ECOWOOD Mervi Kokkila 1.2.2002 Digital elevation models (DEM) in trafficability analysis
1. Introduction
Site topography affects on trafficability at least two ways. First, it affects on the performance of the vehicle and secondly it affects on direction and intensity of water and soil material movement. Information about site topography, together with geomorphological knowledge, can be in a great help when assessing the locations of different soil deposits and thus the bearing capacity of the terrain.
The basic assumption in soil attribute prediction is that topography is one of the most important factor affecting water and solute movement in terrain. Thus topographic attributes can characterise water flow paths and those soil attributes which are connected with soil water content. It is also assumed, that there are no point sources or sinks of water and thus water does not incidentally disappear from or appear in the system. (Gallant, 2000)
Digital elevation model (DEM) describe the topography in a numerical way. There are basically three different ways to represent the surface in an elevation model. In a grid-based model the surface is described by a regularly-spaced point network. In a TIN-model the point network is irregular and consists of the sample of surface specific points. Contour-based models use contours as a base in polygonal network formation. (Moore et al. 1991; Tokola et al. 2000) Examples of a raster DEM, TIN and a contour-based element network are in Figure 1.
Figure 1. Methods of structuring a network of elevation data: (a) square-grid network showing a moving 3x3 sub-matrix centred on node 5; (b) triangular irregular network (TIN);
(c) contour-based element network (After Moore et al. 1991)
The numerical elevation model allows easy quantification of the topographic attributes of a landscape. Primary attributes are calculated directly from a DEM and include variables such as slope, aspect, plan and profile curvature, flow path lengths and specific catchment area. All of these primary terrain attributes can be used when assessing the hydrological responses of a catchment to a rainfall. In addition, there are some secondary attributes, which are calculated from the primary ones.
Different wetness indices are the most widely used secondary attributes to describe the effects of the topography on the distribution of the soil moisture in a landscape level. The calculation of the wetness index is based on logical ideas of downslope water movement and accumulation of water at the base of slopes and in depressions or swales where there is convergence of flow. Although the approach in the wetness index calculation is simple, the calculation includes the topography, which is seen as a key factor regulating the soil water system behaviour. It may provide a quick way to assess the relative differences in the soil moisture between the sites and within the site and thus also a way to assess the relative differences in trafficability.
2. Primary attributes derived from DEM
The surface shape is controlled by changes in elevation from one place to another. These changes are mathematically represented as spatial derivatives, which on regular grids are approximated by finite differences (Figure 2)
Figure 2. Centred finite differences which are used to estimate the derivatives of the topographic surface; (After Gallant and Wilson, 1996)
h z z x zx z
2
4 6
2 4 5 6 2
2
2
h z z z x z
xxz
2 8 5 2 2
2 2
h z z z y zyy z
2 9 7 3 1 2
4h z z z z y x
z
xyz
p zx2 z2y h is the grid spacingp s
FDx x x
y
FD
z
z z
z 90
arctan 180
Basic information about some primary attributes is given in the following text. Examples of the calculation results are in the next chapter. Slope measures the rate of change in elevation.
It is calculated by using finite differences (Eq. 1) or by determining the steepest descent slope.
Aspect describes the orientation of the steepest slope measured in degrees clockwise from north (Eq. 2). Contributing area is a measure of the upslope area that delivers water to a point, grid cell or a given length of contour.
The contributing area is dependent on the flow routing method used in the calculation. A single flow direction method (D8- method) is a flow routing method, in which all water is routed from a cell to its steepest downslope neighbour. One example of routing method, which routes water from a cell to multiple neighbouring cells is a multiple flow direction (FD8-method), in which water is routed from a cell to all its downslope neighbours and routing is weighted by slope. (Gallant and Wilson, 1996)
3. Compound attributes derived from DEM 3.1. Topographic wetness index
Calculation of wetness index is based on the idea of local slope and upslope contributing area affecting the soil moisture status in the calculation unit (eg. Moore et al., 1991). The index in its simplest form is given in Eq. 3.
wT = ln (As / T tan ) (3)
In which, As is the upslope contributing area from which water is directed into the calculation unit; tan is slope of the ground surface in the calculation unit, is slope angle and T is transmissivity of the ground. If the soil transmissivity is considered uniform over the catchment and equals unity, index is (Eq. 4)
w = ln (As / tan ) (4)
The calculation of the index is based on several assumptions. The flow conditions are assumed to be at the steady state, which means that the water flow is even and every calculation unit gets contribution from its entire upslope contributing area. The rate of
(1) (2)
groundwater recharge is assumed to be uniform over the area, meaning that there is no special groundwater sinks in the area. The slope of the ground surface must equal that of the groundwater table. This means that there is a coincidence between the surface and subsurface areas draining to each unit length of contour and the surface slope can thus be used when calculating the direction of subsurface flow. In addition, the conductivity profile is assumed to be exponential and identical over the area and no downhill damming or drainage from downhill is allowed, i.e. downhill conditions have no influence on the calculated wetness in an area element. (Moore et al., 1991; Barling et al., 1994; Rodhe et al. 1999)
When considering the techniques and schemes used for calculating the index value, two important factors can be distinguished. The first one is the resolution and representation of the topographic data and the second one the way the primary attributes are calculated. The influence of the raster DEM data resolution on wetness index calculations has been studied by e.g. Zhang and Montgomery (1994) and Thompson and Moore (1996). Moore et al. 1988 have developed a contour based methods for calculating the terrain parameters, as a response to critics which have been posed against the use of a raster DEM in hydrological analysis.
Zhang and Montgomery (1994) have studied the effect of the DEM grid size on the hydrologic simulations. They noticed that, a 10-m grid size provides a substantial improvement over 30-m data. However, in flow simulations they used single flow algorithms and elevation models were not hydrologically corrected. Single flow algorithms allow water flow only to a single cell downslope and e.g. Moore (1996) and Desmet & Govers (1996) have been criticised the use of them in the hydrologic models. By the hydrologically correct elevation model, developed by Hutchinson (1989), is meant an elevation model, which is corrected with the information about the actual streamlines.
Thompson and Moore (1996) studied the relations between topographic indices and water table depth as well as the effect of DEM resolution on the predictive power of these relations in a shallow forest soil. The existence of the statistically significant relation between the water table depth and the topographic wetness index was noticed. However, accuracy of water table depth predictions varied among cases (time of observation) and measurement points (wells). Also in this study the single flow algorithm was used to delineate the flow paths.
3.2 Dynamic wetness index
In the calculation of the basic wetness indices it is assumed that there are uniform hydraulic properties across the catchment, similar surface and subsurface flow directions and steady
state flow conditions; i.e. every point in a catchment is experiencing drainage from its entire upslope contributing area. This is, however, hardly ever the case because of the small velocities of the subsurface flow. Thus most points in the catchment receive only contributions from a small proportion of their total upslope contributing area. The basic assumption of the specific upslope contributing area as an appropriate surrogate for the subsurface flow rate is thus violated. (Barling et al. 1994) Also the assumption about the uniform hydraulic properties across the catchment seems quite unrealistic.
The static wetness indices don’t take into account the local differences in topography. This is illustrated in Figure 3, which describes four different hillslope profiles that have similar wetness index values but will clearly respond differently to the same precipitation input.
Another defect in the static wetness index is that the largest specific catchment area naturally occur along the main drainage pathways of a whole catchment. As the slope angle for those points tend to be small, the wetness index values are further increasing. (Barling et al., 1994)
A A A A
Figure 3. Four different hillslope profiles that have similar wetness index values in point A
Because of these limitations Barling et al. (1994) introduced a concept for calculating the dynamic wetness index which allows varying hydraulic properties over the catchment and takes into account the velocity of the subsurface flow in the calculation of the effective catchment area. The dynamic wetness index thus relaxes the assumption of the steady state flow.
The assumptions behind the index are that the saturated throughflow is parallel to an impermeable layer, the soil is near field capacity and a uniform rainfall occurs over the specified drainage period. From these assumptions the last one is clearly violated in reality.
However, the results indicate that even though the non-uniform rainfall violates the theoretical basis of the dynamic wetness index, it still provides a useful method for determining the spatial distribution of soil water. (Barling et al. 1994)
4. DEM-based attributes: demonstrations and tests 4.1. Study area
The study area, which is used in demonstrations is located in northern Finland nearby Kajaani (64.05 N, 27,41 E). The altitude in the site varies from 180 m to 275 m, meaning that the whole site has been above the highest sea level during the Glacier melting phase. Because of that, the soils in the area are mainly fine-textured tills and are not pre-washed by the sea phases of the Baltic Sea. However, the lowest parts of the site belong to the run off area of Sotkamo-Pielinen glacial lake and are thus gravelly sandy tills (Kemiläinen, 1988). The glacier flow direction in Finland has usually affected on the thickness of the soil cover in hills in such a way that the soil cover is thin in the north-west sides of the hills and much thicker in the south-east sides (Kemiläinen, 1988). Thus in this area soil cover is quite thin and also some bare rock areas are seen (Atlas of Finland,1987).
Based on the geological map (Havola, 1987), the bedrock in the area is characterised by the resistant rock quartzite, which hasn’t eroded as much as the rocks in the surrounding areas. In addition, some nutritious rocks are found in the area. This has affected on the vegetation, which is quite rich (Kukko-oja et al 1988). The study area is illustrated in the Figure 4.
The small 1-ha study site was used to test the relationship between wetness index and volumetric soil moisture content. The location of the site is given in Figure 4 with a red rectangle. The terrain profile was S-shaped with ~3 % slope in the lowest part of the site in a small stream valley, ~23 % slope in the middle part and ~9 % slope in the upper part. The calculated upslope contributing area varied from ~600 m2 in the upper part to ~48000 m2 in the stream valley.
Figure 4. General view over the study area. Peat-covered areas are described with green, fields with yellow, waterways with blue and the location of the small study site with red colour
4.2 Material and methods
Two raster DEMs over the area were constructed with Arc/Info topogridtool based on the contour datasets of NLS and mapping centre of Kajaani. The resolution of the first model (NLS dataset) was 10 m. Another contour dataset was a bit more precise and allowed a construction of the DEM with the resolution of 5 m. Primary and secondary terrain attributes were calculated with the program TAPES-G. Multiple drainage direction method with the slope weighting algorithm was used in the catchment area computations. A depressionless DEM was not created, because that would have removed all sinks from DEM and thus also some real small depressions. Slope was calculated with the finite difference algorithm. Files of streamlines or artificial flowlines were not used as an input data in the DEM creation, because one of the ideas was to test how the flow routes calculated from DEM correspond to the actual streamlines.
The soil moisture content in a small 1-ha site was measured with TDR (Tektronix) three times during the summer (19-20.6., 4.-5.7., 10.7.2001). The measuring points located regularly over the site and the distance between the points was 10 m. The points were placed in position with compass and measuring tape and the corner point was located by measuring from the known point. The measuring depth of the soil moisture content was 20 cm from the surface of
Dataset National Land Survey of Finland N
the mineral soil. The thickness of the organic layer was usually under 5 cm but in the south- west corner under a very dense Picea abies canopy the organic layer was about 10 cm. The vegetation in the site is roughly described in the Figure 5. Four soil samples were taken to determine the mean grain size and the texture of the soil. Samples were taken from the C- horizon (65-95 cm). Samples were air-dried and analysed by screening and by the COULTER laserdiffractiometer.
Figure 5. Vegetation in the small study site
4.3 Demonstrations
The values of the simplest terrain parameters, slope and aspect, are visualised in the Figures 6 and 7. Slope is given in % and a 45-degree slope is 100 %. The slope angle can be calculated as arctan (slope/100). Aspect is the direction of steepest downwards slope measured degrees clockwise from North. Slope is very useful in trafficability assessment and in routing. Aspect can give some additional information about the radiation conditions and wetness of the site.
S1 S2 S3 S4 S5 S6 S7 S8 S9
Picea abies, ~8 years, ~1,5 m
Picea abies, ~20 years, ~7 m
Picea abies, ~35 years, ~10 m
Soil sample N
Slope, %
0 10 20 30 40 50 60
0-5 % 5-10 % 10-15
%
15-20
%
20-25
%
25-30
%
30- %
% of area
Figure 6. Raster map of slope together with contours (top) and distribution of the slope values over the area (left)
Dataset National Land Survey of Finland
Aspect, in degrees
0 2 4 6 8 10 12 14 16 18 20
0-40 320-360 40-80 180-320 80-120 240-280 120-160 160-200 200-240
% of area
Dataset National Land Survey of Finland
Figure 7. Raster map of aspect together with contours (top) and distribution of the aspect values over the area (left)
In addition to the wetness index calculation, the upslope contributing area of a raster cell can be used when determining the stream network. An example of this is given in the Figure 8 in which the DEM-based calculated flow network is illustrated together with the flow network from the topographic map database. The correspondence between these two networks is quite good. In this area, based on the visual observations in the field, the calculated flow network gives even some additional information about water flowpaths and this might help to delineate the sensitive sites more precisely.
Although the map dataset should include only the streamlines and artificial drains it included also some terrain type boundaries, which clearly had been saved to the dataset with the wrong terrain code number. These kind of errors weaken the usability of the dataset as an input in the creation of the hydrologically correct DEM.
The values of the static topographic wetness index are illustrated in the Figure 9. In addition to wetness index values, also the peat-covered areas, roads and water flowpaths are described.
The figure gives quite clear view about the water movement and about the areas where flow conditions are such that the soil may be temporarily water-logged during rainy periods. When visually comparing the high wetness index values to the boundaries of the peat-covered areas the correspondence is also very good. The small study site where the soil moisture
Figure 8. The raster map of upslope contributing area (brown colour) and the Flow network from the map dataset (blue lines)
Dataset National Land Survey of Finland
measurements were made is located in the south-west part of the area and is described with the black rectangle.
Figure 9. Raster map of the static topographic wetness index values together with contours, roads, streams and peat-covered areas
4.4. Test of wetness index as soil moisture indicator
A linear relationship between wetness index and soil water table depth has been found in many studies (e.g. Troch et al., 1993, Thompson and Moore, 1996) though also critics have been posed against such a simple assumption. Linear relationship may be valid in very humid conditions where regular rains maintain the steady state water flow conditions and thus guarantee that the basic assumption behind the wetness index is valid.
In till soil profile the groundwater level largely follows the topography of the terrain.
However, at upslope locations the hydraulic conductivity of the soil is usually higher throughout the soil profile than in the wet soil types at the slope foot. This means that the soil profile dries quickly to the field capacity level i.e. freely moving water has drained from the
Dataset Kajaanin kaupunki
soil pores. There is also a rapid drainage of water supplying downslope soil types. Thus the groundwater level in the upslope locations may be in few meters depth while in the downslope locations, the groundwater level is often found in the uppermost soil layers. (Lind and Lundin, 1990) Thus after the freely moving water has drained, the topsoil in upslope locations only get contribution from rain and not from the upper contributing area (As). Based on that, it is quite clear that the relationship between topsoil water content and wetness index is not linear.
The measured soil moisture content and calculated wetness index values are described in Figure 10 with series 1 and 2 being closest to stream and series 8 and 9 in the uppermost parts of the site. The location of the series is illustrated in Figure 12.
Figure 10. The measured soil moisture content and the calculated topographic wetness index
The soil moisture content in the driest parts of the terrain varies from 7 to 10 %, which means that the soil is way under its field capacity. In the wettest part of the site, the soil moisture content varies from 9 to 22 %. This variation is probably caused by the microtopographical positions of the measuring points. This topographical variation is described in Figure 11, in which are the results of the topographical survey of the points in the series 1 and 2. Under the chart are the measured soil moisture values.
0.00 0.05 0.10 0.15 0.20 0.25
3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5
SWI
MC vol %
Series1 Series2 Series3 Series4 Series5 Series6 Series7 Series8 Series9
The spatial correspondence between the topsoil moisture content and the topographic wetness index can visually be observed from the Figure 12. In this site the correspondence is quite good. For example, wetness index values are high in the eastern part of the site and a similar moisture pattern is seen in the measured values. Moist conditions were also noticed in the soil survey, in which clear gleyic properties (colour and rust marks) were seen in the easternmost soil sample point in the depth of 60 cm. This indicates that the groundwater level is high in that part of the site throughout the year. Based on the Figure 12, also in the middle of the site is seen a similar spatial correspondence between the soil moisture content and the index values.
There was a very dry period after the first measurement and this was seen in the soil moisture content values of the two other measurements. However, the spatial distribution of the soil moisture content values was similar in all three measurements.
5. Conclusions
Digital elevation model is one of the most important GIS dataset in trafficability assessment.
It provides easy quantification of the terrain attributes and it is a base for hydrological models.
In hydrological modelling most of the applications are grid-based though contour-based models might provide a better approach to assess water flowpaths. In grid-based DEM, the grid resolution is in central role and in most terrain profiles a 10-meter resolution is usually good enough to describe the variation in topography.
S2 Figure 11. Local topography in
the lowest part of the site (top) and the corresponding soil moisture values (left)
14 16 11 12 9 12 9 14 9 14 10 10 11 S2 (series 2) 13 18 15 20 19 22 22 20 21 17 15 10 13 S1 (series 1)
0 2 4 6 8
altitude, m
Local topography
6-8 4-6 2-4 0-2
S1
Calculation of the wetness index may provide some additional information about the site wetness pattern. However, because of the strict assumptions behind the calculation, it should be used with a great care.
Dataset Kajaanin kaupunki
Figure 12. Spatial distribution of the soil moisture content values and the corresponding wetness index values in the site
S1 S2 S3 S4 S5 S6 S7 S8 S9
Soil moisture content 19.6.-20.6.2001
N
References
Atlas of Finland,1987. Relief and landforms. Folio 121-122. Appendix. National board of survey, Geographical society of Finland. 10 p.
Barling, R.D., Moore, I.D. and Grayson, R.B. 1994. A quasi-dynamic wetness index for characterizing the spatial distribution of zones of surface saturation and soil water content.
Water resources research. Vol. 30 (4) p. 1029-1044.
Desmet, P.J.J. and Govers, G. 1996. Comparison of routing algorithms for digital elevation models and their implications for predicting ephemeral gullies. Int. geographical information systems. Vol.10. No. 3. p. 311-331.
Gallant, J. 2000. Terrain analysis. Lecture notes.
http://incres.anu.edu.au/hydweb/johng/Terrlect.html. Received: 20.12.2000.
Gallant, J.C. and Wilson, J.P. 1996. TAPES-G: a grid-based terrain analysis program for the environmental sciences. Computers and geosciences. Vol. 22. No.7. p. 713-722.
Havola, M. 1997. Suomen geologinen kartta, kallioperäkartta. Lehti 3431, Kajaani. Scale 1:
100 000. ISSN 0786-2814. Map, GTK.
Hutchinson, M.F. 1989. A new procedure for gridding elevation and stream line data with automatic removal of spurious pits. Journal of hydrology. Vol. 106. No. 3-4. p. 211-232.
Kemiläinen, H. 1988. Kajaanin kaupungin luonnonsuojelualueiden ja –kohteiden kartoitus.
Osa 1. Geomorfologinen inventointi. Ympäristönsuojelulautakunta, erillistutkimukset.
Kajaani 1988. p. 1-30.
Kukko-oja, K., Heikkilä, H. and Vainio, M. 1988. Kajaanin kaupungin
luonnonsuojelualueiden ja –kohteiden kartoitus. Osa 2. Kasvipeiteinventointi.
Ympäristönsuojelulautakunta, erillistutkimukset. Kajaani 1988. p. 32-96
Lind, B.B. and Lundin, L. 1990. Saturated hydraulic conductivity of scandinavian tills.
Nordic hydrology, 21. p. 107-118.
Moore, I.D., O’Loughlin, E.M. and Burch, G.J. 1988. A contour-based topographic model for hydrological and ecological applications. Earth surface processes and landforms. Vol. 13 (4).
p. 305-320.
Moore, I.D., Grayson, R.B. and Ladson, A.R. 1991. Digital terrain modelling: a review of hydrological, geomorphological and biological applications. Hydrological processes. Vol.5. p.
3-30.
Moore, I.D. 1996. Hydrologic modelling and GIS. In: GIS and environmental modeling:
progress and research issues. GIS world books 1996.
Rodhe, A. Seibert, J. 1999. Wetland occurrence in relation to topography: a test of
topographic indices as moisture indicators. Agricultural and forest meteorology. v. 98-99. p.
325-340.
Thompson, J.C. and Moore, R.D. 1996. Relations between topography and water table depth in shallow forest soil. Hydrological processes. v.10. p. 1513-1525.
Tokola, T., Soimasuo, J., Turkia, A., Talkkari, A., Store, R. and Uuttera, J. 2000. Metsät paikkatietojärjestelmissä. Silva Carelica 33. Joensuun yliopisto, metsätieteellinen tiedekunta.
111 p.
Troch, P.A., Mancini, M., Paniconi, C. and Wood, E.F. 1993. Evaluation of a distributed catchment scale water balance model. Water resources research. Vol 29. No. 6. p. 1805-1817.
Zhang, W. and Montgomery, D.R. 1994. Digital elevation model grid size, landscape representation and hydrologic simulations. Water resources research. Vol. 30. No.4. p. 1019- 1028.
