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Abstract. An alternative to spatial distribution is presented for physically based process modeling of catchment flow and solute transport. The approach is based on an integral relation for catchment streamflow which describes the accumulation through the stream network of the hillslope contributions. This relation is redefined from integration with respect to position along the stream to an integral that is with respect to the physical properties determining the hillslope flow and transport with probability distributions to represent the range of parameter values and areas associated with these. Since the integrand is now a relatively smooth function of the variables of integration, standard numerical integration can be used to evaluate the catchment totals. The assumptions allowing this redefinition are that hillslope hydrology is primarily determined by driving forces that are local to the hillslope and that catchment flow can be lumped in time so that streamflow routing is not required. The interpolation of the integrand involved in the numerical integration results in significant savings over physically based spatially distributed catchment flow and transport models. The methodology is tested through application to an irrigated catchment where model simulations of flow and transport were found to be in close agreement with those observed.

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