Scales and similarities in runoff processes with respect to geomorphometry

Jochen Schmidt - Kirsten Hennrich - Richard Dikau
Department of Geography, University of Bonn, Germany


Numerous investigations using various techniques have been carried out towards a more detailed understanding of relationships and interactions between catchment morphometry and rainfall-runoff processes. Recently, this research question has become more relevant through the need for hydrologic computer models simulating the water balance of large areas. Moreover, advances in the analysis of landform morphometry through the availability of high resolution Digital Elevation Models (DEMs) and powerful Geo-Information Systems (GIS) enhance research efforts within this topic.

In this study several computer techniques and models were applied to investigate the effects of geomorphometry on rainfall-runoff processes at different scales. The sensitivity of dynamic hydrologic processes to comparatively static boundary conditions requires different methods for modelling, analysis and visualisation of different kinds of data. Therefore an approach integrating several geocomputational concepts, including spatial analysis of different types of geo-data, static modelling of spatial structures, dynamic 4D-modelling of hydrologic processes and statistical techniques was chosen.

Geomorphometric analysis of the research areas was carried out with GIS packages (including Arc/Info and GRASS), special purpose software and self developed tools. Soil-morphometry relationships were modelled within a GIS environment. Hydrologic models (SAKE and TOPMODEL) were used to simulate rainfall runoff processes. Statistical tools and sensitivity analysis were applied to gain an insight into the hydrologic significance of geomorphometric properties.

The results demonstrate the importance of small parts of the catchment area, which are related to low slope angles, low flow lengths and concavities. The spatial distribution of soil types has a significant relationship to the modelled runoff. Spatial distributions of soil types are partly related to morphometry and can be captured by means of soil - morphometry models. Further results show that catchments which differ significantly in morphometry show different runoff responses and different hydrologic sensitivity to changes in boundary conditions. A crude derivation of geomorphometric - hydrologic landform types could be reached. Therefore geomorphometric classifications of catchment types could be a promising method to support large scale hydrologic modelling. Models describing soil distribution in relation to geomorphometry could assist regionalisation of spatial heterogeneity and structure of soil parameters relevant in hydrologic modelling. Moreover, quantification of geomorphometric catchment structure, e.g. in terms of contributing areas, is needed to describe significant geomorphometric catchment characteristics.

keywords: hydrologic modelling, geomorphometry, GIS, DEM, soil-morphometry relation

1. Introduction

Regionalisation issues have been main research tasks in hydrology especially over the past decade (Blöschl and Sivapalan, 1995; Gupta et al., 1986). Recently, scaling problems have become more relevant through the need for hydrologic computer models simulating the water balance of large areas. These models are useful in, for example, flood forecasting or improving atmospheric circulation models. Large scale models cannot incorporate detailed and physically based description of processes, because of unknown boundary conditions and limited computing capacities. Parametrisation of boundary conditions and simplification of models are therefore two necessary steps towards the development of hydrologic models for larger scales. One research objective within this broad range of topics is the definition of parameters describing effects of landform structure and toplogy on hydrologic processes, which we term 'effective geomorphometric parameters'.

On a qualitative basis, it is well known that hydrologic processes are influenced by geomorphometric properties like local slope angle, convergencies or drainage density (Gregory and Walling, 1973). There exist some approaches quantifying these relations through drainage basin parameters (Moore et al., 1991) and model conceptions, like the geomorphic instantaneous unit hydrograph (Blöschl and Sivapalan, 1995; Moore et al., 1991). However, a general quantification of these effects is still a research task. Recent advances in the analysis of landform morphometry through the availability of high resolution Digital Elevation Models (DEMs) and powerful Geo - Information System (GIS) packages enhance research efforts within this topic.

With respect to the significance of geomorphometric properties in hydrology, scaling effects have to be considered, meaning that (1) runoff-morphometry relations, which tend to be invariant over certain spatial ranges and (2) spatial thresholds affecting changes in these relations have to be determined (Blöschl and Sivapalan, 1995; Wood, 1995).

Figure 1:   Scales in hydrology and geomorphology. The figure shows in a crude way some dominant features of each discipline in a spatial and spatio-temporal context. Translating scale properties from one discipline to the other is an open research question (Anderson and Burt, 1990).
Scales in hydrology and geomorphology.

In general, local scale, hillslope scale and catchment scale are often used to distingiush different spatial scales in hydrology (figure 1)(Kirkby, 1988). On the local scale water flow path geometries, flow velocities and quantities are influenced directly by parameters like slope angle and upslope drainage area. Additionally, geomorphometry affects hydrologic processes indirectly through their dependency on several other factors (like soil parameters). The hillslope scale is dominated by runoff production mechanisms influenced by soil properties (partitioning of overland flow and subsurface flow) and hillslope form. Extracting of typical 'hillslope stripes' has been one strategy to represent hillslope hydrology within larger scale catchments. On the basin scale the hydrograph is influenced by basin morphometry which can be expressed by representative attributes for catchment height distribution (relief indices), length and form of the basin (form indices) and parameters describing the drainage network (Cooke and Doornkamp, 1990; Gregory and Walling, 1973; Schmidt and Dikau, submitted). It is also well known that mesoscale or macroscale landform types affect hydrologic characteristics significantly.

Regarding these scaling effects, different research methodologies have to be applied in the study of the problem. GIS provide sets of useful techniques and tools for investigations on different spatial levels (given that sufficient data is available).

In 1991, the Deutsche Forschungsgemeinschaft (German Research Council, Bonn) established the project 'Regionalisation in Hydrology'. The general aim of this project is to develop methods transfering hydrologic models and parameters from small spatial scales to larger spatial scales (Kleeberg, 1992). One part of this project concerns the definition and regionalisation of geomorphometric characteristics and attributes with hydrologic relevance on different spatial scales. This part of the project was carried out by research groups at the University of Bonn and the University of Heidelberg using several computational techniques. In this paper some results of this investigation are presented (Hennrich et al., in press; Schmidt and Dikau, submitted; Schmidt et al., in press).

2. Study areas  

Two main study areas have been focused on throughout this investigation: (1) the Weiherbach catchment (6.3 km2) for small scale studies and test purposes, (2) the Leineturm catchment (991 km2) for comparing the Weiherbach results and for large scale studies (figure 2).

Figure 2:   Research areas used in this study: The small Weiherbach catchment (6.3 km2) is located in the Kraichgau loess region in south-west Germany. The Leineturm catchment (991 km2) lies within the mountainous Harz region in the central part of Germany.
Research areas.

The Weiherbach catchment is located in the Kraichgau loess region in south-west Germany. The catchment has been extensively investigated and therefore a wide variety of field data has been collected, including meterological, hydrological, landuse and soil data (Merz and Bárdossy, in press; Merz and Plate, 1997; Schmidt et al., in press). A high resolution (12.5 m grid size) digital elevation model was produced. These data serve as a useful basis for small scale morphometry-runoff investigations. The Weiherbach catchment shows an asymmetry, caused by Pleistocene processes, between smaller, steeper, and highly eroded west-facing subcatchments and larger, gentler, and loess-covered east-facing subcatchments (figure 2). Elevation ranges from 140m to 250m. The area has been dominated by intensive agricultural landuse. Main soil types are loess soils.

The Leineturm catchment is located in the central part of Germany, south of Hannover (figure 2). It is the catchment of the upper Leine river, a part of the Weser catchment. Its south-eastern part lies within the mountainous Harz region. The lower part of the catchment is dominated by agricultural landuse, the upper part is mainly forested. Elevation ranges from 120m to 520m. Climatologic and hydrologic data is available from several stations throughout the catchment. Moreover, a DEM with 31m grid size was available.

3. Methodology

Sensitivity of dynamic hydrologic processes varying in time and space to comparatively static boundary conditions, landsurface morphometry and soil features requires different methods for modelling, analysis and visualisation of data. Therefore an approach integrating several geocomputational concepts, including spatial analysis of different types of data, static modelling of spatial structures, dynamic 4D-modelling of hydrologic processes, and statistical analysis techniques was chosen.

Figure 3:  Structure of methods, tools and parameters. The small arrows indicate data transfer and data processing steps. The large, dotted arrows indicate the main analysis procedures described in section 4: Analysis of (1) primary geomorphometric parameters and spatial hydrologic variables, (2) soil-morphometry relationship and its implications for rainfall-runoff modelling, (3) representative catchment parameters and runoff indices, (4) meso-scale landform types and runoff characteristics.
Structure of methods, tools and parameters.

Investigations of the effects of geomorphometry on rainfall - runoff processes require as basic information a quantitative description of the topography and hydrologic characteristics of the study area. In our study hydrologic features have been synthetically produced by means of physically based hydrologic catchment models (see section 3.1). In order to extract relationships between morphometry and model output, the model runs were carried out under homogeneous boundary conditions (landuse, soil parameters, precipitation) and the same initial conditions (soil moisture). Parameter values were chosen according to typical measured values and validation model runs. However, several sensitivity studies were carried out in the small Weiherbach test catchment to investigate the influence of variable boundary and initial conditions. The modelled hydrologic variables include event based runoff hydrographs and overland flow depth. The spatial model input and output was stored within GRASS and Arc/Info GIS software as local hydrologic attributes. Hydrographs were used to produce a series of hydrologic indices (Hennrich et al., in press), which were stored as hydrologic catchment attributes. These indices were used in a cluster procedure to obtain hydrologic catchment types (see section 4.3).

Topography has been analysed using a collection of geomorphometric GIS-tools and self-developed algorithms (Schmidt and Dikau, submitted) (see section 3.2). Additionally, GIS tools were applied to analyze and produce soil-morphometry relations for the Weiherbach catchment, allowing investigations of interactions between soil type distribution and relief attributes for hydrologic modelling (Hennrich et al., in press; Schmidt et al., in press).

Statistical packages (mainly SAS and some self developed tools) were employed in the analysis of runoff - morphometry relations on the basis of the above data (see section 4). Additionally, model scenarios were produced to investigate model sensitivity to several input parameters. The complete structure of the methods used is presented in figure 3 (Schmidt and Gärtner, submitted).

3.1 Hydrologic models  

Two hydrologic models with different parameter and computational requirements have been used to cover different scale issues in this study.

The quasi-three dimensional model SAKE (Simulationsmodell für Abflüsse kleiner Einzugsgebiete, trans.: runoff simulation model for small catchments) has been utilised for modelling rainfall runoff processes in the Weiherbach catchment. SAKE works with a regular horizontal grid and an uneven vertical discretisation (soil horizons). The different hydrologic fluxes through the cells are modelled by differential equations (Merz and Bárdossy, in press; Merz and Plate, 1997; Schmidt et al., in press). SAKE is an event based model working with a fixed temporal resolution of one minute (the internal timesteps may vary according to the stability of numerical solutions). Some of the required spatial boundary conditions (DEM, landuse, soil types, initial moisture conditions) can be easily stored, manipulated and provided to the hydrologic model by GIS tools. SAKE produces different types of output. As temporal data, hydrographs of runoff, soil moisture and some other hydrologic variables can be produced for each grid point in the catchment. Moreover, spatio-temporal distributions of hydrologic variables such as overland flow depth and soil moisture can be simulated for each time step. Calibration and validation of SAKE was carried out in a highly instrumented subcatchment of the Weiherbach (Schmidt et al., in press).

The hydrologic model TOPMODEL is based on the concept of variable source areas contributing to runoff production through saturated overland flow (Beven and Kirkby, 1979). Formation of contributing areas is related to the topographic parameter $ln(a/tan\beta)$, where a is the upslope area drained per unit contour length and $\beta$ is the slope angle. Model inputs are the frequency distribution of $ln(a/tan\beta)$ (easily provided by GIS), daily precipitation and evapotranspiration time series and several lumped soil and routing parameters. Model outputs are the runoff hydrograph, water balances and contributing areas. The model was calibrated for the Leineturm catchment (Hennrich et al., in press), and the calibrated soil parameters were used as constant values throughout this study.

3.2 Geomorphometric analysis  

Various approaches have been used and applied to describe landform surfaces quantitatively. For the research problem investigated in this study several morphometric concepts have been chosen to describe landforms on different spatial scales (figure 3 and table 1) (Schmidt and Dikau, submitted). On the local scale primary geomorphometric parameters, like the slope angle $\beta$ have been extracted to investigate morphometric influences on hydrologic variables like overland flow depth and velocity. Moore et al. (1991) and Schmidt et al. (in press) have proposed several primary geomorphometric parameters with local hydrologic significance. In particular compound parameters are supposed to be strongly related to hyrologic processes. Most of these parameters could be easily derived by standard GIS tools in GRASS or Arc/Info. Some parameters were derived by special geomorphometric software packages or self developed GIS tools (Schmidt and Dikau, submitted).

At the catchment scale a series of drainage basin parameters (Hennrich et al., in press) were tested for hydrologic relevance. Again, most of them could be derived by standard GIS algorithms, but in several cases our own algorithms had to be developed.

Derivation of landform units can be carried using various approaches, including classification of morphometric parameters, filter techniques and cluster analysis (Dikau et al., 1995; Dikau, 1989, 1994; Schmidt and Dikau, submitted; Sulebak et al., 1997). We applied a classification technique proposed by Hammond (1964), and applied by Dikau et al. (1995) within a geocomputational environment, and cluster analysis in order to derive meso-scale landform units homogeneous in morphometry in the Leineturm study area (Hennrich et al., in press).

Table 1:   Geomorphometric parameters and objects on different scales (Moore et al., 1991; Schmidt and Dikau, submitted) with some examples related to this study.
Geomorphometric parameters and objects on different scales

4. Results  

Some of the research results presented here have been partly published elsewhere (Hennrich et al., in press; Schmidt and Gärtner, submitted; Schmidt et al., in press). It is the purpose of this paper to present them embedded in a framework, including (1) the hierarchical methodological aspects and (2) the scale issues of our work and to show (3) possible links between scales. In Figure 4, the research themes of the next sections on different scales are shown within a sketch of this framework.

Figure 4:  Different levels of investigation in our study. Small arrows indicate data processing and calculation/derivation steps. Large arrows indicate the main analysis procedures as described in the following sections (compare figure 3): Comparison and statistical analysis of primary geomorphometric analysis and spatial hydrologic variables; statistical analysis of representative catchment parameters and runoff indices; comparison and statistical analysis of meso-scale landform types and runoff characteristics.
Different levels of investigation in our study.

4.1 Local scale  

The local scale approaches included investigations of the relevance of morphometric control of local hydrologic processes (index (1) in figure 3) and the utility of soil-morphometry relations in hydrologic modelling (index (2) in figure 3).

The hydrologic model SAKE simulates overland flow depth for each time step (minutes) and the defined spatial discretisation (compare section 3.1). We applied GIS visualisation and map algebra tools to analyse the spatio - temporal development of overland flow depth resulting from model runs in subcatchments of the Weiherbach area (figure 5). The results show a period of fast convergence of overland flow to a comparatively small part (<10%) of the catchment area directly after precipitation ended and a second period of slow runoff of overland flow from the concentration areas (Schmidt and Gärtner, submitted; Schmidt et al., in press). The first period is related to the hydrograph peaks and the second to the falling part of the hydrographs. These two phases were used to define thalweg catchment areas with high relevance for overland flow due to their comparatively long incorporation in overland flow. Multiple regression of simulated overland flow depth and several primary geomorphometric parameters and discriminant analysis on the basis of the defined contributing areas and geomorphometric parameters revealed the high relevance of the topographic parameter $ln(a/tan\beta)$ for overland flow concentration processes.

Figure 5:  Local scale studies: Overland flow depths were analysed using GIS tools (see text) for model runs of SAKE in the Weiherbach subcatchments. The spatial pattern of runoff concentration show strong convergence to the thalwegs. The temporal development of overland flow depth indicates fast concentration to small areas for all catchments after precipitation ended. Statistical analysis revealed the relevance of the parameter $ln(a/tan\beta)$ for this concentration process.
Click on image to view a short video of simulated overland flow
Click on image to view a short video of simulated overland flow

As a first result, it can be stated that the hydrologic significance of a point in a catchment in terms of its contribution to overland runoff, measured by its covering with overland flow depth, is strongly influenced by local morphometric properties. Fast convergence of overland flow is considered to distingiush 'areas of different hydrologic significance' within a catchment (Anderson and Burt, 1978a,b). These findings have some implications for spatial patterns of other boundary conditions used in hydrologic modelling such as soil parameters or initial moisture (see below).

Soil properties used in hydrologic modelling show high variablities depending on measurement methods and sampling location (Hendrickx, 1990). The determination of sufficient soil parameters is one crucial problem in dynamic modelling of hydrologic processes. Additionally, in distributed modelling, the problem of spatial parameter distributions or 'effective parameter values' for certain areas arises. Effective parameter values are often derived by simple statistical measures, which assumes a spatial stochastic variability of parameter values. However, often statistical measures are not appropriate, because parameter values show spatial patterns or structured variability in space (Merz and Bárdossy, in press; Merz and Plate, 1997). In the Weiherbach area, for example, there was a clearly detectable relationship between saturated water content and soil type. The definition of appropriate units (e.g. soil units) showing an internal stochastic variability of parameter values and a clear external distinction from other areas is an important approach, and contributed to the concept of hydrologic response units. One method for coping with this problem is to identify relationships between soil types and soil properties. Another possibilty is to relate soil attributes to other information available at a better spatial resolution, such as digital elevation models or remotely sensed data (Moore et al., 1993). The latter approach is often appropriate, because soil genesis is a result of geomorphic and pedologic processes, strongly influenced by several factors including geology, climate, vegetation and morphometric properties (such as slope angle or local convergence/divergence).

Figure 6:  A soil - morphometry model applied to the Weiherbach area revealed good model results for predicting colluvial soils. The model based on a failure rate analysis using ten geomorphometric parameters.
A soil - morphometry model applied to the Weiherbach area.

In the Weiherbach area we found good prediction quality of a simple soil morphometry model for colluvial soils in the thalwegs (figure 6) (Schmidt et al., in press). The question of whether such models can be useful for parameter estimation is also related to the findings concerning hydrologic significance of geomorphometric catchment positions, which will be shown in the following.

Figure 7:  Local scale studies: Different spatial patterns of model parameters show the effect of geomorphometric structured distributions. The parameter values were coupled to geomorphometric parameters with a random influence to vary spatial autocorrelation (degree of strusture). The upper diagrams show modelled hydrographs for west-facing subcatchments, the lower diagrams represent a east-facing subcatchment. The degree of structure show a significant influnce on modelled hydrograph for the east-facing subcatchment.
Local scale studies.

The model SAKE uses several soil attributes, including saturated hydraulic conductivity and saturated water content, as threedimensional boundary conditions. SAKE was used in sensitivity analysis of the influence of the spatial distribution of these parameters on model results. As a first step, different spatial distributions based on the same frequency distributions of parameter values for conductivity and saturated water content were artificially produced (figure 7). The parameter values were coupled with geomorphometric position using GIS tools in such a way that parameter patterns with different spatial autocorrelation strength resulted. These artificial spatial patterns were used as input parameters for the model (Merz and Bárdossy, in press; Merz and Plate, 1997; Schmidt and Gärtner, submitted; Schmidt et al., in press). For most subcatchments, the simulated hydrographs show a strong dependency on the degree of spatial structuring (figure 7). Further analysis, varying parameter values in different geomorphometric positions, showed the high significance of morphometric positions in the thalweg areas (Schmidt et al., in press).

These results show that runoff concentration processes in small catchments to some extent define areas within catchments that have varying significance for hydrologic catchment response. These catchment areas show strong dependencies on geomorphometric position. This implies, that other parameters relevant in hydrologic modelling should be of varying significance in these areas as a function of their different length of coverage with considerable overland flow depth. Sensitivity studies showed that local parameter values of saturated hydraulic conductivity and saturated water content have varying hydrologic relevances according to geomorphometric position. This means that spatially structured variability and in particular morphometric structured variability of parameters used in hydrologic modelling has to be modelled (Merz and Bárdossy, in press; Merz and Plate, 1997; Schmidt et al., in press). Soil - morphometry relationships are one contribution to the modelling of spatial distribution of soil units and to the derivation of spatial distribution of soil parameters in a process-related manner. Moreover, morphometric modelling can help in estimating the hydrologic significance of parameters. Putting this together, morphometric analysis can assist in (1) defining landform units with relatively homogeneous (stochastic) parameter values, (2) modelling spatial distributions of parameter values, (3) calculating effective parameter values incorporating structured variability, (4) defining appropriate measurement programs for soil parameters (due to the variable model sensitivity), and (5) estimating errors in hydrologic modelling due to parameter uncertainties.

However, we couldn't verify the described relationships and statements for all our test catchments. There was an obvious relationship between catchment morphometry and the hydrologic sensitivity to local parameter variations. As a first statement, there are catchments, in general with steeper gradients and side slopes and smaller thalwegs (west-facing subcatchments in the Weiherbach area), which are less sensible to variation in the spatial patterns of soil parameters and to total changes of parameter values (compare diagrams in figure 7). This leads to the question of geomorphometric catchment characterisation adressed in sections 4.2 and 4.3.

4.2 Catchment scale  

Relations between drainage basin parameters and hydrologic indices have been investigated in numerous studies. Cooke and Doornkamp (1990) and Gregory and Walling (1973) provide useful discussion of these issues. Quantitative description of basin morphology and landuse and the establishment of functional relationships between these parameters and hydrologic catchment characteristics has been found to be useful for modelling (Gupta et al., 1980; Rodriguez-Iturbe and Valdes, 1979, e.g.) and prediction (Acreman and Sinclair, 1986; Sauer et al., 1983, e.g.).

In our studies, we investigated the influence of basin morphometry on runoff in order to identify geomorphometric parameters on the catchment scale (termed 'representative geomorphometric parameters', see section 3.2, table 1), that have hydrologic relevance ('effective parameters'). This part of our study relates to index (3) in figure 3. The simulated hydrographs were used to extract a series of hydrologic indices (Hennrich et al., in press). In order to identify relationships between morphometry and hydrology, the model runs were carried out under the same homogeneous soil, landuse and initial moisture conditions. As decribed in section 3.2, catchment parameters were extracted using a collection of tools, including standard GIS tools, special software and specially developed algorithms. Regression techniques were applied to get relationships between hydrologic indices and catchment parameters (table 2) (Hennrich et al., in press; Schmidt et al., in press). The following conclusions can be drawn:

Table 2:   Correlation matrix of selected morphometric catchment parameters and simulated hydrograph indices for model runs of SAKE in the Weiherbach subcatchments. The hydrograph indices are grouped into attributes describing hydrograph rise, volume and fall. Additionally the peak value of calculated unit hydrograph is included. The table presents some of the best correlation results of the analysis.
Correlation matrix of morphometric catchment parameters and hydrograph indices.

The relations derived for the 23 subcatchments in the Weiherbach area were tested in the Leineturm area. Almost 1000 GIS - derived subcatchments were used to check whether the relations remain stable with a larger data base. In this case, model runs with SAKE and TOPMODEL were used to produce hydrograph indices. The results show the significance of the slope angle, $ln(tan\beta/l)$, $ln(a/tan\beta)$ and relief thickness for simulations in the Leineturm area (table 3).

Table 3:   Correlation coefficients of selected relationships for model runs of SAKE and TOPMODEL in almost 1000 subcatchments in the Leineturm area. Because of the larger data base the correlation coefficients decline, although some of the principal relations identified in table 2 remain stable. As the frequency distribution of $ln(a/tan\beta)$ is a direct TOPMODEL input, the correlation of $ln(a/tan\beta)$ is very high.*
Correlation coefficients of selected relationships.

Various subcatchment sizes have been produced for the Leineturm area. Therefore, the question is whether, and how, the derived relationship is influenced by catchment size. Threshold analysis of hydrologic indices and morphometric parameters revealed that there are significant changes in attribute variances with catchment size (Dikau, 1994; Hennrich et al., in press; Wood et al., 1990; Wood, 1995). We analysed vriation in the derived relationships with changing catchment size by comparing correlation coefficients for certain ranges of catchment size (table 4). The size ranges were extracted from variance diagrams of hydrologic indices and geomorphometric parameters against catchment size as used by Dikau (1994) and Wood (1995) (Hennrich et al., in press). For this procedure, the model results of TOPMODEL for the Leineturm catchment were used. The results show that on different spatial scales significance and 'effectiveness' of parameters change. The parameter $ln(a/tan\beta)$ shows high correlation on all scales, but correlation strength declines at smaller scales. At small catchment scales (< 1km2), the index of relief thickness shows high correlations. Intermediate correlations could be found for flowlength l and the parameter $ln(tan\beta/l)$ on all scales.

Table 4:   Correlation coefficients for selected relationships for model runs of TOPMODEL in different size ranges of the Leineturm subcatchments. The correlation coefficients of $ln(a/tan\beta)$ decline with decreasing catchment size. At small catchment scales (< 1km2), the index of relief thickness shows high correlations. The parameter $ln(tan\beta/l)$ shows intermediate correlations on several scales.
Correlation coefficients for selected relationships.

There are three problems that have to be mentioned in the context of the results presented in this chapter. First, there still remains a considerable amount of scatter in the data and it is questionable whether it is possible and/or useful to improve the derived relation by more sophisticated methods, such as multivariate and nonlinear statistics. The problem still remains whether the relations remain constant under variable boundary conditions (compare section 5). Moreover, the question of whether, and how, these correlations can improve hydrologic modelling is unsolved. From our point of view, one way in using the identified parameters and relationships could be to typify catchments and/or landform units. The simulations in the Weiherbach area revealed the existence of two types of subcatchment, one with steeper gradients and side slopes and smaller thalwegs the other with thalwegs, which are more broad and extended (compare section 4.1). The former tend to produce simple hydrographs (quick runoff response) and tend to be less sensitive to spatial variations in input parameter values. The latter tend to produce more complicated (e.g. double peaked) hydrographs and show a considerable dependency to spatial variations in input parameters (compare figure 7). Based on these findings, the next step in our studies was trying to establish a quantitative measure for catchment types.

4.3 Regional scale  

A general aim of the regional scale studies was to define meso-scale geomorphometric landform types, reflecting similarities in their hydrologic behaviour. This part of the paper relates to index (4) in figure 3. The methodological basis of the approach and the connections to the previous sections can be seen as a sketch in figure 4.

Principal component analysis and cluster analysis using the statistical package SAS were applied to produce regional units with similarities in their hydrologic behaviour. Hydrological indices produced by SAKE and TOPMODEL from model runs on subcatchments of the Leineturm area (compare section 4.2) served as a data base for this procedure. Discriminant analysis using these hydrologic units and representative geomorphometric parameters calculated for the subcatchments (compare section 3.2 and 4.2) gave evidence of explanatory geomorphometric parameters for the hydrologic classification. On the other hand geomorphometric landform units were classified by implementing an algorithm proposed by Hammond (1964) (Dikau et al., 1995; Hennrich et al., in press) within GRASS. Again discriminant analysis was used to check hydrologic significance of the classification against the hydrograph indices simulated by SAKE and TOPMODEL. Finally, a hydrologic - morphometric landform classification was produced from the previous results.

Figure 8:   Results of cluster analysis based on the hydrograph indices simulated by SAKE and TOPMODEL. The modelled areas are landform units similar in their hydrologic response. The results for the two different models show similarities in their spatial structure and correspondence to landform characteristics.
Results of cluster analysis based on the hydrograph indices

The units in figure 8 were generated using clustering methods based on the hydrographs produced by SAKE and TOPMODEL. The hydrologic units produced by the two different models show certain similarities: the mountainous areas and the plains near the river Leine can be distinguished by visual comparison with the DEM for the Leineturm area. Discriminant analysis using geomorphometric catchment parameters revealed high explanatory values only for some of the geomorphometric parameters already identified in section 4.2 ($ln(a/tan\beta)$). Within this study, much simpler parameters, mainly statistical measures for relief height and slope (e.g. average height or slope) could be identified as explanatory variables for hydrologic clusters. Therefore the question is whether simpler landform descriptions could be useful in relating landform morphometry to hydrologic characteristics.

The geomorphometric landform classification scheme of Hammond (1964) classifies areas within a DEM according to the parameters relief, percentage of low slope angle and percentage of low slope angle at lower elevation using a moving window algorithm. This comparatively simple classification procedure produces units describing the meso - scale character of landform (compare figure 9). However, the landform units produced for the Leineturm area show similarities with the produced hydrologic clusters (figure 8), which was quantitatively determined by discriminant analysis. Based on this discriminant analysis, a combination of the TOPMODEL clusters and the Hammond units was produced. The result (figure 9) leads to a simple segmentation in hilly / mountainous areas with high discharge values and plains with low hydrograph characteristics.

Figure 9:   Derivation of geomorphometric - hydrologic landform types. An algorithm for landform classification (Dikau et al., 1995; Hammond, 1964) was applied to generate geomorphometric landform units. Comparing this map and the hydrologic clusters in figure 8 reveals significant similarities. A discriminant analysis based on the factors used in the hydrologic cluster procedure showed that the hydrologic factors could explain the morphometric classification. Reclassifying the hydrologic factors using these results generated a map with two hydrologic - geomorphometric landform units: (1) plains and plains with hills with lower discharge and (2) hills and mountains with higher peak discharge and overland flow.
Geomorphometric - hydrologic landform types

5. Conclusions  

Geomorphometry provides theoretical basics, methods and techniques for landform analysis on different scales. Although there are still some basic problems in quantitaive analysis of terrain (Schmidt and Dikau, submitted), recent computer capabilities, especially GIS tools, provide a sufficient framework for deriving geomorphometric objects and attributes on different scales, ranging from local parameters to landform units. The availability of these tools and the data they require (DEM's) poses the question of whether, and how, these tools could help in modelling landsurface related processes (Moore et al., 1991). This study presents an approach, quantifying relations between geomorphometric attributes and hydrologic variables by linking hydrologic models with GIS modelling techniques. The coupled use of spatial modelling tools (GIS), statistical packages and hydrologic models provides a powerful combination for investigating landform structure in relation to landform processes. However, basic problems within this framework are (1) storage and exchange of various data types used in geomorphology and hydrology and (2) a missing interoperability of different methods and investigation techniques (Schmidt and Gärtner, submitted).

The methodology used in this study suffers from two fundamental difficulties. First, it remains open as to whether the derived relationsships between morphometry and hydrology remain constant under variable boundary conditions. Although sensitivity studies of the influence of parameter variations on the proposed relationships were carried out, it was not feasible to check all possible parameter combinations. Generally speaking, the complex system of hydrologic catchment response to precipitation input was simplified in this study to a morphometry - hydrology interaction, leaving all other influences constant. Second, the analysed interaction was based purely on model results, and the question of whether it is possible to transfer these findings into real situations remains to be verified.

Nevertheless, we see several challenges coming out of this work. In investigating the spatio-temporal structure of runoff concentration processes in small catchments, it can be shown that there are catchment areas of different hydrologic significance according to geomorphometric positions. Quantifying geomorphometry in terms of its hydrologic influence on small scales requires capturing geomorphometric catchment structure (Schmidt et al., in press). The definition of areas with different hydrologic efficiency is a useful and process-related method to quantify geomorphometric structure, because overland flow tends to concentrate very rapidly in small catchment areas. Hydrologic efficiancy as a function of morphometric position implies that other process - relevant boundary conditions have different efficiency according to their morphometric position. This means morphometry can help to estimate the effects of uncertainties of input parameters. Soil - morphometry models are helpful tools in terms of estimating spatial soil type and soil parameter distributions, given that soil genesis is strongly related to gravitational and/or erosional processes (e.g. colluvial soils). These models should be extended to other predictor variables available in a high spatial resolution. Combining soil - morphometry models with morphometric decriptors for hydrologic efficiency could be helpful in regionalising point measurements of soil parameters. Effects of catchment morphometry has been investigated by numerous studies and several catchment parameters have been proposed to reflect hydrologic behaviour (Cooke and Doornkamp, 1990; Gregory and Walling, 1973). However, it is difficult to generate stringent and general relationships within this respect. We propose to use these parameters in the definition of areas showing similar hydrologic response. We showed that a crude hydrologic - geomorphometric landform classification is possible using a predefined model of terrain classification. Quantifying hydrologic similarity on the catchment scale could be a helpful tool in terms of hydrologic regionalisation, and potentially useful for various process modelling approaches.


This research has been supported by the Deutsche Forschungsgemeinschaft (German Research Council, Bonn) within the project ''Regionalization in Hydrology''.


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