A stochastic‐conceptual analysis of rainfall‐runoff processes on a hillslope

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Abstract
A stochastic‐conceptual mathematical model of hydrologie processes on a hillslope is utilized to investigate the influence of the spatial stochastic properties of the hillslope parameters on the statistical properties of the resulting runoff events. The model utilizes a stochastic rainfall generator and allows the generation of overland flow by both the Horton mechanism and the Dunne mechanism. Streamflow statistics are determined on the basis of an event‐based Monte Carlo simulation. The simulated hillslope runoff events are individually and statistically representative of actual runoff events reported in the literature from experimental watersheds. Results indicate that each of the parameters representing the spatial stochastic properties of the hydraulic conductivity distribution on a hillslope exerts an important influence on the statistical properties of runoff events arising from a hillslope under a given climatic regime. The mean value is the most important parameter; the standard deviation is quite important; the autocorrelation function is the least important. If one tries to represent a heterogeneous hillslope by an ‘equivalent’ homogeneous hillslope, the statistical properties of the predicted runoff generated from a given stochastic sequence of storm events may be greatly in error. Results of the simulations reported in this paper suggest that the distribution of hydraulic conductivities over a watershed should be included in parametric representations of the unit hydrograph, in conceptual predictions of flood exceedance probabilities, and in physically based assessments of the autocorrelation structure of the Streamflow sequences. Results of this study also infer a close relationship between climate, hydraulic conductivity, and geomorphic landform development.