Rockfall and snow avalanche hazard mapping using the Energy ...

imProved Accessibility: Reliability and securityof Alpine transport infrastructurerelated to mountainous hazards in a changing climateRockfall and snow avalanche hazardmapping using the Energy Line Angleconceptversion: 01, PP10PARAmount is supported by means of the European Regional Development Fund (ERDF)

1 The concept of the Energy Line AngleThe first step for elaborating an efficient risk prevention policy is to provide to experts and decisiontakers a clear and global vision of what could potentially happen in the territory that they aremanaging. This territorial overview on geo hazards potentialities can only be done at a global scalewhich is commonly the regional ones. With such information risk managers and decision takers areable to determine where local scale expertises are needed and to fix priorities in term of technicalinterventions and funds allocations.The general principle of hazard mapping procedure is 1) to determine the localisation of the hazard’spotential and active release areas, and 2) to estimate from these release areas what are the maximalpossible run-out distances.Working at a regional scale means that modelling tools, for which high resolution data and fieldsurveys are needed, are not directly usable. Due to the resolution and the accuracy of the dataavailable at a regional scale, the use of process based 3d propagation models needs to aggregate andsimplify the input parameters and so to deteriorate the domain of validity of the results obtainedwith such models. This kind of models is also time consuming and needs high storage numericalfacilities. So, for providing a robust and usable regional analysis the experts have to use modelsneeding the lowest amount of input data, data which should be easily available without specific fieldinvestigations. Probabilistic empirical models based on the analysis of past events database areclearly answering to these needs.The advantage of such models is that for identifying potential release and propagation zones they donot required any meteorological or geological data. Effectively these models are only based ontopographic criteria and so the only input datum is a digital terrain model (DTM). Nowadays DTM areavailable for all the alpine space countries and so empirical models can be easily used for a firsthazard geographical assessment and pre-mapping.Historically, the concept used for building up the first empirical model has been established by Heimin 1932 for rockfalls hazard. This concept is the one of the Energy Line Angle (ELA). This conceptstates that the maximal run out distance of a rockfall is corresponding to the point resulting of thegraphical intersection between the horizontal plan and a virtual line (the energy line) starting at therelease point and having a specific slope angle (). The following figure illustrates this concept.PARAmount page 2 of 57

Figure 1: The rockfalls Energy line Angle conceptHeim has also proved that the determination of the run out distance can be done using two differentangle of energy line. The calculation can be done 1) using the geometric angle which is calculatedusing the horizontal projection of the direct slope line between the release point and stopping one,or 2) using the travel angle which is calculated from the length of the horizontal projection of theline corresponding to the water flow direction along the slope. The travel angle is always flatter thanthe geometric ones, because the distance derived from the water flow direction is longer than theone calculated along the direct slope and so the ratio of height and horizontal length is smaller (cf.Fig.2).PARAmount page 3 of 57

Figure 2: The difference between the Energy Line geometric angle (in red) and the Energy Line travelangle (in blue).Since 1932 all the published field observations shows that the magnitude of the Energy Line Angle iswithin a certain range and above a certain limits with little variation (see below the chapter onrockfalls zoning). Therefore, it’s possible to get a realistic order of magnitude of the rockfalls run-outlength from a known release point.The Energy Line Angle concept of Heim has been adapted by Scheller in 1970 in order to calculate themaximal run out point using the foot of the cliff and not its top. This author has so defined theshadow angle (). The figure 3 presents these two angles and the formula to be used for calculatingthe Energy Line Angle (the z has to be adapted for the calculation of the shadow angle). Meissl in1998 has determined that the difference between the geometric angle and the travel ones is lessthan 1 degree. The geometric angle is the easiest one to determine both in the field with aninclinometer or using a DTM.Figure 3: The difference between the Energy Line Angle () and the shadow ones ().PARAmount page 4 of 57

Dorren and Berger (2003) have confirmed the possibility of estimating the maximal speed of a rockusing the maximal difference of altitude between the energy line angle and the slope profile (cf. Fig.4).Figure 4: How to determine the maximal speed of a rock using the Energy line Angle.The Energy Line Angle concept is perfectly adapted to a regional scale assessment if a past rockfallsevents data base is available. For each past event the energy line angle can be calculated and so astatistical model can be calibrated.This simple concept based on the principle of the friction angle has been also tested for predictingsnow avalanche maximal run out distance. The first author who has transposed this concept to snowavalanche problematic is Körner in 1976. In 1979 Lied has proposed, for the Norway topographicconditions, the first snow avalanche maximal run out distance predictive model derived from theenergy line angle concept of Heim. Since then, the protocol used by this author for building up hismodel is the international reference for calibrating snow avalanche maximal run out distanceempirical models. This protocol is presented in the next chapter. As for rockfalls the calibration ofenergy line snow avalanche model needs a paste event data base for building up the statistical law tobe used.The simplicity of the ELA concept and the fact that the statistical laws used by the ELA models arecalibrated using past events data, make that the resulting hazard mapping allowed risk managers tohave a first rough and quick preliminary estimation of potential run out distances and to determinegeographical sectors for which local scale expertises have to be performed. Mapping using the ELAconcept can be very quickly provided using terrain and grid calculation modulus of GIS tools.PARAmount page 5 of 57

Within the Paramount project, the French partner IRSTEA has developed two regional scale modelsbased on the ELA concept, the first one Avalfor LIN is dedicated to snow avalanche hazard mappingand the second one Rockfor LIN to rockfalls hazard mapping. These models, if they are able to displaythe geographical areas potentially affected by these hazards, are also providing (if the forest map isavailable for the concerned study area) the zoning of the forest areas having a potential protectionagainst these two natural hazards. As these models are dedicated to a regional scale mapping, theycan be then used both for risk prevention and forest management strategic planning. The two mainobjectives of these models are to identify in a study area if human infrastructures are potentiallyendangered and if forest stands located above these infrastructure can provide a protective function.The general principle for this mapping is based on answering to the following questions:1. Where are the release areas?2. What is the maximum propagation area envelope?3. Is any human infrastructure located in the propagation area and if so, is it endangered?4. Are any forest stands located in the release area and/or in the propagation area above thehuman infrastructure endangered?If the answer to the third question is yes, then a specific expertise has to be conducted in order toassess the need of protective works. If the answer to the fourth question is yes, then these foreststands serve a protective function, and an investigation at a local scale is needed in order to qualifyand/or quantify the efficiency of this protection.PARAmount page 6 of 57

Flow chart 1 : The general flow chart of Rockfor LINDepending on the objectives, the input data needed are:PARAmount page 8 of 57

ObjectivesRelease zones mappingRun-out zones mappingRisk mappingProtection forest mappingInput data : raster maps (the resolutions can be different but theminimal resolution is the one of the DTM)DTMPast eventcadastres or anygeo-localizedinformationHumaninfrastructuresForest mapTable 1: The input data need for using Rockfor LINThe following maps illustrate the 3 main input data.Map 1: The 25x25m resolution DTM of the French case study “département des Hautes-Alpes” (5549km2)PARAmount page 9 of 57

Map 2: The map of the issues of the French case study “ département des Hautes-Alpes”PARAmount page 10 of 57

Map 3: The forest map of the French case study “ département des Hautes-Alpes”2.1 Rockfalls release areas mapping with Rockfor LINRockfor LIN can only be used if all potential rockfalls release points have been mapped. This mappingcan be done via field surveys, aerial photography analysis, past events data base analysis ornumerical processing on the DTM. Rockfor LIN offers the possibility to perform a DTM analysis foridentifying rockfalls potential release areas.The assumption which has been used is that the release areas depend only on the topographicconditions of the case study. So, a simple slope threshold can be applied to the slope surface raster(computed from the raster Digital Terrain Model [DTM]). The resolution and the accuracy of the DTMaffect the results. At least a DTM resolution of 25x25m is necessary. According to the results ofDorren and Berger (2003), the equation used in Rockfor LIN is:α = 55 x RES -0.075 , where RES is the DTM resolutionAll cells with values higher than the threshold α are qualified as potential release zones for rockfalls.This equation has been established using a multi-resolution analysis of slope gradient in knownexisting rockfalls source area in five sites: France (1), Austria (2), Switzerland (1) and Lichtenstein (1).The table below gives the threshold values for determining rockfalls release area for DTM mainresolutions.DTM resolution/cell size [m]Threshold slope gradient[°]1 555 4910 4625 43Table 2: Threshold values for determining rockfalls release area for DTMs’ main resolutionsWithin Rockfor LIN the user has to enter the DTM’s resolution and then 1) the slope threshold isautomatically calculated and 2) the potential rockfalls release areas map is automatically produced. Ifthe user wants to work with another slope threshold value this is possible and he has to enter thevalue he wants to work with. It’s important to keep in mind that the slope threshold value calculationusing a DTM could generates local errors and that this way of calculation can only determine releaseareas with a minimal height. So the resulting map has to be validated by local experts.PARAmount page 11 of 57

Effectively in a DTM the real curvature of a slope is expressed by the slope value of the cells. Forexample a slope of 43° in a 25x25m DTM can represent very different curvatures profiles asexpressed in the figure below:Figure 6: Example of variation of release area configuration expressed with a slope threshold of 43°.So in one cell the potential release vertical height is depending on: the value () and the length (valuemax = the DTM resolution) of the slope below the foot of the release area and, on the value of theslope angle threshold () used (cf. Fig.7).Figure 7: The parameters influencing the potential release vertical height.The table below gives for 1x1, 10x10 and 25x25m DTMs’ resolutions the potential Vertical ReleaseHeight (VRH) with ≤ and slope length = DTM resolution.PARAmount page 12 of 57

DTMResolution Slope threshold : [°][m]1,00 55,00Slope : [°]Vertical release height : VRH[m]0 1,435 1,3410 1,2515 1,1620 1,0625 0,9630 0,8535 0,7340 0,5945 0,4350 0,2455 0,00DTMResolution Slope threshold [°][m]10,00 46,28Slope : [°]Vertical release height : VRH[m]0 10,465 9,5810 8,6915 7,7820 6,8225 5,7930 4,6835 3,4540 2,0645 0,4646,28 0,00DTMResolution Slope threshold [°][m]25,00 43,20Slope : [°]Vertical release height : VRH[m]0 23,485 21,2910 19,0715 16,7820 14,3825 11,8230 9,0535 5,9740 2,5043,2 0,00Table 3 : Value of the potential Vertical Release Height for 1x1, 10x10 and 25x25m DTMs’ resolutionswith ≤ and slope length = DTM resolution.The use of the angle threshold is perfectly well adapted for identifying vertical release height of:≥23.5m in a DTM having a resolution of 25x25m, ≥10.5m in a DTM having a resolution of 10x10m,≥1.5m in a DTM having a resolution of 1x1m. These values are delimitating the domain of validity ofthis method. For lowest DTM resolutions than 1m, the slope gradient release areas method allowsthe expert to obtain a pre-map which will identify all the potential release area having a verticalheight at minima equal to the DTM resolution. So the expert has to check the validity of this pre-mapfor release area having a vertical height lowest than the DTM resolution. One solution is to use alowest angle threshold. In this case some “false” release area can be detected and the validation ofthe pre-mapping by the expert is obligatory. This validation can be done by sampling check point inthe field.The following map illustrates the results obtained with this method in the French case study of theParamount project.PARAmount page 13 of 57

Map 4: Map of rockfalls release zones obtained with Rockfor LIN (French case study “ département desHautes-Alpes”)2.2 Rockfalls potential maximal run-out areas mapping with Rockfor LINFrom each of the identified potential release areas, RockFor LIN simulates the maximal probablepropagation envelopes. For performing this calculation RockFor LIN uses based on the Energy Lineprinciple (Heim, 1932), and on the use of a lateral spread off angle. The lateral spread off angle isused for characterized the potentiality of lateral deviation of a rock along the most probabletrajectory path. The value of this angle has been fixed, using literature data (Dorren and Berger 2003,Jaboyedoff and Labiouse 2011), to 20°.Concerning the chose of value of the Energy Line Angle, the same approach based on a state of theart has been initially used. The table below gives the available value in the literature of the EnergyLine Angle.Author/SourceEnergy Line AngleBetween brackets the value for the geometrical angleMinimum or interval ofvaluesAverage valuePARAmount page 14 of 57

Shreve (1968) (26.57° - 38.66°) ---Hsü (1975) 31° (32°) ---Onofri & Candian (1979)Grunder ( 1984)Moser (1986)28.34° – 40.73°(28,84 ° - 41,73°)32.6° - 33.4°(33.1° - 34.4°)33° - 42°(34° - 43°)Domaas(1985 in Toppe 1987) 32° (33°) ---Mac ewen (1989) (30.96°) ≈ (31°)Gerber (1994)Meissl (1998)Heinimann et al. (1998)Focardi & lotti (2001)33°- 37°(33.5° - 38°)29° – 47,5°(29.5°- 48.5°)33° - 37°(33.5° - 38°)27° - 29°(27.5° - 30°)------------38° (38°)Ayala-carcedo et al. (2001) (29.1° - 38.9°) (31,9°)Jaboyedoff & Labouise (2003) 32° (33°) ---Jaboyedoff & Labouise (2011) (32,6° - 35,6°) 34°Corominas et al. (2003)Dorren & Berger (2005,2006)26° - 54°(27° 55°)31.3° - 37°(31.9° - 38 °)Copons et al.(2009) site a (36.87° - 56,3°) ---Copons et al.(2009) site b (28.81° - 42.0°) ---Hutter et al. (2005) reduce scaleexperiments------------(30° - 37°) ---Scheidegger (1973) (29.68° - 39,69°) ---Marquinez et al. (2002) site 1 (32.5° - 40.9°)Marquinez et al. (2002) site 2 (29.4° -38.5°)Antoniou & Lekkas (2009) (35°) ---Deparis et al (2008) (31,61° - 47,20°) ---(31.5° - 40.2°)PARAmount page 15 of 57

Hyndman & Hyndman (2009) (33°) ---Berger et al. (2009) with forest (27.67° - 33.88°) ---Berger et al. (2009) without forest (31.32° - 37.86°) ---Berger et al. (2009) reduce scaleexperiments(32.57° - 48.99°) ---Table 4: State of the Art on the Energy Line Angle valuesA statistical analysis has been performed on the data of the table 4, the table 5 presents the resultsof this analysis.StatisticsMinimal GeometricalAngleMaximal GeometricalAngleMean 31.14° 39.30°Min 26.57° 30°1 st quartile 29.45° 36,97°2 nd quartile 31.61° 38.583 rd quartile 33° 41.80°Max 36.87° 48.99°Table 5: Statistical distribution of the published minimal and maximal geometrical Energy LineAngleIn parallel to this State of the Art, the French Northern Alps rockfalls data base has been used for astatistical analysis of the observed values’ distribution (cf. tab.6). the geometrical Energy Line Angleis surveyed since 2010 and for each event occurring in the French Northern Alps and for which a fieldsurvey has been done. .StatisticsVolume(m 3 )Energy LineAngle (°)CentileEnergy LineAngle (°)CentileEnergy LineAngle (°)Minimum 0.02 24.65 0.001% 24.65 4.00% 28.00Maximum 200.00 58.42 4.00% 28.00 20.00% 32.00MeanvalueStandarddeviation6.46 36.69 9.00% 30.00 40.00% 35.0018.88 5.54 35.00% 34.00 65.00% 38.00Median 1.50 36,00Total 194PARAmount page 16 of 57

number ofeventsTable 6: Results of the statistical analysis on the geometrical ELA in the French Northern Alpsrockfalls data baseAll these data have been used for defining a matrix of rockfalls propagation probabilities dependingon the value of the geometrical Energy Line Angle (β). This matrix, given below, is the one usedwithin RockFor LIN for run-out zone calculation.Geometrical Energy LineAngle thresholdsProbability of rockfallspropagation≥ 38°High35°≤

Map 5 : Rockfalls probable propagation zones map obtained with RockFor LIN ,and using a 25x25mDTM, for the French case study “ département des Hautes-Alpes”.PARAmount page 18 of 57

a) b)Map 6 : a) Probable rockfalls propagation zones (in orange, in red the release areas) determined withan ELA of 32° and using a 25x25m DTM for the Queyras area (zoom of the map at the scale of the“département des Hautes-Alpes”- b) Probable rockfalls propagation zones (in orange, in red therelease areas) determined with an ELA of 38° and using a 25x25m DTM for the Queyras area (zoomof the map at the scale of the “departement des Hautes-Alpes”.PARAmount page 19 of 57

Map 7: Probable rockfalls propagation zones including the probable reaching frequency (in red therelease areas) determined with an ELA of 32° and using a 1x1m LiDAR DTM for Forte buso case study(Italy).Map 8: Probable rockfalls propagation zones including the probable reaching frequency (in red therelease areas) determined with an ELA of 38° and using a 1x1m LiDAR DTM for Forte buso case study(Italy).PARAmount page 20 of 57

Map 9: Probable rockfalls propagation zones including the probable reaching frequency (in red therelease areas) determined with an ELA of 38° and using a 20x20m DTM for Tognazza Cavallazza casestudy (Italy).Map 10: Probable rockfalls propagation zones including the probable reaching frequency (in red therelease areas) determined with an ELA of 32° for the Austrian case study.PARAmount page 21 of 57

Map 11: Probable rockfalls propagation zones including the probable reaching frequency (in red therelease areas) determined with an ELA of 32° for Baca case study (Slovenia).2.4 Validation of Rockfor LINThe model RockFor LIN has been validated using 20 well documented past events. Each time themaximal run-out distance is at least included in the 32° ELA. The example below is the one of SaintPaul de Varces in France. In this district a rockfalls happened the 28 th December 2008. The observedtrajectories fit with the 38° ELA propagation zone (the versant is forested). RockFor LIN has been ableto identify the release area (circle in yellow on the map and the photo) and the maximal run-outpoint (green circle on the map and the photo).PARAmount page 22 of 57

Map 12: An example of validation of the results obtained with RockFor LIN , the event of the28/12/2008 in the district of saint Paul de Varces in France.This is very important to remind to the users that the results obtained with RockFor LIN have always tobe compare to the known events in the case study. If the observed run-out distances are length thanthe one calculates with RockFor LIN then the value of the ELA has to be adapted.2.5 Rockfalls risk mapping with Rockfor LINThe last step of a risk mapping is to determine if socio-economic issues are endangered by thenatural hazard studied. Good information on the location of facilities is then required. At a regionalscale, each of the Alpine Space countries can find this information in the geographic database of theirrespective national geographic institutes.Usually these databases list and correspondently map all human infrastructures: public facilities,dwellings, industries, as well as communication, electrical, gas and water infrastructure, etc.According to their importance or their extent, all these items can be classified into protection prioritylevels. This ranking is not obligatory, but facilitates the definition of priority levels for specificprotection actions depending firstly on the importance of the issues and secondly on the hazard’sPARAmount page 23 of 57

specifications. This ranking is required to be performed jointly with all actors involved in riskprevention policy of the study area.By combining this map with the rockfalls run-out envelope map, the potentially endangeredinfrastructure can be identified by selecting all the items located between release points and run-outenvelopes. The map obtained includes the endangered issues and the associated release and run-outzones.If the “issues” map is available then RockFor LIN performs automatically this analysis by maps crossing.The following maps illustrate different way of presenting the results of this risk analysis.a) b)Map 13 : a) Probable rockfalls 32° ELA propagation zones (in orange) and human infrastructureslocalization for the Queyras area (zoom of the map at the scale of the “département des Hautes-Alpes”- b) Probable rockfalls 38° ELA propagation zones (in orange) and human infrastructureslocalization for the Queyras area (zoom of the map at the scale of the “département des Hautes-Alpes”.PARAmount page 24 of 57

a) b)c)Map 14 :Illustration of the identification of endangered issues using the rockfalls propagation mapprovided by RockFor LIN for the case study Mittewald in Italy a) 1x1m LiDAR DTM ;b) the 32° ELArockfalls propagation zone including the reaching probability; c) identification of the sections of theroad endangered and risk ranking using the reaching probability : section in black = high level of risk,section in dark grey = medium level of risk, section in soft grey = low level of risk, no colour = no riskPARAmount page 25 of 57

Map 15: Probable rockfalls propagation zones including the probable reaching frequency (in red therelease areas) determined with an ELA of 32° and localization of the railway for Podbrdo case study(Slovenia).2.4 Rockfalls protection forest mapping with Rockfor LINThe protection forest mapping is the last step of the risk analysis than can be done with RockFor LIN .The general principle is to cross the map of endangered issues with the map of the geographicalextension of forest stands. This forest map can be the one provided by National Forest Inventories orthe one available in the forest services. As the mapping is made at a regional scale, thedendrometrical description of the forest stands is not required. The information required is thesurfaces covered by forest. Identification of forest stands potentially serving a protection function isthen obtained by combining the endangered items map with the forest cover map, and by selectingall forested areas located above an endangered item and on/or between the associated release andrun out zones. This selection is provided automatically by RockFor LIN .PARAmount page 26 of 57

This map of potential protection forest areas is required to be validated by a field survey. But beforethis, it can be used to define an area within which forest management dedicated to the improvementof the protection function needs to be applied. In other terms, this map defines the potential area ofuse of protection forest management guidelines.The strength of this methodology lies in its ability to display the area within which forests are able toprovide a protective function against rockfalls; often such areas are unknown having not beenpreviously identified. A decrease in forest canopy in these protection forest areas could havedramatic consequences requiring adaptations to forest management to ensure the sustainability ofthis protective function.The following maps present examples of the results of the potential protection forest mappingperformed with RockFor LIN .PARAmount page 27 of 57

Map 16: Rockfalls potential protection forest map obtained with RockFor LIN , and using a 25x25mDTM, for the French case study “ département des Hautes-Alpes”.PARAmount page 28 of 57

Map 17: Rockfalls potential protection forest (in green) map obtained with RockFor LIN , and using a25x25m DTM, for the French case study Queyras (zoom of the map at the scale of the“département des Hautes-Alpes”)RockFor LIN is the property of Irstea, for any information or expertise get incontact with:frederic.berger@irstea.fr.PARAmount page 29 of 57

3 Snow avalanche hazard mapping with Avalfor LINAs seen in the introductive chapter, the snow avalanche hazard mapping general process is based onanswering to the following questions:1. Where are the release areas?2. What is the maximum propagation area envelope?3. Is any human infrastructure located in the propagation area and if so, is it endangered?4. Are any forest stands located in the release area and/or in the propagation area above thehuman infrastructure endangered?With regard to the quality of the results obtained for rockfalls risk assessment with our toolRockfor LIN , we have decided to use the same concept for snow avalanches risk assessment. So wehave developed the model Avalfor LIN . This model allows natural risk experts to provide a snowavalanche risk assessment on a large geographical scale as the regional one. As for Rockfalls the inputdata necessary to use Avalfor LIN are: a DTM, the map of socio-economic issues, the forest map and, ifpossible, the past event cadastre.As Rockfor LIN , Avalfor LIN is a 2D raster GIS model developed by Irstea. The general flow chart ofAvalfor LIN has been based on the one of Rockfor LIN . This flow chart is given the following diagram.The main differences between Rockfor LIN and Avalfor LIN are:1. The number of criteria to be used for determining the potential release areas2. The use of a double angles Energy Line Angle model3. The calculation are made using the travel angleAs for rockfalls risk assessment conducted with Rockfor LIN , the one made with Avalfor LIN need a fieldsurvey for its validation. Due to the fact that only topographic criteria are used and according to theDTM resolution and accuracy, some risk conditions can be under or over-estimated. Only theconfrontation to past events cadastre, and/or a campaign of field investigation can identify this overor under-estimation. If this validation phase is not provided then the results obtain with Avalfor LINallow only to propose a pre-mapping which gives a first overview on the potential situation.Depending on the objectives, the input data needed for using Avalfor LIN are the following ones:ObjectivesInput data : raster maps (the resolutions can be different but theminimal resolution is the one of the DTM)DTMPast eventcadastres or anygeo-localizedinformationHumaninfrastructuresForest mapPARAmount page 30 of 57

Release zones mappingRun-out zones mappingRisk mappingProtection forest mappingPARAmount page 31 of 57

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Flow chart 2 : The general flow chart of Avalfor LIN3.1 Snow avalanches release areas mapping with Avalfor LINAvalfor LIN can only be used if all potential rockfalls release points have been mapped. This mappingcan be done via field surveys, aerial photography analysis, past events data base analysis ornumerical processing on the DTM. Avalfor LIN offers the possibility to perform a DTM analysis foridentifying snow avalanches potential release areas on a large geographical sector.The assumptions which have been used are that the release areas depend only on the topographicconditions and the altitude of the case study. So, simple slope thresholds can be applied to the slopesurface raster (computed from the raster Digital Terrain Model [DTM]). The resolution and theaccuracy of the DTM affect the results. The release area modulus of AvalforLIN has been initiallydeveloped for a DTM’s resolution of 25x25m. For lowest DTM‘s resolution, as for example LiDARDTM of 1x1m, Avalfor LIN automatically generates a DTM of 20x20m and then applied the criteria andthe associated thresholds used for a 25x25m resolution.For snow avalanches the four criteria used for release area mapping are the curvature, the slope, thealtitude and the surface. The thresholds of these criteria depend on regional and geo-climaticconditions. Commonly in the European Alps, all cells in 25x25m raster DTM with a slope of 28- 55degrees, a convex form, an altitude higher than 1000m and a minimal surface of 500m² areconsidered as potential release zones for avalanches. Z min = f(geo loc) PARAmount page 33 of 57

Figure 8: The main criteria for snow avalanche release areas determination using a raster DTMThe table below gives the thresholds of the criteria used within Avalfor LIN for snow avalanchesrelease areas determination with a 20x20m or a 25x25m DTM. These criteria and the associatedthresholds have been selected from the scientific literature published on this subject.Alpine region Slope ( 1 )Northern andWestern AlpsSouthern andWestern AlpsCentral AlpsJuraMinimalareaConvexity index(based on thecurvature function ofArcGIS and related to 2 - 1 )28 - 55° ≥ 500m² -0.5Altitude min(Zmin)800m1250m1000m700mTable 8: The criteria’s thresholds, using a 20x20m or 25x25m raster DTM, for snow avalanche releaseareas determination within Avalfor LINThe first action to be done by the expert using Avalfor LIN is to select the alpine region and the countryin which the analysis will be provided. The thresholds and the values of the propagation model to beused are then automatically selecting by Avalfor LIN .The following figure and maps present the results obtain with a 1x1m LiDAR DTM resampled to20x20 m for the Italian case studies and with a 25x25m DTM for Austrian and French case studies.For the Italian and the French case studies the maps present also the validation phase using the pastevent cadastre.With the snow avalanche release area modulus of Avalfor LIN , each recorded past event has at least inthe upper part of its mapped envelop one release area according to the criteria used withinAvalfor LIN .PARAmount page 34 of 57

Figure 9: 3D view (derived form a 1x1m LiDAR DTM) of the Italian case study “Passo Rolle” with thedraping of the snow avalanches past events cadastreMap 18: Snow avalanches past events cadastre of the Italian case study “Passo Rolle”PARAmount page 35 of 57

Map 19: Snow avalanches release areas (in pink) determined with Avalfor LIN for the Italian case study“Passo Rolle”. The initial 1x1m Lidar DTM has been resampled to 20x20m.PARAmount page 36 of 57

Map 20: The DTM (expressed using the altitudinal range) of the Austrian case study of the Paramountproject.Map 21: The localization, using Avalfor LIN , of potential snow avalanche release areas (in pink) in theAustrian case study of the Paramount project.PARAmount page 37 of 57

Map 22: The localization, using Avalfor LIN , of potential snow avalanche release areas (in yellow) inone of the French sites of the Paramount project. The envelops in red correspond to the past eventcadastre (called CLPA in French)3.2 The snow avalanches potential maximal run-out areas mapping with Avalfor LINPARAmount page 38 of 57

AvalFor LIN for avalanches is also based on the Energy Line Angle concept initially formalised by Heimin 1932 and adapted with success to the snow avalanche context by Lied in 1979.As for rockfalls, the maximal probable snow avalanche run-out envelope is determined by thecreation of an intersect point between the ground and an imaginary line drawn from the releasepoint with a calibrated angle.The first difference with the ELA for rockfalls is that for snow avalanches this angle () is determinedusing the value of an intermediary Energy Line Angle () calculated for the first upper point on theslope for which the slope angle is equal to 10° (cf. Fig.9).The correlation between and , = a* + b, is determined using recorded and mapped pastevents.Initial release pointMaximal run out point = 0,97 – 1,5 R 2 = 0,85Figure 9: The snow avalanche Energy Line Angle conceptThe second difference with the ELA for rockfalls is that for snow avalanches these are the travelangles that are used and not the geometrical ones. So, the calibration of this () model needs todetermine the travel path using the principle of water flow direction calculation along the steepestslope. Most of the GIS are able to provide such calculation using raster DTM.PARAmount page 39 of 57

The robustness of the model calibrated using past events data depends on both the accuracy of themapped past events’ envelopes and on the resolution of the DTM used for the data processing. InFrance the site of Chamonix has been used for the calibration of a French () model and for theanalysis of the influence of the DTM resolution on the model’s parameters. A 25x25m DTM and a1x1m Lidar DTM have been used. The map 23 presents an extract of the French snow avalanche pastevents cadastre of this site and the travel path used for the calibration of the () model. With the25x25m DTM the linear correlation between iswith a regression coefficient ofR 2 = 0.82 and with the 1x1m LiDAR DTM this coefficient rise up to 0.94 and the relation is (cf. Fig.10 and 11). It’s important to notice that for the minimal value (27.02°) ofcited in the literature, the difference between the calculated with these two models is only of0.64°.Map 23: Tan extract of the geographical data used for the () model calibration for the Frenchtopographical conditions of the valley of Chamonix. The black lines represent the limits of thepropagation envelopes of the past events and the coloured ones the travel path associated to eachenvelope.PARAmount page 40 of 57

alphaα4545αStastistical Snow Avalanches EnergyLine Angle extrem run-out zone modelReprésentation linéaire linéaire du du modèle modèle "Français""Français"40403535y = y 0,97x = 0,97x - 1,50- 1,50R 2 R = 2 0,82= 0,82303025252020Angles Angles Snow des des couloirsAvalanchecouloirsd'avalanchesd'avalanchesEnergy Line AngleLinéaire Linéaire (Angles des couloirsLinear(Angles regression des couloirsd'avalanches)d'avalanches)15β1515 15 20 20 25 25 30 30 35 35 40 40 4545βFigure 10: The () model calibration using a 25x25m DTM for the French topographical conditionsof the valley of Chamonix50α4545αStastistical Snow Avalanches EnergyLine Angle extrem run-out zone modelReprésentation linéaire linéaire du du modèle modèle "Français""Français"Calage modèle norvégien4540353025201540403535303025252020β15 1520 25 30 35 40 45 50 5515 15 20 20 25 25 30 30 35 35 40 40 4545betay = y 1.0018x-1.6698= y 0,97x = 0,97x - 1,50- 1,50R R 2 2 = = 0.94R 2 0,82= 0,82Angles Angles Snow des des couloirsAvalanchecouloirsd'avalanchesd'avalanchesEnergy Line AngleLinéaire Linéaire (Angles des couloirsLinear(Angles regression des couloirsd'avalanches)d'avalanches)βFigure 11: The () model calibration using a 1x1m DTM for the French topographical conditions ofthe valley of ChamonixPARAmount page 41 of 57

Many authors have tested this () model in different region of the world. The table below gives theavailable value in the literature of this (,) model for different countries ( in red the parametersusable within the European space) and the statistics obtained with these data.Country/ region a b R 2 N Mean Mean Norway0,93 0,86 2,10 1920,94 0,20 0,89 1,74 127423 31,000,96 -1,40 0,92 2,30 200 18,00Western Norway 0,90 0,87 127 29,40 32,60Austria 0,95 -0,83 0,92 1,50 80Iceland 0,85 0,52 2,20 44Canadian mountains(High resolution)Canadian mountains(Low resolution)0,93 0,89 1,10 350,93 0,89 1,05 35Canadian Rockies 0,93 0,75 1,75 126 27,80 29,80Canadian Rockies 0,90 0,15 0,80 1,57 125 28,50 30,60Canadian CoastMountains0,90 0,74 1,70 31 26,80 29,50British Columbia 0,87 0,23 0,61 2,10 31Catalan pyrenees 0,86 1,05 0,75 1,98 64 24,70 27,30Alaska 0,86 0,58 52 25,40 29,60Alaska 0,81 0,32 0,67 1,84 52Colorado 0,80 0,50 130 22,60 27,40Colorado 0,77 0,14 0,51 2,31 130Sierra Nevada 0,76 0,60 90 20,70 26,10Switzerland 50 28 (min 22°)French Northern Alps(Chamonix Highresolution)French Northern Alps(Chamonix+ ChablaisHigh resolution)French Northern Alps(Chamonix Lowresolution)0,98 -1,00 0,90 1031,00 -1,67 0,94 1280,97 -1,50 0,82 103Italy (Magafosse) 0,91 0,05 0,97 10Mean 25,72 29,11PARAmount page 42 of 57

3.94 2,09min 21,41 27.02max 29,57 31.20Table 9: State of the Art and associated statistics on the Energy Line Angle values, () model, forsnow avalancheWithin the Paramount project, an () model has been calibrated for the French, Italian andAustrian topographic conditions. These models are:France: = 1.0018* – 1.6698; R 2 = 0.94Italy: = 0.9074* + 0.0506; R 2 = 0.97Austria: = 0.95* – 0.8; R 2 = 0.92The following table gives the different and the differences of angle obtained with each oftheses models and using the minimal, mean and maximal values of the table 9.min (°) mean (°) max (°)France 25,40 27,49 29,59Italy 24,57 26,47 28,36Austria 24,87 26,85 28,84min (°) mean (°) max (°)F-I 0,83 1,03 1,22F-At 0,53 0,64 0,75I-At -0,30 -0,39 -0,48Table 10: The different and the differences of angle obtained with the French, Italian and Austrianmodels.From the table 9 and the differences expressed in the table 10, the concept of regional models risesup. The same model could be used for Austria an Italy, but not for France. Due to the geographicalproximity between Austria and Slovenia, the authors of the Avalfor LIN model have decided to use theAustrian model for the Slovenian geographic conditions.As () models are 2D ones using water flow direction algorithms, they are not able to representavalanches’ spread off in the run-out zone. This is the reason why in Avalfor LIN the potentiality ofspread off in the run-out zone is expressed using a buffer zone around the calculated maximal runoutpoint. The width of this buffer zone depends on the local slope morphology. The maximal widthof the buffer zone has been fixed at 220m. This value corresponds to the standard deviation (5.17°)PARAmount page 43 of 57

of calculated with the data set for the calibration of the regional models. The use of this bufferzone increases the confident interval of the models.The following maps present for the Italian case study (Passo Rolle) the data used for the )model calibration and the snow avalanche hazard mapping obtained with Avalfor LIN .Map 24: Snow avalanches past events data used for the calibration of the Italian model for the Italiancase study “Passo Rolle”. The initial 1x1m Lidar DTM has been resampled to 20x20m.PARAmount page 44 of 57

Map 25: Snow avalanches hazard mapping with Avalfor LIN for the Italian case study “PassoRolle”. The initial 1x1m Lidar DTM has been resampled to 20x20m. In red the release areas,in grey the run-out zones and in blue the recorded past event data.The following maps present for the Austrian case study the result of the snow avalanche mappingobtained with Avalfor LIN . The map 26 gives an illustration of the watershed and water flow directioncalculations within Avalfor LIN . The map 27 represents only the travel paths and the buffer zonescalculated at the run-out point.PARAmount page 45 of 57

Map 26: The result of the watershed analyses (in yellow, green and blue) including thedetermination of the travel paths, and of the buffer zones (in pink) calculation at the run-out pointusing Avalfor LIN , in the Austrian case study of the Paramount project.Map 27: The result of the travel paths, and of the buffer zones (in pink) calculation at the run-outpoint using Avalfor LIN , in the Austrian case study of the Paramount project.The maps below present the results for the Slovenian and French case studies.PARAmount page 46 of 57

Map 28: Extract of the snow avalanches hazard map for one of the Slovenian cases studies. In red therelease areas, in blue and yellow simulated avalanche paths and run-out zones.PARAmount page 47 of 57

Map 29: Snow avalanche hazard map obtained with Avalfor LIN , and using a 25x25m DTM, for theFrench case study “ département des Hautes-Alpes”.PARAmount page 48 of 57

Map 30: Snow avalanches hazard map obtained with Avalfor LIN , and using a 25x25m DTM, for theFrench case study Queyras (zoom of the map at the scale of the “département des Hautes-Alpes”)3.3 Validation of Avalfor LINThe model Avalfor LIN has been validated using for each case study some past events which have notnee used for the () model calibration. Each time the maximal run-out distance is at least includedin buffered run-out zone calculated with Avalfor LIN . The validation of this tool has also been madeusing past event cadastre in an other place than the ones of he case studies. The map belowpresents, for a French site located in another administrative district (department de l’Isère) than thePARAmount page 49 of 57

one of the Département des Hautes Alpes (Paramount French case study), the confrontation of theAvalfor LIN ’s results to the past event cadastre.Map 31: An example of validation of the results obtained with Avalfor LIN using the past event database of another French site than the one used for the calibration of the French () model.During the winter 2011-2012, an avalanche occurred in a French ski resort and this event has beenvery well documented. Avalfor LIN has been used, without any post calibration, in order to test therelease area and run-out algorithms. Avalor LIN has been able to identify the release area (circle inPARAmount page 50 of 57

yellow on the map and the photo) and the travel path of the snow avalanche. This event hasdestroyed a chairlift station (green circle on the map and the photo), this chairlift stationcorresponds also to the run-out of this event.Map 32: An example of validation of the results obtained with Avalfor LIN using a real event which hadoccurred in another region than the one use for the for the calibration of the French () model. Inred the release are determined with Avalfor LIN , in blue the travel path determined with Avalfor LIN , inthe circles the real zones (yellow = release area, green = stopping point)This is very important to remind to the users that the results obtained with Avalfor LIN have always tobe compare to the known events in the case study. If the observed run-out distances are longer thanthe one calculates with Avalfor LIN then the () model used has to be changed by selecting anotheralpine region proposed by Avalfor LIN or by recalibrating the model.3.4 Snow avalanches risk mapping with Avalfor LINThe process used within Avalfor LIN for identifying the human infrastructures endangered by snowavalanches is exactly the same than for Rockfalls with Rockfor LIN . Here is the copy of the “Rockfallrisk mapping with Rockfor LIN ” :The last step of a risk mapping is to determine if socio-economic issues are endangered by the naturalhazard studied. Good information on the location of facilities is then required. At a regional scale,each of the Alpine Space countries can find this information in the geographic database of theirrespective national geographic institutes.PARAmount page 51 of 57

Usually these databases list and correspondently map all human infrastructures: public facilities,dwellings, industries, as well as communication, electrical, gas and water infrastructure, etc.According to their importance or their extent, all these items can be classified into protection prioritylevels. This ranking is not obligatory, but facilitates the definition of priority levels for specificprotection actions depending firstly on the importance of the issues and secondly on the hazard’sspecifications. This ranking is required to be performed jointly with all actors involved in riskprevention policy of the study area.By combining this map with the snow avalanche run-out envelope map, the potentially endangeredinfrastructure can be identified by selecting all the items located between release points and run-outenvelopes. The map obtained includes the endangered issues and the associated release and run-outzones.If the “issues” map is available then Avalfor LIN performs automatically this analysis by maps crossing.The following map illustrates for the French case study the results of this risk analysis with Avalfor LIN .PARAmount page 52 of 57

Map 33: Snow avalanches hazard and human infrastructures localization obtained with Avalfor LIN ,and using a 25x25m DTM, for the French case study Queyras (zoom of the map at the scale of the“département des Hautes-Alpes”)3.5 Snow avalanches protection forest mapping with Avalfor LINThe protection forest mapping is the last step of the risk analysis than can be done with Avalfor LIN .The general principle is to cross the map of endangered issues with the map of the geographicalextension of forest stands. This forest map can be the one provided by National Forest Inventories orthe one available in the forest services. As the mapping is made at a regional scale, thedendrometrical description of the forest stands is not required. The information required is thesurfaces covered by forest. Identification of forest stands potentially serving a protection function isthen obtained by combining the endangered items map with the forest cover map, and by selectingPARAmount page 53 of 57

all forested areas located above an endangered item and on the associated release zones. Effectivelya forest can have a potential efficient protective role only if it’s located in the release area of a snowavalanche. This selection is provided automatically by Avalfor LIN .This map of potential protection forest areas is required to be validated by a field survey. But beforethis, it can be used to define an area within which forest management dedicated to the improvementof the protection function needs to be applied. In other terms, this map defines the potential area ofuse of protection forest management guidelines.The strength of this methodology lies in its ability to display the area within which forests are able toprovide a protective function against snow avalanches; often such areas are unknown having notbeen previously identified. A decrease in forest canopy in these protection forest areas could havedramatic consequences requiring adaptations to forest management to ensure the sustainability ofthis protective function.The following maps present some examples of the analysis processes performed by Avalfor LIN forproducing the potential protection forest mapping and some results of potential protection forestmaps.PARAmount page 54 of 57

Map 34: Snow avalanches potential release areas under forest canopy map obtained with Avalfor LIN ,for the Austrian case study.Map 35: Snow avalanches run –out zones simulated from the potential release areas under forestcanopy map obtained with Avalfor LIN , for the Austrian case study.PARAmount page 55 of 57

Map 36: Snow avalanches potential protection forest map obtained with Avalfor LIN , and using a25x25m DTM, for the French case study “ département des Hautes-Alpes”.PARAmount page 56 of 57

Map 37: Snow avalanches potential protection forest (in yellow) map obtained with Avalfor LIN , andusing a 25x25m DTM, for the French case study Queyras (zoom of the map at the scale of the“département des Hautes-Alpes”)Avalfor LIN is the property of Irstea, for any information or expertise get incontact with:frederic.berger@irstea.fr.PARAmount page 57 of 57