Fig. 1
D.-I. Müller-Wohlfeil, W. Lahmer, V. Krysanova, A. Becker
The paper is focused on the applicability assessment of two models for large scale hydrological simulation, both of which are based on the topographic index concept. With the first one, TOPMODEL, scaling studies were performed in a number of catchments of different size. Subsequently, an integrated approach coupling the other simplified hydrological model WET with a GIS was applied to the Elbe drainage basin to delineate those areas that are vulnerable as regards water availability. The potential use of TOPMODEL for large scale applications was investigated by studying the effects of different spatial resolutions, area size and topographic conditions on the simulation results. It was shown that runoff estimations are scale-dependent. However, differences in discharge can be compensated by changing the mean transmissivities. Based on these results from the scaling studies with TOPMODEL, application of WET was justified for larger scales. After some modifications with respect to distributed soil and climate data, WET was applied for the Elbe basin. The analysis of water availability was performed in three steps: 1) calculation of the long-term average monthly soil moisture index and evapotranspiration, 2) delineation of subwatersheds in the Elbe basin, 3) identification of critical subbasins from the distribution of the soil moisture index in summer months. The method allows delineation of critical subareas within the study region and can be used for preassessment in large scale hydrological and water quality studies.
Human induced global climate and land use changes directly affect water and biogeochemical cycles, vegetation structure and plant productivity. However, spatial and temporal patterns of changes may differ in different regions, like the patterns of temperature and precipitation derived from simulation runs performed with general circulation models (GCMs). New methods must be developed to predict regional and local changes in terrestrial ecosystems, as the control measures may be regionally specific. On the other hand, it is necessary to provide inputs and feedback mechanisms to global models of climate and biogeochemistry.
Topography-based models like TOPMODEL (Beven and Kirkby, 1979), TOPOG (O'Loughlin, 1981) and WET (Moore et al., 1993) provide a simple way to introduce lateral flow components into regional or global ecosystem models. TOPMODEL and WET are based on the assumption that local soil moisture dynamics strongly depends on the size of the upslope area (a) drained through an observed catchment point, the local surface topographic slope (tan ß) representing the hydraulic gradient for saturated water flow, and the downslope soil transmissivity (T).
In the first part of this study the suitability and shortcomings of TOPMODEL in large scale hydrological studies are investigated. The model was applied to various smaller catchments and to the German part of the Elbe drainage basin (96,000 km²) as a whole. In the second part of our investigation an integrated approach coupling the simplified hydrological model WET (based on a concept similar to that of TOPMODEL) with a GIS was applied to the Elbe drainage basin to delineate vulnerable subareas.
The Elbe drainage basin is one of the largest river basins in Western Europe. The elevation varies from sea level in the Pleistocene slightly hilly lowlands up to 1161 m in the mountainous areas in Saxony. A significant proportion of sandy soils with high infiltration, low amounts of precipitation, and a high water demand (both climatic and anthropogenic) characterize the high hydrological vulnerability (Becker et al., 1995).
Two smaller basins (Stör in the Elbe basin and Vils in southern Germany) and their subcatchments were chosen for scaling studies. The upper Stör subbasin (1153 km²) is dominated by older glacial and glacifluvial sediments. Dominant soil texture classes are sands with different percentages of loam. More detailed simulations were performed for the Buckener Au subcatchment (58 km²), which is dominated by cropland and forest areas. The maximum elevation is about 93 m a.s.l..
The Vils catchment (756 km²) is part of a dry hilly upland region with elevations between 356 and 613 m a.s.l. Soil texture is sandy to loamy and the vegetation cover is dominated by pine forest and agriculture plants. The Frankenohe subcatchment (45.1 km²), studied separately, is located in the northern part of the Vils catchment.
The simulations in the Stör and Vils basins were based on DEM data sets with a spatial resolution of 1 arcsecond (equivalent to a grid size of about 33 m x 33 m and 29 m x 29 m, respectively) provided by the "Amt für Militärisches Geowesen" (Federal Armed Forces Geographic Office, Euskirchen, Germany FAFGO). For the simulation runs in the Elbe basin a 30 x 50 arcseconds (~ 1000 m x 1000 m) DEM of the "Institut für Angewandte Geodäsie" (IFAG, Frankfurt, Germany) was used.
Main goals of the study were
In addition, we intended to check whether simplified models (including only some key factors of system behaviour) can be effective tools for the analysis and preassessment of the hydrological cycle in watersheds.
In order to investigate potential limitations in regional applications, simulations based on high resolution DEMs (1 arcsecond) were commenced, which were subsequently aggregated to low resolution DEMs (up to 1 km mesh size). Following Beven (1995), the effects of subgrid heterogeneity are expected to be more important with increasing scale and mesh size. Other physiogeographical factors like geology, vegetation, and land use are not considered. The only additional spatially distributed information are soil data in the case of the WET model applications.
Critical areas for water availability can be defined in a number of ways. In general, the dynamics of soil moisture patterns reflect the overall water balance and can be considered the most important variable defining water availability for vegetation. In order to define critical areas we estimated the long-term average monthly soil moisture dynamics as a component of the water balance, based on long-term average climatic data, topography, and soil. After averaging the soil moisture distribution for subareas of interest (larger grid cells, subbasins or administrative subunits), vulnerable subregions can be delineated.
TOPMODEL (Beven and Kirkby, 1979) is best suited for small to medium catchments (500 km²) with shallow soils and moderate topography which do not suffer from excessively long dry periods. Input data are DEMs and time series data for precipitation and potential evapotranspiration. Data for measured discharges can be used for validation. Output data include simulated discharges, actual evapotranspiration, and information on the build-up of soil moisture and averaged soil moisture deficit.
The ln(a/tanß) values were calculated from digital elevation data for every single grid cell of the catchment using a modified version of the GRIDATB programme (kindly provided by Dr. Quinn/ADAS, Wolverhampton).The algorithms of GRIDATB allow multidirectional flow in 8 directions. In order to suppress the generation of very large ln(a/tanß) values, the upslope drainage area for each cell can be limited by a threshold (Channel Initiation Threshold CIT) which supports the creation of a virtual river net (Quinn et al., 1995b).
In order to ensure potential flow from each grid cell to its neighbours, the raw elevation data had to be cleaned (i.e. sinks and plateaus had to be removed) before creation of the ln(a/tanß) distributions. A modified version of the program SINKS (also provided by Dr. Quinn) was used for this purpose.
Climatic input were daily data of precipitation and potential evapotranspiration, calculated by the algorithm of Priestley and Taylor (1972) and by a method using only daily values of air temperature and potential sun shine hours (Leavesley et al., 1983) respectively.
The WET model developed at the Australian National University (Moore et al., 1993) is based on a topographic index very similar to that of TOPMODEL. It allows the estimation of the spatial distribution of the long-term average soil moisture and evaporation using an equilibrium approach. Originally the WET model was applied to a small forested catchment (27 km ²) in Australia to estimate spatial patterns of average annual soil moisture and evapotranspiration. The simulations were based on a 30 x 30 m DEM, using a single precipitation value (average annual) for the whole catchment, and without accounting for variation in transmissivity. The annual and monthly time steps are suggested by the authors for WET application (Moore et al., 1993).
The potential evapotranspiration is estimated from the Priestley & Taylor equation for well-watered vegetation under conditions of minimal advection. The equations for the wetness index, potential and actual evapotranspiration are solved iteratively using the Newton-Raphson method, beginning with the element of highest elevation and finishing with the element of lowest elevation at the catchment outlet. WET uses some outputs of the TAPESG (accumulation areas) and SRAD (net radiation) submodels included in the TAPES-G package (Moore et al., 1993). The specific catchment area is estimated by a quasi-random "Rho8"-algorithm that permits drainage from a node to multiple nearest neighbors on a slope-weighted basis. The Geographical Information System GRASS (U.S.Army, 1987) was additionally used for spatial analysis of map layers.
The delineation of vulnerable areas was performed for the Elbe drainage basin in three steps:
Scaling studies to identify potential sources and the magnitude of errors in low resolution topography-based applications have mainly been performed with TOPMODEL. In most of these studies the grid size varied between 2 m and 480 m (Franchini et al., 1996; Bruneau et al., 1995; Quinn et al., 1995a; Wolock and McCabe, 1995; Wolock and Price, 1994; Zhang and Montgomery, 1994; Charait and Delleur, 1993).
Other studies have used components of the TOPMODEL concept with high resolution Digital Elevation Models (DEM) for multiscale or macroscale modelling of hydrological processes and soil-vegetation-atmosphere interaction (e.g. Famiglietti and Wood, 1994; Quinn et al., 1995b).
The main reasons why approaches based on the topographic index (particularly TOPMODEL and WET) have rarely been applied to large areas are that:
Since regional modelling approaches have to cope with that data which is available it was decided to apply TOPMODEL at the regional scale with low spatial and temporal resolution. Currently, the spatial resolution of DEM data available world-wide is not better than 1 km (Arnell, 1993) and the temporal resolution of climate data measured operationally is rarely better than 1 day. On the other hand, even for low resolution data, the average location of the upper groundwater table may be well correlated to topography. Smaller scale topography-induced dynamics may have effects on the overall catchment behaviour even in flatter areas and topographic influences cannot be neglected in regional studies. Phenomena like subsurface stormflow and saturation excess overland flow need not be locally limited but may exceed areas larger than the grid size of, e.g., 1 km² (Blöschl and Sivapalan, 1995). Their effects should be maintained within the model at this scale.
The influence of spatial resolution and catchment size on the ln(a/tanß) distributions and the simulation results were analysed in detail for the Stör and Vils catchments. The simulation runs performed for the Elbe basin were focused on studies of the topographic index in order to extend this analysis to a whole landscape. However, no calibration was possible due to missing measured discharge time series data.
In order to study spatial resolution effects, small time period simulations were performed at different resolutions for the Buckener Au subcatchment (32 to 250 m), the Upper Stör catchment (250 to 1000 m) and the Vils catchment (50 to 1000 m). DEM aggregation was performed by the GRID resampling procedure of the Geographic Information System ARC/INFO (ESRI,1991) using the nearest neighbour relationship.
The ln(a/tanß) distribution functions are influenced by the spatial resolution as follows:
- Since the number of samples contributing to the ln(a/tanß) distributions decreases with decreasing resolution, distributions of high resolution DEMs are smoother than those of low DEMs for the same area.
- Minimum, mean, and maximum of the ln(a/tanß) distributions increase with decreasing spatial resolution, due to increasing grid cell area and decreasing slope related to smoothing effects (smaller tanß values).
Table 1 summarizes the statistics of the ln(a/tanß) distributions obtained for all catchments and spatial resolutions.
| ln(a/tanb) | |||||
|---|---|---|---|---|---|
| catchment | area [km²] | spatial resolution [m] | CIT [km²] | range | mean |
| Buckener Au | 58 | 33 | 0.1 | 3.26 -14.75 | 8.94 |
| 110 | 2 | 5.80 - 17.74 | 10.41 | ||
| 250 | 4 | 7.05 - 18.29 | 11.22 | ||
| Stör | 1780 | 250 | 4 | 6.91 - 18.46 | 12.56 |
| 500 | 8 | 8.550 - 19.20 | 13.08 | ||
| 1000 | 30 | 9.53 - 20.68 | 13.77 | ||
| Frankenohe | 45 | 29 | 0.03 | 4.16 - 13.57 | 8.01 |
| 110 | 1 | 7.35 - 13.76 | 9.97 | ||
| 250 | 2 | 7.35 - 14.64 | 10.16 | ||
| Vils | 756 | 50 | 1 | 3.40 - 16.60 | 9.23 |
| 100 | 2 | 4.40 - 18.00 | 9.78 | ||
| 250 | 4 | 6.40 - 18.80 | 10.78 | ||
| 500 | 8 | 7.40 - 19.80 | 11.85 | ||
| 1000 | 30 | 8.40 - 20.80 | 12.67 | ||
For the same spatial resolution (250 m) and the same CIT value (4 km²), the ln(a/tanß) distributions obtained for the four subcatchments studied in detail do not show a general trend, though one could presume a larger range of potential ln(a/tanß) combinations for larger catchments (more complex landscapes).
The effects of topography and area size on the ln(a/tanß) distributions are most evident for the rather different subcatchments of the Elbe basin. For the German part of the Elbe basin 57 subcatchments were derived using the r.watershed function of GRASS (mean area 1762 km²). In general, the mean ln(a/tanß) values are lower in mountainous and small subcatchments (smaller a and higher tanß values) than in flat and large catchments. The mean ln(a/tanß) values varied between 11.73 in the southern mountainous regions and 14.94 in extremely flat areas (i.e. the Elbe outlet).
Spatial resolution and area size cause changes in the predicted runoff. The simulation results confirm conclusions drawn by Wolock and Price (1994) according to which the ratio of overland flow to total flow increases with decreasing spatial resolution. Simultaneously, the efficiency (defined as ratio of the variance of the residuals to the variance of the observed discharges according to Nash and Sutcliffe, 1979) is reduced by up to about 41% (see Table 2).
| a) identical parameter sets | b) calibrated parameter sets | |||||||
|---|---|---|---|---|---|---|---|---|
| catchment | resolution [m] | mean ln(a/tanb) | ln(T0) | eff-diff [%] | diff Qb/Qtot [%] | ln(T0) | eff-diff [%] | diff Qb/Qtot [%] |
| Buckener Au | 33 | 8.94 | 1.72 | -20.1 | +21.4 | 0.25 | -0.1 | +0.7 |
| 110 | 10.41 | 1.72 | 0 | 0 | 1.72 | 0 | 0 | |
| 250 | 11.22 | 1.72 | -5.9 | -13.4 | 2.53 | +0.5 | -0.3 | |
| Stör | 250 | 12.56 | 4.36 | -1.3 | +1.1 | 3.84 | -7.2 | -5.7 |
| 500 | 13.08 | 4.36 | 0 | 0 | 4.36 | 0 | 0 | |
| 1000 | 13.77 | 4.36 | -15.1 | -10.2 | 5.05 | -0.1 | +3.0 | |
| Frankenohe | 29 | 8.01 | 0.32 | -22.4 | +31.6 | -1.64 | +0.2 | +0.4 |
| 110 | 9.97 | 0.32 | 0 | 0 | 0.32 | 0 | 0 | |
| 250 | 10.16 | 0.32 | -5.6 | -4.4 | 0.51 | -3.1 | -0.6 | |
| Vils | 50 | 9.23 | 0.20 | -15.6 | +26.7 | -1.35 | -0.4 | -2.0 |
| 100 | 9.78 | 0.20 | -8.5 | +18.6 | -0.80 | +0.6 | -0.2 | |
| 250 | 10.78 | 0.20 | 0 | 0 | 0.20 | 0 | 0 | |
| 500 | 11.85 | 0.20 | -10.8 | -23.9 | 1.27 | -1.4 | -2.7 | |
| 1000 | 12.67 | 0.20 | -34.7 | -40.8 | 2.09 | -1.8 | -4.5 | |
By shifting ln(T0) (lateral transmissivity when the soil is just saturated) according to the mean ln(a/tanß) values, one gets almost identical efficiencies and flow ratios. One main reason for the importance of TO in recalibration can be directly derived from basic equations used in TOPMODEL for the calculation of base flow. The results presented here indicate that discharge differences can largely be compensated by changing the mean transmissivity T0. After this compensation other discharge simulation results are almost independent of scale, supporting the results of Franchini et al., 1996; Wolock and McCabe 1995; Bruneau et al., 1995 and Quinn et al., 1995a).
Maps representing single pixel saturation counts show artificial chessboard-shaped patterns in large parts of the Stör and some parts of the Vils catchment (see Fig. 1).
Fig. 1
All these areas characterized by flat orography are exposed to significant manipulation by the SINKS program. The patterns are due to assigning a gradient to flat area cells and are an indication for general problems in applying TOPMODEL, even though discharge curves are well reproduced.
Apart from this problem which is specific for flat regions, the simulation results can be summarized as follows:
Catchment averaged values for counts of full saturation are almost identical for all spatial resolutions. Differences can be explained by spatial aggregation and corresponding smoothing effects on the relief in the DEM and by changes in relief caused by the SINK program.
The highest saturation frequencies are independent of resolution as well. Saturation in converging zones increases if no CIT is specified.
In the case of the saturation patterns obtained for the Vils catchment with and without a CIT, linkages between some adjacent saturated pixels get lost when a CIT is specified. This fits the observation that increased CIT cause higher mean ln(a/tanß) values, which in turn enhance overland flow. Still, the maximum number of saturation counts stays the same if other parameter values are kept constant.
The saturation patterns obtained for the Buckener Au are comparable to soil patterns. Highest values for saturation counts occur where peaty soils are dominant, supporting observations of Merot et al. (1995).
The saturation maps of both the Frankenohe and the Vils catchment show that in steeper parts saturation is often limited to single grid cells. Due to missing spatially distributed data about topography-dependent soil moisture patterns for these catchments, the investigations here were simply focused on the question of, how moisture patterns based on high resolution DEMs differ from those obtained with low resolution DEMs. In case of large-scale TOPMODEL applications, heterogeneity observed for high resolution simulations cannot be represented in detail. However, for the Buckener Au at 110 m and 250 m resolution, the effects of small scale heterogeneity are better maintained since the subcatchment is orographically smoother.
While TOPMODEL was mainly used to investigate scaling issues, WET was applied to a large drainage basin as a whole. There are two main reasons for this strategy to use different modelling approaches for the different scales. Firstly, WET is more suitable for low temporal resolution (annual or monthly time steps). On the other hand, the correlation between temporal and spatial resolutions and scales is well known (Blöschl and Sivapalan, 1995). Further, it was possible to modify WET for use with spatially distributed data of both climate and soil, whereas the distribution version of TOPMODEL does not account for differences in any hydrological important feature except topography.
While TOPMODEL includes dynamics of different subsurface storages, an apriori assumption has been made for WET about vertical drainage from the unsaturated zone to deep ground water (through the deep drainage term D). This means, that WET is more intended to represent the overall influence of topography on the longer-term hydrological behaviour of catchments and different compartments of lateral flow. In addition, the scaling study with TOPMODEL demonstrated that patterns in soil moisture distribution can be maintained for coarser resolution through a simple modification of parameter values. By this, the application of WET to 1 km resolution data was justified. Still, modifications were needed to include the distributed climate and soil parameters.
First of all, the topographic index was calculated in GRASS (Fig. 2).
Fig. 2
The distribution function of the topographic index is comparable to those of other watershed studies (Quinn et al., 1995; Zheng et al., 1995) and the river network is well reproduced.
For such a large drainage basin it was necessary to account for spatially distributed precipitation and soil properties. On the basis of long-term monthly mean values of temperature and precipitation available for 48 meteorological stations in the region (years 1950-1980), spatially distributed monthly means of precipitation and temperature were calculated for every 1 x 1 km grid cell by the spline interpolation method (Hutchinson et al., 1993). Available soil water capacity was derived from soil maps. The program code was modified to include the distributed climate and soil parameters.
One crucial problem in the WET application was related to the actual evapotranspiration accounting for summer months, when potential evapotranspiration is quite high. The problem is directly related to the simplicity of the model, which does not take into account vegetation distribution, root depth, or root density. Including such additional information would improve the evapotranspiration component. On the other hand, the model should be kept as simple as possible for larger-scale applications. As a compromise, we used the soil moisture distribution of a previous month to get more reasonable results, restricting the actual evapotranspiration by precipitation plus change in soil moisture (following the water balance accounting procedure by Thornthwaite and Mather, 1957). By this, a quasi-dynamic element was introduced into the static equilibrium approach, which is reasonable for monthly time steps.
The results for the evapotranspiration and soil wetness index are quite reasonable. In April the mean monthly evapotranspiration is low and almost homogeneous for the whole region. In summer it is higher in the south, where precipitation and water-holding capacity of soils are higher. The distribution of the mean monthly soil wetness index differs essentially for winter and summer months, while the patterns for subsequent summer months are similar. A significant part of the territory is saturated (wetness index = 1) in winter, while certain areas are under water stress in summer (Fig. 3)
Fig. 3
Since WET does not calculate discharge time series, model validation must be performed on the basis of spatial patterns of subsurface moisture (i.e. soil moisture or ground water). However, neither field observations nor remote sensing methods provide data for the validation of results on soil moisture or evapotranspiration in the study region. Therefore, indirect methods had to be used. The results were compared to existing ground water maps (WASY GmbH, scale 1: 50000, see fig 4. ) and some results of the independent terrestrial modelling performed in Germany (Wendland et al., 1993).
Fig. 4
The map of mean ground water depths for eastern Germany and the soil moisture index map generated by WET show similar patterns. Areas of high saturation occur mainly along riparian areas or zones of topographic convergence. On the other hand, dry areas defined by deep ground water tables and low wetness indices appear mainly in loess areas in the southern part of the basin. Comparison to the map of mean annual percolation rates (Wendland et al.,1993) was quite satisfactory as well. This indicates that a topography-based hydrologic approach focused on long-term dynamics is appropriate for time-averaged estimations of subsurface moisture patterns in a large region.
The distribution of the soil wetness index distribution in summer months (from May to August) was used to estimate soil moisture deficit in percent missing from the 50% of field capacity on average in summer months (Fig. 5).
Fig. 5
Averaging the soil moisture deficit values for subbasins (areal average), we identified several classes of vulnerability, and, consequently, the vulnerable subbasins (classes 4 and 5, Fig. 6 ).
Fig. 6
The TOPMODEL results show how differences in topography potentially cause differences in hydrologic patterns and soil moisture dynamics. They further show that the model may be applied to some lowland regions, if high resolution DEMs are available and the limits of application are carefully studied.
It was shown that runoff estimations are scale dependent and differences in discharge (mainly due to differences of mean ln(a/tanß) values) can to a large extent be compensated by changes in mean values of transmissivities T0, even for the 1000 m grid scale. After this compensation, spatially aggregated saturation patterns are more or less independent of scale for the chosen conditions.
Nevertheless, large scale DEM smoothing effects on topography may very much mislead the topography-dependent estimation of dynamic soil moisture patterns, especially if differences in vegetation and soil physical properties are not considered. It may be particularly important to account for intrapatch heterogeneity according to Avissar (1991) and Bruneau et al. (1995). In order to account for heterogeneity the high resolution ln(a/tanß) distribution functions should at least implicitly be included via assumptions based on the known relationship between these distributions for low and high resolution DEMs .
The approach described here allows critical subareas in relatively large drainage basins to be delineated. It can be used for preassessments in large-scale hydrological studies. Based on the knowledge on vulnerable areas, dynamic process-based models can then be applied to better understand the hydrological and biogeochemical processes and to reveal the feedback mechanisms of complex climate - biosphere interactions.
Our study demonstrates that even simplified models which include only the key factors determining system behaviour can be effective tools for the analysis and preassessment of the hydrological cycle in a watershed. A further improvement of equilibrium water balance modelling with monthly time steps would be possible for regions where distributed data on land cover and soil properties are available.
Thanks particularly to Paul Quinn (ADAS, Wolverhampton) and Keith Beven (Lancaster University, GB) who kindly provided the TOPMODEL, SINKS and GRIDATB codes and were always open for fruitful and constructive discussions. The TAPES-G package was obtained from the Centre for Resource and Environmental Studies, The Australian National University. We are grateful to Dr. J. Gallant for useful discussions.
The paper would not have been possible without the distributed climate data provided by Wolfgang Cramer (PIK), who also contributed through lots of useful comments.
The authors would like to thank Prof. Ripl (Free University of Berlin) and the Projektzentrum Ökosystemforschung, the "Landesamt für Wasser und Küste", the Univ. of the Armed Forces, Munich, and the German Weather Service (DWD) for providing data.
We are grateful to the Deutsche Forschungsgemeinschaft (DFG) and the Federal Ministry for Education, Science, Research and Technology (BMBF), which made the present work possible by providing financial support to the authors.
Arnell N. W. (1993). Data requirements for macroscale modelling of the hydrosphere. In: Wilkinson W.B. Macroscale modelling of the hydrosphere. Proceedings of an international Symposium, Yokohama, Japan 21 July 1993. IAHS Publications 214, 139-150.
Avissar, R. (1991). A statistical-dynamical aroach to parameterize subgrid-scale land surface heterogeneity in climate models. Surv. Geophys. 12, 155-178.
Becker, A., Krysanova V, Lahmer W. and Müller-Wohlfeil D.-I. (1993). Modelling of Hydrological and Hydrochemical Variablity under Environmental Change Impact. Acta Geologica Hispanica, No.2-3, 37-43.
Beven K. (1995). Linking parameters across scales: subgrid parameterizations and scale dependent hydrological models. Hydrol. Process., 9, 507-525.
Beven K.J. and Kirkby M.J. (1979). A physically based variable contributing area model of basin hydrology. Hydrol. Sci. Bull., 24, 43-69.
Beven K.J. and Quinn P.F. (1994). Similarity and scale effects in the water balance of heterogeneous areas. In: Proceedings of a AGMET Group Conference on The Balance of Water - present and Future , Dublin, Ireland, pp. 69-86.
Blöschl G. and Sivapalan M. (1995). Scale Problems in Hydrological Modelling. Hydrol. Process., 9, 251-289.
Bruneau P., Gascuel-Odoux C., Robin P., Merot Ph., Beven K. (1995): Sensitivity to space and time resolution of a hydrological model using digital elevation data. Hydrol. Process., 9, 1, 69-81.
Chairat, S. and Delleur J.W. (1993). Effects of the topographic index distribution on predicted runoff using GRASS. Water Resources Bulletin, 29, 1029-1034.
Environmental Systems Research Institute, Inc. (ESRI) (1991). ARC/INFO 6.0. User's guide. Cell based modelling with GRID.
Famiglietti J.S. and Wood E.F. (1994). Multiscale modelling of spatially variable water and ebergy balance process. Water Res. Research, 30, 11, 3062-3078.
Franchini M., Wendling J., Obled C. and Todini E. (1996). Physical interpretation and sensitivity analysis of the TOPMODEL. J. Hydrology , 175, 293-338
Hutchinson M.F., Bischof R.J. (1993). A new method for estimating the spatial distribution of mean seasonal and annual rainfall applied to the Hunter Valley, New South Wales. Austral. Met. Mag. 31:179-184.
Leavesley G.H., Lichty R.W., Troutman B.M. and Saindon L.G. (1983). Precipitation-Runoff Modelling System: Users's manual. U.S. Geological Survey. Water Resources Investigation Report, 83/4238.
Merot Ph., Ezzahar B., Walter C. and Aurousseau P. (1995). Mapping waterlogging od soils using digital terrain models. Hydrol. Process. 9, 1, 27-34.
Moore I.D., Norton T.W. and Williams J.E. (1993). Modelling environmental heterogeneity in forested landscapes. J. Hydrol., 150, 717-747.Nash J.E. and Sutcliffe J.V. (1979). River flow forecasting through conceptional models, 1. A discussion of principles. J. Hydrol., 10, 282-290.
Nash J.E. and Sutcliffe J.V. (1979). River flow forecasting through conceptional models, 1. A discussion of principles. J. Hydrol., 10, 282-290.
O' Loughlin E.M (1981). Saturation regions in catchments and their relation to soil and topographic properties. J. Hydrol., 53, 229-246.
Priestley C.H.B. and Taylor R.J. (1972). On the assessment of surface space heat flux and evaporation using large scale porometers. Mon. Weath. Rev. 106, 81-92 .
Quinn P.F., Beven K.J. and Lamp R. (1995a). The In(a/tan ß) index: how to calculate it and how to use it within the TOPMODEL framework, Hydrol. Process. 9, 2, 161-182.
Quinn P.F., Beven K.J. and Culf A. (1995b). The introduction of macroscale hydrological complexity into land surface - atmosphere transfer models and the effect on planetary boundary layer development. J. Hydrol., 166, 421-445
Thornthwaite C.W. and Mather J.R. (1957). Instructions and tables for computing potential evapotranspiration and the water balance. Publications in Climatology, Laboratory of Climatology, vol 10, no 3
U.S.Army (1987). GRASS reference manual. USA CERL, Champaign, IL.
Wendland F., Albert H., Bach M., Schmidt R. (1993). Atlas zum Nitratstrom in der Bundesrepublik Deutschland, 96 S., Berlin: Springer-Verlag .
Wolock D. M. and McCabe, G. J. (1995). Comparison of single and multiple flow direction algorithms for computing topographic parameters in TOPMODEL. Water Res Research, 31, 5, 1315-1324.
Wolock D.M. and Price C.V. (1994). Effects of digital elevation model and map scale and data resolution on a topography-based watershed model, Water Res Research, 30, 11, 3041-3052.
Zhang W. H. and Montgomery D.R. (1994). Digital elevation model grid size, landscape representation and hydrologic simulation. Water Res. Research, 30, 1019-1028.
Zheng D., Hunt, E.R. and Running, S.W. (1995). Comparison of available water capacity estimated from topography and soil series information. Landscape Ecology, in press.
D.-I. Müller-Wohlfeil, W. Lahmer, V. Krysanova & A. Becker
Potsdam Institute for Climate Impact Research (PIK)
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E-mail: dirkingm@pik-potsdam.de, lahmer@pik-potsdam.de, valen@pik-potsdam.de, becker@pik-potsdam.de