GIS-based components for rainfall-runoff models

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1 HydroGIS 96: Application of Geographic Information Systems in Hydrology and Water Resources Management (Proceedings of the Vienna Conference, April 1996). IAHS Publ. no. 235, GIS-based components for rainfall-runoff models ANDREAS H. SCHUMANN & ROLAND FUNKE Institute of Hydrology Water Resources Management and Environmental Techniques, Ruhr University Bochum, D Bochum, Germany Abstract The utilization of GIS for the parameterization of three processoriented physically-based hydrological model components is described. The heterogeneity of soil and vegetation in a catchment can be expressed with distribution functions of soil storage capacities which are derived efficiently by an overlay of a soil map with land use characteristics. These distribution functions are used to consider the nonlinear distribution of actual soil saturation within a catchment with regard to its impact on surface runoff and interflow during a storm event. The lateral flow of water on the land surface is the second process described by a GIS-based procedure. The runoff between areas of different soil and vegetation attributes is modelled with a new statistical parameter, the transition frequency. These probabilities are estimated by analysing the geomorphological characteristics of flow paths on the land surface. The third GIS-based model component describes the concentration of runoff in the river by an two-dimensional impulse response function. The distribution of the runoff along the river network is estimated by parameterization which is based on the Strahler ordering of the river network. The three new developed model components and their parameterization by GIS were successfully applied to seven catchments with an area between 18 and 576 km 2. INTRODUCTION In distributed hydrological models the spatial heterogeneity of catchment characteristics is usually discretized into small area elements which are considered homogeneous. Physically-based models are in most cases only applicable in micro-scale. As they need defined physical conditions (e.g. soil parameters which are known only for homogeneous soils) their utilization for area elements of some hundred square meters is not justified. As a result "effective" parameters are needed to calibrate these models to real world conditions. Many distributed physically-based models are only a special category of lumped conceptual models (Beven, 1989) as they are used with lumped parameters. In this paper, new approaches are described to consider the spatial heterogeneity of hydrological characteristics within a catchment in meso-scale modelling. The aim is not the transition of physically-based models from meso-scale or macro-scale but the development of new scale-independent model components and their parameterization. These models should be useable in modelling of river basins from 10 to km 2 in size. For three different processes such GIS-based components were developed: - for the runoff formation in the upper, non-saturated soil zone;

2 478 Andreas H. Schumann & Roland Funke - for the lateral flow of water on the land surface under consideration of interactions between different soil and vegetation combinations; - for the runoff concentration within a river network. A DISTRIBUTION FUNCTION OF SOIL STORAGE CAPACITY WITHIN A CATCHMENT If we want to use a physically-based infiltration model (e.g. the Green- Ampt Model) the physical characteristics of the soil (hydraulic conductivity, porosity, field capacity, wetting front suction) should be known. In relation to soil texture classes these parameters can be estimated (e.g. Rawls et al., 1983). Unknown is mostly the depth of the upper soil zone within a catchment. If we apply the classical definition of soil horizons we can estimate the depth of upper (rooted) soil in relation to the type of vegetation. Our hypothesis is that the storage capacity of upper, non-saturated soil can be expressed by the product of effective soil porosity and root depth. Both characteristics vary within a catchment. If we differentiate between soil texture classes, different types of vegetation are represented within each of these classes. This heterogeneity can be considered by area distribution functions of soil storage capacity (Schumann, 1993). Through an overlay of the soil texture map and land use in a GIS, such distribution functions can be derived for each soil texture class. The step by step discretized area soil storage capacity functions can be approximated by analytical functions. These functions describe the spatial variability of soil storage capacity and can be used to consider the temporal and spatial distribution of saturation and saturated areas within the catchment (e.g. Wood, 1991). The methodology for estimation and use of these functions is shown in Fig. 1. TRANSITION FREQUENCIES AS SURFACE FLOW CHARACTERISTICS The velocity of surface runoff depends on slope and surface roughness. Under the assumption that the Manning equation can be used, the local velocity of surface runoff is: v = k r H 2l3 JT (D where k r is roughness (depends on land use), / is slope, and H is the depth of water at the soil surface. As the slope varies strongly within a small scale, a grid-based process description was chosen. Each grid element with a width of 50 m is characterized by its slope, flow direction, vegetation and soil type. In relation to its width Ax, and flow direction <p, a relative time can be defined in which the surface runoff with a depth of one unit passes a grid cell: t = if tanv < 1 (2) k r \JTcos <p Ax,, t = if tan<p > r (3) k \ff sin<p

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4 480 Andreas H. Schumann & Roland Funke The total relative time T, in which a water droplet leaves a certain soil-vegetation combination depends on its flow path. They can be estimated by totalizing the relative times in which water passes the different grid cells of its pathway. If we are not looking for a certain droplet but for the total amount of surface runoff produced at a certain soil-vegetation combination, we can estimate a distribution function showing temporal distribution of the area which drains into other soil-vegetation combinations. The interaction of different soil-vegetation combinations is being considered in the following way: we can estimate the number of grid elements for each soil-vegetation combination i which drains into another soil-vegetation combination,/ (i.e. which has a common border with a combination y in flow direction). We receive a matrix of transition numbers with «-runoff producing soil-vegetation combinations in its lines and (n + l)-runoff receiving elements (including the river network in its rows). The elements Ky of this matrix are the number of grid cells which drain directly from combination i into combination/'. The transition frequencies can be estimated by: k u = 5L_ 11» (4) ** The methodology for estimation of these frequencies is shown in Fig. 2. Fig. 2 Estimation of transition frequencies.

5 GIS-based components for rainfall-runoff models 481 In each time step of simulation At, a part a i IA i of the total area A t of combination / drains into neighbouring combinations. The relative size (for one unit runoff) of this area can be estimated through the cumulative area-time distribution. The direction of drainage is considered through transition probabilities. The total inflow into a certain soil-vegetation combination,/ or into the river network can be estimated as n Qj = E*,VM- 1=1 where Qj is inflow of surface runoff within one time interval, R t is surface runoff, ky is transition probability, and a t is partition of the total area of combination i which drains within one time interval to other soil-vegetation combinations. In the water receiving area, the surface runoff infiltrates or will be translated if this area is saturated. (5) GIS-BASED ESTIMATION OF A TWO-DIMENSIONAL INSTANTANEOUS UNIT HYDROGRAPH The linear advection-dispersion equation which can be derived from the Saint-Venant equation is an often used model for single-channel flow, which can be described by a two-dimensional response function on a Dirac impulse: h(x,t) = A exp - *J4irDt 3 ' ADt with: c advective velocity, D dispersion coefficient, t time and x distance along the longitudinal axis of the water course. The shape of this function is shown in Fig. 3. With increasing distance of the impulse the steepness of the response is reduced. The outflow from the system can be derived from the following equation: t Q(t) q (x,t)h(x,t-t)àràx ( 7 ) /=o If the inflow q z into the river network is normalized we get a distribution function of inflow along the channel network: w(x,t) = q z (x,t)/ J q z (x,t)dx (8) [zv..,. / With the assumption that the inflow distribution is time independent we get the impulse response function for any point along the river: fit) = [ w(x)h(x,t)dx (9) *=0 (6)

6 482 Andreas H. Schumann & Roland Funke pathways drainage area in relation to the total catchment area 0.3 -, ~i r il distance from outlet (length of pathways) Fig. 3 Example of a two-dimensional impulse response function. One possibility for the parameterization of this inflow distribution was suggested by Snell & Sivapalan (1994). If the river network is orderly according to the Strahler ordering scheme (Strahler, 1957) we can divide allflowpaths into a number of pathways describing the transition of water between the initial order o> into which a droplet is injected and higher-and higher ordered streams until the outlet with order Q is reached. Each of these pathways drains a certain partition of the total catchment. The probability of a droplet of runoff produced at any point within the catchment running via a certain pathway ij to the outlet can be computed by: A.. n-i n/>«0" < j, (i,j) s y) A ' 'J with: A a area which drains directly into a stream with the initial order u> of this pathway; Py probability that a stream of order / runs into a stream of order j (where i and y are elements of pathway y; A total area of the catchment; 0 order of the stream at the outlet. The typical length of a pathway, L y is estimated from the average length of its elements by summarization. The inflow distribution function w(x) is defined at the points x = L y only: (10) w(x) = p y w(x) = 0 if x = L y if x = L (11) (12)

7 GIS-based components for rainfall-runoff models 483 The impulse response function can be estimated by: 1 fit) E^A ex jl P y -cty (13) 4Dt AirDt 3 7 We resolve the total river network into single pathways each draining a certain part of the catchment. In Fig. 4, this methodology is shown schematically. \2 Fig. 4 Methodology for estimation of area-length relationship. CASE STUDY, SUMMARY The three model components presented above were combined in a rainfall-runoff model which was applied to seven catchments between 18 and 576 km 2 within the Mosel River basin in Germany. In the first step, the digital soil map of the catchment was combined with the land use classification to estimate for each soil texture class the areal distribution functions of soil storage capacity. These functions were used to compute the surface runoff, the actual values of water storage and soil moisture within each time step. The interflow was computed also in relation to the actual soil moisture. After estimation of the two runoff components, the horizontal division of the model was changed. Now different combinations of soil and vegetation were considered in their areal distribution. For each soil-vegetation combination the drainage area-time function was estimated under consideration of slope and surface roughness. The transition frequencies were computed and the transfer of surface runoff from one soil-vegetation combination to the others was estimated in each time step. As a result, we got the hillslope runoff from each soil-vegetation combination in its two components, namely interflow and surface runoff. For the ordered river network, the two-dimensional impulse response function was estimated. Its two parameters (advective velocity and diffusion coefficient) were calibrated with measured rainfall-runoff events. The different distributions of soil and vegetation types on the drainage areas of each pathway were considered by different characteristics of the subcatchments of the initial streams of each

8 484 Andreas H. Schumann & Roland Funke Table 1 Results of an application of the developed model on some catchments in Germany. Gauge Pruem River Pruem Catchment area. (km 2 ) 53 Number of flood events 8 Computational error of peak flow (mean in %) 14.0 Computational error of runoff volume (mean in %) 5.4 Sinspelt Enz Echterhausen Pruem Pruemzurlay Pruem Giesdorf Nims Seffern Nims Alsdorf Nims pathway. The different steps of parameterization of our rainfall-runoff model are realized by utilization of the GIS ARC/INFO for the estimation of the catchment characteristics, mentioned above. The results of the model application are shown in Table 1. With relative low efforts for model calibration, the rainfall-runoff relationships during flood events in all catchments are well-represented. By application of GIS technology, a new generation of hydrological models for meso- and macro-scale can be developed under consideration of catchment characteristics and their spatial heterogeneity. The three presented tools should be a contribution to this aim. REFERENCES Beven, K. J. (1989) Changing ideas in hydrology - the case of physically-based models. /. Hydrol. 105, Rawls, W. J., Brakensiek, L. & Miller, N. (1983) Green-Ampt infiltration parameters from soil data. /. Hydraul. Engng Div. ASCE109, Schumann, A. H. (1993) Developmentof conceptualsemi-distributed hydrological models and estimationof their parameters with the aid of GIS. Hydrol. Sci. J. 38, Snell, J. D. & Sivapalan.M. (1994) On geomorphologicaldispersion in natural catchments and the geomorphological unit hydrograph. Wat. Resour. Res. 30, Strahler, A. N. (1957) Quantitative analysis of watershed geomorphology. EOS, Trans. AGU 38, Wood, E. F. (1991) Global scale hydrology: advances in land surface modelling. Rev. Geophys., Supplement, April,