Soil moisture modelling using TWI and satellite imagery in the ... - KTH

Soil moisture modelling using TWI
and satellite imagery in the
Stockholm region
Jan Haas
Master’s of Science Thesis in Geoinformatics
TRITA-GIT EX 10-001
School of Architecture and the Built Environment
Royal Institute of Technology (KTH)
100 44 Stockholm, Sweden
March 2010

TRITA-GIT EX 10-001
ISSN 1653-5227
ISRN KTH/GIT/EX--10/001-SE

Abstract
Soil moisture is an important element in hydrological land-surface processes as well as landatmosphere
interactions and has proven useful in numerous agronomical, climatological and
meteorological studies. Since hydrological soil moisture estimates are usually point-based
measurements at a specific site and time, spatial and temporal dynamics of soil moisture are difficult
to capture. Soil moisture retrieval techniques in remote sensing present possibilities to overcome
the abovementioned limitations by continuously providing distributed soil moisture data at
different scales and varying temporal resolutions. The main purpose of this study is to derive
soil moisture estimates for the Stockholm region by means of two different approaches from a
hydrological and a remote sensing point of view and the comparison of both methods.
Soil moisture is both modelled with the Topographic Wetness Index (TWI) based on digital
elevation data and with the Temperature‐Vegetation Dryness Index (TVDI) as a representation
of land surface temperature and Normalized Difference Vegetation Index (NDVI) ratio.
Correlations of both index distributions are investigated. Possible index dependencies on
vegetation cover and underlying soil types are explored. Field measurements of soil moisture
are related to the derived indices.
The results indicate that according to a very low Pearson correlation coefficient of 0.023, no
linear dependency between the two indices existed. Index classification in low, medium and high
value categories did not result in higher correlations. Neither index distribution is found to be
related to soil types and only the TVDI correlates alongside changes in vegetation cover
distribution. In situ measured values correlate better with TVDIs, although neither index is
considered to give superior results in the area due to low correlation coefficients. The decision
which index to apply is dependent on available data, intent of usage and scale. The TWI surface
is considered to be a more suitable soil moisture representation for analyses on smaller scales
whereas the TVDI should prove more valuable on a larger, regional scale. The lack of correlation
between the indices is attributed to the fact that they differ greatly in their underlying theories.
However, the synthesis of hydrologic modelling and remote sensing is a promising field of
research. The establishment of combined effective models for soil moisture determination over
large areas requires more extensive in situ measurements and methods to fully assess the
models’ capabilities, limitations and value for hydrological predictions.
Keywords: TWI, TVDI, soil moisture
i

Acknowledgement
I would like to express my sincere gratitude to my supervisors Ulla Mörtberg and David
Gustafsson, Department of Land and Water Resources Engineering, School of Architecture and
the Built Environment, KTH ‐ Royal Institute of Technology for their continuous help and
guidance, data and literature provision as well as conducting fieldwork together and data post‐
processing.
I also gratefully acknowledge the support and advice given to me by Dr. Yifang Ban, Head of
Department of Urban Planning and Environment, School of Architecture and Built Environment,
KTH ‐ Royal Institute of Technology. I would also like to express my gratitude towards Tuong
Thuy Vu, Dorothy Furberg and Maria Irene Rangel Luna of the same department for their help,
trust and technical support.
Furthermore I would like to thank Else‐Marie Wingqvist from Sveriges Meteorologiska och
Hydrologiska Institut (SMHI) for the provision of detailed temperature and precipitation data
for several gauging stations in and around Stockholm.
ii

Table of Contents
Abstract ................................................................................................................................................................................... i
Acknowledgement ............................................................................................................................................................. ii
Table of Contents ............................................................................................................................................................. iii
List of Tables ....................................................................................................................................................................... vi
List of Figures ................................................................................................................................................................... vii
List of Appendices .......................................................................................................................................................... viii
List of Acronyms ................................................................................................................................................................ ix
1 Introduction ............................................................................................................................................................. 11
2 Background .............................................................................................................................................................. 12
2.1 Topography‐based Hydrological Model (TOPMODEL) ................................................................ 12
2.2 Topographic Wetness Index (TWI) ...................................................................................................... 12
2.3 Digital Elevation Data ................................................................................................................................ 13
2.3.1 Gridded data (DEM) .......................................................................................................................... 13
2.3.2 Triangular irregular networks (TIN) ......................................................................................... 14
2.3.3 Contour Data ........................................................................................................................................ 14
2.3.4 DEM resolution ................................................................................................................................... 14
2.3.5 Depression removal in DEMs ........................................................................................................ 18
2.4 Flow direction algorithms ........................................................................................................................ 19
2.4.1 Single Flow Direction (SFD) algorithms ................................................................................... 19
2.4.2 Biflow Direction (BFD) algorithms ............................................................................................. 20
2.4.3 Multiple Flow Direction (MFD) algorithms ............................................................................. 21
2.4.4 Algorithm comparison ..................................................................................................................... 24
2.5 Soil moisture retrieval in remote sensing ......................................................................................... 26
2.5.1 Soil moisture retrieval techniques .............................................................................................. 27
2.5.2 Landsat program ................................................................................................................................ 28
2.5.3 Landsat 7 Enhanced Thematic Mapper (ETM+) ................................................................... 29
2.5.4 Normalized Difference Vegetation Index (NDVI) ................................................................. 30
iii

2.5.5 Temperature‐Vegetation Dryness Index (TVDI) ................................................................... 31
3 Study area and data description ..................................................................................................................... 35
3.1 Study area ....................................................................................................................................................... 35
3.2 Satellite image ............................................................................................................................................... 35
3.3 Digital Elevation Model ............................................................................................................................. 36
3.4 Contour data .................................................................................................................................................. 37
3.5 Land cover data ............................................................................................................................................ 37
3.6 Soil data ........................................................................................................................................................... 38
3.7 Precipitation and temperature data .................................................................................................... 39
4 Methodology ............................................................................................................................................................ 40
4.1 TWI calculation ............................................................................................................................................. 40
4.1.1 DEM preparation ................................................................................................................................ 40
4.1.2 SCA and slope grid calculation ...................................................................................................... 40
4.1.3 TWI surface generation ................................................................................................................... 41
4.2 TVDI surface generation ........................................................................................................................... 43
4.2.1 Satellite image pre‐processing ..................................................................................................... 43
4.2.2 NDVI surface ........................................................................................................................................ 45
4.2.3 Surface temperature ......................................................................................................................... 47
4.2.4 TVDI surface ......................................................................................................................................... 47
4.3 Surface comparisons .................................................................................................................................. 49
4.4 In situ measurements ................................................................................................................................ 50
5 Results ........................................................................................................................................................................ 52
5.1 TWI calculation ............................................................................................................................................. 52
5.1.1 Filled/unfilled/noData and filled DEM ..................................................................................... 52
5.1.2 Slope 0/+0.1 ......................................................................................................................................... 53
5.1.3 Slope calculation method ................................................................................................................ 53
5.1.4 TWI calculation comparison .......................................................................................................... 54
5.1.5 TWI/TVDI correlations .................................................................................................................... 55
5.1.6 TWI/TVDI and vegetation class correlation ........................................................................... 57
iv

5.1.7 TWI/TVDI and soil class correlation .......................................................................................... 57
5.1.8 TWI/TVDI and soil/vegetation class correlation ................................................................. 58
5.2 Correlation coefficients ............................................................................................................................. 59
5.3 Classification into low, medium and high categories .................................................................... 62
5.4 Correlation with in situ data ................................................................................................................... 62
6 Discussion ................................................................................................................................................................. 64
7 Conclusion ................................................................................................................................................................ 67
References .......................................................................................................................................................................... 68
Appendix ............................................................................................................................................................................. 78
v

List of Tables
Table 1 Technical specifications of Landsat missions 1 to 7 ....................................................................... 29
Table 2 Summary of Landsat 7 ETM+ satellite sensor characteristics .................................................... 29
Table 3 Landsat 7 ETM+ band characteristics ................................................................................................... 30
Table 4 Landsat scene information ........................................................................................................................ 36
Table 5 Land cover classification table ................................................................................................................. 37
Table 6 Vegetation class definition table ............................................................................................................. 38
Table 7 Summary of soil types and distribution ............................................................................................... 38
Table 8 Summary of day mean temperatures and precipitation ............................................................... 39
Table 9 DEM surface statistics before and after pit removal ....................................................................... 40
Table 10 Band constants for radiance calculation from DNs ...................................................................... 46
Table 11 Classes and index surfaces for combination .................................................................................... 49
Table 12 Overview of all surface combinations ................................................................................................ 49
Table 13 Surface classification summary ............................................................................................................ 50
Table 14 TWI surface statistics summary ........................................................................................................... 55
Table 15 Correlation between TVDI/TWI for vegetation classes .............................................................. 59
Table 16 Correlation between TVDI/TWI for soil classes ............................................................................ 59
Table 17 Correlation between TVDI/TWI for vegetation and soil classes ............................................ 60
Table 18 TVDI and TWI surface comparison statistics .................................................................................. 62
Table 19 Numerical comparison between ground truth and calculated TWI and TVDI values ... 63
vi

List of Figures
Figure 1 Simplified representation of the Ts/NDVI space from Lambin and Ehrlich (1996) ........ 33
Figure 2 Ts/NDVI space as TVDI taken from Sandholt et al. (2002) ......................................................... 34
Figure 3 Geometrically corrected Landsat 7 ETM+ satellite image .......................................................... 36
Figure 4 Flow direction angle definition in the Dinf approach taken from Tarboton (1997) ....... 41
Figure 5 Final TWI surface ......................................................................................................................................... 42
Figure 6 Cloud mask ..................................................................................................................................................... 45
Figure 7 Haze mask ....................................................................................................................................................... 45
Figure 8 Final TVDI surface ....................................................................................................................................... 48
Figure 9 In situ data collection site Törnskogen ............................................................................................... 51
Figure 10 Sample point overview ........................................................................................................................... 51
Figure 11 Unfilled DEM (pits and sinks visible) ............................................................................................... 52
Figure 12 Filled DEM (pits and sinks removed) ............................................................................................... 52
Figure 13 TWI surface without prior pit removal ............................................................................................ 52
Figure 14 Slope for TWI calculation in degrees ................................................................................................ 54
Figure 15 Slope for TWI calculation in percent ................................................................................................ 54
Figure 16 Slope calculated in TauDEM ................................................................................................................. 54
Figure 17 Scatterplot of the complete TWI and TVDI surfaces with regression line ........................ 56
Figure 18 Visual comparison between ground truth and calculated TWI and TVDI values ......... 63
vii

List of Appendices
Appendix A Original 50 metre resolution DEM as acquired from Lantmäteriet ................................ 78
Appendix B Precipitation over Stockholm in mm during July 2002 ........................................................ 79
Appendix C Average temperature around Stockholm in °C during July 2002 ..................................... 80
Appendix D D∞ flow direction grid surface for TWI calculation within TauDEM ............................ 81
Appendix E D∞ slope grid surface for TWI calculation within TauDEM ............................................... 82
Appendix F D∞ contributing area surface for TWI calculation within TauDEM ............................... 83
Appendix G NDVI surface calculated by Landsat 7 ETM+ bands 3 and 4 .............................................. 84
Appendix H Temperature in °C derived from the ETM+ thermal band on August 4th, 2002 ....... 85
Appendix I TWI surface calculation variants for 'NoData' ........................................................................... 86
Appendix J TWI surface calculation variants for 'unfilled' ........................................................................... 87
Appendix K TWI surface calculation variants for 'filled' .............................................................................. 88
Appendix L TWI/TVDI scatterplots for vegetation classes 0 to 7 ............................................................. 89
Appendix M TWI/TVDI scatterplots for soil classes ....................................................................................... 90
Appendix N TWI/TVDI scatterplots for soil class bog and vegetation classes 0 to 7 ........................ 91
Appendix O TWI/TVDI scatterplots for soil class clay and vegetation classes 0 to 7 ....................... 92
Appendix P TWI/TVDI scatterplots for soil class rock and vegetation classes 0 to 7 ...................... 93
Appendix Q TWI/TVDI scatterplots for soil class sand and vegetation classes 0 to 7 ..................... 94
Appendix R TWI/TVDI scatterplots for soil class till and vegetation classes 0 to 7 .......................... 95
Appendix S TVDI surface combination statistics.............................................................................................. 96
Appendix T TWI surface combination statistics ............................................................................................... 97
Appendix U TWI/TVDI and TVDI/TWI quantile classification scatterplots ......................................... 98
Appendix V TWI/TVDI and TVDI/TWI natural breaks classification scatterplots ............................ 99
viii

List of Acronyms
ASCII ‐ American Standard Code for Information Interchange
ATCOR ‐ ATmospheric CORrection
BFD ‐ BiFlow Direction
CMP ‐ Common MidPoint
CSV ‐ Comma‐Separated Values
DEMON ‐ Digital Elevation MOdel Networks
DN ‐ Digital Number
EOS ‐ Earth Observation Satellite
ETM ‐ Enhanced Thematic Mapper
FAPAR ‐ Fraction of Absorbed Photosynthetically Active Radiation
FOV ‐ Field‐Of‐View
GA ‐ Genetic Algorithm
GCP ‐ Ground Control Points
GLCF ‐ Global Land Cover Facility
IRS‐WiFS ‐ Indian Remote Sensing Satellites Wide Field Sensor
LAI ‐ Leaf Area Index
LiDAR ‐ Light Detection And Ranging
MFD ‐ Multiple Flow Direction
MIR ‐ Mid‐InfraRed
MSS ‐ MultiSpectral Scanner
NASA ‐ National Aeronautics and Space Administration
NOAA ‐ National Oceanic and Atmospheric Administration
NDVI ‐ Normalized Difference Vegetation Index
NIR ‐ Near InfraRed
PBMR ‐ Push Broom Microwave Radiometer
RBV ‐ Return Beam Vidicon
ix

RMSE ‐ Root‐Mean Square Error
SCA ‐ Specific Catchment Area
SFD ‐ Single Flow Direction
SGU ‐ Sveriges Geologiska Undersökning
SMHI ‐ Sveriges Meteorologiska och Hydrologiska Institut
SPOT ‐ Satellite Pour l'Observation de la Terre
SWEREF99 ‐ SWedish REerence Frame 1999
TauDEM ‐ Terrain analysis using Digital Elevation Models
TDRSS ‐ Tracking and Data Relay Satellite System
TFD ‐ Tracking Flow Direction
TI ‐ Topographic Index
TIN ‐ Triangulated Irregular Network
TIR ‐ Thermal InfraRed
TOPMODEL ‐ TOPography‐based hydrological MODEL
TVDI ‐ Temperature‐Vegetation Dryness Index
TWI ‐ Topographic Wetness Index
USGS ‐ United States Geological Survey
VWC ‐ Vegetation Water Content
WI ‐ Wetness Index
x

1 Introduction
Knowledge about soil moisture status and the processes defining moisture distribution is, and
has always been essential in many respects. Starting to be of importance with the advent of
agriculture in human history, information about soil moisture plays nowadays an important role
in a much broader field, e. g. hydrology, meteorology and climatology, ecology, land surface
modelling and most recently studies on global environmental changes (Verstraeten et al., 2006;
Kerr et al., 2001; Kerr, 2007 and Gruhier et al., 2008). As environmentally related issues
increase, the demand for information on environmental parameters grows simultaneously. To
gather and derive these is therefore a crucial task.
The understanding of hydrological processes and accurate determination of soil moisture has
been subject of numerous studies in the field of hydrology. Soil moisture is usually expressed as
indices in hydrological modelling. One broadly used index is the Topographic Wetness Index
(TWI) originally developed by Beven and Kirkby (1979). It is based on surrounding topography
and describes the tendency of a point to become saturated. Air‐ and spaceborne soil moisture
retrieval has been a promising research field in remote sensing since the early 1970s. Relations
between measured land surface temperature, vegetation and soil moisture could be found and
expressed by the ‘triangle’ method. The Temperature‐Vegetation Dryness Index (TVDI) by
Sandholt et al. (2002) is an index representing the abovementioned relations. Both indices have
shown to be reasonable estimators of surface soil moisture, although some questions of validity
remain. However, there seems to be a lack of knowledge about index correlations and if one
particular index can be considered to give superior results in the region of interest.
One purpose of this study is to compare both index distributions to each other with respect to
different soil types, varying vegetation cover and to explore possible correlations and
dependencies among these. Furthermore, the results and methods are related to in situ
measured soil moisture. Another purpose is to gain insight into current soil moisture
distribution for the region of Stockholm that can be used in further analyses, research and might
help in decision making and future planning.
11

2 Background
2.1 Topography­based Hydrological Model (TOPMODEL)
The TOPMODEL framework initially proposed by Beven and Kirkby (1979) is a compilation of
different concepts for distributed hydrological modelling. It is based on the two fundamental
assumptions that downslope subsurface flows can be adequately represented by a succession of
steady state water table positions and that there is an exponential relationship between local
storage (or water table level) and downslope flow rate. Furthermore it is assumed that the
hydraulic gradients of the saturated zone can be approximated by local surface topographic
slopes �tan β�, thus requiring a detailed analysis of catchment topography (Quinn, 1991 and
Beven, 2004).
2.2 Topographic Wetness Index (TWI)
The TWI is a mathematically simple parameterisation of soil moisture status that has been
applied in numerous studies. The index is based and calculated on slopes and depends therefore
on digital terrain data. The TWI is firstly suggested within the TOPMODEL framework by Beven
and Kirkby (1979) and can be calculated as:
����⁄ ��� ��
(1)
where α = the cumulative upslope area draining through a point (per unit contour length)
tan β = the slope angle at that point
The index describes the tendency of water to accumulate at any point in a catchment (in terms
of α) and the tendency for gravitational forces to move that water downslope (expressed in
terms of tan β as an approximate hydraulic gradient) (Quinn, 1991). Thus, wet areas can arise
either from large contributing drainage areas or from very flat slopes, whereas areas with low
index values are drier, resulting from either steep slopes or small contributing drainage areas.
TOPMODEL is able to predict both distributed water tables and hydrographs. Modification of the
local water table depth can give an estimate of local soil moisture status. Calculated local water
table depths are dependent on the value of the index at a point (Quinn et al., 1995).
12

Statistical distributions and spatial patterns of the TWI vary greatly depending on calculation
parameters (Quinn et al., 1995). The two most critical issues here are the resolution of the
underlying elevation model and the choice of the appropriate flow routing algorithm. For
successful TWI calculations it is assumed that any problems involved in DEM creation, i.e. sink
and dam removal are resolved. Quinn et al. (1995) also noted that there is no standard solution
for calculating the ln�α⁄ tan β� index but that its parametres need to be optimized according to
the corresponding catchment.
Limitations and issues of validation and predictive uncertainty of the concept were investigated,
detailed analyses of the model’s capabilities, underlying theories and basic assumptions were
performed and improvements were suggested in several works (Franchini et al., 1996; Ambroise
et al., 1996; Beven, 1997; Mendicino and Sole, 1997; Seibert et al., 1997; Brasington and
Richards, 1998; Güntner et al., 1999 and Sørensen et al., 2006).
2.3 Digital Elevation Data
Digital elevation data is traditionally represented in three forms; gridded data, triangular
irregular networks and contour based elevation models. All of them can be used in hydrological
modelling.
2.3.1 Gridded data (DEM)
Digital elevation models are readily available and commonly used as representation of elevation
information. Grid DEMs store height information in matrix form. Each matrix node of equal
resolution is assigned one particular elevation value. Grid based DEMs are widely used in
analyses of hydrologic problems but are disadvantageous in some respects. They lack e. g. the
possibility of sufficiently representing elevation discontinuities. Another disadvantage is that
mesh resolution affects the results and computational efficiency. Furthermore it is stated that
grid spacing needs to be based on the roughest terrain in the catchment which results in
redundancy in smoother areas and finally that the computed flow paths tend to zigzag instead of
to follow drainage lines, thus becoming too long. Holmgren (1994) noted that grid based DEMs
were relatively unsuitable for hydrological modelling before the development of more
sophisticated flow direction algorithms, as runoff could only be modelled in a simplified way
(limited to eight discrete directions).
13

2.3.2 Triangular irregular networks (TIN)
The representation of elevation data in TINs is based on the connection of nodes with stored 3‐
dimensiondal coordinates (x, y and z). The nodes are connected with edges to form triangles.
Additional information such as slope, aspect, surface length and area can then be derived for
each of the resulting triangular facets. The TIN has become a rather unpopular format in recent
years (Holmgren, 1994).
2.3.3 Contour Data
Contours are lines that connect points of equal (elevation) values. As the spacing between the
contours widens, height differences become smaller and vice versa. Contour data is usually
derived from digitizing of maps and represents height distribution continuously. Contour based
models are superior to other forms of elevation data because they explicitly state in which
direction the runoff flows (always perpendicular to the contours) (Holmgren, 1994). Aryal and
Bates (2008) found that contour DEMs are less sensitive to changes in resolution than grid DEMs
and provide more consistent estimates of TWIs at moderate to high DEM resolutions.
The quality of elevation data used in the analyses is of great importance. Yet, according to Quinn
et al. (1995), Wolock and McCabe (1995), Beven (1997) and Mendicino and Sole (1997), there is
no standard and superior set of digital elevation data as basis for TWI calculation.
2.3.4 DEM resolution
Selecting the optimal spatial resolution is a central issue in environmentally related analyses
including digital elevation data (Rodhe, 1999; Aryal and Bates, 2008). The appropriate
resolution should be chosen according to the modelling goals but is unfortunately often
determined by data availability and economic aspects. The spatial resolution should always be
modelled to fit the scale of the area under consideration (Vaze and Teng, 2007; Wu et al., 2007).
For example smaller areas with more detailed information require higher spatial resolutions. If
the resolution becomes too low and hillslope lengths are comparatively small, no meaningful
TWI can be derived (Beven, 1997). Studies show that highest resolutions do not always produce
the most accurate prediction model (Wu et al., 2008). The studies of Refsgaard (1997), Molnár
and Julien (2000) and Vázquez et al. (2002) highlighted the variability in hydrologic response to
grid size and suggested an appropriate resolution as a trade‐off between minimized
computational effort and retention of realistic model performance. Endreny and Wood (2003)
found that runoff flows differently with varying spatial resolutions. Many studies found the TWI
14

concept to respond sensitively to grid cell resolution (Wolock and Price, 1994; Gallant and
Hutchinson, 1996; Saulnier et al., 1997; Brasington and Richards, 1998; Higy and Musy, 2000;
Vivoni et al., 2005; Vaze and Teng, 2007; Wu et al., 2007; Wu et al., 2008), even in resolutions
higher than 10 m (Hancock, 2005). Rather coarse data may not represent some important slope
features whereas a too high resolution can introduce unwanted perturbations to flow directions
and slope angles. This coincides with the findings of Wolock and Price (1994), Zhang and
Montgomery (1994), Bruneau et al. (1995) and Thieken et al. (1999), who stated that low
resolution DEMs generally show smoother terrains and shorter flow paths by statistics of slopes
and topographic indices than high resolution data. Vaze and Teng (2007) found that maximum
and mean slope values drastically decrease with a decrease in DEM resolution. TWI distribution
is dependent on the degree of spatial resolution of elevation data. The findings in several studies
show that a lower grid cell resolution results in higher TWI mean values and a broader range of
smaller slope percentages (Hutchinson and Dowling, 1991; Jenson, 1991; Quinn et al., 1991 and
1995; Wolock and Price, 1994; Zhang and Montgomery, 1994; Saulnier et al., 1997; Wolock and
McGabe, 1995; Wolock and McGabe, 2000; Hjerdt et al., 2004; Sørensen and Seibert, 2007; Wu et
al., 2007 and 2008 and Aryal and Bates, 2008). Wu et al. (2008) additionally noticed that the
standard deviation of plan curvature decreased with increasing DEM cell size.
Not only directly derived elevation attributes are dependent on resolution, but also the form of
the index distribution (Iorgulescu and Jordan, 1994; Wolock and Price, 1994; Zhang and
Montgomery, 1994; Bruneau et al., 1995; Quinn et al., 1995; Franchini et al., 1996; Saulnier et al.,
1997 and Mendicino and Sole, 1997). Wolock and Price (1994) studied the effects of topography
on watershed hydrology. They showed that DEM resolution has an effect on water table depth
prediction, the ratio of overland flow to total flow, peak flow and variance and skew of predicted
stream flows. It was found that predicted mean depths to water tables decreased and maximum
daily flow increased with coarser DEMs. Wolock and McGabe (2000) compared 100 m and 1000
m resolution DEMs and found that slopes calculated from 1000 m resolution DEMs are generally
smaller, whereas specific catchment area (SCA) and the TWI are larger compared to 100 m
resolution DEMs. The reasons for these changes are attributed mainly to terrain discretization
effects (dividing the terrain into a different amount of grid cells than initially present) and are
found to be independent of underlying terrain types. Wu et al. (2007) examined the effects of
elevation data resolution on the performance of topography based watershed runoff simulations.
Twelve DEMs of different grid sizes were compared in terms of their influence upon TWI
distribution. It was found that the total watershed discharge increases continuously as
resolutions decrease. Sørensen and Seibert (2007) also found decreasing variations in TWI
between neighbouring cells with an increase in cell size. By increasing the resolution, TWI
distributions turned out to become rather similar, but quite different patterns were to be
15

expected as well. Brasington and Richards (1998) examined frequency distributions of
slope, tan �, upslope contributiong area and TWI on DEMs with varying resolutions from 20 m to
500 m. They found a significant distribution dependency on grid size with most prominent
changes in DEM resolutions from 100 m to 200 m. Saulnier et al. (1997) based their study on
digital terrain maps with resolutions ranging from 20 m to 120 m with 20 m increments from
initially digitized 10 m contour lines. Further scale dependence in the calibrated value of the
saturated conductivity parameter K0 could be identified.
Horizontal Resolution
Different DEM resolutions as basis for calculation of topographic parameters were explored and
used in numerous studies with varying goals. The resolutions under consideration range from
meter level up to several kilometres.
Murphy et al. (2009) used two different data sets: A 1 m resolution Light Detection And Ranging
(LiDAR) DEM and a 10 m conventional photogrammetric DEM. Both DEMs showed good results
in comparison to field‐mapped conditions. The LiDAR DEM produced slightly better results.
Warren et al. (2004) compared slopes on different DEM resolutions and found the highest
resolution of 1 m to be most adequate. Freer et al. (1997) calculated the TWI for subsurface
storm flow analysis on two small catchments with 1 m and 2 m DEM resolutions. Zhang and
Montgomery (1994) and Wu et al. (2008) based their analyses on 2 m resolution DEMs. Wu and
Archer (2005) used DEM grids of 4 m resolution in their study. Sulebak et al. (2000) related soil
moisture to primary and secondary topographic attributes on a 5 m resolution DEM. Sørensen
and Seibert (2007) examined the scale dependency of a decreasing DEM resolution upon the
TWI by resampling a 5 m resolution LiDAR DEM to 10, 25, and 50 m respectively and observed
TWI values to be considerably sensitive to different grid resolutions whereas the estimation of
upslope areas is even more affected than calculated slopes. Thompson et al. (2001) compared
terrain attributes and quantitative soil‐landscape models on different horizontal resolutions (10
m – 30 m) and vertical precisions (0.1 m – 1 m). It could be observed that a decrease in
horizontal resolution resulted in lower slope gradients on steeper slopes, steeper slope
gradients on flatter slopes, narrower ranges in curvature, larger SCAs in upper landscape
positions and lower SCAs in lower landscape positions. Zinko et al. (2006) calculated ground
water flow based on a 20 m resolution DEM. Kim et al. (2008) investigated the strength of
correlations between different soil properties and found a TWI at a 25 m resolution as best. Vaze
and Teng (2007) also suggested a grid cell resolution of 25 m or higher (up to 1 m) to capture
the scale of surface processes. The resolution is however determined by landscape variations.
Tombul (2007) used a 30 m resolution DEM for a comparison of wetness index (WI) and
topographic index (TI). Prasad et al. (2005) explored the relationship of hydrologic parameters
16

and nutrient loads using a 30 m resolution DEM with moderate success. Garbrecht and Martz
(1993) showed that most drainage features can be produced with a 30 m resolution DEM.
Endreny and Wood (2003) examined the spatial congruence of observed and DEM‐delineated
overland flow networks with a 30 m resolution DEM. Cai and Wang (2006) observed that there
are no significant changes in TWI values when comparing 30 m and 90 m resolution DEMs in
landscapes with high elevation variation. Kim and Jung (2003) found a pixel size threshold
between 30 m and 50 m for stable and consistent computation of spatial flow distribution
patterns. Lineback Gritzner et al. (2001) calculated the TWI with DYNWET on a 30 m resolution
DEM. Soil moisture could not be related to landslide risk. The authors suggest that a too coarse
spatial resolution might account for the lack of correlation. This would be consistent with the
findings of Zhang and Montgomery (1994) stating that a resolution of 30 to 90 m could be too
large for modelling complex topography. Wu et al. (2007) examined the influence of DEM
resolution upon TWI distributions by means of comparisons between twelve different DEMs
ranging from 30 m to 3 km. Conoscenti et al. (2008) based their studies on a 40 m resolution
DEM. Lin et al. (2007) successfully explored the relationships of topography and spatial
variations in groundwater and soil morphology using a 40 m resolution DEM. Bruneau et al.
(1995) considered even a resolution as low as 50 m to be sufficient if the model calibration is
able to compensate aggregation effects. Quinn et al. (1995) considered grid sizes of 100 m or
more as too coarse for meaningful TWI calculations. The depiction of the topographic form of
individual hillslopes required higher resolutions. A direct effect on the calculation of
accumulated contributing areas could be observed for different grid resolutions. Hutchinson and
Dowling (1991) examined a 2.5 km resolution DEM. Jain et al. (1992) conducted their study on
distributed modelling even on a 4 km resolution.
Overall, a 10 m horizontal resolution was found most suitable in many studies and is therefore
suggested (Wolock and Price, 1994; Zhang and Montgomery, 1994; Irvin et al., 1997; Saulnier et
al., 1997; Thieken et al., 1999; Chaplot and Walter, 2003 and Fei et al., 2007).
Vertical Precision
A sufficiently high vertical precision is needed in order to determine accurate spatial locations of
channel segments and thus the channel network (Thieken et al., 1999). Chaplot and Walter
(2003) used a 0.3 m vertical resolution and a 10 m horizontal resolution DEM in their studies
and achieved good correlations between the soil wetness and topographic attributes at all
depths. Nelson and Jones (1995) point out the necessity of roundoff error removal in low
vertical resolution DEMs before delineation of stream networks and basins of a watershed. They
presented a method of smoothing already rounded digital terrain models with the effect of
restoring the smoothness of the natural terrain as well as the removal of flat regions. The results
17

show that their algorithm is able to restore the natural slope of large flat areas where the lack of
elevation can be attributed to roundoff errors in the elevation data. Different studies show that a
decrease in vertical precision does not have any significant influence on slope gradients or SCAs
(Quinn et al., 1991; Wolock and Price, 1994; Zhang and Montgomery, 1994 and Gyasi‐Agyei et al.,
1995). However, Thompson et al. (2001) identified various points with zero slope gradients and
zero slope curvature alongside a decrease in vertical precision. Pan et al. (2004) found that
errors in all compared flow direction algorithms increase as the vertical resolution decreases.
This suggests calculating the TWI on the highest vertical resolution possible.
2.3.5 Depression removal in DEMs
Digital elevation models often contain unrealistic local depressions that affect calculations of
flow directions and flow accumulation. These depressions sometimes reflect the real situation
but are often introduced during the generation of the DEM through interpolation errors. Müller‐
Wohlfeil et al. (1996) and Irvin et al. (1997) emphasized the need of getting rid of DEM
depressions which are described as spurious low spots that are generally relics of the DEM
generation. This confirms the findings of O’Callaghan and Mark (1984) who stated that pits or
depressions are usually rare topographic features (e. g. natural holes or quarries) or absent in
most terrain types, but not uncommon in digital elevation models. They are therefore
considered as errors. Nelson and Jones (1995) also identified depressions and pits as spurious
and attribute them to errors in elevation data. Beven (1997) also noted the common problem of
sinks in flow pathway determination in digital terrain analysis. Qin et al. (2007) pointed out the
necessity of DEM pre‐processing for removal of depressions and flat areas preceding TWI
calculation. Present flow direction algorithms need depressionless DEMs as input lest the flow
be stopped in a sink. O’Callaghan and Mark (1984) introduced the techniques of elevation
smoothing (reducing the number of artificial pits by a weighted sum of a point and its eight
neighbours) and iterative interior pit removal. Elevation smoothing only identifies and removes
shallow pits whereas deeper sinks remain. Pit removal involves identifying the point of a basin
where water would overflow from the pit basin. This point lies on the boundary of the pit with
minimum elevation difference to the pit. Another approach is to fill the identified pits, i.e. e. to
match one particularly low elevation value to the lowest value of the surrounding pixels. Jenson
and Domingue (1988) refined pit removal implementing neighbourhood techniques and
iterative spatial techniques. Planchon and Darboux (2001) present a new method for filling
depressions in DEMs. This new approach inundates the whole DEM surface and removes the
excessive water afterwards instead of gradually identifying pits and filling them. The process is
18

simple to implement with low computational complexity. Furthermore, it is possible to add
slope to the filled sinks to overcome the limitations of flow direction algorithms in flat areas.
2.4 Flow direction algorithms
Flow direction algorithms decide about how flow propagates from one grid cell to other grid
cells. Thus, they determine the total upslope area entering one grid cell and the effective contour
length orthogonal to the flow direction. The cumulative upslope area α needed in the TWI can
then be calculated from the relationship:
���⁄ �
(2)
where α = cumulative upslope area
A = total upslope area
L = effective contour length
Hillslope geometry and flow partitioning greatly affect the spatial patterns of the TWI (Aryal and
Bates, 2008). The mixture of convex and concave features (Kim and Lee, 2004) as well as errors
in elevation data (Walker and Willgoose, 1999) complicate the essential choice of the
appropriate flow direction algorithm, which greatly influences the calculation of upslope
contributing areas, flow accumulation and other processes, e. g. sediment transport capacity
(Wilson et al., 2007). Furthermore it is impractical to prefer one specific flow direction
algorithm to another. The algorithm should rather be chosen according to the underlying
topography. One particularly critical issue related to the determination of flow paths that has not
been resolved satisfactorily yet is flow direction routing in flat areas with no or only little height
difference. Existing flow direction algorithms have resolved this problem more or less successful
but it remains a limitation to most approaches.
2.4.1 Single Flow Direction (SFD) algorithms
SFD algorithms restrict the surface and subsurface runoff from a single grid cell to only one
other cell without considering any other surrounding cells. No flow bifurcation and dispersive
flow is possible. Water only flows to the cell with the highest gradient (the steepest slope). SFDs
have been criticized for the lack of not being able to take flow dispersion into account, e. g. by
Aryal and Bates (2008). The SFD is furthermore incapable of returning the right flow path if the
19

steepest gradient might coincidentally fall between two of the eight cardinal and diagonal
directions (Wolock and McCabe, 1995).
D8
The D8 (deterministic eight‐node) algorithm is the first method of calculating flow directions
from one cell to one of its eight neighbours by O’Callaghan and Mark (1984). It is rather simple
and does not account for dispersive flow. Because flow is only assigned to the surrounding cell
with the steepest downwardslope gradient, grid bias is introduced (Tarboton, 1997). The D8
method works well in valleys but produces many parallel flow lines and problems near
catchment boundaries.
Rho8
Fairfield and Leymarie (1991) suggested a new method to overcome the limitations of the D8
algorithm by introducing a probability distribution proportional to altitude difference (slope)
between the centre and neighbouring cells. In their method, parallel flow paths are broken up
and a mean flow direction equal to the aspect is generated (Wilson et al., 2000). The flow
distribution pattern results in more cells with no upslope connections but is uniquely generated
each time. The randomness of the probability function has been criticised by Tarboton (1997)
because SCAs are deterministic quantities and should therefore be calculated in a stable,
repeatable way.
2.4.2 Biflow Direction (BFD) algorithms
Two Directional Edge­Centred Routing
The two directional edge‐centred routing algorithm (2D‐Lea) by Lea (1992) creates a planar
surface prior to flow direction determination. Elevation information is interpolated and stored
on the edges of four surrounding DEM cells, creating a plane. Flow is then expressed as a flow
vector following the route a ball would take when put on the centre of a cell on the plane. This
method allows flow to be determined precisely and expressed continuously with an angle
between 0 and 2π. Flow is then directed and split towards the two cells closest to the angle. The
method lacks the possibility to disperse flow into more than two cardinal directions.
Two Directional Block­Centred Routing
Jensen’s two directional block‐centred routing algorithm (2D‐Jensen) is based on the same
planar concept as in 2D‐Lea with the difference that not only four but nine cells are used to
determine the plane which is defined by averaging cell centre values rather than edges (Jensen,
20

2004). Both the SFD and BFD algorithms are problematic in finding the right flow directions in
flat areas (Pan et al., 2004).
2.4.3 Multiple Flow Direction (MFD) algorithms
The MFD algorithm was initially proposed by Quinn et al. (1991) to improve the representation
of convergence and divergence of flow. Unlike the SFD and BFD algorithms, the MFD algorithm
allows dispersive flow from one grid cell proportionately to multiple surrounding cells. As the
D8 algorithm, the MFD algorithm is based upon finding the steepest slope to the surrounding
eight cells. Downward elevation gradients are determined for each possible direction and
multiplied with the corresponding contour lengths, respectively. This implies that flow is always
divided proportionally to all surrounding cells. Tarboton (1997) noted that this could introduce
unwanted errors because dispersive flow from one pixel is not necessarily directed towards all
pixels in the vicinity with lower elevation.
Quinn et al. (1991) used a slightly different formula for the contour length calculation than
Wolock and McGabe (1995) who first described the implementation of the MFD algorithm in the
ARC/INFO framework. According to Wolock and McCabe (1995), MFDs tend to give more
realistic‐looking spatial patterns of accumulating area than single‐directional flow algorithms
where flow is expressed in distinct lines. Although the MFD algorithms can not overcome the
limitation of flow determination in flat areas where slope values become rather small, they still
provide better results than the SFD and BFD algorithms (Pan et al., 2004). Kim and Lee (2004)
pointed out another limitation of the initial MFD algorithm. Dispersive flow is only possible
towards eight discrete directions. This drawback has been resolved by the concept of a flow tube
network within the Digital Elevation Model Networks (DEMON) algorithm by Costa‐Cabral and
Burges (1994) which enables flow in continuous directions from 0 to2π. Another disadvantage
of the MFD is flow overdissipation and braiding near channel pixels especially in convex‐shaped
topography as has been pointed out by Quinn et al. (1995).
FD8
The limitation of D8 algorithm only being able to direct flow to one of eight surrounding cells
has been overcome by the FD8 algorithm that allows catchment spreading and flow dispersion
to be represented (Moore et al., 1993). The algorithm allows dispersive flow in upland areas
(above defined channels) but uses the initial SFD D8 algorithm below channel initiation points.
Although the problems of parallel flow and single flow could be resolved, some issues still
remain. Mendicino and Sole (1997) noted that the FD8 algorithm simulates flow poorly in
certain topographic conditions (e. g. alluvial plains). In these areas a pronounced expansion of
21

surface runoff along the alluvial plains occurs instead of a well delineated stream channel
network.
FRho8
As the FD8 is for the D8 algorithm, the FRho8 is an advancement of the Rho8 algorithm. FRho8
can be described as the combination of the MFD algorithm by Quinn et al. (1991) and the SFD
algorithm Rho8. Firstly, the algorithm identifies all downslope neighbouring points to a channel
initiation point and respectively calculates the slope gradients. Secondly, flow is distributed
among the surrounding cells according to the Rho8 procedure. The upslope contributing and
SCAs are then determined using the flow width and flow accumulation approaches as in the D8
algorithm. The improvements made result in more realistic contributing areas and solve the
problem of parallel flow paths. Wilson and Gallant (1996) noted that the flow dispersion
algorithm should best be disabled in high contributing areas, because stream lines are usually
quite well defined. According to Mendicino and Sole (1997), the algorithm leads to problems in
channel network definition.
MFD­md
Qin et al. (2007) developed a modified MFD as proposed by Quinn et al. (1991). The MFD‐md
algorithm is adaptive to local terrain conditions and uses ���� as a linear function of maximum
downslope gradient. Thus, the flow accumulation can be modelled more reasonably. In
comparison to the original MFD algorithm, MFD‐md achieves fewer errors in the calculated
cumulative upslope area α.
The MFD‐md algorithm results in smoother spatial TWI distributions which gives a more
realistic state of flow, especially in flat areas. Additionally, TWI values tend to be slightly smaller
than the ones calculated with the approach based on Quinn et al. (1991). As other MFD
algorithms, the MDF‐md algorithm still can not get rid of the problems occurring in flat areas
where soil moisture distribution should be homogeneous. Initial removal of sinks and pits is also
necessary.
DEMON
The DEMON algorithm was developed by Costa‐Cabral and Burges (1994) and is based on the
planar representation as initially described by Lea (1992). DEMON was created to overcome
existing restrictions of the D8 algorithm. Flow is represented in two dimensions and directed by
aspect in a flow tube network. Flow is generated at each source pixel and routed down a stream
tube until a sink is encountered or the DEM boundaries are reached. The stream tubes are
constructed from points of intersections of lines drawn in gradient direction and grid cell edges.
22

Contributing and dispersal areas can be determined. Main advantages as pointed out by Costa‐
Cabral and Burges (1994) are those of contour based models according to Moore et al. (1988).
Furthermore, DEMON is able to represent varying flow width over non planar topography and
can be calculated on rectangular grid DEMs. Additionally, the DEMON algorithm represents the
hillslope aspect better than the D8 algorithm. Curved flow paths are also represented in contrast
to the D8 algorithm (Costa‐Cabral and Burges, 1994). Another advantage as pointed out by
Wilson and Gallant (1996) is that DEMON shows the differences between convergent and
divergent areas more accurately than the FD8 and FRho8 algorithms. However, the DEMON
algorithm has problems with unwanted indentations in isolines which occur by the
approximation of conical surfaces by a mosaic of planes. These could only be resolved by a non‐
planar surface fitting. However, this would yield large computational expenses and a high risk of
error introduction and is therefore unsuitable. This limitation could be fixed by the D1 algorithm
by Tarboton (1997) who found the DEMON algorithm not working correctly in flat areas and
when exceptions in data sets occur.
D∞
The D∞ algorithm was invented by Tarboton (1997). It is based on the concept of MFD
algorithms but incorporates the idea of a block‐centred surface fitting scheme as the 2‐D Lea, 2‐
D Jensen and DEMON algorithms. The new approach of flow dispersion is based on the
calculation of a single angle between 0 and 2π being the steepest downward slope on the eight
triangular facets centered at each pixel. Then, upslope area is determined by dividing the flow
between two downslope pixels according to how close this flow direction is to the direct angle to
the downslope pixel. Flow in flat areas is treated as proposed by Garbrecht and Martz (1997).
The algorithm is considered advantageous because of its abilities to minimise unrealistic
dispersion in the calculation of the cumulative upslope area α and to handle ridges, pits and flat
areas in natural catchments.
Tracking Flow Direction (TFD) algorithm
The TFD algorithm was created by Pan et al. (2004) to overcome the limitations of TWI
calculation in flat areas. It treats minimum slope values as in Wolock and McGabe (1995) while
the flow direction is determined according to the ARC/INFO flow direction module. The TFD
algorithm is found to give superior results in flat areas in comparison to the other flow direction
algorithms.
Spatially distributed flow apportioning algorithm (SDFAA)
Kim and Lee (2004) propose a new integrated flow determination algorithm. A spatially varying
flow apportioning factor is introduced in order to distribute the contributing area from upslope
23

cells to downslope cells. An iterative process of parameter optimization using a Genetic
Algorithm (GA) is implemented.
The SDFAA was found advantageous to existing approaches. A field example showed less
overdissipation problems near channel cells, a robust parameter determination and the
connectivity feature of river cells. However, and in contrast to other algorithms, the SDFAA
requires the channel location as an additional input. Similar to other flow direction models, the
removal of depressions and flat areas in elevation data is necessary prior to algorithm
application. The SDFAA further resolves valley bottom overdissipation problems of the MFD and
provides a more flexible allowance of flow distribution to downslope cells. Furthermore it
reduces some problems concerning flow determination in complicated field topography.
However, the application of the spatially distributed flow apportioning algorithm to other
watersheds still needs to be investigated (Kim and Lee, 2004).
2.4.4 Algorithm comparison
Wolock and McCabe (1995) found that mean TWI values increase and that smoother TWI
patterns across the DEM surface result when using MFD algorithms in comparison to SFD
algorithms. Desmet and Govers (1996) examined the influence of different flow routing
algorithms on upslope contributing areas which are considerably smoother for multiple flow
algorithms and the prediction of ephemeral gullies. The latter could be modelled more
accurately with multiple flow models because single flow routing algorithms are highly sensitive
to small errors in elevation data. On the whole, Desmet and Govers (1996) found the D8 and 2D‐
Lea algorithms superior for they visually seem to correlate better with the main drainage lines.
Mendicino and Sole (1997) noted that the D8 and Rho8 procedures, although conceptually
different, produce similar distribution functions of the TI. The FRho8 and DEMON procedures
were additionally identified to behave similarly as the Rho8 algorithm. For this reason it is
suggested to calculate flow directions with a mixed procedure, based on the method of Quinn et
al. (1995).
Gallant and Wilson (1996) stated that the FD8 and FRho8 algorithms are superior to the D8
algorithm because they result in more realistic distributions of contributing areas in upslope
areas and their ability to resolve the problem of parallel unrealistic flow paths.
The DEMON and 2D‐Lea algorithms have the advantage that they are able to determine flow
directions precisely and that they are deterministic. Errors may however be introduced in
creating the plane through grid cells (Tarboton, 1997). Flow according to MFD as proposed by
24

Quinn et al. (1991) follows the topographic slope but introduces significant dispersion. Tests on
the basis of the evaluation of test statistics and examination of influence and dependence maps
on DEMs with different resolutions show that the D∞ algorithm performs better than D8, 2D‐
Lea and MFD as proposed by Quinn et al. (1991) in terms of upslope area calculation. Tarboton
(1997) found the D∞ and DEMON algorithms to generally work best. They both produce
smallest errors in the comparison of calculated and theoretical upslope. The D∞ algorithm
additionally overcomes the problems of loops and inconsistencies of the DEMON and other
plane‐fitting models.
Wilson et al. (2000) examined the effects of DEM source, grid resolution and choice of flow
direction routing algorithms on five topographic attributes. SFD algorithms result in more cells
with rather small upslope contributing areas. FRho8 and DEMON agreed best with each other in
surface comparison.
According to Zhou and Liu (2002) the infinite flow direction algorithm proposed by Tarboton
(1997) achieves better drainage configurations than other algorithms when using rasterized
topographic data to calculate catchment areas.
Endreny and Wood (2003) explored the congruence which is explained as the overlap between
field‐sketched flow path networks observed during a storm and the calculated moisture indices
of observed and DEM‐delineated overland flow networks on a 30 m horizontal resolution DEM.
Five common flow direction algorithms were compared in terms of their spatial congruence. The
D8 and MFD algorithms were assigned the lowest congruence ratings whereas the 2D‐Lea and
D∞ algorithms, which direct flow to a maximum of two neighbours, produced the highest
congruence ratings. The modifications to the D8 and MFD methods allowing limited dispersive
flow could increase congruence. Dispersive flow to two or three surrounding cells is suggested
as an optimum.
Pan et al. (2004) evaluated the performance of six different floating algorithms (combinations of
flow direction and slope algorithms) by Root‐Mean‐Square Error (RSME) comparison on three
different idealized hillslopes (planar, convergent and divergent (concave and convex)) and two
combinations of vertical and horizontal terrain data resolutions, respectively. Among the tested
algorithms, the MFD algorithm was found to be most accurate in all examined cases, followed by
the BFD and SFD algorithms which especially produced significant errors when contour lines
were not parallel to one of the eight cardinal flow directions. In all cases it could be observed
that TWI errors decreased with an increasing vertical resolution independent on the underlying
flow direction algorithm. The differences in algorithm‐based determination of contour lengths
did not greatly affect the results. Additionally it could be found that the RMSE of the calculated
25

topographic indices compared to initial slopes and contour lengths increases with increasing
slope values. The TFD worked best in flat areas where the SFD and BFD have problems resolving
the right flow direction. Since the MFD algorithm calculates dispersive flow it propagates to a
broader region than the SFD and BFD algorithms.
Güntner et al. (2004) recommended an intermediate approach between SFDs and MFDs.
Results from different studies (Wolock and McCabe, 1995; Desmet and Govers, 1996; Tarboton,
1997; Wilson et al., 2000 and Endreny and Wood, 2003) show that existing algorithms behave
differently according to the underlying landscape (e. g. planar, conical, hilly and steep or flat).
The current state of research is not yet able to recommend a specific flow routing model suitable
for all of the varying landforms. Wilson et al. (2007) compared the performance of several flow
direction algorithms on a 10 m resolution DEM across six different fuzzy‐defined landscape
classes and tested the hypotheses that the performance of five flow routing algorithms does not
change with the flow descending from steeper to flatter terrain (1) and that the performance of
those algorithms does not vary across different fuzzy‐classified landscapes (2). The lowest mean
SCA occurred on hilltops and ridgelines becoming higher as the terrain became flatter. Overall,
landscape can be divided into two groups (high elevation and low elevation) based on the SCA
calculation results. All in all, the results of the comparison show which flow routing algorithms
give similar or different results and where differences lie, but they can not indicate which
algorithm works best for what landscape type in regard of measured soil moisture or hydrologic
theory. All in all, the results suggest that the D∞, MFD, and DEMON algorithm performed better
than the D8 and Rho8 algorithms.
Sørensen et al. (2006) compared TWIs calculated with different modifications and evaluated
them in terms of their correlations with five soil moisture related parameters. Upslope area,
creek cell representation and slope were determined according to different theories. Although
correlations could be observed, no TWI combination was found superior for all measured
variables. It is therefore assumed that the best method varies and is site specific.
2.5 Soil moisture retrieval in remote sensing
With readily available high resolution and consistent, long‐term remote sensing records and
progress in digital image processing techniques as well as the tendency towards macro scale
modelling, the combination of remote sensing and hydrological modelling becomes more and
more promising. Remote sensing can provide large scale distributed data sets where ground
based measurements are unavailable. However, the determination of small scale hydrologic
26

features is not sufficient. Determination of fluxes and parameterization of hydrologic processes,
e. g. evaporation, infiltration, runoff or drainage still require detailed hydrological models
(Dubayah et al., 1995). There have already been some attempts to combine remote sensing and
hydrologic modelling (Milly and Kabala, 1985; Houser et al., 1998; Bauer et al. 2006). Lin et al.
(1994) compared remotely sensed and simulated moil moisture over a heterogeneous
watershed and found both techniques to be consistent with ground measurements. Kite and
Pietroniro (1996) presented a comprehensive overview of remote sensing applications in
hydrologic modelling.
2.5.1 Soil moisture retrieval techniques
Soil moisture retrieval with remote sensing techniques can be achieved in all regions of the
electromagnetic spectrum. Comprehensive comparisons between different retrieval techniques
can be found in Bryant et al. (2003) and Moran et al. (2004). Engman and Gurney (1991) present
an overview of soil moisture retrieval techniques and analyse their capabilities, advantages and
disadvantages. The following methods mentioned have been successfully used to model soil
moisture and are briefly described:
Gamma radiation techniques
The detection of soil moisture is based on the different natural gamma radiation flux emitted
from dry and wet soils and captured by airborne sensors at a height of 100 m to 200 m, because
the atmosphere attenuates the radiation flux. Background soil moisture and gamma count rate
need to be obtained by antecedent calibration flights as additional parameters.
Hyperspectal techniques
Reflected solar radiation is measured. Soil moisture can be estimated by unequal albedos (wet
soils have lower albedos than dry soils). Many confounding factors such as surface roughness,
angle of incidence, vegetation cover and soil colour and texture complicate moisture
determination.
Thermal techniques
Thermal techniques make use of the relation of diurnal surface temperature change and soil
moisture. Surface temperature is primarily dependent on thermal inertia of soil, which in turn is
related to thermal conductivity and heat capacity. With increasing soil moisture, both the
thermal conductivity and heat capacity rise. Using thermal techniques requires anterior
knowledge of the soil type, is limited to bare, unvegetated soils and retrieves soil moisture only
27

in the top five centimetres of the soil layer. Pratt and Ellyet (1979) give further information on
thermal techniques.
Microwave techniques
Microwave techniques can be separated into active and passive techniques. Passive systems
measure emission intensity from soil surfaces with a radiometer at longer wavelengths (more
than five centimetres). Active systems measure backscattered radar waves and directly relate
them to soil moisture. Both techniques have different advantages but make use of the same
principle ‐ the dielectric properties of soils. These vary greatly with changing moisture
conditions. For wet soils, the dielectric constant is considerably higher than for dry soils. For
passive systems, an increase in the dielectric constant would result in a decreased emissivity
whereas active systems would measure higher radar backscatter. The dielectric properties of
soils are defined through soil texture. The dielectric constant changes according to soil
composition (e. g. the relative amount of sand, silt or clay). Soil composition must therefore be
known to be able to accurately determine soil moisture. Microwave remote sensing is unaffected
by cloud cover but vegetation canopies attenuate microwave reflectance. For a more
comprehensive review of microwave techniques for soil moisture retrieval beginning in the
early 1970s, the works of Schmugge (1978), Schmugge (1983), Wang et al. (1983), Fung and
Eom (1985), Jackson and Schmugge (1989), Kostov (1993), Engman and Chauhan (1995), Njoku
and Enthekabi (1996), Schmugge (1998), Schmugge et al. (2002) and Wagner et al. (2007) are
recommended.
2.5.2 Landsat program
The National Aeronautics and Space Association’s (NASA) Landsat program started with the
launch of the satellite Landsat 1, the world’s first Earth Observation Satellite (EOS) in 1972. The
program consists of a series of satellites that photographically capture and monitor the earth’s
surface with the intention of studying the planet as a global environmental system. Currently,
the two Landsat missions 5 and 7 are circling the globe, collecting and delivering continuous
high resolution multispectral data of earth from space. Landsat imagery has been broadly used
both in science and public to study and analyse global processes at moderate spatial resolutions.
Landsat satellites carry multiple remote sensors and data relay systems along with altitude‐
control and orbit‐adjust subsystems, power supply and receivers for ground station commands
and transmitters to send the data to ground receiving stations.
28

The following table provides an overview of all Landsat missions and their technical
specifications:
System Activity I(s) Resolution (m) Communication A R D
Landsat 1 1972‐1978 RBV/MSS 80/80 D. d. with recorders 917 18 15
Landsat 2 1975‐1982 RBV/MSS 80/80 D. d. with recorders 917 18 15
Landsat 3 1978‐1983 RBV/MSS 40/80 D. d. with recorders 917 18 15
Landsat 4 1982‐1993 MSS/TM 80/30 D. d. TDRSS 705 16 85
Landsat 5 since 1984 MSS/TM 80/30 D. d. TDRSS 705 16 85
Landsat 6 1993 ETM 15 (pan)/30(ms) D. d. with recorders 705 16 85
Landsat 7 since 1999 ETM+ 15 (pan)/30(ms) D. d. with recorders 705 16 150
I = Instrument(s)
A = Altitude in kilometres
R = Revision rate in days
D = Data rate in Mpbs
RBV = Return Beam Vidicon
MSS = MultiSpectral Scanner
TM = Thematic Mapper
ETM = Enhanced Thematic Mapper
pan = panchromatic
ms = multispectral
D. d. = Direct downlink
TDRSS = Tracking and Data Relay Satellite System
Table 1 Technical specifications of Landsat missions 1 to 7
2.5.3 Landsat 7 Enhanced Thematic Mapper (ETM+)
Landsat 7 is the latest NASA satellite that was launched in 1999. It is the only Landsat satellite to
carry the ETM+ instrument, a passive sensor that measures solar radiation reflected or emitted
by the earth's surface. The instrument records data on eight bands with wavelengths of 0.45 µm
to 12.5 µm. In addition to bands of visible and infrared wavelengths, the instrument includes a
high resolution panchromatic and a thermal band. The satellite provides global coverage
between latitudes of 81 degrees north and 81 degrees south.
The following table summarizes Landsat 7 ETM+ satellite sensor characteristics:
Launch date 15 th of April, 1999 (Vandenberg Air Force Base, California)
Spatial resolution 15 to 90 metres
Orbit 705 +/‐ 5 kilometres (at the equator) sun‐synchronous
Orbit inclination 98.2 +/‐ 0.15
Orbit period 98.9 minutes
Swath width 183 kilometres
Grounding track repeat cycle 16 days (233 orbits)
Table 2 Summary of Landsat 7 ETM+ satellite sensor characteristics
29

The ETM+ sensor records data on eight bands with different spectral ranges, whose
characteristics are depicted in the following table:
Band Spectral range (µm) Ground resolution (m) Description
1 0.45 ‐ 0.52 30/28.5 blue‐green
2 0.52 ‐ 0.60 30/28.5 green
3 0.63 ‐ 0.69 30/28.5 red
4 0.76 ‐ 0.90 30/28.5 near‐infrared (NIR)
5 1.55 ‐ 1.75 30/28.5 mid‐infrared (MIR)
6 10.4 ‐ 12.5 60/57 thermal infrared (TIR)
7 2.08 ‐ 2.35 30/28.5 mid‐infrared (MIR)
panchromatic 0.50 ‐ 0.90 15/14.25 black/white
Table 3 Landsat 7 ETM+ band characteristics
The spectral bands used in this study for index calculations are briefly described as follows:
Band 3: 0.63 µm ­ 0.69 µm (red)
Band 3 absorbs chlorophyll of green vegetation and is therefore often analysed in vegetation
discrimination. In addition, it was found useful in soil‐boundary and geological boundary
mapping. Atmospheric influences are reduced but not avoided.
Band 4: 0.76 µm ­ 0.90 µm (NIR)
Band 4 especially responds to vegetation biomass (appearing bright) because vegetation reflects
approximately half of the incident near‐infrared radiant flux. It is therefore of use for vegetation
type identification and vegetation monitoring. Furthermore it has proven valuable in soil
moisture mapping, water body discrimination and in emphasizing soil‐crop contrasts.
Band 6: 10.4 µm ­ 12.5 µm (TIR)
The TIR band measures the amount of emitted infrared radiant flux (heat). The apparent
temperature is a function of the emissivity and true (kinetic) temperatures of surface objects.
Band 6 is used in locating geothermal activity, volcanic monitoring, thermal inertia mapping, soil
moisture studies, vegetation classification, vegetation stress analysis and cloud differentiation.
Moreover, band 6 is able to capture unique information on topographic aspect differences in
mountainous regions.
2.5.4 Normalized Difference Vegetation Index (NDVI)
The NDVI was developed by Rouse et al. (1973) and is one of the most commonly used
vegetation indices. The underlying principle of the index is the fact that chlorophyll pigments in
vigorous vegetation absorb the radiation in visible red wavelengths. The reflectance behaves
inversely to the absorption. The more chlorophyll that is present in plant leaves, the fewer
waves are reflected. Near‐infrared radiation is however scattered by internal leaf structures and
30

then either reflected or transmitted, allowing multiple layers of leaves to influence the overall
reflectance. The ratio of difference and sum of reflectance within both wavelength boundaries
received by a spaceborne satellite sensor is expression of vegetation health and vegetation
density. The NDVI also differentiates between green vegetation and soil background and is
useful for land cover classification (Yilmaz et al., 2008). It can additionally be used to derive
further vegetation indices, e. g. Leaf Area Index (LAI), Vegetation Water Content (VWC) or the
Fraction of Absorbed Photosynthetically Active Radiation (FAPAR). The index is calculated as:
���� � r ��� � r ���
r ��� � r ���
where r NIR = near‐infrared reflectance
r ��� = visible red reflectance
Ratio values range from ‐1 to +1. Positive values close to 1 denote healthy green vegetation
whereas negative values describe clouds or other areas with no vegetation cover such as water
bodies, snow‐covered areas or rocks and bare soils. Low values around 0 represent sparsely
vegetated areas, aged and dead vegetation.
The usefulness of the NDVI for soil moisture retrieval has been investigated and proven in
numerous studies (Price, 1990; Jackson et al., 2004; Walthall et al., 2004; Wang et al., 2004;
Wang et al., 2007 and Yilmaz et al., 2008).
2.5.5 Temperature­Vegetation Dryness Index (TVDI)
The strong correlation of remotely sensed surface temperature as measured by TIR emissions
and NDVI has been shown to be related to surface soil moisture in numerous studies (Goward
and Hope, 1989; Nemani et al., 1992; Goetz, 1997; Sandholt et al., 2002; Wang et al., 2004 and
2005; Zeng et al., 2004; Zhan et al., 2004; Naira et al., 2007; Wang et al., 2007; Yue et al., 2007
and Zhang et al., 2007).
Additionally to the direct estimation of soil moisture status, the relationship has been shown to
be of value in deriving further information: Nemani and Running (1989) and Price (1990) first
made use of the temperature/vegetation relationship to estimate evapotranspiration. Moran et
al. (1994) used the relationship to estimate crop water deficit. Nemani and Running (1997)
successfully utilized the Ts/NDVI space for land cover characterization. Gillies and Carlson (1995)
developed a method based on the relationship of NDVI and surface temperature to infer
31
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estimates of fractional vegetation cover and regional patterns of surface moisture availability
which could verified later by Gillies et al. (1997).
Several investigations concerning the validity of the relationship were made and modifications
to improve soil moisture estimates were tested (Carlson et al., 1995; Roy, 1997; Goward et al.,
2002; Claps and Laguardia, 2004; Kimura, 2006; Carlson, 2007 and Hassan et al., 2007).
The approach of a simplified land surface dryness index, often referred to as the ‘triangle’
method as proposed by Sandholt et al. (2002) was chosen in this study. It is an interpretation of
the Ts/NDVI space in terms of surface soil moisture status and is based on the assumption that
remotely sensed surface temperatures are related to vegetation canopy cover. The emitted heat
flux from the vegetated surface is lower than from bare soil because of a higher thermal inertia
in vegetation and stomatal transpiration control. Thus, remotely sensed surface temperatures
vary as a function of both thermal inertia and moisture availability of green vegetation. The
different response of surface temperature and vegetation to water stress in combination can be
related to surface moisture conditions. Chlorophyll concentration and thus reflectance in green
vegetation responds only weakly to immediate water stress, whereas surface temperatures of
unvegetated terrains quickly respond to changing moisture conditions. Sandholt et al. (2002)
identify the factors relevant for the location of the pixel in the Ts/NDVI space as
evapotranspiration, fractional vegetation cover, thermal properties of the surface, net radiation,
atmospheric forcing and surface roughness and some additional interacting factors.
The Ts/NDVI values plotted against each other ideally result in a triangular shape whose edges
represent either dry (limited water availability and low evapotranspiration) or moist (unlimited
water availability and maximum evapotranspiration) conditions. The following simplified figure
taken from Lambin and Ehrlich (1996) clarifies this relationship:
32

Figure 1 Simplified representation of the Ts/NDVI space from Lambin and Ehrlich (1996)
The TVDI can be calculated with the following formula:
���� � �� � �����⁄ ������������� (5)
where T S = observed surface temperature in ±C
T S���
= minimum surface temperature in the triangle
a, b = parameters defining the dry edge of the triangle
NDVI = observed Normalized Difference Vegetation Index
The parameters a and b are estimated as a linear fit to data with the following formula:
� ����
� � � ����� (6)
where T S��� = maximum surface temperature observation for a given NDVI
A more comprehensive understanding of how the parameters are related to each other can be
obtained in Sandholt et al. (2002) and observed in the following figure:
33

Figure 2 Ts/NDVI space as TVDI taken from Sandholt et al. (2002)
34

3 Study area and data description
3.1 Study area
The analysis is performed around Vallentuna municipality, Stockholms län. The area under
consideration reaches from Danderyd municipality in the south up to Arlanda airport in the
north and covers approximately 800 km2 of predominately clay, till, sand and rock soil as well as
bogs and fens. The area shows only little elevation differences and is mostly covered by open
fields and pasture, coniferous forest and built‐up areas. Lakes or branches of the Baltic Sea make
up about 10 percent of the area. Being close to Stockholm, the capital and political and
economical centre of Sweden, the region is of significance for a large part of the Swedish
population. The population of Stockholm was 825.000 people in autumn 2009 and is expected to
grow steadily over the next decades reaching one million residents in 2030. By then, the
Stockholm‐Mälaren region is estimated to have risen up to 3.5 million inhabitants. This increase
requires detailed information on all aspects of the region for future planning.
3.2 Satellite image
The Landsat 7 ETM+ satellite image used in the analysis dates from August, 4th, 2002. All bands
were acquired online from the Global Land Cover Facility (GLCF)
(http://www.landcover.org/data/gls/) and composed in PCI Geomatica 9.1. The satellite image
was applied the Swedish Reference Frame 1999 (SWEREF99) reference system. Figure 3 below
shows the satellite image after band composition and geometric correction:
35

Figure 3 Geometrically corrected Landsat 7 ETM+ satellite image
The following table depicts further Landsat scene information:
Author NASA Landsat Program
Publication date 2004
Collection name Landsat ETM+ 30m scene
Processing level L1G
Image name L7CPF20020701_20020930_02
Publisher United States Geological Survey (USGS)
Publisher location Sioux Falls, South Dakota
Product coverage date 2002‐08‐04
Table 4 Landsat scene information
3.3 Digital Elevation Model
A 50 x 50 metre horizontal resolution DEM with a 0.1 metre vertical precision in the underlying
SWEREF99 reference system was obtained from Lantmäteriet, the Swedish mapping, cadastral
and land registration authority. Elevation ranges from 0.1 m to 102.3 m with an average
elevation of 16.9 m above sea level. The DEM in its original form is presented in Appendix A.
36

3.4 Contour data
A vector data set of 5 m interval contour lines and 3 m and 6 m bathymetry contours in the RT90
2.5 gon coordinate system was reprojected to the SWEREF99 reference system and used in the
geometric correction process of the satellite image.
3.5 Land cover data
Land cover data was also acquired in form of the ‘marktäcke’ raster file from Lantmäteriet in 25
x 25 m resolution with the SWEREF99 reference system (later resampled to 28.5 m).
Information on land cover is necessary in order to relate soil moisture status to vegetation
distribution. Land cover classes as initially present in the file were reclassified according to the
amount of vegetation inherent in each land cover class, respectively. The less green vegetation is
present, the lower the vegetation class. The reclassification results are listed in table 5 below:
Land cover class description Newly assigned vegetation class
Urban areas 0
District larger than 200 inhabitants and less green areas 0
District larger than 200 inhabitants and more green areas 0
Solitary houses and courtyards 0
Industrial, commercial and public areas 0
Gravel and sand deposits 0
Landfills 0
Lakes and dams with open water surface 0
Lakes and dams with vegetation 0
Urban green areas 1
Sport fields 1
Ski slopes 1
Parks (not urban) 1
Fields 2
Pasture 3
Clear‐cut areas 3
Deciduous forest neither upon bog nor rock 4
Deciduous forest upon bog 4
Coniferous forest upon lichen soil 5
Coniferous forest not upon lichen soil 7‐15 m 5
Coniferous forest not upon lichen soil >15 m 5
Coniferous forest upon bog 5
Coniferous forest upon rock 5
Mixed forest neither upon bog nor rock 6
Mixed forest upon rock 6
Young forest 6
Wet bog 7
Other bog 7
Table 5 Land cover classification table
37

The vegetation class definition is summarized in the following table:
3.6 Soil data
Vegetation class description Vegetation class
Built‐up and water 0
Short grass 1
Pasture 2
Field 3
Deciduous forest 4
Coniferous forest 5
Mixed forest 6
Mire 7
Table 6 Vegetation class definition table
A soil map from the region of interest was integrated in the study. The data was issued by the
Sveriges Geologiska Undersökning (SGU) in the RT90 2.5 gon reference system and changed to
the SWEREF99 reference system. Soil moisture status should not only be related to vegetation,
but also to the underlying soil type. In order to explore the influences of vegetation and soil type
on soil moisture as calculated by the TWI and TVDI, soil type distribution is needed. The
following table shows the summarized soils and their distribution:
Soil type Pixels Area (km²) Percentage
Bog 7380 4.6 0.58
Fen 32829 20.5 2.58
Detritus mud 4333 2.7 0.34
Alluvial sediment, clay ‐ coarse silt 253 0.2 0.02
Mud – clay 42821 26.8 3.36
Clay 423808 264.9 33.27
Sand 54075 33.8 4.25
Gravel 4675 2.9 0.37
Cobbles 293 0.2 0.02
Esker 10475 6.5 0.82
Water 134905 84.3 10.59
Till 349754 218.6 27.46
Land fill (artificial/unknown) 130 0.1 0.01
Rock 207958 130.0 16.33
∑ 1273689 796.1 100.00
Table 7 Summary of soil types and distribution
Index distribution was investigated on the five predominant soil types clay, till, rock, sand and
bog/fen, which constitute about 95% of all soils present in the map (water bodies included).
38

3.7 Precipitation and temperature data
Precipitation and temperature data for July 2002 were obtained from SMHI for several stations
around the area under consideration. The data was used to identify weather conditions during
four weeks anteceding satellite image acquisition. The in situ measurements were scheduled
according to matching weather conditions. Otherwise, soil moisture status from field
measurements and the ones derived from the satellite image would be incomparable.
Temperatures range from monthly averages of 17.6 ±C to 19.2 ±C. The overall average
temperature is 18.3 ±C. Precipitation greatly varies from 67.4 mm/month to 178.8 mm/month.
Average precipitation over the whole area is 105.3 mm/month and total precipitation measured
at all stations sums up to 1264.10 mm/month. Table 8 below summarizes temperature and
precipitation data for all relevant weather stations:
Station Day mean temperature (°C) Total precipitation (mm)
Adelsö 18.3 126.5
Gnesta no data 175.8
Gustavsberg no data 74.6
Husarö 18.3 69.6
Rimbo no data 75
Skjörby no data 123.5
Stavsnäs 18.3 no data
Stockholm 19.2 113.8
Svanberga 17.8 78.8
Södertälje 18.3 178.8
Tullinge 17.6 101.5
Ultuna 18.5 78.8
Vallentuna no data 67.4
Average 18.3 105.3
Table 8 Summary of day mean temperatures and precipitation
The surfaces were generated in ArcGIS 9.3 by interpolating station data using the spline method.
Precipitation and temperature distribution maps are presented in Appendix B and C.
39

4 Methodology
For the objective of pixel by pixel soil moisture surface index comparison, data synchronisation
is needed. This implies matching the spatial resolution, surface extent and reference system of
all data sets, which was done in ArcGIS 9.3 and PCI Geomatica 9.1.
4.1 TWI calculation
4.1.1 DEM preparation
The DEM was resampled to a higher resolution to match the satellite image resolution (28.5 m).
The average elevation increased to 26 m above sea level when reducing the size by matching the
DEM boundaries to the smallest data set in the study, the soil map. The DEM is basis for TWI
calculation and therefore requires the removal of spurious sinks and pits, as mentioned earlier.
This was done with the FILL function in ArcGIS 9.3. The following table shows DEM statistics
before and after pit removal:
DEM type Min Max Mean Standard deviation
unfilled 0.10 102.30 26.01 19.65
filled 0.10 102.30 26.30 16.61
Table 9 DEM surface statistics before and after pit removal
4.1.2 SCA and slope grid calculation
SCA and slope grid were determined with the Terrain analysis using Digital Elevation Models
(TauDEM) software version 3.1 in ArcGIS 9.3. The D∞ flow direction approach was chosen. The
relevant functions in the Basic Grid Analysis menu require the pit filled elevation grid as input.
The ‘Dinf flow directions’ function generates both a flow direction surface and slope grid as a
first step. Flow direction is assigned to one or two neighbours based upon the steepest
downslope gradient on a triangular facet and expressed as a continuous angle from 0 to2π, as
the following figure clarifies:
40

Figure 4 Flow direction angle definition in the Dinf approach taken from Tarboton (1997)
Slope was calculated from the tangent of the slope angle. If no positive slope angles are present,
the flow determination method for flat areas after Garbrecht and Martz (1997) was used. This
method includes two independent slope gradients ‐ one gradient away from higher terrain and
the other towards lower terrain. The linear combination of both gradients is sufficient to identify
the drainage pattern (Garbrecht and Martz, 1997).
From the pit filled DEM, a flow direction grid (Appendix D) along with the slope grid (Appendix
E) were generated. SCA was then recursively calculated from the flow direction grid.
Contribution at each cell increases with the amount of upslope cells from which flow is
proportioned to the cell. After the identification of all contributing cells, SCA is calculated as the
amount of contributing cells multiplied by grid cell size (Appendix F).
4.1.3 TWI surface generation
With the SCA surface and slope grid, the TWI surface could be calculated for each pixel with
formula (1). This was done in ArcGIS 9.3 using the ArcModelBuilder. The arctangent of the slope
was calculated and then multiplied with the SCA. The TWI is expressed as the product’s natural
logarithm. The final TWI surface is presented in the following figure:
41

Figure 5 Final TWI surface
TWI surface generation was performed with varying settings to find the most realistic index
distribution and to study the differences in index values. Three unequal slope calculation
42

methods were tested (slope calculated in ArcGIS in both degrees and percent and slope as
calculated with TauDEM). The effect of a slight slope increase by 0.1 for all slope calculation
methods on the index was investigated to overcome the algorithm’s limitation of flat areas.
Additionally, the effect of variations in the underlying DEM upon the TWI was explored. DEMs
before and after pit removal and with removed water bodies were tested. These combinations
resulted in twelve different TWI surfaces which are discussed in the results section.
4.2 TVDI surface generation
The TVDI surface requires surface temperature and NVDI as input. Before they can be derived,
satellite image pre‐processing, geometric and atmospheric correction need to be performed. All
necessary steps and relevant intermediate results are described in processing order in the
following sections.
4.2.1 Satellite image pre­processing
All image pre‐processing was performed in PCI Geomatica Focus 9.1. The image was
downloaded in single bands that needed to be combined first. The band files were unzipped and
converted to .pix files. Format options in the ‘Import to PCDISK‘ function were set as ‘Band
Interleaved’, the overview options are set to ‘Nearest neighbor downsampling’.
In order to perform an atmospheric correction and to calculate the Ts/NDVI ratio, all bands need
to be applied the same spatial resolution. Therefore, the thermal bands (ETM+ 6.1 and ETM+ 6.2)
were reprojected with the PCI Geomatica ‘Reprojection’ function to match the resolution of the
other bands (from 57 m to 28.5 m). The reprojection bounds and were kept. The resampling
method was set to nearest with an exact transform order and a sampling interval of 1.
Each band was investigated in terms of random bad pixels (shot noise), line start problems and
(partial) line or column drop‐outs and striping. No line start problems and (partial) line or
column drop‐outs and striping could be identified. Bands one to seven (excluding the
panchromatic band) were then transferred into one file with the ‘Transfer layers’ function.
To precisely match the extents and boundaries of all surfaces, the TWI surface as generated in
ArcGIS 9.3 was added as an additional band to the file after atmospheric and geometric
correction. The already existing bands were clipped to the extent of the TWI surface.
43

Geometric correction
A geometric correction of the image was performed to correct potential spatial distortions in the
image using the Geomatica OrthoEngine. Exactly matching the image bands to the TWI surface is
crucial for a pixel to pixel comparison.
The first order polynomial math modelling method was chosen and the projection parameters
were defined to match the SWEREF99 system. Eight Ground Control Points (GCP) were manually
collected. A geocoded vector data set of 5 metre interval contour lines was used as ground
control source. An overall RMSE of 0.58 image pixels could be achieved (RMSE of 0.33 in X and
0.48 in Y direction).
After GCP collection, the ETM+ image was corrected with all bands. A sampling interval of four
was chosen and resampling method set to nearest.
Atmospheric correction
When extracting biophysical parameters from vegetation such as biomass, chlorophyll, leaf area,
percent canopy closure and other indices, atmospheric correction of the satellite image is
needed. Atmospheric influences are significant to the NDVI and can contribute up to more than
50 percent over sparse vegetation cover (Jensen, 2004). Absolute radiometric correction of
atmospheric attenuation turns the digital brightness values recorded by a remote sensing
system into scaled surface reflectance values (Du et al., 2002). An atmospherically corrected
TVDI surface is necessary for comparison with the TWI, which is free from atmospheric
influence.
There are two modules in PCI Geomatica to perform atmospheric corrections: ATCOR2 is used
for correcting satellite imagery over flat terrain and ATCOR3 for rugged terrain. Both modules
work with a database of atmospheric correction functions and have been developed mainly for
satellite sensors with a small swath angle such as Landsat and Satellite Pour l'Observation de la
Terre (SPOT), but some wide Field‐Of‐View (FOV) sensors such as Indian Remote Sensing
Satellites Wide Field Sensor (IRS‐WiFS) are also supported. Since the area shows only little relief,
an absolute radiometric correction of atmospheric attenuation with the ATCOR2 module was
chosen. Elevation was set to the mean elevation of the area (26.01 m). Sensor type, pixel size and
date were chosen according to the image attributes. The ‘etm_standart1’ calibration file of PCI
Geomatica was used. Atmospheric definition area was set to rural and the condition to mid‐
latitude summer. Correction parameters were specified according to the satellite image
metadata file (sun elevation at 45.4 decimal degrees). Visibility and adjacency were kept to 30
km and 1 km, respectively. The blue‐green, red, near‐infrared and thermal band (1, 3, 4 and 6)
44

were corrected. Additionally, haze and clouds were removed from the image. Haze and cloud
masks were defined automatically with a large area haze mask and the correction mode for thin
to medium haze. In the advanced options settings of the haze and cloud definition panel, the
average surface temperature was set to 18.91 °C. This value is the average temperature
calculated from weather stations located in the area (Stockholm and Adelsö) on satellite image
acquisition date. Emissivity was kept as a constant of 0.98. Visibility data was automatically
calculated. The cloud and haze masks are shown in the following figures 6 and 7:
Figure 6 Cloud mask Figure 7 Haze mask
4.2.2 NDVI surface
After satellite image pre‐processing, geometric and atmospheric correction, the NDVI could be
calculated. Image pixels in Geomatica are scaled as Digital Numbers (DN) from 1 to 255 and do
not represent real spectral reflectance as measured by the sensor. These values however need to
be obtained first in order to calculate spectral indices. First, radiance was calculated from the
DNs. From radiance, reflectance could be calculated. Bands 3 and 4 were exported to American
Standard Code for Information Interchange (ASCII) files. The header was removed and the
remaining absolute values were imported into Microsoft Excel, where all calculations were
performed. The radiance values were derived using the following formula:
� l �
� ���l � � ���l
���� ��� � ���� ���
� ����� � ���� ��� � � � ���l (7)
where L l = the spectral radiance at the sensor’s aperture in watts per steradian, µm and m 2
45

L ���l = the spectral radiance scaled to ���� ��� in watts per steradian, µm and m 2
L minl = the spectral radiance scaled to ���� ��� in watts per steradian, µm and m 2
QCAL = the quantized calibrated pixel value in DNs
QCAL min = the minimum quantized calibrated pixel value
QCAL max = the maximum quantized calibrated pixel value
The values for the three bands needed for NDVI and surface temperature calculation, are
respectively specified in the Landsat 7 science data user’s handbook (Irish, 2000) or can be
taken from the satellite image metadata file and are presented in the following table:
Values Band 3 (high gain) Band 4 (low gain) Band 6.2 (high gain)
QCAL ��� 255 255 255
QCAL ��� 1 1 1
L ���l ‐5.0 ‐5.1 3.2
L ���l 152.9 241.1 12.65
ESUN � 1533 1039 ‐
Table 10 Band constants for radiance calculation from DNs
The NDVI is based upon surface reflectance. Therefore, the calculated radiance needed to be
further converted into spectral reflectance values according to the formula:
� � �
�·� �·� �
���� � ·��� ��
where ρ �= unitless planetary reflectance
L � = spectral radiance at the sensor’s aperture
d = Earth‐sun distance in astronomical units (216th day of year = 1.0145779)
ESUN λ = mean solar exoatmospheric irradiances in watts per µm and m 2
θ � = solar zenith angle in degrees
The earth‐sun distance was obtained from a Microsoft Excel table published in the Landsat 7
science data user’s handbook (Irish, 2000). The solar zenith angle was calculated with the Solar
Position Calculator provided by the National Oceanic and Atmospheric Administration (NOAA)
Surface Radiation Research Branch.
From reflectance values, the NDVI could be calculated using equation (3). The final NDVI surface
is shown in Appendix G.
46
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4.2.3 Surface temperature
Surface temperature was calculated from the satellite image’s thermal band in high gain mode
(band 6.2). Similar to the previous NDVI calculation, surface temperature can not be determined
directly from the thermal bands DNs. The recorded brightness values needed to be converted to
spectral radiances first with the same formula (7). Surface temperature could then be obtained
from radiance values with the following formula:
��
��
�� � ��
� l � �� (9)
where T = effective temperature in Kelvin
K2 = calibration constant 2 in watts per steradian, µm and m 2 (1282.71)
K1 = calibration constant 1 in watts per steradian, µm and m 2 (666.09)
L l = spectral radiance at the sensor’s aperture in watts per steradian, µm and m 2
The resulting surface was then transformed from Kelvin to degree Celsius (°C). By exploring the
frequency distribution of temperature values, very few extremely high and low values could be
detected, identified as outliers and changed to the next realistic higher or lower value. Maximum
and minimum values then range from 8°C over the Baltic Sea to up to 40°C over densely built‐up
areas with an average temperature of 21°C. The temperature surface is shown in Appendix H.
4.2.4 TVDI surface
Both the NDVI and the temperature surfaces were rounded to three decimals and exported to
two Comma‐Separated Value (CSV) files, respectively. They were plotted against each other in
Matlab to identify the regression lines defining the upper and lower edges of the triangle.
Minimum and maximum temperature values for given NDVIs can thus be calculated as follows:
� ���� � 13.452 � 8.046 � ���� (10)
� ���� � 51.955 � 36.450 � ���� (11)
With the minimum and maximum values and the parameters a �51.955� and b �36.450� known,
the TVDI could be calculated according to formula (5) in Microsoft Excel. The calculated TVDI
values were then exported as ASCII file for surface generation in ArcGIS and as CSV file for
correlation analyses in Matlab. The final TVDI surface is shown in the following figure:
47

Figure 8 Final TVDI surface
48

4.3 Surface comparisons
In order to explore the statistical relationship between TWI and TVDI and to investigate possible
dependencies on other factors, the two surfaces were reclassified. Pixels of both TWI and TVDI
surfaces with different underlying soil types and vegetation classes were identified and
respectively extracted into separate surfaces. Five predominating soil classes (bog and fen, clay,
rock, sand and till) and eight distinct vegetation classes (0‐7, higher values denote stronger
vegetated areas) were used for reclassification. All resulting surfaces were converted into CSV
files and imported into Matlab. Table 11 below shows an overview of all 13 unique classes and
the two index surfaces:
Soil class Vegetation class Index surface one Index surface two
Bog and fen 0 TWI TVDI
Clay 1
Rock 2
Sand 3
Till 4
5
6
7
Table 11 Classes and index surfaces for combination
For each index surface, those pixels were extracted that belong to vegetation class 0 to 7 and to
one of the five soil types. All resulting combined surfaces are shown in the following table:
Combinations Number of surfaces
Soil and TWI 5 � 1 = 5
Soil and TVDI 5 � 1 = 5
Soil and vegetation and TWI 5 � 8 � 1 = 40
Soil and vegetation and TVDI 5 � 8 � 1 = 40
Vegetation and TWI 8 � 1 = 8
Vegetation and TVDI 8 � 1 = 8
Table 12 Overview of all surface combinations
Minimum, maximum, mean, standard deviation, amount of pixels and area percentage were
calculated for each surface combination, respectively. Pearson pairwise correlation coefficients
were calculated for each surface comparison between TWI and TVDI for equal class
combinations.
Additionally, the TWI and TVDI surfaces were both classified into the three categories of low,
medium and high values to detect further correlations. There is no optimum classification
method and optimum number of classes for comparing the two surfaces because of their
unequal value distribution. Therefore, two classification methods were tested (natural breaks
classification and quantile classification). The natural breaks classification after Jenks distributes
values into classes according to their natural breaks. This however means that values classified
49

y a natural break in one surface do not belong to a natural break in the other surface. The
quantile classification however assigns an equal amount of values to each class. This is most
suitable for linearly distributed data. One surface was classified for each of the three categories
with the two different classification methods. The corresponding surface was then created by
identifying and matching the cells of the initially classified surface. The following table shows the
classification summary:
Surface type Classification method Category Min Max
TVDI quantile low 0 0.187891
TVDI quantile medium 0.187891 0.269103
TVDI quantile high 0.269103 1
TVDI natural breaks low 0 0.249766
TVDI natural breaks medium 0.249766 0.427656
TVDI natural breaks high 0.427656 1
TWI quantile low 0 2.882193
TWI quantile medium 2.882193 5.572232
TWI quantile high 5.572232 12,5215
TWI natural breaks low 0 1.761344
TWI natural breaks medium 1.761344 3.240865
TWI natural breaks high 3.240865 12.5215
Table 13 Surface classification summary
Quantile and natural breaks classification result in different category boundaries as can be seen
from the table above. For TVDI values, quantile classification breaks lie considerably lower than
for the natural breaks classification. The reverse can be observed for TWI values. The natural
breaks classification results in narrower classes. This dissimilarity between the surfaces
demonstrates a natural difference in value distribution, e. g. two thirds of TVDI values lie
approximately only within the first quarter of the range (0.27), whereas two thirds of TWI
values lie roughly within half of the range (5.57).
4.4 In situ measurements
In order to compare the results obtained from the TVDI and TWI surfaces, soil moisture ground
truth values were gathered in situ with ground‐penetrating radar (GPR) at ten selected sites of
varying soil types and different TVDI and TWI indices. Soil moisture in the surface layer of the
soil to a depth of approximately 50 cm was derived from the dielectric constant of the soil using
the empirical Topp equation (Topp et al., 1980). The dielectric constant of the soil was measured
by means of the common‐midpoint method. Two GPR antennas, 800 MHz (Malå Geoscience)
were used to make small scale common‐midpoint measurements with a maximum antenna
separation of about 2 m. The CMP data were analysed using the software Reflex Win 4.5
(Sandmeier software, Germany). The following maps show the location of measurements taken
in Törnskogen, approximately 20 km north of Stockholm:
50

Figure 9 In situ data collection site Törnskogen Figure 10 Sample point overview
Soil moisture in volume fraction was determined by calculating the arithmetic mean of the
measured moisture values for each sample point. The amount of measurements taken per point
varies between two and three. The sample points were determined in advance of the actual
collection. The TWI surface was classified into three categories: low, medium and high values. A
map of five soil types (bog/fen, clay, rock, sand and till) was additionally created. Three
locations for each combination of TWI and soil class could be identified in the sample area. It
was not possible to measure soil moisture for all 36 points due to unsuitable weather conditions.
51

5 Results
5.1 TWI calculation
Results of the TWI calculation with varying settings as previously described are shown in the
following paragraphs.
5.1.1 Filled/unfilled/noData and filled DEM
TWIs that were calculated based on the unfilled DEM clearly show a lot of wrongly calculated
cells with no data values spread all over the area. This leads to the conclusion and confirms the
findings in other studies that a pit filled DEM has to be used in any case. The two following
figures show excerpts from the DEM with and without sink removal prior to TWI calculation:
Figure 11 Unfilled DEM (pits and sinks visible)
Figure 13 TWI surface without prior pit removal
52
Figure 12 Filled DEM (pits and sinks removed)

An excerpt of the TWI surface based on a DEM without antecedent sink removal is shown in the
figure above. The white cell aggregations (mostly four quadratically arranged cells) are sinks
with no data values.
The algorithm used in TauDEM can not distinguish whether larger flat areas with slope values of
0 should be water bodies or belong to the land surface. To ensure these areas to be correctly
processed, all water bodies present were taken out of the index calculation. These were
identified according to the ‘marktäcke’ data from Lantmäteriet. The raster was added in ArcMap
and clipped to shape. It was then reclassified, assigning ‘1’ to all other values and ‘noData’ to
water bodies. The mask was then multiplied with the filled DEM, assigning all water bodies an
elevation of ‘noData’. To omit calculating TWI values for water bodies, it is suggested to use the
data set where water bodies are excluded.
5.1.2 Slope 0/+0.1
The removal of water bodies does not solve the problem that zero TWI values are calculated for
large flat land covered areas with 0 slope values in the DEM. These areas should obviously be
assigned positive TWI values, since water tends to eventually flow towards them from higher
slopes. To overcome this problem, a very slight artificial slope of 0.1 was added to every cell in
the DEM. This resulted in successfully calculating TWI values for all cells (excluding ‘noData’
cells). The results show that this leads to higher minimum values, a higher mean and smaller
standard deviation. Maximum values are not affected.
5.1.3 Slope calculation method
TWIs based on slope in percent and degrees are higher than the ones based on TauDEM
calculated slope, which give better TWI results in flat areas. Neither visual interpretation nor
statistical analysis show significant differences in TWI distribution based on slope or degrees.
53

The following three figures show the slopes used as basis for TWI calculation:
Figure 14 Slope for TWI calculation in percent
Figure 16 Slope calculated in TauDEM
5.1.4 TWI calculation comparison
TWI surface generation results with different settings (filled/unfilled/noData and filled DEM,
slope increase +0/+0.1, and slope calculation method in degrees/percent/TauDEM) are
presented in Appendix I‐K. The following table presents a statistical summary of the different
TWI surface variations:
54
Figure 15 Slope for TWI calculation in degrees

DEM type Slope Slope calculation method Min Max Mean Standard deviation
filled/noData +0 degrees 0 14.62 4.39 1.95
filled/noData +0 percent 0 14.72 4.54 1.96
filled/noData +0 TauDEM 0 11.54 1.25 1.29
filled/noData +0.1 degrees 1.04 14.63 4.66 1.68
filled/noData +0.1 percent 1.04 17.72 4.80 1.68
filled/noData +0.1 TauDEM 1.04 12.52 2.84 1.57
Unfilled +0 degrees 0 14.32 3.94 2.13
Unfilled +0 percent 0 14.37 4.07 2.17
Unfilled +0 TauDEM 0 9.21 1.16 1.23
Unfilled +0.1 degrees 1.04 14.32 4.45 1.58
Unfilled +0.1 percent 1.04 14.37 4.57 1.59
Unfilled +0.1 TauDEM 1.04 11.98 2.79 1.40
Filled +0 degrees 0 16.68 3.70 2.42
Filled +0 percent 0 16.75 3.83 2.46
Filled +0 TauDEM 0 14.20 1.05 1.28
Filled +0.1 degrees 1.04 16.68 4.50 1.85
Filled +0.1 percent 1.04 16.75 4.61 1.86
Filled +0.1 TauDEM 1.04 14.67 2.97 1.75
Table 14 TWI surface statistics summary
Flat land surface areas could be discriminated from water bodies by removing these from the
DEM. On flat areas, flow could be determined when a slight artificial slope was added. For these
reasons and the fact that a DEM without sinks is needed as data input, the in table 14 highlighted
TWI calculation method is considered to be the most suitable one. This surface was eventually
compared to the TVDI surface.
5.1.5 TWI/TVDI correlations
When attempting to correlate both surfaces, the ‘noData’ values of removed water bodies
(designated as ‘‐9999’) in the TWI surface distort the scatterplot. Therefore, those values and the
corresponding ones in the TVDI surface needed to be removed.
The two final TWI and TVDI surfaces were converted to CSV files, read in Matlab and compared
to each other. The resulting scatterplot is shown in the following figure:
55

dry TWI wet
Scatterplot TWI/TVDI
wet TVDI dry
Figure 17 Scatterplot of the complete TWI and TVDI surfaces with regression line
The triangular shape of the scatterplot suggests a correlation of the two soil moisture indices.
High TWI values describe the tendency of soil to get saturated after rainfall, whereas low values
denote drier areas where no water accumulates, e. g. hilltops or ridges. Lower TVDI values on
the other hand express wet areas and high values dry ones. Several observations can be made
from the shape of the triangle. One observation is that with an increase in TVDI values, the
corresponding TWI values decrease along the blue line in the figure above (estimated regression
line). If this assumption is true, the TWI can be used as a predictor of the TVDI and vice versa
along the diagonal. Considering the left upper peak of the triangle, it seems that most points with
a high TWI are also wet according to a low TVDI. When considering maximum TVDI values, only
very few points indicate a high TWI (both index values represent dry soil).
However, these relations do not hold true in the lower part of the triangle where values are
evenly distributed. Numerous points being denoted as wet by the TVDI vary greatly in the TWI
index distribution. Additionally, very wet areas according to the TVDI surface (between 0 and
0.1) are contrarily assigned a rather dry status in the TWI surface.
56

Another observation that can be made from the scatterplot concerns the maximum and
minimum TVDI values. It seems that a lot of cells have either the exact value 0 or 1. This happens,
because few points marginally exceeded the limits for TVDIs (ranging from zero to one) due to
errors and noise in the initial satellite image derived thermal and NDVI surfaces. Values
exceeding one have been set to one and values that fall below zero have been set to zero,
respectively. All in all, 11145 cells out of 3450482 (0.3%) were changed (734 below zero and
10411 above one). The Pearson pairwise correlation coefficient for the TWI/TVDI surface is
0.023 with a p‐value of 0.00283, indicating a low but statistically significant correlation.
The comparison of all the combined TWI and TVDI surfaces with the soil and vegetation surfaces
is described in the following sections and the corresponding scatterplots are shown in Appendix
L to R.
5.1.6 TWI/TVDI and vegetation class correlation
The first observation that can be made is that the triangular shape is still visible in all
correlations but narrows as the amount of cells decreases with each vegetation class increment.
The values concentrate in the lower left corner of the triangle.
It also becomes apparent that the classification into the eight vegetation classes correlates with
the TVDI distribution. The higher the vegetation class, the lower TVDI values which indicates a
moister soil. This clearly validates the TVDI as a predictor of soil moisture since a sufficient
amount of available water results in an increase in growth and biomass. The right edge of the
triangle (expressed through the blue diagonal shown in Figure 17) becomes gradually steeper as
TVDI values decrease. This means that more cells with low TWI values disappear with an
increase in vegetation class than cells with high values, as it should be. Similar to the initial
comparison of the complete surfaces, areas denoted as moist by the TVDI still vary greatly in
TWI distribution.
5.1.7 TWI/TVDI and soil class correlation
There does not seem to be a significant variation in the triangular shape of the scatterplots for
different soil types. Therefore it can be reasoned that the correlation between TWI and TVDI as
the indices it selves are independent on the underlying soil type. The only visible difference is
the amount of cells. Clay and till are predominant, whereas bog and fen show least occurrences.
57

5.1.8 TWI/TVDI and soil/vegetation class correlation
TWI/TVDI correlation for bogs and fens
In all scatterplots except the one for vegetation class 0, the characteristic triangular shape is
visible. Points accumulate within TWI value boundaries of one and five and vary greatly from 0.1
to 1 on the TVDI axis. A correlation is least observable. Point quantity decreases with higher
vegetation classes. TVDI values also decrease continuously with a higher vegetation class. More
distinct shapes should become apparent as vegetation classes increase because all areas in the
soil map identified as bogs and fens naturally should also belong to a high vegetation class.
Therefore not many cells with a low vegetation class are expected to be denoted as bogs and
fens.
TWI/TVDI correlation for clay soils
The scatterplots all show the well‐known triangular shape, although it is least visible for
vegetation classes zero and seven. There are by far most pixels (42%) on clay soils in vegetation
class two followed by pixels in class zero (18%) and three (14%) indicating that clayey soils
tend to be covered by vegetation of lower classes, mostly fields and meadows. One difference
that can be observed is that there are more cells with higher TWI values than 10 in comparison
to other soil types. One simple reason for this might be that most of all points identified (40%)
lie on clay soil which means a higher chance that high values fall unto that class. Another reason
might be that water tends to accumulate rather there than on other soils or that clay seems to be
the predominant soil type in the lowest parts of the watershed or underneath streams where
highest TWIs are expected.
TWI/TVDI correlation for rock soils
As in the correlation on clay soils, the triangle is distinguishable for all vegetation classes except
for the highest one. There, only very few cells (0.1%) could be identified. They are simply not
enough values to form a visible triangle. The correlation plots are similar to the ones for the
other soils. One observation is that nearly half of all points (47%) fall into vegetation class five.
All other soil types except till have considerably less cells in that class.
TWI/TVDI correlation for sand soils
Similar to the scatterplots with the other underlying soil types, the triangular shape is visible but
less clear. The right edge is more difficult to define. The combination surface of sand and
vegetation class seven is undefined. Only 41 cells of that unique combination could be identified
which is least of all possible combinations between soil and vegetation and constitutes only 0.1
58

percent of all areas on sandy soil. Sandy soils are second rarest in the region and are
predominantly covered by vegetation of lower classes (vegetation class five to seven cover only
26%).
TWI/TVDI correlation for till soils
The correlations on till soil mostly resemble the correlations on rock soil. Most cells could be
identified in vegetation class five (39%) followed by vegetation class zero (19%) and three
(14%). Similar to correlations on other soils, the triangular shape is least visible for the lowest
and highest vegetation class, respectively.
5.2 Correlation coefficients
The following tables show correlation results for all TWI and TVDI combinations. Surface
statistics of all compared surfaces are presented in Appendix S and T.
Surface combination Pearson pairwise correlation coefficient p­value
TVDI/TWI for vegetation class 0 ‐0.038

Surface combination Pearson pairwise
correlation coefficient
p­value
TVDI/TWI for soil class bog and vegetation class 0 ‐0.022 0.178
TVDI/TWI for soil class bog and vegetation class 1 0.062 0.0147
TVDI/TWI for soil class bog and vegetation class 2 0.063

the triangle but a large amount lies scattered outside it, especially towards higher TVDI values
with slightly decreasing TWI values. Large variations in TWI values are expected since they are
only based on slopes and independent on land cover. As vegetation class zero denotes built‐up
areas, high TVDI values implying less vegetation are also expected. Considering all the combined
surfaces, it becomes apparent that most points accumulate in the lower left corner of the triangle.
This also show the means of the surfaces, which are 2.84 for the TWI surface and 0.26 for the
TVDI surface, respectively. This indicates that most points that are identified as moist by the
TVDI are indicated rather dry by the TWI in respect to the range of both indices.
Another interesting aspect of the statistics concerns the distribution of cells in respect to
vegetation and soil classes. Cells on the lowest vegetation class constitute a considerable
percentage in all classes (13% to 32%, average 18%). Most cells lie on the predominant soil type
clay (40%). Main vegetation class is five (27%). Other vegetation classes are rather equally
distributed. Vegetation class five is mostly found on till and rock and least on clay soils. The
highest vegetation class is nearly only found in bogs and fens and constitutes only about 1
percent of vegetation classes. Most cells are found to lie on clay soils in vegetation class 2.
TVDI
Mean and maximum values for each unique TVDI combination decrease with an increase in
vegetation class according to TVDI theory. As there are a lot of minimum values in all classes, no
change with variation of soil type and vegetation class can be observed. The highest four
vegetation classes (4 to 7) have similarly low values. The biggest difference in means and
maximum values can be observed in the transition from vegetation class 3 (pasture, grasslands
and meadows) to 4 (deciduous forest). This becomes especially apparent when exploring the
combination of TVDI and vegetation only (TVDI0 to TVDI7). Furthermore there seems to be a
correlation of vegetation class and standard deviations. The standard deviations decrease as
vegetation increases. It can therefore be reasoned, that most cells with high vegetation are also
denoted as wet and least cells incorrectly denoted as dry. On the other hand, high standard
deviations in lower vegetation classes mean that a number of cells identified as dry by the TVDI
varies in vegetation class.
TWI
Minimum values are equal for each surface combination due to the calculation method.
Minimum values denote points with no tendency to accumulate water. Maximum values vary
marginally with an average of 11.87. Maximum TWI values are highest on clay soil (12.52) and
lowest on sand soil (10.46). They do not change within different vegetation classes. Highest
mean values can be observed for soil classes bog and fen (3.13) and clay (3.10), lowest on rock
61

(2.45). Very high standard deviations explain that values deviate greatly from the mean. All
combinations of surfaces are statistically spoken comparatively similar which makes it difficult
to discover variations in value distributions and patterns that soil types or vegetation classes
can account for.
5.3 Classification into low, medium and high categories
The TWI/TVDI and TVDI/TWI scatterplots for quantile and natural breaks classifications are
shown in Appendix U and V. The following table summarizes correlation statistics.
Surface Pearson pairwise Norm of
Regression line p­value
correlation coefficient residuals
TVDI quantile l ‐0.057 794.90 � � �6.17 � � � 3.82

significant result. It is important to note that weather conditions (dry) at the time and three
weeks before the samples were collected are similar to the ones of the satellite image acquisition
date. Measurements for the soil type and TWI class combinations ‘low clay’, ‘medium bog’ and
‘medium clay i’ could be carried out before rain set in. The other samples might be affected by
rainfall, although it is unclear to what extent. Some of the measurements were conducted in
open field whereas others took place under canopies. The following table shows the measured
soil moisture for all points with underlying pixel values of the TWI and TVDI surfaces,
respectively.
Point description # samples Average volume fraction (m³/m³) TWI TVDI
low clay 2 0.185 4.8052 0.15
low fen 3 0.188 1.4625 0.18
low till 3 0.374 4.6549 0.19
medium bog 3 0.670 2.036 0.17
medium clay i 3 0.247 1.8015 0.16
medium clay ii 2 0.277 1.9055 0.15
medium till i 3 0.136 2.0794 0.15
medium till ii 3 0.200 2.4293 0.16
high clay 3 0.398 6.1129 0.14
Table 19 Numerical comparison between ground truth and calculated TWI and TVDI values
Figure 18 Visual comparison between ground truth and calculated TWI and TVDI values
63

6 Discussion
The purpose of this study was to estimate soil moisture status around Stockholm based on two
different approaches and to compare the results. Soil moisture distribution could be modelled
with the in hydrology commonly used TWI and the remotely sensed TVDI. Index distribution
dependence on both soil type and vegetation cover was investigated. The results indicate that no
linear dependency between the two indices exists (Pearson correlation coefficient 0.023, p‐value
0.00283). Index classification in low, medium and high value categories did not result in higher
correlations. Although Seibert et al. (2007) found the TWI related to soil properties, neither
index distribution is found to be dependent on the underlying soil type. It should be noted that
the bog/fen class is not a soil class. Bogs and fens are different and should not have been merged
into one class although both can be summarized as wetlands. No connection between TWI
distribution and vegetation cover could be detected. TVDI values however change with
vegetation distribution. Areas indicated as wet by the TVDI are also assigned a higher vegetation
class according to index theory. In situ measured soil moisture did not agree well with either
index. However, the amount of measured values was too small to achieve statistically significant
results. This weak accordance and the lack of correlation between the indices raise questions of
index validity, suitability and comparability. Here it should also be mentioned that the results
are largely dependent on the actual data that were used. Higher resolutions and further varitions
in TWI calculation might produce different results. The TWI model in fact was a good predictor
for dry areas according to high TVDI and low TWI values, but failed much more in mid and wet
areas. It can be reasoned that areas with small upslope areas are correctly identified as dry, but
that points with larger upslope areas are more often wrongly classified.
There rest degrees of uncertainty if the TWI is able to represent soil moisture sufficiently
accurate. Although often successfully applied, different studies compared TWIs with distributed
field measurements and often found weak correlations (Burt and Butcher, 1985; Iorgulescu and
Jordan, 1994; Thompson and Moore, 1996; Seibert et al., 1997 and Murphy et al., 2008).
Iorgulescu and Jordan (1994) suggested topography being a relevant factor but not sufficient in
determination of saturated areas. Soil and geological factors needed to be incorporated as well.
Beven (1997) questions the reliability of the TOPMODEL concept. According to his findings it
only sometimes produces reasonable results. The reasons for this are attributed to the facts that
the index greatly simplifies catchment dynamics and that its underlying theory is rather
restrictive. Güntner et al. (1999) as well as others emphasize the need of validation methods for
hydrological models or spatially distributed simulations. Their multi‐criterial validation of
TOPMODEL identified limitations of the TOPMODEL concept in comparison to the real situation.
64

Sulebak et al. (2000) also concluded that the predictive power of the TWI is still unclear and has
yet to be fully assessed. Güntner et al. (2004) tried to validate TOPMODEL with various
modifications in respect to saturated areas. Although improvements could partially be achieved
with the modified index, the question to what extent the TWI is able to correctly reflect the
distribution of saturated areas still remains. Murphy et al. (2009) identified limitations to the
concept as over‐dependence on convergent flow, dispersive flow in lower landscape positions
and the failure to account for local downslope topography effects and hydrologic conditions.
A central issue in TWI calculation is DEM resolution. As stated earlier, a 10 m spatial resolution
is recommended to obtain TWI values that represent soil moisture status most accurately.
Therefore, TWIs are expected to correlate better with the actual soil moisture when calculated
on a higher resolution DEM. However, no correlation improvement with TVDI values is expected
due to differences in underlying index theories. As the TWI’s crucial criterion for surface soil
moisture status is slope, the TVDI is solely based upon surface temperature and vegetation cover.
These initial factors stand only in little relation to each other. Especially when considering scale
differences. Large forest areas, e. g. vary little in surface temperature and NDVI but might be
spread over rugged terrain with high variations in slope and relief, where water availability
differs greatly. Vegetation over large areas is less defined by local slope variations than by
climate (especially temperature and precipitation). The TWI might therefore be rather suitable
for small scale analyses limited to single catchments than to large scale determination of soil
moisture. The TVDI on the other hand would be of little use to determine where exactly water
would accumulate within a catchment. Not only the TWI, but also the TVDI concept lacks
complete validation. Carlson et al. (1995) compared soil water contents derived with the
‘triangle’ method (similar concept as for the TVDI) and with the Push Broom Microwave
Radiometer (PBMR) to in situ ground measurements and found weak correlations. Similar to the
findings in this study a full range in surface soil moisture availability was present over varying
vegetation cover. Soil water content was also found to greatly vary at different depths. Spatial
variations of surface soil water content were greater for the ‘triangle’ method. Furthermore, it is
argued that the triangular shape of the distribution seemed to be dependent on the amount of
pixels and not on the resolution. The combined microwave and triangle methods gave better
results than one method alone. In the study it was reasoned that to fully validate the triangle
method, further research would be needed.
65

Neither of the indices was able to accurately represent soil moisture status with respect to the
measured soil water content. The reason might be that simply too few measurements could be
conducted, which also might be affected by rainfall to some unknown extent. To gain further
insight into the correlations between soil moisture, vegetation cover, underlying soil type and
both indices, extensive soil moisture measurements would be a valuable contribution.
66

7 Conclusion
The study examined two completely different methods of surface soil moisture estimation. Soil
moisture was derived and expressed by two indices. Topographic Wetness Index (TWI) and
Temperature‐Vegetation Dryness Index (TVDI) were calculated for an area of approximately
800 km2 north of Stockholm, Sweden. The two approaches, one from a hydrological modelling
point of view and the other in the remote sensing field of soil moisture retrieval using satellite
imagery were compared to each other. In situ soil moisture measurements were taken and
related to the derived moisture indices. Index dependencies on vegetation cover and soil type
were investigated. No significant correlation between the two indices could be detected. Index
distribution was found to be independent on different soil types and only the TVDI seems to be
related to vegetation cover. Both indices showed only weak correlations with in situ measured
soil moisture. Larger sample size could result in statistically significant results. Extensive soil
moisture measurements in the area would greatly contribute to result interpretation. However,
the fact that both indices correlate considerably better with in situ measured soil moisture than
with themselves suggests that both methods can be used to model soil moisture in this area for
different purposes and possibly also complete each other. At the same time it can be reasoned
that the underlying index theories fundamentally differ. The TWI calculated only with elevation
information and the TVDI making use of the land surface temperature and vegetation
distribution relation have no common basis which the lack of correlation clearly expresses. The
question of which index gives the better results or is superior can not be answered. The choice of
which index to use should be dependent on the intention of usage and reference scale. The
results of this study hopefully contribute to ongoing actual research about integrating remotely
sensed soil moisture into hydrological modelling. As a result, two soil moisture index surfaces
were generated that can be used for further analyses, research purposes in hydrology and
remote sensing, decision making or for any other purpose. The TWI surface is considered a more
suitable soil moisture representation for analyses on smaller scales or for single catchments
whereas the TVDI should prove more valuable on a larger, regional scale. However, the synthesis
of hydrologic modelling and remote sensing is a promising field of research. The establishment
of combined effective models for soil moisture determination over large areas requires more
extensive in situ measurements and methods to fully assess the models’ capabilities, limitations
and value for hydrological predictions.
67

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Appendix
Appendix A Original 50 metre resolution DEM as acquired from Lantmäteriet
78

Appendix B Precipitation over Stockholm in mm during July 2002
79

Appendix C Average temperature around Stockholm in °C during July 2002
80

Appendix D D∞ flow direction grid surface for TWI calculation within TauDEM
81

Appendix E D∞ slope grid surface for TWI calculation within TauDEM
82

Appendix F D∞ contributing area surface for TWI calculation within TauDEM
83

Appendix G NDVI surface calculated by Landsat 7 ETM+ bands 3 and 4
84

Appendix H Temperature in °C derived from the ETM+ thermal band on August 4th, 2002
85

Appendix I TWI surface calculation variants for 'NoData'
86

Appendix J TWI surface calculation variants for 'unfilled'
87

Appendix K TWI surface calculation variants for 'filled'
88

Appendix L TWI/TVDI scatterplots for vegetation classes 0 to 7
89

Appendix M TWI/TVDI scatterplots for soil classes
90

Appendix N TWI/TVDI scatterplots for soil class bog and vegetation classes 0 to 7
91

Appendix O TWI/TVDI scatterplots for soil class clay and vegetation classes 0 to 7
92

Appendix P TWI/TVDI scatterplots for soil class rock and vegetation classes 0 to 7
93

Appendix Q TWI/TVDI scatterplots for soil class sand and vegetation classes 0 to 7
94

Appendix R TWI/TVDI scatterplots for soil class till and vegetation classes 0 to 7
95

Surface Min Max Mean Std. deviation Pixel count Area percentage
tvdi 0.01 1.00 0.26 0.12 874879 100
tvdi0 0.01 1.00 0.39 0.14 156469 18
tvdi1 0.01 1.00 0.29 0.10 55281 6
tvdi2 0.03 1.00 0.27 0.10 194685 22
tvdi3 0.01 1.00 0.24 0.08 122934 14
tvdi4 0.03 0.72 0.18 0.04 37713 4
tvdi5 0.05 0.92 0.18 0.04 235067 27
tvdi6 0.03 0.84 0.19 0.05 64594 7
tvdi7 0.08 0.37 0.19 0.03 5661 1
tvdibog 0.04 1.00 0.23 0.12 29542 4
tvdiclay 0.01 1.00 0.28 0.12 323124 40
tvdirock 0.05 1.00 0.23 0.09 148101 18
tvdisand 0.01 1.00 0.28 0.14 40143 5
tvditill 0.01 1.00 0.23 0.11 260309 32
tvdibog0 0.11 1.00 0.44 0.18 3813 13
tvdibog1 0.13 0.79 0.26 0.10 1539 5
tvdibog2 0.04 0.71 0.23 0.09 2888 10
tvdibog3 0.06 0.86 0.22 0.09 4641 16
tvdibog4 0.08 0.58 0.16 0.03 3417 12
tvdibog5 0.07 0.86 0.17 0.04 8928 30
tvdibog6 0.06 0.60 0.17 0.04 3197 11
tvdibog7 0.11 0.33 0.18 0.33 1157 4
tvdiclay0 0.01 1.00 0.41 0.14 58932 18
tvdiclay1 0.09 1.00 0.31 0.10 22165 7
tvdiclay2 0.03 1.00 0.28 0.10 135716 42
tvdiclay3 0.06 0.88 0.24 0.08 45677 14
tvdiclay4 0.09 0.71 0.18 0.04 10221 3
tvdiclay5 0.08 0.77 0.18 0.04 34563 11
tvdiclay6 0.05 0.68 0.19 0.05 15348 5
tvdiclay7 0.11 0.36 0.19 0.05 252 0
tvdirock0 0.09 1.00 0.35 0.13 23351 16
tvdirock1 0.09 1.00 0.26 0.09 8740 6
tvdirock2 0.05 0.95 0.29 0.09 11193 8
tvdirock3 0.08 0.96 0.24 0.07 18500 13
tvdirock4 0.09 0.54 0.18 0.04 5020 3
tvdirock5 0.05 0.73 0.19 0.04 69239 47
tvdirock6 0.07 0.80 0.19 0.05 11525 8
tvdirock7 0.08 0.37 0.19 0.04 200 0
tvdisand0 0.10 1.00 0.40 0.14 12782 32
tvdisand1 0.12 1.00 0.29 0.11 3925 10
tvdisand2 0.08 0.99 0.27 0.10 5331 13
tvdisand3 0.01 0.96 0.26 0.09 5165 13
tvdisand4 0.10 0.54 0.18 0.05 1954 5
tvdisand5 0.09 0.92 0.18 0.05 7931 20
tvdisand6 0.10 0.50 0.19 0.05 2989 7
tvdisand7 0.12 0.27 0.18 0.03 41 0
tvditill0 0.01 1.00 0.38 0.14 48650 19
tvditill1 0.01 1.00 0.27 0.10 14654 6
tvditill2 0.03 0.96 0.24 0.08 16075 6
tvditill3 0.01 1.00 0.24 0.07 36846 14
tvditill4 0.03 0.72 0.18 0.04 14087 5
tvditill5 0.09 0.76 0.18 0.03 101545 39
tvditill6 0.03 0.84 0.18 0.04 27947 11
tvditill7 0.11 0.37 0.18 0.04 320 0
Appendix S TVDI surface combination statistics
96

Surface Min Max Mean Std. deviation Pixel count Area percentage
twi 1.04 12.52 2.84 1.65 874879 100
twi0 1.04 12.52 2.81 1.61 156469 18
twi1 1.04 12.20 2.87 1.66 55281 6
twi2 1.04 12.43 3.13 2.03 194685 22
twi3 1.04 12.31 2.83 1.65 122934 14
twi4 1.04 11.04 2.91 1.60 37713 4
twi5 1.04 11.27 2.61 1.26 235067 27
twi6 1.04 11.32 2.79 1.44 64594 7
twi7 1.04 11.88 3.28 2.31 5661 1
twibog 1.04 10.99 3.13 2.03 29542 4
twiclay 1.04 15.52 3.10 1.31 323124 40
twirock 1.04 11.50 2.45 1.13 148101 18
twisand 1.14 10.46 2.94 1.63 40143 5
twitill 1.04 11.67 2.62 1.27 260309 32
twibog0 1.04 10.56 3.11 2.06 3818 13
twibog1 1.04 10.29 3.27 2.15 1539 5
twibog2 1.04 10.94 3.45 2.31 2888 10
twibog3 1.04 10.93 3.29 2.21 4641 16
twibog4 1.04 10.98 3.24 2.10 3417 12
twibog5 1.04 9.94 2.89 1.74 8928 30
twibog6 1.04 10.87 3.06 1.86 3197 11
twibog7 1.04 10.99 3.31 3.37 1157 4
twiclay0 1.04 11.52 3.08 1.87 58932 18
twiclay1 1.04 12.20 3.08 1.86 22165 7
twiclay2 1.04 12.17 3.18 2.07 135716 42
twiclay3 1.04 12.10 3.04 1.82 45677 14
twiclay4 1.04 11.04 3.11 1.72 10221 3
twiclay5 1.04 11.27 2.96 1.53 34563 11
twiclay6 1.04 11.07 3.03 1.64 15348 5
twiclay7 1.04 11.47 3.06 2.10 252 0
twirock0 1.04 10.76 2.43 1.14 23351 16
twirock1 1.04 10.60 2.45 1.08 8740 6
twirock2 1.04 11.42 2.70 1.55 11193 8
twirock3 1.04 11.00 2.45 1.20 18500 13
twirock4 1.04 10.64 2.61 1.24 5020 3
twirock5 1.04 9.45 2.38 1.01 69239 47
twirock6 1.04 11.32 2.54 1.18 11525 8
twirock7 1.04 11.50 2.53 1.55 200 0
twisand0 1.04 10.22 2.78 1.55 12782 32
twisand1 1.04 10.46 2.94 1.61 3925 10
twisand2 1.04 10.29 3.13 1.91 5331 13
twisand3 1.04 10.11 2.89 1.65 5165 13
twisand4 1.04 8.99 3.05 1.66 1954 5
twisand5 1.04 9.37 2.90 1.56 7931 20
twisand6 1.04 9.78 2.98 1.62 2989 7
twisand7 1.04 6.11 2.71 1.41 41 0
twitill0 1.04 10.66 2.60 1.31 48650 19
twitill1 1.04 10.60 2.63 1.25 14654 6
twitill2 1.04 11.13 2.67 1.44 16075 6
twitill3 1.04 11.67 2.60 1.30 36846 14
twitill4 1.04 10.96 2.75 1.36 14087 5
twitill5 1.04 9.59 2.58 1.20 101545 39
twitill6 1.04 11.18 2.70 1.30 27947 11
twitill7 1.04 11.50 3.04 2.07 320 0
Appendix T TWI surface combination statistics
97

Appendix U TWI/TVDI and TVDI/TWI quantile classification scatterplots
98

Appendix V TWI/TVDI and TVDI/TWI natural breaks classification scatterplots
99

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The TRITA-GIT Series - ISSN 1653-5227
2009
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