine reproduzierbare Methode 

erforderlich, welche mit den Spülversuchen entwickelt und im Laufe der Zeit immer weiter 

verbessert worden ist, um ein möglichst breites Spektrum an Informationen generieren zu 

können. Neben Abtragswerten können auch hydraulische Parameter erfasst bzw. aus erfassten 

Daten abgeleitet werden. Die letzte hier vorgestellte Version des Versuchsaufbaus ist ein 

Etappenziel, weitere Verbesserungen und Erweiterungen sind bereits in der Erprobungsphase. 

Die Methode kann zudem innerhalb anderer Fragestellungen im Bereich Oberflächenabfluss 

27


und Bodenabtrag erfolgreich eingesetzt werden, Untersuchungen zur Ziegenerosion 

profitieren bereits von der Methode „Spülversuch“. 

Eine Schwachstelle der aktuellen Versuchsversion liegt in der fehlenden Information 

bezüglich der tatsächlichen Quelle des bewegten Sedimentes. Bisher können diese Quellen 

nur durch Beobachtungen während des Versuches erfasst werden. Dabei ist jedoch eine 

Quantifizierung nicht möglich, des Weiteren werden auf diese Weise nur sehr große und 

damit deutlich sichtbare Ereignisse berücksichtigt. Aktuell wird überprüft, ob die Erstellung 

von Differenzbildern eines DGMs (digitales Geländemodell) aus Stereoluftbildpaaren der 

Aufnahmehöhe 1 m über Grund geeignet ist, Aussagen bezüglich der Menge des beim 

Spülversuch bewegten/abgetragenen Sediments zu machen. Dabei handelt es sich um eine 

Anpassung der bereits erprobten Methode des großmaßstäbigen Luftbildmonitorings, welches 

seit Jahren in der Arbeitsgruppe der Physischen Geographie an der Universität Trier unter 

Leitung von Herrn Prof. Ries verwendet wird, um die Entwicklung von Gullys zu erfassen. 

Statt einer fliegenden Kameraplattform wird hier ein terrestrisches Trägersystem verwendet. 

Die Versuchsanordnung soll sicherstellen, dass beide Kameras mit gleichbleibendem Abstand 

über die Geländeoberfläche geführt werden und in Abständen von ca. 1 m Bildpaare von der 

Versuchsfläche aufnehmen. Die Berechnung der Flughöhe über Grund erfolgt überschlägig 

anhand der gültigen Formeln für Abbildungsmaßstab und technischer Daten des 

Kameraherstellers. Zur Volumenberechnung anhand der Differenzbilder ist die zu bespülende 

Geländeoberfläche vor und nach der Durchführung des Spülversuchs mit einer Serie von 

Stereoluftbildpaaren unter Beachtung der für die Luftbilderstellung üblichen Überdeckung 

von ca. 60 % lückenlos abzudecken. Nach Durchführung erster Tests ist eine Konstruktion 

vergleichbar einem Turmdrehkran auf Basis eines Vermessungsstatives hergestellt worden. 

Diese Stereoluftbildpaare sollen mit dieser in Abbildung 12 dargestellten Versuchsanordnung 

aufgenommen werden, wobei durch die niedrige Aufnahmehöhe von ca. 1 m über Grund 

sichergestellt wird, dass auch kleine Mengen des umgelagerten Sediments erfasst werden 

können. 

28


Abbildung 12: Drehkrankonstruktion: A: Gesamtgestell, B: Kameraaufhängung, C: maximale 

Reichweite, D: minimale Reichweite 

Zu behebende Probleme liegen zum einen in der Tatsache, dass hohe Temperaturen 1) die 

Akkulaufzeit auf ca. 10 min begrenzen und 2) sich die Kameragehäuse verziehen. Das 

Akkuproblem kann provisorisch über eine modifizierte Stromversorgung (Autobatterie 

Umformer 12 V auf 220 V Handyladegerät Akkudummy) gelöst werden. Eine 

Abschattung der Rinne verringert die Hitze und verbessert die Licht- und damit auch die 

Bildqualität. Zum anderen verhindert die Ausführung mit nur zwei Kameras die Aufnahme 

von Überhängen in den Rinnenwänden. Dazu sollen in Zukunft zwei weitere, schräg 

angebrachte Kameras an der Kameraschiene montiert werden. Die Auswertung der Bilder 

erfolgt über das Standardprogramm Leica Photogrammetry Suite. 

Ein weiterer Ansatzpunkt für die Auswertung der erstellten Fotos liegt in der Verwendung 

einer Kombination von kommerziellen und open source - Programmen zur 3-D Visualisierung 

von Rinnen und zur automatischen Berechnung von Umlagerungsvolumina. Das erste zu 

verwendende Programm ist MS-Photosynth©. Dieses Programm stellt aus einer Vielzahl von 

Einzelfotos ein Gesamtbild zusammen. Dabei werden nicht mehr, wie bisher üblich, 

29


bestimmte Passpunkte benötigt, die in jedem der Fotos vorhanden sein müssen, das Programm 

erkennt vielmehr selbstständig Punktcluster (Übereinstimmung bezüglich Helligkeitswerten, 

Farbwerten, Kontrastwerten), die in überlappenden Fotopaaren vorhanden sind. Anhand 

dieser feature-points, also Punkthaufen, die in den Fotos zu finden sind, werden räumliche 

Markierungen gesetzt, anhand derer die Einzelbilder in Übereinstimmung gebracht und soweit 

entzerrt werden, dass ein passgenaues Panorama entsteht. Dadurch können Fotos kombiniert 

werden, die aus sehr unterschiedlichen Winkeln aufgenommen worden sind. Als nächster 

Schritt wird die Punktwolke aus MS-Photosynth© extrahiert. Jeder Punkt der Punktwolke 

weist zu diesem Zeitpunkt relative x-, y-, und z- Koordinaten auf. Dieses Zwischenergebnis 

wird in open source - Programmen weiterverarbeitet. In PMVS2 (Patch-Based Multi-View 

Stereo) und CMVS (Clustering for Multi-View Stereo) wird die Punktwolke mit den 

vorhandenen Bildinformationen überlagert. Mesh Lab trianguliert zwischen den jeweils 

benachbarten Punkten der Punktwolke, es entsteht ein dreidimensionales Gitternetz. 

Probleme liegen v.a. in der unbekannten Genauigkeit und dem Fehlen eines Maßstabes dieser 

in MS-Photosynth© erstellten Höhenmodelle. Weiterhin lassen die mit MS-Photosynth© 

erstellten Punktwolken immer wieder Bereiche ohne Werte erkennen. Diese Bereiche führen 

in der Volumendifferenzberechnung zu großen Fehlern. Das Ziel der Versuche liegt jedoch 

darin, auch möglichst kleine Mengen von verlagertem Substrat zu erfassen, die Gesamt- 

Fehlergröße liegt jedoch geschätzt um mehrere Größenordnungen über der theoretisch durch 

das Aufnahmesystem möglichen Genauigkeit. Des Weiteren muss MS-Photosynth© als 

black-box-Modell angesehen werden, die verwendeten Algorithmen sind nicht bekannt und 

dadurch fehlt die Kontrolle über Fehlergrößen, -mengen und -quellen. Angedacht für die 

Zukunft ist zunächst die Verwendung eines nicht cloud-basierten Programmes als Alternative 

zu MS-Photosynth©. Dadurch soll das Auftreten von unkontrollier- und unkorrigierbaren 

Fehlern schon im ersten Verarbeitungsschritt ausgeschlossen werden. Nach Herstellung der 

endgültigen Einsatzbereitschaft wird diese Methode eine kostengünstige Variante zum sehr 

viel kostenintensiveren Laserscanning darstellen. 

Des Weiteren soll zukünftig die Fließgeschwindigkeit im Bereich von einem Meter ober- und 

unterhalb der Messstellen mit Hilfe von einfachen Webcams gemessen werden. Dadurch kann 

Personal eingespart und Messkampagnen selbst mit kleineren Teams realisiert werden. Die 

Auswertung des Filmmaterials und die Ermittlung der Fließgeschwindigkeit kann im 

Anschluss an die Geländearbeit durchgeführt werden. 

Ein wünschenswertes Ziel wäre es, mithilfe der gewonnenen Daten und Beobachtungen ein 

funktionierendes Bodenerosionsmodell bzw. Submodell rill erosion zu entwickeln. Fraglich 

30


bleibt jedoch, ob die Vielzahl verschiedener Prozesse - jeder mit hoher räumlicher und 

zeitlicher Variabilität - mittels empirischer Formeln ausreichend genau beschrieben werden 

kann. Ein neuer Ansatz besteht in der Verwendung von Wahrscheinlichkeits- 

Dichtefunktionen. Die erfolgversprechendste, aber noch nicht einsatzbereite Version ist von 

Sidorchuk (Sidorchuk, 2002; Sidorchuk et al., 2004; Sidorchuk, 2005 a, b; Sidorchuk et al., 

2008; Sidorchuk, 2009 a, b) entwickelt worden. Diese stochastischen Modelle reduzieren die 

Anzahl der empirischen Komponenten, wodurch das theoretische und das Prozesswissen 

erhöht und der black-box-Charakter der empirischen Modelle verhindert werden kann. Es 

wird nicht mehr ein einzelner Wert als Eingangsgröße sondern Wahrscheinlichkeits- 

Dichtefunktionen (probability density functions, pdf’s) des gemessenen Parameters 

verwendet. Das Problem dieser Modelle der dritten Generation (Sidorchuk, 2009 b) ist, dass 

der Typ der Wahrscheinlichkeits-Dichtefunktion noch nicht bekannt ist. Es gibt eine große 

Anzahl von Boden- und Umweltparametern, welche die Erosionsresistenz beeinflussen, und 

es ist nicht klar, ob dieses komplexe Konzept durch Wahrscheinlichkeits-Dichtefunktionen 

beschrieben werden kann. Aufgrund der benötigten Anzahl von Wahrscheinlichkeits- 

Dichtefunktionen und der benötigten Computerleistung scheint dieser Ansatz laut Knapen et 

al. (2007) zu kompliziert zu sein, sodass bis auf Weiteres nicht auf experimentelle 

Bodenerosionsforschung verzichtet werden kann; zum einen zur Verbesserung des 

Grundlagenwissens, zum anderen zur Ermittlung der pdf’s in der stochastischen 

Bodenerosionsmodellierung. 

Zwei Dinge sind zu unserer Arbeit nötig: Unermüdliche 

Ausdauer und die Bereitschaft, etwas, in das man viel 

Zeit und Arbeit gesteckt hat, wieder wegzuwerfen. 

Albert Einstein 

31


Quellenangaben 

Anderson, D.M., Macdonald, L.H. (1998): Modelling road surface sediment production using 

a vector geographic information system. Earth Surface Processes and Landforms 23, 

95–107. 

Appelboom, T.W., Chescheir, G.M., Skaggs, R.W., Hesterberg, D.L. (2002): Management 

practices for sediment reduction from forest roads in the coastal plains. Transactions 

of ASAE 45(2), 337–344. 

Auerswald, K., Fiener, P., Dikau, R. (2009): Rates of sheet and rill erosion in Germany - A 

meta-analysis. Geomorphology 111(3-4), 182-193. 

Avni, Y. (2005): Gully incision as a key factor in desertification in an arid environment, the 

Negev highlands, Israel. Catena 63, 185-220. 

Beuselinck, L., Govers, G., Hairsine, P., Sander, G., Breynaert M. (2002): The influence of 

rainfall on sediment transport by overland flow over areas of net deposition. Journal of 

Hydrology 257, 145-163. 

Brodie, I., Rosewell C. (2007): Theoretical relationships between rainfall intensity and kinetic 

energy variants associated with stormwater particle washoff. Journal of Hydrology, 

340(1-2), 40-47. 

Brunton, D.A., Bryan, R.B. (2000): Rill network development and sediment budgets. Earth 

Surface Processes and Landforms 25, 783-800. 

Bryan, R.B., Poesen, J. (1989): Laboratory experiment on the influence of slope length on 

runoff, percolation and rill development. Earth surface processes and Landforms 14, 

211-231. 

Bryan, R.B. (2000): Soil erodibility and processes of water erosion on hillslope. 

Geomorphology 32(3-4), 385-415. 

Casali, J., Loizu, J., Campo, M., De Santisteban, L., Alvarez-Mozos, J. (2006): Accuracy of 

methods for field assessment of rill and ephemeral gully erosion. Catena 67(2), 128- 

138. 

Cerdan, O., Le Bissonnais, Y., Couturier, A., Bourennane, H., Souchère, V. (2002): Rill 

erosion on cultivated hillslopes during two extreme rainfall events in Normandy, 

France. Soil and Tillage Research 67(1), 99-108. 

Constantin, P. (2001): Some open problems and research directions in the mathematical study 

of fluid dynamics. Mathematics unlimited-2001 and beyond, 353-360. 

32


Eastaugh, C. S., Rustomji, P. K., Hairsine, P. B. (2008): Quantifying the altered hydrologic 

connectivity of forest 23 roads resulting from decommissioning and relocation. 

Hydrological Processes 22, 2438–2448. 

Faust, D., Schmidt, M. (2009): Soil erosion processes and sediment fluxes in a Mediterranean 

marl landscape, Campina de Cádiz, SW Spain. Z.Geomorph. N.F. 52 (2), 247-265. 

Fefferman, C.L. (2006): Existance and smoothness of the Navier-Stokes equation, The 

millennium prize problems. Clay Math. Inst., Cambridge, MA, 57-67. 

Gilley, J.E., Kottwitz, E.R., Simanton, J.R. (1990): Hydraulic characteristics of rill. 

Transactions of the ASAE 33, 1900-1906. 

Giménez, R., Govers, G. (2002): Flow Detachment by Concentrated Flow on Smooth and 

Irregular Beds. Soil Sci Soc Am J 66(5), 1475-1483. 

Govers, G. (1987): Spatial and temporal variability in rill development processes at the 

Huldenberg experimental site. Catena Supplement 8, 17-34. 

Govers, G., Everaert, W., Poesen, J., De Ploey, J., Lautridou, J.P. (1990): A Long flume study 

of dynamic factors affecting the resistance of loamy soil to concentrated flow erosion. 

Earth surface processes and landforms 15, 313-328. 

Govers, G. (1991): Time-dependency of runoff velocity and erosion: the effect of the initial 

soil moisture profile. Earth Surface Processes and Landforms 16, 713-729. 

Govers, G. (1992): Evaluation of transporting capacity formulae. In: Parsons, A.J., Abrahams, 

A.D. (Eds.): Overland flow – Hydraulics and erosion mechanics. UCL-Press, 

Guildford, 243-273. 

Govers, G., Giménez, R., Van Oost, K. (2007): Rill erosion: Exploring the relationship 

between experiments, modelling and field observations. Earth-Science Reviews 84(3- 

4), 87-102. 

Grayson, R.B., Haydon, S.R., Jayasuriya, M.D.A., Finlayson, B.L. (1993): Water quality in 

mountain ash forests—separating the impacts of roads from those of logging 

operations. Journal of Hydrology 150: 459–480. 

Huang, C., Bradford, J.M., Laflen, J.M. (1996): Evaluation of the detachment-transport 

coupling concept in the WEPP rill erosion equation. Soil Science Society American 

Journal 60, 734-739. 

Knapen, A., Poesen, J., Govers, G., Gyssels, G., Nachtergaele, J. (2007): Resistance of soils 

to concentrated flow erosion: A review. Earth-Science Reviews 80(1-2), 75-109. 

Kuhn, N., Bryan, R.B., Navar, J. (2003): Seal formation and interrill erosion on a smectiterich 

Kastanozem from NE-Mexico. Catena 52, 149-169. 

33


Kuhn, N., Bryan, R. (2004): Drying, soil surface condition and interrill erosion on two 

Ontario soils. Catena 57, 113-133. 

Le Bissonnais, Y., Cerdan, O., Lecomte, V., Benkhadra, H., Souchère, V., Martin, P. (2005): 

Variability of soil surface characteristics influencing runoff and interrill erosion. 

Catena 62, 111-124. 

Loch, R.J. (2000): Using Rainfall simulation to guide planning and management of 

rehabilitated areas: Part I. Experimental methods and results from a study at the 

northparkes mine, Australia. Land Degradation and Development 11, 221-240. 

Mancilla, G.A., Chen, S., McCool, D.K. (2005): Rill density prediction and flow velocity 

distribution on agricultural areas in the Pacific Northwest. Soil and Tillage Research 

84, 54-66. 

Marzolff, I., Ries, J.B., Poesen, J. (2011): Short-term vs. medium-term monitoring for 

detecting gully-erosion variability in a Mediterranean environment. Earth Surface 

Processes and Landforms 36, 1604–1623. 

Merz, W. (1993): Experimentelle Untersuchungen zur Rillenerosion auf landwirtschaftlich 

genutzten Böden in Kanada und der Volksrepublik China. Freiburger Geographische 

Hefte, Heft 40, Selbstverlag des Institutes für Physische Geographie der Albert- 

Ludwig-Universität Freiburg i.Br., Freiburg, 147 pp. 

Meyer, L.D., Forster, G.R., Römkens, M.J.M. (1975): Source of soil eroded by water from 

upland slopes. Proc. 1972 Sediment Yield Workshop, US Dept. of Agric. Sediment. 

Lab., Oxford, Mississippi: 177-189. 

Morgan, R.P.C., Martin, L., Noble, C.A. (1987): Soil erosion in the United Kingdom: a Case 

Study from Mid-Bedfordshire, England. Occasional Paper No.14. 

Motha JA, Wallbrink PJ, Hairsine PB, Grayson RB. (2003): Determining the sources of 

suspended sediment in a forested catchment in southeastern Australia. Water 

Resources Research 39(3): 1056. DOI: 10.1029/2001WR000794. 

Nearing, M.A., Bradford, J.M., Parker, S.C. (1991): Soil detachment by shallow flow at low 

slopes. Soil Science Society of America Journal 55 (2), 339-344. 

Nearing, M.A., Parker, S.C. (1994): Detachment of soil by flowing water under turbulent and 

laminar conditions. Soil Sci. Soc. Am. J. 58 (6), 1612-1614. 

Nearing, M.A. (1998): Why soil erosion models over-predict small soil losses and underpredict 

large soil losses. Catena 32, 15-22. 

Poesen, J. (1987): Transport of rock fragments by rill flow – a field study. In: Bryan, R.B. 

(Ed.): Rill erosion - process and significance. Catena Supplement 8, 35-54. 

34


Polyakov, V.O., Nearing, M.A. (2003): Sediment transport in rill flow under deposition and 

detachment conditions. Catena 51, 33-43. 

PTB Mitteilungen (2007): Das Internationale Einheitensystem (SI). Amts- und 

Mitteilungsblatt der Physikalisch-Technischen Bundesanstalt, 117. Jahrgang. Heft 2, 

Braunschweig und Berlin. 

Regüés, D., Balasch, J.C., Castelltort, X., Soler, M., Gallart, F. (2000): Relación entre las 

tendencias temporales de producción y transporte de sedimentos y las condiciones 

climáticas en una pequeña cuenca de montaña mediterránea (Vallcebre, Pirineos 

Orientales). Cuadernos de Investigación Geográfica 26, 41-65. 

Richter, G. (2001): Bodenerosion – Analyse und Bilanz eines Umweltproblems. 

Wissenschaftliche Buchgesellschaft, 264 Seiten. 

Ries, J.B., Marzolff, I. (2003): Monitoring of gully erosion in the Central Ebro Basin by large 

scale aerial photography taken from a remotely controlled blimp. Catena 50, 309-328. 

Ries, J.B. (2011): Bodenerosion. In: Gebhardt, H., Glaser, R., Radtke, U., Reuber, P. (Hrsg.): 

Geographie – Physische Geographie und Humangeographie. 2. Auflage, Spektrum 

Akademischer Verlag, 506-517. 

Ries, J.B., Andres, K., Wirtz, S., Tumbrink, J., Wilms, T., Peter, K.D., Burczyk, M., Butzen, 

V., Seeger, M. (subm. 2011) Sheep and goat erosion – experimental geomorphology 

as an approach for the quantification of underestimated processes. Zeitschrift für 

Geomorphologie. 

Scherer, U. (2008): Prozessbasierte Modellierung der Bodenerosion in einer Lösslandschaft. 

Dissertation, Fakultät für Bauingenieur-, Geo- und Umweltwissenschaften, Universität 

Fridericiana zu Karlsruhe (TH), Karlsruhe, Germany. 

Schneider, G. (2008): Ein Millenniumsproblem: Die globale Existenz und Eindeutigkeit 

glatter Lösungen der dreidimensionalen Navier-Stokes-Gleichungen. Mathematik- 

Online: Beiträge zu berühmten, gelösten und ungelösten Problemen, Nummer 2. 

Seeger, M., Errea, M.P., Beguería, S., Arnáez, J., Martí, C., García-Ruiz, J.M. (2004): 

Catchment soil moistureand rainfall characteristics as determined factors for discharge 

/ suspended sediment hysteretic loops in a small headwater catchment in the Spanish 

Pyrenees. Journal of Hydrology 288, 299-311. 

Seeger, M., Errea-Abad, M.-P., Lana-Renault, N. (2005): Spatial Distribution of Soils and 

their Properties as Indicators of Degradation/Regradation Processes in a Highly 

Disturbed Mediterranean Mountain Catchment. Journal of Mediterranean Ecology 6 

(1), 53-59. 

35


Seeger, M. (2007): Uncertainity of factors determining runoff and erosion processes as 

quantified by rainfall simulations. Catena 71 (1), 56-67. 

Seiler, R. (2002): Die Navier-Stokes-Gleichung. Elemente der Mathematik 57, 109-114. 

Sidorchuk, A. (2002): Stochastic Modelling of soil erosion and deposition. Proceedings of the 

12 th ISCO Conference, Beijing, China, 26-31 May 2002, 136-142. 

Sidorchuk, A., Smith, A., Nikora, V. (2004): Probability distribution function approach in 

stochastic modelling of soil erosion. Sediment transfer trough the fluvial system. 

IHAS Publ. 288, 345-353. 

Sidorchuk, A. (2005a): Stochastic components in the gully erosion modelling. Catena 63, 

299-317. 

Sidorchuk, A. (2005b): Stochastic modelling of erosion and deposition in cohesive soils. 

Hydrol. Process. 19, 1399-1417. 

Sidorchuk, A., Schmidt, J., Cooper, G. (2008): Variability of shallow overland flow velocity 

and soil aggregate transport observed with digital videography. Hydrological 

Processes 22, 4035-4048. 

Sidorchuk, A. (2009a): High-Frequency variability of aggregate transport under water erosion 

of well-structured soils. Eurasian Soil Sci. 42 (5), 543-552. 

Sidorchuk, A. (2009 b): A third generation erosion model: The combination of probabilistic 

and deterministic components. Geomorphology 110 (1-2), 2-10. 

Stroosnijder, L. (2005): Measurement of erosion: Is it possible? Catena 64, 162-173. 

Temam, R. (2000): Some developments on Navier-Stokes equations in the second half of the 

20 th century. Development of mathematics 1950-2000, Birkhäuser, Basel, Switzerland, 

1049-1106. 

Wiegner, M. (1999): The Navier-Stokes equations – a neverending challenge? Jahresbericht 

Deutsch. Math.-Verein 101 (1), 1-25. 

Wirtz, S., Seeger, M., Ries, J.B. (2010): The rill experiment as a method to approach a 

quantification of rill erosion process activity. Zeitschrift für Geomorphologie 54 (1), 

47-64. 

Wirtz, S., Seeger, M., Ries, J.B. (2012a): Field experiments for understanding and 

quantification of rill erosion processes. Catena 91, 21-34. 

Wirtz, S., Iserloh, T., Rock, G., Hansen, R., Marzen, M., Seeger, M., Betz, S., Remke, A., 

Wengel, R., Butzen, V., Ries, J.B. (2012b): Soil erosion on abandoned land in 

Andalusia – a comparison of interrill – and rill erosion rates. ISRN Soil Science, 

doi:10.5402/2012/730870. 

36


Wirtz, S., Seeger, M., Zell, A., Wagner, C., Wagner, J.-F., Ries, J.B. (subm. 2012): 

Applicability of different hydraulic parameters to describe soil detachment in eroding 

rills. PLoSOne. 

Wirtz, S., Seeger, M., Remke, A., Wengel, R., Wagner, J.-F., Ries, J.B. (2013): Do 

deterministic sediment detachment and transport equations adequately represent 

process-interactions in eroding rills? An experimental field study. Catena 101, 61-78. 

37


Kapitel 2 

Wirtz et al. (2012b): Soil erosion on abandoned land in Andalusia – a comparison 

of interrill– and rill erosion rates. ISRN Soil Science, doi: 10.5402/2012/730870. 

38


Soil erosion on abandoned land in Andalusia – a comparison of interrill- and rill erosion 

rates 

Wirtz, S. (1); Iserloh, T. (1); Rock, G. (2); Hansen, R. (1); Marzen, M. (1); Seeger, M. (1); 

Betz, S. (1); Remke, A. (1); Wengel, R. (1); Butzen, V. (1); Ries, J.B. (1) 

(1): Trier University, Dep. of Physical Geography, Behringstraße, 54286 Trier, Germany 

(2): Trier University, Remote Sensing Department, Behringstraße, 54286 Trier, Germany 

Abstract 

The present paper is based on several field investigations (monitoring soil and rill erosion by 

aerial photography, rainfall simulations with portable rainfall simulators and manmade rill 

flooding) in southern Spain. Experiments lead now to a closer understanding of the dynamics 

and power of different soil erosion processes in a gully catchment area. 

The test site Freila (Andalusia, SE Spain) covers an area of 10.01 ha with a rill density of 169 

m ha -1 , corresponding to a total rill length of 1694 m. Assuming an average rill width of 0.15 

m, the total rill surface can be calculated at 250 m² (0.025 ha). This given, the surface covered 

by rills makes up only 0.25 % of the total test site. Since the rill network drains 1.98 ha, 20 % 

of the total runoff comes from rills. The rills’ sediment erosion was measured and the total 

soil loss was then calculated for detachment rates between 1685 g m -2 and 3018 g m -2 . The 

interrill areas (99.75 % of the test site) show values between 29-143 g m -2 . This suggests an 

important role of rill erosion concerning runoff and soil detachment. 

Keywords 

Soil erosion, water erosion, rill erosion, interrill erosion, rainfall simulation 

1 Introduction 

Soil erosion by water involves different physical processes at variable spatial and temporal 

scales. The two main processes are interrill and rill erosion by runoff water, the mechanisms 

of these two processes are completely different. The soil detachment in interrill erosion is 

induced and enhanced by splash and shallow overland flow [1]. In addition, it is influenced by 

the intrinsic characteristics of the soils [2, 3, 4] and rainfall intensity [5, 6]. In contrast, rill 

erosion is caused by a concentrated overland flow [6, 7, 8]. This is considered to be the most 

important process of sediment erosion and soil loss [9, 10]. As a result, the new rills can 

39


become persistent and form gullies, potentially constraining further land use [11, 12, 13, 14]. 

Especially on fallow and shrub land, rills can develop without being disturbed by land 

management measures like ploughing. Since huge areas in the Mediterranean are covered by 

fallow and shrub land [15], rill erosion can be assumed to be a major process of soil erosion in 

the Mediterranean. 

The outstanding importance of linear erosion for all intents and purposes (geomorphology, 

hydrology and economy) can be explained by the amount of kinetic energy of water, running 

as a concentrated runoff in channels. When concentrated, water reaches its maximum impact 

concerning erosion and transport [16]. The percentage of interrill-, rill- and gully erosion on 

the total soil loss in a catchment area is difficult to determine, and results of many research 

groups differ considerably in comparing the effectiveness of the different soil erosion 

processes. 

Results concerning the proportion of gully erosion on total soil erosion vary between 10 % 

and more than 90 % [17]. Gullies need high-intensity rainfall events to be activated. Most 

thunderstorms do not activate the gully in a catchment, but are able to generate or reactivate 

smaller forms, the rills. Faust & Schmidt [18] considered the geomorphologic importance of 

gullies as quite low, corresponding to the rare activity of the gullies. They state an activity 

frequency of one single event in 20 years, compared with an assumed activity of the rills of 

about four times per year. On that account, the rills deliver smaller sediment quantities, but 

this can occur several times within one year. Meyer et al. [19] suggested a triplication of 

erosion rates due to rill development. Cornfields in Bedfordshire (Great Britain) lost as much 

as 9 to 21 times more sediment by rill erosion, compared with erosion only affected by 

interrill erosion [20]. Cerdan et al. [9] reported the soil loss by rill erosion in Normandy 

during only a few heavy rainfall-events to be up to 90 % of the total soil loss. 

During the last decades, several approaches have been developed to describe and predict soil 

detachment and sediment transport in rills in a reliable way [7, 21, 22]. In contrast, the factors 

influencing the development and the behaviour of rills have not been comprehensively 

assessed yet. The relationships between factors influencing these processes remain unclear as 

well. Knapen et al. [8] attribute this to the lack of comparable data that could be used for a 

meta-analysis on rill erosion. Furthermore, there is still little known about the function of rills 

in specific environments. 

In this paper, the results of a set of experimental methods are used to draw conclusions from 

the differences between interrill- and rill erosion dynamics on a gully catchment in Andalusia 

(Spain). Three main questions were to be answered: 

40


1. Which proportion of the test site area is drained by rill networks? 

2. Which runoff intensities appear in the rills, which on the interrill-areas? 

3. How effective is the rill erosion compared to the interrill erosion in the catchment? 

2 Material and Methods 

2.1 Study Area 

The study area Freila is situated in the Hoya de Baza sedimentary basin (see figure 1) in 

Andalusia (Southeast Spain). The bedrock mostly consists of Pliocene sedimentary rocks, i.e. 

marls and fine grained sandstones. At the surface the marls and sandstones are weathered to 

calcareous loamy to sandy lithosols. The semi-arid climate is characterised by a mean annual 

temperature of about 14.2 °C. The annual precipitation is down to only 368 mm, with a high 

inter-annual variability. The vegetation is dominated by low shrub-land of Thymus vulgaris 

and Stipa tenacissima grassland. The land use on the southern lake-side of the Negratin 

reservoir is dominated by abandoned cereal fields, which are extensively grazed by flocks of 

sheep. Agricultural land use comprises mainly cereal dry-farming [23]. At the top of the 

catchment, a gully has developed. 

Figure 1: Test site in Andalusia (UTM: 509864 E – 4154369 N) 

41


2.2 Methods 

During the field work, we combined the experimental methods rill experiment and rainfall 

simulation with field mapping. As a geodetic control of the maps we used large scale aerial 

photographs, taken with our own equipment. 

2.2.1 Rill experiment 

During the rill experiments, water was pumped into an existing erosion rill using a motor 

driven pump. For low flow experiments (LFEs) we used a constant discharge at the inlet of 9 

L min -1 for 8 minutes. The total amount of water was 72 L. In the high flow experiments 

(HFEs) we used a pump with a capacity between 250 and 330 L min -1 . During 3 to 4 minutes 

we reached a water discharge of about 1000 L. The mobilisation of sediments due to 

turbulences of water at the inlet of the measuring channel was suppressed by a special inlet 

construction. 

Each rill experiment consisted of two runs. In the first run the rill was tested under field (dry) 

conditions and in a second run, about 15 min later, the same rill was tested under wet 

conditions. The flow velocity within the rill was measured by recording the travel times of the 

waterfront and of two applied colour tracers. In the LFEs, the colour tracers were used after 

the flow stabilisation (3 and 6 minutes) and in the HFEs after 1 and 2 minutes. Accordingly, 

three velocity curves were recorded and changes in flow dynamics can be detected. The used 

colour tracers were the food colourings E 124 (red) and E 13 (blue). 

The rill's slope was measured using a spring bow of 1 m range with a digital spirit level. It has 

to be considered, that slope measuring provided only average slopes for each meter of the rill 

length, so steps or knick-points in the rill were not captured. However, the position of each 

step or knick-point and also the heights were separately recorded. 

At each of the three measuring points (MP) along the rill, four water samples were taken: the 

first directly when the waterfront has reached the sampling point, the second 30 sec later, the 

third after 90 sec and the fourth 150 sec after the arrival of the waterfront. The sediment 

concentration of each sample was determined by filtration in the laboratory. [24, 25] 

At each MP, the rill cross section was measured by means of a yardstick (LFEs) or a laser 

rangefinder (HFEs). The distance between ground level and sensor respectively, and rill 

bottom was measured in 0.02 m steps. This method allowed an accurate calculation of the 

rill’s cross section area and also an estimation of the rills’ volume at the MP. 

The water height was measured simultaneously with the time of sampling by means of a 

yardstick in the LFEs or continuously by ultrasonic sensors (HFEs) at each measuring point. 

42


2.2.2 Rainfall Simulations 

The test plot was circular, with a diameter of 60 cm and an area of 0.28 m 2 . It was delimited 

by a steel ring of 7 cm height, which was introduced into the soil for at least 3 cm. The outlet 

was V-shaped and was placed at the deepest point of the plot at surface level. The commercial 

full cone nozzle (Lechler 460.608) was fed with a pressure of about 40 kPa (0.4 bars) at a 

height of 2 m. The water flow was regulated by a flow metre (Type KSK-1200HIG100) 

positioned on a separate pole in 1.5 m height. The resulting rainfall intensity was maintained 

throughout the experiments at around 40 mm h -1 , which is considered to be mean 

thunderstorm rainfall intensity with a return period of about 2 years [26]. The complete runoff 

was collected and runoff and soil detachment was determined gravimetrically. [23, 27, 28, 29, 

30]. The standard deviation of the rainfall intensity is < 5 % [28]. 

Plot surface parameters were rock fragment cover, separated in embedded and overlying, 

vegetation cover, bare soil area, separated in crusted and uncrusted and finally the slope of the 

plot. These parameters were optically estimated in the field and validated again with the help 

of digital photographs taken from every plot, and preferably taken at an angle of 90° to the 

plot surface. The slope was measured by a clinometer. 

For comparing the variability of the different parameters, we calculated the average of the 

relative measurement errors (RME) following the DIN 1319-1 [31]. This error is defined as 

xa 

xr 

f = 100 

Eq. (1) 

x 

r 

where x a are the measured values and x r are “correct” values; we used the mean of the 

measured values as x r . This value describes the deviation of each single experiment from the 

mean of all experiments. 

2.2.3 Small Format Aerial Photography (SFAP) 

The photos were taken using three different camera carriers depending on the wind 

conditions, requested flight level (photographed area) and available manpower: a hot air 

blimp, a kite or an unmanned aerial vehicle (UAV). A detailed description of the camera 

carriers and aerial photography in general is to find in Aber et al. [32]; the hot air blimp is 

also described in Ries & Marzolff [33]. 

The first used camera was a Canon 350D with a Canon EF-S 20 mm objective, the maximum 

solution of the photos is 8 MP, the resulting stereoscopic images show a ground resolution 

between 0.5 and 11 cm, depending on the flying height. 

43


The second used camera was a Nikon Coolpix S6000 digital compact camera with a 

maximum solution of 14.48 MP. The zoom-objective has an aperture angle dynamic between 

28 and 144 mm and a light intensity between 2.8 and 5.6. 

Aerial photographs were used during field work as a basis for the mapping and the 

classification in “vegetation areas” and “no vegetation areas”. 

2.2.4 Field mapping and GIS Analysis 

The field mapping based on the self-made aerial photographs should deliver information 

about the spatial distribution of linear erosion forms, the catchment areas of these forms and a 

total rill length on the test site. With this information, different parameters can be calculated. 

The total rill area is calculated as follows: 

A =W L 

(Eq. 2) 

R 

R 

R 

Where A R = total rill area [m²], W R = estimated average rill width [m] and L R = total rill 

length in the test site [m]. 

The rill density is calculated using the following equation (eq. 3): 

D R 

= L R 

A T 

(Eq. 3) 

Where D R = rill density [m ha -1 ], L R = total rill length in the test site [m] and A T = test site 

area [ha]. 

The rill drainage index is calculated as follows: 

I R 

= C R 

A T 

(Eq. 4) 

Where I R = rill drainage index [ha ha -1 ], C R = total area of all rill catchments [ha] and A T = 

test site area [ha]. 

2.2.5 Classification of the aerial photographs 

In order to obtain spatial information about the different land cover types and distribution, a 

classification of digital UAV imagery has been performed. First, an unsupervised 

classification was done for identifying the classes that can be statistically distinguished. As a 

result, only three classes could be distinguished, i.e. “vegetation”, “no vegetation/soil” and 

“shadow”. A drawback of classifying UAV imagery was the fact, that for such a large area, 

multiple flights were needed to cover the whole site. This led to a change of the illumination 

conditions for the different flights’ images. Considering these facts, every tile of the mosaic 

needed to be classified individually. Using manually digitised training areas, the maximum 

44


likelihood classifier was chosen. After classification of every single tile, a mosaic was 

calculated. 

3 Results and Interpretation 

3.1 Rill experiments 

The rill experiments were accomplished in five different rills, one rill was tested three times, 

once in a LFE and two times in a HFE. The catchment areas of the tested rills were between 

190 and 1600 m², the tested rill parts showed lengths between 15 and 21 m and widths 

between 0.4 and 2.1 m, resulting in rill areas between 6 and 44 m². These values are 

summarised in table 1. 

Table 1: Setup parameters of the tested rills 

Experiment rill Inflow intensity Inflow Catchment Tested rill Estimated Rill area 

[L min -1 ] duration [min] area [m²] length [m] rill width [m] [m²] 

RE1_2008 1 9 8 415 15 0.4 6 

RE2_2008 2 9 8 203 21 0.4 8.4 

RE3_2008 3 9 8 579 15 0.5 7.5 

RE4_2009 1 250 4 415 16 0.4 6.4 

RE5_2009 4 250 4 187 17 0.4 6.8 

RE6_2009 5 330 3 1641 21 2.1 44.1 

RE7_2009 1 250 4 415 16 0.4 6.4 

Figure 2 shows the results of the rill experiments. The sediment concentrations in the rill 

experiments with an inflow intensity of 9 L min -1 showed a data range between 0.8 

(RE1_2008b) and 4.5 g L -1 (RE2_2008a), the average sediment concentration was 2.3 g L -1 . 

The rill experiments with an inflow intensity higher than 250 L min -1 showed sediment 

concentrations between 5 (RE4_2009b, RE5_2009b and RE7_2009b) and 20 g L -1 

(RE5_2009a), the average sediment concentration in these experiments was 8.6 g L -1 , that 

means about 3.5 times higher than in the experiments with an inflow intensity of 9 L min -1 . 

The runoff coefficients RCs showed a data range between 11 and around 95 %. In the 

experiments with an inflow quantity of 1000 L per run, nearly the complete water amount 

reached the end of the tested rill part. Using the RC and the flow length of the LFEs, we could 

calculate an average infiltration rate in L m -1 . This value was used to calculate the RC of the 

HFEs. The percentages of infiltrated water in the HFEs were between 3 % and 6 % so we 

used RCs between 94 % and 97 %. These values are summarised in table 2. The RMEs 

describe the variations between the single experiments and an average value. Most RMEs in 

45


the 9 L min -1 – experiments ranged between 67.5 (75 % quartile) and 42.8 % (25 % quartile), 

in the 250 L min -1 – experiments most RMEs were between 51.3 and 29.9 %. The highest 

RMEs were 93.1 and 131.4 %, the lowest values were 9.5 and 26.7 %; the medians were 55.8 

and 41.3 %. The RCs showed lower variations than the sediment concentrations, most RMEs 

were between 48.3 and 13.9 %, the maximum value was 75.4 %, the minimum 0.3 % and the 

median 20.8 %. The reason for the higher variations in sediment concentrations were “special 

events” such as bank failure and headcut retreat. Such processes increased the sediment 

concentration for a certain time period while the runoff stayed about constant. 

Figure 2: Results of the rill experiments: Sediment concentrations of the 6 runs of the 3 rill 

experiments with an inflow intensity of 9 L min -1 (A), sediment concentrations of the 8 runs 

of the 4 rill experiments with an inflow intensity higher than 250 L min -1 (B), runoff 

coefficients of all rill experiments (C), relative measurements errors of the sediment 

concentrations (separated in experiments with an inflow intensity of 9 L min -1 and an inflow 

intensity higher than 250 L min -1 ) and the runoff coefficients (D). 

46


Table 2: Sediment concentrations and runoff coefficients of the rill experiments 

Experiment rill sediment runoff 

concentration [g L -1 ] coefficient [%] 

RE1_2008a 

2.10 11.27 

1 

RE1_2008b 0.82 37.75 

RE2_2008a 

4.48 45.61 

2 

RE2_2008b 1.23 56.78 

RE3_2008a 

3.91 51.56 

3 

RE3_2008b 1.36 71.54 

RE4_2009a 

6.30 94.00 

1 

RE4_2009b 5.00 94.00 

RE5_2009a 

19.90 97.00 

4 

RE5_2009b 5.10 97.00 

RE6_2009a 

6.00 96.00 

5 

RE6_2009b 6.10 96.00 

RE7_2009a 

15.50 94.00 

1 

RE7_2009b 5.00 94.00 

3.2 Rainfall Simulations 

In this study, the results of 33 rainfall experiments were used; the plots of all simulations are 

shown in figure 3. In most cases, the rock fragments were embedded into the soil surface and 

the bare soil areas were crusted. Only in some special cases, e.g. after a mechanical 

disturbance (goat trampling) and the resulting destruction of the crusts, the rock fragments 

were overlying. Most test plots showed a sparse vegetation cover and showed either a crusted 

soil surface or a cover with embedded rock fragments. Rainfall experiment 23 showed a dense 

vegetation cover, plots with mechanical treatment are 5-7 and 12-15. The influence of these 

parameters on runoff and erosion are discussed in Ries et al. [27] and Ries & Marzolff [33] 

for example. The percentages of the different surface parameters and the slope values of the 

different plots are summarised in table 3. 

47


Figure 3: Surfaces of the used rainfall simulation plots 

48


Table 3: Plot parameters and results of the 33 rainfall simulations: RFC e = Rock fragment 

cover embedded, VC = Vegetation cover, BS c = Bare soil crusted, RFC o = Rock fragment 

cover overlying, BS u = Bare soil uncrusted, RC = runoff coefficient, SQ = sediment quantity, 

SSC = sediment concentration 

Id RFCe VC BS c RFC o BS u Slope RC SQ SSC 

[%] [%] [%] [%] [%] [°] [%] [g] [g L -1 ] 

01 85 14 0 1 0 9 72.0 5.8 1.4 

02 1 1 98 0 0 11 53.3 4.9 1.7 

03 63 36 0 1 0 15 80.6 5.1 1.1 

04 6 35 58 1 0 13 65.9 8.7 2.4 

05 1 0 0 11 88 5 94.6 70.8 13.4 

06 1 0 0 13 86 5 73.5 52.2 12.7 

07 1 0 0 40 59 5 112.6 50.6 8.0 

08 25 6 68 1 0 9 51.0 13.2 4.6 

09 25 18 56 1 0 11 95.2 57.6 10.8 

10 91 0 8 1 0 15 43.2 14.9 6.2 

11 99 0 0 1 0 15 66.9 11.3 3.0 

12 1 3 0 4 92 15 12.2 4.9 7.2 

13 1 2 0 11 86 15 5.6 0.4 1.4 

14 1 3 0 4 92 15 53.1 25.0 8.4 

15 1 2 0 11 86 15 84.4 49.4 10.4 

16 18 0 81 1 0 12 39.5 1.9 0.9 

17 9 4 86 1 0 10 47.7 6.9 2.6 

18 96 0 3 1 0 16 138.0 98.5 12.7 

19 27 15 57 1 0 13 53.4 4.1 1.4 

20 60 1 38 1 0 11 54.1 4.5 1.5 

21 25 10 64 1 0 16 76.3 12.0 2.8 

22 1 17 82 0 0 6 58.2 8.1 2.5 

23 1 99 0 0 0 11 42.0 3.6 1.5 

24 22 17 60 1 0 6 86.8 22.9 4.7 

25 77 16 6 1 0 9 39.5 6.7 3.0 

26 1 19 80 0 0 4 79.8 7.2 1.6 

27 1 10 89 0 0 1.8 46.6 5.9 2.3 

28 96 2 1 1 0 19 58.2 17.9 5.5 

29 20 8 71 1 0 12.3 57.0 11.2 3.5 

30 0 6 94 0 0 2 61.3 20.0 5.8 

31 85 2 12 1 0 8 29.6 13.9 8.3 

32 52 0 47 1 0 7.5 68.4 30.9 8.1 

33 97 0 2 1 0 17 36.6 4.4 2.2 

49


Figure 4: Results of the rainfall simulations: Runoff Coefficients (A), sediment quantities (B) 

and sediment concentrations (C). The limits between extremely high, very high, high, middle, 

low and very low are marked. D: Relative Measuring errors of the runoff coefficients (RC), 

the sediment quantities (SQ) and the sediment concentrations (SSC) of the rainfall 

simulations. 

The runoff coefficients, the amounts of eroded material and the sediment concentration of the 

experiments were classified in 6 classes from very low (class 0) to extreme high (class 5) as 

shown in table 4. Each class was symbolised by a box in a certain colour in figure 7. The first 

box represented the runoff coefficient, the second the sediment quantity and the third the 

sediment concentration. In a fourth box, the average class value from these three parameters 

was calculated. These values describe the hazard class of the tested plot against the called 

parameters. The class limits for runoff coefficient and sediment quantity were defined on the 

basis of the experience from about 400 rainfall simulations of the working group in semi-arid 

landscapes in North Africa and Spain during the past 16 years [e.g. 23, 27, 34]. For the 

definition of the sediment concentration class limits, we did not divide the sediment quantity 

and the runoff quantity, we defined other limits. The reason for this decision was, that in the 

other case, nearly all rainfall simulations would show “very high” or even “extreme high” 

sediment concentrations even in cases of low sediment quantities (and low runoff values). So 

we defined the limits “independent” of runoff coefficient and sediment quantity. 

50


Table 4: Classification of the rainfall simulations regarding runoff coefficient (RC), sediment 

quantity (SQ) and sediment concentration (SSC). 

Value RC [%] SQ [g] SSC [g L -1 ] Colour 

Extreme high 5 > 75 > 40 > 10 

Very high 4 50.1 – 75 8.1 – 40 8.1 – 10 

High 3 30.1 – 50 4.1 – 8 6.1 – 8 

Middle 2 10.1 – 30 1.1 – 4 4.1 – 6 

Low 1 1 – 10 0.1 – 1 2 – 4 

Very low 0 < 1 < 0.1 < 2 

Regarding Figures 7 and 8: First (left) box: RC class value; second box: SQ class value; third box: 

SSC class value; fourth (right) box: average class value 

Regarding runoff coefficients (Fig 4 A), a wide range from 5.6 % to 100 % could be 

observed. In two cases the maximum RC of 100 % was exceeded with values of 112.6 % and 

138 % due to seepage of water from outside the plot ring. We still did not omit them because 

91 % of the rainfall simulation experiments showed high (21 %), very high (42 %) or extreme 

high (27 %) runoff coefficients. Only 9 % showed middle (6 %) or low (3 %) values and no 

RC was very low. 

Also 91 % of the sediment quantity values were high (33 %) very high (39 %) or extreme 

high (18 %) and also only 9 % showed middle (6 %) or low (3 %) values (Fig 4 B). The range 

of sediment quantity was between 0.4 g and 98.5 g. 

Sediment concentrations of the rainfall simulation experiments ranged between 0.9 g L -1 and 

13.4 g L -1 (Fig 4 C). 33 % of these values were high (9 %), very high (9 %) and extreme (15 

%). 67 % were middle (12 %), low (27 %) and very low (27 %). 

Most of the RMEs were between 13.5 (25 % quartile) and 40.7 % (75 % quartile) for the 

runoff coefficients, between 43.4 and 81.8 % for the sediment quantities and between 43.4 

and 71.8 for the sediment concentrations. The sediment quantity showed the highest 

maximum RME (394.7 %) and the highest median RME (70.4 %). The runoff values 

generally showed lower RME values than the erosion parameters, suggesting that the single 

values showed lower differences from an average value. 

Regarding runoff coefficient classes, sediment quantity classes and sediment concentration 

classes separated following the 3 groups (1) with mechanical treatment, (2) without 

mechanical treatment and (3) high vegetation cover, a clear statement could be made: plots 

with a vegetation cover of maximal about 1/3 (highest value in these groups: 36 %) and 

without mechanical treatment showed average class values of 3.9 (very high) for runoff 

coefficient, 3.6 (very high) for sediment quantity and 1.5 (low-middle) for sediment 

51


concentration. Although absolute values showed differences, we found this an appropriate 

method for classification of sub-areas. The mechanical treated plots representing goat trails 

also showed “very high” runoff coefficient and sediment quantity values (3.7 and 4.0). The 

sediment concentration showed in contrast to the other group also the class “very high” (3.7). 

That means, we defined for the test site area without vegetation without goat trampling a very 

high RC (50.1 – 75 % runoff under a rainfall event of 40 mm h -1 for 30 minutes), a very high 

detachment rate (8.1 – 40 g per 0.28 m², that means 29 – 143 g m -2 under the simulated 

rainfall event) and a middle sediment concentration (4.1-6 g L -1 ). The only rainfall simulation 

(Id 23) with high vegetation cover (99 %) showed lower class values, the RC was still “high” 

(30 – 50 %), the sediment loss could be classified as “middle” (4 – 14 g m -2 ) and the sediment 

concentration as “very low” (< 2 g L -1 ). 

52


Table 5: Class values separated following “crusted soil”, “rock fragment cover embedded” 

and “rock fragment cover overlying”. 

Rainfall Sim. Id RC class SQ class SSC class Average class 

Group 1: with mechanical treatment 

5 5 5 5 5 

6 4 5 5 5 

7 5 5 3 4 

12 2 3 4 3 

13 1 1 0 1 

14 4 4 4 4 

15 5 5 5 5 

Average Group 1 3.7 4.0 3.7 3.9 

Group 2: without mechanical treatment 

1 4 3 0 2 

2 4 3 0 2 

3 5 3 0 3 

4 4 4 1 3 

8 4 4 2 3 

9 5 5 5 5 

10 3 4 3 3 

11 4 4 1 3 

18 5 5 5 5 

16 3 2 0 2 

17 3 3 1 2 

19 4 3 0 2 

20 4 3 0 2 

21 5 4 1 3 

22 4 4 1 3 

24 5 4 2 4 

25 3 3 1 2 

26 5 3 0 3 

27 3 3 1 2 

28 4 4 2 3 

29 4 4 1 3 

30 4 4 2 3 

31 2 4 4 3 

32 4 4 4 4 

33 3 3 1 2 

Average Group 2 3.9 3.6 1.5 2.9 

Special Group: Vegetation cover 

53


23 3 2 0 2 

3.3 Mapping, GIS analyses and aerial photography 

Figure 5 shows the positions of the 5 tested rills and the positions of 33 rainfall simulations. 

The different colours represent the year of accomplishment. Additionally, the outlines of the 

test site are marked. Figure 6 includes the mapped rills and their catchment areas; in figure 7 

the classification of the rainfall simulations is added. The classification system is presented in 

table 4. In figure 8, the soil coverage, divided in “vegetation” and “no vegetation”, is 

presented additionally. 

Figure 5: Positions of the rainfall simulations and the rill experiments 

54


Figure 6: Additionally: Mapped rills and their catchments 

55


Figure 7: Additionally: Classification of runoff coefficient, sediment quantity, sediment 

concentration and average assessment of the rainfall simulations 

56


Figure 8: Additionally: soil surface coverage 

Table 6 lists the calculated test site parameters. The total rill length in the study area (10.01 

ha) was 1694 m. These rills drained an area of 1.98 ha, which was about 20 % of the whole 

test area. The measured rills had an average width of 0.15 m (based on field mapping and 

SFAP), so there was an estimated rill area of about 0.025 ha (0.25 % of the study area). 

Accordingly, we could calculate the total interrill area at about 9.99 ha (99.75 % of the study 

area). The rill density was 169 m ha -1 . In the study area, a total trail length of about 365 m was 

mapped, the average width of these trails was about 1 m. That means, an area of 365 m² was 

covered with uncrusted soil and/or overlying rock fragments what makes up for only 0.5 % of 

the non-vegetated area. 

57


Table 6: Different test site parameters 

Parameter 

Value 

Total rill length L R [m] 1694 

Area of the test site A T [ha] 10.01 

Catchment area of all rills C R [ha] 1.98 

Estimated average rill width W R [m] 0.15 

Total rill area A R [ha] 0.025 

Interrill area A I [ha] 9.99 

Rill amount on total test site [%] 0.25 

Interrill amount on total test site [%] 99.75 

Rill density D R [m ha -1 ] 169 

Rill drainage index I R [%] 20 

Trail length [m] 365 

Trail area [m²] 365 

4 Combination of the results and discussion 

To compare both, the results of the rill experiments and the rainfall simulations, we wanted to 

calculate the inflow intensity which would reach the rill under a real rainfall event of 40 mm 

h -1 , an event simulated in our rainfall experiments. From the inflow intensity we could 

estimate the average sediment concentration following figure 9. In this figure, we ignored two 

peaks: In RE5_2009a was a technical problem in sampling and in RE7_2009a 600 goats were 

crossing the rill before the measurement, so the quantity of lost material was too high. We 

therefore assumed in both cases the same sediment concentration as measured in run b of the 

experiment. 

58


Figure 9: Relationship between the inflow intensity and the sediment concentration in the rill 

experiments 

The relationship between runoff and the sediment concentration gave a high significance R² in 

our experiments but the data base is still too small for general statements of these correlations. 

So in this study we used the relationship only for this test site and only for an approximate 

estimation of the sediment concentration, caused by runoff of a 40 mm h -1 rainfall event. The 

relationship between runoff and sediment yield is to be found in several studies. Parsons et al. 

[35] e.g. measured runoff and eroded material from 8 runoff plots during 10 natural storm 

events and described a clear correlation between runoff coefficient and the sediment yield. 

A critical point in upscaling the results from rainfall simulator area to catchment area scale 

was the well-known scale problem [36]. The plot size used in the rainfall simulations (0.28 

m²) is too small for rill initiation. On the other hand, only much longer plot or slope lengths 

can cause rill development and – in consequence – initiate soil loss processes and runoff 

change. An important condition for the initiation of soil erosion in general is exceeding a 

certain threshold determined by soil parameters, such as soil shear strength or critical shear 

stress, via hydraulic parameters (shear stress, unit length shear force, stream power). Those 

values are used to calculate transport and detachment capacities. Soil erosion can occur as 

long as the transport or detachment rate does not exceed the transport or detachment capacity. 

Exceeding this threshold will cause sedimentation of the excess material [e.g. 37]. Different 

research groups defined different thresholds that separate the interrill erosion from the 

59


initiation of rill erosion. Emmett [38] found, that flowing water on entirely flat surfaces runs 

partially in preferred runoff paths with higher flow velocity, runoff depth and consequently 

with different erosional behaviour. Other research groups stated 2-3° [39, 40] or 3-7° [41] as 

critical slope for rill initiation. When we assume a critical slope of 3°, only two (6 %) of our 

rainfall plots showed lower values, 8 plots (24 %) showed slope values lower than 7°. That 

denotes that upscaling the results from the rainfall simulation plots to a greater area will 

underestimate the real erosion and runoff values. Another critical value for rill initiation is a 

Froude number between 2.4 and 3 [39] or 1+0.0035*D, were D is the median of grain size in 

µm [42]. Giménez & Govers [43] and Giménez [44] assume that there is a threshold Froude 

number. In laboratory experiments, they found that the flow velocity in natural (rough) rills 

was independent of the slope angle because of a feedback between rill bed morphology and 

flow parameters. The frequency of macro roughness (steps, pools) increased with slope and, 

as a consequence, an increase of the flow velocity was prevented. With increasing slope, the 

water accelerated until a Froude number between 1.3 and 1.7 was reached. At this point, an 

“hydraulic jump” occurred and a plungepool could develop [44, 45]. The Froude number of 

the runoff on our rainfall simulation plots was clearly below 1, so the mentioned critical 

values were not reached. In contrast to the cited research groups, Torri et al. [46] and Merz & 

Bryan [47] stated, that the Froude number was not applicable to discriminate between rill and 

interrill flow because runoff in rills was not implicit supercritical. 

A third possible factor influencing the rill initiation is the runoff intensity. Loch & Donnollan 

[48] observed rill development on clay soils with a slope angle of 2.3°, where the runoff 

reached an intensity of 0.3 to 0.6 L sec -1 . Moss et al. [49] determined a value of 0.6 L sec -1 on 

non-cohesive quartz sand with a slope of 0.2 – 0.3°. Loch & Thomas [50] found much higher 

values: they determined minimum runoff intensities of more than 3 L sec -1 . In our rainfall 

experiments, 100 % runoff was 5.6 L 30 min -1 , that means an average value of 0.003 L sec -1 . 

In consequence to the reported critical runoff intensities of the research groups, none of our 

rainfall simulation plots was able to develop any rills. Merz [16] doubts the importance about 

the runoff as a significant value for rill initiation. In his studies, the runoff was measured at 

the lowermost part of a test plot. These values could not describe a reliable average of the 

hydraulic situation since the runoff was not constant over the whole plot. Merz [16] assumed 

that different critical runoff values in both studies are based on variations in cohesive forces 

of the substratum and other soil physical parameters. Therefore, the critical runoff should not 

be used as a confirmed parameter for rill development. 

60


More detailed results of soil and water movement under defined conditions are listed below in 

Table 7. The conditions for the precipitation were: 40 mm h -1 rainfall event within 30 min. 

The field mapping provided size and position of catchments areas. The classification of the 

surface in “vegetation” and “no vegetation” was done by aerial images. We assumed that the 

complete runoff from “no vegetation” areas can reach the rills. Rainfall experiments of Cerdà 

[51] in south-east Spain on Stipa tenacissima areas showed, that surface runoff and erosion 

was negligible in the tussock and quite high in bare areas. So we could calculate the rainfall 

quantity that reaches to uncovered surface areas of the rill catchments by multiplying the “novegetation” 

area in each catchment with 20 (40 mm h -1 but duration just 30 min). The rainfall 

simulations were accomplished on areas with very low vegetation cover and the classification 

of the rainfall experiments showed a “very high” (class 4) runoff coefficient between 50 % 

and 75 %, independent of the soil surface cover (crusted, overlying or embedded rock 

fragments). Because of the range in the runoff classification, we also got a range in the runoffand 

erosion parameters in table 7. We could calculate the runoff quantity and the runoff 

intensity. Based on the runoff values of our rill experiments, we assumed that there was an 

average infiltration rate of 2.5 L m -1 in the rill so we could calculate the water quantity and the 

runoff intensity which was able to cause erosion. Figure 7 shows the correlation between the 

runoff intensity and the sediment concentration calculated from the results of the rill 

experiments. Using the now known runoff intensity in the rill and the equation in figure 7, we 

could calculate the sediment concentrations in the rills. Runoff quantity, rill lengths and the 

average rill widths were known, so we could calculate the absolute erosion quantity and the 

erosion rate per unit area. 

Table 7: Runoff and erosion parameters of the rill catchments. The presented values base on 

the class limits. 

Rill Catchment 

Rill 

Id. 

No- Runoff Rill Runoff 

Erosion 

Area Vegetation 

SSC 

vegetation quantity length intensity 

rate 

[m²] area [m²] 

[g L -1 ] 

area [m²] [L] [m] [L min -1 ] 

[g m -2 ] 

1 415 89 326 3256 - 4884 26 106 - 161 3 - 4 34 - 61 

2 1346 477 869 8695 - 13042 106 281 - 426 6 - 7 54 - 107 

3 87 3 84 843 - 1264 26 26 - 40 3 - 3 23 - 38 

4 1852 382 1470 14696 - 22044 121 480 - 725 8 - 11 78 - 160 

5 59 23 36 365- 547 16 11 - 17 2 - 2 21 - 34 

6 280 17 263 2633 - 3950 51 84 - 127 3 - 4 31 - 54 

7 466 63 403 4033 - 6049 32 132 - 199 4 - 5 37 - 68 

61


8 448 64 384 3839 - 5759 35 125 - 189 4 - 4 36 - 66 

9 41 11 30 299 - 449 10 9 - 14 2 - 2 21 - 34 

10 61 19 42 424 - 636 16 13 - 20 2 - 2 21 - 35 

11 66 25 41 407 - 610 19 12 - 19 2 - 2 21 - 34 

12 66 17 49 489 - 733 4 16 - 24 2 - 3 24 - 37 

13 43 32 11 110 - 166 5 3 - 5 2 - 2 20 - 32 

14 133 21 112 1121 - 1682 24 35 - 54 3 - 3 25 - 41 

15 1616 393 1223 12235 - 18352 60 403 - 607 7 - 9 69 - 140 

16 622 231 391 3913 - 5870 49 126 - 192 4 - 5 36 - 66 

17 692 41 651 6513 - 9770 67 212 - 320 5 - 6 46 - 89 

18 81 30 51 513 - 770 18 16 - 24 2 - 3 22 - 35 

19 155 17 138 1379 - 2068 17 45 - 68 3 - 3 27 - 44 

20 443 11 432 4323 - 6484 21 142 - 214 4 - 5 39 - 71 

21 491 0 491 4909 - 7363 31 161 - 243 4 - 5 41 - 76 

22 1658 253 1405 14053 - 21079 48 464 - 699 8 - 11 77 - 157 

23 255 33 222 2222 - 3333 12 73 - 110 3 - 4 30 - 52 

24 177 31 146 1460 - 2189 22 47 - 71 3 - 3 27 - 45 

25 408 63 345 3454 - 5182 58 110 - 168 4 - 4 34 - 62 

26 1120 345 775 7752 - 11629 62 253 - 382 5 - 7 51 - 100 

27 916 232 684 6844 - 10267 38 225 - 339 5 - 6 48 - 93 

28 183 57 126 1265 - 1897 15 41 - 62 3 - 3 26 - 44 

29 109 28 81 811 - 1216 17 26 - 39 3 - 3 24 - 39 

30 579 92 487 4870 - 7305 26 160 - 241 4 - 5 41 - 76 

31 49 16 33 334 - 500 8 10 - 16 2 - 2 22 - 35 

32 37 10 27 268 - 402 6 8 - 13 2 - 2 22 - 34 

33 250 90 160 1598 - 2397 20 52 - 78 3 - 3 27 - 46 

34 46 10 36 364 - 545 10 11 - 17 2 - 2 22 - 35 

35 195 67 128 1285 - 1927 19 41 - 63 3 - 3 26 - 43 

36 237 93 144 1444 - 2166 30 46 - 70 3 - 3 26 - 44 

37 151 15 136 1363 - 2045 11 45 - 67 3 - 3 27 - 45 

38 117 18 99 986 - 1479 8 32 - 49 3 - 3 26 - 41 

39 365 96 269 2689 - 4034 73 84 - 128 3 - 4 30 - 54 

40 128 30 98 978 - 1466 24 31 - 47 3 - 3 24 - 40 

41 132 26 106 1058 - 1587 34 32 - 50 3 - 3 24 - 40 

42 68 10 58 579 - 869 12 18 - 28 2 - 3 23 - 37 

43 15 4 11 109 - 164 6 3 - 5 2 - 2 19 - 31 

44 224 42 182 1824 - 2736 34 58 - 88 3 - 3 28 - 48 

45 259 80 179 1791 - 2686 38 57 - 86 3 - 3 27 - 47 

46 188 42 146 1456 - 2183 33 46 - 70 3 - 3 26 - 44 

47 171 26 145 1447 - 2171 21 46 - 71 3 - 3 27 - 45 

48 79 14 65 649 - 973 9 21 - 32 2 - 3 24 - 38 

62


49 297 44 253 2534 - 3801 21 83 - 125 3 - 4 31 - 55 

50 203 35 168 1675 - 2513 26 54 - 82 3 - 3 27 - 47 

51 1641 306 1335 13352 - 20028 187 429 - 652 7 - 10 71 - 146 

410 30 4 26 257 - 386 12 8 - 12 2 - 2 20 - 33 

It has to be considered, that the rill catchments were only used to calculate the runoff for the 

rills, erosion only taking place directly in the rills. That means the rill catchments were on the 

“rill site” regarding the runoff but on the “interrill site” concerning the erosion parameters. 

Table 8 summarises the results of table 7: the complete interrill areas without gully covered 

100079 m², 19750 m² of which were catchments for rills which covered 254 m² resulting from 

the total rill length and an average rill width. 21912 m² were covered with vegetation, 78167 

m² showed bare soil. The erosion rates in the rills reached values between 1685 and 3018 g m - 

2 (under a 40 mm h -1 rainfall event of 30 min), whereas the soil loss in the interrill areas was 

only between 29 and 143 g m -2 (20-60 times less). This relationship is confirmed by Morgan 

[52], who stated that rill sediment transport exceeded interrill transport by a factor of 40 on an 

11° slope. Due to the much larger area of the interrill areas, the total soil loss quantity was 

about 5 to 15 times higher than in the rills. The runoff intensity of the water from the interrill 

area was about 5 times higher than the runoff intensity of the rill flow. Regarding the runoff 

intensity per square meter, the rills’ value exceeded the interrills’ value by the factor 50. 

Table 8: Comparison of rill and interrill areas. The erosion values are only valid for the rill 

areas, not for the rill catchment areas (specific explanation in the text) 

Rills / rill catchments Interrill Area without gully 

Area complete [m²] 254 / 19750 100079 

Area, Vegetation [m²] X / 4174 21912 

Area, no vegetation [m²] X / 15576 78167 

Erosion rate [g m -2 ] 1685-3018 / X 29-143 

Erosion quantity [kg] 425-762 / X 2267-11178 

Runoff intensity [m³ s -1 ] 0.08-0.13 / X 0.43-0.65 

Runoff intensity per m² [cm s -1 ] 0.03-0.05 / X 0.0006-0.0008 

One ignored point in our study is the gully in the test site. This is acceptable in so far as the 

gully is not active. An active gully would certainly raise the runoff and erosion values on the 

gully-bottom. 

63


We probably underestimated the rill erosion values: during a real rainfall event, the water 

would fill the rill from upstream and from both sides whereas in the experiments, the water 

entered the rill at a single point. The measured sediment concentrations in the rills (maximum 

19.9 g L -1 in RE5_2009a) showed relatively low values. In the surrounding area of the 

presented test site, we still measured much higher sediment concentrations of up to 438 g L -1 

caused by an inflow intensity of only 9 L min -1 [25]. This means, the rill effectiveness could 

be even higher than the presented results implicate. Unfortunately, we do not (yet) have 

enough data of the surrounding test sites for a comparison of the different areas. 

5 Conclusions 

The aim of this study was to compare the effectiveness of rill and interrill areas concerning 

soil erosion on one abandoned land site in Andalusia. The results are only valid for the tested 

area, they cannot easily be adapted to other areas or used as general statement about the 

relation between rill- and interrill erosion. We combined the results of rill experiments, 

rainfall simulations, field mapping and small scale aerial photographs to get an idea about the 

dimension of the soil loss caused by rill- and interrill flow. In our test site, the rills reached 

much higher erosion rates than the interrill erosion (20-60 times higher). Because of the much 

larger interrill area, the absolute erosion values of the interrill areas were 5-15 times higher 

than these of the rill area. The rills in our study area drained 19800 m² of the 100079 m² study 

area; this means 0.25 % of the study area were responsible for 20 % of the area providing 

runoff. The results clearly proved the importance of the rills as sediment provider as well as 

runoff accumulator. The possible influence of the gully in our study area was ignored in this 

study, so we cannot state the possibly erosion-activating effect of our applied rainfall intensity 

of 40 mm h -1 . We know about the problems and the limitations of upscaling experimental 

field assessments but as we only presented ranges or class limits, we assume that the results 

remain in realistic dimensions. 

Acknowledgement 

The research was supported by the 'Internationales Graduiertenzentrum' of Trier University, 

by the Deutsche Forschungsgemeinschaft (DFG) project numbers Ri 835/2 and Ri-835/6-1 

and by the 'Freundeskreis Trierer Universität e.V.'. Additionally we thank all participants of 

the field trips to Andalusia in September 2006, September 2008 and September 2009 who 

supported the accomplishment of the experiments. Special thanks go to Dr. A. Keller for the 

support in data analysis. Finally, we would like to thank the reviewers for their remarks. 

64


References 

1. Beuselinck, L., Govers, G., Hairsine, P., Sander, G. and Breynaert, M.: The influence 

of rainfall on sediment transport by overland flow over areas of net deposition, 

Journal of Hydrology, 257, 145-163, 2002. 

2. Kuhn, N. and Bryan, R.: Drying, soil surface condition and interrill erosion on two 

Ontario soils, Catena, 57, 113-133, 2004. 

3. Kuhn, N., Bryan, R.B. and Navar, J.: Seal formation and interrill erosion on a 

smectite-rich Kastanozem from NE-Mexico, Catena, 52, 149-169, 2003. 

4. Le Bissonnais, Y., Cerdan, O., Lecomte, V., Benkhadra, H., Souchère, V. and 

Martin, P.: Variability of soil surface characteristics influencing runoff and interrill 

erosion, Catena, 62, 111-124, 2005. 

5. Brodie, I. and Rosewell, C.: Theoretical relationships between rainfall intensity and 

kinetic energy variants associated with stormwater particle washoff, Journal of 

Hydrology, 340(1-2), 40-47, 2007. 

6. Bryan, R. B.: Soil erodibility and processes of water erosion on hillslope, 

Geomorphology, 32(3-4), 385-415, 2000. 

7. Govers, G., Giménez, R. and Van Oost, K.: Rill erosion: Exploring the relationship 

between experiments, modelling and field observations, Earth-Science Reviews, 

84(3-4), 87-102, 2007. 

8. Knapen, A., Poesen, J., Govers, G., Gyssels, G. and Nachtergaele, J.: Resistance of 

soils to concentrated flow erosion: A review, Earth-Science Reviews, 80(1-2), 75- 

109, 2007. 

9. Cerdan, O., Le Bissonnais, Y., Couturier, A., Bourennane, H. and Souchère, V.: Rill 


France, Soil and Tillage Research, 67(1), 99-108, 2002. 

10. Poesen, J.: Transport of rock fragments by rill flow – a field study. In: R.B. Bryan 

(Editor): Rill erosion - process and significance, Catena, Supplement 8, Cremlingen, 

35-54, 1987. 

11. Oostwoud Wijdenes, D.J., Poesen, J., Vandekerckhove, L. and Ghesquiere, M.: 

Spatial distribution of gully head activity and sediment supply along an ephemeral 

channel in a Mediterranean environment, Catena, 39, 147-167, 2000. 

65


12. Vandekerckhove, L., Poesen, J., Oostwoud Wijdenes, D. and De Figueiredo, T.: 

Topographical thresholds for ephemeral gully initiation in intensively cultivated areas 

of the Mediterranean, Catena, 33, 271-292, 1998. 

13. Woodward, D. E. 1999. Method to predict cropland ephemeral gully erosion. Catena, 

37(3-4), 393-399. 

14. Hancock, G.R., Crawter, D., Fityus, S.G., Chandler, J. and Wells, T.: The 

measurement and modelling of rill erosion at angle of repose slopes in mine spoil, 

Earth Surface Processes and Landforms 33, 1006-1020, 2008. 

15. Ries, J.B.: Landnutzungswandel und Landdegradation in Spanien – Eine Einführung, 

in: Marzolff, I., Ries, J.B., De La Riva, J. and Seeger, M. (Eds): 

Landnutzungswandel und Landdegradation in Spanien, 11-29, 2003. 

16. Merz, W.: Experimentelle Untersuchungen zur Rillenerosion auf landwirtschaftlich 

genutzten Böden in Kanada und der Volksrepublik China. Freiburger Geographische 

Hefte, Heft 40, Selbstverlag des Institutes für Physische Geographie der Albert- 

Ludwig-Universität Freiburg i.Br., Freiburg, 147 pp., 1993. 

17. Poesen, J., Valentin, C., Nachtergaele, J. and Verstraeten, G.: Gully erosion and 

environmental change: importance and research needs, Catena, 50(2–4), 91–133, 

2003. 

18. Faust, D. and Schmidt, M.: Soil erosion processes and sediment fluxes in a 

Mediterranean marl landscape, Campina de Cádiz, SW Spain, Z.Geomorph. N.F. 52 

(2), 247-265, 2009. 

19. Meyer, L.D., Forster, G.R. and Römkens, M.J.M.: Source of soil eroded by water 

from upland slopes, Proc. 1972 Sediment Yield Workshop, US Dept. of Agric. 

Sediment. Lab., Oxford, Mississippi, 177-189, 1975. 

20. Morgan, R.P.C., Martin, L. and Noble, C.A.: Soil erosion in the United Kingdom: a 

Case Study from Mid-Bedfordshire, England, Occasional Paper No.14., 1987. 

21. Giménez, R., and Govers, G. 2002. Flow Detachment by Concentrated Flow on 

Smooth and Irregular Beds. Soil Sci Soc Am J, 66(5), 1475-1483. 

22. Hessel, R. and Jetten, V. 2007. Suitability of transport equations in modelling soil 

erosion for a small Loess Plateau catchment. Engineering Geology, 91(1), 56-71. 

23. Seeger, M.: Uncertainty of factors determining runoff and erosion processes as 

quantified by rainfall simulations, Catena, 71(1), 56-67, 2007. 

66


24. Wirtz, S., Seeger, M. and Ries, J.B.: The rill experiment as a method to approach a 

quantification of rill erosion process activity, Zeitschrift für Geomorphologie, 54,1, 

47-64, 2010. 

25. Wirtz, S., Seeger, M. and Ries, J.B.: Field experiments for understanding and 

quantification of rill erosion processes, Catena 91, 21-34, 2012. 

26. Ministerio de Fomento, Secretaria de Estado de Infraestructuras y Transportes, 

Directión General de Carreteras: Máximas illuvias diarias en la espana peninsular, 

1999. 

27. Ries, J.B., Langer, M. and Rehberg, C.: Experimental investigations on water and 

wind erosion on abandoned fields and arable land in the Central Ebro Basin, 

Aragón/Spain, Z. Geomorphol. N.F. (Supplement 121), 91– 108, 2000. 

28. Iserloh, T., Fister, W., Seeger, M., Willger, H. and Ries, J.B.: A small portable 

rainfall simulator for reproducible experiments on soil erosion. Soil and Tillage 

Research 124, 131-137, 2012. 

29. Ries, J.B., Seeger, M., Iserloh, T., Wistorf, S. and Fister, W.: Calibration of simulated 

rainfall characteristics for the study of soil erosion on agricultural land, Soil & Tillage 

Research 106, 109-116, 2009. 

30. Fister, W., Iserloh, T., Ries, J.B. and Schmidt, R.-G.: Comparison of rainfall 

characteristics of a small portable rainfall simulator and a combined portable wind 

and rainfall simulator. Zeitschrift für Geomorphologie, 55(3), 109-126, 2011. 

31. DIN 1319-1.: Grundlagen der Messtechnik – Teil 1: Grundbegriffe, Deutsches Institut 

für Normung e.V., Ausgabe: 1995-01 , Deutsch, 1995. 

32. Aber, J. S., Marzolff, I., and Ries, J. B.: Small-Format Aerial Photography: 

Principles, techniques and geoscience applications., Elsevier, Amsterdam, 2010. 

33. Ries, J. B. and Marzolff, I.: Identification of sediment sources by large-scale aerial 

photography taken from a monitoring blimp, Phys. Chem. Earth, 22 (3-4), 295-302, 

1997. 

34. Ries, J.B.: Methodologies for soil erosion and land degradation assessment in 

mediterranean-type ecosystems, Land Degradation & Development, 21, 171-187, 

2010. 

35. Parsons, A.J., Brazier, R.E., Wainwright, J. and Powell, D.M.: Scale relationships in 

hillslope runoff and erosion, Earth Surf. Process. Landforms, 31, 1384-1393, 2006. 

67


36. Amore, E., Modica, C., Nearing, M.A. and Santoro, V.C.: Scale effect in USLE and 

WEPP application for soil erosion computation from three Sicilian basins, Journal of 

Hydrology, 293, 100-114, 2004. 

37. Scherer, U.: Prozessbasierte Modellierung der Bodenerosion in einer Lösslandschaft, 

Ph.D. thesis, Fakultät für Bauingenieur-, Geo- und Umweltwissenschaften, 

Universität Fridericiana zu Karlsruhe (TH), Karlsruhe, Germany, 2008. 

38. Emmett, W.W.: The hydraulics of overland flow on hillslopes, US Geological Survey 

Professional Paper 662-A, United States Government Printing Office, Washington, 

1970. 

39. Savat, J. and De Ploey, J.: Sheetwash and rill development by surface flow, in: 

Badland geomorphology and Piping, Geo Books, Norwich, 1982. 

40. Govers, G.: Spatial and temporal variability in rill development processes at the 

Huldenberg experimental site, in: Rill erosion, Catena Supplement 8, Catena Verlag, 

Braunschweig, 17-34, 1987. 

41. Evans, R.: Water erosion in british farmers’ fields, Progress in Physical Geography, 

14, 2, 198-219, 1990. 

42. Boon, W. and Savat, J.: A Nomogram for the Prediction of Rill Erosion, in: Soil 

Conservation: Problems and Prospects, John Wiley & Sons Ltd., Cranfield, Bedford, 

303-319, 1981. 

43. Giménez, R. and Govers, G.: Interaction between bed roughness and flow hydraulics 

in eroding rills, Water resources Research, 37,3, 791-799, 2001. 

44. Giménez, R.: The interaction between rill hydraulics, rill geometry, and sediment 

detachment: an experimental approach, Proefschrift ingedient tot het behalen van de 

graad van Doctor in de Wetenschappen, Katholieke Universiteit Leuven, Faculteit 

Wetenschappen, Department Geografie-Geologie, 2003. 

45. Giménez, R., Planchon, O., Silvera, N. and Govers, G.: Longitudinal velocity patterns 

and bed morphology interaction in a rill, Earth Surface Processes and Landforms, 29, 

105-114, 2004. 

46. Torri, D, Sfalanga, M. and Chisci, G.: Threshold conditions for incipient rilling, in: 

Rill erosion, Catena, Supplement 8, Catena Verlag, Braunschweig, 97-105, 1987. 

47. Merz, W. and Bryan, R.B.: Critical conditions for rill initiation on sandy-loamy 

Brunisols – laboratory and field experiments in Southern Ontario, Canada, Geoderma, 

57, 4, 357-385, 1993. 

68


48. Loch, R.J. and Donnollan, T.E.: Field rainfall simulator studies on two clay soils of 

the Darlington Downs, Queensland: I. The effect of plot length and tillage orientation 

on erosion processes and runoff and erosion rates, Australien Journal of Soil 

Research, 21, 33-46, 1983. 

49. Moss, A.J., Green, P. and Hutka, J.: Small channels: Their experimental formation, 

nature, and significance, Earth surface processes and landforms, 7, 401-415, 1982. 

50. Loch, R.J. and Thomas, E.C.: Resistance to rill erosion: observations on the efficiency 

of rill erosion on a tilled clay soil under simulated rain and run-on water, in: Rill 

erosion – processes and significance, Catena Supplement 8, Catena Verlag, 

Braunschweig, 71-83, 1987. 

51. Cerdà, A.: The effect of patchy distribution of Stipa tenacissima L. on runoff and 

erosion, Journal of Arid Environments, 36, 37-51, 1997. 

52. Morgan, R.P.C.: Soil erosion in the United Kingdom: field studies in the Silsoe area, 

1973-75, National College of Agricultural Engineering Occasional Paper 4, 1977. 

69


Kapitel 3 

Wirtz et al. (2010): The rill experiment as a method to approach a quantification 

of rill erosion process activity. Zeitschrift für Geomorphologie 54 (1), 47-64. 

70


The rill experiment as a method to approach a quantification of rill erosion process 

activity 

Wirtz S. (1), Seeger M. (1,2) & Ries J.B. (1) 

(1) Dep. of Physical Geography, Trier University (2) Dep. of Land Degradation and 

Development, Wageningen University 

with 9 figures and 6 tables 

Summary 

Within this paper a standardized method to quantify sediment transport and runoff in natural 

rills is described. In order to achieve this, several rill experiments (RE) were accomplished in 

March 2007 in the Arnás catchment in the Spanish Pyrenees. Both, anthropogenically 

initiated and naturally developed rills were flushed with a total water quantity of 72 l in 8 

minutes (equivalent to 9 l min -1 ). Following the developed experimental routine flow 

velocities are recorded along the whole flushed rill, sediment concentrations are measured at 

different points and different times during the experiment and runoff values are measured 

after 25 m. For the characterisation of the rill, slope is measured and micromorphological 

features like scours are registered. 

By means of the developed rill experiments it becomes possible to assess the effectivity of 

single rills in a catchment. However, the assessments can not be generalized because it is 

impossible to project the behaviour of one rill to other rills, even if the spatial distance in 

between is small. But it gets possible to detect the qualitative process activity in a rill. 

The average slopes oscillated between 7.6° and 11.3°, the highest slope was 16°. The 

sediment concentrations reached average values between 0.69 and 2.21 g l -1 , the maximum 

values ranged between 1.59 and 6.31 g l -1 . Comparing the sediment concentrations measured 

in the rills to the sediment concentrations in the runoff of the river Arnás, it can be stated that 

the concentrations in the rills are usually higher. 

Keywords: soil erosion, rill erosion, field experiments, quantification of process activity, 

Arnás catchment 

71



Soil erosion is a complex process, which involves different processes at variable spatial and 

temporal scales. Rill erosion is considered to be the most important process affecting soils. 

Not only because of the large amounts of eroded soil material, but also due to the generation 

of more or less persisting forms, which can develop into gullies and disable further land use. 

(OOSTWOUD WIJDENES et al. 2000, VANDEKERCKHOVE et al. 1998, WOODWARD 

1999, HANCOCK et al. 2008) 

The outstanding role of linear erosion in geomorphological, hydrological and economical 

aspects can be explained by the fact that the runoff water reaches its maximal power as both, 

eroding and transporting medium, when concentrated in a rill (MERZ 1993). Runoff depth 

and flow velocity reach higher values than within diffuse sheet flow, thus the forces affecting 

soil particles are multiplied as compared to sheet flow (POESEN 1987). Consequently, more 

energy for mobilization and transport of soil material is available (MERZ 1993) leading to a 

clear increment in erosion rates. MEYER et al. (1975) noticed a triplication of the erosion 

rates due to rill development. Corn fields in Bedfordshire, England for example produce 9-21 

times as much sediment with rill erosion under corn as a comparable field only affected by 

sheet erosion (MORGAN et al. 1987). According to CERDAN et al. (2002) up to 90 % of soil 

loss in several heavy rainfall-events in Normandy was caused by rill erosion. 

Despite the efforts made for understanding rill erosion processes and building models to 

explain the retreat of headcuts (e. g. FLORES-CERVANTES et al. 2006) or to model gully 

erosion by identification of stochastic components (SIDORCHUK 2005) there is still much 

work to do for a comprehensive modelling of rill erosion and to the development of field 

methods for understanding and quantifying the rill erosion processes. The lack of rill erosion 

models is all that weighty, if is compared with the approaches for modelling sheet erosion 

(BRUNO et al. 2008). 

BRUNO et al. (2008) tested the evolution of a rill network under natural rainfall on testplots 

in Sicily. Investigating the effect of initial conditions, rill headcut development and the most 

important hydraulic variables, they tried to compile simple mathematical models. Their results 

are remarkable, because they demonstrate that the erosion occurs within the upper part of the 

rill, but the eroded material is only passed through the lower rill section. 

Correct and reproducible measurement of rill erosion processes are needed for the 

understanding and the correct model building of a rill erosion model. CASALI et al. (2006) 

tested three frequently used methods to quantify the intensity of rill erosion processes and 

showed that different methods offer clear differences in resulting data. Depending on the 

72


method used, the form of the tested rill, as well as position and distance between the measured 

cross sections, the measuring error was up to 40 %. So it is clear, that results taken with 

different methods still cannot be compared and a standardized method is needed. These 

methods are useful to quantify erosion, but it remains impossible to give a statement about the 

dynamics in the rill. 

Still not all factors influencing the evolution and the behaviour of rills are known, and the 

knowledge of the relationship between factors is weak as well. KNAPEN et al. (2007) 

attribute this to the lack of comparable data that can be used for a comparative investigation 

of different studies on rill erosion. Furthermore, there is still little known about the function of 

rills in specific environments, this is: what is the rill's contribution to the sediment dynamics? 

How effective are rills for the routing of surface runoff? 

In the present paper, a field method is presented for the accomplishment of comparable 

experiments on ephemeral rill types in different landscapes. Hereby, a contribution to 

understand the functioning of natural rills and their role concerning runoff concentration and 

erosion is made. Additionally, the interconnection of the rills with their environment, 

especially the contributing areas, is seized by means of rainfall simulations. Some of the 

possibilities will be shown exemplarily on experiments performed in the Central Spanish 

Pyrenees. 


Study area: 

The Arnás catchment is located in the Upper Aragón River Basin, a northern tributary of the 

Ebro River. The bedrock is Eocene Flysch with alternating sandstones with carbonate 

cementation and marl layers sloping northward, which is characteristic of a wide sector of the 

Central Spanish Pyrenees. The climate is mountainous Mediterranean sub-humid. The 

average annual precipitation is about 1100 mm, mostly concentrated from October to May but 

divided by a secondary minimum in March. The average annual temperature is 10ºC. The 

Arnás ravine drains a 284 ha headwater catchment into the Lubierre River, a small tributary of 

the Aragón River. The highest peak is at 1330 m a.s.l. and the outflow at about 900 m a.s.l. 

The ravine runs from west to east, building up a valley with a strong contrast between the 

steep south facing slope and the gentle north facing slope. The morphology of the slopes is 

characterised by big rotational landslides and earthflows. Some poorly drained areas can be 

found related to the rotational landslides, especially in the shady aspect. They are mostly 

disconnected from the drainage network. Most of the catchment is covered by shrubs 

73


(SEEGER et al. 2005). Due to sheep grazing, the vegetation succession is strongly retarded 

and absent on many trails (RIES et al. 2000b; RIES et al. 2003). 

Figure 1 shows the Arnás catchment with the dominating runoff processes in winter, when the 

experiments were carried out and the positions of the rill experiments. The tested rills have 

developed in regions with dominating surface runoff generation processes: the first rill in a 

Hortonian overland flow (HOF) area, rill 2 and rill 3 in an saturation overland flow (SOF) 

area. 

Fig. 1: Overview over the Arnás catchment with the dominating runoff processes in winter: 

HOF= Horton overland flow, SOF=saturation overland flow, SSF= subsurface flow, DP= 

deep percolation (modified according to BUTZEN et al. 2009 submitted). 

Tested rills: 

In the Arnás catchment the experiment was accomplished in three rills that are very similar to 

each other for the first 12 m. The slope stays constant at about 8° in rill 1 whereas rill 2 and 

rill 3 become steeper. (Fig. 3). All three rills drain over a track and finish with a step at the 

track scarp. 

The first rill has developed along a motorcycle trail, thus it is an anthropogenically initiated 

rill with an average slope of 7.6°, the maximum slope is 12°. The rill is weakly developed, the 

width is between 1 and 10 cm, the depth between 1 and 5 cm. The rill is nearly completely 

74


covered with grass. The rock fragment cover is about 10%. The dominating runoff process 

mapped for this rill is HOF. 

The second rill is a naturally developed rill on an abandoned field with an average slope of 

11° and a maximum slope of 16°. This medium developed rill (width between 5 and 20cm, 

depth between 5 and 10 cm) shows a dense rock fragment cover (about 30%) and is only 

partially (about 10%) grass-covered. The dominating runoff process is the SOF. 

Rill 3 is also a naturally developed rill, that has cut into an old slump. The average slope is 

11.3° and the maximum slope 14.5°. The rill is rather deeply incised with width between 10 

and 50 cm and depth between 15 and 20 cm. It shows a dense rock fragment cover of about 

30% and almost no vegetation cover (about 5%). Rill 3 was just tested over 15 m, because it 

was expected that the water would not reach the 25 m standard test length on the slump 

material. So, also the slope was just measured over the 15 m. (Fig. 3) The dominating runoff 

process is also SOF. 

Fig. 2: Profiles of the 3 rills. The measuring points are also marked. 

75


Fig. 3: The three tested rills. 

Table 1: Rill parameters of the three tested rills 

Factor RE 1 RE 2 RE 3 

Tested length [m] 25 25 15 

Average slope [°] 7.6 11 11.3 

Maximum slope [°] 12 16 14.5 

Catchment area [m²] 450 400 ND 

Rock fragment cover [%] 10 30 30 

Vegetation Cover [%] 90 10 5 

depth [cm] 1-5 5-10 15-20 

width [cm] 1-10 5-20 10-50 

runoff process HOF SOF SOF 

Rainfall simulations: 

For the characterisation of the rill catchments there were performed rainfall simulations, with 

a small mobile rainfall simulator based on the one used by CALVO CASES et al. (1988), 

LASANTA et al. (1994) and CERDÁ & GARCÍA-FAYOS (1994-95). The plot is bounded 

by a steel ring of 60 cm in diameter (0,28 m²) and 6 cm height, it has an outlet of 10 cm width 

with a narrowing runoff collector (RIES et al. 2000a, PFAHLS et al. 1999). The rainfall 

intensity is 40 mm/h, the fall height is 2 m. The suitability of this method for the explanation 

of the influence of external factors on runoff generation and erosion with this methodology 

was demonstrated in the same catchment by SEEGER (2007). 

76


Rill experiment: 

The objective of the rill experiment is to simulate concentrated runoff without the effect of 

splash or additional inflow into a rill. Each experiment consists of two runs: first the rill is 

tested under dry conditions; in a second run, about 15 min later, the same rill is tested under 

wet conditions. 

With a motor driven pump, a constant discharge of 9 l min -1 is maintained during 8 minutes, 

resulting in a total water inflow of 72 l. 

In order to reduce the flow velocity of the inflowing water and consequently avoiding the 

mobilization of soil material at the starting point, the water inflow is initiated through the 

“Field-Adapter-Tool A” (FAT-A) (Fig.4). This is a longish 55x30 cm plastic plate on which 

plastic pipes and an inverted meadow of synthetic turf are fixed. The hose can be adapted to 

the pipe system with a compressed air adapter. The flow velocity is firstly reduced by the 

course of the pipes and secondly by the flow path under the artificial turf. In this way, 

accelerated erosion can be avoided, as the water leaves the plastic plate through a cut and 

flows into the rill in a rather 'natural' speed. 

Fig.4: Device for water inflow into the rill (Fat-A). 

The travel time of the waterfront and of two colour tracers are measured for each meter using 

a chronograph. The first colour tracer is induced after three minutes at the starting point, the 

second follows after six minutes. By means of this procedure, three velocity curves are 

recorded and changes in flow dynamics can be detected. As colour tracers, food colourings (E 

124 (red) and E 13 (blue)) are used for reasons of safety. 

The experiment ends after 25 m flow length. For the continuous measurement of the water 

level by means of a pressure transducer (Ecotech DL/n, V2.35), the FAT-Z (Fig. 5) has been 

designed. It consists of a metal sheet with a plastic drainpipe with a junction. The sheet is 

driven into the ground as far until the opening of the drainpipe is on rill’s ground level. The 

77


pressure transducer is installed at the junction piece, and this is filled with water so that the 

water level sensor is permanently awashed. For calibrating the gauge, the runoff at the 

outflow is measured volumetrically in regular intervals. 

Fig. 5: Mobile flume (FAT-Z). 

The rills slope is measured with a spring bow of 1m range and a digital air lever (Fig. 6), thus 

dividing it into 25 segments. It has to be considered, that the slope measuring provides only 

average slopes for 1 meter. A step or a knickpoint in the rill is not accounted. The positions 

and the heights of the steps are noted. 

78


Fig. 6: The 1m-spring bow. 

For gathering intermediate data on suspended sediment transport, three adequate sampling 

points are selected. Small knickpoints in the rill have proven to be adequate to collect water 

samples without having to press the bottle into the rill bottom. At these points in the rills 

longitudinal profile, four water samples are taken: the first directly after the waterfront has 

reached the sampling point, the second after 30 seconds, the third after 1:30 min and the 

79


fourth 2:30 min after the arrival of the water. The sampling disturbs flow behaviour, so it 

should be taken quickly. There is no default quantity, but the sample should be enough for 

filtration and determination of sediment concentration. 

Laboratory analysis and data processing: 

The samples are filtered with a 25 µm and a 2 µm pore size filter from Schleicher & Schuell 

Company (Whatman 589/1 black ribbon and Whatman 589/3 black ribbon) and the sediment 

quantity is determined gravimetrically. The calculated sediment amounts are related to the 

water quantity in the sample to get a sediment concentration in g l -1 . 

Data evaluation: 

The experiments are characterised by means of the following indicators, where the water 

flowing out of the rill system is considered as runoff: 

intensity factor: the relationship between the maximum runoff value and the inflow 

intensity, I = RI / II 

duration factor: the relationship between the runoff duration and the inflow duration, 

DF = RD / ID 

detention: the difference between the runoff start and the inflow finish, D = RS - IF 

time factor: the relationship between these two values, T = RS / IF 

runoff rate: relationship between runoff quantity and inflow quantity. This factor 

neglects the influence of the flow length, but it is an indicator to the infiltration 

characteristics within the rill, R = RQ / IQ 

r-l-factor (runoff-length-factor): the relationship between the runoff- and the inflow 

quantity, depending on the flow length: r-l-factor = (runoff quantity / inflow quantity ) 

* length [m], RL = (RQ / IQ ) * L 

For characterising the rainfall simulations, we used the overall runoff coefficient. With this, 

the size of the contributing area is determined, which is needed to produce a runoff of 9 l min - 

1 at the starting point of each rill with a rainfall intensity of 40 mm h -1 . With a given 

catchment area size and a known runoff coefficient of the rainfall simulations, the RR (Rill 

runoff caused by a rainfall intensity of 40 mm h -1 in the catchment [l s -1 ] ) can be calculated, 

at least the dimension. 

The runoff of a river catchment can not easily be compared to a runoff in a rill. In the Arnás 

catchment, runoff and sediment concentration values were measured (SEEGER et al. 2005). 

We can calculate the dimension of the theoretical runoff, a runoff quantity that the Arnás river 

80


would offer if he had not his real catchment area size but the catchment area size of the rills. 

This value is calculated as follow: 

runoff Arnás * area rill catchment 

Theoretical runoff = 

area Arnás catchment 

It is not possible to compare the absolute runoff values of a river and a rill catchment, so we 

calculated the specific runoff, the theoretical runoff relating to 1 ha for the Arnás catchment 

and the rill catchments. 

For the Arnás catchment, the specific average runoff is calculated as follow: 

average runoff min average runoff max 

Specific average runoff = / 2 

catchment area catchment area 

The specific runoff peak is calculated respectively. 

The values for the rill catchments are calculated as follow: 

RQ run a RQ run b 

Specific average runoff = 

/ (2 * catchment area) 

RD run a RD run b 

Specific runoff peak = 

RI run a RI run b 

2 * catchment area 

with RQ = runoff quantity [l], RD = runoff duration [s] and RI = maximum runoff intensity [l 

s -1 ]. 

3 Results 

Table 2: Results of the rainfall simulations: ND = No Data 

Factor RE 1 RE 2 RE 3 

Sed.Conc. rainfall simulation 1 [g l -1 ] 0.7 0.9 ND 

Sed.Conc. rainfall simulation 2 [g l -1 ] ND 1.86 ND 

Runoff of rainfall simulation 1 [%] 25 80 ND 

Runoff of rainfall simulation 2 [%] ND 100 ND 

Start runoff rainfall simulation 1 [s] 99 61 ND 

Start runoff rainfall simulation 2 [s] ND 14 ND 

RR = Rill runoff caused by a rainfall intensity of 40 mm h -1 in the 

catchment [l s -1 ] 

1.3 4.15 ND 

In the 450m² catchment area of rill 1, one rainfall simulation was accomplished. This 

simulation showed a runoff coefficient of 25% and a average sediment concentration of 0.7 g 

l -1 . The runoff started after 99 s. The RR reaches 1.3 l s -1 . 

81


The catchment of rill 2 has an area of 400m², in this area two rainfall simulations were 

accomplished. The runoff coefficients were 80% and 100%, the average sediment 

concentrations 0.9 and 1.86 g l -1 . The runoff started after 61 s in the first simulation and still 

after 14 s in the second simulation. The RR reaches 4.15 l s -1 . 

In the catchment area of rill 3, no rainfall simulation was accomplished . 

Table 3: Overview over the runoff values of the rill experiments: n.D. = no Data 

rill 1 rill 2 rill 3 

Factor 1a 1b 2a 2b 3a 3b 

L = length [m] 25 25 25 25 15 15 

IQ = inflow quantity [l] 72 72 72 72 72 72 

II = inflow intensity [l s -1 ] 0.15 0.15 0.15 0.15 0.15 0.15 

IF = inflow finish [s] 480 480 480 480 480 480 

ID = inflow duration [s] 480 480 480 480 480 480 

RQ = runoff quantity [l] 8.41 17.01 20 49.23 n.D. 10.09 

RI = maximum runoff intensity [l s -1 ] 0.042 0.059 0.066 0.102 n.D. 0.052 

RS = runoff start [s] 554 398 608 414 n.D. 442 

RF = runoff finish [s] 904 832 1420 1612 n.D. 796 

RD = runoff duration [s] 350 434 812 1198 n.D. 354 

I = intensity factor 0.28 0.39 0.44 0.68 n.D. 0.34 

DF = duration factor 0.73 0.90 1.69 2.5 n.D. 0.74 

D = detention [s] 74 -82 128 -66 n.D. -38 

T = time factor 1.15 0.83 1.27 0.86 n.D. 0.92 

R = runoff rate [%] 11.68 23.63 27.78 68.38 n.D. 14.01 

RL = r-l-factor 2.92 5.91 6.94 17.09 n.D. 2.1 

82


Fig. 7: Runoff values after 25m, respectively. 15m for rill experiment 3. 

In run A of RE 1 8.41 l of the 72 l inflow reached the measuring point at 15 m this is 

equivalent to a runoff rate of 11.68 %. The maximum runoff at the outlet is 0.042 l s -1 that 

means 28% of the inflow intensity. The runoff period counts 350 s and it begins 74 s after 

stopping inflow. In the second run, 17.01 l reached the 25 m with a maximum intensity of 

0,059 l s -1 , (39% of the inflow intensity) corresponding to a runoff rate of 23.63 %. The 

duration is longer in the second run (434 sec) and starts earlier, 82 s before stopping 

discharge. The r-l-factor in the first run is 2.92, in the second run 5.91. (Fig. 7a) 

83


The first run of RE 2 leads to a total runoff of 20 l, thus representing a proportion of 27.78 %, 

at the end of the rill. The runoff peak reaches 0.066 l s -1 , 44% of the inflow intensity. During 

the second run, 49.23 l reach the gauge at 25 m, indicating a runoff rate of 68.38%. Also the 

runoff intensity is higher than in the other experiments, the maximum value reaches 0.102 l s -1 

(68% of the inflow intensity). In the first run the runoff lasts for 812 s and starts 128 s after 

the water input is stopped, in the second run, 66 s before stopping the discharge, the runoff 

duration of 1198 s starts. The r-l-factor is 6.94 for the first run and 17.09 for the second run. 

(Fig. 7b) 

In RE 3A the water did not reach the measuring point after 15 m. In the second run (RE 3B) 

10.09 l (14.01%) reached the measuring point with a maximum intensity of 0.052 l s -1 (34% 

of the inflow intensity). The runoff starts 38 s before the pump is stopped and goes on for 354 

s The r-l-factor is calculated here with 2.1. 

Table 4: Overview over the flow velocities of the rill experiments: n.D.= no data 



MEAN water front [m s -1 ] 0.05 0.04 0.05 0.07 0.02 0.03 

MEAN Tracer 1 [m s -1 ] 0.1 0.11 0.09 0.1 0.06 0.07 

MEAN Tracer 2 [m s -1 ] 0.1 0.1 0.17 0.13 0.05 0.08 

MAX waterfront [m s -1 ] 0.12 n.D. 0.13 0.11 0.04 0.06 

MAX Tracer 1 [m s -1 ] 0.23 0.24 0.52 0.38 0.25 0.27 

MAX Tracer 2 [m s -1 ] 0.2 0.24 1.35 1.09 0.11 0.28 

84


Fig. 8: Flow velocities of the 3 rill experiments. 

In the first experiment it is plain to see that the waterfront flows much slower than the two 

tracers. The front is even outrun by tracer 1 after 22 m. Run a and run b also show similar 

average and maximum velocity values. In the first run, the waterfront shows flow velocities 

between 0.02 and 0.12 m s -1 , the average is 0.05 m s -1 , in the second run the flow velocity 

could not be measured for the first 20 m. Tracer 1 is similar in the two runs, the velocities 

range between 0.23 and 0.02 m s -1 in the first run and between 0.24 and 0.04 m s -1 in the 

second run. The averages are 0.10 and 0.11 m s -1 respectively. Tracer 2 is very similar to 

Tracer 1, the values are between 0.2 and 0.04 m s -1 in the first, and between 0.24 and 0.03 m 

s -1 in the second run. The averages are both 0.10 m s -1 . 

In experiment 2 are no big differences between the waterfront and the two tracers. In both 

runs the highest flow velocities are reached over the first 3-4 m, at this place also the highest 

differences in velocity between the waterfront and the tracers can be observed. The course is 

very constant. The flow velocities of the waterfront range between 0.13 and 0.02 m s -1 in the 

first run and between 0.11 and 0.03 m s -1 in the second run. The averages are 0.05 and 0.07 m 

85


s -1 . Tracer 1 shows a higher maximum value in the first run (0.52 m s -1 ) than in the second run 

(0.38 m s -1 ), whereas the mean values are similar reaching 0.09 m s -1 in the first and 0.1 m s -1 

in the second run. The maximum velocity value of tracer 2 is measured in the first run with 

1.35 m s -1 compared to 1.09 m s -1 in the second run. The average is also higher in the first run 

with 0.17 m s -1 against 0.13 m s -1 in the second run. The minimum velocities are 0.03 m s -1 in 

the second run for the waterfront, tracer 1 and also tracer 2; in the first run, the minimum of 

front and first tracer is 0.02 m s -1 , the lowest flow velocity of tracer 2 is 0.04 m s -1 . 

In experiment 3 variations can be detected as well but they are not as high as in the first 

experiment. The water does not reach the rill's end in the first run but the movement stops 

after 11m. The waterfront shows again the lowest flow velocities and is cached by tracer 1 in 

the first run after 6.5 m, in the second run after 13 m. The two tracers show again very similar 

flow velocities, until tracer 1 outruns the waterfront and turns into the waterfront itself. The 

maximum velocity of the waterfront is 0.04 m s -1 in the first run and 0.06 m s -1 in the second 

run. The averages are 0.02 m s -1 and 0.03 m s -1 respectively. Tracer 1 reaches 0.25 m s -1 in the 

first run and 0.27 m s -1 in the second run, the average is 0.06 m s -1 and 0.07 m s -1 . Also tracer 2 

shows a higher maximum in the second run with 0.28 m s -1 against 0.11 m s -1 in the first run 

and mean values of 0.05 m s -1 in the first and 0.08 m s -1 in the second run. The minimum 

values are 0.01 m s -1 for the front, tracer 1 and tracer 2 in both runs. 

Table 5: Overview over the sediment concentrations of the rill experiments 



MAX [g l -1 ] 2.06 2.31 2.37 6.31 2.31 1.59 

MIN [g l -1 ] 0 0.05 0 0.3 0 0 

MEAN [g l -1 ] 0.78 0.69 0.82 2.21 0.83 0.88 

86


Fig.9: Sediment concentrations of the 3 rill experiments: MP=Measuring point, n.D.= no data. 

In the first experiment, the maximum sediment concentrations are 2,06 g l -1 in the first run 

and 2.31 g l -1 in the second run. Minimum values are 0 g l -1 (no sediment detected) in the first 

run and 0.05 g l -1 in the second run. The averages are 0.78 g l -1 and 0.69 g l -1 . 

The second experiment shows a maximum sediment concentration of 2.37 g l -1 in the first and 

6.31 g l -1 in the second run, the minimum values are 0 g l -1 for the first run and 0.3 g l -1 for the 

second run. The averages are 0.82 and 2.21 g l -1 . 

In the third experiment, the last measuring point is not reached by the water in the first run, so 

no samples could be collected there. regarding the first two measuring points, the first run 

shows a maximum of 2.31 g l -1 , a minimum of 0 g l -1 and an average of 0.83 g l -1 . In the 

second run, all three measuring points offered samples. The maximum value is 1.59 g l -1 , the 

minimum 0 g l -1 and the average 0.88 g l -1 . 

Concerning the sediment concentrations, high differences are to notice. The highest value is 

reached with 6.31 g l -1 in experiment 2b. But there are also several samples where no 

sediment could be detected. The averages of the experiments mostly range below 1 g l -1 that is 

87


even slightly below the sediment concentrations of the rainfall simulations in the rill 

catchments. Experiment 2b is an exception with several samples reaching values between 2 

and 4 g l -1 , and a maximum value of over 6 g l -1 . 

4 Discussion 

POLYAKOV & NEARING (2003) tested in laboratory experiments the behaviour of rills 

under different inflow quantities and rill lengths on a loamy substrate. The sediment 

concentrations reached values between 10 and 130 g l -1 . LOCH (2000) tested the influence of 

vegetation on soil erosion. In one of his plots, both interrill and rill erosion was observed. The 

sediment concentrations of this plot reached a maximum value of 210 g l -1 . In the experiments 

accomplished in the Arnás-catchment, the maximum sediment concentration reached only 

6.31 g l -1 . The low sediment concentrations may be explained by the fact that the induced 

water inflow rate is not sufficient to activate a further incision of the rill. Also the take-up of 

loose material from the rill's ground does not raise the sediment concentrations significantly 

because directly before the experiments, snow melt removed the available material. The 

necessary presuppositions for further rill incision are a higher discharge rate and/or the 

preparation of transportable material e.g. by frost weathering. 

For all rill experiments the total runoff is higher in the second run, in experiment 2b for 

example 49 l of the 72 l inflow reach the end of the rill at 25 m, this is a rate of about 68 %. 

The lowest runoff rate (11,68%) reaches the 25 m in experiment 1a. The third experiment is 

not directly comparable to the other two experiments because of the changed flow lengths. 

After 15 m, there is certainly still a higher water quantity in the rill as after 25 m. The rate 

reaches 14 % here. Regarding the r-l-factor, experiment 3 shows the lowest value, it is even 

still lower than the r-l-factor of experiment 1a. In experiment 3, the runoff was measured only 

in run b, because in run a, over a flow length of 15m, 100% of the 72 l of inflow could 

infiltrate into the substrate. 

For each rill experiment, the second run shows a negative detention, indicating that the water 

reaches the measuring point before the inflow is finished. The lower the detention is, the 

faster the water reaches the measuring point. The second runs show higher maximum runoff 

quantities and so also higher intensity factors, the earlier runoff starts and the longer the 

period. Here we can deduce, that the moisture status of the rill not only has an influence on 

the infiltration within the rill, but also has a positive relation with the flow velocity. 

The three tested rills show different starting and developing conditions. The first rill is 

anthropogenically initiated and has developed on a motorcycle trail, the two other rills are 

88


naturally developed. Rill 3 has developed on an old rotational slump and is the deepest incised 

of the three rills. The deep incision suggests a more intense activity of the rill, but in the 

experiments, the used 72l water did not reach the rill’s end. That means, that for development 

and evolution of this rill, a much higher water quantity is needed as used in the experiments. 

The estimated area of the catchments of rill 1 and rill 2 was 450 and 400 m² respectively. In 

the rill catchments rainfall simulations were accomplished and the results are used to get a 

ballpark estimation of the water amounts that can reach the rill at least for the given soil 

moisture situation and the experimental rainfall intensity of 40 mm h -1 . Under a rainfall 

intensity of 40 mm h -1 , rill 1 can expect a runoff of about 1.3 l s -1 , rill 2 even 4.15 l s -1 , these 

values are about 10 to 25 times higher than the used input discharge rate of 0.15 l s -1 for each 

rill. The rainfall simulation in the catchment of rill 1 reached a sediment concentration of 0.7 

g l -1 , the average of the two runs of RE1 was 0.73 g l -1 , so there is no clear difference between 

rill erosion and sheet erosion in this case, because the used quantity of water was not 

sufficient to lead to further rill incision. The two rainfall simulations in the catchment of rill 2 

reached an average sediment concentration of 1.38 g l -1 , the two runs of RE2 reached an 

average of 1.52 g l -1 . 

At the outlet of the Arnás catchment, SEEGER et al. (2005) measured runoff values as well as 

sediment concentrations. The average sediment concentrations ranged between 0.03 and 2.29 

g l -1 , with maximum values between 0.09 and 4.8 g l -1 . In the rill experiments, the maximum 

sediment concentrations ranged between 1.59 and 6.31 g l -1 thus being in the same range than 

the values of the whole Arnás catchment. It is not possible to compare the runoff values of the 

rill experiments with the runoff values of the catchment because rill and river are different 

forms and there are different processes proceeding. What we can do is to compare the runoff 

values of the rill's catchment with the Arnás catchment: The area of the Arnás catchment is 

284 ha, the average runoff values are between 48 and 708 l s -1 . For a catchment of 450 m² (rill 

1) and 400 m² (rill 2) the theoretical runoff values would reach values between 0.008 and 0.11 

l s -1 and between 0.007 and 0.1 l s -1 . The maximum values between 87 and 2347 l s -1 of the 

Arnás catchment calculated for the rill catchments are between 0.014 and 0.37 l s -1 and 

between 0.012 and 0.34 l s -1 . The used inflow was 0.15 l s -1 and this value caused the same 

sediment concentration range as measured at the Arnás catchment outlet. The rainfall 

simulations in the rill catchments show, that a rainfall intensity 40 mm h -1 could cause an 

inflow in the rills of 1.3 for rill 1 or even 4.15 l s -1 for rill 2 (table 2). 

89


Table 6: Comparison of the runoff values of the Arnás catchment and the rill catchments; c.a. 

= catchment area 

Arnás c.a. 284 ha RE1 c.a. 450 m² RE2 c.a. 400 m² 

specific average runoff [l s -1 /m²] 0.0001 0.00007 0.00008 

specific runoff peak [l s -1 /m²] 0.0004 0.0001 0.0002 

It is to notice, that the connectivity between rill and river is not given in each case. The 

sediment and the water from the rill may not reach the river. The river transports the material 

from those areas that have a connectivity to the river. The trails improve the connectivity, but 

in some cases, it is not sufficient. 

Accordingly the rills can be regarded as very effective sediment providers for the receiving 

waters in a catchment because they can cause heavy sediment losses with relatively low 

runoff amounts: the calculated specific runoff values of the rills are clearly lower than the 

specific runoff values of the Arnás catchment. But this lower specific runoffs reach the same 

sediment concentrations as the Arnás catchment (table 6). 

The results clearly indicate that the rill erosion in the Arnás catchment, despite the relatively 

low measured values, is characterized by a high efficiency. 

The given standardized experimental setup makes it possible to compare different rills and to 

take statements about their efficiency for runoff and sediment budget of a catchment. Only 

with comparable conditions concerning water quantity and inflow intensity, it becomes 

possible to achieve appropriate statements on the basis of the measured results and to compare 

single experiments to each other at least qualitatively or semi-quantitatively. 

Measuring the slope is very important, but it has to be considered, that only average values 

over 1 meter slope length are measured. The position and the elevation of the knickpoints in 

the rill must be recorded exactly and accounted in the analysis. 

Using colour tracers, it became possible to record changes in flow velocity. This can be 

caused for example by the overflow of a plunge pool, a process, that delivers a lot of water 

and sediment in a short time. Without the knowledge of a change in flow velocity, the notice 

of an increase in sediment concentration could cause a wrong conclusion. 

In these experiments, 72 l of water are discharged with an intensity of 9 l min -1 into a rill, an 

intensity also used in laboratory experiments by POLYAKOV & NEARING (2003). They 

measured clearly higher sediment concentrations. That means, under other conditions, this 

water quantity is sufficient to cause higher sediment loss. The Arnás catchment is still as 

90


much degraded, that the most erodible material is removed and the rill's bottoms still reached 

the Flysch-plates . But it is a fact, that even in the slump material rills are developed. But for 

developing or increasing much higher water quantities and runoff intensities are needed. 

Considering the influence of initial soil moisture, one experiment consists of two runs. The 

influence of initial soil moisture was accounted by GOVERS et al. (1990) and GOVERS 

(1991). In their experiments under dry conditions the sediment concentrations almost reached 

the runoff's transport capacity, under higher initial soil moistures, the sediment concentrations 

were lower. In the rill experiments in the Arnás-catchment, the transport capacity was not 

reached because of the lack of transportable material and the low water amount. The influence 

of the initial soil moisture was clearly to notice, in the second run under saturated conditions 

the flow velocities and the runoff values were higher than in the first run with a soil moisture 

of about field capacity caused by snow melt . The starting moistures of the rainfall 

simulations were between 22 and 24 grav. %. But some experiments also show higher 

sediment concentrations under the higher initial soil moisture conditions in the second run 

(almost saturated). Under wet conditions, the flow velocities are higher and the cohesion 

forces are weaker, but there is less loose material in the rill. Under dry conditions, (in this 

case: less wet) the sediment concentrations are higher if there is a high quantity of lose 

material in the rill, if all this material is removed in the first run and if the higher flow 

velocities in the second run cannot cause an incision into the rill’s bed. 

5 Conclusion 

Three rill experiments according the described method were executed in the Arnás-catchment 

in the Pyrenees. 

In these experiments, as well naturally developed rill, anthropogenically induced rills like rills 

developed from motorcycle trails as real lanes were tested. The used 72 liters of water, that 

were disposed with an intensity of 9 l min -1 into the rill, caused material loss in the rill, but the 

dimensions were really different. There were samples without detectable sediment, the highest 

sediment concentrations reached values of 6.31 g l -1 . These results indicate that in the Arnás 

catchment, the rills have developed and are still active today under higher runoff intensities 

than the ones used in the experiments. 

From the induced 72 l of water, between about 8 and 49 l reached the end of the test length, 

what means a rate between 11 and 68 %. Is the passed flow length accounted, r-l-factors of 

between 2.1 and 17.1 were calculated. This factor is necessary, because in the third 

91


experiment, the flow length was reduced from 25 m to 15 m for accounting the given 

conditions. It is clearly to detect, that the different rills have a different efficiency for runoff 

and sediment budget. 

By recording the flow velocities, slope, sediment concentrations and runoff values, the 

behaviour of the three tested rills in the Arnás catchment could be comprehended. But the 

results can only be applied to this three tested rills, it is not possible to give a statement about 

the behaviour of rills in a catchment. Despite similar experiment conditions, the factors slope, 

different development state of the rill (depth and width) and position of the rill in the 

landscape determine the behaviour of the rills. The furthermost developed rill shows the 

lowest r-l-factor, the water can’t reach the measuring point after 15 m in the first run. So, it 

must be assumed, that this rill has formed under much higher rainfall-runoff situations as 

simulated in the experiments. It is necessary to go on testing rills with a standardised method 

like the rill experiments to collect more information about a rill's behaviour concerning runoff 

and sediment transport, and maybe to give universal statements. This rill experiments offer 

qualitative or semi-quantitative analysis of single rills. 

References 

- BRUNO, C., DI STEFANO, C. & FERRO, V. (2008): Field investigation on rilling in 

the experimental Sparacia area, South Italy. - Earth Surface Processes and Landforms 

33: 263-279. 

- BUTZEN, V., SEEGER, M. & CASPER, M. (2009 submitted): Spatial pattern and 

temporal variability of runoff processes in Mediterranean Mountain environments - 

coupling experimental measurement and GIS-analysis. - Zeitschrift für 

Geomorphologie; submitted. 

- CALVO -CASES, A., GISBERT, J.M., PALAU, E. & ROMERO, M. (1988): Un 

simulador de lluvia portátil de fácil construcción. - In: Sala, M. & Gallart, F. (eds.): 

Métodos y técnicas para la medición en el campo de processo geomorfológicos: 6-15. 

- CASALI, J., LOIZU, J., CAMPO, M.A., DE SANTISTEBAN, L.M. & ÁLVAREZ- 

MOZOZ, J. (2006): Accuracy of methods for field assessment of rill and ephemeral 

gully erosion. - Catena 67: 128-138. 

- CERDÁ, A. & GARCÍA-FAYOS, P. (1994-95): Relaciones entre las pérdidas de agua 

y semillas en zonas acarcavadas. Influencia de la pendiente. - Cuadernos I Geográfica 

20-21: 47-63. 

92


- CERDAN, O., LE BISSONNAIS, Y., COUTURIER, A., BOURENNANE, H. & 

SOUCHÈRE, V. (2002): Rill erosion on cultivated hillsplope during two extreme 

rainfall events in Normandy, France. - Soil & Tillage Research 67: 99-108. 

- FLORES-CERVANTES, J.H., ISTANBULLUOGLU, E. & BRAS, R.L. (2006): 

Development of gullies on the landscape: A model of headcut retreat resulting from 

plunge pool erosion. - J. Geophys. Res. 111: F01010, doi:10.1029/2004JF000226. 

- GOVERS, G., EVERAERT, W., POESEN, J., DE PLOEY, J. & LAUTRIDOU, J.P. 

(1990): A Long flume study of dynamic factors affecting the resistance of loamy soil 

to concentrated flow erosion. - Earth surface processes and landforms 15: 313-328. 

- GOVERS, G. (1991): Time-dependency of runoff velocity and erosion: the effect of 

the initial soil moisture profile. - Earth Surface Processes and Landforms 16: 713-729. 

- HANCOCK, G.R., CRAWTER, D., FITYUS, S.G., CHANDLER, J. & WELLS, T. 

(2008): The measurement and modelling of rill erosion at angle of repose slopes in 

mine spoil. - Earth Surface Processes and Landforms 33: 1006-1020. 

- KNAPEN, A., POESEN, J., GOVERS, G., GYSSELS, G. & NACHTERGAELE, J. 

(2007): Resistance of soils to concentrated flow erosion: A review. - Earth-Science 

Reviews 80: 75-109. 

- LASANTA, T., PÉREZ RONTOMÉ, M.C. & GARCÍA RUIZ, J.M. (1994): Efectos 

hidromorfológicos de differentes alternativas de retirada de tierras en ambientes 

semiáridos de la depressión del Ebro. - In: García Ruiz, J.M. & Lasanta, T. (eds.): 

Efectos geomorfológicos del abandono de tierras: 69-82; Sociedad Española de 

Geomorfología. 

- LOCH, R.J. & THOMAS, E.C. (1987): Resistance to rill erosion: observations on the 

efficiency of rill erosion on a tilled clay soil under simulated rain and run-on water. - 

In: Bryan, R.B. (ed.): Rill erosion – processes and significance: 71-83; Catena Verlag. 

- LOCH, R.J. (2000): Using rainfall simulation to guide planning and management of 

rehabilitated areas: part I Experimental methods and results from a study at the 

Northparkes mine, Australia. - Land degradation and development 11: 221-240. 

- MERZ, W. (1993): Experimentelle Untersuchungen zur Rillenerosion auf 

landwirtschaftlich genutzten Böden in Kanada und der Volksrepublik China. - 

Freiburger Geographische Hefte, Heft 40, Selbstverlag des Institutes für Physische 

Geographie der Albert-Ludwig-Universität Freiburg i.Br., Freiburg, 147 pp. 

93


- MEYER, L.D., FORSTER, G.R. & RÖMKENS, M.J.M. (1975): Source of soil eroded 

by water from upland slopes. - Proc. 1972 Sediment Yield Workshop, US Dept. of 

Agric. Sediment. Lab., Oxford, Mississippi: 177-189. 

- MORGAN, R.P.C., MARTIN, L. & NOBLE, C.A. (1987): Soil erosion in the United 

Kingdom: a Case Study from Mid-Bedfordshire, England. - Occasional Paper No.14. 

- OOSTWOUD WIJDENES, D.J., POESEN, J., VANDEKERCKHOVE, L. & 

GHESQUIERE, M. (2000): Spatial distribution of gully head activity and sediment 

supply along an ephemeral channel in a Mediterranean environment. - Catena 39: S. 

147-167. 

- PFAHLS, C., SEEGER, M. & SAUER, T. (1999): Infiltrationsmessungen, 

Niederschlagssimulationen, TDR- und Einstichtensiometermessungen sowie 

konventionelle gravimetrische Bodenwassererhebungen – ein Methodenvergleich. - 

APT-Berichte 4, Nr. 10: 51-77. 

- POESEN, J. (1987): Transport of rock fragments by rill flow – a field study. - In: 

Bryan R.B. (ed.): Rill erosion – processes and significance: 35-54; Catena Verlag. 

- POLYAKOV , V.O. & NEARING, M.A. (2003): Sediment transport in rill flow under 

deposition and detachment conditions. - Catena 51: 33-43. 

- RIES, J.B., LANGER, M. & REHBERG, C. (2000a): Experimental investigations on 

water and wind erosion on abandoned fields and arable land in the central Ebro Basin, 

Aragón/Spain. - Zeitschrift für Geomorphologie N.F. Suppl.-Bd. 121: 91-108. 

- RIES, J.B., MARZOLFF, I. & SEEGER, M. (2000b): Der Einfluss von Beweidung 

auf die Vegetationsbedeckung und Bodenerosion in der Flyschzone der spanischen 

Pyrenäen. - In: G. Zollinger (ed): Aktuelle Beiträge zur angewandten physischen 

Geographie der Tropen, Subtropen und der Regio Trirhena: 167-194; Freiburger 

Geographische Hefte. 

- RIES, J.B., MARZOLFF, I. & SEEGER, M. (2003): Einfluss der Beweidung auf 

Vegetationsbedeckung und Geomorphodynamik zwischen Ebrobecken und Pyrenäen. 

- Geographische Rundschau 55(5): 52-59. 

- SEEGER, M., ERREA-ABAD, M.-P. & LANA-RENAULT, N. (2005): Spatial 

Distribution of Soils and their Properties as Indicators of Degradation/Regradation 

Processes in a Highly Disturbed Mediterranean Mountain Catchment. - Journal of 

Mediterranean Ecology Vol. 6 No.1: 53-59. 

- SEEGER, M., ERREA, M.-P., LANA-RENAULTE, N., BEGUERÍA, S., ARNÁEZ, 

J., MARTÍ, C., REGÜÉS, D. & GARCÍA-RUIZ, J.-M. (2005): Charakteristika des 

94


Sedimenttransportes in einem Kleineinzugsgebiet der Aragonesischen Pyrenäen. - 

Zeitschrift für Geomorphologie N.F. Suppl.-Bd. 138: 211-228. 

- SIDORCHUK, A. (2005): Stochastic components in the gully erosion modeling. - 

Catena 63: 299–317. 

- VANDEKERCKHOVE, L., POESEN, J., OOSTWOUD-WIJDENES, D. & DE 

FIGUEIREDO, T. (1998): Topographical thresholds for ephemeral gully initiation in 

intensively cultivated areas of the Mediterranean. - Catena 33: 271-292. 

- WOODWARD, D.E. (1999): Method to predict cropland ephemeral gully erosion. - 

Catena 37: 393-399. 

95


Kapitel 4 

Wirtz et al. (2012a): Field experiments for understanding and quantification of rill 

erosion processes. Catena 91, 21-34. 

96


Field experiments for understanding and quantification of rill erosion processes 

Wirtz S. a , Seeger M. b , Ries J.B. a 

a: Dep. of Physical Geography, Trier University 

b: Dep. of Land Degradation and Development, Wageningen University 

Abstract 

Despite many efforts over the last decades to understand rill erosion processes, they remain 

unclear. This paper presents the results of rill experiments accomplished in Andalusia in 

September 2008 using a novel experimental set up. 72 L of water are introduced with an 

intensity of 9 L min -1 into a rill. Rill cross sections, slope values, flow velocities and sediment 

concentrations were measured and these values were used to calculate sediment detachment 

and transport. Each experiment was repeated once within 15 min. With this new experimental 

setup it is possible to calculate several hydraulic parameters like hydraulic radius, wetted 

perimeter, flow cross section, transport rate and transport capacity which are usually 

estimated from coarse flow and rill parameters. In rill experiments, four different natural rills 

were flooded with the same experimental setup. Several processes like transport of loose 

material, erosion, bank failure and knickpoint retreat and the runoff effectiveness showed 

different and variable intensities. The sediment concentrations ranged between 5.2 – 438 g L - 

1 . In most cases, detachment rates are close to the transport capacity and, in some cases, the 

transport capacity is even exceeded. This can be explained by the occurrence of different 

erosion processes within a rill (e.g. detachment, bank failure, headcut retreat) which are not 

all explained by the given equations. The results suggest that the existing soil erosion 

equations based on shear forces exerted by the flowing water are not able to describe rill 

erosion processes satisfactory. Too many different processes with a high spatial and temporal 

variability are responsible for rill development. 

Key words: soil erosion, rill erosion, experimental method, quantification of process activity 

Introduction 

Soil erosion in general, and the development of rills in special, is the result of a very complex 

interaction of soil properties with a high spatial and temporal variability (Nachtergaele et al., 

97


2001, 2002; Poesen et al., 1999) in which the morphology of a rill and the rill's headcut 

morphology (Flores-Cervantes et al., 2006) may be determinant as well as stochastically 

driven processes (Sidorchuk, 2005). This leads to great difficulties in quantifying soil erosion 

processes and makes soil erosion measurements hardly comparable (Knapen et al., 2007; 

Auerswald et al., 2009; Stroosnijder, 2005). 

The two main processes in soil erosion are inter-rill and rill erosion by flowing water, 

however the mechanisms of these two processes are completely different. The detachment in 

inter-rill erosion is caused and enhanced by drop-impact (Beuselinck et al., 2002) and, in 

addition to the soil’s intrinsic characteristics (Kuhn and Bryan, 2004; Kuhn et al., 2003; Le 

Bissonnais et al., 2005), is thought to depend mainly on rainfall intensity (Brodie and 

Rosewell, 2007; Bryan, 2000). Rill erosion is, in contrast, caused by the concentrated flow of 

water (Bryan, 2000; Govers et al., 2007; Knapen et al., 2007) and is considered to be the most 

important process of sediment production (and thus, soil loss) (Cerdan et al., 2002; Poesen, 

1987). The resulting rills may be persistent and develop into gullies, hindering further land 

use (Woodward, 1999; Vandekerckhove et al., 1998). Especially on fallowland and shrubland, 

rills can develop without disturbance by land management measures like ploughing. In the 

Mediterranean, huge areas of fallowland and shrubland exist (Ries, 2003) thus rills can 

develop very fast and cause high soil losses. 

Generally, rill erosion is understood as the effect of flowing water exceeding a certain 

threshold of soil resistance (Knapen et al., 2007). During the last decades, several approaches 

to describe and predict soil detachment and sediment transport in rills have been developed, 

and great effort has been made to evaluate their suitability for that purpose (Giménez and 

Govers, 2002; Govers et al., 2007; Hessel and Jetten, 2007). Unfortunately, the different 

approaches to describe this phenomenon have turned out to be at least weak, if not 

contradictory (Giménez and Govers, 2002; Govers et al., 2007; Merz and Bryan, 1993). This 

is attributed mainly to methodological differences in all monitoring and experimental set-ups 

to achieve the rills (Knapen et al., 2007; Merz and Bryan, 1993). It also appears that particle 

detachment and sediment transport may be controlled by different characteristics of the 

flowing water and, therefore, a comprehensive description may not be possible (Govers et al., 

2007). However, soil erosion measurements are still lacking (Stroosnijder, 2005) and there is 

a recognized need to perform field experiments to ascertain the role of rills in soil erosion 

(Govers et al., 2007). As the observation of erosion in the field is subordinated to the 

stochastic character of the erosion events (Auerswald et al., 2009) and to a high dependency 

of the measurement technique (Casali et al., 2006), standardized and reproducible field 

98


experiments are needed, in which the relevant parameters of runoff and sediment transport 

can be measured and which, at the same time, can produce data to characterise the rill's 

behaviour in its environment. 

Most experimental work about rill erosion that has been carried out, both in the laboratory 

(Brunton and Bryan, 2000; Bryan and Poesen, 1989; Gilley et al., 1990; Huang et al., 1996; 

Mancilla et al., 2005) as well as under field conditions (De Santisteban et al., 2005; Helming 

et al., 1999; Rejman and Brodowski, 2005) used soils with different textures and natural or 

simulated rainfall. The aim of the research groups was to observe rill network formation 

(Bruno et al., 2008; Mancilla et al., 2005), define the initial conditions for rilling (Bruno et al., 

2008, Bryan et al., 1998; Govers and Poesen, 1988; Slattery and Bryan, 1992; Torri et al., 

1987), study the development of rill head morphology (Bruno et al., 2008; Brunton and 

Bryan, 2000), estimate the main hydraulic variables like cross-section area, wetted perimeter, 

hydraulic radius, mean velocity and shear stress (Bruno et al., 2008; Foster et al., 1984; Gilley 

et al., 1990; Giménez et al., 2004; Govers, 1992b) or propose mathematical models for 

estimating soil loss due to rill erosion (Favis Mortlock, 1998; Favis Mortlock et al., 2000; 

Bruno et al., 2008; Foster, 1982; Nearing et al., 1989). 

In most laboratory experiments the effort is made to find relationships between different 

factors. The influence of runoff on soil detachment is an often investigated question. Other 

parameters often tested are slope length, percolation, rill development, critical Froude 

number, critical shear stress different soil characteristics, slope, rainfall intensity, flow 

velocity or flow velocity distribution, bed morphology and flow area. 

In such a way, Bryan and Poesen (1989) tested, in laboratory experiments, the relationship 

between slope length, percolation, runoff and rill development. The flume used had a 

maximum length of 24.5 m, consisting of ten segments of 2.45 m. At the end of the flume, 

runoff was measured. They showed that runoff is not a simple function of rainfall excess and 

slope length but a more complex process dominated by surface sealing, rill development and 

headcut incision. Rill initiation is controlled by established threshold hydraulic conditions, the 

further development of the rills and headcuts is complex and depending on different 

thresholds. Torri et al. (1987) related in laboratory experiments, with variable slope, runoff 

and rainfall intensity, the critical Froude number and the critical shear stress to some soil 

characteristics. Critical shear stress was found to be correlated to soil shear strength. But this 

result could not be confirmed in all further studies. In an other laboratory study, Nearing et al. 

(1991) measured flow shear stresses ranged from 0.5 to 2 Pa, while tensile strengths ranged 

from 1 to 2 kPa, a difference in magnitude of 1000. Despite this conflict, detachment rates of 

99


nearly 300 g m -2 s -1 were measured. He explained this result with turbulent burst events which 

are much greater than the average flow shear stresses. 

Giménez et al. (2004) tested, in a laboratory flume experiment, the velocity distribution in 

rills and the relationship between flow velocity and rill bed morphology. They showed that 

bed roughness increases with slope while flow velocity decreases. Flow velocity increases 

until a threshold Froude number between 1.3 and 1.7 is reached, and a hydraulic jump occurs 

leading to the formation of a pool. Govers (1992b) tested, in another laboratory flume, the 

relationship between discharge, flow velocity and flow area. He showed that mean flow 

velocity is not at the front of the water, but where the water reached 80-90% of its maximum 

width. The mean flow velocity and cross-sectional flow area can be related to discharge for 

rills eroding loose, non layered materials like agricultural soils. Soil characteristics and slope 

appear to be of minor importance in this study. 

The main problem with these laboratory experiments is that the results cannot be easily 

transferred to natural rills. In the laboratory, flumes with compacted soil material are used, but 

Giménez & Govers (2002) showed that most of the data attained on rill models with smooth 

beds cannot be applied to naturally developed rills with rough beds. In many cases, hydraulic 

parameters are extracted from equations created to describe flow behaviour in rivers. Govers 

(1992a) and Govers et al. (2007) showed that these parameters cannot simply be transferred to 

flow behaviour in rills. This process oriented research needs also to be conducted in natural 

rills, using a mixture of process oriented (laboratory) experiments and field research. 

However field research is often in pursuit of other targets. Experimental work is very rare. 

Interests are adjusted to catchment areas, long-term-observations on plots or, in best cases, the 

measurement of different parameters under natural rainfall. Some examples are given here. 

De Santisteban et al. (2005) tested two different indices to characterise the influence of 

watershed topography on channel erosion. The first is defined as the product of watershed 

area and the partial area-weighted average slope. The other one is similar but uses the slope as 

the weighting factor, i.e. it is the product of watershed area and the length-weighted average 

slope. It was shown, that for a wide range of soil, climate, soil use and management 

conditions, the close relationship between soil erosion and topography can be quantified using 

the two indices. Govers & Poesen (1988) observed on a 7500 m² field plot the evolution of a 

rill and gully system. The periodic survey started on 15.11.1983 and finished at 3.10.1984. 

They measured detachment rates and used splash cups to get data about splash erosion. The 

sediment being detached by splash on inter-rill areas is transported to the channel system 

mainly by inter-rill wash. Rill and gully erosion is more important than inter-rill erosion, but 

100


the relative importance of inter-rill erosion varies in time and space, due to changes of the 

inter-rill surface characteristics and the activation of sidewall and gullying processes in the 

channel network. Bruno et al. (2008) accomplished field investigations under natural rainfall. 

They measured cross sections, runoff and soil loss and proposed a simple mathematical model 

for estimating soil loss. The analysis of the measured erosive events allowed establishment of 

the proportion of both rill erosion and inter-rill erosion on total soil loss. The measurements 

showed that rill erosion increases the total sediment transport efficiency because rill flow is 

able to transport both the inter-rill eroded sediments and sediment particles eventually 

detached from the rill wetted perimeter. The measurements also allowed verification of a 

relationship between rill length and rill volume, which was theoretically deduced by the 

dimensional analysis and self-similarity theory. This equation shows that rill length can be 

usefully employed as a severity index of the rilling process. The morphological evolution of 

the rill cross-section showed that in the first part of the rill length the channelized flow is able 

to erode the wetted perimeter and to transport the eroded particles, while in the terminal part 

of the rill the actual sediment load is high and the flow is only able to transport the particles 

coming from upstream without scouring the rill perimeter. The shear stress profile along the 

rill length confirmed that in the terminal part of the rill the flow is able to transport the 

upstream eroded sediment particles, but not able to detach additional material. 

The review of the experimental research on rill erosion processes shows the weak and 

partially contradictory results of attempts to understand rill erosion processes. This can be 

seen in the large number of studies dealing with the relationships between flow parameters 

and particle detachment and transport. This is even clearer regarding the rills' development 

and behaviour in the field. There is still a lack of direct observation of the throughflow and 

sediment transport/detachment characteristics in natural rills. On the other hand, rills and their 

behaviour in the landscape can give insight to the main dominating soil erosion processes and 

their magnitude and frequency. But for this we have to understand their functioning with 

determined amounts of throughflowing water. Therefore, a novel and simple method for 

characterizing the rills hydraulic effectiveness and the erosion dynamics within was 

developed. 

In the landscape context the following questions have to be addressed: 

1. What is the rill's contribution to soil erosion? 

2. How effective are rills for routing water and sediments through their environment? 

The rill flow and erosion experiments are thought to provide insights to contribute finding 

answers. This experiment should be able to reflect, at different levels of detail, the rill's 

101


hydraulic and erosion dynamics within the landscape in which they developed. Experiments 

have been designed so that they can be easily adapted to different rill sizes and morphologies 

as well as to variable runoff, thus providing information about the different processes 

involved in rill erosion. Within, we attempt to approach standardised description methods for 

the rill erosion processes. 

The aim of the novel experimental field setup presented here is to provide a reproducible tool, 

in which the magnitude of rill erosion processes can be understood, and at the same time 

contribute to understanding the effect of rills in their environment. The new method can be 

used to test existing rills in field experiments and generate information about their hydraulic 

effectiveness and erosion dynamics. This experimental setup only allows to identify and to 

compare different processes and their activity within a specific rill. Similar to the uncertain 

erosion behaviour of replicated test plots (Nearing, 1998; Nearing et al., 1999) a direct 

comparison of results from different experiments is not valid. 

Material and Methods 

Study areas 

The four study areas in Andalusia are located at Negratin, Freila, Salada and Belerda as 

presented in Figure 1. UTM coordinates of the tested rills are given in Table 1. 

Fig. 1: Location of the test areas in South East Spain 

102


Negratin and Freila: The areas are located within the Hoya de Baza sedimentary basin and 

composed of marls, in which calcareous Regosols have developed. The climate is semi-arid 

and vegetation is dominated by low shrubs and Stipa tenacissima grass tussocks. The land 

cover at the south side of the Negratin-dam is dominated by abandoned cereal fields, which 

are extensively grazed by sheep and agricultural land use is comprised mainly of cereal dryfarming 

and almond grooves (Seeger, 2007). 

Salada: Located at the SE-margin of the Betic range (SE-Spain), inside the penibetic complex. 

The area is composed of conglomerates with a clayey to loamy matrix in which Regosols as 

well as to fairly developed (Calcic) Cambisols have developed. Vegetation is similar to that 

found in the Freila and Negratin-area. The climate is semi-arid too, but less accentuated than 

in the previously mentioned area (Seeger, 2007). Here we can find a mixed pattern of rainfed 

agricultural areas, mainly cereals, olives and almonds, and abandoned or uncultivated areas. 

Belerda: This test area is located in the Guadix basin. The parent material consists of tertiary 

and quaternary conglomerates, sands, silts and clays. The soil texture class following the FAO 

is a silty clay loam. The land use is separated into cultivated areas, with almond and olive 

groves, and abandoned agricultural fields (Vandekerckhove et al., 2003). The climate is, 

though still semi-arid, characterised by higher average annual temperatures and precipitations 

in comparison with the other test areas. 

The climatic parameters of the test fields are summarized in Table 1. 

Table 1: Temperature, precipitation, northing and easting of the four test areas. 

Tested Rill meteorological station average annual temperature annual precipitation easting rill northing rill 

Negratin Baza 14.2°C 368 mm 505835 4156275 

Freila Baza 14.2°C 368 mm 504874 4152414 

Salada Embalse Valdeinfierno 13.4°C 311 mm 595759 4187298 

Belerda Granada 15.6°C 473 mm 477694 4132866 

Tested rills 

An overview of the main descriptors of the rills is given in Table 2. Particle size analysis was 

conducted following AD-HOC-Arbeitsgruppe Boden (2005). Soil texture is classified 

following FAO guidelines (FAO, 2006). 

103


Table 2: Rill parameters; NCA = needed catchment are to reach a runoff of 9 L min -1 ; gravel 

content refers to total soil, the rest only to fine earth fraction. Particle-size class limits are 

determined following AD-HOC-Arbeitsgruppe Boden 2005. 

Negratin Freila Salada Belerda 

Ø Slope [°] 20.6 9.7 7.7 17.1 

max. Slope [°] 31 19 11 28 

tested flow length [m] 20 21 15 16 

catchment area [m²] 1200 1100 170 5400 

texture class L SiL SiCL L 

Gravel [%] > 2000 μm 1 13 1 13 

coarse sand [%] 2000-630 μm 10 1 2 10 

middle sand [%] 630-200 μm 10 6 2 10 

fine sand [%] 200-125 μm 8 2 1 8 

very fine sand [%] 125-63 μm 17 9 7 17 

coarse silt [%] 63-20 μm 13 28 17 13 

middle silt [%] 20-6.3 μm 13 22 17 13 

fine silt [%] 6.3-2 μm 14 17 24 14 

Clay [%] < 2 μm 15 15 29 15 

organic matter [%] 11.5 11.5 8.7 12.15 

starting soil moisture [% w/w] 5.08 2.4 4.48 5.87 

Kt [s² m 0,5 kg -0,5 ] 0.0095 0.0095 0.0095 0.0091 

location WEPP dataset Frederick Frederick Frederick Opequion 

maximum width [m] 0.3 0.3 0.3 0.3 

maximum depth [m] 0.1 0.2 0.2 0.2 

vegetation cover [%] ~ 5 ~ 0 ~ 0 ~ 10 

rock fragment cover [%] ~ 5 ~ 5 ~ 5 ~ 10 

volume [m³] 0.2 0.26 0.23 0.19 

MP 1 

cross section [m²] 0.0107 0.0217 0.0221 0.0140 

slope [°] 30 3 6 14 

MP 2 


slope [°] 19 19 11 18 

MP 3 


slope [°] 15 10 7 18 

grain density [kg m -3 ] 2650 2710 2660 2610 

dry bulk density [kg m -3 ] 1410 1510 1320 1450 

runoff rainfall simulations [%] 71.5 90 85 51 

NCA [m²] 19 15 16 27 

The rill in Negratin (Fig. 2, upper left) is situated on the steepest slope (average 20.6°) of the 

tested rills with a catchment area of the rill’s headcut of about 1200 m². The total rill length 

tested was 20 m in length with a maximum width of about 0.3 m and a maximum depth of 0.1 

m. Vegetation and rock fragments cover only approximately 5% of the rill. The areas of the 

three measured cross sections are 0.0107 m² at 6 m, 0.0102 m² at 10 m and 0.016 m² at 16 m 

of the tested rill's length. With these values, the total volume was estimated to be about 0.2 

m³. The rill was carved into a loamy soil with a moderate bulk density of 1410 kg m -3 (BD3, 

104


(FAO, 2006)), in which the particle density was measured to be 2.65 g cm -3 . Starting soil 

moisture was 5.08 % w/w. 

The rill at Freila (Fig 2, upper right) developed on a leveled field. The maximum depth of the 

rill is about 0.2 m, the maximum width 0.25 m. Vegetation cover is not detectable, rock 

fragment cover is about 5%. Using the cross sections of 0.0217 m² (5 m), 0.016 m² (12.5 m), 

0.01 m² (15.5 m) and the flow length of 21 m, a volume of about 0.26 m³ was estimated for 

the whole rill. The soil texture is classified as medium clay silt, with a particle density of 2.71 

g cm -3 and a moderate bulk density of 1510 kg m -3 (BD3). Starting soil moisture was 2.4 % 

w/w. 

The rill at the Salada site (Fig 2 bottom left) formed on an unpaved road with an average 

slope of 7.7°. The rill's headcut catchment covers an area of about 170 m². The maximum 

width within the 15 m length tested is about 0.3 m, the maximum depth round 0.2 m. Only 5 

% of the rill is covered by rock fragments, and there is no vegetation cover in the rill. The 

cross section at the first measuring point at 4 m has an area of 0.0221 m², after 7 m, a cross 

section of 0.0244 m² was measured and after 12 m, the cross section was 0.0144 m². For the 

tested length of 15 m, there is a volume of 0.23 m³ calculated. The soil texture is classified as 

silty clay loam, with a low bulk density (BD2) of 1320 kg m -3 . The particle density value 

reaches 2.66 g cm -3 . Starting soil moisture was 4.48 % w/w. 

The Belerda rill (Fig 2 bottom right) developed in a loam soil with a high content of sand (45 

% of the fine soil) and coarse fragments (13 % of the total soil). It is located on a steep 

agricultural road with an average slope of 17.1° and a catchment area of about 5400 m². We 

tested 16 m of rill length, with a maximum width of 0.3 m and a maximum depth of 0.2 m. 

Vegetation and rock fragments cover about 10%. The cross sections were measured at 4.5 m, 

at 8 m and at 11 m, they reach areas of 0.014 m², 0.020 m² and 0.021 m² respectively leading 

to an estimated rill volume of about 0,19 m³ . The bulk density is with 1450 kg m -3 moderate 

(BD3), the grain density is only 2.61 g cm -3 . Starting soil moisture was 5.87 % w/w. 

105


Fig. 2: The 4 tested rills: top left Negratin; top right Freila; bottom left Salada; bottom right 

Belerda 

Rill experiment 

The rill experiments consist of two runs: first the rill is tested under field conditions (“dry”); 

in a second run, about 15 min later, the same rill is tested under “wet” conditions. 

With a motor driven pump, a constant discharge of 9 L min -1 is maintained for 8 minutes, 

resulting in a total water inflow of 72 L. To avoid mobilization of soil particles by the 

inflowing water at the starting point of the experiment, the inflow velocity and pressure are 

reduced with an inflow device, which allows the water to enter the rill as a light stream (Wirtz 

et al., 2010). 

The flow velocity within the rill is characterized in three steps: the travel time of the 

waterfront and of two different colour tracers is measured for every meter using a 

106


chronograph. The first colour tracer is introduced at the starting point after three of the eight 

minutes of experiment time, the second follows at six minutes. By means of this procedure, 

three velocity curves are recorded and changes in flow dynamics can be detected. For safety 

reasons, food colourings (E 124 (red) and E 13 (blue)) are used as colour tracers. 

The runoff height is continuously measured in a small flume at the end of the rill by a 

pressure transducer (Ecotech DL/n, V2.35). For runoff curve calibrating, runoff at outflow is 

measured volumetrically at regular intervals. With this, a constant measurement of the 

discharge is possible in high temporal resolution and throughout the whole experiment. 

The rill's morphology is characterized by measuring its slope with a spring bow of 1m range 

and a digital air lever. It should be noted that slope measuring provides only average slopes 

per 1 meter. A step or a knick-point in the rill is not accounted for, however its position and 

height are recorded. 

For gathering intermediate data on suspended sediment transport, three suitable measuring 

points (MP) are selected. Small knickpoints in the rill have proven to be useful sampling 

points because there is no need to press the bottle into the rill bottom. Four water samples are 

taken: the first as soon as the waterfront has reached the sampling point, the second after 30 

seconds, the third after 1:30 and the fourth 2:30 after the arrival of the water. The sediment 

concentration is determined by filtration of the samples in laboratory (Wirtz et al., 2010). 

The rill cross section was measured at each measuring point. With thin metal sticks, the 

distance between ground level and rill bottom was measured in 0.02 m steps. This allows an 

accurate calculation of the rills transversal area and an estimation of the rills volume. 

Descriptors of rill experiment 

Several simple descriptors are used for characterizing the hydraulic function of the rills: 

The total runoff volume at the outlet V R [L] is calculated. When divided by the inflow 

volume, V I [L] , the runoff coefficient (RC) [without unit] is obtained by 

V 

V 

R 

RC = 

(eq. 1) 

I 

To compare runoff values measured in rill experiments with different experimental lengths, 

we calculate the runoff length factor (RC L ) [m] by multiplying the runoff coefficient by the 

tested length [m]. It is an expression of runoff effectiveness and an inverse measure for 

infiltration capacity within the rill: 

VR 

RC 

L 

= L 

(eq. 2) 

V 

I 

107


The maximum runoff intensity Q m [L s -1 ] is set into relation with the inflow intensity Q I [L s - 

1 ], leading to Q f [without unit], which is the intensity factor. Some additional factors of the 

flow duration are calculated as they are also indicators of the transformation of the input pulse 

such as the begin and end times of the outflow at the end of the rill and the flow duration (t S 

[s], t E [s] and T R [s] respectively). The changes in flow duration are indicated by the quotient 

(d T ) [without unit] between runoff duration and inflow duration T I [s]. 

Velocity is recorded as an average value (v a ) [m s -1 ] and the maximum (v max ) [m s -1 ] value for 

each of the 3 measurements in each experiment. The flow velocity at which each of the 

samples was collected is estimated as follows: We assume linear changes between the 

measured flow velocities (front, tracer 1 and tracer 2). Knowing the exact time of arrival of 

the water front to the sampling point, we estimate the flow velocity for each of the samples 

collected interpolating between the measured velocities. 

Taking into account the rill’s morphology, the estimated velocity at the sampling location, the 

points in time and the sediment concentration, we calculated the maximum hydraulic shear 

stress τ [Pa] (eq. 3) according to Nearing et al. (1997). 

τ = ρgRS 

(eq. 3) 

where ρ represents the fluid density [kg m -3 ] which was calculated taking into account the 

sediment concentration in the samples, g the gravitational acceleration (9.81 m s -2 ), R the 

hydraulic radius [m], and S the effective slope (sin(slope angle)). The hydraulic radius is 

calculated as follow: 

A 

R (eq. 4) 

WP 

with A = flow cross section [m²] and WP = wetted perimeter [m]. Flow cross section is 

calculated using the runoff and the flow velocity: 

Q 

A (eq. 5) 

v 

with Q = runoff [m³ s -1 ] and v = flow velocity [m s -1 ]. The runoff, needed to calculate the 

hydraulic radius at the measuring points, was set equal to inflow (0.00015 m 3 s -1 ), so the 

calculated values can be understood as the maximum possible. Using the known flow cross 

section and the rill cross section, water level and wetted perimeter can be determined. 

The sediment transport within the rill was characterized by the sediment concentration in the 

samples. Additionally, we calculated the sediment transport per unit time and unit rill length 

(D L [kg m -1 s -1 ]) and per unit rill bed area (D A [kg m -2 s -1 ]). 

108


The transport capacity T C [kg s -1 ] at each of the sampling points was calculated according to 

WEPP (Foster et al., 1995): 

3 

2 

T 

C 

= k t f 

(eq. 6) 

where k t is the transport coefficient [m 0.5 s 2 kg -0.5 ] and τ f is the flow shear stress [Pa]. Here we 

used the maximum hydraulic shear stress calculated as mentioned above. 

Rainfall simulations 

For the characterisation of the rill catchments rainfall simulations were performed with a 

small mobile rainfall simulator based on the type of Calvo Cases et al. (1988), Lasanta et al. 

(1994) and Cerdá and García-Fayos (1994-95). The plot was bounded by a steel ring of 0.6 m 

in diameter (0.28 m²) and 0.006 m height, having an outlet of 0.1 m width with a narrowing 

runoff collector (Ries et al., 2000; Ries et al., 2009). The rainfall intensity was 40 mm h -1 , the 

fall height 2 m. The suitability of this method for the explanation of the influence of external 

factors on runoff generation and erosion with this methodology was demonstrated by Seeger 

(2007). 

The results gathered from the rainfall simulations were used to estimate the minimum area 

needed to generate the runoff which was used to perform the rill experiments (9 L min -1 ). This 

information provides insight regarding the possibility of runoff in the rill. This factor called 

“needed catchment area” (NCA) is calculated as follow: 

NCA 

I 

RO 

RS 

100 

RE 

* I 

RS 

(eq. 7) 

with I RE = inflow intensity of the rill experiment, in this study, the value is 9 L min -1 . RO RS is 

the runoff of the rainfall simulation [%] and I RS is the rainfall intensity of the rainfall 

simulation per area in L min -1 m -2 . 

Results 

Runoff dynamics 

In the Negratin-rill catchment the runoff coefficient of the rainfall simulations reached 71.5%. 

Only 19 m² of the catchment is needed to generate the experiments' runoff during a moderate 

heavy rain (Table 2). 

In the Freila test site, the runoff coefficient increased to 90 %, reducing the needed 

contributing area to only 15 m 2 . Salada showed similar values, (RC=85 %), for which only 16 

109


m 2 would be necessary to generate the experimental runoff in the rill. Due to the considerably 

lower RC in Belerda (51 %), the contributing area was estimated to be 27 m 2 (Table 2). 

Rill hydraulics 

The descriptors of the rills’ hydraulics are summarized in Table 3. 

After the given flow length, only 19 L water reach in the first run in Salada the end of the 

tested rill part. The highest value (59 L) is measured in the second run in the Belerda 

experiment. 

The highest maximum runoff intensity was measured in the first run in the Belerda 

experiment (0.15 L s -1 ), the lowest maximum runoff intensity in the first run of the Salada 

experiment (0.07 L s -1 ). 

The relationship between inflow intensity and runoff intensity shows the highest value in the 

first Belerda run, here the inflow and the runoff intensity are equal. The lowest value is 

measured in Salada, run a (0.47). 

The highest runoff coefficient is measured in Belerda run b, here 82 % of the inflow water 

reach the runoff measuring point. In the first Salada run, only 27 % reach the end of the tested 

rill part. 

The runoff-length-factor shows its lowest value in Salada run a (3.96 m) the highest value is 

measured in Freila run a (13.71 m). In all experiments, the second run shows higher values 

than the first run but in the second run in Freila, there are no data available because of 

technical problems. 

The runoff at the rill’s end starts in the second run in the Belerda experiment still after 70 sec., 

in the first run of the Freila experiment, the water reaches the rill’s end after 175 sec. After 

593 sec., the runoff ends in the first run of the Salada experiment, in the first run of the Salada 

experiment, the runoff has finished after 866 sec. The runoff shows the longest duration in the 

first run in Negratin (700 sec.), the fastest runoff wave has been noticed in the first run in 

Freila (88 sec.). 

The relationship between runoff duration and inflow duration shows the highest value in 

Negratin run a (1.46), the lowest value in Salada run a (0.92). 

Average flow velocities show the highest values in Freila run b (Front), Negratin run a 

(Tracer 1) and Salada run b (Tracer 2), the lowest values in Freila and Salada run a (Front), 

and Belerda run b (Tracer 1 and Tracer 2). The maximum flow velocities show the highest 

values in Freila run b (Front) and Negratin run a (Tracer 1 and Tracer 2), the lowest values are 

measured in Freila run a (Front), Freila run b (Tracer 1) and Belerda run b (Tracer 2). 

110


Table 3: Hydraulic parameters, ND = no data, F = waterfront, T1 = tracer 1, T2 = tracer 2 


run a b a b a b a b 

VR [L] 26 44 47 ND 19 55 43 59 

Qm [L s -1 ] 0.08 0.11 0.13 ND 0.07 0.13 0.15 0.14 

Qf 0.53 0.73 0.87 ND 0.47 0.87 1 0.93 

RC [-] 0.36 0.61 0.65 ND 0.27 0.76 0.6 0.82 

RCL [m] 7.22 12.22 13.71 ND 3.96 11.46 9.56 13.11 

tS [s] 166 108 175 ND 155 70 118 110 

tE [s] 866 666 663 ND 593 726 646 794 

TR [s] 700 558 88 ND 438 656 528 684 

va [m s -1 ] 

vmax [m s -1 ] 

dT 1.46 1.16 1.02 ND 0.92 1.37 1.15 1.43 

F 0.16 0.21 0.12 0.27 0.12 0.25 ND 0.15 

T1 0.36 0.3 0.29 0.28 0.29 0.31 0.26 0.25 

T2 0.32 0.31 0.35 0.34 0.38 0.39 0.29 0.24 

F 0.36 0.44 0.18 0.70 0.22 0.49 ND 0.29 

T1 1.05 0.78 0.42 0.37 0.44 0.46 0.49 0.5 

T2 0.93 0.85 0.65 0.56 0.6 0.61 0.44 0.38 

Erosion dynamics 

The erosion dynamic parameters are all summarized in table 4. 

Negratin: The average sediment concentration in the first run (run a) was 270 g L -1 with an 

average maximum flow velocity of 0.28 m s -1 . The maximum sediment concentration of 428 

g L -1 was measured after 30 sec at MP3. In the second run (run b), the average sediment 

concentration reached only 58 g L -1 , with an average maximum flow velocity of 0.27 m s -1 . 

The maximum sediment concentration increased to only 111 g L -1 and was measured at the 

waterfront at MP3 (figure 3). 

Freila: In the 1 st run, the average sediment concentration reached 224 g L -1 with an average 

maximum flow velocity of 0.25 m s -1 . In the second run 189 g L -1 and 0.3 m s -1 were 

reached. The maximum sediment concentration in the first run increased to 438 g L -1 , 

measured at MP3 after 2:30 min. In run b, a maximum value of 267 g L -1 was measured at 

MP2 after 2:30 min (figure 4). 

Salada: The average sediment concentration in the 1 st run reached 183 g L -1 and increased to 

295 g L -1 in the 2 nd run. The average maximum flow velocities were 0.27 and 0.32 m s -1 . The 

111


maximum sediment concentration in both runs was measured after 2:30 min at MP2, reaching 

in run a 302 g L -1 , and 402 g L -1 in run b (figure 5). 

Belerda: In this experiment, the average sediment concentration in the first run reached 28 g L 

-1 at an average maximum flow velocity of 0.25 m s -1 . It should be noted that in this 

experiment the flow velocity of the waterfront could not be measured. The waterfront of the 

first run always shows the lowest flow velocity, so the 0.25 m s -1 mentioned here is too high. 

In the second run, the average sediment concentration decreased to 16 g L -1 . The average 

maximum flow velocity (waterfront included) reached 0.21 m s -1 . In the first run, the 

maximum sediment concentration reached was 54 g L -1 at the waterfront at MP3. In the 

second run, the waterfront at MP1 reached 29 g L -1 (figure 6). 

The average detachment rate shows the highest values in most cases at the second measuring 

point. In experiments Negratin b and Freila a, the highest values were reached at MP3, in 

experiment Belerda b, the highest value was reached at MP1. The maximum detachment rates 

also reach the highest values mostly at MP2, although Negratin b and Freila a reached them at 

MP3, and Negratin a at MP1. 

The highest average sediment flux values are reached at MP 3 for experiments Negratin a and 

b and Freila a; at MP 2 for experiment Freila b, Salada a and b and Belerda a. Belerda b 

reached the highest value at MP1. The maximum sediment flux values show the same trend, 

except that in experiment Belerda a the highest value is not reached at MP2 but at MP3. 

The transport capacity also shows a variable trend. In Negratin, the highest values were 

reached at the first measuring point, in Freila at the second measuring point. In Salada, the 

highest values were reached at the third measuring point. Only the maximum T C for the 

second run was reached at the second measuring point. In the second Belerda run, the highest 

values were reached at the third measuring point. 

112


Table 4: Erosion dynamic parameters, ND = no data 


run a b a b a b a b 

1 0.0683 0.0113 0.0489 0.0350 0.0614 0.1060 ND 0.0086 

Ø Da [kg s -1 m -2 ] 2 0.0785 0.0149 0.0688 0.0784 0.0994 0.1545 ND 0.0054 

3 0.0652 0.0191 0.0844 0.0604 0.0559 0.0993 ND 0.0054 

1 0.1081 0.0197 0.0734 0.0444 0.0928 0.1279 ND 0.0117 

max. Da [kg s -1 m -2 ] 2 0.1063 0.0179 0.0963 0.0988 0.1543 0.1976 ND 0.0117 

3 0.0898 0.0239 0.1198 0.0686 0.0801 0.1256 ND 0.0063 

1 0.0366 0.0058 0.0259 0.0178 0.0238 0.0394 0.0040 0.0030 

Ø Qs [kg s -1 ] 2 0.0393 0.0072 0.0274 0.0337 0.0311 0.0503 0.0044 0.0019 

3 0.0454 0.0131 0.0474 0.0334 0.0273 0.0431 0.0040 0.0020 

1 0.0633 0.0106 0.0368 0.0226 0.0343 0.0483 0.0071 0.0044 

max. Qs [kg s -1 ] 2 0.0550 0.0087 0.0339 0.0400 0.0453 0.0602 0.0076 0.0041 

3 0.0641 0.0166 0.0656 0.0376 0.0349 0.0542 0.0081 0.0025 

1 0.3204 0.2265 0.0085 0.0045 0.0208 0.0150 ND 0.3197 

Ø Tc [kg s -1 ] 2 0.0719 0.0421 0.1365 0.1574 0.0444 0.0581 ND 0.3358 

3 0.1107 0.0689 0.0426 0.0299 0.0685 0.2412 ND 0.4060 

1 0.5549 0.3070 0.0127 0.0049 0.0274 0.0179 ND 0.3788 

max. Tc [kg s -1 ] 2 0.1070 0.0508 0.2795 0.1819 0.0526 0.0722 ND 0.2864 

3 0.1746 0.0882 0.0538 0.0333 0.1382 0.0143 ND 0.4970 

Fig. 3: Results RE Negratin 

113


Fig. 4: Results RE Freila 

Fig. 5: Results RE Salada 

114


Fig. 6: Results RE Belerda 

Discussion 

The estimation of the contributing areas for the experimental runoff shows that these are 

considerably smaller than the catchments of the rills. This leads to the conclusion that the 

runoff used within these experiments represents a low magnitude-high frequency event. 

Therefore, the measured amounts of erosion and hydraulic dynamic have to be valued as low. 

This should be remembered when considering or comparing sediment concentrations. 

The sediment concentrations measured in our experiments are interesting and important when 

compared with previous experiments. Polyakov and Nearing (2003) tested, in laboratory 

experiments, the behaviour of rills in al loamy substrate under different inflow quantities (6 

and 9 L min -1 ) and rill lengths. The sediment concentrations in their experiment reached 

values between 10 and 130 g L -1 . Loch (2000) tested the influence of vegetation on soil 

erosion. In one of his plots, both inter-rill and rill erosion were observed. The sediment 

concentrations of this plot reached a maximum value of 210 g L -1 . The maximum value 

measured in our rill experiments in Andalusia was 437.6 g L -1 , which is about double the 

maximum value in the experiments of Loch (2000) and about 3.5 times higher than the values 

in the laboratory experiments of Polyakov and Nearing (2003). This is remarkable because, in 

115


laboratory experiments, the rills are formed in a relatively loose substrate while the rills tested 

in our experiments developed in natural soils or on heavily compacted areas. In our 

experiments, the sediment concentrations showed a large range, from a low value of 5.2 g L -1 , 

measured in Belerda, to the highest value (437.6 g L -1 ) in Freila. Sediment concentrations 

used to parametrize WEPP ranged from 0.1 to 415 g L -1 (Elliot et al., 1989). Our results show 

that in Mediterranean sedimentary basins, on abandoned fields, the erosion rates may exceed 

the upper limits of the parametrization data set of WEPP. Taking into account the low runoff 

used here, it can be assumed that the parameterization dataset does not cover the range of soils 

that can be found in practice. This confirms the assumption of Sidorchuk (2009), who 

postulates that most empirical data used for establishing erosion models is too narrow to cover 

the variability of erosion controls and processes. 

The reason for such a large range of sediment concentrations could be the fact that several 

processes take place in the rill: the transport of lose material, erosion or both processes 

together. Erosion processes can be separated into deepening of the rill's bottom caused by the 

shear forces of water (and transported sediments), but the main sediment load is supplied by 

other processes. Rill erosion is the result of the combination of different processes including 

headcut erosion, sidewall sloughing, tunnelling, micro-piping, slaking piping and sapping 

(Bryan et al. 1989, Bryan 1990, Knapen et al. 2007, Owoputi & Stolte 1995, Rapp 1998, Zhu 

et al. 1995). Zhu et al. (1995) concluded in laboratory experiments that the contribution of 

headcutting in detachment processes was four times larger than the contribution of bed scours. 

Kohl (1988) found that headcutting accounted for up to 60% of total rill erosion for the soil 

erodibility data of WEPP. Stefanovic and Bryan (2009) tested in laboratory experiments the 

development of rills on a loamy sand and on a sandy loam. They also showed that 

concentrated flow causes sediment production primarily from knickpoints, chutes, meanders 

and bank failure. Govers (1987) distinguished between hydraulic erosion, mass wasting 

processes on rill sidewalls, gullying and piping. During his study in Huldenberg, the loamy 

hilly region of Flandres, the field was conventionally tilled and a seedbed was prepared. 

Hydraulic rill erosion mostly occurs during three observed runoff events with peak discharges 

between 70 and 90 L s -1 (4200 – 5400 L min -1 ). Runoff rates during other events were always 

below 25 L s -1 (1500 L min -1 ). We used runoff rates of 9 L min -1 however this rate turned out 

to be too low to produce hydraulic rill erosion. With our runoff rates, we can cause mass 

wasting processes on rill sidewalls. In the observed runoff events (Govers 1987), mass 

wasting processes caused 37% of total erosion in rills. But in erosion modelling, rill erosion is 

considered to be only dependant of the erosive power of the flowing water, represented by 

116


shear stress, unit length shear force or stream power. The process of gullying, the retreat 

erosion at knickpoints and headcuts is not considered in rill erosion formulas. This process 

caused about 12% of rill erosion rates in the study of Govers (1987). In our experiments, we 

only cause mass wasting and gullying processes, so the relations between hydraulic 

parameters and sediment concentration are mostly low. But the hydraulic rill erosion only 

occurs in extreme runoff events, in most cases, the runoff values are too low to cause this 

process (Govers 1987). All these observations agree with our own observations and 

measurements. In these cases, we can also observe that the areas with high erosion rates 

exceed the calculated transport capacities and show a trend towards an increase with flow 

duration. This suggests that sediment production by knickpoints, chutes, etc. is important for 

understanding rill behaviour. Nevertheless, they are highly variable throughout a single rill, 

and the combination of the processes can change between run a and run b of one experiment. 

The different processes can be identified by comparing the sediment concentrations, the flow 

velocities and the absolute level of the sediment concentrations. 

The first process is the “bulldozer-effect” (Seeger et al., 2005, Regües et al., 2000), a 

mobilisation of the loose material available in the rill before an experiment starts. The highest 

sediment concentration at the MP is collected with the water front despite the lowest flow 

velocity. This effect can be detected in the first run of the Negratin experiment. The flow 

velocity in run a and run b are close but in the first run the average sediment concentration is 

clearly higher. The material transport within the second run has to be attributed only to the 

erosion effect of the flowing water (bulldozer-effect (marginal) + erosion (low)), since the 

loose material has removed in the first run, mostly by the water front (bulldozer effect (high) 

+ erosion (low)). In run a, the bulldozer-effect is more powerful than the erosion process. If 

the erosion process is more powerful, the sediment concentrations increase at the MP from the 

first to the last sample. The waterfront only mobilizes the available loose material, but 

because of the low flow velocity, the erosion process starts later and the sediment 

concentration increases (bulldozer-effect (lower) + erosion (higher)). This can be observed in 

the first run of the Freila experiment. In the second run, the sediment concentrations are 

lower, because the bulldozer-effect is able to mobilize only the material left behind after run a 

(bulldozer-effect (marginal) + erosion (high)). If there is no available loose material and the 

erosion process is very active from the beginning, the sediment concentrations increase at 

each measuring point and the run with the higher flow velocity shows the higher average 

sediment concentration. This was given in the Salada experiment: run a (bulldozer-effect 

(marginal) + erosion (high)) had a lower average flow velocity and a lower average sediment 

117


concentration than run b (bulldozer-effect (marginal) + erosion (even higher)) with a higher 

average flow velocity and also a higher average sediment concentration. In some rills the 

erosion process could not be activated with the inflow intensity and water quantity used. Even 

the higher flow velocity in the second run was not sufficient to start erosion processes. In this 

case the available loose material is removed by the slowly flowing waterfront of the first run. 

This situation occurred in the Belerda experiment, where the highest sediment concentrations 

were measured at the waterfront run a (bulldozer-effect (high) + erosion (marginal)), while in 

run b both the bulldozer-effect and erosion processes were very low (bulldozer-effect 

(marginal) + erosion (marginal)). 

The differences in runoff-length-coefficient between the two runs can be seen clearly. In 

Salada, the RC L factor in run b is about twice as high as in run a, in Salada even the factor 3 is 

observed. In Belerda, the differences between the two runs are not significant, but the absolute 

values show that this rill is an effective runoff collector for the gully. In Freila only the first 

run could be measured, but this first run had the highest RC L factor of all runs. This is likely 

due to the fact that the rills in this area show a low infiltration rate, which corresponds to the 

high bulk densities measured. It also shows that, in these areas, flow concentration and the 

runoff accelerating effect of the rills within the landscapes are considerable regardless of the 

erosion processes inside the rills. 

Differences in the flow velocities of the water fronts between the two runs are particularly 

noteworthy. The velocities of the waterfronts in the first runs are clearly lower than all other 

velocity curves. This may be attributed, in part, to the higher transporting activity the water 

has to perform during the first runs, combined with a higher infiltration rate in most cases, 

resulting in considerably higher loss of water mass during the experiment. But the other, and 

surely most important, factor is that of initial soil moisture as was reported also by Govers et 

al. (1990) and Govers (1991): higher soil moisture reduces the infiltration rate which results in 

more water flowing along the experimental length. Higher soil moisture at the surface layer of 

the soil reduces the water repellency of the soils. This can be important for the dynamics of 

the water front under dry conditions. This was observed, even under very moist conditions, in 

the Pyrenees (Wirtz et al., 2010). Here we have that the observed velocities during the first 

run may underestimate the runoff during a rainfall event, as the rain producing the runoff 

would moisten the rill at the same time, thus generating the conditions for fast flow. 

The influence of initial soil moisture on sediment transport was reported by Govers et al. 

(1990) and Govers (1991). In their experiments under dry conditions the sediment 

concentrations almost reached the runoff's transport capacity while, under higher initial soil 

118


moistures, the sediment concentrations were lower. In three of our rill experiments, the first 

run (dry conditions) showed higher sediment concentrations than the second run (wet 

conditions). Only in the experiment at Salada, were higher sediment concentrations reached in 

the second run. The differences between run a and run b are caused by the differences in the 

supply of loose material, which is normally higher in the first run, and the detachment, which 

is normally higher in the second run (higher flow velocity). 

The ranges of transport capacity calculated are within the same orders of magnitude within 

the rills as reported by Giménez and Govers (2002). Plotting the sediment flow rate Q s against 

the transport capacity T c shows some differences between the tested rills (Fig. 7 - 10). In 

Negratin and Belerda the measured values are below the calculated transport capacity, due to 

a limitation in sediment supply or sediment detachment. This is especially accentuated in the 

Belerda experiment. Both Negratin and Belerda have loam soils, however Belerda has in 

addition a high coarse fragment content and the higher organic matter content which may be a 

reason for the lower detachment rates. Within the tested rills of Freila and Salada, the 

observed sediment load is at least partially above the calculated sediment transport capacity. 

Here, transport of sediments within the rill should be limited by the transport capacity 

however gravitational processes like bank failure and headcut retreat at knickpoints are the 

main sediment producing processes rather than erosive deepening of the rill's bottom. As a 

result it is possible for the sediment load to surpass the transport capacity. As Q s and T c have 

been calculated based on the inflow into the rill, both values are doubtless lower than the 

values given here, but as T c decreases more quickly (flow shear stress with an exponent 1.5, 

Q S with an exponent 1) the relationship is expected to shift towards exceeding the transport 

capacity as runoff decreases. However a common observation in all experiments was the fact, 

that at each measuring point and at each run we found a wide range of values for the transport 

capacity and the sediment load. We even found shifts between exceeding the transport 

capacity and dropping below at the same measuring point. This is a clear indicator of the 

spatially (along the rill) and temporally (during different stages of the water flow) variable 

processes and process intensities. The variability of erosion processes was tested from 

different research groups. Nearing (1998) tested the variability between replicated soil erosion 

field plots under natural rainfall and determined the principal factor or factors which correlate 

to the magnitude of variability. The coefficient of variation ranged on the order of 14 % for a 

measured soil loss of 20 kg m -2 to grater than 150 % for a measured soil loss of less than 0.01 

kg m -2 . Ruttiman et al. (1995) analysed statistically the data of four sites, each with five to six 

reported treatments; each of them with three replications. The coefficients of variation in soil 

119


loss ranged from 3.4 % to 173.2 %, with an average value of 71 %. Wendt et al. (1986) 

measured soil erosion rates on 40 experimental plots. All plots were cultivated and treated 

identically. The coefficients of variation for 25 storms ranged from 18 % to 91 %, with a 

clearly decreasing variability of soil loss with increasing erosivity of the storms: 15 storms 

with erosion rates higher than 0.1 kg m -2 were noted and 13 showed coefficients of variation 

of less than 30 %. Risse et al. (1993) applied the USLE to a large data-set of plot-years and 

natural runoff plots. Annual values of measured soil loss averaged 3.51 kg m -2 , the average 

magnitude of prediction error was 2.13 kg m -2 , that means 60 %. Zhang et al. (1996) tested the 

WEPP-model in a similar way. The average soil loss was 2.18 kg m -2 with an average 

prediction error of 1.34 kg m -2 this means 61% of the mean. Liu et al. (1996) compared 

measured values with WEPP-calculated values. For one of the tested catchments, the 

sediment yield was underpredicted by approximately 50 %. Govers (1991) tested the rill 

erosion rates on arable land in Central Belgium. The relevant characteristics of the selected 

fields were similar; the highest standard deviation was 65 m in length and 25.5 % in sand 

content. Mean rill erosion rate from 156 measurements reached 0.36 kg m -2 , with a maximum 

of 3.5 kg m -2 , but also no erosion was observed. The results reflected here show the high 

variability of soil erosion measurements, even under controlled (this is experimental) 

conditions. This is partially the result of non-homogeneous parameters concerning soil 

characteristics and rainfall. On experimental plots, infiltration rates and soil aggregate 

stability can be highly variable (Ajayi & Horta 2007) as well as the rainfall shows a high 

spatial and temporal variability (Dunkerley 2008). Therefore, the input parameters to the 

different measurements reflected in the mentioned studies were not really comparable. 

Nevertheless, the results also make clear, that modelling soil erosion has to tackle with 

uncertainty in model input as well as in the data that can be used for model calibration and 

validation. 

In the field, the spatial and temporal variability of soil conditions cannot be avoided, and is, 

furthermore, part of the investigations. Therefore, additional input parameters as rainfall or 

flow should be maintained constant to generate reproducible data. 

120


Fig. 7: Sediment flux vs. transport capacity RE Negratin 

Fig. 8: Sediment flux vs. transport capacity RE Freila 

121


Fig. 9: Sediment flux vs. transport capacity RE Salada 

Fig. 10: Sediment flux vs. transport capacity RE Belerda 

Conclusions 

In Andalusia, four rill experiments were conducted. The aim of these experiments was to 

estimate the effectiveness of different rills as sediment sources and runoff pathways and to 

detect the processes having the most influence on the rills’ behaviour. To accomplish this, 72 

122


L of water were induced with an intensity of 9 L min -1 into the rill. Flow velocities, sediment 

concentrations, rill cross sections, water levels, runoff values and slope were measured and 

different hydraulic parameters were calculated. It was noticeable that, despite the low inflow 

intensity, extremely high sediment concentrations were reached in some cases, with the 

transport of loose material having in some cases a higher, and in other cases a lower, 

influence on the sediment budget. In one experiment, where only low erosion activity took 

place, the measured sediment concentrations were mainly caused by the removal of the loose 

material. The runoff effectiveness showed very different values, and the higher effectiveness 

was reached in each case under conditions of higher initial soil moisture. 

During the experiment, the main sediment delivering processes were observed to be retreat 

erosion at knickpoints or steps and bank failure processes. Depending on the tested rill, a 

simple cutting in the rill's bottom also played an important role. In some cases, the high 

sediment concentrations during the first run indicate that the mobilisation of loose material 

may be important too. This may lead to loose material dominating the amount of transported 

material unless the other processes described above occur. 

In most cases, the erosion rate was near the transport capacity. In each experiment, the 

transport capacities and the sediment loads showed high variability even at a single measuring 

point. In some cases, samples exceeded the traditionally calculated transport capacity. This 

behaviour is a clear indicator of variable processes and process intensities in the natural 

environment. The limitation of detachment or transport equations is that important sediment 

preparing processes, like headcut retreat, step-pool effects or bank failure, are not considered. 

Measured total rill erosion rates are the sum of erosion rates caused by a combination of 

different soil erosion processes with different spatial and temporal distribution. There are two 

different ways. The first way is to modify existing physical based model concepts or, the 

second way, to start a new direction, the concept of stochastic soil erosion modelling. In both 

cases, much more field experiments are needed to provide the required data and the question 

is, if the actual used experimental setups can deliver the requested data or if a totally new 

experimental setup must be created. 

The novel method for monitoring rill processes presented here allows a lot of data which are 

useful for understanding the behaviour of rills in a catchment area to be directly measured or 

calculated from the measured data. 

123


Acknowledgements 

The research was supported by the Internationale Graduiertenzentrum of Trier University. We 

want to acknowledge the reviewers for their valuable comments. They were very helpful in 

clarifying the objectives and the discussion. 

References 

AD-HOC-Arbeitsgruppe Boden 2005. Bodenkundliche Kartieranleitung. 5. verbesserte und 

erweiterte Auflage, Hannover. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart. 

Ajayi, A.E., Horta, I.D.M.F. 2007. The effect of spatial variability of soil hydraulic properties 

on surface runoff processes. Anais XIII Simpósio Brasileiro de Sensoriamento 

Remoto, Florianópolis, Brasil, 21-26 abril 2007, p. 3243-3248. 

Auerswald, K., Fiener, P. and Dikau, R. 2009. Rates of sheet and rill erosion in Germany - A 

meta-analysis. Geomorphology, 111(3-4), 182-193. 

Beuselinck, L., Govers, G., Hairsine, P., Sander, G. and Breynaert M. 2002. The influence of 

rainfall on sediment transport by overland flow over areas of net deposition. Journal of 

Hydrology, 257, 145-163. 

Brodie, I and Rosewell C. 2007. Theoretical relationships between rainfall intensity and 

kinetic energy variants associated with stormwater particle washoff. Journal of 

Hydrology, 340(1-2), 40-47. 

Bruno, C., Di Stefano, C. and Ferro, V., 2008. Field investigation on rilling in the 

experimental Sparacia area, South Italy. Earth Surface Processes and Landforms, 33, 

263-279. 

Brunton, D.A. and Bryan, R.B., 2000. Rill network development and sediment budgets. Earth 

Surface Processes and Landforms, 25, 783-800. 

Bryan, R.B. 1990. Knickpoint evolution in rillwash. Catena 17, 111-132. 

Bryan, R. B. 2000. Soil erodibility and processes of water erosion on hillslope. 

Geomorphology, 32(3-4), 385-415. 

Bryan, R.B. and Poesen, J., 1989. Laboratory experiment on the influence of slope length on 

runoff, percolation and rill development. Earth surface processes and Landforms, 14, 

211-231. 

Bryan, R.B., Govers, G., Poesen, J. 1989. The concept of soil erodibility and some problems 

of assessment and application. Catena, 16 (4-5), 393-412. 

124


Bryan, R.B., Hawke, R.M. and Rockwell, D.L., 1998. The influence of subsurface moisture 

on rill system evolution. Earth Surface processes and Landforms, 23, 773-789. 

Calvo -Cases, A., Gisbert, J.M., Palau, E. and Romero, M. 1988. Un simulador de lluvia 

portátil de fácil construcción. In: M. Sala, F. Gallart (Editors), Métodos y técnicas 

para la medición en el campo de processo geomorfológicos. pp. 6-15. 

Casali, J., Loizu, J., Campo, M., De Santisteban, L. and Alvarez-Mozos, J. 2006. Accuracy 

of methods for field assessment of rill and ephemeral gully erosion. Catena, 67(2), 

128-138. 

Cerdá, A. and García-Fayos, P. 1994-95. Relaciones entre las pérdidas de agua y semillas en 

zonas acarcavadas. Influencia de la pendiente. Cuadernos I Geográfica, 20-21, 47-63. 

Cerdan, O., Le Bissonnais, Y., Couturier, A., Bourennane, H. and Souchère, V. 2002. Rill 


France. Soil and Tillage Research, 67(1), 99-108. 

De Santisteban, L.M., Casalì, J., Lòpez, J.J., Giràldez, J.V., Poesen, J. and Nachtergaele, J., 

2005. Exploring the role of topography in small channelerosion. Earth Surface 

Processes and Landforms, 30, 591-599. 

Dunkerley, D. 2008. Rain event properties in nature and in rainfall simulation experiments: a 

comparative review with recommendations for increasingly systematic study and 

reporting. Hydrological Processes, 22, 4415-4435. 

Elliot, W.J., Liebenow, A.M., Laflen, J.M. and Kohl, K.D., 1989. A compendium of soil 

erodibility data from WEPP cropland soil field erodibility experiments 1987 and 1988. 

NSERL Report No. 3, The Ohio State University and USDA Agricultural Research 

Service. 

FAO 2006. Guidelines for soil description. 4. ed. Rome. 

Favis-Mortlock, D. 1998. A self-organizing dynamic systems approach to the simulation of 

rill initiation and development on hillslopes. Computers and Geosciences, Vol. 24, No. 

4, 353-372 

Favis-Mortlock, D., Boardman, J., Parsons, A.J. and Lascelles, B. 2000. Emergence and 

erosion: a model for rill initiation and development. Hydrological Processes, 14, 2173- 

2205. 

Flores-Cervantes, J. H., Istanbulluoglu, E. and Bras, R. L. 2006. Development of gullies on 

the landscape: A model of headcut retreat resulting from plunge pool erosion. J. 

Geophys. Res., 111, F01010, doi:10.1029/2004JF000226. 

125


Foster, G.R., 1982. Modelling the erosion process. In: H.P. Johnson, D.L. Brakensiek 

(Editors), Hydraulic Modelling of Small Watersheds. ASAE monograph 5, Hann CT, 

St. Joseph, MI, pp. 295-380. 

Foster, G.R., Huggins, L.F. and Meyer, L.D., 1984. A laboratory study of rill hydraulics: I. 

Velocity relationsships. Transactions of ASAE, 27, 790-796. 

Foster, G., Flanagan, D., Nearing, M., Lane, L., Risse, L. and Finkner, S. 1995. Hillslope 

Erosion Component. USDA-Water Erosion Prediction Project (WEPP). West 

Lafayette, pp. 11.1-11.12. 

Gilley, J.E., Kottwitz, E.R. and Simanton, J.R., 1990. Hydraulic characteristics of rill. 

Transactions of the ASAE, 33, 1900-1906. 

Giménez, R., and Govers, G. 2002. Flow Detachment by Concentrated Flow on Smooth and 

Irregular Beds. Soil Sci Soc Am J, 66(5), 1475-1483. 

Giménez, R., Planchon, O., Silvera, N. and Govers, G., 2004. Longitudinal velocity patterns 

and bed morphology interaction in a rill. Earth Surface Processes and Landforms, 29, 

105-114. 

Govers, G. 1987. Spatial and temporal variability in rill development processes at the 

Huldenberg experimental site. Catena Supplement, 8, 17-34. 

Govers, G. 1991. Rill erosion on arable land in central Belgium: Rates, controls and 

predictability. Catena, 18, 133-155. 

Govers, G. 1992 a. Evaluation of transporting capacity formulae. In: A.J. Parsons, A.D. 

Abrahams (Editors), Overland flow – Hydraulics and erosion mechanics. UCL-Press, 

Guildford, pp. 243-273. 

Govers. G., 1992b. Relationship between discharge, velocity and flow area for rills eroding 

loose, non layered materials. Earth Surface Processes and Landforms, 17, 515-528. 

Govers, G. and Poesen, J., 1988. Assesment of the interrill and rill contributions to total soil 

loss from an upland field plot. Geomorphology, 1, 343-354. 

Govers, G., Giménez, R. and Van Oost, K. 2007. Rill erosion: Exploring the relationship 

between experiments, modelling and field observations. Earth-Science Reviews, 84(3- 

4), 87-102. 

Helming, K., Römkens, M.J.M., Prasad, S.N. and Somme, H., 1999. Erosional development 

of small scale drainage networks. In: S. Hergatren, H.J. Neugebauer (Editors), Process 

Modelling and Landform Evolution. Lecture Notes in Earth Science 78. Springer, 

Berlin, pp. 123-146. 

126


Hessel, R. and Jetten, V. 2007. Suitability of transport equations in modelling soil erosion for 

a small Loess Plateau catchment. Engineering Geology, 91(1), 56-71. 

Huang, C., Bradford, J.M. and Laflen, J.M., 1996. Evaluation of the detachment-transport 

coupling concept in the WEPP rill erosion equation. Soil Science Society American 

Journal, 60, 734-739. 

Knapen, A., Poesen, J., Govers, G., Gyssels, G. and Nachtergaele, J. 2007. Resistance of 

soils to concentrated flow erosion: A review. Earth-Science Reviews, 80(1-2), 75-109. 

Kohl, K.D., 1988. Mechanics of rill headcutting. Ph.D. Thesis, Iowa State University, Ames. 

Kuhn, N. and Bryan, R. 2004. Drying, soil surface condition and interrill erosion on two 

Ontario soils. Catena, 57, 113-133. 

Kuhn, N., Bryan, R.B. and Navar, J. 2003. Seal formation and interrill erosion on a smectiterich 

Kastanozem from NE-Mexico. Catena, 52, 149-169. 

Lasanta, T., Pérez Rontomé, M.C. and García Ruiz, J.M. 1994. Efectos hidromorfológicos de 

differentes alternativas de retirada de tierras en ambientes semiáridos de la depressión 

del Ebro. In: J.M. García Ruiz, T. Lasanta (Editors), Efectos geomorfológicos del 

abandono de tierras. Sociedad Española de Geomorfología, pp. 69-82. 

Le Bissonnais, Y., Cerdan, O., Lecomte, V., Benkhadra, H., Souchère, V. and Martin, P. 

2005. Variability of soil surface characteristics influencing runoff and interrill erosion. 

Catena, 62, 111-124. 

Liu, B.Y., Nearing, M.A., Baffaut, C., Ascough II, J.C., 1996. The WEPP watershed model: 

III. Comparisons to measured data from small watersheds. Transactions of the ASAE, 

40, 945-951. 

Loch, R.J. 2000. Using Rainfall simulation to guide planning and management of 

rehabilitated areas: Part I. Experimental methods and results from a study at the 

northparkes mine, Australia. Land Degradation and Development, 11, 221-240. 

Mancilla, G.A., Chen, S. and McCool, D.K., 2005. Rill density prediction and flow velocity 

distribution on agricultural areas in the Pacific Northwest. Soil and Tillage Research, 

84, 54-66. 

Merz, W. and Bryan, R. B. 1993. Critical conditions for rill initiation on sandy loam 

Brunisols: laboratory and field experiments in southern Ontario, Canada. Geoderma, 

57(4), 357-385. 

Nachtergaele, J., Poesen, J., Sidorchuk, A. and Torri, D. 2002. Prediction of concentrated 

flow width in ephemeral gully channels. Hydrological Processes, 16, 1935-1953. 

127


Nachtergaele, J., Poesen, J., Steegen, I., Takken, L., Beuselinck, L., Vandekerckhove, L. 

and Govers, G. 2001. The value of a physically based model versus an empirical 

approach in the prediction of ephemeral gully erosion for loess-derived soils. 

Geomorphology, 40, 237-252. 

Nearing, M.A., Bradford, J.M., Parker, S.C. 1991. Soil detachment by shallow flow at low 

slopes. Soil Science Society of America Journal, 55 (2), 339-344. 

Nearing, M.A., 1998. Why soil erosion models over-predict small soil losses and underpredict 

large soil losses. Catena, 32, 15-22. 

Nearing, M.A., Govers, G. and Norton, L.D. 1999. Variability in Soil Erosion Data from 

Replicated Plots. Soil Science Society of America Journal, 63, 1829-1835. 

Nearing, M. A., Norton, L. D., Bulgakov, D. A., Larionov, G. A., West, L. T. and 

Dontsova K. M. 1997. Hydraulics and Erosion in Eroding Rills. Water Resources 

Research, 33 (4), 865-876. 

Nearing, M.A., Foster, G.R., Lane, L.J. and Finkner, S.C., 1989. A process-based soil erosion 

model for USDA - Water Erosion Predict Project technology. Transactions of the 

ASAE, 32, 1587-1593. 

Owoputi, L.O., Stolte, W.J., 1995. Soil detachment in the physically based soil erosion 

process: a review. Transactions of the ASAE, 38 (4), 1099-1110. 

Poesen, J., De Luna, E., Franca, A., Nachtergaele, J. and Govers, G. 1999. Concentrated 

flow erosion rates as affected by rock fragment cover and initial soil moisture content. 

Catena, 36, 315-329. 

Poesen, J. 1987. Transport of rock fragments by rill flow – a field study. In: R.B. Bryan 

(Editor), Rill erosion - process and significance. Catena, Supplement 8, Cremlingen, 

pp. 35-54. 

Polyakov, V.O. and Nearing, M.A., 2003. Sediment transport in rill flow under deposition and 

detachment conditions. Catena, 51, 33-43. 

Rapp, I., 1998. Effects of soil properties and experimental conditions on the rill erodibilities 

of selected soils. Ph. D. Thesis, Faculty of Biological and Agricultural Sciences, 

University of Pretoria, South Africa. 

Regüés, D., Balasch, J.C., Castelltort, X., Soler, M., Gallart, F., 2000. Relación entre las 



Orientales). Cuadernos de Investigación Geográfica, 26, 41-65. 

128


Rejman, J. and Brodowski, R., 2005. Rill characteristics and sediment transport as a function 

of slope length during a storm event on loess soil. Earth Surface Processes and 

Landforms, 30, 231-239. 

Ries, J.B., Langer, M. and Rehberg, C. 2000. Experimental investigations on water and wind 

erosion on abandoned fields and arable land in the central Ebro Basin, Aragón/Spain. 

Zeitschrift für Geomorphologie N.F. Suppl.-Bd. 121, 91-108. 

Ries, J.B., Seeger, M., Iserloh, T., Wistorf, S. and Fister, W. 2009. Calibration of simulated 

rainfall characteristics for the study of soil erosion on agricultural land. Special issue 

on "soil erosion and degradation on agricultural land "Soil and Tillage Research 106,1, 

109-116. 

Ries, J.B. 2003 Landnutzungswandel und Landdegradation in Spanien – Eine Einführung. In: 

I. Marzolff, J.B. Ries, J. De La Riva., M. Seeger (Editors), Landnutzungswandel und 

Landdegradation in Spanien, pp.11-29. 

Risse, L.M., Nearing , M.A.., Nicks, A.D., Laflen, J.M., 1993. Assessment of error in the 

universal soil loss equation. Soil Sci. Soc. Am. J. 57, 825-833. 

Ruttimann, M., Schaub, D., Prasuhn, V., Ruegg, W., 1995. Measurement of runoff and soil 

erosion on regulary cultivated fields in Switzerland – some critical considerations. 

Catena, 25, 127-139. 

Seeger, M. 2007. Uncertainty of factors determining runoff and erosion processes as 

quantified by rainfall simulations. Catena, 71(1), 56-67. 

Seeger, M., Errea, M.P., Beguería, S., Arnáez, J., Martí, C., García-Ruiz, J.M., 2004. 

Catchment soil moisture and rainfall characteristics as determinant factors for 

discharge/suspended sediment hysteretic loops in a small headwater catchment in the 

Spanish Pyrenees. Journal of Hydrology, 288, 299–311. 

Sidorchuk, A. 2005. Stochastic modelling of erosion and deposition in cohesive soils. 

Hydrological Processes, 19(7), 1399-1417. 

Sidorchuk, A. 2009: A third generation erosion model: The combination of probabilistic and 

deterministic components. Geomorphology, 110 (1-2), 2-10. 

Slattery, M.C. and Bryan, R.B., 1992. Hydraulic conditions for rill incision under simulated 

rainfall: a laboratory experiment. Earth Surface Processes and Landforms, 8, 97-105. 

Stroosnijder, L. 2005. Measurement of erosion: Is it possible?. Catena, 64, 162-173. 

Torri, D., Dfalanga, M. and Chisci, G., 1987. Threshold conditions for incipient rilling. In: 

R.B. Bryan (Editor): Rill Erosion. Catena Supplement, 8, 97-105. 

129


Vandekerckhove, L., Poesen, J. and Govers, G. 2003. Medium-term gully headcut retreat 

rates in Southeast Spain determined from aerial photographs and ground 

measurements. Catena, 50, 329-252. 

Vandekerckhove, L., Poesen, J., Oostwoud Wijdenes, D. and de Figueiredo,T. 1998. 

Topographical thresholds for ephemeral gully initiation in intensively cultivated areas 

of the Mediterranean. Catena, 33(3-4), 271-292. 

Wendt, R.C., Alberts, E.E., Hjelmfelt, Jr., 1986. Variability of runoff and soil loss from 

fallow experimental plots. Soil Sci. Soc. Am. J. 50, 730-736. 

Wirtz, S., Seeger, M. and Ries, J.B. 2010. The rill experiment as a method to approach a 

quantification of rill erosion process activity. Zeitschrift für Geomorphologie, 54,1, 

47-64. 

Woodward, D. E. 1999. Method to predict cropland ephemeral gully erosion. Catena, 37(3-4), 

393-399. 

Zhang, G., Liu, B., Liu, G., He, X., Nearing, M.A., 2003. Detachment of undisturbed soil by 

shallow flow. Soil Science Society of America Journal 67, 713-719. 

Zhu, J.C., Gantzer, C.J., Peyton, R.L., Alberst, E.E., Anderson, S.H., 1995. Simulated smallchannel 

bed scour and head cut erosion rates compared. Soil Science Society of 

America Journal, 59 (1), 211-218. 

130


Kapitel 5 

Wirtz et al. (2013): Do deterministic sediment detachment and transport equations 

adequately represent process-interactions in eroding rills? An experimental field study. 

Catena 101, 61-78. 

131


Do deterministic sediment detachment and transport equations adequately represent the 

processes interactions in eroding rills? An experimental field study. 

Stefan Wirtz • Manuel Seeger • Alexander Remke • René Wengel • Jean-Frank Wagner • 

Johannes B. Ries 

Dep. of Physical Geography, Trier University 

Abstract 

This paper tackles two main questions by linking observations, determination of hydraulic 

parameters and measurement of sediment transport with the formulae used in soil erosion 

models. First, do constant shear stress values in different rills with constant soil parameters 

result in the same soil detachment values? Secondly, deterministic soil erosion models make 

the assumption that there is a relationship (often further assumed to be linear) between shear 

stress and soil detachment; is this suitable for representing real erosion process combinations 

in natural rills? Following most process based deterministic soil erosion models, derived 

hydraulic and erosion parameters should be similar. However, the results from the different 

experiments showed clear differences in sediment concentration, transport rates and other 

measured as well as calculated values. In contrast to our experimental results, a model 

simulation would produce erosion parameters with low variations, represented by the relative 

measurement error and the empirical variation coefficient. This reveals the general problems 

of using process based deterministic models for erosion in shallow rills. While soil erosion 

models simulate the processes resulting from the shear forces of flowing water on the soil 

surface, other processes like side wall failure, headcut retreat and plunge pool dynamics are 

not taken into account. Our results suggested that these other processes may contribute 

substantially to rill erosion processes. The results of this study strongly suggested that the 

model concept of most physical based soil erosion models is inadequate for modeling rill 

erosion processes. Measured total rill erosion rates were the sum of erosion rates caused by a 

combination of different soil erosion processes with different spatial and temporal 

distribution. This combination cannot be described by a single equation. 

Keywords Experimental field work • Process based soil erosion model • Rill erosion • Soil 

erosion 

132



Modelling the results of the processes of soil erosion by water is an important task for 

geomorphologic research. Soil erosion models are also used to evaluate land use systems, and 

derive guidelines for land use management. Model concepts can be empirical (e.g. USLE; 

Wishmeier and Smith, 1965, 1978) or based on physical process description (e.g. WEPP; 

Laflen et al., 1997; EUROSEM; Morgan et al., 1998; LISEM; De Roo et al., 1996). There are 

also stochastic approaches found in the literature for describing and modelling sediment 

detachment and transport (Einstein, 1937, Mirtskhoulava, 1988, Wilson, 1993a, Govindaraju 

and Kavvas, 1994, Lisle et al., 1998, Hairsine and Rose, 1991, Govers, 1991, Nearing, 1991, 

Shaw et al., 2008, Sidorchuk, 2002, Sidorchuk et al., 2004, Sidorchuk, 2005 a, Sidorchuk, 

2005 b, Sidorchuk et al., 2008, Sidorchuk, 2009). However to date no no practical, field-scale 

or catchment-scale, model exists which uses stochastic approaches. Different approaches are 

currently under construction; RillGrow 1 and RillGrow 2 are examples for model 

developments which represent detachment from a distributional perspective (Favis-Mortlock 

et al., 1998, 2000). 

What is the background of process based soil erosion models? 

Many current soil erosion models are described as physically based, or process-based. Knapen 

et al. (2007) distinguish between excess shear stress models and excess stream power models. 

In the first case, transport and detachment capacities are calculated using shear stress alone 

and in the other, shear stress is replaced by stream power which is the product of shear stress 

and flow velocity. In both cases, a critical soil parameter (critical shear stress or critical 

stream power) is exceeded by a hydraulic factor (shear stress or stream power) which enables 

an entrainment of soil particles. Shear stress is therefore a fundamental factor for the process 

based soil erosion models, describing the drag force exerted by the flow on the bed (Giménez 

and Govers, 2002). For inferring shear stress and the derived detachment and transport 

capacity in soil erosion modelling, a set of input parameters are typically used in slightly 

varying combinations: slope, liquid density, flow velocity, hydraulic radius, wetted perimeter, 

flow cross section and water depth (Knapen et al., 2007). Due to the deterministic nature of 

process based models, the same input parameters will always deliver the same results. 

Moreover, these models often assume a linear relation between shear stress and soil 

detachment (Lyle and Smerdon, 1965, Torri et al., 1987, Ghebreiyessus et al., 1994, Nearing 

et al., 1997). 

133


Where have experiments been conducted and what questions have been addressed? 

Following Kleinhans et al. (2010) there are several ways for geoscientists to create results or 

data sets. These are (i) field observations, (ii) field experiments, (iii) laboratory experiments 

or (iv) a model simulation. 

Measurements of soil erosion have been conducted in both the field and experimentally in the 

lab. In laboratory experiments, the initial and boundary conditions can be well controlled. Soil 

parameters, rill forms and slope can be adapted to specific questions. In this way, physical 

laws can be tested in a relatively precise environment. However, Giménez and Govers (2002) 

showed that parameters determined under laboratory conditions cannot be easily transferred to 

natural environments. The main reason is that in laboratory experiments smooth beds are 

often used while in natural rills the beds are always irregular. Nonetheless, laboratory 

experiments have given detailed insight into different processes of soil erosion and have been 

used to derive empirical relationships between descriptors of the forces exerted by flowing 

water and sediment detachment and transport. For example, Brunton and Bryan (2000) and 

Bryan and Poesen (1989) showed in laboratory experiments that headcut incision and bank 

collapse are important processes in the development of rills and rill networks. But the 

consideration of these processes has not found its way into applied soil erosion modelling. 

Different research groups have often presented different shear stress – based factors like: unit 

length shear force (Giménez and Govers, 2002), stream power (Bagnold, 1977, Hairsine and 

Rose, 1992, Elliot and Laflen, 1993, Nearing et al., 1997, Zhang et al., 2003), unit stream 

power (Yang,1972, Moore and Burch, 1986) and effective stream power (Bagnold, 1980, 

Govers, 1992a), which show a more or less good fit with soil detachment rates measured in 

their experiments. These experimentally deduced factors are highly dependent on the 

experimental setup, due to a none standardised experimental method available. Casali et al. 

(2006) clearly shows the consequences of comparing the results from different methods. 

These results are often used in process based soil erosion models. As a result, soil erosion 

models which make use of these experimentally deduced factors have a clear empirical 

foundation (Stroosnijder, 2005). However, this is not always adequately acknowledged. 

The United States Department of Agriculture (USDA) made great efforts in field 

experimental research for developing the Universal soil loss equation USLE (Flanagan et al., 

2003). 

Nevertheless, most field data about runoff and erosion in rills have been gained from 

observations during natural rainfall and runoff events or long-term-plot measurements; in only 

few cases controlled experiments have been conducted (Abrahams and Li, 1996, De 

134


Santisteban et al., 2005, Helming et al., 1999, Parsons et al., 1999, Parsons and Wainwright, 

2006, Rejman and Brodowski, 2005). The aim of these studies was: 

- to observe rill network formation (Bruno et al., 2008, Mancilla et al., 2005), 

- to define the initial conditions for rilling (Bruno et al., 2008, Bryan et al., 1998, 

Govers and Poesen, 1988, Slattery and Bryan, 1992, Torri et al., 1987), 

- to study the development of rill head morphology (Bruno et al., 2008, Brunton and 

Bryan, 2000), 

- to estimate the main hydraulic variables like cross-section area, wetted perimeter, 

hydraulic radius, mean velocity and shear stress for calculating other hydraulic 

parameters which could not be measured or estimated (Abrahams and Li, 1996, Bruno 

et al., 2008, Foster et al., 1984, Gilley et al., 1990, Giménez et al., 2004, Govers, 1992 

b), to validate existing models (Huang et al., 1996), 

- to measure the transmission losses in rills (Parsons et al., 1999) or 

- to propose mathematical models for estimating soil loss due to rill erosion (Bruno et 

al., 2008, Foster, 1982, Nearing et al., 1989) or for rill initiation (Parsons and 

Wainwright, 2006). 

Field data are as close to reality as possible. But observations can be collected from a long 

term plot measurement or only by scientists who are in the right place at the right time. This is 

not always possible, so field experiments are used to trigger the processes to be observed 

when the measurement team is on site. However, both observations and experiments have 

certain disadvantages: (i) Measurement techniques may disturb the processes being observed, 

(ii) the time scale of human observations is shorter than that of the process under study, (iii) 

some processes cannot easily be measured and (iv) some processes are apparently chaotic and 

their spatial and temporal variations are difficult to capture (Favis-Mortlock and de Boer, 

2003, Kleinhans et al., 2010). 

Nevertheless, simplified experimental setups are ruled by the same natural laws as the 

processes found in nature. Thus, experimental observations can be considered as a simplified 

but valid representation of the reality (Paola et al., 2009). A model is always simpler than the 

thing which it aims to represent (Favis-Mortlock et al., 2001). 

Mathematical models describe reality in terms of mathematical equations. Physical laws are 

often simplified to allow numerical solutions, but in many cases it is not clear which laws 

apply and to what extent simplification is possible. Model parameters are always the result of 

simplifications. Values of some parameters are not well known, so the model has to be 

calibrated. Here, the phenomenon of equifinality is a problem: A wide range of parameters 

135


can produce the same result. Or, as Favis-Mortlock et al. (2001, p. 487) state, models can give 

“the right answer for the wrong reason”. Another problem is that parameters for rill hydraulics 

are often taken from equations for describing flow behaviour in rivers. Govers (1992 a) and 

Govers et al. (2007) showed that these equations are not suitable for rill erosion processes. 

Therefore, there is often a mismatch between model results and observed or measured 

“reality” (Kleinhans et al., 2010). 

What is our scientific question? 

As discussed above, models can give rise to large uncertainties. This is, in some cases, the 

result of poor quality or inappropriate input data. At the same time, field experiments deliver 

reliable data, as processes run under natural conditions. Field experiments enable a direct 

observation of the processes involved in rill dynamics. Hence, to bridge the gap between 

models, parameterisation and observations, the field experiments in this study were performed 

with specific attention given to the basic hydraulic parameters needed to calculate shear 

stress. By linking the observations, the determination of hydraulic parameters and the 

measurement of sediment transport with fundamental formulae used in soil erosion models, 

we aimed to tackle the following questions: 

1. Do constant shear stress values in different rills on the same field with constant 

soil parameters (critical shear stress for example) always result in the same soil 

detachment values? 

And as a consequence of this question: 

2. Is the model concept of a linear relation between shear stress and soil detachment 

suitable for real erosion process combinations in natural rills? 

The characteristics of the field site and the experimental set up allowed a set of experiments 

with very similar boundary conditions to be conducted under natural conditions. All necessary 

parameters could be measured directly, thus avoiding the need for estimates. As a 

consequence, it was expected that the shear stress exerted by the flowing water would remain 

within the same order of magnitude for all experiments. 

2 Materials and methods 

2.1 Study area 

The Natural Park Bardenas Reales, a 425 km² semiarid landscape, is located in northeast 

Spain (Navarra), in the Ebro-Basin (Fig. 1). It is bounded by the Aragón River on the north 

and the Ebro on the south (Desir and Marín, 2007, Murelaga et al., 2002, Sancho et al., 2008). 

136


The tertiary and quaternary sediments in the Bardenas Reales consist of open playa-lake 

deposits, red, grey and green clayey marl and pockets of lacustrine, limestone-like, sandy and 

gypsum-containing sediments as well as massive marly and lacustrine limestones that form 

cuestas (Desir and Marín, 2007, Murelaga et al., 2002, Sancho et al., 2008). The climate in the 

test area is semi-arid and characterised by irregular, heavy rainfall events with an average of 

380 mm a -1 , the average annual temperature is 19.2°C, and the potential evapotranspiration 

rate reaches 1084 mm. In summer and winter, only sporadic rainfall events reach the test 

areas; the convective precipitation occurs in spring and autumn (Causapé et al., 2006, 

Causapé et al., 2004, Desir and Marín, 2007, Sancho et al., 2008). 

Fig. 1 Location of the Bardenas Reales 

The position of our experimental site was 624817 E 4681907 N (UTM Zone 30). With highdefinition 

aerial photography it was possible to estimate area and length values and to 

describe soil surface characteristics such as vegetation cover or rills. 

On a part of the 0.75 ha field with nearly bare soil, i.e. vegetation cover was only 1% and rock 

fragments cover 2%, approximately 20 furrows have developed into rills in different stages of 

development (Fig. 2). Average rill length was 10 m, thus we calculated a total rill length of 

200 m. The relationship between rill length and area (rill density) was 267 m ha -1 . This is 

lower than on the fields which were treated by the ‘ripping’ technique (a kind of deep 

137


loosening) where furrows were opened but higher than on a ploughed field in the study of 

Hagmann (1996). The informations about area size and rill lengths have been derived from 

self-made large scale aerial photographs. The camera used for acquiring the photos was a 

Canon 350D with a Canon EF-S 20 mm objective. The maximum resolution of the photos 

was 8 MP, the resulting stereoscopic images showed a ground resolution between 0.5 and 11 

cm, depending on the flying height. We used a low flight level, so the ground resolution of 

our photos is at about 1 cm. This is accurate enough for calculating rill lengths and area sizes. 

Other informations like cross sections or rill width are not calculated from aerial 

photographies but directly measured in the field. For these tasks, the ground resolution would 

not be appropriate. 

Four of these rills were randomly chosen for the experiments. 

Fig. 2 Field with the tested rills: The crawler as scale in the photo on the right has a length of 

about 1.5m. RE = rill experiment 

On our test site, texture class was at the threshold between poor silty sand and poor loamy 

sand, gravel content was 1%. Main texture class was fine and very fine sand, nearly half of 

the fine soil material showed a grain size between 0.2 and 0.063 mm. Grain density and dry 

bulk density have been estimated as 2.65 g cm -3 and 1.68 g cm -3 , respectively, following the 

138


Ad-hoc-Arbeitsgruppe Boden (2005). Soil material contained 2.2% organic matter, and the 

starting soil moisture was 7.5%. The tested rills developed in this homogeneous substrate 

show neither steps nor plungepools but had different slopes and flow length. The rill 

descriptors with different values for each rill are summarized in Table 1, the constant setup, 

soil and climate factors are presented in Table 2. 

Table 1 Rill descriptors and values by test rill. MP = Measuring Point 

Factor Rill 1 Rill 2 Rill 3 Rill 4 

Tested flow length [m] 10 14 6 6.5 

Ø Slope [°] 4.3 3.1 2 2.9 

Max. Slope [°] 9.4 5.8 3.1 7.1 

Min. Slope [°] 1.8 1.2 0.7 1 

Standard deviation slope [°] 2.1 1.3 0.9 1.9 

MP 1 position [m] 3 4 1.5 2 

MP 1 slope [°] 1.8 3.5 2.8 3.7 

MP 1 depth [m] 0.109 0.115 0.075 0.105 

MP 1 width [m] ~ 0.52 ~ 0.56 ~ 0.25 ~ 0.28 

MP 2 position [m] 6 7 3 3.5 

MP 2 slope [°] 4.6 3 3.1 1.6 

MP 2 depth [m] 0.115 0.189 0.076 0.101 

MP 2 width [m] ~ 0.6 ~ 0.52 ~ 0.28 ~ 0.20 

MP 3 position [m] 9 12 4.5 5 

MP 3 slope [°] 3.3 2.1 1.5 1 

MP 3 depth [m] 0.108 0.161 0.085 0.093 

MP 3 width [m] ~ 0.6 ~ 0.42 ~ 0.28 ~ 0.24 

139


Table 2 Constant parameters 

Parameter Factor Value 

Discharge intensity [ L min -1 ] 9 

Setup Discharge quantity [L] 72 

Discharge time [min] 8 

Soil texture 

Loamy sand 

Organic matter [%] ~ 2.2 

Land use 

Arable land 

Transport Coefficient K t [s 2 m 0.5 kg -0.5 ] 0.0107 

Soil Vegetation cover [%] ~ 1 

Rock fragment cover [%] ~ 2 

Starting soil moisture [%] ~ 7.5 

Grain density [g cm -3 ] 2.65 

Dry bulk density [g cm -3 ] 1.68 

Average precipitation [mm a -1 ] 380 

Climate 

Average annual temperature [°C] 19.2 

Evapotranspiration rate [mm a -1 ] 1084 

Characterisation 

Semi arid 

2.2 Rill experiment 

The rill experiment consisted of two runs: in the first run the rill was tested under dry 

conditions; in a second run, 15 min later, the same rill was tested under wet conditions, 

therefore the influence of the initial soil moisture could be considered. 

For each run, a motor driven pump was used to maintain a constant discharge of 9 L min -1 for 

8 minutes, resulting in a total water flow of 72 L (Wirtz et al., 2010, Wirtz et al., 2012). In the 

used range of water quantity and pressure the fluctuations were very low so we can assume 

that the inflow was stable. 

The flow velocity within the rill was characterized by the travel time of the waterfront and of 

two colour tracers (food colourings (E 124 red and E 13 blue started at 3 and 6 minutes after 

the start of the experiment) measured for every meter using a chronograph. By means of this 

procedure, three velocity curves with the maximum flow velocities were recorded and 

changes in flow dynamics could be detected. Following Govers (1992b) we assumed that the 

mean flow velocity is reached, where the waterfront reaches 80 – 90 % of its maximum width. 

In our experiments, the difference between the front and this point could not easily be 

140


distinguished and the time difference between these two points defined our measurement 

accuracy because of the relatively diffuse form of the waterfront and the flow velocity. The 

measured flow velocities were not equal to the flow velocities at sampling time. We assumed 

a linear increase or decrease between the three measured flow velocities so we could calculate 

the velocities between those points to get the velocities for the sampling time. This procedure 

is shown in Fig. 3. 

Fig 3 Calculation of the flow velocities 

At the end of the rill, the runoff was continuously measured by a pressure transducer (Ecotech 

DL/n, V2.35). For calibration of the discharge curve, runoff at the outflow was measured 

volumetrically at regular intervals. This allowed constant measurement of the discharge at 

high temporal resolution and throughout the whole experiment. 

The rill's slope was measured using dividers with a range of 1m and a digital spirit level as it 

was used in Wirtz et al. (2010). It is important to note that slope measurement provided only 

an average slope over the 1 meter. 

At three measuring points (MPs) along the rill four water samples were taken: the first as soon 

as the waterfront reached the sampling point, the second 30 seconds later, and the third and 

fourth after 1:30 min and 2:30 min total time from arrival of the water. The measurement of 

sediment passing given points is measurements of flux. Changes in flux at different points and 

at different times enable the identification of processes leading to spatial and temporal sources 

and sinks of sediment (Parsons et al., 2006). The sediment concentration was determined by 

filtration of the samples in the laboratory (Wirtz et al., 2010). The reason for this sampling 

141


scheme was that we could not collect the whole water at a MP, so we had to take aliquots. At 

the beginning we expected the highest fluctuations, hence the distance between sample 1 and 

2 was lower than between sample 2 and 3 and sample 3 and 4. Depending on the flow length 

to the MP it was possible that after 3 minutes the runoff stopped at this point, we had to take 

the samples before this occurred. 

At each MP, rill cross section was measured. With thin metal sticks, the distance between 

ground level and rill bottom was measured in 0.002 m steps. This allowed an accurate 

calculation of the rill’s cross section area and an estimation of the rill’s volume. Additionally, 

the water depth at a certain point in the rill was measured several times using a yardstick. By 

combining the rill cross section and the water depth it was possible to calculate flow area, 

wetted perimeter and hydraulic radius using the georeferencing tool of a GIS. 

2.3 Descriptors for soil detachment 

The relationship between detachment rate and detachment capacity and respectively the 

relationship between transport rate and transport capacity are important values for assessing 

different processes acting in the rill. These variables were calculated as follow: 

DC = K 

r 

(τ τcr 

) (Foster et al., 1995) Eq. (1) 

T 

1.5 

C 

= K 

t 

R τ 

(modified from Wagenbrenner et al., 2010) Eq. (2) 

SC 

V A 

DR = 

Eq. (3) 

L WP 

TR = SC 

V A 

Eq. (4) 

with D C = detachment capacity [kg m -2 s -1 ], K r = rill erodibility factor [s m -1 ], τ = shear stress 

[Pa], τ cr = critical shear stress [Pa], T C = transport capacity [kg s -1 ], K t = transport coefficient 

[s² m 0.5 kg -0.5 ], R = hydraulic radius [m], D R = detachment rate [kg m -2 s -1 ], S C = sediment 

concentration [g L -1 ], V = flow velocity [m s -1 ], A = flow area [m²], L = flow length [m], WP 

= wetted perimeter [m], T R = transport rate [kg s -1 ]. 

The rill erodibility factor K r can be calculated for cropland or rangeland; in this case, we used 

the equation of Flanagan and Livingston (1995) for cropland. Parameters are very fine sand 

content (vfs) and organic material content (org.Mat.). 

K 

1.84(org. 

Mat. 

) 

r 

= 0.00197 + 0.0003 (vfs) + 0.03863 

Eq. (5) 

Depending on land use, the parameters for the critical shear stress are clay content and very 

fine sand content (Flanagan and Livingston, 1995). 

τ c 

= 2.67 + 0.065 (clay) 0.058 (vfs) 

Eq. (6) 

142


Shear stress was calculated as follow: 

τ = ρ g R S (Giménez and Govers, 2002) Eq. (7) 

with ρ = fluid density [kg m -3 ], g = gravitational acceleration (9.81 m s -2 ), R = hydraulic 

radius [m] and S = effective slope (sin(slope angle)). 

The transport coefficient value was taken from the WEPP-database (Elliot et al., 1989). We 

used the value of the soil that is most similar to the soil in the test area. In this case, the 

location is Amarillo, the K t value is 0.0107 s 2 m 0.5 kg -0.5 . 

For comparing the variability of the different parameters, we calculated first the average of 

the relative measurement errors (RME) following the DIN 1319-1 (1995). This error is 

defined as 

xa 

xr 

RME = 100 

Eq. (8) 

x 

r 

with x a as measured value and x r as “correct” value, we used the mean of the measured values 

as x r . The variance and the standard deviation are still in the unit of each parameter, therefore 

the variances of different parameters are not comparable. 

The RME describes the difference between the average value of all experiments and the 

average values of one run. From our measuring values, we calculated the average value of 

each run. The average of these “run-values” is the x r in Eq. (8), the average of each run is 

presented by the x a . The given values in Table 4 are the average of the values of the 8 runs. 

The RME would be much higher if we would calculate the RME between average values of 

all 96 samples and the single, directly measured sample. 

As second value for describing the variation, we calculated the empirical variation coefficient 

EVC. It was calculated as follows: 

standard 

deviation 

EVC = 

average 

Eq. (9) 

The calculation for this factor is similar to the calculation of the RME values: We did not use 

the mean standard deviation and the average of all samples, because of the different 

conditions we calculated the average values for each run and averaged these results. 

3 Results 

Sediment concentrations at the MPs 

We use a number-letter-system to identify our runs. The first number is the number of the 

experiment, a or b means the first or the second run and the last number is the number of the 

measuring point. 

143


Generally we could distinguish between seven different sediment concentration curves 

(Figure 4-7). (1) The first trend was defined by a decrease from the first to the last sample, 

only one sample with increasing value disturbed this trend. This form was found in 1a1, 1a2, 

1b1, 2a2, 2a3 and 3a3. (2) In the second form, the decreasing trend was not disturbed by any 

increasing value. This trend was shown by 1a3. (3) The next trend type was defined by an 

increase from the first to the second sample, after that, the values remained almost constant: 

1b2, 2b1, 3a1, 3b1, 3b2, 3b3, 4a2, 4b1, 4b2, and 4b3. (4) It was also possible that the values 

stayed about constant from the first to the last sample, this form was found in 1b3 and 4a3. (5) 

In 2a1, the values increased from sample 1 to sample 3, after that the value decreased at 

sample 4. (6) In version 6, we observed a decrease from sample 1 to sample 2 and an increase 

from sample 2 up to sample 4. This was found in 2b2, 3a2 and 4a1. (7) The last version found 

at 2b3 showed a decrease from sample 1 to sample 2 followed by a constant trend which was 

disturbed by one sample with increasing value. 

Flow velocities along the rill profile 

In experiment 1 and 4, the flow velocity curves showed similar forms: In the first runs, the 

two tracers are similar over the rill profile; the water front didn’t reach the same velocity. In 

run 2, the velocity of the waterfront increased and tracers and water front showed similar 

values. In experiment 3, the differences between the tracers and the front were also low in the 

second run, but the roughly parallel trend of the tracers in run 1 was disturbed in run 2. In the 

first run of experiment 2, the tracers showed similar values, the waterfront showed lower 

values again. But in run 2, the water front showed a very irregular trend with fewer 

similarities to the tracer curve. Because of technical problems, the velocity of tracer one in 

experiment 2b was not measured. 

Runoff values at the end of the tested rill part 

In most cases, the increase of the runoff curve is very fast, only run 1 in experiment 1 showed 

a slower increase. In all cases, the runoff in run 1 started later as in the second run and the 

values were lower, this difference was very noticeable in the first experiment. Also the runoff 

duration was longer in the second runs of all experiments. Because of technical problems, the 

runoff of run 1 in experiment 4 was not measured but the observations confirmed the 

measurements of the other experiments. 

144


Fig. 4 Results of RE 1 

145



146



147



Average values for the different runs: 

All factors for each run of the four REs are presented in Table 3. Whether values were 

measured or calculated is also noted. The average values in this table were calculated from 12 

samples (3 MPs x 4 samples in each run). 

148


Table 3 Average values of all factors for all experiments. Shear stress 1 includes the sediment 

concentration and grain density in the liquid density calculation, shear stress 2 is calculated 

using a constant liquid density of 1 g cm -3 . c = value is calculated, equation number is given, 

m = value is measured. SSC = Sediment concentration. The r-l-factor describes the 

relationship between runoff and flow length: inflow/runoff * length. 

Factor Unit m/c 1a 1b 2a 2b 3a 3b 4a 4b 

Transport rate [kg s -1 ] c 4 0.0055 0.0057 0.0112 0.0152 0.0006 0.0004 0.0015 0.0013 

SSC [g L -1 ] m 16.32 13.53 44.02 37.51 2.56 1.78 10.19 9.41 

Detachment rate [kg s -1 m -2 ] c 3 0.0051 0.0054 0.0123 0.0146 0.0007 0.0006 0.0033 0.0037 

Shear stress 1 [Pa] c 7 7.17 7.15 5.88 6.24 3.64 4.75 2.77 3.5 

Shear stress 2 [Pa] c 7 7.09 7.09 5.73 6.12 3.64 4.75 2.76 3.49 

Hydraulic Radius [cm] m 1.28 1.28 1.16 1.19 0.90 1.13 0.74 0.87 

Slope [°] m 3.2 3.2 2.9 2.9 2.4 2.4 2.1 2.1 

Flow velocity [m s -1 ] m 0.15 0.18 0.16 0.21 0.14 0.17 0.16 0.19 

Liquid density [g cm -3 ] m 1.010 1.008 1.027 1.023 1.002 1.001 1.006 1.006 

r-l-factor [m] m 1.27 4.25 6.39 7.95 3.09 4.29 ND 3.34 

Runoff coefficient [%] m 12.68 42.47 45.61 56.78 51.56 71.54 ND 51.33 

RE1 showed the highest average values in both shear stress forms (constant liquid density and 

liquid density including sediment concentration and grain density), in the hydraulic radius 

values and in slope. Lowest values were measured for r-l-factor and runoff coefficient (1a). 

In RE2 the highest values for transport rate (2b), sediment concentration (2a), detachment rate 

(2b), flow velocity (2b), liquid density (2a) and r-l-factor (2b) were measured. 

RE 3 only showed the highest runoff coefficient (3b). Instead of highest values, many lowest 

values have been measured or calculated: transport rate, sediment concentration, detachment 

and liquid density in 3b and flow velocity in 3a. 

RE4 provided the lowest shear stress values, the lowest hydraulic radius (4a) and the lowest 

slope. 

In a model simulation, in most cases average values are used. The external parameters are 

constant on the whole field (see Table 2), so the 4 different rills would be described by one 

mean value. We calculated mean values of all samples (4 experiments x 2 runs x 3 MPs x 4 

samples = 96 samples) which are presented in Table 4. To compare the variability of the 

different parameters, we also calculated the relative measurement error (RME) and the 

empirical variation coefficient (EVC) for each of them. The RME values for the tested 

parameters are presented in Fig. 8, the EVC values in Fig. 9 and they are summarized in Table 

4. 

149


Fig. 8 The relative measurement errors of the tested parameters: Shear stress 1 includes the 

sediment concentration and grain density in the liquid density calculation, shear stress 2 is 

calculated using a constant liquid density of 1 g cm –3 

Fig.9 The empirical variation coefficient of the tested parameters: Shear stress 1 includes the 

sediment concentration and grain density in the liquid density calculation, shear stress 2 is 

calculated using a constant liquid density of 1 g cm –3 

150


Table 4 Variability of different runoff and erosion factors, hydraulic and rill parameters. 

RME is the relative measurement error. EVC is the empirical variation coefficient Shear 

stress 1 includes the sediment concentration and grain density in the liquid density 

calculation, shear stress 2 is calculated using a constant liquid density of 1 g cm –3 . Uncertainty 

= standard deviation * data quantity -1/2 

Factor Average RME [%] EVC Uncertainty 

Transport rate [kg s -1 ] 0.0052 81.7 0.69 0.009 

Sediment Concentration [g L -1 ] 16.9 70.5 0.54 1.793 

Detachment rate [kg s -1 m -2 ] 0.0057 67.5 0.74 0.001 

Shear stress 1 [Pa] 5.1 28.6 0.33 0.299 

Shear stress 2 [Pa] 5.1 28 0.33 0.295 

Hydraulic radius [cm] 1.1 16.4 0.09 0.035 

Slope [°] 2.7 14.7 0.28 0.104 

Flow velocity [m s -1 ] 0.2 10.2 0.27 0.005 

Liquid density [g cm -3 ] 1.01 0.7 0.006 0.001 

The highest average RME was calculated for the transport rate. RME values of more than 

60% were also calculated for sediment concentration and detachment rate. RME values 

between 20 and 40% were calculated for both shear stress variations. RME values below 20% 

were measured for flow velocity and for the input parameters of the shear stress equation 

hydraulic radius, slope and liquid density. 

The comparison of the EVC (empirical variation coefficient) showed similar results: High 

EVCs were calculated for transport and detachment rate and the sediment concentration. The 

shear stress values showed again middle values, the flow velocity and the slope were in the 

EVC-ranking in a middle position, in the RME-ranking they were in a back position. Low 

EVCs were determined for the hydraulic radius and the liquid density. 

Concerning the ranges of the RME values (Fig. 8) it is notable that the erosion parameters 

transport and detachment rate and sediment concentration showed the highest range between 

maximum and minimum value as well as between the 75 % and the 25 % quantile. Middle 

ranges (here defined as values between 20 and 40 %) between maximum and minimum values 

were determined in both shear stress variations, hydraulic radius and flow velocity, low 

ranges < 20 % in slope and liquid density. Regarding only the range between the 75 and the 

151


25 % quantile, nearly all parameters showed a low range, only the shear stress with constant 

liquid density showed a middle range. 

Regarding the ranges of the EVC (Fig. 9) it is notable that all parameters showed the same 

range class between maximum and minimum value as well as between the both quantiles. The 

detachment rate showed high ranges, transport rate, sediment concentration, hydraulic radius, 

slope and flow velocity middle ranges and low ranges were determined for both shear stress 

variations and the liquid density. 

4 Discussion 

Errors in measurement 

The statistical uncertainty of the different parameters (Table 4) showed the highest value in 

sediment concentration, contrasting, and the flow velocity showed a very low uncertainty. 

However, a formal statistical analysis of errors is problematic for this study, since extreme 

high or low values in sediment concentration would be regarded as outliers, and perhaps 

discarded or discounted. But, from our observations, these extreme values result from a 

process change and thus should certainly not be ignored. This problem is also found in the 

model concepts: The processes which cause the extreme values (rill bank failure for example) 

are not described by the used equations. Regarding the measurement methods for the 

sediment concentration and the flow velocity, the number of possible errors in velocity 

measurement is much higher than in sediment concentration measurement. The problem of 

flow velocity measurement was described for example by Govers (1992b) and Ali (2011). In 

some cases, a constant correction factor was used to calculate the mean flow velocity from the 

often measured maximum flow velocity of the waterfront. This factor changed depending on 

experimental setup, Govers (1992 b) determined 0.94. Ali (2011) analysed the variability of 

the correction factor depending on grain size, testing four different grain sizes in the sand 

group. The correction factors were 0.44, 0.77 and two times 0.82. Other authors found out that 

the correction factor depends on slope and Reynolds number (Li et al., 1996) or on slope, 

Reynolds number and sediment discharge (Zhang et al., 2010) 

Rate vs. Capacity 

Theoretically, the relationship between a rate and a capacity should not exceed 1 because 

sedimentation processes reduce this value when the rate is higher than the capacity (Scherer, 

2008). However, in our experiments, 67 of 96 samples (75%) showed higher transport rates 

than transport capacities, especially in higher sediment concentration ranges (Fig. 10). 

152


The transport rate exceeded the transport capacity in 77% of the samples (dry runs) 

respectively in 63% (wet runs) of the samples. But regarding the average values of the 

relationships between transport rate and transport capacity (only the values higher than 1) the 

second runs (b-runs) showed a higher value than the first runs (a-runs) (7 vs. 5.7). In the a- 

runs, the transport of loose material was the main process, in the b-runs the bank failure and 

the headcut retreat. Sediment supply was not limited due to the low flows during the 

experiment. Fig. 11 shows clearly that still at low runoff values the transport rate was much 

higher than the transport capacity. In most of the cases, the transport of loose material was 

responsible for the high transport rates. 

Fig.10 Relationship between transport rate and transport capacity vs. sediment concentration. 

The equilibrium line is shown 

153


Fig. 11 Relationship between transport rate and transport capacity vs. runoff. The equilibrium 

line is shown 

Variability in soil erosion measurements 

The input parameters for calculating shear stress showed average RME values below 20%: 

hydraulic radius with 16.4%, slope with 14.7% and liquid density with 0.7%. The calculated 

shear stress values were also similar; the variability was 28.6% when liquid density with 

sediment concentration considered was used and 28% if the liquid density of clear water was 

assumed. In models, a commonly-used idea is that there is a linear relation between shear 

stress and soil detachment volumes. This means that the variability of soil loss parameters 

should also be in the same order of magnitude. For transport and detachment rate, input 

parameters are still flow velocity and sediment concentration. Flow velocity showed a low 

variability of 10.2%. On the other hand sediment concentration (70.5%), transport rate 

(81.7%) and detachment rate (67.5%) showed very high variability, all values being over 

60%. This variation in values contrasts with the approach used in models. In a model 

simulation the variations of the input parameters and the soil loss parameters would be 

similar. This means that in this case, there was no simple linear relation between shear stress 

and soil detachment. 

The results of the research reported by Govers (1991), Liu et al. (1996), Nearing (1998, 1999 

a), Risse et al. (1993), Ruttiman et al. (1995), Wendt et al. (1986) and Zhang et al. (1996) 

underscore the problems. Nearing (1998) tested the variability between replicated soil erosion 

154


field plots under natural rainfall to determine the principal factor or factors which correlate 

with the magnitude of variability. The coefficient of variation ranged in the order of 14% for a 

measured soil loss of 20 kg m -2 to greater than 150% for a measured soil loss of less than 0.01 

kg m -2 . Ruttiman et al. (1995) analysed statistically the data of four sites, each with five to six 

reported treatments; each of them with three replicates. The coefficients of variation in soil 

loss ranged from 3.4% to 173.2%, with an average value of 71%. In a classic study, Wendt et 

al. (1986) measured soil erosion rates on 40 experimental plots. All plots were cultivated and 

treated identically. The coefficients of variation for 25 storms ranged from 18% to 91%, with 

a clearly decreasing variability of soil loss with increasing erosivity of the storms: 15 storms 

with erosion rates higher than 0.1 kg m –2 were noted and 13 showed coefficients of variation 

less than 30%. Risse et al. (1993) applied the USLE to a large data-set of plot-years and 

natural runoff plots. Annual values of measured soil loss averaged 3.51 kg m –2 , the average 

magnitude of prediction error was 2.13 kg m –2 , that means 60%. Zhang et al. (1996) tested the 

WEPP-model in a similar way. The average soil loss was 2.18 kg m –2 with an average 

prediction error of 1.34 kg m -2 which is 61% of the mean. Liu et al. (1996) compared 

measured values with WEPP-calculated values. For one of the tested catchments, the 

sediment yield was under-predicted by approximately 50%. Govers (1991) tested the rill 

erosion rates on arable land in Central Belgium. The relevant characteristics of the selected 

fields were similar; the highest standard deviation was 65 m in length and 25.5% in sand 

content. Mean rill erosion rate from 156 measurements reached 0.36 kg m –2 , with a maximum 

of 3.5 kg m –2 , but also no erosion was observed. The cited results are mostly from plot 

measurements which often do not show any rills but the results reflected here show the high 

variability of soil erosion measurements, even under controlled, experimental conditions. 

Different processes 

At most MPs, the sediment concentration showed a decreasing trend while the flow velocity 

increased. That means the available loose material was washed out. This process has been 

called “bulldozer-effect” (Seeger et al., 2004, Regüés et al., 2000, Wirtz et al., 2012) and was 

detectable in 1a3, 1b1, 3a1, 3b1, 3b2, 3b3, 4b1 and 4b2 (The number after the experiment 

number is the MP again). This trend could be disturbed by some higher sediment 

concentration peaks which represent in most cases side wall failures or knickpoint 

undercutting and retreat (1a1, 1a2, 1b2, 2a1, 2a2, 2a3, 3a3). Another observed process was the 

combination of the bulldozer-effect and increasing incision into the bottom of the rill. This 

combination was detectable by a constant (starting with the first or also with the second 

155


sample at the MP) or even increasing sediment concentration (1b3, 2b1, 2b2, 3a2, 4a1, 4b3). 

The combination of all three processes is also possible, first the bulldozer-effect, followed by 

incision in the rill’s bottom disturbed by a sidewall failure (2b3, 4a2, 4a3). 

The very large variability is likely to be in part the result of non-homogeneous parameters 

used for soil characteristics and rainfall. On experimental plots, infiltration rates and soil 

aggregate stability can be highly variable (Ajayi and Horta, 2007). Even simulated rainfall 

shows a high spatial and temporal variability (Assouline, 2009, Dunkerley, 2008, Lascelles et 

al., 2000) on plot size thus, we can assume that natural rainfall events show at least a similar 

variability. The variability is likely higher under natural rainfall because rainfall simulators 

are mostly constructed to create spatially uniform rainfall conditions. Therefore, the input 

parameters for the different measurements reflected in the studies mentioned above were not 

really comparable. Nevertheless, the results also make clear that modelling soil erosion 

involves uncertainty in model input as well as in the data that can be used for model 

calibration and validation. In the field, the spatial and temporal variability of soil conditions 

cannot be avoided, and is, furthermore, part of the investigations. Therefore, additional input 

parameters such as rainfall or flow should be kept constant in the experiments to generate 

comparable data. There is a high variability in soil erosion processes that cannot be 

represented by a single factor e.g. shear stress. The shear stress equation implies that drag 

forces are the dominant forces controlling erosion. But rill erosion is the result of the 

combination of different processes including headcut erosion, sidewall sloughing, tunnelling, 

micro-piping, slaking, piping and sapping (Bryan et al., 1989, Bryan, 1990, Knapen et al., 

2007, Owoputi and Stolte, 1995, Rapp, 1998, Zhu et al., 1995). These processes are not 

explicitly accounted for in shear stress equations, although there is ample evidence to support 

their importance. Zhu et al. (1995) concluded from laboratory experiments that the 

contribution of headcutting in detachment processes was four times higher than the 

contribution of bed scours. Kohl (1988) found that headcutting accounted for up to 60% of 

total rill erosion for the soil erodibility data of WEPP. Stefanovic and Bryan (2009) tested, in 

laboratory experiments, the development of rills on a loamy sand and on a sandy loam and 

showed that concentrated flow causes sediment production primarily from knickpoints, 

chutes, meanders and bank failure. Govers (1987) distinguished between hydraulic erosion, 

mass wasting processes on rill sidewalls, gullying and piping. During his classic study in 

Huldenberg, the loamy hilly region of Flandres, the field was conventionally tilled and a 

seedbed was prepared. Hydraulic rill erosion mostly occurred during three observed runoff 

events with peak discharges between 70 and 90 L s –1 (4200 – 5400 L min –1 ). Runoff rates 

156


during other events were always below 25 L s –1 (1500 L min -1 ). We used runoff rates of 9 L 

min –1 which turned out to be too low to produce hydraulic rill erosion. However, it was 

sufficient to cause mass wasting processes on rill sidewalls and exceeding transport capacity. 

In the observed runoff events (Govers, 1987), mass wasting processes caused 37% of total 

erosion in rills. But in erosion modelling, rill erosion is considered to be only dependent on 

the erosive power of the flowing water, represented by shear stress, unit length shear force or 

stream power. The retreat erosion at knickpoints and headcuts (in Govers (1987) called 

“gullying”), is not considered in rill erosion equations. This process caused about 12% of rill 

erosion rates in the study of Govers (1987). In our experiments, we only cause mass wasting 

and headcut retreat, so the relations between hydraulic parameters and sediment concentration 

are mostly low. However, hydraulic rill erosion only occurs in extreme runoff events 

suggesting that, in most cases, runoff values are too low to cause this process (Govers, 1987, 

Nearing, 1991). All these observations agree with our own observations and measurements. In 

addition, there are several studies and models looking at headcut retreat (Bennett, 1999, 

Robinson et al., 2000, Alonso and Bennett, 2002, Bennett and Alonso, 2005, Bennett and 

Alonso, 2000, Flores-Cervantes et al., 2006, Gordon et al., 2007) and bank failure (Parker, 

1983, Kovacs and Parker, 1994). These results have not (yet) been applied in soil erosion 

models. Some of the interacting sub-processes in an eroding rill are summarized in Kinnell 

(2005) and especially in figure 1 of this paper. He distinguished between raindrop detachment 

with transport by raindrop splash, raindrop detachment with transport by raindrop-induced 

flow transport, raindrop detachment with transport by flow and flow detachment with 

transport by flow. In our experiments, we only activated the last process, all raindropdependant 

processes were not represented in our experimental setup. Following Kinnell 

(2005) the flow detachment does not occur unless a critical value is exceeded. As we just 

measured the effect of one sub-process, our sediment concentrations would have been higher 

in a real rainfall event. The hydraulic parameters and hence the results of a model simulation 

would not have been affected. 

Soil loss and the hydraulic parameters 

Knapen et al. (2007) calculated the correlation of shear stress, unit length shear force, stream 

power and Reynolds number with the detachment capacity using several WEPP datasets. The 

best average correlation was determined for stream power with R² = 0.59. The R² values for 

the shear stress variable used in the WEPP datasets were never strong. Knapen et al. (2007, p. 

80f.) describes the shear stress as follows: ”Although the use of flow shear stress as soil 

157


detachment predictor can be contested, critical shear stress (τ cr ) and concentrated flow 

erodibility KC (...) have been selected as the most universal parameters to describe soil 

erosion resistance to concentrated flow.“ The correlations between these factors and the soil 

detachment capacities in our study showed very different results. There was not a single 

parameter that always showed the best correlation. 

Other groups have found linear correlations between a hydraulic parameter and an erosion 

parameter as well as in laboratory flume experiments (Partheniades and Paaswell, 1970, 

Nearing et al., 1997, Ghebreiyessus et al., 1994, Torri et al., 1987, Giménez and Govers, 

2002) and in field research (Elliot et al., 1989, Nearing et al., 1997, Nearing et al., 1999 b). 

We could not confirm these observations, in our field experiments there was no linear 

relationship between any hydraulic parameter and any erosion parameter. 

In a laboratory study, Nearing et al. (1991) measured flow shear stresses ranging from 0.5 to 2 

Pa, while tensile strengths ranged from 1 to 2 kPa, a difference in magnitude of 1000. Despite 

this, detachment rates of nearly 300 g m –2 s –1 were measured. Nearing explained this as being 

the result of turbulent burst events which are much greater than the average flow shear 

stresses. Nearing and Parker (1994) further investigated the influence of turbulence on shear 

stress. They showed that under turbulent flow conditions the same shear stress value results in 

a clearly higher detachment rate. Differences between detachment rates caused by turbulent 

and laminar flow increased with increasing shear stress value. 

This means that the influence of turbulence on soil erosion will be higher when hydraulic 

conditions lead to a high shear stress value than when shear stress values are in the lower 

range. This can be the reason that soil erosion models often over-predict small soil losses and 

under-predict large soil losses. Nearing (1998) explained this by the presence of natural 

variations in model data, which the model is not capable of capturing. These variations will 

affect a bias in the erosion predictions relative to values on the higher end versus those on the 

lower end of the range of measured values (Nearing 1998). 

Origin of the used equations 

Another reason for wich the use of the shear stress equation as it is commonly used does not 

deliver satisfactory results is the origin of this equation. The shear stress equation is deduced 

from the Navier-Stokes equations which describe the motion of fluids. The equations arise 

from applying Newton’s second law to fluid motion (net force on a particle is equal to the 

time rate of change of its linear momentum in an inertial reference frame), combined with the 

assumption that the fluid stress is the sum of a diffusing viscous term plus a pressure term. 

158


Using one of the Navier-Stokes equations, an incompressible fluid can be completely 

described; thus reducing hydrodynamic questions to a mathematical problem. But this 

problem consists of a system of second order nonlinear partial differential equations which 

require the most powerful computers to numerically solve even the easiest cases. For the 

general, 3-dimensional case, existence- uniqueness- and regularity statements are not yet 

proven. Indeed, the Clay Mathematics Institute (CMI) included this in their “Millennium 

Prize Problems” which represent the most important open problems in mathematics, and has 

offered a prize of US$ 1,000,000 for a solution or a counter example (Constantin, 2001, 

Fefferman, 2006, Seiler, 2002, Schneider, 2008, Temam, 2000, Wiegner, 1999). 

The inconsistencies between the experimental results and the process based model 

assumptions can be the consequence of several reasons, such as uncertainties in measurements 

on the one hand or, on the other hand, inconsistent and incomplete process representations 

within the models. Uncertainty in the measurement of soil erosion has been a strong point of 

discussion (Stroosnijder, 2005), which is certainly still not fully resolved. The experimental 

setup applied in this study aimed to minimize systematic errors and their propagation. The 

design of the inlet, the flume for runoff measurement and the monitoring of flow and 

sediment transport reduced disturbance to a minimum (Wirtz et al., 2010, Wirtz et al., 2012). 

The results of measurements were also within the range measured in other experiments (e.g. 

Knapen et al., 2007). This, in combination with qualitative process observations made during 

the experiments, allows us to draw the conclusion that the source of errors is found in the 

model concepts. 

In models, different parameters play an important role. It is to distinguish between the 

hydraulic parameter flow shear stress τ and the soil parameter critical shear stress τ c or τ cr . 

Shear stress exerted by flow must exceed the critical shear stress to cause erosion. In critical 

shear stress calculations, soil parameters like dry bulk density, grain size distribution and 

organic content are used, in shear stress calculation hydraulic parameters, roughness, flow 

velocity and fluid density are variables. Different research groups deleted or added different 

factors to adapt the equation to their research topic. As a consequence, the equations for 

calculating transport and detachment capacity, critical shear stress and shear stress have 

different forms in different publications. 

We assumed that shear stress or critical shear stress values are always defined in the unit [Pa 

= kg m -1 s -2 ]. Note that in each paper where the units of the variables were not always given, 

we assumed [Pa] when no other unit was defined by the author and calculated the unknown 

units of the used parameters considering this default. For a better comparison with the original 

159


literature, we did not homogenize the labelling of the different parameters, but used the ones 

given by the authors. That means different parameters can be labelled equally. As it can be 

seen in Table 5, for the calculation of shear stress exerted by flowing water, many different 

parameters have been taken into account. Even the physical definition of the parameter “shear 

stress” seems to be unclear. Some factors have been developed from empirical studies 

(equation 10, equation 11). In most cases, the theoretical basis of the equations is not clear. 

Equation 12 is derived from Landau and Lifchitz (1971). The critical shear stress is the force 

needed to detach a soil particle, so it corresponds to a soil parameter and therefore input for 

calculation should also be depending on soil characteristics. In the WEPP model (Table 6, 

equation 26-28), the critical shear stress is calculated using only soil parameters like texture, 

organic matter content and dry bulk density. However in some equations the so called 

“critical” shear stress consists of hydraulic parameters like water depth, water width or fluid 

density (Table 6, equations 17-20). In equation 21 hydraulic and soil parameters are used 

equally. In equation 22, 23 and 24 the empirical nature of the development is clear. According 

to equation 23 and 24 the critical shear stress is only dependent on a constant value and the 

relationship between given particle size and the subsurface d 50 . In equation 26, the typical 

parameters for calculating shear stress of flowing water are used to define critical shear stress. 

This method uses additionally the Manning friction factor, which is a descriptor of the soils 

surface roughness. Thus, the use of the term “critical shear stress” seems to be very unclear. 

The different equations for detachment and transport capacity were developed from data sets 

created from controlled laboratory experiments, field observations or field experiments. In 

equations 29-32 (Table 7), neither critical shear stress nor shear stress is used for calculation 

of the transport capacity. In equation 33, shear stress is used to calculate transport capacity, in 

equation 34 transport rate is calculated using shear stress and critical shear stress and in 

equation 35 the detachment capacity is calculated using critical shear stress and shear stress 

(see Table 7). Equation 33 is a modification of the Yalin (1963) equation from 1963 (Foster et 

al., 1995). In equation 34 and 35 it is clear to see that shear stress and critical shear stress are 

opponents, the important parameter is the difference between these two variables. If critical 

shear stress is higher than shear stress, no erosion can occur. A summary of these equations is 

given by Reid and Dunne (1996), on the EPA-homepage (2009) and in Hessel and Jetten 

(2007).It has been shown that the physical definition of the parameters is not clear and their 

mostly empirical foundation does not fit the high temporal and spatial variability of processes 

within a rill. Different processes dominate at different intensities and this fact causes high 

160


variability in sediment concentration, transport and detachment rates. But the spatial and 

temporal distribution of the different processes is apparently highly random. 

Table 5 Equations for calculating shear stress. 

Eq. 

Equation 

10 

τ = γ 

y 

b 

y 

( 

y 

a 

s b 2 

eff 

p 

i 

C 

it 

) 

τ = shear stress [Pa], γ = weight density of water (force/volume) [Pa], y = flow depth assuming 

laminar flow [m], b = time weighting factor in finite difference equation for continuity, s = sine 

of slope angle, y b /y p = the ratio of the flow depth on a smooth surface to that in the ponds from 

depressions and “dams” [m m -1 ], a = a coefficient to be estimated i eff = effective rainfall 

intensity [m s -1 ] 

C 

it 

y 

p 

= exp [ 0.21 ( 1)] 

y 

Foster (1982) 

11 = a (ρ ρ) g D 

12 

τ 

s 

b 

1.18 

ρ S = specific weight of the sediment [kg m -3 ], ρ = specific weight of the water [kg m -3 ] D = the 

particle size [m], a = an empirical factor between 0.039 and 0.09 

Shields (1936), Miller et al. (1977), Parker et al. (1982), Diplas (1987), Parker (1990), Komar 

(1987 a,b), Andrews (1983), Ashworth and Ferguson (1989 a,b), Komar and Carling (1991) 

τ = (σ 

g) 

2 

3 

( 3 

υ) 

1 

3 

*sin 

2 

3 

α 

q 

1 

3 

σ = fluid density [kg m -3 ], g = gravitation [9.81 m s -2 ], υ = kinematic viscosity [m 2 s -1 ] 

α = slope angle, q = runoff discharge rate per unit of width [kg m -1 s -1 ] 

Chisci et al. (1985) 

13 = σ g R* tan(γ) 

τ r 

τ r = runoff shear stress [Pa], σ = fluid density [kg m -3 ], g = acceleration of gravity [9.81 m s -2 ], R 

=hydraulic radius [m], γ = slope angle [°] 

Torri et al. (1987) 

γ 

τ = 

h 

L 

14 L 

R 

15 

γ = unit density of water [kg m -3 ], h L = head loss due to friction [m 2 s -2 ], R = hydraulic radius 

[m], L = channel length [m] 

Ghebreiyessus et al. (1994) 

τ 

s 

= ρ 

w 

g S R 

f 

f 

s 

tot 

ρ w = water density [kg m -3 ], g = gravitation factor [9.81 m s -2 ], S = slope, R = hydraulic radius 

[m], f s and f tot = Darcy-Weisbach friction factors for the bare soil and composite surface, 

161


respectively 

Nearing et al. (1997) 

16 τ = ρ g R S 

ρ = density of the fluid [kg m -3 ], g = gravitation factor [9.81 m s -2 ], R = hydraulic radius [m], S = 

sin(slope) 

Giménez and Govers (2002) 

Eq. 

17 

18 

19 

20 

21 

τ b 

τ b 

τ w 

τ w 

= γ 

= γ 

= γ 

= γ 

S 

S 

S 

S 

Table 6 Equations for calculating critical shear stress. 

D 

( 1 

B D 

for 

4 B 

D 

B 

for 0 

D 

) for 0 

B 

1 

2 

D 

B 

1 

2 

D 

B 

B B D 

( 1 ) for 

2 4 D B 

Equation 

1 

2 

1 

2 

τ b = critical bed shear stress, τ w = critical walls shear stress [Pa], γ = fluid density [kg m - 

3 ], S = slope [m m -1 ], D = water depth [m], B = water width [m] In Eq. 17, Ott and van 

Uchelen (1936) uses instead of D/2 the term D/B. 

Shields (1936), Ott and van Uchelen (1936) 

τ 

c 

D S 

γs 

γ 

( ) 

γ 

d 

D = mean depth [m], S = water surface slope [m m -1 ], γ = specific weight of fluid [kg m - 

3 ], γ S = specific weight of sediment [kg m -3 ], d = particle diameter [m] 

22 

23 

Graf (1971) 

τ 

α n 

= ( ) 

1.486 

2 

c 

γ w 

τ c = critical boundary shear stress [pounds per square foot], α = an empirical factor, n = 

Manning’s friction coefficient [m 1/3 s -1 ], γ w = unit weight of water [pounds per square 

foot] 

Partheniades and Paaswell (1970) 

τ 

c 

di 

= 0.0834 ( ) 

d 

50 

0.872 

162


24 di 

0.887 

τc 

= 0.0384 ( ) 

d50 

d i 

d 50 = relationship between given particle size and the subsurface d 50 

Andrews (1984), Andrews and Erman (1986) 

25 

26 

27 

28 

τ 

cr 

= ρ 

(ρ g 

u 

2 

cr 

n 

0.66 

= (ρ 

q 

g R 

0.66 

S 

0.7 

S) 

) 

cr 

cr 

ρ = density of the water [kg m -3 ], u cr = shear velocity [m s -1 ], g = gravitation factor [9.81 

m s -2 ], R = hydraulic radius [m], S = sin (slope), n = Manning friction factor [m 1/3 s -1 ], q 

= unit discharge [m 7/6 s] 

De Ploey (1990) 

τ c 

= 2.67 + 0.65 CLAY 0.058 VFS 

for cropland > 30 % sand 

τ c 

= 3.5 

for cropland < 30 % sand 

τ = 3.23 0.056 SAND 0.244 ORGMAT + 0.9 for rangeland 

c 

BD dry 

Clay = clay content [%], VFS = very fine sand content [%], SAND = sand content [%], 

ORGMAT= organic matter content [%] (1.724 times organic carbon content), BD dry = 

dry soil bulk density [g cm -3 ] 

Flanagan and Livingston (1995) 

Table 7 Equations for calculating transport and detachment capacity. 

No. 

Equation and Variables 

TC 

f 

TC = 

29 

TC 

( 1 

ρ 

S 

f 

) 

TC = transport capacity in clear water [g L -1 ], TC f = transport capacity in sedimentwater 

[g L -1 ], ρ S = density of solid material [kg m -3 ] 

Govers (1990) 

qb 

w 

TC = 

30 Q 

ρ 

S 

TC = transport capacity in clear water [g L -1 ], q b = volumetric bedload transport per 

unit width [m² s -1 ], w = flow width [m], ρ S = density of solid material [kg m -3 ], Q = 

runoff [m³ s -1 ] 

Abrahams et al. (2001), Low (1989), Rickenmann (1990) 

163


qS 

w 

TC = 

31 Q 

32 

33 

34 

35 

TC = transport capacity in clear water [g L -1 ], ρ S = density of solid material [kg m -3 ], w 

= flow width [m], Q = runoff [m³ s -1 ] 

Yalin (1993), Bagnold (1980) 

ρ 

f 

TC = 

( 1 

CP 

1E6 

CP 

) 

1E6 

TC = transport capacity in clear water [g L -1 ], ρ f = fluid density [kg m -3 ], C P = 

concentration [ppm] 

Yang (1973) 

1.5 

TC = k t 

τ 

f 

TC = transport capacity [kg s -1 ], k t = transport coefficient [m 0.5 s² kg -0.5 ], τ f = hydraulic 

shear acting on the soil [Pa] 

Foster et al. (1995) 

11.2 (τ τ 

QB 

= 

3 

(τ ) 

c 

c 

) 

4.5 

Q B = transport rate per unit of width [kg 1.5 m -1.5 s -3 ], τ c = threshold value of τ required to 

initiate particle motion, τ = shear stress [Pa] 

Parker (1979) 

D 

C 

= K 

r 

(τ 

τ 

cr 

) 

D C = detachment capacity [kg m -2 s -1 ], K r = rill erodibility factor [s m -1 ], τ = shear stress 

[Pa], τ cr = critical shear stress [Pa] 

Foster et al. (1995) 

Constant soil parameters? 

Another important fact which cannot be handled by the process based models is the 

heterogeneity in critical shear stress. In this study, we performed our experiments on one field 

with uniform treatment, hence the soil parameters are as constant as possible. As a 

consequence, we assumed the critical shear stress to be constant in our experiments. In a 

typical model, the critical shear stress for cropland with a sand content > 30% (at our test side: 

about 80%, mainly middle, fine and very fine sand) is calculated using the clay and the very 

fine sand content and these values are constant. This assumes a constant critical shear stress 

but in reality, this homogeneity is not found. The critical shear stress can also change between 

164


experiments or within one experiment caused by wetting and drying or by sealing and 

crusting. These changes are not represented in models. 

Better ideas? 

The results reported here do not show a simple linear relation between a single hydraulic 

parameter and soil detachment rate. Depending on the model purpose and scale, these factors 

can be used to predict the magnitude of rill detachment but they are not applicable for the 

simulation of rill erosion with high-resolution spatial and temporal change in processes. A 

promising approach is to use probability density functions to predict soil detachment. The 

newest, although not yet operational, version of this approach has been developed by 

Sidorchuk (Sidorchuk, 2002, Sidorchuk et al., 2004, Sidorchuk, 2005 a, Sidorchuk, 2005 b, 

Sidorchuk et al., 2008, Sidorchuk, 2009). But two decades ago Nearing et al. (1991) 

demonstrated mathematically the stochastic nature of the „critical hydraulic shear stress“ and 

recognize that shear stress as well as local soil resistance have to be thought of and 

characterized in terms of probability density functions instead of singular values. A stochastic 

approach is not itself new: The idea of process-based stochastic modelling of erosion dates 

back to the fundamental work of H.A. Einstein (1937). According to Sidorchuk (2005b), the 

main ideas which made the stochastic approach attainable for the conditions of shallow, 

rough-bed flows and cohesive soils have been formulated by Mirtskhoulava (1988, cited in 

Sidorchuk, 2005b). Other approaches to stochastic soil erosion modelling are those published 

by Wilson (1993a,b) and Nearing (1991), who presented a simple probabilistically based 

mathematical model for the detachment of cohesive soil particles by shallow turbulent flow. 

Govindaraju & Kavvas (1994) also developed and tested a spectral stochastic theory for 

analysing rill distribution and profiles on a hillslope. Lisle et al. (1998) derive a stochastic 

model of sediment particle motion which, given suitable averaging, is consistent with the 

ideas of Einstein (1937) and with the model proposed by Hairsine and Rose (1991). The 

conceptualization of this model has been corroborated experimentally by Shaw et al. (2008). 

On the basis of the aforementioned conceptual work, Sidorchuk (2005b) developed a 

stochastic model of cohesive soil erosion and deposition which is denoted hereafter a 3 rd 

generation soil erosion model. It is noticeable that the 3 rd generation models are not obtained 

by merely imposing probability distributions on the input variables of 2 nd generation models 

but constitute a new, physical approach. The RillGrow 1 and 2 models use the stochastic 

approach (Favis-Mortlock et al., 1998, 2000). That approach is capable of explicitly 

specifying the spatial location of the initiation and subsequent development of rills. 

165


Following the authors, RillGrow 1 has three main limitations: (1) many process descriptions 

(e.g. infiltration and deposition) are omitted, (2) the approach is very demanding of 

computational resources and (3) the model demands a great deal of data regarding 

microtopography (Favis-Mortlock et al., 1998). RillGrow 2 circumvents several but not (yet) 

all shortcomings (Favis-Mortlock et al., 2000). Following a personal communication from 

Favis-Mortlock (2012), RillGrow is now at version 6, and it is much more process-focused 

than earlier versions. The stochastic detachment relationship of Nearing (1991) is now used 

for flow detachment. Favis-Mortlock is currently writing up this version. 

5 Conclusions 

The results of this study clearly showed that the model concept of most process based soil 

erosion models is not suitable for modelling rill erosion processes. These models assume a 

linear relation between shear stress and soil detachment. That means, when input parameters 

for calculating shear stress are constant, or at least in a limited range, the erosion parameters 

should also be in a similar, limited range. In our experiments, hydraulic radius, flow velocity, 

slope and liquid density showed similar values but the resulting erosion parameters of 

sediment concentration, and detachment and transport rates showed variability values of more 

than 60%. The total measured rill erosion rates are the sum of erosion rates caused by a 

combination of different soil erosion processes with different spatial and temporal 

distribution. This combination cannot be described by one single equation. 

There are two different ways to address this conundrum. The first is to modify existing 

physical based model concepts so that different processes can be taken into account; the 

second is to head in a new direction, using the concept of stochastic soil erosion modelling. In 

both cases, much more field experimentation will be needed to provide the required data. A 

big question is whether or not the experimental setups currently employed can deliver the 

required data, or if totally new experimental setups will need to be developed. 

Following Rees (2002), there are three great frontiers in science: the very big, the very small, 

and the very complex. And erosion, which depends on turbulent behavior, is an example of 

the very complex. 

Acknowledgements 

This research was supported by the Internationales Graduiertenzentrum of Trier University. 

We thank all participants of the field trip to the Bardenas Reales in spring 2009 which 

supported the accomplishment of the experiments. A special thank goes (1) to our native 

166


speakers, which revised the complete paper and (2) to the reviewers whose comments helped 

to improve significantly the quality of the paper. 

References 

Abrahams, A.D., Li, G., 1996. Rill hydraulics on a semiarid hillslope, southern Arizona. Earth 

Surface Processes and Landforms, 21: 35-47. 

Abrahams, A.D., Gao, P., Aebly, F.A., 2000. Relation of sediment transport capacity to stone 

cover and size in rain-impacted interrill flow. Earth Surf Proc Land, 25: 497-504. 

Ad-hoc-Arbeitsgruppe Boden, 2005. Bodenkundliche Kartieranleitung. 5. Auflage, 

Bundesamt für Geowissenschaften und Rohstoff in Zusammenarbeit mit den staatlichen 

Geologischen Diensten der Bundesrepublik Deutschland. 

Ajayi, A.E., Horta, I.D.M.F., 2007. The effect of spatial variability of soil hydraulic properties 

on surface runoff processes. Anais XIII Simpósio Brasileiro de Sensoriamento Remoto, 

Florianópolis, Brasil, 21-26 April 2007, pp. 3243-3248. 

Ali, M., 2011. Sediment transport capacity for soil erosion modelling at hillslope scale: an 

experimental approach. Dissertation, Wageningen University 

Alonso, C.V., Bennett, S.J., Stein, O.R., 2002. Predicting headcut erosion and migration in 

upland flows. Water Resour Res, 38 (12): 1303-1317. 

Andrews, E.D., 1983. Entrainment of gravel from naturally sorted riverbed material. Geol Soc 

Am Bull, 94: 1225-1231. 

Andrews, E.D., 1984. Bed-material entrainment and hydraulic geometry of gravel-bed rivers 

in Colorado. Geol Soc Am Bull, 95(3): 371-378. 

Andrews, E.D., Erman, D.C., 1986. Persistence in the size distribution of superficial bed 

material during an extreme snowmelt flood. Water Resour Res, 22: 191-197. 

Ashworth, .PJ., Ferguson, R.I., 1989a. Size-selective entrainment of bed load in gravel bed 

streams. Water Resour Res, 25: 627-634. 

Ashworth, P.J., Ferguson, R.I., 1989b. Quantifying gravel deposition on river bars using 

flexible netting. J Sediment Res, 59(4): 623-624. 

Assouline, S., 2009. Drop size distributions and kinetic energy rates in variable intensity 

rainfall. Water Resour.Res, 45: W11501, doi: 10.1029/2009WR007927. 

Bagnold, R.A., 1963. Mechanics of marine sedimentation. In: M.N. Hill (Editor), The Sea: 

Ideas and Observations on Progress in the Study of the Seas, Vol. 3 – The Earth Beneath 

the Sea. Wiley-Interscience, London, pp. 507-528. 

167


Bagnold, R.A., 1966. An approach to the sediment transport problem from general physics. 

Geological Survey Professional paper 422-1, 37 pp. 

Bagnold, R.A., 1977. Bed load transport by natural rivers. Water Resour Res, 13: 303-312, 

Bagnold, R.A., 1980. An empirical correlation of bedload transport rates in flumes and natural 

rivers. Proc. Royal Society Series, A372: 453-473. 

Bell, J.B., Garcia, A.L., Williams, S.S., 2007. Numerical methods for the stochastic Landau- 

Lifshitz Navier-Stokes equations. Phys Rev E 76. 

Bennett, S.J., 1999. An Experimental Study of Headcut Growth and development in upland 

concentrated flows. USDA and Agricultural Research service Research report No. 13, 

190 pp. 

Bennett, S.J., Alonso, C.V., 2005. Kinematics of flow within headcut scour holes on 

hillslopes. Water Resour Res 41:W09418, doi:10.1029/2004WR003752. 

Bennett, S.J., Alonso, C.V., Prasad, S.N., Rönkens, M.J.M., 2000. Experiments on headcut 

growth and migration in concentrated flows typical of upland areas. Water Resour Res, 

36: 1911-1922. 

Bruno, C., Di Stefano, C., Ferro, V., 2008. Field investigation on rilling in the experimental 

Sparacia area, South Italy. Earth Surf Proc Land, 33: 263-279. 

Brunton, D.A., Bryan, R.B., 2000. Rill network development and sediment budgets. Earth 

Surf Proc Land, 25: 783-800. 

Bryan, R.B., 1990. Knickpoint evolution in rillwash. Catena, 17: 111-132. 

Bryan, R.B., Poesen, J., 1989. Laboratory experiment on the influence of slope length on 

runoff, percolation and rill development. Earth Surf Proc Land, 14: 211-231. 

Bryan, R.B., Govers, G., Poesen, J., 1989. The concept of soil erodibility and some problems 

of assessment and application. Catena, 16 (4-5): 393-412. 

Bryan, R.B., Hawke, R.M., Rockwell, D.L., 1998. The influence of subsurface moistureon rill 

system evolution. Earth Surf Proc Land, 23: 773-789. 

Casali, J., Loizu, J., Campo, M.A., De Santisteban, L.M., Álvarez-Mozos, J., 2006. Accuracy 

of methods for field assessment of rill and ephemeral gully erosion. Catena, 67: 128-138. 

Causapé, J., Quílet, D., Aragüés, R., 2004. Salt and nitrate concentrations in the surface 

waters of the CR-V irrigation district (Bardenas I, Spain): Diagnosis and prescriptions for 

reducing off-site contamination. J Hydrol, 295: 87-100. 

Causapé, J., Quílet, D., Aragüés, R., 2006. Groundwater quality in CR-V irrigation district 

(Bardenas I, Spain): Alternative scenarios to reduce off-site salt and nitrate 

contamination. Agr Water Manage, 84: 281-289. 

168


Chisci, G., Sfalanga, M., Torri, D., 1985. An experimental model for evaluating soil erosion 

on a single-rainstorm basis. In: S.A. El Swaify, W.C. Moldenhauer, A. Lo (Editors), Soil 

Erosion and Conservation. Soil conservation Society of America, Ankeny, Iowa, pp. 558- 

565. 

Constantin, P., 2001. Some open problems and research directions in the mathematical study 

of fluid dynamics. Mathematics unlimited-2001 and beyond. pp 353-360. 

De Ploey, J., 1990. Threshold conditions for thalweg gullying with special reference to loess 

areas. Catena Supplement, 17: 147-151. 

De Roo, A.P.J., Wesseling, C.G., Jetten, V.G., Ritsema, C.J., 1996. LISEM – a physically 

based hydrological and erosion model incorporated in a GIS. IAHS Publ. 235: 395-403. 

De Santisteban, L.M., Casalì, J., Lòpez, J.J., Giràldez, J.V., Poesen, J., Nachtergaele, J., 2005. 

Exploring the role of topography in small channelerosion. Earth Surf Proc Land, 30: 591- 

599. 

Desir, G., Marín, C., 2007. Factors controlling the erosion rates in a semi-arid zone (Bardenas 

Reales, NE-Spain). Catena, 71: 31-40. 

DIN 1319-1., 1995. Grundlagen der Messtechnik – Teil 1: Grundbegriffe. Deutsches Institut 

für Normung e.V., Ausgabe: 1995-01 , Deutsch. 

Diplas, P., 1987. Bedload transport in gravel-bed streams. J Hydraul Eng ASCE, 113: 277- 

292. 

Dunkerley, D., 2008. Rain event properties in nature and in rainfall simulation experiments: a 

comparative review with recommendations for increasingly systematic study and 

reporting. Hydrol Process, 22: 4415-4435. 

Einstein, H.A., 1937. Der Geschiebetrieb als Wahrscheinlichkeitsproblem, Dissertation, ETH 

Zürich. 

Elliot, W.J., Laflen, J.M., 1993. A Process-based rill erosion model. T. ASAE, 36(1): 35-72. 

Elliot, W.J., Liebenow, A.M., Laflen, J.M., Kohl, K.D., 1989. A compendium of soil 

erodibility data from WEPP cropland soil field erodibility experiments 1987 and 1988. 

NSERL Report No. 3, The Ohio State University, and USDA Agricultural Research 

Service, pp. 186. 

EPA-homepage: Channel Processes: Bedload transport. United States Environmental 

protection agency http://water.epa.gov/scitech/datait/tools/warsss/bedload.cfm. Accessed 

14 September 2010. 

Fan, J., Gao, H., Guo, B., 2010. Regularity criteria for the Navier-Stokes-Landau-Lifshitz 

system. J Math Anal Appl, 363: 29-37. 

169


Favis-Mortlock, D., Guerra, T., Boardman, J., 1998. A self-organizing dynamic systems 

approach to hillslope rill initiation and growth: model development and validation. IAHS 

Publ., 249: 53-61 

Favis-Mortlock, D.T., Boardman, J., Parsons, A.J., Lascelles, B., 2000. Emergence and 

erosion: a model for rill initiation and development. Hydrol. Process., 14: 2173-2205. 

Favis-Mortlock, D., Boardman, J., MacMillan, V., 2001. The limits of erosion modelling: 

why we should proceed with care. In: R.S. Harmon, W.W. Doe (Editors), Landscape 

erosion and evolution modeling. Kluuwer Academic/Plenum, New York, pp. 477-516. 

Favis-Mortlock, D., de Boer, D., 2003. Simple at heart? Landscapes as a self-organizing 

complex system. In: S. Trudgill, A. Roy (Editors), Contemporary meanings in Physical 

Geography: From what to why? Arnold Publishers, London. 

Fefferman, C.L., 2006. Existance and smoothness of the Navier-Stokes equation. The 

millennium prize problems. Clay Math. Inst., Cambridge, MA, pp. 57-67. 

Flanagan, D.C., Livingston, S.J., 1995. WEPP user summary, USDA-water erosion prediction 

project. NSERL Report No. 11. National soil erosion research Laboratory, pp. 141. 

Flanagan, D.C., Laflen, J.M., Meyer, L.D., 2003. Honoring the Universal Soil Loss Equation. 

American Society of Agricultural Engineers, Historic Landmark Dedication. 

Flores-Cervantes, J.H., Istanbulluoglu, E., Bras, R.L., 2006. Development of gullies on the 

landscape: A model of headcut retreat resulting from plunge pool erosion. J Geophys 

Res, 111:F01010, doi:10.1029/2004JF000226. 

Foster, G.R., 1982. Modelling the erosion process. In: C.T. Haan, H.P. Johnson, D.L. 

Brakensiek (Editors), Hydraulic Modelling of Small Watersheds. ASAE monograph 5, 

Hann CT, St. Joseph, MI, pp. 296-379. 

Foster, G.R., Huggins, L.F., Meyer, L.D., 1984. A laboratory study of rill hydraulics: I. 

Velocity relationships. T. ASAE, 27: 790-796. 

Foster, G.R., Flanagan, D.C., Nearing, M.A., Lane, L.J., Risse, L.M., Finkner, S.C., 1995. 

Hillslope erosion component. In: D.C. Flanagan, M.A. Nearing (Editors), USDA Water 

Erosion Prediction Project: Hillslope Profile and Watershed Model Documentation, 

Chapter 11, USDA-ARS NSERL Report 10. 

Ghebreiyessus, Y.T., Gantzer, C.J., Alberts, E.E., Lentz, R.W., 1994. Soil erosion by 

concentrated flow: shear stress and bulk density. T. ASAE, 37 (6): 1791-1797. 

Gilley, J.E., Kottwitz, E.R., Simanton, J.R., 1990. Hydraulic characteristics of rills. T. ASAE, 

33: 1900-1906. 

170


Giménez, R., Govers, G., 2002. Flow Detachment by Concentrated Flow on Smooth and 

Irregular Beds. Soil Sci Soc Am J, 66(5): 1475-1483. 

Giménez, R., Planchon, O., Silvera, N., Govers, G., 2004. Longitudinal velocity patterns and 

bed morphology interaction in a rill. Earth Surf Proc Land, 29: 105-114. 

Gordon, L.M., Bennett, S.J., Wells, R.R., Alonso, C.V., 2007. Ephemeral gully headcut 

development and migration in stratified soil. In: J. Casalí, R. Giménez (Editors). Progress 

in Gully Erosion Research, IV International Symposium on Gully erosion, Pamplona, 

Spain, 17-19 September 2007, pp. 52-53. 

Govers, G., 1987. Spatial and temporal variability in rill development processes at the 

Huldenberg experimental site. Catena Supplement, 8: 17-34. 

Govers, G., 1990. Empirical relationships for transport capacity of overland flow. IAHS 

publication, 189: 45-63. 

Govers, G., 1991. Rill erosion on arable land in central Belgium: Rates, controls and 

predictability. Catena, 18: 133-155. 

Govers, G., 1992a. Evaluation of transport capacity formulae for overland flow. In: A.J. 

Parsons, A.D. Abrahams (Editors), Overland flow: hydraulics and erosion mechanics, 

UCL Press, London, pp. 243-273. 

Govers, G., 1992b. Relationship between discharge, velocity and flow area for rills eroding 

loose, non layered materials. Earth Surf Proc Land, 17: 515-528. 

Govers, G., Poesen, J., 1988. Assessment of the interrill and rill contributions to total soil loss 

from an upland field plot. Geomorphology, 1: 343-354. 

Govers, G., Giménez, R., van Oost, K., 2007. Exploring the relationship between 

experiments, modelling and field observations. Earth Sci Rev, 84 (3-4): 87-102. 

Govindaraju, R.S., Kavvas, M.L., 1994. A spectral approach for analysing the rill structure 

over hillslopes. Part I. Development of stochastic theory. J Hydrol, 158(3-4): 333-347. 

Graf, W.H., 1971. Hydraulics of sediment transport. McGraw-Hill, New York. 

Hairsine, P.B., Rose, C.W., 1991. Rainfall detachment and deposition: Sediment transport in 

the absence of flow-driven processes. Soil Sci Soc Am J, 55 (2): 320-324. 

Hairsine, P.B., Rose, C.W., 1992. Modeling water erosion due to overland flow using 

physical principles, 2. Rill flow. Water Resour Res, 28: 245-250. 

Hagmann, J., 1996. Mechanical soil conservation with contour ridges: cure for, or cause of, 

rill erosion? Land Degrad Dev, 7: 145-160. 

Helming, K., Römkens, M.J.M., Prasad, S.N., Somme, H., 1999. Erosional development of 

small scale drainage networks. In: S. Hergarten, H.J. Neugebauer (Editors), Process 

171


Modelling and Landform Evolution, Lecture Notes in Earth Science, 78, Springer, 

Berlin, pp. 123-146. 

Hessel, R., Jetten, V., 2007. Suitability of transport equations in modelling soil erosion for a 

small Loess plateau catchment. Eng Geol, 91: 56-71. 

Huang, C., Bradford, J.M., Laflen, J.M., 1996. Evaluation of the detachment-transport 

coupling concept in the WEPP rill erosion equation. Soil Sci Soc Am J, 60: 734-739. 

Kinnell, P.I.A., 2005. Raindrop-impact-induced erosion processes and prediction: a review. 

Hydrol. Process., 19: 2815-2844. 

Kleinhans, M.G., Bierkens, M.F.P., van der Perk, M., 2010. HESS opinions. On the use of 

laboratory experimentation: „Hydrologists, bring out shovel and garden hoses and hit the 

dirt“. Hydrol Earth Syst Sc, 14: 369-382. 

Knapen, A., Poesen, J., Govers, G., Gyssels, G., Nachtergaele, J., 2007. Resistance of soils to 

concentrated flow erosion: A review. Earth Sci Rev, 80(1-2): 75-109. 

Kohl, K.D., 1988. Mechanics of rill headcutting. Dissertation, Iowa State University, Ames. 

Komer, P.D., 1987a. Selective grain entrainment by a current from a bed of mixed sizes: A 

reanalysis. J Sediment Petrol, 57: 203-211. 

Komar, P.D., 1987b. Selective gravel entrainment and the empirical evolution of flow 

competence. Sedimentology, 34: 1165-1176. 

Komar, P.D., Carling, P.A., 1991. Grain sorting in gravel-bed streams and the choice of 

particle sizes for flow-competence evaluations. Sedimentology, 38: 489-502. 

Kovacs, A., Parker, G., 1994. A new vectorial bedload formulation and its application to the 

time evolution of straight river channels. J Fluid Mec, 267: 153-183. 

Laflen, J.J., Elliott, W.J., Flanagan, D.C., Meyer, C.R., Nearing, M.A., 1997. WEPPpredicting 

water erosion using a process-based model. Journal of Soil and Water 

Conservation, 52: 96-102. 

Landau, L., Lifchitz, E., 1971. Mécaniques des fluids. MIR, Moscow. 

Lascelles, B., Favis-Mortlock, D.T., Parsons, A.J., Guerra, A.J.T., 2000. Spatial and temporal 

variation in two rainfall simulators: Implications for spatially explicit rainfall simulation 

experiments. Earth Surf. Process. Landforms, 25: 709-721. 

Li, G., Abrahams, A.D., Atkinson, J.F., 1996. Correction factors in the determination of mean 

velocity of overland flow. Earth Surface processes and Landforms, 21: 509-515. 

Lisle, I.G., Rose, C.W., Hogarth, W.L., Hairsine, P.B., Sander, G.C., Parlange, J.-Y., 1998. 

Stochastic sediment transport in soil erosion. J Hydrol, 204 (1-4): 217-230. 

172


Liu, B.Y., Nearing, M.A., Baffaut, C., Ascough, II J.C., 1996. The WEPP watershed model: 

III. Comparisons to measured data from small watersheds. T. ASAE, 40: 945-951. 

Low, H.S., 1989. Effect of sediment density on bed-load transport. J. Hydraul. Eng. ASAE, 

115: 124-138. 

Lyle, W.M., Smerdon, E.T., 1965. Relation of compaction and other soil properties to erosion 

resistance of soils. T. ASAE, 8: 419-422. 

Mancilla, G.A., Chen, S., McCool, D.K., 2005. Rill density prediction and flow velocity 

distribution on agricultural areas in the Pacific Northwest. Soil Till Res, 84: 54-66. 

Miller, M., McCave, I.N., Komar, P.D., 1977. Threshold sediment motion under 

unidirectional currents. Sedimentology, 24: 507-527. 

Mirtskhoulava, T.Y., 1988. Principles of Physics and Mechanics of Channel Erosion. 

Gidrometeoizdat: Leningrad (in Russian). 

Moncoqut, F., 2003. Le desert de Bardenas Reales et sa region. Editions Lavielle. 

Moore, I.D., Burch, G.J., 1986. Sediment transport capacity of sheet and rill flow: Application 

to unit stream power theory. Water Resour Res, 22: 1350-1360. 

Morgan, R.P.C., Quinton, J.N., Smith, R.E., Govers, G., Poesen, J.W.A., Auerswald, K., 

Chisci, G., Torri, D., Styczen, M.E., 1998. The European soil erosion model 

(EUROSEM): a dynamic approach for predicting sediment transport from field and small 

catchments. Earth Surface Processes and Landforms, 23: 527-544. 

Murelage, X., Suberbiola, X.P., De Lapparent de Broin, F., Rage, J.-C., Duffaud, S., Astibia, 

H., Badiola, A., 2002. Amphibians and Reptiles from the Early Miocene of the Bardenas 

Reales of Navarre (Ebro Basin, Iberian Peninsula). Geobis, 35: 347-365. 

Nearing, M.A., 1991. A probabilistic model of soil detachment by shallow turbulent flow. T. 

ASAE, 34 (1): 81-85. 

Nearing, M.A, 1998. Why soil erosion models over-predict small soil losses and under-predict 

large soil losses. Catena, 32: 15-22. 

Nearing, M.A., Parker, S.C., 1994. Detachment of soil by flowing water under turbulent and 

laminar conditions. Soil Sci Soc Am J, 58 (6): 1612-1614. 

Nearing, M.A., Foster, G.R., Lane, L.J., Finkner, S.C., 1989. A process-based soil erosion 

model for USDA - Water Erosion Predict Project technology. T. ASAE, 32: 1587-1593. 

Nearing, M.A., Bradford, J.M., Parker, S.C., 1991. Soil detachment by shallow flow at low 

slopes. Soil Sci Soc Am J, 55(2): 339-344. 

Nearing, M.A., Norton, L.D., Bulgakov, D.A., Larionov, G.A., West, L.T., Dontsova, K.M., 

1997. Hydraulics and Erosion in Eroding Rills. Water Resour Res, 33 (4): 865-876. 

173


Nearing, M.A., Govers, G., Norton, L.D., 1999a. Variability in soil erosion data from 

replicated plots. Soil Sci Soc Am J, 63: 1829-1835. 

Nearing, M.A., Simanton, J.R., Norton, L.D., Bulygin, S.J., Stone, J., 1999b. Soil erosion by 

surface water flow on a stony, semiarid hillslope. Earth Surf. Process. Landforms, 24: 

677-686. 

Ott, W.P., van Uchelen, J.C., 1936. Application of similarity principles and turbulence 

research to bed.load movement. Hydrodynamics Laboratory California Institute of 

Technology Publication No. 167, Soil conservation Service. 

Owoputi, L.O., Stolte, W.J., 1995, Soil detachment in the physically based soil erosion 

process: a review. T. ASAE, 38 (4): 1099-1110. 

Paola, C., Straub, K., Mohrig, D., Reinhardt, L., 2009. The "unreasonable effectiveness" of 

stratigraphic and geomorphic experiments. Earth Sci Rev, 97(1-4): 1-43. 

Parker, G., 1979. Hydraulic geometry of active gravel rivers. J. Hydr. Eng. Div. ASCE, 105: 

1185-1201. 

Parker, G., 1983. Discussion of “lateral bed load transport on side slopes” by S. Ikeda. J 

Hydraul Eng ASCE, 109: 197-199. 

Parker, G., 1990. Surface-based bedload transport relation for gravel rivers. J Hydraul Res, 

28: 417–436. 

Parker, G., Klingeman, P.C., McLean, D.G., 1982. Bedload and size distribution in paved 

gravel-bed streams. J. Hydr. Eng. Div. ASCE, 108: 544-571. 

Parsosn, A.J., Wainwright, J., Stone, P.M., Abrahams, A.D., 1999. Transmission losses in rills 

on dryland hillslopes. Hydrol. Process., 13: 2897-2905. 

Parsons, A.J., Wainwright, J., 2006. Depth distribution of interrill overland flow and the 

formation of rills. Hydrol. Process., 20: 1511-1523. 

Parsons, A.J., Wainwright, J., Brazier, R.E., Powell, D.M., 2006. Is sediment delivery a 

fallacy? Earth Surf. Process. Landforms, 31: 1325-1328. 

Partheniades, E., Paaswell, R.E., 1970. Erodibility of channels with cohesive boundary. J 

Hydr Eng Div ASCE: 755-771. 

Rapp, I., 1998. Effects of soil properties and experimental conditions on the rill erodibilities 

of selected soils. Dissertation, Faculty of Biological and Agricultural Sciences, 

University of Pretoria, South Africa. 

Rees, M., 2002. Our cosmic habitat. Princeton University Press, New Jersey. 

Regüés, D., Balasch, J.C., Castelltort, X., Soler, M., Gallart, F., 2000. Relación entre las 


174



Orientales). Cuadernos de Investigación Geográfica, 26: 41–65. 

Reid, D.M., Dunne, T., 1996. Rapid evaluation of sediment budgets. Catena Verlag, 

Reiskirchen, Germany. 

Rejman, J., Brodowski, R., 2005. Rill characteristics and sediment transport as a function of 

slope length during a storm event on loess soil. Earth Surf Proc Land, 30: 231-239. 

Rickenmann, D., 1991. Hyperconcentrated flow and sediment transport at steep slopes. J 

Hydraul Eng ASCE, 117: 1419-1439. 

Risse, L.M., Nearing, M.A., Nicks, A.D., Laflen, J.M., 1993. Assessment of error in the 

universal soil loss equation. Soil Sci Soc Am J, 57: 825-833. 

Robinson, K.M., Bennett, S.J., Casali, J., Hanson, G.J., 2000. Processes of headcut growth 

and migration in rills and gullies. Int J Sediment Res, 15(1): 69-82. 

Ruttimann, M., Schaub, D., Prasuhn, V., Ruegg, W., 1995. Measurement of runoff and soil 

erosion on regulary cultivated fields in Switzerland – some critical considerations. 

Catena, 25: 127-139. 

Sancho, C., Benito, G., Munoz, A., Pena, J.L., Longares, L.A., McDonald, E., Rhodes, E., 

Saz, M.A., 2007. Actividad alluvial durante la pequena Edad del Hielo en Bardenas 

Reales de Navarra. Geogaceta, 42: 111-114. 

Sancho, C., Pena, J.L., Munzo, A., Bonito, G., McDonald, E., Rhodes, E.J., Longares, L.A., 

2008. Holocene alluvial morphopedosedimentary record and environmental changes in 

the Bardenas Reales Natural Park (NE Spain). Catena, 73: 225-238. 

Scherer, U., 2008. Prozessbasierte Modellierung der Bodenerosion in einer Lösslandschaft. 

Dissertation, Fakultät für Bauingenieur-, Geo- und Umweltwissenschaften, Universität 

Fridericiana zu Karlsruhe (TH), Karlsruhe, Germany. 

Schneider, G., 2008. Ein Millenniumsproblem: Die globale Existenz und Eindeutigkeit glatter 

Lösungen der dreidimensionalen Navier-Stokes-Gleichungen. Mathematik-Online: 

Beiträge zu berühmten, gelösten und ungelösten Problemen, Nummer 2. 

Seeger, M., Errea, M.P., Beguería, S., Arnáez, J., Martí, C., García-Ruiz, J.M., 2004. 

Catchment soil moisture and rainfall characteristics as determinant factors for 

discharge/suspended sediment hysteretic loops in a small headwater catchment in the 

Spanish Pyrenees. Journal of Hydrology, 288: 299–311. 

Seiler, R., 2002. Die Navier-Stokes-Gleichung. Elemente der Mathematik, 57: 109-114. 

Shaw, S.B., Makhlouf, R., Walter, M.T., Parlange, J.-Y., 2008. Experimental testing of a 

stochastic sediment transport model. J Hydrol, 348(3-4): 425-430. 

175


Shields, A., 1936. Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die 

Geschiebebewegung. Dissertation, TU Berlin, Berlin, Germany. 

Sidorchuk, A., 2002. Stochastic Modelling of soil erosion and deposition. Proceedings of the 

12 th ISCO Conference, Beijing, China, 26-31 May 2002, pp. 136-142. 

Sidorchuk, A., 2005a. Stochastic components in the gully erosion modelling. Catena, 63: 299- 

317. 

Sidorchuk, A., 2005b. Stochastic modelling of erosion and deposition in cohesive soils. 

Hydrol Process, 19: 1399-1417. 

Sidorchuk, A., 2009. High-Frequency variability of aggregate transport under water erosion of 

well-structured soils. Eurasian Soil Sci, 42(5): 543-552. 

Sidorchuk, A., Smith, A., Nikora, V., 2004. Probability distribution function approach in 

stochastic modelling of soil erosion. In: V. Golosov, V. Belyaev, D.E. Walling (Editors), 

Sediment transfer trough the fluvial system, IHAS Publ. 288, pp. 345-353. 

Sidorchuk, A., Schmidt, J., Cooper, G., 2008. Variability of shallow overland flow velocity 

and soil aggregate transport observed with digital videography. Hydrol Process, 22: 

4035-4048. 

Slattery, M.C., Bryan, R.B., 1992. Hydraulic conditions for rill incision under simulated 

rainfall: a laboratory experiment. Earth Surf Proc Land, 8: 97-105. 

Stefanovic, J.R., Bryan, R.B., 2009. Flow energy and channel adjustments in rills developed 

in loamy sand and sandy loam soils. Earth Surf Proc Land, 34: 133-144. 

Stroosnijder, L., 2005. Measurement of erosion: Is it possible? Catena, 64: 162-173. 

Temam, R., 2000. Some developments on Navier-Stokes equations in the second half of the 

20 th century. In: J.-P. Pier (Editor), Development of mathematics 1950-2000, Birkhäuser, 

Basel, Switzerland, pp. 1049-1106. 

Torri, D., Dfalanga, M., Chisci, G., 1987. Threshold conditions for incipient rilling. Catena 

Supplement, 8: 97-105. 

Wagenbrenner, J.W., Robichaud, P.R., Elliot, W.J., 2010. Rill erosion in natural and disturbed 

forests: 2. Modeling Approaches. Water Resour Res, 46:doi:10.1029/2009WR008315. 

Wendt, R.C., Alberts, E.E., Hjelmfelt, J.R., 1986. Variability of runoff and soil loss from 

fallow experimental plots. Soil Sci Soc Am J, 50: 730-736. 

Wiegner, M., 1999. The Navier-Stokes equations – a neverending challenge? Jahresbericht 

Deutsch. Math.-Verein, 101 (1): 1-25. 

Wilson, B.N., 1993a. Development of a fundamentally-based detachment model. T. ASAE, 

36 (4): 1105-1114. 

176


Wilson, B.N., 1993b. Evaluation of a fundamentally-based detachment model. T. ASAE, 36 

(4): 1115-1122. 

Wirtz, S., Seeger, M., Ries, J.B., 2010. The rill experiment as a method to approach a 

quantification of rill erosion process activity. Z Geomorphol, 54 (1): 47-64. 

Wirtz, S., Seeger, M., Ries, J.B., 2012. Field experiments for understanding and quantification 

of rill erosion processes. Catena, 91: 21-34. 

Wishmeier, W.C., Smith, D.D., 1965. Predicting Rainfall Erosion Losses from Cropland East 

of the Rocky Mountains. Agricultural Handbook No. 282. US Department of 

Agriculture, Washington DC. 

Wishmeier, W.C., Smith, D.D., 1978. Predicting Rainfall Erosion Losses – A Guide to 

conservation Planning. Agricultural Handbook No. 537. US Department of Agriculture, 

Washington DC. 

Yalin, M.S., 1963. An expression for bedload transportation. J Hydr Eng Div ASCE, 89: 221- 

250. 

Yang, C.T., 1972. Unit stream power and sediment transport. J Hydr Eng Div ASCE, 98: 

1805-1825. 

Yang, C.T., 1973. Incipient motion and sediment transport. J Hydr Eng Div ASCE, 99: 1679- 

1703. 

Zhang, X.C., Nearing, M.A., Risse, L.M., McGregor, K.C., 1996. Evaluation of runoff and 

soil loss predictions using natural runoff plot data. T. ASAE, 39: 855-863. 

Zhang, G., Liu, B., Liu, G., He, X., Nearing, M.A., 2003. Detachment of undisturbed soil by 

shallow flow. Soil Sci Soc Am. J, 67: 713-719. 

Zhang, G., Luo, R., Cao, Y., Shen, R., Zhang, X.C., 2010. Correction factor to dye-measured 

flow velocity under varying water and sediment discharges. Journal of Hydrology, 389: 

205-213. 

Zhu, J.C., Gantzer, C.J., Peyton, R.L., Alberst, E.E., Anderson, S.H., 1995. Simulated smallchannel 

bed scour and head cut erosion rates compared. Soil Sci Soc Am J, 59 (1): 211- 

218. 

177


Kapitel 6 

Wirtz et al. (subm.2012): Applicability of different hydraulic parameters to describe soil 

detachment in eroding rills. PLoSOne. 

178


Applicability of different hydraulic parameters to describe soil detachment in eroding 

rills 

Wirtz S. a , Seeger M. a,b , Zell A. c , Wagner C. c , Wagner J.-F. d , Ries J.B. a 

a: Dep. of Physical Geography, Trier University, Germany; b: Dep. of Land Degradation and 

Development, Wageningen University, The Netherlands; c: Dep. 7.3- Technical Physics, 

Saarland University, Germany; d: Dep. of Geology, Trier University, Germany 

Abstract 

This paper presents the comparison of experimental results with assumptions used in 

numerical models. The aim of the field experiments is to test the linear relationship between 

different hydraulic parameters and soil detachment. The correlations between shear stress, 

unit length shear force, stream power, unit stream power and effective stream power and the 

detachment rate show that there is not a single parameter that continuously displays the best 

correlation. The best match not only changes from one experiment to another, but also from 

one measuring point to another. Different processes in rill erosion are responsible for the 

changing correlations. However, not all these procedures are considered in soil erosion 

models. Hence, hydraulic parameters alone are not sufficient to predict detachment rates. 

They predict the fluvial incising in the rill's bottom, but the main sediment sources are not 

considered sufficiently in its equations. The results of this study show that there is still a lack 

in understanding of the physical processes underlying soil erosion. Exerted forces, soil 

stability and its expression, the abstraction of the detachment and transport processes in 

shallow flowing water are still subject of unclear description and dependence. 

Keywords 

Soil erosion, rill hydraulics, shear stress, rill erosion, dynamic viscosity, field experiments 


Soil erosion models use different composite factors to describe and predict soil detachment 

and transport capacity. The factors used most frequently are average shear stress [1-4], unit 

length shear force [5], stream power [4, 6-9], unit stream power [10, 11] and effective stream 

power [12, 13]. Giménez and Govers [5] define the different hydraulic parameters as follows: 

179


(1) shear stress is the drag force exerted by the flow on the bed, (2) stream power is defined as 

the energy of the flow dissipated to the bed based on total discharge, (3) unit stream power is 

a product of slope and flow velocity, (4) the effective stream power can be seen as the power 

over a given rill cross section and (5) the unit length shear force is a hydraulic parameter 

calculated on a unit length basis [5]. 

In most cases, a linear equation describes the relation between the hydraulic parameters 

mentioned above and the detachment rate. By exceeding a certain threshold, erosion by 

concentrated flow begins and detachment rate increases. This threshold has a positive x-axis 

intercept, which means, there is no detachment below this point. 

Another option is to consider concentrated flow erosion as a nonlinear threshold phenomenon 

or as a two-part linear threshold phenomenon: below the threshold soil detachment takes place 

(first linear relationship) but after exceeding the threshold, detachment rate increases much 

faster (second linear relationship) [14]. But is this linear relationship really suitable? 

Knapen et al. [14] calculated the correlation between shear stress, unit length shear force, 

stream power and Reynolds number and the detachment rate from several WEPP datasets. 

The best average correlation was determined for stream power with R² = 0.59. The WEPPused 

shear stress is a variable that reaches only low R² values for all of the tested data sets. 

Knapen et al. [14, p. 80f.] describes the shear stress as follows: “Although the use of flow 

shear stress as soil detachment predictor can be contested, critical shear stress (τ cr ) and 

concentrated flow erodibility KC (...) have been selected as the most universal parameters to 

describe soil erosion resistance to concentrated flow.” The correlations between these factors 

and the soil detachment rate show very different results. There is not a single parameter that 

always shows the best correlation. These considerations lead to 2 main questions: 

- Are soil erosion, detachment and transport, directly dependent on water flow 

characteristics? 

- Are these concepts, as implemented in soil erosion models, suitable to describe rill 

erosion? 

These questions have been tackled by many research groups that have been searching for the 

equation that suits their observations best [1-13, 15-42]. However, taking into consideration 

the numerous and variable results, a deeper insight into the rill erosion processes on hillslopes 

is needed. To get this insight, different strategies can be applied [43]: (I) Modelling, (II) 

laboratory experiments (III) field observations and (IV) field experiments. Each of these 

methods shows different advantages and disadvantages. 

180


Due to difficulties to measure certain parameters, models have to be calibrated. During this 

process, the phenomenon of equifinality can appear: different parameter sets show the same 

result. Another point of criticism in model developing methods is that parameters for rill 

hydraulics are often adapted from equations made for describing flow behaviour in rivers. 

Govers and his colleagues [13, 44] showed that these equations are not suitable for rill erosion 

processes. Therefore, there is often a mismatch between model results and observed or 

measured “reality” [43]. Additionally, models only project the concepts of the designer, not 

necessarily the reality. Herein, there is a reproducibility of the modelling results, contrasting 

with the measurements, which often have a high inconsistency and can be modelled by a 

flexible set of input variables. 

In laboratory experiments, the initial and boundary conditions are well controlled. Soil 

parameters are well known and rill forms and slope can be adapted to the specific question. 

Thus, physical laws can be tested/ controlled in a well defined environment. However, 

Giménez and Govers [5] showed that parameters determined under laboratory conditions are 

not easily transformable to natural environments. One disadvantage of former laboratory 

experiments or field observations is that in most cases only total runoff and sediment output 

are measured while the relative contribution of the individual processes is not considered [45]. 

Field data is as close as possible to reality. Nevertheless, observations as well as experiments 

show certain disadvantages: (I) Measurement techniques may disturb the observed processes, 

(II) time scale of human observations is shorter than that of the process under study, (III) 

some processes cannot be measured directly or indirectly and (IV) some processes are chaotic 

and the spatial and temporal variations are difficult to specify 

[43]. 

The linear or two-part-linear relationship between soil detachment and hydraulic parameters 

used in soil erosion models is in most cases deduced from laboratory experiments. The 

question to be answered is: Are these relationships suitable for erosion processes in natural 

rills? Thus, the experiments have been accomplished in the field and not in artificial 

laboratory rills. The setup used enables to measure the input parameters for calculating 

hydraulic parameters. Therefore, it is no need to build on estimations as it is done in the small 

number of published field experiments. The advantages of laboratory experiments are 

combined with the advantage of testing natural rills. That means in all experiments, the same 

experimental setup was used (similar inflow intensity, same water quantity, same sampling 

scheme, same measurement of hydraulic parameters) and these experiments have been 

accomplished under field conditions (no artificial laboratory rills in bulk substrates but 

181


naturally developed rills in naturally developed soils). The purpose of the field experiments 

was to quantify in a detailed temporal and spatial resolution the soil erosion dynamics in 

natural rills under concentrated flow and to compare the measured sediment dynamics with 

those calculated by means of the most common detachment and transport equations. 

The aims of this paper are 

1) to elucidate the relationship between hydraulic parameters such as shear stress, unit 

length shear force, unit stream power, stream power, effective stream power and the 

Reynolds number and soil detachment in natural rills. 

2) An additional aim is to explain the reasons for the obvious problems of the physically 

based soil erosion models in reflecting the processes in rills. 

3) Finally a basic consideration is employed: Are the currently used model approaches 

able to describe rill erosion with all involved processes in general? 

The overall aim of this paper is to have a critical view on concepts for modeling rill erosion 

based on experiments performed in naturally developed rills. 


Ethics Statement: 

No specific permits were required for the described field studies. The mayors of the towns 

next to the study sites or the owners of the fields were informed about the intended activities 

and were asked for permission. The test sites Freila, Negratin and Salada are abandoned fields 

which are sporadically used as pasture for goats or sheep and in Belerda the experiment was 

accomplished on an almond field. The locations Freila, Negratin end Salada are not privatelyowned 

and permission was granted from the owner of the study site Belerda. None of the 

study sites are protected in any way and the field studies did not involve endangered or 

protected species. 

Study areas: 

The four study areas in Andalusia are located at Negratin, Freila, Salada and Belerda. UTM 

coordinates of the tested rills are given in Table 1. 

182


Table 1 Temperature, precipitation, northing and easting of the four test areas. 

Tested Rill 

Meteorological 

station 

Average 

annual 

temperature 

Annual 

precipitation 

Northing of 

the rill 

Easting of 

the rill 

Freila 1+3 Baza 14.2 °C 368 mm 4154368 509860 

Freila 2 Baza 14.2 °C 368 mm 4154398 509826 

Negratin Baza 14.2 °C 368 mm 4156324 505710 

Salada 

Embalse 

Valdeinfierno 

13.4 °C 311 mm 4187266 595761 

Belerda Granada 15.6 °C 473 mm 4133440 478070 

Negratin and Freila: The areas are located within the Hoya de Baza sedimentary basin and 

composed of marls, in which calcareous Regosols have developed. The climate is semi-arid 

and vegetation is dominated by low shrubs and Stipa tenacissima grass tussocks. The land 

cover at the south side of the Negratin-dam is dominated by abandoned cereal fields, which 

are extensively grazed by sheep and agricultural land comprised mainly of cereal dry-farming 

and almond grooves [46]. 

Salada: Located at the SE-margin of the Betic range (SE-Spain), inside the penibetic complex. 

The area is composed of conglomerates with a clayey to loamy matrix, in which Regosols as 

well as to fairly developed (Calcic) Cambisols have developed. Vegetation is similar to that 

found in the Freila and Negratin-area. The climate is semi-arid too, but less accentuated than 

in the previously mentioned area [46]. Here a mixed pattern of rainfed agricultural areas, 

mainly cereals, olives and almonds, and abandoned or uncultivated regions is to find. 

Belerda: This test area is located in the Guadix basin. The parent material consists of tertiary 

and quaternary conglomerates, sands, silts and clays. The soil texture class following the FAO 

[47] is a silty clay loam. The land use is separated into cultivated areas, with almond and olive 

groves, and abandoned agricultural fields [48]. The climate is, though still semi-arid, 

characterised by higher average annual temperatures and precipitations in comparison with 

the other test zones. 

The climatic parameters of the test fields are summarized in table 1. 

Tested rills: 

The main descriptors of the rills are summarized in table 2; photographies of the rills are 

presented in figure 1. 

183


Figure 1 Photographies of the tested rills 

Table 2 Rill parameters: Grain size class limits are from [49], texture class is determined 

following [47]. 

Freila 1 Freila 2 Freila 3 Negratin Salada Belerda 

Ø Slope 

[°] 

9.4 7.7 9.4 5.6 25.6 16.9 

Max. Slope 

[°] 

15.2 14.1 15.2 12.9 7.3 12.5 

Tested flow 

length [m] 

16 21 16 30 17 23 

Texture class SL SL SL SiL SiCL L 

Gravel > 2000 µm [%] 30 30 30 1 1 13 

Sand 2000-630 µm [%] 14 14 14 1 2 10 

630-200 µm [%] 14 14 14 5 2 10 

184


200-125 µm [%] 13 13 13 6 1 8 

125-63 µm [%] 16 16 16 11 7 17 

Silt 63-20 µm [%] 13 13 13 11 17 13 

20-6.3 µm [%] 10 10 10 20 17 13 

6.3-2 µm [%] 11 11 11 24 24 14 

Clay < 2 µm [%] 9 9 9 21 29 15 

Starting soil 

moisture [% w/w] 

3.1 3.5 3.1 3.1 5.8 2.4 

K t 

[s 2 m 0.5 kg -0.5 ] 

Location 

WEPP dataset 

Maximum 

width [m] 

Maximum 

depth [m] 

Vegetation 

cover [%] 

Rock fragment 

cover [%] 

Grain density 

[g cm -3 ] 

Dry bulk density 

[g cm -3 ] 

Org. material 

[%] 

Critical shear 

stress [Pa] 

0.0090 0.0090 0.0090 0.0095 0.0096 0.0093 

Academy Academy Academy Frederick Mexico Caribou 

~ 0.4 ~ 2.2 ~ 0.4 ~ 0.4 ~ 0.5 ~ 0.3 

~ 0.05 ~ 0.7 ~ 0.05 ~ 0.2 ~ 0.25 ~ 0.15 

~ 40 ~ 40 ~ 40 ~ 0 ~ 15 ~ 5 

~ 80 ~ 80 ~ 80 ~ 5 ~ 20 ~ 50 

2.69 2.69 2.69 2.65 2.66 2.61 

1.44 1.55 1.44 1.57 1.52 1.68 

1.29 1.29 1.29 1.75 2.97 1.34 

1.97 2.07 1.97 2.93 3.20 2.77 

Land use rangeland rangeland rangeland rangeland rangeland cropland 

The tested rills in Freila have developed on a sandy loam with high gravel content. Sand 

content is 57 % with a relatively homogeneous contribution between coarse, medium, fine and 

very fine sand. The same is true in the silt fraction, the 34 % are homogeneously contributed 

in the complete silt fraction between 63 and 2 µm. The rills show all a dense rock fragment 

cover and the highest vegetation cover of the four test sides. 

In Negratin, the soil material is nearly gravel free, coarse, medium and fine sand also show 

low amounts, most of the fine material is in the grain size class < 20 µm. The rock fragment 

185


cover in the rill is higher than the gravel content of the soil material thus it is possible that 

residual rock fragment accumulation has occurred. 

In Salada the grain size distribution is similar to Negratin. The highest account of the fine soil 

material is in the class < 63 µm. The residual rock fragment accumulation is formed even 

more clearly as in Negratin; the vegetation cover is relatively high compared to the other test 

sites. 

The rill in Salada is the only rill that has developed in an actually used agricultural field. The 

soil material is composed by a mixture of all particle size classes from gravel to clay. The 

rock fragment cover is high compared to the other test sites and the vegetation cover 

comparatively low. This test site shows the highest dry bulk density which can be declared by 

the actual agricultural use. 

Methods: 

Rill experiment (RE): 

The rill experiments consist of two runs: first the rill is tested under field conditions (run a); in 

a second run (run b), approximately 15 minutes later, the same rill is tested under almost 

saturated soil conditions. With a motor driven pump, a constant discharge of 250 or 330 L 

min -1 is maintained during 4 respectively 3 minutes, resulting in a total water inflow of 1,000 

L. Mobilisation of material at the inflow has been avoided. The flow velocity within the rill is 

characterized by the travel time of the waterfront and of two colour tracers (started at 1 and 2 

minutes of the experiment), measured for every meter using a chronograph. By means of this 

procedure, three velocity curves are recorded and changes in flow dynamics can be detected. 

As colour tracers, food colourings (E 124 (red) and E 13 (blue)) are used for reasons of safety. 

The rill's slope is characterized by measuring with a spring bow of 1m range and a digital 

spirit level. It must be considered that slope measuring provides only average slopes for 1 

meter. A step or a knick-point in the rill is not accounted, but its position and height are 

recorded. 

At three measuring points (MP1-3) always four water samples are taken: the first one as soon 

as the waterfront has reached the sampling point, the second 30 seconds later, the third after 

1:30 minutes and the fourth 2:30 minutes after the arrival of the water. The (suspended) 

sediment concentration SSC is determined by filtration of the samples in laboratory [50]. 

At each measuring point, rill cross section was measured. With a laser rangefinder, the 

distance between sensor and rill bottom was measured in 0.002 m steps. This allows an 

accurate calculation of the rills cross section area and an estimation of the rills volume. 

186


Water level was continuously measured by ultrasonic sensors at each measuring point. 

Descriptors for soil detachment: 

Soil detachment can be described by shear stress τ, unit length shear force Γ, stream power ω, 

unit stream power ω U and effective stream power ω eff . 

* g * R * S 

[Pa] Eq. (1) 

* g * A* 

S * 

[N m -1 ] Eq. (2) 

W P 

* g * R * S * v * v [W m -2 ] Eq. (3) 

U 

S * v 

[m s -1 ] Eq. (4) 

1.5 1.5 

( * v) 

eff 

[W m -1 ] Eq. (5) 

2 

2 

3 

3 

d d 

with ρ = liquid density [kg m -3 ], g the gravitational acceleration (9.81 m s -2 ), R the hydraulic 

radius [m], A the flow cross section area [m²], S the effective slope (sin(slope angle)), W P the 

wetted perimeter [m], v the flow velocity [m s -1 ] and d the water depth [m]; abbreviations of 

the units are Pa = Pascal, N = Newton, W = Watt. 

Reynolds number describes the balance between the inertial flow forces represented by the 

product in the numerator and the viscous forces as described by the dynamic viscosity in the 

denominator. It is a criterion for stability of a flowing medium. When Reynolds number is 

small, viscous forces dominate the motion and inertial ones can be ignored whereas at high 

Reynolds numbers inertial forces dominate and it is often possible to ignore viscosity [51]. 

Reynolds Number Re is calculated as follows: 

*v * R 

Re Eq. (6) 

with ρ = liquid density [ kg m -3 ], v = flow velocity [m s -1 ], R = hydraulic radius [m] and η = 

dynamic viscosity [Pa s]. 

Liquid density is calculated using sediment concentration and grain density. The use of 

water’s density is not practicable due to sediment concentrations of more than 400 g L -1 . 

Grain density was measured by a capillary pycnometer following DIN 18124 [52]. Flow 

velocity for each sample is interpolated between three measured velocities (arrival of the 

waterfront and arrival of the two colour tracers). Hydraulic radius and wetted cross section 

area can be calculated by measuring water level and the rill profile. 

The viscosity of the sediment suspensions was measured with a shear rate controlled 

rheometer (Haake MARS from Thermo Fisher Scientific, Karlsruhe, Germany) and a cone- 

187


plate geometry with an angle of 2° and a diameter of 60 mm [53]. The shear rate γ is defined 

as: 

dv 

dy 

Eq. (7) 

with v = fluid velocity and y = the gap between the cone and base plate. The rheomter 

controls the shear rate and measures the shear stress τ, from which the viscosity η is 

calculated via 

Eq. (8) 

The sample volume was always 2.0 ml and the cell was tempered to 20 °C +/- 0.01 °C. Data 

points were taken at shear rates between 150 s -1 and 1500 s -1 . The viscosity does not depend 

on the shear rate. This is according to theoretical considerations. For a suspension of 

monodisperse particles one expects a linear relation [54, 55] for volume concentrations up to 

approximately 10%. 

Detachment rate D R [kg s -1 m -2 ] is calculated from the measured sediment concentrations and 

different hydraulic parameters: 

D 

R 

SSC * v * A 

L * W 

P 

with SSC = sediment concentration [g L -1 = kg m -3 ] and L = flow length [m]. 

Eq. (9) 

For the calculation of the critical shear stress, the equations from the WEPP model [34] is 

used. It is to separate between “cropland with sand content > 30%” and “rangeland”. 

cr 

( cropland ) 2.67 0.065*(% clay ) 0.058*(% very fine sand ) 

Eq. (10) 

cr 

( rangeland ) 3.23 0.056*(% sand ) 0.244*(% org. 

mat.) 

0.9*( dry bulk density ) 

Eq. (11) 

For quantification of the different processes in the rill, the transport rate T R [kg s -1 ] and the 

transport capacity T C [kg s -1 ] are to calculate: 

T R 

SSC * v* 

A 

Eq. (12) 

1.5 

T C 

R * K t 

* 

Eq. (13) 

Kt [s 2 m 0.5 kg -0.5 ] is a transport coefficient depending on soil substrate. The Kt value of the 

WEPP substrate which was most similar to the given test site conditions was used. 

3 Results 

3.1 Initial data 

188


The used parameters show a wide range of data. In most cases (12 of 19), the standard 

deviation is higher than the mean values, the highest standard deviation – mean - percentage 

reaches the transport capacity (224 %), the effective stream power (188.9 %), the sediment 

concentration (168.3 %) and detachment and transport rate (both 150 %). The lowest 

percentage is calculated for sample density (0.5 %). All initial data are presented in 

supporting information tables S1-S18 and the statistical values of the data in table 3. 

Table 3 Statistical values of the initial data. 

Maximum Minimum Mean Standard Deviation Percentage from Mean 

SSC [g L -1 ] 422.30 0.001 52.15 87.78 168.3 

D R [kg s -1 m -2 ] 0.96 0.001 0.10 0.15 150.0 

T R [lg s -1 ] 2.06 0.001 0.16 0.24 150.0 

р [g cm -3 ] 1.26 1.00 1.03 0.005 0.5 

Slope [°] 24.50 1.70 9.73 6.90 70.9 

T C [kg s -1 ] 3.38 0.001 0.25 0.56 224.0 

v [m s -1 ] 2.94 0.04 0.79 0.49 62.0 

η [kg s -1 m -1 ] 0.00311 0.00100 0.00126 0.00044 34.9 

Water depth [cm] 21.00 0.20 3.99 4.23 106.0 

A [cm²] 877.69 0.80 149.21 195.84 131.3 

W P [cm] 107.58 4.85 38.21 24.16 63.2 

R [cm] 9.65 0.10 2.92 2.12 72.6 

τ [Pa] 246.70 0.96 52.38 55.18 105.3 

Г [N m -1 ] 172.58 0.10 23.99 35.10 146.3 

ω [W m -2 ] 365.28 0.31 41.54 55.91 134.6 

ω U [m s -1 ] 0.88 0.001 0.14 0.17 121.4 

ω eff [W m -1 ] 37864.55 5.81 3807.14 7192.32 188.9 

Re [ ] 86918.88 237.00 19053.94 16226.56 85.2 

τ - τ cr [Pa] 244.73 -1.46 49.89 55.11 110.5 

3.2 Dynamic viscosity 

The measured liquid's dynamic viscosities show a clear correlation to sediment concentration 

(see figure 2), and increases with sediment concentration. Visible deviations from the trend 

line were noted in samples with low sediment concentrations, which were often rich on 

transported organic material. The small branchlets with low weight implicate a low sediment 

concentration, but in rheometer measurements, they tilt and a high shear stress is erroneously 

measured. The trend line equation has been calculated for samples from different test sites, 

the R²-value of 0.92 indicates that this equation can be used for further experiments. 

189


Figure 2 Correlation between sediment concentration and the dynamic viscosity 

3.3 Correlations between detachment rate and hydraulic parameters 

The correlations between the detachment rate and different hydraulic parameters show the 

complete possible range from R² = 0 up to R² = 0.99 (see Table 4). Trend lines are increasing, 

decreasing and about constant, it is not possible to find any clear regularity. Only 40 of 252 

correlations (about 16 %) show an increasing trend line with an R² value ≥ 0.7. The highest 

average R²-value is calculated for the (τ-τ cr ) – detachment rate - relationship if all R² values 

are used (0.53), if only the R²- values with increasing trend line are considered in calculation, 

the τ – detachment rate relationship shows the highest average R² (0.55). Separating the 

experiments into two groups, Freila 1-3 with low sediment concentrations (LSSC) and 

Negratin, Salada, Belerda with high sediment concentrations (HSSC), it is noticeable that the 

LSSC-experiments clearly show higher R²-values than the HSSC-experiments, whether all R²values 

or only the R²-values of correlations with increasing trend line are used. Indicating 

that, the influence of hydraulic parameters is higher for low sediment concentrations or in 

other words, high sediment concentrations are not caused by hydraulic parameters. 

Table 4 R² - values between hydraulic parameter and the detachment rate. 

τ Г ω ω U ω eff Re τ - τ cr 

Freila 1 run a MP 1 0.29 0 0.12 0 0.02 - 0.02 - 0.00 0 0.02 - 0.29 0 

MP 2 0.49 0 0.55 0 0.49 + 0.01 0 0.48 + 0.49 + 0.49 0 

MP 3 0.18 + 0.18 + 0.01 + 0.94 - 0.01 - 0.02 - 0.18 + 

Freila 1 run b MP 1 0.03 0 0.06 0 0.41 - 0.47 - 0.33 - 0.51 - 0.03 0 

MP 2 0.95 0 0.98 0 0.95 + 0.30 0 0.94 + 0.95 + 0.95 0 

MP 3 0.16 + 0.15 + 0.00 0 0.15 - 0.02 - 0.00 0 0.16 + 

Freila 2 run a MP 1 0.81 + 0.91 + 0.17 + 0.45 - 0.32 - 0.01 + 0.81 + 

190


MP 2 0.08 - 0.08 - 0.58 - 0.61 - 0.37 - 0.61 - 0.08 0 

MP 3 0.8 - 0.79 - 0.97 - 0.78 - 0.94 - 0.98 - 0.80 - 

Freila 2 run b MP 1 0.84 - 0.85 - 0.99 - 0.84 - 0.92 - 0.99 - 0.84 - 

MP 2 0.99 - 0.99 - 0.58 - 0.53 - 0.19 - 0.62 - 0.99 - 

MP 3 0.92 - 0.92 - 0.22 - 0.08 - 0.13 - 0.27 - 0.92 - 

Freila 3 run a MP 1 0.97 + 0.98 + 0.14 - 0.69 - 0.43 - 0.36 - 0.97 - 

MP 2 0.88 - 0.82 - 0.89 - 0.92 + 0.89 - 0.94 - 0.88 - 

MP 3 0.80 + 0.81 + 0.62 - 0.99 - 0.86 - 0.78 - 0.80 + 

Freila 3 run b MP 1 0.96 + 0.96 + 0.93 - 0.99 - 0.94 - 0.94 - 0.96 + 

MP 2 0.64 - 0.60 - 0.68 + 0.72 + 0.74 + 0.79 + 0.64 - 

MP 3 0.93 + 0.93 + 0.26 + 0.03 + 0.09 + 0.19 + 0.93 + 

Negratin run a MP 1 0.03 - 0.03 - 0.16 - 0.23 - 0.01 + 0.20 - 0.03 - 

MP 2 0.60 + 0.53 + 0.22 + 0.05 + 0.06 + 0.14 + 0.60 + 

MP 3 0.31 - 0.09 + 0.19 + 0.96 + 0.15 0 0.23 0 0.05 0 

Negratin run b MP 1 0.86 - 0.86 - 0.53 - 0.51 - 0.00 0 0.58 - 0.86 - 

MP 2 0.14 + 0.19 + 0.16 + 0.08 + 0.17 0 0.14 + 0.14 + 

MP 3 0.31 + 0.27 + 0.39 + 0.24 + 0.99 0 0.79 0 0.31 0 

Salada run a MP 1 0.44 + 0.45 + 0.70 + 0.64 + 0.70 + 0.67 + 0.44 + 

MP 2 0.78 + 0.81 + 0.22 + 0.00 0 0.02 + 0.12 + 0.78 + 

MP 3 0.09 - 0.07 - 0.00 0 0.02 0 0.01 0 0.00 0 0.09 - 

Salada run b MP 1 0.23 - 0.18 - 0.19 - 0.27 - 0.17 - 0.20 - 0.23 - 

MP 2 0.86 + 0.87 + 0.01 - 0.18 - 0.05 - 0.03 - 0.86 + 

MP 3 0.00 - 0.00 - 0.03 0 0.02 0 0.05 0 0.02 0 0.00 0 

Belerda run a MP 1 0.35 - 0.35 - 0.25 + 0.28 + 0.26 + 0.08 + 0.34 - 

MP 2 0.71 + 0.55 + 0.02 0 0.85 - 0.92 - 0.23 - 0.71 + 

MP 3 0.27 + 0.19 + 0.47 + 0.31 + 0.78 + 0.00 0 0.27 + 

Belerda run b MP 1 0.12 + 0.07 + 0.05 - 0.46 - 0.59 - 0.37 - 0.12 + 

MP 2 0.06 + 0.20 + 0.00 0 0.01 0 0.02 - 0.16 - 0.06 + 

MP 3 0.71 + 0.74 + 0.88 + 0.86 + 0.83 + 0.72 + 0.71 + 

Mean 1 0.52 0.50 0.37 0.43 0.40 0.39 0.53 

Mean 2 0.55 0.52 0.40 0.46 0.45 0.39 0.53 

Mean 3 0.65 0.65 0.50 0.53 0.48 0.53 0.65 

Mean 4 0.69 0.70 0.43 0.56 0.56 0.49 0.64 

Mean 5 0.38 0.36 0.25 0.33 0.32 0.26 0.39 

Mean 6 0.44 0.41 0.39 0.43 0.52 0.35 0.45 

MP = measuring point, τ = shear stress, Г = unit length shear force, ω = stream power, ω U = unit stream power, ω eff = 

effective stream power, Re = Reynolds number, + indicates increasing trend line, - indicates decreasing trend line, 0 indicates 

a nearly constant trend line, Mean 1 = all values, Mean 2 = only values with increasing trendline, Mean 3 = all Freila 

experiments, Mean 4 = Negratin, Salada, Belerda all values, Mean 5 = Freila only values with increasing trend line, Mean 6 = 

Negratin, Salada, Belerda only values with increasing trend lines 

3.4 Quantification of different erosion processes 

The quantification of the different processes consists of several steps. One further model 

assumption is, that the transport rate cannot exceed the transport capacity, sedimentation 

191


processes would reduce the transport rate to the transport capacity [56]. Transport capacity 

calculation uses shear stress, meaning if transport rate is higher than the capacity, proceses 

without link to shear stress such as bank failure and headcut retreat provide the material. 

Therefore, it is possible to calculate the percentage of shear-stress-independent-providedmaterial. 

The transport of loose material is somewhere in between, it is caused by shear stress 

but dry bulk density and hence the critical shear stress which has do be exceeded is lower than 

on “non loosened” substrate. Figure 3 shows the relationships between the measured transport 

rates and the predicted transport capacities. From 144 samples, in 82 cases the transport rate 

exceeds the capacity, this is about 57 %. Table 5 presents the differences between transport 

rates and transport capacities as well as the percentage of transport rate exceeding the capacity 

and hence the percentage of processes which are not controlled by the influence of shear 

stress. The percentage of material which is transported by processes independent of shear 

stress is 41.5 % in mean. The distribution is uneven: in the three Freila-experiments, the mean 

is 24.3 % and in Negratin, Salada and Belerda, the value is 58.7 %. The second group shows 

clearly higher sediment concentrations that means, the processes independent of shear stress 

provide higher sediment concentrations than the shear stress-based processes. 

Figure 3 Transport rate vs. Transport capacity 

192


Table 5 Transport rates vs. Transport capacities. 

run-MP-time Freila1 Freila 2 Freila 3 Negratin Salada Belerda 

Transport rate T R [kg s -1 ] - Transport capacity T C [kg s -1 ] 

a - 1 - 0:00 0.016496 0.208367 0.299736 0.356133 0.090648 0.449332 

a - 1 - 0:30 0.009216 -0.000042 -0.002630 0.388589 -0.068663 0.658430 

a - 1 - 1:30 0.028119 -0.009571 -0.011526 0.302982 -0.008596 0.347591 

a - 1 - 2:30 0.003356 0.008419 -0.018163 0.377529 0.129568 0.340157 

a - 2 - 0:00 0.000700 0.016861 -0.122188 0.080985 -0.049255 0.206128 

a - 2 - 0:30 0.000594 -0.003886 -1.661911 0.239944 -0.227338 0.075105 

a - 2 - 1:30 0.000078 -0.003910 -2.256325 0.167504 -0.360192 0.036567 

a - 2 - 2:30 -0.070511 -0.009096 -3.036197 0.191535 -0.060043 0.035613 

a - 3 - 0:00 0.218935 0.034645 0.337938 0.039447 0.126165 0.725246 

a - 3 - 0:30 0.036412 -0.594298 0.059926 0.039858 -0.158184 1.890184 

a - 3 - 1:30 0.012344 -0.618707 0.021373 0.035472 -0.289620 0.162081 

a - 3 - 2:30 0.005022 -0.637078 0.000277 0.040050 -0.421114 0.126305 

b - 1 - 0:00 0.058696 0.033665 -0.109527 0.544266 0.005208 0.093669 

b - 1 - 0:30 -0.000152 0.000836 -0.062758 0.311392 -0.161699 0.210084 

b - 1 - 1:30 0.000136 -0.005232 -0.033282 0.268657 -0.151983 0.007109 

b - 1 - 2:30 -0.001141 -0.007456 -0.038459 0.232281 -0.219765 0.006954 

b - 2 - 0:00 0.000120 0.027868 -1.587432 0.109482 -0.443133 0.478729 

b - 2 - 0:30 -0.000007 -0.011142 -2.043042 0.152084 -0.356465 0.023048 

b - 2 - 1:30 -0.068115 -0.014524 -2.539236 0.124697 -0.119275 0.165872 

b - 2 - 2:30 -0.001477 -0.013833 -3.356041 0.183860 -0.202332 0.071039 

b - 3 - 0:00 0.001240 0.188280 0.178267 0.038147 -0.132203 -0.044270 

b - 3 - 0:30 0.003910 -0.641102 0.033766 0.025673 -0.369358 0.379557 

b - 3 - 1:30 -0.198913 -0.656871 -0.020963 0.013890 -0.582478 0.584281 

b - 3 - 2:30 -0.230061 -0.693729 -0.041146 0.016264 -0.734992 0.764599 

Percentage of T R exceeding T C 

a - 1 - 0:00 92.9 78.0 78.9 94.0 55.4 96.8 

a - 1 - 0:30 87.8 0 0 93.0 0 97.6 

a - 1 - 1:30 95.6 0 0 91.3 0 95.4 

a - 1 - 2:30 72.7 42.6 0 91.7 41.8 87.9 

a - 2 - 0:00 96.5 49.9 0 97.1 0 85.1 

a - 2 - 0:30 65.0 0 0 92.7 0 89.0 

a - 2 - 1:30 4.8 0 0 91.4 0 94.1 

a - 2 - 2:30 0 0 0 87.4 0 86.1 

a - 3 - 0:00 91.1 12.0 81.4 99.7 40.0 82.7 

a - 3 - 0:30 86.8 0 68.8 99.8 0 91.8 

a - 3 - 1:30 43.5 0 44.1 99.7 0 54.5 

a - 3 - 2:30 20.4 0 0.6 99.6 0 42.6 

b - 1 - 0:00 97.8 90.3 0 95.9 6.8 78.8 

193


b - 1 - 0:30 0 5.8 0 91.5 0 92.9 

b - 1 - 1:30 9.7 0 0 90.4 0 58.9 

b - 1 - 2:30 0 0 0 87.5 0 22.9 

b - 2 - 0:00 94.9 62.1 0 97.3 0 92.6 

b - 2 - 0:30 0 0 0 88.7 0 59.4 

b - 2 - 1:30 0 0 0 84.5 0 96.4 

b - 2 - 2:30 0 0 0 83.9 0 82.3 

b - 3 - 0:00 0.5 42.2 59.0 99.7 0 0 

b - 3 - 0:30 32.5 0 44.1 99.4 0 72.4 

b - 3 - 1:30 0 0 0 99.4 0 80.9 

b - 3 - 2:30 0 0 0 99.3 0 84.1 

Mean 41.4 16.0 15.7 94.0 6.0 76.1 

Mean 24.3 58.7 

Mean 41.5 

4 Discussion 

A comparison with results of other research groups shows that the measured values are in a 

realistic range. Ghebreiyessus [3] measured shear stress values up to 40 Pa, in the experiments 

of Nearing et al. [4] Reynolds numbers up to 100000 and unit stream power values up to 10 m 

s -1 were reached. Giménez & Govers [5] found unit stream power values up to 0.4 m s -1 and 

unit length shear force values up to 6 N m -1 , in the paper of Zhang et al. [9], shear stress 

values up to 30 Pa and unit stream power values up to 0.5 m s -1 are published. Govers [13] 

measured shear stress values up to 100 Pa and effective stream power values up to 10000 W 

m -1 . The presented measurements are in the same order of magnitude and therefore realistic. 

But in contradiction with the cited papers, there are no clear linear correlations between 

hydraulic parameters and erosion parameters in the results of the field experiments. Therefore, 

these outcomes indicate that linear models are not applicable for description of experimental 

processes in natural rills. The question to be answered is: why doesn’t this concept that has 

been used for over 30 years work? 

In literature, four possible reasons can be found. (I) Unclear calculation and definition of the 

used parameters, (II) disregarding the influence of turbulence, (III) responsibility of processes 

which are not controlled by shear stress for material transport and (IV) a high spatial and 

temporal variability of those processes. 

The first reason could be the unclear calculation of shear stress. It is to differentiate between 

flow shear stress τ, a hydraulic parameter, and critical shear stress τ c or τ cr , a soil parameter 

which is similar to soil strength. Shear stress exerted by flow must exceed the critical shear 

stress to cause erosion. 

194


For calculation of shear stress exerted by flowing water, hydraulic parameters, roughness, 

flow velocity and fluid density have been taken into account. The actual version of the shear 

stress equation calculates the average shear stress by depth averaging of momentum equation 

for steady uniform flow per area and time, but this definition doesn’t fit to all definitions used 

in literature. Some factors have been developed from empirical studies [15-26]. In most cases, 

the theoretical basis of the equations is not clear. The formula used in Chisci et al. [27] is 

derived from Landau and Lifchitz [57]. Other versions of the Landau-Lifchitz equation are to 

find in literature [2-5]. 

The critical shear stress is the force needed to detach a soil particle. So it corresponds to a soil 

parameter and therefore, input for calculations should also be depending on soil 

characteristics. Only in the WEPP model [34], the critical shear stress is calculated using only 

soil parameters like texture, organic matter content and dry bulk density. But in some 

equations the so called “critical” shear stress consists of hydraulic parameters like water 

depth, water width, Manning friction factor or fluid density [16, 28, 33], hydraulic and soil 

parameters are used equally [34]. In the studies of Partheniades & Paaswell [30], Andrews 

[31] and Andrews & Erman [32] the empirical nature of the development is clearly noticeable. 

That means the equations are not deduced from physical laws but from empirical studies. 

In many studies [12, 35, 37-41], neither critical shear stress nor shear stress are used for the 

calculation of the transport capacity. In other studies shear stress is used to calculate transport 

capacity and detachment capacity [36] or transport rate [42] and critical shear stress to 

calculate the detachment capacity [36]. In both cases it is clear that shear stress and critical 

shear stress operate against each other, the important parameter is the difference between 

these two variables. 

A summary of these equations can be found in Reid and Dunne [66], on the EPA-homepage 

[67] and in Hessel and Jetten [68]. 

The second reason for the bad correlations between hydraulic parameter and soil detachment 

can be the lack of turbulence parameters in the equations. 

In the study of Knapen et al. [14] the Reynolds number shows very different correlations to 

the detachment rate, the same is to notice in the given results of this study. The reason could 

be that the turbulence, described by the Reynolds number, does not directly operate on 

substrate, it influences the acting shear stress, that means the calculated shear stress is much 

lower than the operating shear stress. This relation has been confirmed in several studies. 

Nearing et al. [69] found that turbulence can increase the active shear stress by a factor of 

several thousands. They measured flow shear stresses ranged from 0.5 to 2 Pa, while tensile 

195


strengths ranged from 1 to 2 kPa, a difference in magnitude of 1000. Despite this conflict, 

detachment rates of nearly 300 g m -2 s -1 were measured. He explained this result with 

turbulent burst events which are much greater than the average flow shear stresses. Another 

study about the influence of turbulence on detachment rates was published by Nearing & 

Parker [70]. They showed that under turbulent flow conditions the same shear stress value 

caused a clearly higher detachment rate. In their flume experiments the difference between 

detachment rate caused by turbulent and laminar flow increased with increasing shear stress 

value. That means, if given hydraulic conditions lead to a high shear stress value, the 

influence of turbulence on soil erosion is higher than in low shear stress value ranges. 

The shear stress equation as well as those related to the other hydraulic parameters assumes 

that drag forces are dominant for controlling erosion. But rill erosion is the result of the 

combination of different processes including headcut erosion, sidewall sloughing, tunnelling, 

micro-piping, slaking piping and sapping [14, 45, 71-75]. This is the third reason for the 

problems of the model equations. The percentage of headcutting in the different studies 

ranges between “four times higher than the contribution of bed scours” [75] to “60 % of total 

rill erosion” [76]. Stefanovic and Bryan [77] showed that concentrated flow causes sediment 

production primarily from knickpoints, chutes, meanders and bank failure. Govers [45] 

distinguished between hydraulic erosion, mass wasting processes on rill sidewalls, gullying 

and piping. Hydraulic rill erosion mostly occurred during three extreme runoff events. Mass 

wasting processes caused 37 % of total erosion in rills. Gullying, the retreat erosion at 

knickpoints and headcuts caused about 12% of rill erosion rates. In the presented experiments, 

mainly mass wasting and gullying processes occurred, so the correlations between hydraulic 

parameters and detachment rate are mostly low. But the hydraulic rill erosion only occurs in 

extreme runoff events, in most cases, the runoff values are too low to cause this process. The 

percentage of material which is transported independent of shear stress is very high on the 

water front samples. Here the transport of loose material is probably more important than in 

the other samples. That means this process is mainly independent of shear stress. In these 

cases of transport rate vs. transport capacity < 1 the independence of shear stress cannot be 

excluded, in the other cases the processes controlled by shear stress can occur. It is to 

conclude that in the case of T R > T C , not only shear stress controlled processes provide the 

material; at least the difference between T R and T C is caused by processes independent of 

shear stress. 

The presented experiments show that the correlation between hydraulic parameters and 

detachment rate does neither change from one experiment to another nor from one run to 

196


another but from one measuring point and run to another. Thus, sediment producing processes 

change with high spatial and temporal variability. This is the fourth reason for model 

problems. It is very difficult to propose a single factor that always describes the soil 

detachment satisfactory. The high variability of erosion processes, even under controlled 

experimental conditions, has been shown in different studies, measured variability shows a 

wide range between 3.4 and 173.2 % [78-83]. This is partially the result of non-homogeneous 

parameters concerning soil characteristics and rainfall. On experimental plots, infiltration 

rates and soil aggregate stability can be highly variable [84] as well as the rainfall shows a 

high spatial and temporal variability [85]. Therefore, the input parameters to the different 

measurements reflected in the mentioned studies were not really comparable. Nevertheless, 

the results also make clear that modelling soil erosion has to include uncertainty in model 

input as well as in the data used for model calibration and validation. 

In the field, the spatial and temporal variability of soil conditions cannot be avoided, and is, 

furthermore, part of the investigations. Thus, additional input parameters as rainfall or flow 

should be maintained constant in the experiments to generate reproducible data. The high 

variability in soil erosion processes cannot be represented by a single factor like shear stress. 

The results show that there is not a simple linear correlation between a certain hydraulic 

parameter and soil detachment rate. Depending on model purpose and scale, the factors can be 

used to predict the magnitude of rill detachment but they are not applicable for the simulation 

of rill erosion with high-resolution spatial and temporal change in processes. 

A newer approach is the use of probability density functions to predict soil detachment [86, 

87]. Sidorchuk gives two sources of stochasticity in erosion modelling: (1) the necessity of 

spatial and temporal averaging when determining deterministic equations, which describe 

concentrated flow erosion and (2) the fact that the main erosion factors, if these can be 

determined anyway, can only be measured with limited accuracy. This is not the first attempt 

to model erosion by relating the probability of soil detachment with the excess of erosion 

driving forces over soil erosion resistance forces. Other papers were published by Nearing 

[88], Wilson [89] and Sidorchuk [90-95]. One of the earliest publications about stochastic in 

erosion processes has been published by Einstein [96]. These stochastic models reduce the 

number of empirical components, but this approach seems to be too complicated [14] – yet. 

5 Conclusion 

The results show that simple linear correlation between hydraulic parameter and soil 

detachment is not suitable, at least in natural rills. The reason for that is the combination of 

197


different processes that cause different amounts of soil erosion. Shear stress only describes 

one process. The results clearly show that there is not one fixed parameters that always 

predict soil detachment best. Applicability of one certain hydraulic parameter to predict the 

sediment concentration changes at a certain point in time within few minutes because the 

temporal and spatial distribution of the different erosion processes is highly randomly 

determined. Therefore, it might be more useful to formulate results in probalistic terms. This 

is required since the 1990s [89, 91] and implemented since the 2000s especially by the 

working group of Sidorchuk [90, 94-98]. But first, much more field experiments are needed to 

provide the required data. 


The research was supported by the ‘Internationale Graduiertenzentrum’ of Trier University 

and the ‘Freundeskreis Trierer Universität e.V.’. Additionally, we thank all participants of the 

field trip to Andalusia in September 2009 who supported the performance of the experiments 

and Olli and Seta for revising the whole paper. 

References 

1. Lyle WM, Smerdon ET (1965) Relation of compaction and other soil properties to 

erosion resistance of soils. Transactions of the ASAE 8: 419-422. 

2. Torri D, Dfalanga M, Chisci G (1987) Threshold conditions for incipient rilling. 

Catena Supplement 8: 97-105. 

3. Ghebreiyessus YT, Gantzer CJ, Alberts EE, Lentz RW (1994) Soil erosion by 

concentrated flow: shear stress and bulk density. Transactions of the ASAE 37 (6): 

1791-1797. 

4. Nearing MA, Norton LD, Bulgakov DA, Larionov GA, West LT, Dontsova KM 

(1997) Hydraulics and Erosion in Eroding Rills. Water Resources Research 33 (4): 

865-876. 

5. Giménez R, Govers G (2002) Flow Detachment by Concentrated Flow on Smooth 

and Irregular Beds. Soil Sci Soc Am J 66(5): 1475-1483. 

6. Bagnold RA (1977) Bed load transport by natural rivers. Water resources Research 

13: 303-312. 

7. Hairsine PB, Rose CW (1992) Modeling water erosion due to overland flow using 

physical principles, 2. Rill flow. Water resources Research 28: 245-250. 

198


8. Elliot WJ, Laflen JM (1993) A Process-based rill erosion model. Transactions of 

the ASAE 36 (1): 35-72. 

9. Zhang G, Liu B, Liu G, He X, Nearing MA (2003): Detachment of undisturbed 

soil by shallow flow. Soil Science Society of America Journal 67: 713-719. 

10. Yang CT (1972) Unit stream power and sediment transport. J. Hydraulics Div. 

Am. Soc. Civil Eng. 98: 1805-1825. 

11. Moore ID, Burch GJ (1986) Sediment transport capacity of sheet and rill flow: 

Application to unit stream power theory. Water Resour. Res. 22: 1350-1360. 

12. Bagnold RA (1980): An empirical correlation of bedload transport rates in flumes 

and natural rivers. Proc. Royal Society Series A372: 453-473. 

13. Govers G (1992) Evaluation of transport capacity formulae for overland flow. In: 

Parsons AJ, Abrahams AD editors. Overland flow: hydraulics and erosion 

mechanics. London: UCL Press. pp. 243-273. 

14. Knapen A, Poesen J, Govers G, Gyssels G, Nachtergaele J (2007): Resistance of 

soils to concentrated flow erosion: A review. Earth-Science Reviews 80(1-2): 75- 

109. 

15. Foster GR (1982) Modelling the erosion process. In: Johnson HP, Brakensiek DL, 

editors. Hydraulic Modelling of Small Watersheds. St. Joseph, MI: ASAE 

monograph 5, Hann CT. 

16. Shields A (1936) Anwendung der Ähnlichkeitsmechanik und der 

Turbulenzforschung auf die Geschiebebewegung. Berlin: Dissertation, TU Berlin. 

17. Miller M, McCave IN, Komar PD (1977) Threshold sediment motion under 

unidirectional currents. Sedimentology 24: 507-527. 

18. Parker G, Klingeman PC, McLean DG (1982) Bedload and size distribution in 

paved gravel-bed streams. Journal of the Hydraulics Division, American Society of 

Civil Engineers 108: 544-571. 

19. Diplas P (1987) Bedload transport in gravel-bed streams. J. Hydraul. Eng. ASCE 

113: 277-292. 

20. Parker G (1990) Surface-based bedload transport relation for gravel rivers. J. 

Hydraul. Res. 28: 417–436. 

21. Komar PD (1987 a) Selective grain entrainment by a current from a bed of mixed 

sizes: A reanalysis. J. Sediment. Petrol. 57: 203-211. 

22. Komar PD (1987 b) Selective gravel entrainment and the empirical evaluation of 

flow competence. Sedimentology 34: 1165-1176. 

199


23. Andrews ED (1983) Entrainment of gravel from naturally sorted riverbed material. 

Geol. Soc. Am. Bull. 94: 1225-1231. 

24. Ashworth PJ, Ferguson RI (1989 a) Size-selective entrainment of bed load in 

gravel bed streams. Water Resources Research 25: 627-634. 

25. Ashworth PJ, Ferguson RI (1989 b) Quantifying gravel deposition on river bars 

using flexible netting. Journal of Sedimentary Research Vol. 59 No. 4: 623-624. 

26. Komar PD, Carling PA (1991) Grain sorting in gravel-bed streams and the choice 

of particle sizes for flow-competence evaluations. Sedimentology 38: 489-502. 

27. Chisci G, Sfalanga M, Torri D (1985) An experimental model for evaluating soil 

erosion on a single-rainstorm basis. In: El-Swaify SA, Moldenhauer WC, Lo A, 

editors. Soil Erosion and Conservation. Ankeny, Iowa: Soil conservation Society 

of America. pp. 558-565. 

28. Ott WP, van Uchelen JC (1936) Application of similarity principles and turbulence 

research to bedload movement. Hydrodynamics Laboratory California Institute of 

Technology Publication No. 167. Soil conservation Service. 

29. Graf WH (1971) Hydraulics of sediment transport. New York: McGraw-Hill. 

30. Partheniades E, Paaswell RE (1970) Erodibility of channels with cohesive 

boundary. Journal of the Hydraulic Division, Proceedings of the American Society 

of civil Engineers: 755-771. 

31. Andrews ED (1984) Bed-material entrainment and hydraulic geometry of gravelbed 

rivers in Colorado. Geological Society of America Bulletin 95(3): 371-378. 

32. Andrews ED, Erman DC (1986) Persistence in the size distribution of superficial 

bed material during an extreme snowmelt flood. Water Resources Research 22: 

191-197. 

33. De Ploey J (1990) Threshold conditions for thalweg gullying with special 

reference to loess areas. Catena Supplement 17: 147-151. 

34. Flanagan DC, Livingston SJ (1995) WEPP user summary, USDA-water erosion 

prediction project. NSERL Report No. 11. National soil erosion research 

Laboratory. 

35. Yalin MS (1963) An expression for bedload transportation. J. Hydr. Eng. Div. 

ASCE 89: 221-250. 

36. Foster GR, Flanagan DC, Nearing MA, Lane LJ, Risse LM, Finkner SC (1995) 

Hillslope erosion component. In: USDA Water Erosion Prediction Project: 

200


Hillslope Profile and Watershed Model Documentation, Chapter 11, USDA-ARS 

NSERL Report 10. 

37. Govers G (1991) Rill erosion on arable land in central Belgium: Rates, controls 

and predictability. Catena 18: 133-155. 

38. Abrahams AD, Gao P, Aebly FA (2000) Relation of sediment transport capacity to 

stone cover and size in rain-impacted interrill flow. Earth Surf. Proc.Land. 25: 

497-504. 

39. Low HS (1989) Effect of sediment density on bed-load transport. J. Hydraul. Eng. 

ASAE 115: 124-138. 

40. Rickenmann D (1991) Hyperconcentrated flow and sediment transport at steep 

slopes. J. Hydraul. Eng. ASCE 117: 1419-1439. 

41. Yang CT (1973) Incipient motion and sediment transport. J. Hydr. Eng. Div. 

ASCE 99: 1679-1703. 

42. Parker G (1979) Hydraulic geometry of active gravel rivers. Journal of the 

Hydraulics Division, American Society of Civil Engineers 105: 1185-1201. 

43. Kleinhans MG, Bierkens MFP, van der Perk M (2010) HESS opinions. On the use 

of laboratory experimentation: „Hydrologists, bring out shovel and garden hoses 

and hit the dirt“. Hydrology and Earth System Sciences 14: 369-382. 

44. Govers G, Giménez R, van Oost K (2007) Exploring the relationsship between 

experiments, modelling and field observations. Earth-Science Reviews 84 (3-4): 

87-102. 

45. Govers G (1987) Spatial and temporal variability in rill development processes at 

the Huldenberg experimental site. Catena Supplement 8: 17-34. 

46. Seeger M (2007) Uncertainty of factors determining runoff and erosion processes 

as quantified by rainfall simulations. Catena 71 (1): 56-67. 

47. FAO (2006) Guidelines for soil description. Rome: 4. ed. Food and Agriculture 

Organization of the United Nations. 

48. Vandekerckhove L, Poesen J, Oostwoud Wijdenes D, de Figueiredo T (2003) 

Topographical thresholds for ephemeral gully initiation in intensively cultivated 

areas of the Mediterranean. Catena 33(3-4): 271-292. 

49. Ad-hoc-Arbeitsgruppe Boden (2005) Bodenkundliche Kartieranleitung. Hannover: 

5. Auflage, Bundesamt für Geowissenschaften und Rohstoff in Zusammenarbeit 

mit den staatlichen Geologischen Diensten der Bundesrepublik Deutschland. 438 

p. 

201


50. Wirtz S, Seeger M, Ries JB (2010) The rill experiment as a method to approach a 

quantification of rill erosion process activity. Zeitschrift für Geomorphologie Vol. 

54,1: 47-64. 

51. Allen JRL (1994) Fundamental properties of fluids and their relation to sediment 

transport processes. In: Pye K, editor. Sediment transport and depositional 

processes. Blackwell Scientific Publications. pp. 25-88. 

52. DIN 18124 (1997) Baugrund, Untersuchung von Bodenproben - Bestimmung der 

Korndichte - Kapillarpyknometer, Weithalspyknometer. Deutsches Institut für 

Normung e.V., Ausgabe : 1997-07 , Deutsch. 

53. Macosko CW (1994) Rheology: Principles, Measurements and Applications. New 

York: VCH: Wiley-VCH. New York. 

54. Einstein A (1906) Eine neue Bestimmung der Moleküldimensionen. Analen der 

Physik 19: 289-306. 

55. Einstein A (1911) Berichtigung zu meiner Arbeit: „Eine neue Bestimmung der 

Moleküldimensionen“. Analen der Physik 34: 591-593. 

56. Scherer U (2008): Prozessbasierte Modellierung der Bodenerosion in einer 

Lösslandschaft. Karlsruhe: Disserationsschrift, Fakultät für Bauingenieur-, Geound 

Umweltwissenschaften, Universität Fridericiana zu Karlsruhe (TH). 248 p. 

57. Landau L, Lifchitz E (1971) Mécaniques des fluids. Moscow: MIR 

58. Fan, J., Gao, H., Guo, B., 2010. Regularity criteria for the Navier-Stokes-Landau- 

Lifshitz system. J.Math. Anal. Appl. 363, 29-37 

59. Bell, J.B., Garcia, A.L., Williams, S.S. 2007. Numerical methods for the stochastic 

Landau-Lifshitz Navier-Stokes equations. Physical Review E 76 

60. Seiler R (2002) Die Navier-Stokes-Gleichung. Elemente der Mathematik 57: 109- 

114. 

61. Constantin P (2001) Some open problems and research directions in the 

mathematical study of fluid dynamics. Mathematics unlimited-2001 and beyond: 

353-360. 

62. Fefferman CL (2006) Existance and smoothness of the Navier-Stokes equation. 

The millennium prize problems. Cambridge, MA.: Clay Math. Inst. pp. 57-67. 

63. Temam R (2000) Some developments on Navier-Stokes equations in the second 

half of the 20 th century. Development of mathematics 1950-2000: 1049-1106. 

64. Wiegner M (1999) The Navier-Stokes equations – a neverending challenge? 

Jahresbericht Deutsch. Math.-Verein 101, No. 1: 1-25. 

202


65. Schneider G (2008) Ein Millenniumsproblem: Die globale Existenz und 

Eindeutigkeit glatter Lösungen der dreidimensionalen Navier-Stokes-Gleichungen. 

Mathematik-Online: Beiträge zu berühmten, gelösten und ungelösten Problemen, 

Nummer 2. 

66. Reid DM, Dunne T (1996) Rapid evaluation of sediment budgets. Reiskirchen: 

Catena Verlag. 

67. EPA-homepage (2009) Channel Processes: Bedload transport. United States 

Environmental protection agency. Available: 

http://water.epa.gov/scitech/datait/tools/warsss/bedload.cfm, access: 14.9.2010 

68. Hessel R, Jetten V (2007) Suitability of transport equations in modelling soil 

erosion for a small Loess plateau catchment. Eng. Geol. 91: 56-71. 

69. Nearing MA, Bradford JM, Parker SC (1991) Soil detachment by shallow flow at 

low slopes. Soil Science Society of America Journal 55 (2): 339-344. 

70. Nearing MA, Parker SC (1994) Detachment of soil by flowing water under 

turbulent and laminar conditions. Soil Science Society of America Journal 58 (6): 

1612-1614. 

71. Bryan RB, Govers G, Poesen J (1989) The concept of soil erodibility and some 

problems of assessment and application. Catena 16 (4-5): 393-412. 

72. Bryan RB (1990) Knickpoint evolution in rillwash. Catena 17: 111-132. 

73. Owoputi LO, Stolte WJ (1995) Soil detachment in the physically based soil 

erosion process: a review. Transactions of the ASAE 38 (4): 1099-1110. 

74. Rapp I. (1998) Effects of soil properties and experimental conditions on the rill 

erodibilities of selected soils. Pretoria: Ph. D. Thesis, Faculty of Biological and 

Agricultural Sciences, University of Pretoria, South Africa. 

75. Zhu JC, Gantzer CJ, Peyton RL, Alberst EE, Anderson SH (1995) Simulated 

small-channel bed scour and head cut erosion rates compared. Soil Science Society 

of America Journal 59 (1): 211-218. 

76. Kohl KD (1988) Mechanics of rill headcutting. Ames: Phd. Diss. Iowa State 

University. 

77. Stefanovic JR, Bryan RB (2009) Flow energy and channel adjustments in rills 

developed in loamy sand and sandy loam soils. Earth Surface Processes and 

Landforms 34: 133-144. 

78. Nearing MA (1998) Why soil erosion models over-predict small soil losses and 

under-predict large soil losses. Catena 32: 15-22. 

203


79. Ruttimann M, Schaub D, Prasuhn V, Ruegg W (1995) Measurement of runoff and 

soil erosion on regulary cultivated fields in Switzerland – some critical 

considerations. Catena 25: 127-139. 

80. Wendt RC, Alberts EE, Hjelmfelt Jr (1986). Variability of runoff and soil loss 

from fallow experimental plots. Soil Sci. Soc. Am. J. 50: 730-736. 

81. Risse LM, Nearing MA, Nicks AD, Laflen JM (1993) Assessment of error in the 

universal soil loss equation. Soil Sci. Soc. Am. J. 57: 825-833. 

82. Zhang XC, Nearing MA, Risse LM, McGregor KC (1996) Evaluation of runoff 

and soil loss predictions using natural runoff plot data. Trans. ASAE 39: 855-863. 

83. Liu BY, Nearing MA, Baffaut C, Ascough II JC (1996) The WEPP watershed 

model: III. Comparisons to measured data from small watersheds. Transactions of 

the ASAE 40: 945-951. 

84. Ajayi AE, Horta IDMF (2007) The effect of spatial variability of soil hydraulic 

properties on surface runoff processes. Anais XIII Simpósio Brasileiro de 

Sensoriamento Remoto, Florianópolis, Brasil, 21-26 abril 2007, p. 3243-3248. 

85. Dunkerley D (2008) Rain event properties in nature and in rainfall simulation 

experiments: a comparative review with recommendations for increasingly 

systematic study and reporting. Hydrological Processes 22: 4415-4435. 

86. Sidorchuk A (2005 b) Stochastic modelling of erosion and deposition in cohesive 

soils. Hydrological Processes 19: 1399-1417. 

87. Sidorchuk A (2009 b) A third generation erosion model: The combination of 

probabilistic and deterministic components. Geomorphology 110 (1-2): 2-10. 

88. Nearing MA (1991) A probabilistic model of soil detachment by shallow turbulent 

flow. Transactions of the ASAE 34 (1): 81-85. 

89. Wilson BN (1993) Development of a fundamentally-based detachment model. 

Transactions of the ASAE 36 (4): 1105-1114. 

90. Sidorchuk A (2001) Calculation of the rate of erosion in soils and cohesive 

sediments. Eurasien Soil Science 34 (8): 893-900. 

91. Sidorchuk A (2002) Stochastic Modelling of soil erosion and deposition. 12 th 

ISCO Conference, Beijing 2002. 

92. Sidorchuk A, Smith A, Nikora V (2004) Probability distribution function approach 

in stochastic modelling of soil erosion. Sediment transfer trough the fluvial system 

Vol. 288. IHAS Publ., pp. 345-353. 

204


93. Sidorchuk A (2005 a) Stochastic components in the gully erosion modelling. 

Catena 63: 299-317. 

94. Sidorchuk A, Schmidt J, Cooper G (2008) Variability of shallow overland flow 

velocity and soil aggregate transport observed with digital videography. 

Hydrological Processes 22: 4035-4048. 

95. Sidorchuk A (2009 a) High-Frequency variability of aggregate transport under 

water erosion of well-structured soils. Eurasian Soil Science Vol. 42, No. 5: 543- 

552. 

96. Einstein HA (1936) Der Geschiebetrieb als Wahrscheinlichkeitsproblem. Zürich: 

Diss.-Druckerei A.-G. Gebr. Leemann & Co. 112 p. 

205


Table S1 Freila 1 erosion data 

Run - MP - flow length [m]- 

sampling time [min:sec] 

Sediment 

Concentration 

[g L -1 ] 

Detachment 

rate 

[kg s -1 m -2 ] 

Transport 

rate 

[kg s-1] 

Sample 

density 

[g cm -3 ] 

Slope 

[°] 

Transport 

capacity 

[kg s-1] 

a-1-3.4-0:00 10.6 0.0156 0.017750523 1.01 2.4 0.00125 

a-1-3.4-0:30 2.1 0.0092 0.010500304 1.00 2.4 0.00128 

a-1-3.4-1:30 3.3 0.0257 0.029404312 1.00 2.4 0.00129 

a-1-3.4-2:30 0.4 0.0040 0.004617795 1.00 2.4 0.00126 

a-2-8.6-0:00 14.9 0.0008 0.000726251 1.01 7.4 0.00003 

a-2-8.6-0:30 2.4 0.0004 0.000914653 1.00 7.4 0.00032 

a-2-8.6-1:30 1.4 0.0005 0.001633948 1.00 7.4 0.00156 

a-2-8.6-2:30 0.6 0.0010 0.007309575 1.00 7.4 0.07782 

a-3-13.1-0:00 26.6 0.0407 0.240254717 1.02 6 0.02132 

a-3-13.1-0:30 8.0 0.0079 0.041958790 1.01 6 0.00555 

a-3-13.1-1:30 3.1 0.0049 0.028349123 1.00 6 0.01600 

a-3-13.1-2:30 2.5 0.0042 0.024596630 1.00 6 0.01957 

b-1-3.4-0:00 35.1 0.0524 0.060019839 1.02 2.4 0.00132 

b-1-3.4-0:30 0.5 0.0010 0.001109306 1.00 2.4 0.00126 

b-1-3.4-1:30 0.6 0.0012 0.001397038 1.00 2.4 0.00126 

b-1-3.4-2:30 0.1 0.0002 0.000302770 1.00 2.4 0.00144 

b-2-8.6-0:00 4.8 0.0001 0.000126626 1.00 7.4 0.00001 

b-2-8.6-0:30 0.6 0.0001 0.000260038 1.00 7.4 0.00027 

b-2-8.6-1:30 0.7 0.0013 0.010225583 1.00 7.4 0.07834 

b-2-8.6-2:30 0.1 0.0000 0.000132974 1.00 7.4 0.00161 

b-3-13.1-0:00 9.9 0.0336 0.247153306 1.01 6 0.24591 

b-3-13.1-0:30 2.6 0.0021 0.012025713 1.00 6 0.00812 

b-3-13.1-1:30 1.0 0.0042 0.030456868 1.00 6 0.22937 

b-3-13.1-2:30 0.8 0.0047 0.035191499 1.00 6 0.26525 

206


Table S2 Freila 1 runoff data 



Flow 

velocity 

[m s -1 ] 

Dynamic 

viscosity 

[kg s -1 m -1 ] 

Water 

depth 

[cm] 

Flow cross 

section 

[cm²] 

Wetted 

Perimeter 

[cm] 

Hydraulic 

radius 

[cm] 

a-1-3.4-0:00 0.41 0.001053 0.20 40.9 33.5 1.2 

a-1-3.4-0:30 1.20 0.001011 0.30 41.7 33.7 1.2 

a-1-3.4-1:30 2.12 0.001017 0.30 41.7 33.7 1.2 

a-1-3.4-2:30 2.61 0.001002 0.40 42.0 34.2 1.2 

a-2-8.6-0:00 0.34 0.001075 0.30 1.4 10.9 0.1 

a-2-8.6-0:30 0.39 0.001012 1.30 10.0 27.6 0.4 

a-2-8.6-1:30 0.41 0.001007 2.50 28.0 41.1 0.7 

a-2-8.6-2:30 0.41 0.001003 10.30 289.7 88.9 3.3 

a-3-13.1-0:00 0.92 0.001133 3.60 98.3 45.1 2.2 

a-3-13.1-0:30 1.01 0.001040 2.40 51.8 40.5 1.3 

a-3-13.1-1:30 1.05 0.001016 3.10 86.9 44.3 2.0 

a-3-13.1-2:30 1.06 0.001012 3.30 94.9 44.6 2.1 

b-1-3.4-0:00 0.41 0.001176 0.30 41.7 33.7 1.2 

b-1-3.4-0:30 0.57 0.001002 0.40 42.0 34.2 1.2 

b-1-3.4-1:30 0.59 0.001003 0.40 42.0 34.2 1.2 

b-1-3.4-2:30 0.91 0.001000 0.50 47.2 36.3 1.3 

b-2-8.6-0:00 0.32 0.001024 0.50 0.8 10.9 0.1 

b-2-8.6-0:30 0.49 0.001003 1.30 9.4 28.0 0.3 

b-2-8.6-1:30 0.53 0.001003 10.40 290.7 89.0 3.3 

b-2-8.6-2:30 0.46 0.001001 2.40 26.1 37.7 0.7 

b-3-13.1-0:00 0.76 0.001050 9.20 327.5 56.2 5.8 

b-3-13.1-0:30 0.72 0.001013 2.80 64.0 42.8 1.5 

b-3-13.1-1:30 0.98 0.001005 9.20 318.0 55.9 5.7 

b-3-13.1-2:30 1.32 0.001004 9.30 346.0 57.4 6.0 

207


Table S3 Freila 1 hydraulic data 

Run - MP - flow length [m]- τ Г ω 

sampling time [min:sec] [Pa] [N m -1 ] [W m -2 ] 

ω U ω eff 

Re τ - τ cr 

[m s -1 ] [W m -1 ] [ ] [Pa] 

a-1-3.4-0:00 5.05 1.69 2.07 0.02 187.91 4791 3.08 

a-1-3.4-0:30 5.09 1.72 6.10 0.05 725.17 14707 3.12 

a-1-3.4-1:30 5.09 1.72 10.79 0.09 1703.78 25834 3.12 

a-1-3.4-2:30 5.05 1.73 13.18 0.11 1898.77 32015 3.08 

a-2-8.6-0:00 1.68 0.18 0.57 0.04 20.68 420 -0.30 

a-2-8.6-0:30 4.58 1.26 1.77 0.05 42.55 1384 2.61 

a-2-8.6-1:30 8.62 3.54 3.53 0.05 77.65 2776 6.64 

a-2-8.6-2:30 41.19 36.61 16.89 0.05 315.87 13326 39.22 

a-3-13.1-0:00 22.72 10.25 20.90 0.10 876.60 17996 20.75 

a-3-13.1-0:30 13.20 5.34 13.31 0.11 583.29 12474 11.23 

a-3-13.1-1:30 20.14 8.93 21.11 0.11 982.55 20267 18.17 

a-3-13.1-2:30 21.83 9.74 23.08 0.11 1077.88 22237 19.86 

b-1-3.4-0:00 5.20 1.75 2.13 0.02 149.50 4412 3.23 

b-1-3.4-0:30 5.05 1.73 2.90 0.02 196.40 7053 3.08 

b-1-3.4-1:30 5.05 1.73 2.98 0.02 204.64 7245 3.08 

b-1-3.4-2:30 5.33 1.94 4.84 0.04 363.78 11770 3.36 

b-2-8.6-0:00 0.96 0.10 0.31 0.04 5.81 237 -1.01 

b-2-8.6-0:30 4.25 1.19 2.08 0.06 54.38 1644 2.28 

b-2-8.6-1:30 41.30 36.75 21.83 0.07 461.19 17220 39.33 

b-2-8.6-2:30 8.73 3.29 4.00 0.06 96.25 3166 6.76 

b-3-13.1-0:00 60.18 33.79 45.74 0.08 1517.71 42492 58.21 

b-3-13.1-0:30 15.35 6.58 11.01 0.08 396.41 10602 13.38 

b-3-13.1-1:30 58.39 32.63 56.94 0.10 2108.18 55255 56.42 

b-3-13.1-2:30 61.89 35.49 81.83 0.14 3606.26 79497 59.92 

208





Sediment 

Concentration 

[g L -1 ] 

Detachment 

rate 

[kg s -1 m -2 ] 

Transport 

rate 

[kg s-1] 

Sample 

density 

[g cm -3 ] 

Slope 

[°] 

Transport 

capacity 

[kg s-1] 

a-1-4-0:00 16.8 0.0668 0.267274644 1.01 5.7 0.05891 

a-1-4-0:30 2.4 0.0078 0.023207900 1.00 5.7 0.02325 

a-1-4-1:30 1.4 0.0058 0.014046683 1.00 5.7 0.02362 

a-1-4-2:30 2.3 0.0086 0.019756646 1.00 5.7 0.01134 

a-2-8.5-0:00 11.3 0.0079 0.033779926 1.01 3.4 0.01692 

a-2-8.5-0:30 3.9 0.0033 0.014486969 1.00 3.4 0.01837 

a-2-8.5-1:30 2.8 0.0028 0.011787666 1.00 3.4 0.01570 

a-2-8.5-2:30 1.8 0.0023 0.010364921 1.00 3.4 0.01946 

a-3-13.3-0:00 19.2 0.0239 0.287705065 1.01 7.4 0.25306 

a-3-13.3-0:30 6.1 0.0127 0.181365395 1.00 7.4 0.77566 

a-3-13.3-1:30 3.1 0.0070 0.098724460 1.00 7.4 0.71743 

a-3-13.3-2:30 2.3 0.0057 0.079795433 1.00 7.4 0.71687 

b-1-4-0:00 12.4 0.0193 0.037281867 1.01 5.7 0.00362 

b-1-4-0:30 2.0 0.0062 0.014347225 1.00 5.7 0.01351 

b-1-4-1:30 0.8 0.0027 0.006088968 1.00 5.7 0.01132 

b-1-4-2:30 0.4 0.0017 0.003861665 1.00 5.7 0.01132 

b-2-8.5-0:00 12.0 0.0103 0.044903275 1.01 3.4 0.01704 

b-2-8.5-0:30 1.6 0.0018 0.008409765 1.00 3.4 0.01955 

b-2-8.5-1:30 0.8 0.0010 0.005012019 1.00 3.4 0.01954 

b-2-8.5-2:30 0.7 0.0012 0.005702665 1.00 3.4 0.01954 

b-3-13.3-0:00 38.0 0.0371 0.445794531 1.02 7.4 0.25751 

b-3-13.3-0:30 2.9 0.0092 0.132228769 1.00 7.4 0.77333 

b-3-13.3-1:30 1.6 0.0042 0.059490319 1.00 7.4 0.71636 

b-3-13.3-2:30 1.4 0.0016 0.022511209 1.00 7.4 0.71624 

209





Flow 

velocity 

[m s -1 ] 

Dynamic 

viscosity 

[kg s -1 m -1 ] 

Water 

depth 

[cm] 

Flow cross 

section 

[cm²] 

Wetted 

Perimeter 

[cm] 

Hydraulic 

radius 

[cm] 

a-1-4-0:00 0.47 0.001084 4.7 338.62 99.98 3.39 

a-1-4-0:30 0.54 0.001012 2.8 174.04 74.13 2.35 

a-1-4-1:30 0.69 0.001007 2.4 142.28 60.20 2.36 

a-1-4-2:30 0.84 0.001012 1.6 100.62 57.12 1.76 

a-2-8.5-0:00 0.21 0.001057 0.3 142.06 50.60 2.81 

a-2-8.5-0:30 0.24 0.001020 0.5 152.10 52.27 2.91 

a-2-8.5-1:30 0.31 0.001014 0.2 134.99 49.38 2.73 

a-2-8.5-2:30 0.38 0.001009 0.5 152.10 52.27 2.98 

a-3-13.3-0:00 0.32 0.001096 4.2 469.04 90.43 5.19 

a-3-13.3-0:30 0.34 0.001031 8.2 877.69 107.58 8.16 

a-3-13.3-1:30 0.37 0.001016 8 838.70 105.94 7.92 

a-3-13.3-2:30 0.41 0.001012 8 838.70 105.94 7.92 

b-1-4-0:00 0.56 0.001062 0.8 53.72 48.34 1.11 

b-1-4-0:30 0.67 0.001010 1.8 109.04 57.70 1.89 

b-1-4-1:30 0.80 0.001004 1.6 100.62 57.12 1.76 

b-1-4-2:30 0.87 0.001002 1.6 100.62 57.12 1.76 

b-2-8.5-0:00 0.26 0.001060 0.4 143.66 51.04 2.81 

b-2-8.5-0:30 0.31 0.001008 0.8 168.31 56.37 2.99 

b-2-8.5-1:30 0.39 0.001004 0.8 168.31 56.37 2.99 

b-2-8.5-2:30 0.48 0.001004 0.8 168.31 56.37 2.99 

b-3-13.3-0:00 0.25 0.001190 4.2 469.04 90.43 5.19 

b-3-13.3-0:30 0.52 0.001015 8.2 877.69 107.58 8.16 

b-3-13.3-1:30 0.45 0.001008 8 838.70 105.94 7.92 

b-3-13.3-2:30 0.19 0.001007 8 838.70 105.94 7.92 

210





ω U ω eff 

Re τ - τ cr 

[m s -1 ] [W m -1 ] [ ] [Pa] 

a-1-4-0:00 33.35 33.34 15.67 0.05 476.44 14840.13 31.28 

a-1-4-0:30 22.91 16.98 12.47 0.05 477.57 12643.85 20.84 

a-1-4-1:30 23.05 13.87 15.97 0.07 767.17 16276.69 20.98 

a-1-4-2:30 17.19 9.82 14.47 0.08 866.60 14676.93 15.12 

a-2-8.5-0:00 16.45 8.32 3.45 0.01 308.68 5619.61 14.38 

a-2-8.5-0:30 16.97 8.87 4.14 0.01 287.89 6976.46 14.90 

a-2-8.5-1:30 15.93 7.87 4.96 0.02 696.51 8412.52 13.86 

a-2-8.5-2:30 17.36 9.07 6.58 0.02 577.49 11212.34 15.29 

a-3-13.3-0:00 66.33 59.98 21.22 0.04 809.25 15329.03 64.26 

a-3-13.3-0:30 103.48 111.32 34.97 0.04 1095.81 26859.14 101.41 

a-3-13.3-1:30 100.22 106.18 37.48 0.05 1235.77 29202.70 98.15 

a-3-13.3-2:30 100.17 106.12 41.06 0.05 1417.16 32125.42 98.10 

b-1-4-0:00 10.91 5.27 6.11 0.06 377.59 5905.24 8.84 

b-1-4-0:30 18.44 10.64 12.30 0.07 628.24 12503.04 16.37 

b-1-4-1:30 17.17 9.81 13.73 0.08 801.27 14039.07 15.10 

b-1-4-2:30 17.17 9.81 14.92 0.09 908.07 15284.39 15.10 

b-2-8.5-0:00 16.50 8.42 4.29 0.02 352.57 6954.96 14.43 

b-2-8.5-0:30 17.39 9.80 5.34 0.02 308.90 9112.39 15.32 

b-2-8.5-1:30 17.38 9.80 6.84 0.02 447.03 11708.97 15.31 

b-2-8.5-2:30 17.38 9.80 8.25 0.03 592.94 14138.38 15.31 

b-3-13.3-0:00 67.10 60.68 16.78 0.03 568.65 11156.44 65.03 

b-3-13.3-0:30 103.27 111.10 53.49 0.07 2072.79 41729.93 101.20 

b-3-13.3-1:30 100.12 106.07 45.47 0.06 1651.29 35706.89 98.05 

b-3-13.3-2:30 100.11 106.06 19.44 0.03 461.72 15281.78 98.04 

211





Sediment 

Concentration 

[g L -1 ] 

Detachment 

rate 

[kg s -1 m -2 ] 

Transport 

rate 

[kg s-1] 

Sample 

density 

[g cm -3 ] 

Slope 

[°] 

Transport 

capacity 

[kg s-1] 

a-1-2.9-0:00 45.0 0.2958 0.379845863 1.03 4.7 0.08011 

a-1-2.9-0:30 3.0 0.0174 0.017769517 1.00 4.7 0.02040 

a-1-2.9-1:30 1.6 0.0135 0.014059196 1.00 4.7 0.02558 

a-1-2.9-2:30 0.8 0.0081 0.008537001 1.00 4.7 0.02670 

a-2-11-0:00 43.2 0.1264 0.653849085 1.03 15.1 0.77604 

a-2-11-0:30 7.8 0.0298 0.189057846 1.00 15.1 1.85097 

a-2-11-1:30 4.3 0.0173 0.117480752 1.00 15.1 2.37381 

a-2-11-2:30 3.7 0.0161 0.120276643 1.00 15.1 3.15647 

a-3-13.8-0:00 56.3 0.0619 0.414999121 1.04 4.4 0.07706 

a-3-13.8-0:30 11.1 0.0144 0.087141739 1.01 4.4 0.02722 

a-3-13.8-1:30 5.5 0.0080 0.048446063 1.00 4.4 0.02707 

a-3-13.8-2:30 3.9 0.0068 0.043053290 1.00 4.4 0.04278 

b-1-2.9-0:00 3.5 0.0257 0.036744778 1.00 4.7 0.14627 

b-1-2.9-0:30 1.4 0.0178 0.023345189 1.00 4.7 0.08610 

b-1-2.9-1:30 0.4 0.0054 0.006318732 1.00 4.7 0.03960 

b-1-2.9-2:30 0.0 0.0000 0.000000000 1.00 4.7 0.03846 

b-2-11-0:00 10.2 0.0422 0.267669423 1.01 15.1 1.85510 

b-2-11-0:30 3.3 0.0122 0.080111940 1.00 15.1 2.12315 

b-2-11-1:30 1.9 0.0055 0.038627457 1.00 15.1 2.57786 

b-2-11-2:30 1.2 0.0026 0.019920464 1.00 15.1 3.37596 

b-3-13.8-0:00 26.1 0.0421 0.302333459 1.02 4.4 0.12407 

b-3-13.8-0:30 6.1 0.0121 0.076629194 1.00 4.4 0.04286 

b-3-13.8-1:30 2.5 0.0034 0.021755547 1.00 4.4 0.04272 

b-3-13.8-2:30 2.2 0.0002 0.001559311 1.00 4.4 0.04271 

212





Flow 

velocity 

[m s -1 ] 

Dynamic 

viscosity 

[kg s -1 m -1 ] 

Water 

depth 

[cm] 

Flow cross 

section 

[cm²] 

Wetted 

Perimeter 

[cm] 

Hydraulic 

radius 

[cm] 

a-1-2.9-0:00 0.44 0.001225 7.6 191.68 45.06 4.25 

a-1-2.9-0:30 0.65 0.001015 4.3 89.43 35.77 2.50 

a-1-2.9-1:30 0.90 0.001008 4.8 100.07 36.54 2.74 

a-1-2.9-2:30 1.00 0.001004 4.9 103.52 37.15 2.79 

a-2-11-0:00 0.61 0.001216 10.00 248.00 47.02 5.27 

a-2-11-0:30 0.55 0.001039 15.00 436.45 57.68 7.57 

a-2-11-1:30 0.52 0.001022 17.00 517.84 61.88 8.37 

a-2-11-2:30 0.51 0.001018 20.00 638.72 68.08 9.38 

a-3-13.8-0:00 0.35 0.001281 7.00 210.67 48.55 4.34 

a-3-13.8-0:30 0.62 0.001055 5.00 128.02 44.00 2.91 

a-3-13.8-1:30 0.69 0.001027 5.00 128.02 44.00 2.91 

a-3-13.8-2:30 0.68 0.001020 6.00 160.05 45.78 3.50 

b-1-2.9-0:00 0.38 0.001018 9.7 276.10 50.23 5.50 

b-1-2.9-0:30 0.82 0.001007 5.9 204.80 46.02 4.45 

b-1-2.9-1:30 1.33 0.001002 5.7 134.37 41.18 3.26 

b-1-2.9-2:30 1.55 0.001000 5.6 123.89 38.41 3.23 

b-2-11-0:00 0.6 0.001051 15.00 436.45 57.68 7.57 

b-2-11-0:30 0.51 0.001016 16.00 479.77 59.92 8.01 

b-2-11-1:30 0.38 0.001009 18.00 550.13 63.54 8.66 

b-2-11-2:30 0.25 0.001006 21.00 674.83 69.96 9.65 

b-3-13.8-0:00 0.42 0.001130 9.00 276.30 52.05 5.31 

b-3-13.8-0:30 0.78 0.001031 6.00 160.05 45.78 3.50 

b-3-13.8-1:30 0.54 0.001013 6.00 160.05 45.78 3.50 

b-3-13.8-2:30 0.04 0.001011 6.00 160.05 45.78 3.50 

213





ω U ω eff 

Re τ - τ cr 

[m s -1 ] [W m -1 ] [ ] [Pa] 

a-1-2.9-0:00 35.16 15.84 15.47 0.04 339.16 15709.50 33.19 

a-1-2.9-0:30 20.13 7.20 13.13 0.05 387.49 16085.57 18.16 

a-1-2.9-1:30 22.03 8.05 19.74 0.07 664.13 24368.99 20.06 

a-1-2.9-2:30 22.41 8.33 22.33 0.08 788.02 27665.64 20.44 

a-2-11-0:00 138.45 65.10 84.45 0.16 3602.41 27174.42 136.48 

a-2-11-0:30 194.31 112.09 107.33 0.14 3938.82 40414.91 192.34 

a-2-11-1:30 214.45 132.70 111.95 0.14 3859.87 42875.13 212.48 

a-2-11-2:30 240.30 163.61 123.07 0.13 3992.08 47287.94 238.33 

a-3-13.8-0:00 33.81 16.42 11.83 0.03 239.70 12271.29 31.84 

a-3-13.8-0:30 22.05 9.70 13.56 0.05 368.01 17075.36 20.08 

a-3-13.8-1:30 21.97 9.67 15.20 0.05 436.48 19653.60 20.00 

a-3-13.8-2:30 26.38 12.08 17.97 0.05 497.22 23420.27 24.41 

b-1-2.9-0:00 44.28 22.24 16.83 0.03 326.93 20572.31 42.31 

b-1-2.9-0:30 35.80 16.48 29.31 0.07 1046.85 36207.56 33.83 

b-1-2.9-1:30 26.23 10.80 34.84 0.11 1388.43 43265.86 24.26 

b-1-2.9-2:30 25.93 9.96 40.30 0.13 1748.03 50139.66 23.96 

b-2-11-0:00 194.60 112.25 116.76 0.16 4468.98 43466.94 192.63 

b-2-11-0:30 205.03 122.86 105.19 0.13 3660.45 40501.41 203.06 

b-2-11-1:30 221.51 140.75 83.15 0.10 2378.54 32237.17 219.54 

b-2-11-2:30 246.70 172.58 61.60 0.07 1368.60 23964.67 244.73 

b-3-13.8-0:00 40.61 21.14 17.05 0.03 350.70 20049.07 38.64 

b-3-13.8-0:30 26.41 12.09 20.69 0.06 614.06 26675.66 24.44 

b-3-13.8-1:30 26.35 12.06 14.15 0.04 347.22 18563.41 24.38 

b-3-13.8-2:30 26.35 12.06 1.17 0.00 8.22 1533.53 24.38 

214


Table S10 Negratin erosion data 



Sediment 

Concentration 

[g L -1 ] 

Detachment 

rate 

[kg s -1 m -2 ] 

Transport 

rate 

[kg s-1] 

Sample 

density 

[g cm -3 ] 

Slope 

[°] 

Transport 

capacity 

[kg s-1] 

a-1-3.2-0:00 67.3 0.3509 0.378972891 1.04 3.2 0.02284 

a-1-3.2-0:30 55.7 0.3594 0.417851939 1.03 3.2 0.02926 

a-1-3.2-1:30 37.0 0.2853 0.331751054 1.02 3.2 0.02877 

a-1-3.2-2:30 35.2 0.3353 0.411477439 1.02 3.2 0.03395 

a-2-5.1-0:00 128.8 0.1191 0.083361100 1.08 7.7 0.00238 

a-2-5.1-0:30 102.6 0.2553 0.258820005 1.06 7.7 0.01888 

a-2-5.1-1:30 60.6 0.1840 0.183346450 1.04 7.7 0.01584 

a-2-5.1-2:30 41.3 0.1941 0.219213489 1.03 7.7 0.02768 

a-3-11.5-0:00 170.4 0.0370 0.039566213 1.11 1.7 0.00012 

a-3-11.5-0:30 155.3 0.0391 0.039947665 1.10 1.7 0.00009 

a-3-11.5-1:30 95.0 0.0333 0.035583905 1.06 1.7 0.00011 

a-3-11.5-2:30 81.0 0.0364 0.040214682 1.05 1.7 0.00016 

b-1-3.2-0:00 82.1 0.5253 0.567410676 1.05 3.2 0.02314 

b-1-3.2-0:30 35.9 0.2925 0.340134613 1.02 3.2 0.02874 

b-1-3.2-1:30 24.7 0.2555 0.297103809 1.02 3.2 0.02845 

b-1-3.2-2:30 12.4 0.2164 0.265524812 1.01 3.2 0.03324 

b-2-5.1-0:00 128.2 0.1551 0.112506225 1.08 7.7 0.00302 

b-2-5.1-0:30 48.3 0.1641 0.171502072 1.03 7.7 0.01942 

b-2-5.1-1:30 28.8 0.1376 0.147576853 1.02 7.7 0.02288 

b-2-5.1-2:30 28.3 0.1823 0.219256736 1.02 7.7 0.03540 

b-3-11.5-0:00 168.5 0.0358 0.038265903 1.10 1.7 0.00012 

b-3-11.5-0:30 79.8 0.0234 0.025837099 1.05 1.7 0.00016 

b-3-11.5-1:30 52.8 0.0137 0.013972868 1.03 1.7 0.00008 

b-3-11.5-2:30 51.4 0.0153 0.016371852 1.03 1.7 0.00011 

215


Table S11 Negratin runoff data 



Flow 

velocity 

[m s -1 ] 

Dynamic 

viscosity 

[kg s -1 m -1 ] 

Water 

depth 

[cm] 

Flow cross 

section 

[cm²] 

Wetted 

Perimeter 

[cm] 

Hydraulic 

radius 

[cm] 

a-1-3.2-0:00 0.53 0.001336 0.5 106.28 33.75 3.15 

a-1-3.2-0:30 0.59 0.001278 2 126.85 36.33 3.49 

a-1-3.2-1:30 0.71 0.001185 2 126.85 36.33 3.49 

a-1-3.2-2:30 0.82 0.001176 3 143.13 38.35 3.73 

a-2-5.1-0:00 0.64 0.001644 0.4 10.11 13.72 0.74 

a-2-5.1-0:30 0.75 0.001513 2.1 33.86 19.88 1.70 

a-2-5.1-1:30 0.96 0.001303 2 31.49 19.53 1.61 

a-2-5.1-2:30 1.18 0.001207 2.6 44.94 22.14 2.03 

a-3-11.5-0:00 0.46 0.001852 0.40 5.05 9.30 0.54 

a-3-11.5-0:30 0.59 0.001776 0.30 4.33 8.89 0.49 

a-3-11.5-1:30 0.74 0.001475 0.40 5.05 9.30 0.54 

a-3-11.5-2:30 0.81 0.001405 0.50 6.12 9.61 0.64 

b-1-3.2-0:00 0.65 0.001411 0.5 106.28 33.75 3.15 

b-1-3.2-0:30 0.75 0.001180 2 126.85 36.33 3.49 

b-1-3.2-1:30 0.95 0.001123 2 126.85 36.33 3.49 

b-1-3.2-2:30 1.50 0.001062 3 143.13 38.35 3.73 

b-2-5.1-0:00 0.76 0.001641 0.5 11.54 14.22 0.81 

b-2-5.1-0:30 0.99 0.001242 2.3 36.00 20.49 1.76 

b-2-5.1-1:30 1.29 0.001144 2.5 39.73 21.03 1.89 

b-2-5.1-2:30 1.46 0.001141 3 53.06 23.58 2.25 

b-3-11.5-0:00 0.45 0.001843 0.40 5.05 9.30 0.54 

b-3-11.5-0:30 0.53 0.001399 0.50 6.12 9.61 0.64 

b-3-11.5-1:30 0.61 0.001264 0.30 4.33 8.89 0.49 

b-3-11.5-2:30 0.63 0.001257 0.40 5.05 9.30 0.54 

216


Table S12 Negratin hydraulic data 



ω U ω eff 

Re τ - τ cr 

[m s -1 ] [W m -1 ] [ ] [Pa] 

a-1-3.2-0:00 17.96 6.06 9.52 0.03 1004.67 13009.48 15.04 

a-1-3.2-0:30 19.78 7.19 11.70 0.03 543.29 16715.29 16.85 

a-1-3.2-1:30 19.56 7.11 13.84 0.04 698.89 21333.97 16.63 

a-1-3.2-2:30 20.89 8.01 17.08 0.05 730.82 26518.86 17.96 

a-2-5.1-0:00 10.46 1.44 6.70 0.09 687.70 3099.18 7.54 

a-2-5.1-0:30 23.82 4.74 17.75 0.10 982.41 8925.34 20.90 

a-2-5.1-1:30 21.99 4.30 21.12 0.13 1317.11 12329.08 19.06 

a-2-5.1-2:30 27.36 6.06 32.28 0.16 2090.11 20354.33 24.44 

a-3-11.5-0:00 1.75 0.16 0.80 0.01 28.58 1490.41 -1.18 

a-3-11.5-0:30 1.56 0.14 0.92 0.02 42.67 1786.38 -1.37 

a-3-11.5-1:30 1.67 0.16 1.24 0.02 54.86 2890.54 -1.26 

a-3-11.5-2:30 1.95 0.19 1.58 0.02 67.92 3863.99 -0.98 

b-1-3.2-0:00 18.12 6.12 11.78 0.04 1382.74 15249.04 15.20 

b-1-3.2-0:30 19.55 7.10 14.58 0.04 755.90 22575.90 16.62 

b-1-3.2-1:30 19.41 7.05 18.44 0.05 1074.74 29978.88 16.48 

b-1-3.2-2:30 20.60 7.90 30.90 0.08 1778.67 53133.31 17.67 

b-2-5.1-0:00 11.52 1.64 8.76 0.10 886.05 4058.91 8.59 

b-2-5.1-0:30 23.79 4.87 23.45 0.13 1404.17 14369.29 20.86 

b-2-5.1-1:30 25.28 5.32 32.62 0.17 2178.77 21693.14 22.35 

b-2-5.1-2:30 30.10 7.10 44.00 0.20 3022.79 29329.14 27.17 

b-3-11.5-0:00 1.74 0.16 0.79 0.01 27.61 1464.08 -1.18 

b-3-11.5-0:30 1.94 0.19 1.03 0.02 35.72 2528.39 -0.98 

b-3-11.5-1:30 1.47 0.13 0.90 0.02 40.73 2434.20 -1.46 

b-3-11.5-2:30 1.63 0.15 1.03 0.02 41.37 2810.22 -1.30 

217


Table S13 Salada erosion data 



Sediment 

Concentration 

[g L -1 ] 

Detachment 

rate 

[kg s -1 m -2 ] 

Transport 

rate 

[kg s-1] 

Sample 

density 

[g cm -3 ] 

Slope 

[°] 

Transport 

capacity 

[kg s-1] 

a-1-2.3-0:00 65.7 0.2744 0.163638470 1.04 14.9 0.07299 

a-1-2.3-0:30 21.9 0.0840 0.053634448 1.01 14.9 0.12230 

a-1-2.3-1:30 11.4 0.0767 0.044566797 1.01 14.9 0.05316 

a-1-2.3-2:30 15.4 0.4565 0.309609576 1.01 14.9 0.18004 

a-2-4.7-0:00 30.8 0.0812 0.094584461 1.02 24.5 0.14384 

a-2-4.7-0:30 18.3 0.0529 0.070550578 1.01 24.5 0.29789 

a-2-4.7-1:30 40.7 0.2666 0.437682105 1.03 24.5 0.79787 

a-2-4.7-2:30 11.4 0.0980 0.117807544 1.01 24.5 0.17785 

a-3-4.7-0:00 113.4 0.3238 0.315564275 1.07 24.5 0.18940 

a-3-4.7-0:30 42.2 0.1193 0.126580737 1.03 24.5 0.28476 

a-3-4.7-1:30 25.0 0.1295 0.149733833 1.02 24.5 0.43935 

a-3-4.7-2:30 14.7 0.2187 0.282982246 1.01 24.5 0.70410 

b-1-2.3-0:00 36.8 0.1280 0.076308115 1.02 14.9 0.07110 

b-1-2.3-0:30 8.1 0.0812 0.091376454 1.01 14.9 0.25308 

b-1-2.3-1:30 5.8 0.0783 0.081788592 1.00 14.9 0.23377 

b-1-2.3-2:30 7.0 0.1136 0.143162068 1.00 14.9 0.36293 

b-2-4.7-0:00 42.9 0.2433 0.404671007 1.03 24.5 0.84780 

b-2-4.7-0:30 19.7 0.1253 0.189952323 1.01 24.5 0.54642 

b-2-4.7-1:30 9.6 0.0684 0.084120916 1.01 24.5 0.20340 

b-2-4.7-2:30 10.9 0.1511 0.215740177 1.01 24.5 0.41807 

b-3-4.7-0:00 39.0 0.1429 0.151710680 1.02 24.5 0.28391 

b-3-4.7-0:30 9.5 0.0551 0.063738761 1.01 24.5 0.43310 

b-3-4.7-1:30 7.8 0.0905 0.117090916 1.00 24.5 0.69957 

b-3-4.7-2:30 6.6 0.1257 0.174190550 1.00 24.5 0.90918 

218


Table S14 Salada runoff data 

Run - MP - flow length 

[m]- 


Flow 

velocity 

[m s -1 ] 

Dynamic 

viscosity 

[kg s -1 m -1 ] 

Water 

depth 

[cm] 

Flow cross 

section 

[cm²] 

Wetted 

Perimeter 

[cm] 

Hydraulic 

radius 

[cm] 

a-1-2.3-0:00 0.48 0.001328 2.5 51.91 25.92 2.00 

a-1-2.3-0:30 0.35 0.001110 3.2 69.41 27.75 2.50 

a-1-2.3-1:30 0.86 0.001057 2.2 45.47 25.27 1.80 

a-1-2.3-2:30 2.33 0.001077 4.1 86.29 29.49 2.93 

a-2-4.7-0:00 0.62 0.001154 4.7 49.50 24.79 2.00 

a-2-4.7-0:30 0.51 0.001091 3.7 76.10 28.35 2.68 

a-2-4.7-1:30 0.78 0.001204 7.7 137.92 34.93 3.95 

a-2-4.7-2:30 1.84 0.001057 4.1 56.01 25.58 2.19 

a-3-4.7-0:00 0.62 0.001567 5 44.87 20.73 2.16 

a-3-4.7-0:30 0.51 0.001211 6 59.01 22.58 2.61 

a-3-4.7-1:30 0.78 0.001125 7 76.97 24.61 3.13 

a-3-4.7-2:30 1.84 0.001073 8 104.38 27.53 3.79 

b-1-2.3-0:00 0.40 0.001184 2.5 51.91 25.92 2.00 

b-1-2.3-0:30 0.68 0.001041 6.3 164.46 48.91 3.36 

b-1-2.3-1:30 0.95 0.001029 5.9 148.03 45.41 3.26 

b-1-2.3-2:30 0.96 0.001035 7.5 212.97 54.81 3.89 

b-2-4.7-0:00 0.66 0.001214 8.0 143.01 35.38 4.04 

b-2-4.7-0:30 0.87 0.001098 6.6 110.25 32.24 3.42 

b-2-4.7-1:30 1.45 0.001048 4.2 60.45 26.15 2.31 

b-2-4.7-2:30 2.12 0.001054 5.7 93.66 30.39 3.08 

b-3-4.7-0:00 0.66 0.001195 6 59.01 22.58 2.61 

b-3-4.7-0:30 0.87 0.001047 7 76.97 24.61 3.13 

b-3-4.7-1:30 1.45 0.001039 8 104.38 27.53 3.79 

b-3-4.7-2:30 2.12 0.001033 9 124.17 29.48 4.21 

219


Table S15 Salada hydraulic data 



ω U ω eff 

Re τ - τ cr 

[m s -1 ] [W m -1 ] [ ] [Pa] 

a-1-2.3-0:00 52.57 13.63 25.24 0.12 1482.75 7531.25 49.37 

a-1-2.3-0:30 63.95 17.75 22.53 0.09 1061.25 8050.56 60.75 

a-1-2.3-1:30 45.71 11.55 39.35 0.22 3144.11 14760.25 42.50 

a-1-2.3-2:30 74.52 21.98 173.86 0.60 19280.91 64004.64 71.32 

a-2-4.7-0:00 82.79 20.52 51.33 0.26 2823.76 10932.84 79.59 

a-2-4.7-0:30 110.44 31.31 56.09 0.21 3783.55 12635.30 107.23 

a-2-4.7-1:30 164.68 57.53 128.40 0.32 8038.43 26224.38 161.48 

a-2-4.7-2:30 89.70 22.95 165.43 0.76 17895.79 38472.08 86.50 

a-3-4.7-0:00 94.27 19.54 58.44 0.26 3292.10 9166.87 91.06 

a-3-4.7-0:30 109.10 24.64 55.42 0.21 2691.66 11247.11 105.90 

a-3-4.7-1:30 129.22 31.80 100.75 0.32 5953.66 22018.10 126.02 

a-3-4.7-2:30 155.65 42.85 287.09 0.76 26199.37 65737.82 152.45 

b-1-2.3-0:00 51.66 13.39 20.67 0.10 1098.76 6920.70 48.46 

b-1-2.3-0:30 85.25 41.70 58.17 0.18 2802.12 22158.58 82.04 

b-1-2.3-1:30 82.54 37.48 78.04 0.24 4548.92 30059.69 79.33 

b-1-2.3-2:30 98.44 53.96 94.08 0.25 5131.14 36030.09 95.24 

b-2-4.7-0:00 168.82 59.74 111.42 0.27 6334.72 22554.07 165.62 

b-2-4.7-0:30 140.82 45.40 123.21 0.36 8374.20 27572.20 137.61 

b-2-4.7-1:30 94.60 24.74 136.77 0.60 13237.98 32076.24 91.40 

b-2-4.7-2:30 126.24 38.36 267.99 0.88 29621.25 62486.08 123.04 

b-3-4.7-0:00 108.88 24.59 71.86 0.27 3974.97 14785.43 105.68 

b-3-4.7-0:30 127.99 31.50 111.99 0.36 6977.44 26284.46 124.79 

b-3-4.7-1:30 154.99 42.67 224.07 0.60 18065.59 53022.45 151.78 

b-3-4.7-2:30 172.07 50.72 365.28 0.88 34762.59 86918.88 168.87 

220


Table S16 Belerda erosion data 



Sediment 

Concentration 

[g L -1 ] 

Detachment 

rate 

[kg s -1 m -2 ] 

Transport 

rate 

[kg s-1] 

Sample 

density 

[g cm -3 ] 

Slope 

[°] 

Transport 

capacity 

[kg s-1] 

a-1-6-0:00 111.1 0.6584 0.463968090 1.07 11.7 0.01464 

a-1-6-0:30 250.8 0.9576 0.674872393 1.15 11.7 0.01644 

a-1-6-1:30 288.4 0.5173 0.364531283 1.18 11.7 0.01694 

a-1-6-2:30 176.1 0.4415 0.387089673 1.11 11.7 0.04693 

a-2-13-0:00 243.8 0.1124 0.242154919 1.15 15.1 0.03603 

a-2-13-0:30 359.6 0.1026 0.084365950 1.22 15.1 0.00926 

a-2-13-1:30 234.8 0.0617 0.038866537 1.14 15.1 0.00230 

a-2-13-2:30 88.0 0.0533 0.041378347 1.05 15.1 0.00577 

a-3-17-0:00 341.2 0.2734 0.876936459 1.21 15.4 0.15169 

a-3-17-0:30 422.3 0.6314 2.058803483 1.26 15.4 0.16862 

a-3-17-1:30 62.6 0.0887 0.297213079 1.04 15.4 0.13513 

a-3-17-2:30 383.4 0.0896 0.296150064 1.24 15.4 0.16984 

b-1-6-0:00 93.0 0.1522 0.118800584 1.06 11.7 0.02513 

b-1-6-0:30 212.6 0.3207 0.226026124 1.13 11.7 0.01594 

b-1-6-1:30 16.5 0.0211 0.012073263 1.01 11.7 0.00496 

b-1-6-2:30 13.5 0.0389 0.030357874 1.01 11.7 0.02340 

b-2-13-0:00 312.2 0.2399 0.516754731 1.19 15.1 0.03803 

b-2-13-0:30 97.3 0.0387 0.038785872 1.06 15.1 0.01574 

b-2-13-1:30 421.1 0.2325 0.171978951 1.26 15.1 0.00611 

b-2-13-2:30 61.8 0.0860 0.086292771 1.04 15.1 0.01525 

b-3-17-0:00 31.7 0.0240 0.078397448 1.02 15.4 0.12267 

b-3-17-0:30 141.3 0.1565 0.524266143 1.09 15.4 0.14471 

b-3-17-1:30 125.3 0.2185 0.722405305 1.08 15.4 0.13812 

b-3-17-2:30 109.2 0.2682 0.909694568 1.07 15.4 0.14510 

221


Table S17 Belerda runoff data 

Run - MP - flow length 

[m]- 


Flow 

velocity 

[m s -1 ] 

Dynamic 

viscosity 

[kg s -1 m -1 ] 

Water 

depth 

[cm] 

Flow cross 

section 

[cm²] 

Wetted 

Perimeter 

[cm] 

Hydraulic 

radius 

[cm] 

a-1-6-0:00 2.94 0.001556 1.0 14.20 11.75 1.21 

a-1-6-0:30 1.89 0.002254 1.0 14.20 11.75 1.21 

a-1-6-1:30 0.89 0.002442 1.0 14.20 11.75 1.21 

a-1-6-2:30 0.80 0.001881 2.0 27.55 14.61 1.89 

a-2-13-0:00 0.42 0.002219 3.0 23.65 16.57 1.43 

a-2-13-0:30 0.46 0.002798 0.7 5.06 6.33 0.80 

a-2-13-1:30 0.72 0.002174 0.2 2.31 4.85 0.48 

a-2-13-2:30 1.09 0.001440 0.6 4.32 5.98 0.72 

a-3-17-0:00 0.56 0.002706 0.2 45.89 18.87 2.43 

a-3-17-0:30 1.03 0.003111 0.3 47.50 19.18 2.48 

a-3-17-1:30 0.95 0.001313 0.5 50.15 19.70 2.55 

a-3-17-2:30 0.16 0.002917 0.4 48.85 19.45 2.51 

b-1-6-0:00 0.65 0.001465 1.5 19.65 13.01 1.51 

b-1-6-0:30 0.75 0.002063 1.0 14.20 11.75 1.21 

b-1-6-1:30 0.94 0.001083 0.2 7.72 9.52 0.81 

b-1-6-2:30 1.14 0.001068 1.5 19.65 13.01 1.51 

b-2-13-0:00 0.70 0.002561 3.0 23.65 16.57 1.43 

b-2-13-0:30 0.48 0.001486 1.0 8.31 7.72 1.08 

b-2-13-1:30 1.08 0.003105 0.5 3.78 5.69 0.66 

b-2-13-2:30 1.68 0.001309 1.0 8.31 7.72 1.08 

b-3-17-0:00 0.52 0.001159 0.3 47.50 19.18 2.48 

b-3-17-0:30 0.74 0.001706 0.5 50.15 19.70 2.55 

b-3-17-1:30 1.18 0.001627 0.4 48.85 19.45 2.51 

b-3-17-2:30 1.62 0.001546 0.6 51.41 19.95 2.58 

222


Table S18 Belerda hydraulic data 



ω U ω eff 

Re τ - τ cr 

[m s -1 ] [W m -1 ] [ ] [Pa] 

a-1-6-0:00 25.71 3.02 75.58 0.60 14155.26 24423.50 22.94 

a-1-6-0:30 27.78 3.26 52.62 0.38 8224.56 11735.83 25.01 

a-1-6-1:30 28.34 3.33 25.22 0.18 2728.19 5190.96 25.57 

a-1-6-2:30 41.58 6.08 33.17 0.16 2592.39 8864.96 38.81 

a-2-13-0:00 41.96 6.95 17.62 0.11 766.31 3107.72 39.19 

a-2-13-0:30 24.97 1.58 11.58 0.12 1076.71 1619.26 22.19 

a-2-13-1:30 13.93 0.67 10.00 0.19 1991.25 1799.58 11.16 

a-2-13-2:30 19.47 1.16 21.19 0.28 2954.62 5758.07 16.70 

a-3-17-0:00 76.70 14.47 42.95 0.15 17731.56 6092.17 73.92 

a-3-17-0:30 81.32 15.60 83.46 0.27 36654.75 10296.35 78.55 

a-3-17-1:30 68.88 13.57 65.17 0.25 17991.78 19049.17 66.11 

a-3-17-2:30 80.93 15.74 12.80 0.04 1816.39 1683.83 78.16 

b-1-6-0:00 31.78 4.13 20.66 0.13 1543.50 7087.10 29.01 

b-1-6-0:30 27.21 3.20 20.36 0.15 1979.84 4961.43 24.44 

b-1-6-1:30 16.31 1.55 15.41 0.19 3811.70 7155.59 13.54 

b-1-6-2:30 30.30 3.94 34.59 0.23 3345.39 16287.61 27.53 

b-2-13-0:00 43.50 7.21 30.45 0.18 1740.33 4652.71 40.73 

b-2-13-0:30 29.16 2.25 14.00 0.13 1128.08 3684.88 26.39 

b-2-13-1:30 21.39 1.22 23.11 0.28 3798.42 2911.66 18.62 

b-2-13-2:30 28.56 2.20 47.98 0.44 7159.25 14340.51 25.79 

b-3-17-0:00 65.77 12.62 34.20 0.14 9616.37 11330.97 63.00 

b-3-17-0:30 72.10 14.20 53.35 0.20 13326.36 12001.08 69.32 

b-3-17-1:30 70.51 13.71 83.19 0.31 30113.84 19632.98 67.74 

b-3-17-2:30 71.65 14.29 116.06 0.43 37864.55 28811.68 68.87 

223


Kapitel 7 

Ries et al. (subm. 2011): Sheep and goat erosion – experimental geomorphology as an 

approach for the quantification of underestimated processes. Zeitschrift für 

Geomorphologie. 

224


Sheep and goat erosion – experimental geomorphology as an approach for the 

quantification of underestimated processes 

Ries, J.B., Andres, K., Wirtz, S., Tumbrink, J., Wilms, T., Peter, K. D., Burczyk, M., Butzen, 

V. & Seeger, M. 

Dep. of Physical Geography, Trier University, Germany 

with 10 figures and 2 tables 

Abstract 

The grazing of goats and sheep is regarded as an important factor for soil degradation in semiarid 

landscapes. Nevertheless, hardly any data can be found in literature. In the presented 

study, the process dynamics of material disaggregation and translocation directly caused by 

trampling animals is quantified by means of experimental methods on test plots. Gerlach 

troughs are installed in order to quantify material mobilisation in different directions. The 

slope angle as well as the running speed of the animals is varied. Additionally, the amount of 

material that is loosened by the hooves of the goats is measured. 

The translocation rates are surprisingly high and slope as well as running speed turn out to be 

important influencing factors. In downslope direction, each goat can translocate between 0.6 g 

and 6.5 on each square meter, depending on slope. The maximum translocation rate in 

movement direction reaches 4.5 g m -2 per goat for fast running and 1.3 g m -2 per goat for slow 

motion. Additionally, each goat can loosen 14 g of soil material per square meter; this 

material can easily be removed by wind or water. Experiments with marked rock fragments 

on slopes of 4° and 11° showed that a flock of 45 goats translocates rock fragments (ø 3 cm) 

by a mean distance of 8.8 cm. While rock movement occurs in all directions, most often they 

are kicked forward-downslope. Net mean downslope translocation rates vary between 1.5 cm 

and 6.6 cm corresponding with slope and the total number of rock fragments moved. 

Keywords 

erosion, sheep and goats, experimental geomorphology, Mediterranean landscapes 

225



About 40 % of the earth's land-surface is used for grazing and 80 % of this grazing area is 

situated in landscapes with semi-arid and arid climates (e.g. BRANSON et al. 1981, 

MONFREDA et al. 2008, 2009, RAMANKUTTY et al. 2008). Over-grazing is considered the 

main cause of 35 % of world-wide soil degradation (OLDEMANN et al. 1991). On the 

African continent, 49 % of the soil surface is already degraded due to grazing and in Australia 

the affected area is 81 % (EVANS 1998, OLDEMANN et al. 1991). Accordingly, grazinginduced 

soil degradation is one of the most widespread land-degradation phenomena. 

Numerous field surveys in literature focus on the degradation of vegetation due to browsing 

damage by animals (e.g. ALADOS et al. 2004, ANDRESEN et al. 1990, MWENDERA & 

MOHAMED SALEEM 1997b, MWENDERA et al. 1997, NOY-MEIR 1975, 1978, 1995, 

PEARSON et al. 1990, PEGAU 1970, RIES et al. 2003, VALENTIN 1985, WANG et al. 

2002). There are also many studies about the formation of specific grazing-induced vegetation 

patterns (e.g. BARBIER et al. 2006, BOONKORKUEA et al. 2010, BORGOGNO et al. 2009, 

DEBLAUWE et al. 2008, GALLE et al. 2001, GOLODETS & BOEKEN 2006, 

HILLERISLAMBERS et al. 2001, MONTANA 1992, TONGWAY et al. 2001, TONGWAY 

& LUDWIG 2001, WORRALL 1959). Vegetation density and distributions patterns play a 

crucial role in soil erosion processes. According to basic literature (ELWELL & STOCKING 

1976), a vegetation cover of 30-40 % is sufficient to protect soil surfaces against degradation. 

SEUFFERT (1999) confirms these values. Other studies, which deal specifically with 

sediment yields in low open matorral shrublands in Mediterranean mountain regions, assume 

that a considerably higher degree of vegetation cover is needed to contain erosive processes 

(MOLINILLO et al. 1997, RIES 2005). They ascribe this to the patchy pattern of tussocks. 

Spots densely covered with Stipa tenacissima have high infiltration rates and low runoff 

coefficients, while the bare areas around them experience sheet flow and rill erosion. Grazing 

in these areas leads to a higher contrast between tussock patches and bare soil (CERDÀ 

1997). 

ROSTANGO et al. (1991) found a remarkable distinction in terms of infiltration rates and 

chemical and physical soil properties on comparing shrub mounds and inter-mound areas for 

soils in northeastern Patagonia. Similar results were presented by DUNKERLY & BROWN 

(1995) for banded vegetation covers in patterned chenopod shrublands in New South Wales, 

Australia. They divided their areas of investigation into source sections, characterized by high 

runoff rates, and sink sections with vital importance for the redistribution of water. 

226


Furthermore, the article points out the vulnerability of these shrublands against grazinginduced 

erosion. 

Basically, two main theses on the impacts of grazing can be found in literature. The studies 

with a more ecological or botanical focus regard grazing animals as ‘ecosystem engineers’ 

and emphasize the increased biodiversity of grazing areas with different biospheres for other 

biota, as compared with non-grazing areas (e.g. JONES et al. 1994, SCHAICH 2007, STAVI 

et al. 2009). The more soil scientific, geomorphologic and hydrologic studies point out the 

physical compaction phenomena and, accordingly, the reduced infiltration rates of the soils 

(MULHOLLAND & FULLEN 1991, PARIENTE 2002, PIETOLA et al. 2005, PROFFITT et 

al. 1995, STAVI et al. 2008a, b, STAVI et al. 2009, STEWART & CAMERON 1992, 

TABOADA & LAVADO 1993, MWENDERA & SALEEM 1997a). 

In contrast to that, the immediate influence of the trampling of sheep and goat hooves on the 

soil surface are overlooked. The destruction of crusts and the loosening and mobilization of 

soil material for further transport through wind and water are possible effects. Correlating 

geomorphologic rates are also unknown, so far. Only few studies suggest that the impact of 

animal trampling is significant and should not be neglected any more (e.g. UNGAR et al. 

2009, RIES 2005, 2010). 

The issue of rock fragment translocation is treated in even fewer publications. GOVERS & 

POESEN (1998) investigate the translocation of rock fragments by sheep and goat trampling 

in a study area with steep, debris-covered slopes in Turkey, and discovered significant rock 

fragment movements. Particularly, the long-term effects of animal trampling on debriscovered 

slopes should be subject to further investigation (GOVERS & POESEN 1998). 

UNGAR et al. (2009) determine considerable rock fragment movement regardless of their 

size on grazed areas as opposed to the reference area without grazing influence in the Negev 

desert. The vegetation cover is regarded to be the most important factor influencing rockfragment 

movement by animal trampling. On existing trails more rock fragments are moved 

than on densely vegetation-covered areas. NYSSEN et al. (2006) emphasize rock fall and 

material movement as being the most important geomorphologic process induced by animal 

trampling in Ethiopia. On grazed test-areas, up to 95 % of the rock fragments on the soil 

surface were moved in the course of 20 months. 

Only a small number of experimental studies focus on the influence of grazing on vegetation 

cover and geomorphodynamics (RIES et al. 2003, ELDRIDGE 1998, MWENDERA & 

MOHAMED SALEEM 1997a). RIES et al. (2003) observe that sheep and goat trails in dense 

Matorral with intensive grazing can be regarded as the most active surfaces due to the 

227


concentrated trampling impact. They show a tendency to spatial progression, even when shrub 

density increases. By means of rainfall simulations, runoff coefficients of up to 98 % and 

sediment discharges of up to 328 g m -2 could be measured on trails using 40 mm h -1 rainfall 

intensity and a simulated rainfall duration of 30 minutes (RIES 2010). These values are very 

high compared to runoff coefficients and sediment discharges on other surfaces in the same 

study area (runoff up to 76 %, sediment discharge up to 68 g m -2 ). ELDRIDGE (1998) 

determine a higher erodibility, decreasing infiltration rates, increasing overland flow 

generation, a decrease in surface crust-cover and an increase of loose, bare soil, also using 

rainfall simulations on areas with crusted soil surfaces and simulated animal trampling 

(artificial sheep hooves). 

Nevertheless, livestock-induced erosion rates are hitherto practically unknown. The 

fundamental significance of trampling erosion is, however, undisputed. There are few 

quantitative field studies that acquire their measurements from animals in their natural 

surroundings. This lack of research is likely to derive from the complexity of the processes 

involved, being far from thoroughly understood, and non-existing adequate methods. In 

addition, handling live animals and using them as research objects can be difficult and should 

not be underestimated. Particularly, data are missing on: the impact of hooves on dry coherent 

crusted surfaces; the influence of trampling on the translocation of fine material in downslope 

as well as in and against the animals’ moving direction; the influence of slope and moving 

speed on those translocation rates; and the impact of trampling on the translocation of rock 

fragments. 

In this context there is need for comparative studies for the rock translocation experiments in 

the Taurus conducted by GOVERS & POESEN (1998). Even though this phenomenon is 

ubiquitous in nearly all semi-arid and arid regions, the impact of trampling livestock on stonecovered 

surfaces is clearly understudied. Above all, quantitative studies on the distance and 

direction of translocated rock fragments and fine material are missing. Finally, the impact of 

trampling livestock on fluvial erosive forms is of particular interest since little is known about 

how detached material is eroded when flushing occurs, for instance in rills or gullies. 

Following those points, the main objectives of this study are 

1. to develop methods for the quantification of translocation rates of soil-material and 

rock fragments by sheep and goat trampling on in-situ sites, 

2. to present first results concerning ranges of moved rock fragments and soil material 

under these specific experimental setups and 

3. to quantify the effect of animal trampling on sediment availability in rills. 

228


In this way, the directly measured translocation or loosening rates by goat trampling can be 

evaluated and compared with the rates of other erosion processes. In addition, the discussion 

on the methodological development is intended to be encouraged. 


2.1 Study Area 

The study area Freila is located in the Hoya de Baza sedimentary basin (see figure 1). The 

bedrock is composed of Pliocene marls and sandstones on which calcareous Lithosols in 

loamy sand are developed. The semi-arid climate is characterized by an average annual 

temperature of about 14.2 °C and an annual precipitation of 368 mm, with a high inter-annual 

variability. The vegetation is dominated by low shrub-land of Thymus vulgaris and Stipa 

tenacissima grassland. The land-cover on the southern lake-side of the Negratin reservoir is 

dominated by abandoned cereal fields, which are extensively grazed by flocks of sheep and 

goats. Agricultural land-use comprises mainly cereal dry-farming, almond plantations and 

olive orchards (SEEGER 2007). Generally, non-vegetated areas are crusted and rock 

fragments are embedded in the crusts. Only on recently used trails, the crusts are destroyed 

and rock fragments are covering the substrate. 

Figure 1: Localization of the study area in High Andalusia 

229


2.2 Methods: 

All experiments were run on test plots with similar footprints (see fig. 2), installed in contour 

line direction, but carried out on sites with differing surface properties and slopes. The test 

plots are representative for areas used as pasture. 

15 goats were guided over each test plot several times. Meanwhile, translocated material was 

collected and the transport direction recorded. Surface type, slope and running speed were 

varied in accordance with the observed way of natural flock movement patterns. The used 

‘Malaga-goats’ (DOPPELBAUER 2002) and sheep weighed between 45 and 50 kg each. In 

detail, we conducted the following experiments: 

Experiment 1: Translocation quantity in down-slope direction 

Experiment 1 was conducted on slopes of 8.5°, 12° and 20°. Vegetation cover was less than 5 

% on the plots. Plot size was 2 m x 1 m (see fig. 2a). A Gerlach trough with the length of 2 m 

was implemented as a sediment trap at the down-slope end of the plot. 15 goats were guided 

over the plot 4 times in a row (= 60 goats). Afterwards, the sediment traps were emptied and 

weighed. This process was repeated 10 times in order to simulate the impact of the passage of 

a flock of 600 animals. In experiment 1c (slope 20°) we increased the running speed of the 

animals after the 5 th run (= 5 x 60 goats), in the other 2 versions, the running speed was kept 

constant over all runs. 

Experiment 2: Translocation quantity parallel to contour lines 

Experiment 2 was conducted on a 8.5° steep sheep trail. The test plot was covered with 13 % 

vegetation and 18 % rock fragments. The footprint of the experiment was a combination of 

two separate plots (each 2 x 1 m) resulting in a total size of 4 x 1 m. The Gerlach troughs 

(each 1 m in length) were placed at a right angle to the moving direction of the goats at the 

end of those plots (see fig. 2b). Again, the material collected in the troughs was weighed after 

each run of 60 goats. In experiment 2a, the running speed of the goats was increased after the 

5 th run, in experiment 2b the speed was kept constant. 

Experiment 3: Translocation direction and distance of rock fragments 

Experiments 3 a, b and c were conducted on test plots of 2 x 0.6 m (1.2 m 2 ) on 4° (3 a & 3 b) 

and 11° slopes (3 c). On all plots 120, colored and numbered rock fragments (ø ca. 3 cm) 

230


were spread in a 10 x 10 cm pattern (see fig. 2c). After the passing of 3 x 15 goats (= 45 

goats), the translocation vector (distance and angle) of each rock fragment was measured. 

The original position of each fragment was marked by a nail that was driven into the ground. 

The resulting values were categorized into 4 segments according to the measured angles: 

- (1) 0-89° forward-downslope 

- (2) 90-179° backward-downslope 

- (3) 180-269° backward-upslope 

- (4) 270-359° forward-upslope 

Since the bulk of our rock fragments landed in segment 1, this segment was further divided, 

allowing for a more precise interpretation: 

- (1a) 0-44° forward-forward-downslope 

- (1b) 45-89° downslope-forward 

Later on, we applied the law of sines to calculate the vertical up- and downslope translocation 

distances of all moved rock fragments. 

Experiment 4: Loosening quantity 

The test plot of the 4 th experiment had a rectangular footprint of 4 m x 0.5 m (see fig. 2d) and 

was characterized by a flat, crusted surface. It was covered sparsely by dead vegetation (about 

5 %); rock fragments were not present. A flock of 15 goats was guided over the test plot 4 

times (= 60 goats) before it was swept with a regular hand broom. The loosened fine material 

was collected and weighed. This procedure was repeated 10 times in order to simulate the 

gradual loosening process of a soil crust caused by a flock of 600 animals. 

231


Figure 2: Setup of the experiments. 2a: Translocation quantity in down-slope direction; 2b: 

Translocation quantity in running direction; 2c: Translocation direction and distance of rock 

fragments, black dots are the rock fragments; 2d: Loosening quantity 

Experiment 5: Flow detachment of the loosened material 

The rill experiments consist of two runs. First, the rill was tested under field conditions; in a 

second run, about 15 minutes later, the same rill was tested under wet conditions. Using a 

motor driven pump, a constant discharge of 250 L min -1 is maintained during 4 minutes, 

resulting in a total water inflow of 1000 L. The mobilization of material by the water jet at the 

inflow is prevented by covering the substrate with a doormat. For gathering intermediate data 

on suspended sediment transport, three adequate measuring points (MP) were selected. Small 

knick-points in the rill have proven to be the best sampling points because at these points, the 

bottles do not have to be pressed down to the bottom of the rill. Here, four water samples 

were taken. The first was taken immediately on the waterfront’s arrival at the sampling points. 

The second one was taken after 30 seconds, the third after 90 seconds and the fourth 150 

seconds after the arrival of the water. The sediment concentration was determined by filtration 

of the samples in the laboratory. Flow velocity was also measured for each meter flow length 

using a stopwatch (WIRTZ et al. 2010, 2012). 

232


The same rill was tested with and without goat trampling. The rill had an average slope of 

8.8° and a maximum slope of 15.2°. The tested flow length is 16 m. Gravel content was 30%, 

antecedent soil moisture 3 %, vegetation cover about 20 % and rock fragment cover was 60 

%. The maximum depth of the rill was 10 cm and the maximum width about 40 cm. Grain 

density was 2.69 Mg m -3 and (dry) bulk density was 1.44 Mg m -3 . 

Methodology for analysis: 

We used various methodological approaches to describe and illustrate our results: 

In order to describe the results, different methodological approaches were used: 

In experiment 1, the translocation quantity [g] is given. The translocated material is 

removed from a defined test site area and collected in Gerlach Troughs. This quantity refers to 

an area of 2 m² and 60 goats per run; the cumulative values represent 600 goats. As it is a 

downslope mobilization, we can additionally state the translocation flux, i.e. the 

translocation quantity per unit length in downslope direction. As the downslope length is 1 m, 

the translocation flux is equal to the translocation quantity. The translocation quantity is 

measured over the test plot length of 2 m, which leads to the following equation: translocation 

flux [g m -1 ] = translocation quantity / 2. The translocation rate can be calculated from the 

translocation quantity. It refers to 1 m² and one goat: translocation rate = translocation 

quantity / 120. 

In experiment 2 we use the translocation quantity and the translocation rate. The translocation 

flux is not used because the values are not the result of a downslope movement. In this 

experiment it is noteworthy that each trough collects the material from an area of 2 m², so 

cumulated material from both troughs refers to 4 m². Additionally, in experiment 2, we 

discuss a trail erosion rate. This value is given in Mg per ha and 600 goats, calculated from 

the translocation rate in g per m² and goat. This calculation is representative in this case, 

because on trails, the goats run similarily fast and similarily close as in our experiments. 

In experiment 3, we calculate a net mean downslope translocation rate for each individual 

rock fragment per experiment: Net mean downslope translocation rate = (downslope quantity 

x downslope mean distance) - (upslope quantity x upslope mean distance) / all spread out rock 

fragments. 

In experiment 4, the loosening quantity was measured by brushing off and collecting the 

loosened material from the flat test plot. The quantity is given in [g], referring to an area of 2 

m² and 60 goats in each run. The loosening rate refers to 1 m² and 1 goat, leading to: 

loosening rate = loosening quantity / 120. 

233


In experiment 5, the detachment rate [Kg s -1 m -2 ] and the transport rate [Kg s -1 ] are 

presented. They are calculated as follows: 

transport rate = sediment concentration * flow velocity * flow cross section 

detachment rate = transport rate / (flow length * wetted perimeter) 

The sediment concentration is given in [g L -1 ], flow velocity in [m s -1 ], the flow cross section 

in [m 2 ], flow length and wetted perimeter in [m]. 

3 Results and interpretation 

3.1 Translocation quantities in downslope direction 

Figure 3: Translocation quantities in down-slope direction 

The first runs are not taken into account in order to eliminate possible errors due to the 

installation of the Gerlach troughs. 

On the 8.5° slope plot, rock fragments are translocated only in the 4 th run, in all other runs 

only fine material is affected by the trampling. The quantities are similar, they range between 

75 and 41 g, only run 4 with 282 g and run 8 with only 4 g are out of line. The quantities are 

presented in figure 3a. In total, 83 g rock fragments (11 %) and 662 g fine material was 

translocated (figure 3d). The translocation flux is equal to translocation quantity. 

234


The course of the translocation quantity of fine material and rock fragments in down-slope 

direction on a 12° slope is presented in figure 3b. From run 2 to 8, the quantity of fine 

material is higher than the quantity of rock fragments, the percentage of rock fragments on 

total translocated material is between 20 % and 25 % (in runs 4, 6 and 7, it is 0 %). Run 9 and 

10 show an increase in rock fragment quantity, in run 9 the percentage increases to 70 % and 

in run 10 even to 81 %. The translocation rate of fine material is similarily high in runs 2-5, 

while runs 6-10 show lower fine material amounts except for run 8 with a fine material 

amount in the range of the first group. The total translocated fine material is 1245 g, rock 

fragments with 496 g cause 28 % of total sampled material (figure 3d). 

On a 20° slope (figure 3c), the mass of translocated material increases up to a mean value of 

788 g (runs 2-5). From run 6 to 10 the running speed was increased, which can be regarded as 

typical for the more difficult slope segments. The amount of eroded material for the slow runs 

2 to 5 ranges between 475 g and 961 g. In the faster runs 6 to 10, values between 1 573 g and 

1 032 g are measured, which is equivalent to a medial increase of 66 %. The percentage of 

rock fragments of the total mass of eroded material increases from 10 % in the slow runs to 21 

% in the fast runs. In total 8096 g were translocated, 16 % of which were rock fragments. Due 

to comparability reasons, the 10 th runs of the experiments 12° and 20° were not considered in 

figure 3d. 

Interpretation: 

Experiment 1a (8.5° slope) only shows low material translocation rates. The given slope is too 

flat to transport the material to the troughs. The material seems to be loosened and after 

several intermediate storages, the material reaches the troughs in run 4. 

Also in experiment 1b (12° slope), only a low amount of material is translocated with 2.26 kg 

m -2 per goat. The fluctuating amounts of moved soil material can be explained by the fact that 

the material either reaches the Gerlach troughs directly, or it is temporally stored in the still 

existent micro-relief of ridges and furrows. The rock fragments are only mobilized after about 

480 goats have passed. The threshold was crossed this late because the rocks were embedded 

into the soil and re gradually detached by the trampling. 

Due to the increase of slope to 20° in experiment 1c, the translocation rates in the slow runs 

were 3 times higher and reach values of up to 6.6 g m -2 per goat. Again, the translocation rate 

increased with higher running speed up to 10 g m -2 per goat and thereby reaches the same 

range as the loosening rate in experiment 4. Due to the steep slope, the material reached the 

Gerlach trough directly, without intermediate storage. The amount of transported rock 

235


fragments increased considerably in later runs, because a certain number of crossing animals 

is necessary to mobilize the rock fragments from their embedded position. This could already 

be observed on the 12° slope. The increase in running speed also promotes the movement of 

rock fragments. 

3.2 Translocation quantities parallel to contour lines 

236


Figure 4: Translocation quantities parallel to contour lines 

Again, the first run is not taken into account in order to avoid errors resulting from the 

installation of the Gerlach troughs. 

237


Amounts of material which were moved on existing trails parallel to contour lines range 

between the values measured on the abandoned fields in downslope direction with 8.5° and 

12° slopes (experiment 1). 

In a first experiment, we changed the running speed after the 5 th run and measured fine 

material as well rock fragment translocation. In a second experiment with constant slow 

running speed, we wanted to ensure to have measured the influence of different speed in the 

first experiment, not the influence of a longer trampling time and higher animal quantity. 

In the first experiment (figure 4a) rock fragments were not moved in the first 5 slow runs. 

From run 6 onwards, the running speed of the animals was increased so that the goats were 

now really 'running' along the trail, just in a way that can be regarded as typical for faster 

movements of flocks. This faster movement lead to an increase of the translocation quantity 

by the factor five, but with a temporal lag, because it was recorded only in the 7 th run. 

Afterwards this trend decreased. Now, in addition to the higher fine material amount, rock 

fragments were moved in runs 7 to 10. Their proportion rose and fell from 31 % in the 7 th run 

over 35 % and 29 % down to 9 % in the last run. Altogether 4134 g of material was moved in 

this experiment, 1237 g or 30 % of this material were rock fragments (see figure 4a). 

In the second experiment, hardly any rock fragments were present on the plot. In mean, 145 g 

material was moved in each run, this is similar to the 155 g measured in the slow runs in 

experiment 2a. 


The similar mean values of the 4 slow runs in experiment 2a and the 9 runs in experiment 2b 

show that the differences between the slow and the fast runs in experiment 2a are caused by 

the different running speeds and not by trampling time and animal quantity. 

In the trail experiment, the measured translocation rates parallel to contour lines reached 

values around 1.3 g m -2 per goat for the slow runs which is comparable to the values measured 

on the abandoned field. At the higher running speed, as it is more typical for the trails, the 

translocation rate was five times higher with 5.9 g m -2 per goat. In the following experiment, 

it is clearly to see that the speed influences the translocation rate and not the longer trampling 

time and the higher number of animals. That means the running speed is an important 

parameter for the quantity of translocated material. The movement of rock fragments again 

can only be observed after the passing of about 300 goats. 

3.3 Translocation direction and distance of rock fragments 

238


239


Figure 5: Translocation direction and distance of rock fragments. Length of the arrows 

represents the mean translocation distance, width of the arrows the quantity of the rock 

fragments in each segment. 

Figure 5 shows the previously introduced segments, the proportion of rock fragments that was 

translocated into each of them as well as the mean distance the fragments were moved. While 

the number of rock fragments is illustrated by the width of the arrows, their length represents 

the mean movement distance. 

Experiments 3a and b were both conducted on test plots with a slope of 4°. In experiment 3a, 

94% of the rock fragments were moved with a mean distance of 7,4 cm. Of these fragments 

44% were relocated forward downslope, 22% backward downslope, 12% backward upslope 

and 18% forward upslope. The mean transportation distances for the segments 1-4 were 8.4 

cm, 7.0 cm, 8.9 cm, and 5.3 cm, respectively. The values in the sub segments 1a and 1b 

resemble each other closely both in input proportion (22%, 22%) and movement distance (8.4 

cm, 8.3 cm). 

In experiment 3b, 71% of all spread out rock fragments were relocated with a mean distance 

of 5.0 cm. 56% of them were moved forward downslope, 14% backward downslope, 13% 

backward upslope and 16% forward upslope. The corresponding mean translocation distances 

were 7.2 cm, 4.4 cm, 3.6 cm, and 4.6 cm. Again, the sub segments 1a and b have equal input 

proportions (28%, 28%), but this time differ in terms of mean movement distance (8.7 cm, 5.6 

cm). 

Experiment 3c was conducted on a steeper slope (11°) than experiments 3a and b. Here, 90% 

of all spread out rock fragments were moved with a mean transportation distance of 14.1 cm. 

The dominating translocation direction was forward downslope with an input proportion of 

71% of all moved fragments. The input in segment 2 is 15%, in segment 3 it is lowest with 

4% and in segment 4 it is 10%. The mean transportation distances for the 4 segments are 16.8 

cm, 9.3 cm, 11.2 cm and 19.0 cm. The input in sub segment 1a is more than twice as high as 

in 1b (49%, 22%). The mean transportation distance, however, is higher in sub segment 1b 

(14.1 cm, 22.9 cm). 

240


Figure 6: Net up- and downslope translocation 

In contrast to figures 5a-c, figures 6a and b do not distinguish between the four segments, but 

juxtapose the vertical up- and downslope translocation for the three experiments. In 

experiment 3a, 61% of all spread out rock fragments were moved downslope, as opposed to 

the 23% that were pushed upslope. Also, the mean translocation distance was higher 

downslope (5.4 cm) than upslope (3.2 cm). In experiment 3b, 49% of all rock fragments were 

translocated downslope with a mean distance of 3.7 cm. 16% were pushed upslope with a 

mean distance of 2.4 cm. The most contrasting results were generated in experiment 3c, where 

66% of all rock fragments were moved downslope with a mean distance of 11.4 cm, while 

11% were transported upslope with a mean distance of 7.9 cm. 


241


Experiments 3a, b and c show that on average 85 % of all marked rock fragments were 

mobilized after the passing of 45 goats. As figure 5 illustrates, the main direction of 

translocation throughout all 3 experiments is forward downslope (segment 1) with an average 

proportion of 57 % of all moved rock fragments. Also true for all 3 experiments is the fact 

that significantly more rock fragments were pushed forward than backward (on average 62 % 

to 28 %). Hence, the goats’ moving direction and slope direction seem to correlate with the 

translocation direction of our rock fragments. As expected, the results of experiment 3c show 

that gravity plays an increasingly important role once slope is steeper. Here, 86 % of all 

moved rock fragments were relocated downslope, compared with 70 % in experiments 3a and 

b combined. Furthermore, the input proportion in the forward directions (segments 1 and 4) is 

heavily skewed in favor of the forward downslope compartment with a ratio of 71 % to 10 %, 

compared with 44 % to 18 % and 56 % to 16 % in experiments 3a and b, respectively. This 

indicates a change in the trajectory of the kicked rock fragments due to steeper slope. Rock 

fragments that would come to a halt in segment 4 on a flatter slope, now land in segment 1. 

This hypothesis is also nicely supported by the analysis of the sub segments 1a and b. Since 

the input quantities are similar for both sub segments in experiments 3a and b, they do not 

allow for a judgment of whether the goats’ moving direction or slope has a higher impact on 

the rock fragments relocation. In experiment 3c, however, where slope is much steeper (11°), 

the input in segment 1a is more than twice as high as in 1b. Likely, this result can be ascribed 

to an additional input of rock fragments in 1a, which on flatter slopes would have remained in 

segment 4. 

Finally, the distribution of rock fragments across all 4 segments, i.e. all directions, is 

noteworthy. The hooves’ impact cannot be easily translated into a forward-downslope kicking 

direction of rock fragments. While this is true for the lion’s share of all measured rock 

fragments, segments 2, 3 and 4 constantly contained at least some of the total quantity. 

Interestingly, the highest mean translocation distances were not always recorded in the 

forward-downslope direction. In fact, this was only the case in experiment 3b. In experiments 

3a and 3c, the upslope segments 3 and 4, respectively, show the highest values. However, 

since few rock fragments were moved into these segments and the mean is calculated, outliers 

can easily affect the result. 

As expected, the mean translocation distance increases with slope. Whereas it is 6.2 cm for 

experiments 3a and b put together, the impact of gravity clearly surfaces in experiment 3c, 

where it is 14.1 cm. On analyzing the results of the sub segments 1a (forward-forwarddownslope) 

and 1b (downslope-forward) in all 3 experiments, the impetus of the factor slope 

242


becomes evident once more. On the relatively flat surface in experiments 3a and b, the mean 

translocation distances of the sub segments is nearly identical in experiment 3a (8.4 cm, 8.3 

cm) and a little higher in sub segment 1a in experiment 3b (8.7 cm, 5.6 cm). On the steeper 

11° slope in experiment 3c, the mean translocation distance in the downslope-forward sub 

segment (1b) is significantly higher (14.1 cm, 22.9 cm). The difference in experiment 3c can 

probably be explained by the high overlap of the driving forces of initial kicking impulse and 

gravity in sub segment 1b. While we assume that 1a contains some rock fragments that were 

initially kicked in upslope direction, fragments that ended in 1b have likely been kicked in 

downslope direction by the goats right away. In that case, impulse and gravity would meet 

best in 1b, leading to the highest mean translocation distance (22.9 cm) here. 

The mean net downslope translocation rates for experiments 3a, b and c are 2.6 cm, 1.5 cm 

and 6.6 cm. Again, slope appears to be a dominating factor and explains why the highest 

distance is recorded in experiment 3c. The low net mean downslope translocation rate of 1.5 

cm in experiment 3b is caused by the relatively high proportion of unmoved stones. 

3.4 Loosening quantity 

Figure 7: Loosening rate of fine material on a highly crusted plain surface 

243


Figure 7 shows that the loosening quantity increased from 305 g in the 1 st to 1538 g in the 3 rd 

run and stayed at this level until the total of 600 goats passed after the 10 th run. After the 5 th 

run, a slight decrease can be observed, but this is probably not significant. 


The increase in the amount of loosened material from run 1 to 3 can be traced back to a stepby-step 

cracking of the sedimentation crust on the whole test plot. After 180 goats, the crust is 

completely destroyed and the soil material is loosened with 1.5 kg 2 m -2 per 60 goats. The 

slightly decreasing trend can be explained by lower availability of detachable crust material 

and by increasing compaction. The measured loosening rate can be evaluated as high 

regarding the value of 12.5 g m - ² per goat. 

3.5 Flow detachment of loosened material 

Figure 8: Sediment concentrations, transport and detachment rates of the rill experiment with 

and without goat trampling (MP = measuring point) 

244


All three erosion parameters showed higher values in the experiment with goat trampling, but 

the difference is most obvious in the dry run. In the second (wet) run, the values were equal or 

at least similar to the values of the experiments without trampling. Transport and detachment 

rate were about 5 times higher in the dry run with goat trampling as in the runs without 

trampling. Sediment concentration in the dry run with trampling was about 2.5 higher 

compared to the experiment without trampling (see figure 8). 


The rill experiment clearly shows the short-term influence of goat trampling. Livestock’s 

hooves’ impact prepares the soil surface and a large quantity of loose material is made ready 

for transport (see experiment 4). Crucially, this material is removed very fast; the second run 

with trampling still shows nearly the same values as the runs without preceding trampling. 

The sediment concentrations at the waterfront were clearly higher in the experiment with 

trampling, whereas the other samples show similar concentrations. Accordingly, trampling 

provides a large quantity of loose material but its impact on mobilization is only detectable for 

a short time. 

3.6 Statistical analysis 

In table 1, the statistical values of the experiments 1, 2 and 4 are summarized. In experiment 1 

and 2, the first run was not used in the calculations to avoid mistakes caused by the 

installation of the troughs. The difference between mean and standard deviation increases 

with slope, meaning high quantities as well as low quantities of substrate can be translocated. 

The quantity of the mean increases with slope but the values become less stable. This is also 

detectable in figure 8. Regarding the values for the movement parallel to contour lines, the 

differences between mean and standard deviation for trough 1 and 2 in each version are very 

similar, they are in all three cases between 52 and 58 %. But in all three cases, the first trough 

shows clearly higher differences than the second trough. Because of the low n-values, we do 

not want to over-interpret the values and conclude that the high values for trough 1 are caused 

by the jumping-in and -out of the animals at the beginning of the test plot. Once they are 

inside the fenced course, the movements are smoother. Figure 9 shows that again, the fast 

running speed can cause very high values as well as low values, the mean values are clearly 

higher than under slow movement but the values are less stable. The high difference between 

245


mean and standard deviation in the loosening experiment can be explained by the slow 

increase at the beginning due to breaking the crust. 

Table 1: Statistical values of the different experiments. St.Dev. = standard deviation, T1 = 

Gerlach Trough A, T2 = Gerlach Trough B 

Mean [g] Median St.Dev. IMean-St.Dev.I % from mean 

[g] [g] 

Slope 8.5° 93.1 66.1 104.9 11.8 12.7 

Slope 12° 250.5 231.9 132.3 118.2 47.2 

Slope 20° 1047.0 1032.3 299.1 747.9 71.4 

Trail A slow T1 92.3 76.5 34.3 58.0 62.8 

Trail A slow T2 62.6 67.0 32.9 29.7 47.4 

Trail A fast T1 374.2 402.0 120.1 254.1 67.9 

Trail A fast T2 328.8 233.0 169.0 159.8 48.6 

Trail B slow T1 105.1 116.0 25.5 79.6 75.7 

Trail B slow T2 39.6 31.1 28.2 11.4 28.8 

Loosening 1322.2 1431.5 394.8 927.4 70.1 

Figure 9: Boxplots of the different experimental setups. T1 = Gerlach Trough A, T2 = 

Gerlach Trough B 

246


4 Discussion 

The calculated translocation rates increase with slope and with the running speed of the 

animals, thus conforming with theoretical expectations. All values are considered to be 

explicitly higher than a tolerable soil erosion rate for completely mechanized agriculture. The 

influence of slope has also been shown by OOSTWOUD WIJDENES et al. (2001). The 

measured transport rates on a 50 % slope were twice as high as on a 20 % slope. The total 

amount of loosened material by trampling of 6.6 Kg m -2 on the test plots has also to be 

evaluated as very high. The provided loose material can easily be eroded by wind and water 

erosion processes (cf. our rill experiments). 

The trails in the study area are distributed very irregularly (see figure 10). The total trail 

density is 247 m ha -1 ; 13 985 m ha -1 in the trail zone and 68 m ha -1 outside this zone. 

Assuming a mean trail width of 30 cm, the total trail area takes up 705 m²; 545 m² in the trail 

zone and 160 m² outside. Regarding the proportions of the total trail area, the values are 0.7 % 

for the whole study area, 3 % in the trail zone and 0.2 % outside the trail zone (see table 2). 

Table 2: Trails length and area sizes of different landscape units in the test area 

Value 

% of total area 

Trail length in Trail zone [m] 1818 - 

Trail length outside Trail zone[m] 532 - 

Total trail length [m] 2350 - 

Trail zone [m²] 17300 18 

Abandoned fields [m²] 49000 51 

Steep slopes [m²] 27830 29 

Untreated zones [m²] 1300 2 

Total area study site [m²] 95430 - 

On the trails, sheep run similarly fast and close as simulated in our experiments, so we can use 

our measured values to calculate trail erosion rates: Parallel to contour lines (in and against 

running direction), each slow moving goat can translocate 1.3 g m -2 , and, if speed is 

increased, the value can reach 5.9 g m -2 . For an extrapolation, we assume an average value of 

3.6 g m -2 per goat and the same slopes as in our experiments, since the plots were 

representative for trails in the study site. The total area is 9.5 ha, the trail area is 705 m², 

meaning the trail erosion rate reaches 160 Kg ha -1 per 600 goats. This value should clearly be 

247


higher in trail zone (1.7 ha, trail area 545 m²), where the trail erosion rate reaches 692 Kg ha -1 

per 600 goats. Outside the trail zone, the value is 44 Kg ha -1 per 600 goats. 

Figure 10: Trail distribution in the study area 

The translocation of rock fragments results in an almost complete workup of the rock 

fragment cover. According to CERDÀ (2001) rock fragments retard ponding and surface 

runoff and give greater steady state infiltration rates and smaller interrill runoff discharges, 

sediment concentrations and interrill erosion rates. He performed rainfall simulations with 55 

mm h -1 for 120 min, in the middle of which he removed the rock fragment cover. The steadystate 

infiltration rate diminished from 44.5 to 27.5 mm h -1 , the runoff coefficient increased by 

the factor 3, sediment concentration by the factor 33 and the erosion rate by the factor 39. 

That means the rock fragments are an important erosion protection and if they are removed by 

animal trampling, the substrate below becomes vulnerable against other erosion processes. 

248


We measured distance and direction of the rock fragment translocation in experiment 3. The 

mean translocation distance of the 3 experiments only reaches 8.8 cm, thus being much lower 

than the mean displacement distance of 38 cm on Lesvos (Greece) that was determined by 

OOSTWOUD WIJDENES et al. (2001). However, this rather short distance is a consequence 

of the considerably flatter slopes of 4° - 11° in the present study vs. 2° - 24° in OOSTWOUD 

WIJDENES et al. (2001). It is important to notice that OOSTWOUD WIJDENES et al. 

(2001) measured the 38 cm after one year, the grazing peak is between April and June. It is 

not reconstructible how far the rock fragments were displaced after a certain number of sheep. 

Additionally, they corrected the negative distances (upslope movement) by adding the largest 

negative distance plus one centimeter to all negative distances. This transformation resulted in 

a slightly overestimated mean. Our smaller rock fragments are probably not the reason for 

these different results, as OOSTWOUD WIJDENES et al. (2001) showed that the rock 

fragment displacement distance is not depending on mass. The study started in May and in the 

first 7 months the displacement distances are lower than in the second 5 months 

(OOSTWOUD WIJDENES et al. (2000). In the 5-month period, only one of the grazing peak 

months is included; in the 7-month period two of them. That means despite longer measuring 

times and despite a higher trampling intensity, the values are higher in the 5-month period. A 

reason could be the winter months December and January, in which other erosive processes 

influence the displacement distances. This fact emphasizes the need for short-term 

experiments to isolate the influence of animal trampling. 

GOVERS & POESEN (1998) measured an average horizontal displacement distance of 38 cm 

for rock fragments on slopes between 27° and 31°. But the test sites had different widths 

(between 1.4 m and 4.1 m) and the number of sheep and goats ranged between 22 and 100. To 

make the measured values comparable, they calculated a unit displacement distance in cm per 

animal and meter. They presented values between 0.47 cm and 5.6 cm. The highest value was 

calculated for the smallest plot, the lowest value for the largest plot. Again, we used a plot 

width of 0.6 m and 45 goats and measured an average distance of 8.8 cm. Our test plot was 

thus smaller than the smallest one used by GOVERS & POESEN (1998). Calculating the 

same unit displacement distance (displacement distance / (number of animals / plot width)) 

we receive a value of 0.1 cm. Once more, slope is probably responsible for this much lower 

value; its effect covers the fact that the plot width of the smallest Govers-Poesen-plot was 

twice as large as our plot width. In our experiments, the marked rocks were positioned on top 

of given overlying or embedded rock fragments. This means our rocks were probably easier to 

move than naturally occurring rock fragments. Even after considering this, our values are still 

249


much lower than those of GOVERS & POESEN (1998). It is hard to mark existing rock 

fragments and measure their translocation distances because their original position cannot be 

marked as easily. Knowing the exact original position of each rock fragment is paramount, 

however, for recording translocation distances and angels. 

The values of mobilized material indicates severe exceeding of the expectable tramplinginduced 

erosion rates for the whole study area, especially considering the fact that a mediumsized 

flock only crossed our test plots for a single time. The effects of the mobilization of soil 

material by the animals’ hooves has scarcely been regarded in literature until now. There is a 

plethora of studies, however, on the decrease in vegetation cover by grazing animals and the 

consequent increase in bare soil areas that are unprotected from erosion (e.g. ALADOS et al. 

2004, ANDRESEN et al. 1990, DUNKERLEY & BROWN 1995, MWENDERA & 

MOHAMED SALEEM 1997b, MWENDERA et al. 1997, NOY-MEIR 1975, 1978, 1995, 

PEARSON et al. 1990, PEGAU 1970, RIES et al. 2003, VALENTIN 1985, WANG et al. 

2002). CERDÀ (1997) showed that runoff and soil loss increase with decreasing vegetation 

cover. He used rainfall simulations on bare plots (0-3 % vegetation cover), on plots vegetated 

by herbs (30-85 % vegetation cover) and on plots vegetated by tussocks (75- 100 % 

vegetation cover). The mean runoff coefficient after 60 min on bare plots was 31 %, on herbs 

plots 2 % and on tussock plots 0.3 %. The mean erosion rate on bare plots was 37 g m -2 h -1 , on 

herbs plots 1.44 g m -2 h -1 and 0 g m -2 h -1 on tussock plots. Accordingly, the reported processes 

of mobilization of soil material and rock fragments by animal hooves need to be investigated 

in different areas in future studies because our preliminary findings show that the impacts of 

these processes on total erosion rates should be tremendous. 

Nevertheless, the experimental designs should be animatedly discussed and need to be further 

developed. 

5 Conclusions 

Independent from the discussible extrapolation of the measured values to a larger area of 

several hectares, the determined values have to be evaluated as high, regarding the land-use of 

extensive grazing in the test area. Also in comparison to erosion rates on agricultural fields, 

the measured values are considered to be too high for a sustainable land use of Mediterranean 

rangelands. 

Regarding our experimental results, the following conclusions can be drawn: 

- Slope and running speed influence the translocation rates by the factor 2.5 to 5.5. 

250


- Embedded rock fragments appear to be resistant against goat trampling until the 

passing of approx. 300 animals. 

- Rock fragments that rest loosely on top of the soil surface are prone to be moved by 

animal hooves even at low slope angles. 

- Crusted soil surfaces provide a high amount of detachable fine material once the crust 

is destroyed livestock trampling. 

- The provided fine material can be eroded by overland flow within a short time, and is 

immediately available for wind erosion processes, too. 

- The experimental methods have proven to be suitable for the determination of areaand 

animal-number-related rates that are surprising in their magnitude. Nevertheless, 

the methods require further validation and development. 

The results of the present study support the conclusion that sheep and goat erosion is a 

severely underestimated problem. 


We want to thank all students and the voluntary assistants for their work during the field trip. 

Special thanks go to Guidobaldo Hernandez Vico, the herder of the “erosion-goats”. He 

provided the goats and he was the only person who was able to keep the 15 crazy critters 

under control. 

References 

ALADOS, L., ELAICH, A., PAPANASTASIS, V.P., OZBEK, H., NAVARRO, T., 

FREITAS, H., VRAHNAKIS, M., LARROSI, D. & CABEZUDO, B. (2004): Change in 

plant spatial patterns and diversity along the successional gradient of Mediterranean 

grazing ecosystems. - Ecological Modelling 180: 523-535. 

ANDRESEN, H., BAKKER, J.P., BRONGERS, M., HEYDEMANN, B. & IRMLER, U. 

(1990): Long – term changes of salt marsh communities by cattle grazing. – Vegetatio 89: 

137-148. 

BARBIER, N., COUTERON, P., LEJOLY, J., DEBLAUWE, V. & LEJEUNE, O. (2006): 

Self-organized vegetation patterning as a fingerprint of climate and human impact on 

semi-arid ecosystems. – J. Ecol., 94: 537-547. 

BOONKORKUEA, N., LENBURY, Y., ALVARADO, F.J. & WOLLKIND, D.J. (2010): 

Nonlinear stability analyses of vegetation pattern formation in an arid environment. – 

Journal of Biological Dynamics 4, 4: 346-380. 

251


BORGOGNO, F., D’ODORICO, P., LAIO, F. & RIDOLFI, L. (2009): Mathematical Models 

of vegetation pattern formation in ecohydrolgy. – Reviews of Geophysics 47: RG1005, 

doi:10.1029/2007RG000256. 

BRANSON, F.A., GIFFORD, G.F., RENARD, K.G. & HADLEY, R.F. (1981): Rangeland 

hydrology, 2 nd edition. - Kendall/Hunt Pub Co, Dubuque, IA, 340 pp. 

CERDÀ, A. (1997): The effect of patchy distribution of stipa tenacissima L. on runoff and 

erosion. – Journal of Arid Environments 36: 37-51. 

CERDÀ, A. (2001): Effects of rock fragment cover on soil infiltration, interrill runoff and 

erosion. – European Journal of Soil Science 52: 59-68. 

DEBLAUWE, V., BARBIER, N., COUTERON, P., LEJEUNE, O. & BOGAERT, J. (2008): 

The global biogeography of semi-arid periodic vegetation patterns. – Global. Ecol. 

Biogeogr. 17: 715-723. 

DESIR, G. & MARIN, C. (2007): Factors controlling the erosion rates in a semi-arid zone 

(Bardenas Reales, NE Spain). Catena 71: 31-40. 

DOPPELBAUER, J.P. (2002): Ziegenzucht und Ziegenhaltung in der EU und den 

Beitrittsländern. - 1. Fachtagung für Ziegenzüchter und -halter, 12. - 13. November 2002, 

Bundesanstalt für alpenländische Landwirtschaft Gumpenstein, 4 pp. 

DUNKERLEY, D.L. & BROWN, K.J. (1995): Runoff and runon areas in a patterned 

chenopod shrubland, arid western New South Wales, Australa: characteristics and origin. 

– Journal of Arid Environments 30: 41-55. 

ELDRIDGE, D. J. (1998): Trampling of microphytic crusts on calcareous soils and its impact 

on erosion under rain-impacted flow. – Catena 33: 221-239. 

ELWELL, H.A. & STOCKING, M.A. (1976): Vegetal cover to estimate soil erosion hazard 

in Rhodesia. – Geoderma 15: 61–70. 

EVANS, R. (1998): The erosional impacts of grazing animals. – Progress in Physical 

Geography 22, 2: 251-268. 

GALLE, S., BROUWER, J. & DELHOUME, J. P. (2001): Soil water Balance. – In: 

Tongway, D.J., Valentin, C. & Seghieri, J. (eds.): Banded vegetation patterning in arid 

and semiarid environments: ecological processes and consequences for management:77- 

104; Springer-Verlag, New York. 

GOLODETS, C. & BOEKEN, B. (2006): Moderate sheep grazing in semiarid shrubland 

alters small-scale soil surface structure and patch properties. - Catena 65: 285-291. 

GOVERS, G. & POESEN, J. (1998): Field experiments on the transport of rock fragments by 

animal trampling on scree slopes. – Geomorphology 23: 193-203. 

252


HILLERISLAMBERS, R., RIETKERK, M., VAN DEN BOSCH, F., PRINS, H.H.T. & DE 

KROON, H. (2001): Vegetation pattern formation in semi-arid grazing systems. - Ecology 

82(1): 50-61. 

JONES, C.G., LAWTON, J.H. & SHACHAK, M. (1994): Organisms as ecosystem engineers. 

- OIKOS 69: 373-386. 

MOLINILLO, M., LASANTA, T., & GARCIA-RUIZ, J. (1997): Managing mountainous 

degraded landscapes after farmland abandonment in the Central Spanish Pyrenees. - 

Environmental Management 21(4): 587-98. 

MONFREDA, C., RAMANKUTTY, N. & FOLEY, J. A. (2008): Farming the planet: 2. 

Geographic distribution of crop areas, yields, physiological types, and net primary 

production in the year 2000. - Global Biogeochem. Cycles 22: GB1022, 

doi:10.1029/2007GB002947. 

MONFREDA, C., RAMANKUTTY, N. & HERTEL, T.W. (2009): Global Agricultural Land 

Use Data for Climate Change Analysis. – In: Hertel, T.W., Rose, S. & Tol, R.S.J. (eds): 

Economic Analysis of Land Use in Global Climate Change Policy: 33-48; Routledge. 

MONTANA, C. (1992): The colonization of bare areas in two-phase mosaics of an arid 

ecosystem. - Journal of Ecology 80: 315-327. 

MULHOLLAND, B. & FULLEN, M.A. (1991): Cattle trampling and soil compaction on 

loamy sands. - Soil Use and Management 7,4: 189-192. 

MWENDERA, E.J. & MOHAMED SALEEM, M.A. (1997a): Hydrologic response to cattle 

grazing in the Ethiopian highlands. - Agriculture, Ecosystems and Environment 64: 33-41. 

MWENDERA, E.J. & MOHAMED SALEEM, M.A. (1997b): Infiltration rates, surface 

runoff, and soil loss as influenced by grazing pressure in the Ethiopian highlands. - Soil 

Use and Management 13: 29-35. 

MWENDERA, E.J., MOHAMED SALEEM, M. A. & WOLDU, Z. (1997): Vegetation 

response to cattle grazing in the Ethiopian highlands. - Agriculture, Ecosystems and 

Environment 64: 43-51. 

NOY-MEIR, I. (1975): Stability of grazing systems: an application of predator-prey graphs. - 

Journal of Ecology 63: 459-481. 

NOY-MEIR, I. (1978): Grazing and production in seasonal pastures: analysis of a simple 

model. - Journal of Applied Ecology 15: 809-835. 

NOY-MEIR, I. (1995): Interactive effects of fire and grazing on structure and diversity of 

Mediterranean grasslands. - Journal of Vegetation Science 6: 701-710. 

253


NYSSEN, J., POESEN, J., MOEYERSONS, J., DECKERS, J. & HAILE, M. (2006): 

Processes and rates of rock fragment displacement on cliffs and scree slopes in an amba 

landscape, Ethiopia. – Geomorphology 81: 265-275. 

OLDEMANN, L.R., HAKKELING, R.T.A. & SOMBROEK, W.G. (1991): World map of the 

status of humaninduced soil degradation. An explanatory note. Wageningen: International 

Soil Reference and Information Centre/Nairobi: United Nations Environment Programme, 

41 pp. 

OOSTWOUD WIJDENES, D.J., POESEN, J., VANDEKERCKHOVE, L. & KOSMAS, C. 

(2000): The use of marked rock fragments as tracters to assess rock fragments transported 

by sheep trampling on Lesvos, Greece. – In: Foster, I.D.L. (ed): Tracers in 

Geomorphology. John Wiley & Sons, LTD: 201-220. 

OOSTWOUD WIJDENES, D.J., POESEN, J., VANDEKERCKHOVE, L. & KOSMAS, C. 

(2001): Measurements at one-year interval of rock-fragment fluxes by sheep trampling on 

degraded rocky slopes in the Mediterranean. – Zeitschrift für Geomorphologie 45,4: 477- 

500. 

PARIENTE, S. (2002): Spatial patterns of soil moisture as affected by shrubs, in different 

climate conditions. – Environmental Monitoring and Assessment 73: 237-251. 

PEARSON, H.A., BALDWIN, V.C. & BARNETT, J.P. (1990): Cattle grazing and pine 

survival and growth in subterranean clover pasture. – Agroforestry Systems 10: 161-168. 

PEGAU, R.E. (1970): Effect of reindeer trampling and grazing on lichens. – Journal of Range 

Management 23,2: 95-97. 

PIETOLA, L., HORN, R. & YLI-HALLA, M. (2005): Effects of trampling by cattle on the 

hydraulic and mechanical properties of soil. – Soil and tillage research 82: 99 – 108. 

PROFFITT, A.P.B., BENDOTTI, S. & MCGARRY, D. (1995): A comparison between 

continuous and controlled grazing on a red duplex soil. I. Effects on soil physical 

characteristics. - Soil & Tillage Research 35: 199-210. 

RAMANKUTTY, N., EVAN, A. T., MONFREDA, C. & FOLEY, J. A. (2008): Farming the 

planet: 1. Geographic distribution of global agricultural lands in the year 2000. - Global 

Biogeochem. Cycles 22: GB1022, doi:10.1029/2007GB002947. 

RIES, J.B. (2010): Methodologies for soil erosion and land degradation assessment in 

Mediterranean-type ecosystems. – Land Degradation & Development 21: 171-187. 

RIES, J.B., SEEGER, M., ISERLOH, T., WISTORF, S. & FISTER, W. (2009): Calibration of 

simulated rainfall characteristics for the study of soil erosion on agricultural land. - Soil & 

Tillage Research 106:109-116. 

254


RIES, J. B. (2005): Soil Erosion on Abandoned Fields in Mediterranean Mountains - 

Monitoring of Processes and Development. - Journal of Mediterranean Ecology 6,1: 43- 

52. 

RIES, J.B., MARZOLFF, I. & SEEGER, M. (2003): Einfluss der Beweidung auf 

Vegetationsbedeckung und Geomorphodynamik zwischen Ebrobecken und Pyrenäen. - 

Geographische Rundschau 55, 5: 52-59. 

ROSTANGO, C. M., DEL VALLE, H. F. & VIDELA, L. (1991): The influence of shrubs on 

some chemical and physical properties of an aridic soil in north-eastern Patagonia, 

Argentina. - Journal of Arid Environments 20: 179-188. 

SCHAICH, H. (2007): Analyse raum-zeitlicher Prozesse der Vegetationsentwicklung unter 

Beweideeinfluss in der renaurierten Syr-Aue (Luxemburg). – Cultera 51: 179-191. 

SEEGER, M. (2007): Uncertainty of factors determining runoff and erosion processes as 

quantified by rainfall simulations. - Catena, 71(1): 56-67. 

SEUFFERT, O., HERRIG K., OLLESCH G. & BUSCHE, D. (1999): REI - An integrated 

rainfall erosivity index for assessing and correlating rainfall structure, runoff and erosion. 

- Geoökodynamik 20: 1-54. 

STAVI, I., UNGAR, E.D., LAVEE, H. & SARAH, P. (2008a): Grazing-induced spatial 

variability of soil bulk density and content of moisture, organic carbon and calcium 

carbonate in a semi-arid rangeland. – Catena 75: 288-296. 

STAVI, I., UNGAR, E.D., LAVEE, H. & SARAH, P. (2008b): Surface microtopography and 

soil penetration resistance associated with shrub patches in a semiarid rangeland. – 

Geomorphology 94: 69-78. 

STAVI, I., UNGAR, E.D., LAVEE, H. & SARAH, P. (2009): Livestock modify ground 

surface microtopography and penetration resistance in a semi-arid shrubland. – Arid Land 

Research Management 23: 237-247. 

STEWART, D.P.C. & CAMERON, K.C. (1992): Effect of trampling on the soils of the St 

James Walkway, New Zealand. – Soil Use and Management 8,1: 30-36. 

TABOADO, M.A. & LAVADO, R.S. (1993): Influence of cattle trampling on soil porosity 

under alternate dry and ponded conditions. – Soil use and Management 9,4: 139-143. 

TOLLNER, E.W., CALVERT, G.V. & LANGDALE, G. (1990): Animal trampling effects on 

soil physical properties of two southeastern U.S. ultisols. – Agriculture, Ecosystems and 

Environments 33: 75-87. 

255


TONGWAY, D.J., VALENTIN, C. & SEGHIERI, J. (2001): Banded Vegetation Patterning in 

Arid and Semiarid Environments: Ecological Processes and Consequences for 

Management. – Springer, 1 st Edition, New York, 267 pp. 

TONGWAY, D. J. & LUDWIG, J. A. (2001): Theories on the origins, maintenance, 

dynamics, and functioning of banded landscapes. – In: Tongway, D.J., Valentin, C. & 

Seghieri, J. (eds.): Banded vegetation patterning in arid and semiarid environments: 

ecological processes and consequences for management: 20-31; Springer-Verlag, New 

York. 

UNGAR, E. D., STAVI, I., LAVEE, H. & SARAH, P. (2009): Effects of livestock traffic on 

rock fragment movement on hillsides in a semiarid patchy rangeland. - Land Degradation 

& Development 20: 1-8. 

VALENTIN, C. (1985): Effects of grazing and trampling on soil deterioration around recently 

drilled water holes in the Sahelian Zone. – In: El-Swaify, S.A., Moldenhauer, W.L. & Lo 

A. (eds): Soil Erosion and Conservation. Soil Cons. Soc. of America, Ankeny, USA: 51- 

65. 

WANG, Y., SHIYOMI, M., TSUIKI, M., TSUTSUMI, M., YU, X. & YI, R. (2002): Spatial 

heterogeneity of vegetation under different grazing intensities in the Northwest 

Heilongjiang Steppe of China. - Agriculture, Ecosystems and Environment 90: 217-229. 

WIRTZ, S., SEEGER, M. & RIES, J.B. (2010): The rill experiment as a method to approach a 

quantification of rill erosion process activity. – Zeitschrift für Geomorphologie 54,1: 47- 

64. 

WIRTZ, S., SEEGER, M. & RIES; J.B. (2012): Field experiments for understanding and 

quantification of rill erosion processes. – Catean 91:21-34. 

WORRALL, G. A. (1959): The Butana grass patterns. - Journal of Soil Science 10: 34-53. 

256


Angaben zur Person 

Name, Vorname 

Geburtsdatum 

Familienstand 

Wissenschaftlicher Werdegang 

Wirtz, Stefan 

17.01.1982, Saarbrücken 

ledig 

Berufserfahrung 

Seit Januar 2011 

Wissenschaftlicher Mitarbeiter im Fach Physische 

Geographie 

Juli 2008 – Dezember 2010 

Promotions-Stipendiat an der Universität Trier, 

gefördert durch das Land Rheinland-Pfalz (GraFöG) 

Ausbildungsweg 

Juli 2008 - 

Doktorand an der Universität Trier, FB VI 

Geographie/ Geowissenschaften 

September 2002 bis Dezember 2007 

Studium der Angewandte Physische Geographie an 

der Universität Trier, Abschluss: Diplom-Geograph 

Nebenfächer Bodenkunde und Geologie 

Thema der Diplomarbeit: Spülversuche als 

experimentelle Methode zur Rinnenerosionsforschung 

Juli 2001-März 2002 

Wehrdienst Fallschirmjäger FschJgBtl. 261 Lebach 

1992-2001 Realgymnasium Völklingen, Abschluss: Abitur 

257

Dipl. Geogr. Stefan Wirtz; Physische Geographie, Universität Trier, Behringstraße, 54286 Trier 

Lebenslauf 

Persönliche Daten 

Name 

Wirtz, Stefan 

Anschrift privat Thomasstraße 2 

54316 Franzenheim 

Telefon: +496588 982889 

E-Mail: stefanw-170182@t-online.de 

Geburtsdatum 

Geburtsort 

Staatsangehörigkeit 

Familienstand 

17.01.1982 

Saarbrücken 

Deutsch 

ledig 

Ausbildung 

1988-1992 

1992-2001 

Juli 2001-März 2002 

September 2002 

- Dezember 2007 

Juli 2008 – Dezember 2010 

Seit Januar 2011 

Grundschule Viktoria, Püttlingen 

Realgymnasium Völklingen, Abschluss: Abitur 

Wehrdienst Fallschirmjäger FschJgBtl. 261 Lebach 

Universität Trier 

Studiengang Angewandte Physische Geographie 

Nebenfächer Bodenkunde und Geologie 

Abschluss mit Note „sehr gut“ 

Thema der Diplomarbeit: Spülversuche als experimentelle 

Methode zur Rinnenerosionsforschung 

Promotionsstipendium des Landesgraduiertenzentrums der 

Universität Trier 

Wissenschaftlicher Mitarbeiter der Universität Trier, 

Physische Geographie 

258

Dipl. Geogr. Stefan Wirtz; Physische Geographie, Universität Trier, Behringstraße, 54286 Trier 

Arbeitserfahrung 

März/April 2005 

März/April 2006 

Seit August 2012 

Praktikum beim Landesamt für Umweltschutz, Abteilung 

Geologie und Boden, Saarbrücken 

Praktikum bei der NABU Landesgeschäftsstelle Saarland, 

Lebach 

Aushilfe bei der EGP – Gesellschaft für urbane 

Projektentwicklung 

Sprachkenntnisse 

Englisch gut, Französisch Grundkenntnisse 

EDV-Kenntnisse 

MS Office, ArcGIS, Photoshop 

Interessen und Hobbys 

Leichtathletik, Kampfsport (Ju-Jutsu) 

Lehrveranstaltungen: 

Semester Veranstaltung Leitung 

SoSe 2006 2006 Geländepraktikum "Bodenphysik" Schneider, Wirtz 

SoSe 2008 2008 Lehrforschungsprojekt Physische Geographie Geländeseminar Ries, Iserloh, Wirtz 

SoSe 2008 2008 Lehrforschungsprojekt Physische Geographie Vorbereitungsseminar Ries, Iserloh, Wirtz 

WiSe 2008 / 2009 Lehrforschungsprojekt Datenanalyse und Darstellung Ries, Iserloh, Wirtz 



SoSe 2009 2009 Übung Grundlagen der Physischen Geographie II BSc Wirtz 


SoSe 2010 2010 Geländepraktikum "Geomorphologische Kartierübung" Iserloh, Wirtz 

SoSe 2010 2010 Tutorium für Bachelor- Master- Diplomarbeiten Iserloh, Wirtz 



SoSe 2011 2011 Übung Grundlagen der Physischen Geographie II BEd Geographie Wirtz 



WiSe 2011 / 2012 Übung Grundlagen der Physischen Geographie I BEd Geographie Wirtz 

WiSe 2011 / 2012 Übung Grundlagen der Physischen Geographie I Ökozonen der Erde BSc Wirtz 

SoSe 2012 2012 Tutorium für Bachelor- Master- Diplomarbeiten Iserloh, Wirtz 


…………….…………………………………… 

(Dipl. Geogr. Stefan Wirtz) 

259

Stefan Wirtz Vom Fachbereich VI (Geographie/Geowissenschaften ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?