Probabilistic characterization of base flows in river basins: Roles of soil, vegetation, and geomorphology

In this paper we extend previous mathematical results on the probabilistic modeling of base flows driven by spatial and temporal fluctuations of soil moisture and affected by intermittent rainfall forcings and by heterogeneous transport, soil, and vegetation properties. Rainfall is modeled as a zero-dimensional marked Poisson process with exponentially distributed intensity, and various descriptors of spatial heterogeneity are used. The master equation for the probability distribution (pdf) of the base flow (here epitomized by the mean daily flow rate in suitably sized catchments) and its moment-generating function are derived by coupling soil moisture balances with a traveltime formulation of transport. Exact solutions for the flow moments are derived in the following cases: (1) two tributary areas in parallel, (2) the rigorous extension to N subbasins, and (3) a simplified geomorphic arrangement of subbasins. Base flow statistics obtained by naive spatial averages of heterogeneous properties exhibit the same mean of the exact solution but may significantly overestimate higher-order moments. Relatively wet climate conditions seem to enhance the effects of the heterogeneity of soil, vegetation, transport, and geomorphic properties, particularly for low-stage flow regimes. The probabilistic structure of the base flow is explicitly linked to relevant climatic and geomorphologic features in addition to the spatial distribution of soil and vegetation properties, with possible ecohydrological implications on long-term water and nutrient mass balances in river basins.