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Hydrology, Water Resources and Ecology in Headwaters (Proceedings of the HeadWater'98 Conference held at Meran/Merano, Italy, April 1998). IAHS Publ. no. 248, 1998.

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Physically-based hydrological modelling on the hillslope and micro-catchment scale: examples of capabilities and limitations AXEL BRONSTERT Potsdam Institute for Climate Impact Research, PO Box 60 12 03, D-14412 Potsdam, Germany

BERND GLÛSING & ERICH PLATE IHW, University of Karlsruhe, Kaiserstrafie 12, D-76128 Karlsruhe, Germany

Abstract In recent years several comprehensive hillslope hydrological models have been developed which have resulted in the improved representation of hillslope hydrological processes (including their interactions) and in some operational applications. An overview of the objectives for hydrological modelling at the hillslope and micro-catchment scale is presented, an exemplary comprehensive physically-based hillslope model is briefly introduced, and several application examples are demonstrated. The limitations of detailed hillslope hydrological modelling are discussed.

MOTIVATION FOR HILLSLOPE MODELLING In the last two decades there has been an increasing interest in hillslope hydrology (Kirkby, 1988; O'Loughlin, 1990; Gutknecht, 1996), shown by a number of field experiments on hillslopes under different conditions. In many cases, these experiments have been coupled with developing, testing and applying of hillslope hydrological models of different kinds. This paper investigates which hydrological problems have been approached successfully and what limitations of hillslope models are inherent. There are a variety of motivations for the development of hillslope models: (a) to provide a research tool which is capable of calculating various hydrological processes and their interactions on the hillslope scale, (b) to obtain a tool to be used for design purposes in environmental and engineering applications, and (c) to derive the basic unit for a non-grid distributed physically-based catchment model.

SET-UP OF A DETAILED HILLSLOPE MODEL The model summarized here, termed Hillflow, has been presented in detail by Bronstert (1994). Its development was accompanied by an extensive field study, for which the Weiherbach catchment in southwest Germany has been intensively equipped. This catchment is a hilly, almost completely agricultural area of deep loess soil (Plate, 1992). One of the main concerns of the model was to include a fairly

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(1) precipitation (2) throughfall (3) infiltration (microand macropores) (4) surface runoff (5) subsurface stormflow (6) soil-water flow (micropores) (7) interaction m i c r o - / macro-pore system (8) percolation or capillary rise (9) r e t u r n flow (10) r o o t - w a t e r u p t a k e (11) soil evaporation (12) plant t r a n s p i r a t i o n

Fig. 1 Structure of the Hillflow-2D model.

detailed representation of rapid hydrological flow processes, such as infiltration (including effects of macropores), (unsaturated) subsurface stormflow and surface runoff. The model is "physically based" in the sense that its parameters have a physical meaning and can be obtained or derived from field measurements or experiments. Three versions of the model were developed: a one-dimensional (vertical) version, a two-dimensional (horizontal/vertical) version and a quasi threedimensional version. Figure 1 gives a schematic representation of the twodimensional (hillslope) version and lists the processes considered. The approaches for the various processes included in the model are summarized in the following (for details see Bronstert, 1994).

Interception and évapotranspiration Two options are available for interception: the highly parameterized Rutter model, and a much simpler overflow model with canopy storage capacity as its single

Physically-based hydrological modelling on the hillslope and micro-catchment scale

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parameter. Different approaches for évapotranspiration are incorporated into the model system, from which the Penman-Monteith equation is the most detailed.

Infiltration Infiltration is a crucial process in modelling the hydrological response of agricultural hillslopes, in particular under conditions of extreme precipitation. In this model the focus has been laid on soil characteristics increasing the total infiltration capacity through the effects of macropores. Infiltration-reducing processes such as soil freezing and soil crusting have not been included so far. Approximating the different infiltration components observed under field conditions leads to the assumption of two infiltration components. The total infiltration rate I is considered to be the sum of the actual rate into the micropores (or soil matrix), Imic , and the actual rate into the macropores, Imac . The infiltration component into the macropore system is switched on when the net precipitation exceeds the matrix infiltration rate (/^ > Imic). Infiltration-excessoverland flow is generated if the precipitation intensity exceeds the sum of the two infiltration components. The infiltration into the soil matrix, /,„,. , is calculated according to the standard approach of soil matrix potential presented by, for example, Feddes et al. (1978).

Water dynamics in the unsaturated matrix Water movement in the unsaturated soil matrix of the hillslope is approached by approximating the Richard's equation. The lower boundary of the model region is considered to be within the unsaturated zone, i.e. groundwater flow or water flow in fissured rock is not part of the model. Surface runoff For surface runoff computations the diffusion analogy equations are applied. The friction slope is calculated according to the Manning-Strickler equation.

Subsurface stormflow Hillflow assumes that the subsurface hillslope response to heavy rainfall (termed subsurface stormflow) is dominated by unsaturated, lateral, non-Darcian flow through the macropore system. This flux is considered to flow within a soil layer of constant thickness parallel to the surface. Hence, the slope of the subsurface cascade is the same as that of the surface cascade. This subsurface stormflow may occur in the case of high precipitation intensity producing macropore infiltration as mentioned before. The routing algorithm of the subsurface stormflow is analogous to the computation for surface runoff, i.e. the diffusion analogy is adapted in both cases. Two options to calculate the friction of the subsurface stormflow are provided.

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Streamflow routing In the 3D version of the model a streamflow runoff module has been included. The equations used are the diffusion analogy approach and the Manning-Strickler formula for a dentritic channel system. Overtopping of the channel banks and interaction of surface runoff and channel discharge are possible.

APPLICATIONS IN HILLY AND MOUNTAINOUS LANDSCAPES During the last few years, a variety of applications under different environmental conditions have been performed. These have included process studies of hillslope erosion and infiltration, long-term water balance at the hillslope scale, and studies on the fluxes in a sloping landfill cover or on the effects of urbanization in a hilly landscape. The results were documented by Bronstert & Plate (1997). The focus of this chapter will be on the applications in hilly and mountainous landscapes.

A storm event at an agricultural micro-catchment in southwest Germany The 3D-version was applied to the 33-ha subcatchment "Neuenbiirger Pfad" in the Weiherbach for a rainfall period of 16 days, from 19 October until 3 November 1992. The soils in the area are loess, alluvial loess and loamy loess. On the first and last day, TDR measurements were taken at 18 locations (at four depths each) within the area, allowing an areal interpolation of the soil moisture at the beginning and at the end of the simulation period. The total precipitation during this period amounted to 94.5 mm, with an hourly maximum intensity of 36 mm h'1. Both topographic and land-use data were derived from DTM and on-site vegetation assessment. Figure 2 shows the areal soil moisture distribution at the Neuenbiirger Pfad catchment on 3 November 1992 for the 0-150 mm soil layer, where Fig. 2(a) represents the soil moisture based on the interpolation of several TDR measurements and Fig. 2(b) shows the results obtained by the model. Visual comparison shows that the pattern of the areal soil-moisture distribution is well-represented and the higher moisture content in the valley bottoms is shown clearly by the model results. Although the 3D-version performed well for this hilly agricultural catchment, the limitations as regard to a hydrological forecast were quite clear: - The calculated runoff generation by infiltration excess (Hortonian overland flow) responds rather sensitively even to small changes in the soil hydraulic parameters, such as saturated conductivity ks or saturated water content 9^. - Changes in surface roughness (Strickler coefficient kj may cause important changes in runoff volume at the small catchment scale, because the roughness controls surface flow velocity and the remaining time for downslope infiltration after rainfall intensity decreases. The actual rainfall intensity is a precondition for a reliable calculation of infiltration excess overland flow. Average values (e.g. 30 min or 1 h) may result in too low intensities for model input and an underestimation of runoff produced. - Processes representing only a small fraction of the total water budget (for many


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hydrological conditions, e.g. surface runoff or groundwater recharge) are hardly predictable; in the favourable cases the right fraction can be approximated. Some runoff-generating processes which are not covered by the model might be of relevance on catchment scale. In the case reported some agricultural roads proved to be a main source for surface runoff during small rainfall events. Picaninny catchment, Central Highlands of Victoria, Australia The experimental hydrological Picaninny catchment (Central Highlands of Victoria, Australia) has been monitored since 1955 to study runoff generation and evaporation processes, and the effects of vegetation changes on water yield rates. Covering an area of 52.8 ha, it is completely covered by mountain ash forest {Eucalyptus régnons) and is characterized by steep slopes (average surface gradient of 37%) and shallow, highly permeable soils (between 0.5 and 2 m deep) on underlying fractured rock. The average annual precipitation is about 1180 mm and the average évapotranspiration about 800 mm. Though the saturated surface area covers only about 1 % of the catchment area, storm runoff generation is dominated by saturation excess overland flow. This is because of the high (macro-)porosity of the soil, resulting in a high infiltration capacity of the non-saturated area, and because the saturated areas are located close to the channel and respond very quickly to precipitation.


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Glusing (1997) applied the 3D-version to the Picaninny catchment. Two different modelling studies have been performed: a long-term simulation of 19 years (from 1972 until 1991), focusing mainly on the average water budget, and a short-term simulation of 15 days (from 16 till 31 December 1993) on the storm hydrograph and on the variation of saturated contributing areas during a storm event. Figure 3 shows the variation in the soil moisture (average soil depth 0.3-1.5 m; measurements taken at 12 locations) for the period of July 1972-July 1981. It is clear that Hillflow reproduces the seasonal variation of the soil moisture well and coincides satisfactorily with the measured values. The difference in the results reached by Hillflow with those of the Australian TOPOG model (CSIRO, 1992) is due to the different parameterization of the high hydraulic conductivities of the soil. Hillflow uses the double porosity concept and TOPOG a single porous medium. This implies that the high infiltration rates observed in nature have to be represented by high matrix conductivity values (TOPOG) or by high macroporosity and moderate matrix conductivity (Hillflow). Hence, during inter-storm periods, the matrix percolation velocity simulated by TOPOG is much higher than that simulated by Hillflow, resulting in different soil moisture recession characteristics for the two models. Though Hillflow was able to reproduce the average soil moisture fairly well, it did not give a satisfactory result for the calculation of runoff. Figure 4 compares the measured and calculated hydrographs for a storm event on 20 December 1993. It is easy to see that only the quick runoff peaks are reproduced by the model and not the slower reaction and recession after rainfall stops. The model's failure in reproducing

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the slow runoff components is due to the missing groundwater component in Hillflow. The saturated flow in the deeper soil layers or in the fractured rock beneath is not accounted for by the soil moisture calculation approach applied here. Runoff from the Ringelbach catchment in the Vosges, France The limitations of the model in representing the groundwater recession, which became clear in the Picaninny catchment, are almost the same as those which degraded the results in an application to the 36-ha Ringelbach catchment in the Vosges, France. This catchment, described in detail by Ambroise (1994), is an Alpine-type area with shallow and highly permeable soil above fractured rock. Saturation-excess-overland flow is the dominant process for runoff generation during storm periods. The extent and dynamics of the saturated areas and the storm runoff behaviour was represented quite well by the catchment-scale application by Glusing (1995). However, the postrainfall, rather long-lasting discharge recession was not reproduced due to the lack of an adequate model component dealing with groundwater recession. Due to the generally scarce data and the complex geological conditions an addition of a distributed groundwater model as a feasible solution is rather questionable. The lessons learned from these two applications on mountain catchments are as follows: (a) A double porosity approach is appropriate for the compatible modelling of high infiltration rates during high-intensity rainfall storms and relatively slow percolation velocities during inter-storm periods. (b) Modelling overland flow during storm periods requires rainfall data input at a high temporal resolution. Averaged over long time intervals will result in a drastic underestimation of simulated runoff. (c) The reasonable modelling of lateral groundwater flow requires a separate model component. There is some evidence that semi-distributed approaches, adapted to the specific catchment conditions, might be an appropriate approach.

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Hydrological response of experimental hillslopes in the Austrian Alps under extreme precipitation conditions Kirnbauer et al. (1996) presented a study on runoff generation in the small Alpine catchment Lohnersbach located in the eastern Austrian Alps covering an area of 16 km2 and ranging between 1100 and 2200 m a.s.l. It is assumed that catchment storm runoff is mainly created through saturation-excess-overland flow. Runoff coefficients for a monitored saturation area range between 0.3 and 0.9, depending on antecedent moisture conditions and amount of precipitation during the event. For topographic reasons the size of the saturation area does not change and therefore this wide range of runoff coefficients cannot be due to the expansion and shrinkage of the saturation area. The temporal variability of the runoff coefficient can be interpreted as a consequence of microtopography in the saturation area in combination with fluctuating water levels (R. Kirnbauer, 1997, personal communication). The 2D-version was applied to this monitored saturated area of 81 m long, the slope varying from 23 % to 67 %. The simulation period was 92 days during summer and autumn 1992, with heavy precipitation during this period. So far, this application was of little success due to several model-specific and site-specific problems: (a) The hydrological condition of the hillslope mentioned can be summarized as a saturated flow dominated, steep hillslope. In conjunction with the high surface gradient of the topography, the subsurface flow processes are likely to be driven by the piezometric gradient of the subsurface catchment. This type of hydrogeological process is not part of the model applied. (b) The micro-topography of the saturation area is formed by little ponds; this brings about different surface storage and roughness conditions (due to varying water levels in the ponds) as a consequence of changing inflow from the springs. This dynamic behaviour of surface roughness is not included in the model. (c) Preferential flow plays a major role in runoff generation of these steep mountainous hillslopes. Similar situations have also been reported by Scherrer (1997) for several hillslopes in the Swiss Alps. Besides the fact that preferential flow is a fairly frequent phenomenon in mountainous environments, a commonly accepted calculation approach is still lacking. (d) Another open problem degrading the simulation results in the Lohnersbach saturation area is the influence of the boundary conditions of the individual hillslope on runoff generation. As the area considered is part of a larger mountain slope, there is substantial subsurface flow into it from the upslope region. The bottom boundary conditions of the hillslope are, in particular, usually fairly unclear. The study of the model performance in this context is still underway and the conclusions given here have a preliminary character. However, they might be valid for other Alpine environments as well. CONCLUSIONS In general, the quality of the model results depends heavily on the accuracy of the input data (and/or boundary conditions) and their spatial and temporal resolution, as


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well as on the model calibration. The soil hydraulic parameters, in particular, should be adjusted within a reasonable, i.e. physically-based range. But even given detailed data available, an optimal parameter adjusting and an error-free model comprising all relevant processes, considerable uncertainty remains. This uncertainty can be attributed mainly to the scale dependency of the model parameters and the stochastic behaviour of the hydrological processes. The inherent limitations of detailed hillslope hydrological modelling originate in the following: - There is still a lack of knowledge on how to formulate and parameterize certain processes influencing the hydrological response of a hillslope, e.g. surface crusting or sealing and saturated-unsaturated flow in preferential pathways. In many practical applications, the available data will be insufficient to satisfy the requirements of a detailed hillslope model. The soil information, in particular, and the bottom boundary conditions are known only in exceptional cases. Small variations in some state variables can cause large changes in runoff generation. However, this sensitivity is rarely a model artefact; it is rather a representation of the variability and stochasticity of the natural conditions. - Finally, the application of detailed hillslope models encounters problems similar to those faced by any other complex computer model, such as possible constraints of computer power, and the requirement of a bug-free code and a more-or-less user-friendly interface.

REFERENCES Ambroise, B. (1994) Les bassins de recherche vosgiens (The research basins in the Vosges). In: Actes du Seminar National: Du concept de BVRE à celui de zone-atelier dans les recherches menées en eaux continentales, 71-88. CEMAGREF Editions, Paris. Bronstert, A. (1994) Modellierung der AbfluBbildung und der Bodenwasserdynamik von Hângen (Modelling of runoff generation and soil water dynamics of hillslopes). Mitt, des IHW, Nr. 46, Univ. Karlsruhe. Bronstert, A. & Plate, E. J. (1997) Modelling of runoff generation and soil moisture dynamics for hillslopes and microcatchments. J. Hydrol. 198(1-4), 177-195. CSIRO (1992) TOPOG User Guide, V. 4.0. CSIRO, Div. Water Res., Canberra. Feddes, R. A., Kowalik, P.J. & Zaradny, H. (1978) Simulation of Field Water Use and Crop Yield. Simulation Monograph. PUD0C. Glusing, B. (1995) Test und Anpassung des hydrol. Modells HILLFLOW-3D im Hinblick auf eine Anwendung auf das Untersuchungseinzugsgebiet Ringelbach in den Sudvogesen (Test and adaptation of the Hillflow-3D model in the Ringelbach research basin in the southern Vosges). IHW, Univ. Karlsruhe. Glùsing, B. (1997) Anwendung des Modells H1LLFLOW auf das Forschungseinzugsgebiet Picaninny und Vergleich mit Ergebnissen des Modells TOPOG (Application of the Hillflow-3D model in the Picaninny research basin and comparison with the results obtained by the TOPOG-model). IHW, Univ. Karlsruhe. Gutknecht, D. (1996) AbfluBentstehung an Hângen—Beobachtungen und Konzeptionen (Runoff generation at hillslopes— observations and concepts). Ôster. Wasser- und Abfallwirt. 48(5/6), 134-144. Kirkby, M. (1988) Hillslope runoff processes and models. /. Hydrol. 100, 315-339. Kirnbauer, R., Pirkl, H., Haas, P. & Steidl, R. (1996) AbfluBmechanismen—Beobachtung und Modellierung (Runoff mechanisms—observations and modelling). Ôster. Wasser-und Abfallwirt. 48(1/2), 15-26. O'Loughlin, E. M. (1990) Perspectives on hillslope research. In: Process Studies in Hillslope Hydrology (ed. by M. G. Anderson & T. P. Burt), 501-516. John Wiley, Chichester, UK. Plate, E. J. (1992) Prognosemodell fur die Gewâsserbelastung durch Stofftransport aus einem kleinen lândl. Einzugsgebiet (Modelling water and solute transport in a small rural catchment). Mitt, des IHW, Nr. 41, Univ. Karlsruhe. Scherrer, S. (1997) Identifikation von AbfluBprozessen mittels kûnstlicher Niederschlâge (Identifying runoff processes by means of artificial rainfall). Mitt, der VAW, Nr. 147, ETH Zurich.