Author(s): Botter Gianluca; Porporato Amilcare; Rodriguez-Iturbe Ignazio; Rinaldo Andrea
Linked Author(s): Andrea Rinaldo
Keywords: Stochastic models; Water budget; Soil moisture; Baseflows; Eco-hydrology
Abstract: River basins transforms rainfall into runoff by means of complex eco-hydrological processes operating at different spatial and temporal scales. The pronounced temporal variability of runoff thus reflects the random characters of key environmental conditions (e. g., stochastic meteorologic forcings, heterogeneous transport processes). The influence of spatial and temporal fluctuations of soil moisture on the base flow is investigated in this paper by means of a stochastic framework, where the intermittency of precipitation is handled by modelling the incoming rainfall rates as a marked Poisson process with exponentially distributed intensities. The probability distribution function (pdf) of the base flow and/or its moment generating function are derived by coupling a stochastic description of soil moisture dynamics with a simplified flow model based on the formulation of transport via the residence time distribution. Exact solutions are here achieved in a simplified, lumped framework where the basin is characterized by spatially averaged soil, vegetation and transport properties. In particular, we investigate in this note the case of negligible surface runoff, which corresponds to neglect the upper bound of the infiltration rates due to the finite soil storage capacity. The probability density function (pdf) of the slow components of runoff (i. e., of the base flows) is shown to be Gamma distribution, whose shape is chiefly controlled by the ratio between the runoff frequency and the inverse of the mean residence time of subsurface flow. The framework developed allows one to link the probabilistic structure of the slow component of runoff (i. e., base flow) with relatively simple (pluviometric, soil, vegetation and geomorphologic) macroscopic parameters with a clear physical meaning. The framework developed can also include the effect of heterogeneity of soil, vegetation and morphological features and is deemed to have relevant implications for the eco-hydrology of fluvial systems and for drought prediction in ungauged basins.