Basin-scale soil moisture dynamics and the probabilistic characterization of carrier hydrologic flows: Slow, leaching-prone components of the hydrologic response

This paper aims at a first theoretical step toward the probabilistic modeling of nutrient contents in catchment-scale soil states. To this end, we wish to characterize probabilistically the slow, leaching-prone component of the hydrologic response, which chiefly determines the export of dissolved nutrients from soil, as a result of interactions between mobile/immobile phases along the pathways of runoff formation. The influence of temporal fluctuations of soil moisture on slow components of the catchment-scale runoff is thus investigated by means of a stochastic framework, where the intermittency of rainfall is modeled by a marked Poisson process with exponentially distributed intensities. The probability distribution of the relevant runoff components and its moment-generating function are derived by coupling a stochastic description of soil moisture dynamics with a suitably simplified flow model. New exact solutions are achieved in two different cases, namely, when (1) infiltration rates are assumed proportional to the incoming rainfall depths, i.e., when surface runoff is negligible, and (2) infiltration rates are upwardly bounded by episodical soil saturations (e.g., for shallow soils). In both cases, the derived probability density functions of slow components of runoff are well described by a Gamma distribution, whose shape is 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 slow components of runoff with simple (pluviometric, soil, vegetation, and geomorphologic) macroscopic parameters, with implications for the ecohydrology of fluvial systems and for drought prediction in ungauged basins. Comparisons with Monte Carlo simulations of a more detailed rainfall-runoff model to a real catchment located in northeastern Italy suggest the ability of the approach proposed to capture the main features of runoff probability distributions in heterogeneous catchments.