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

摘要

This paper aims at a first theoretical step toward the probabilistic modeling of nutrientcontents in catchment-scale soil states. To this end, we wish to characterizeprobabilistically the slow, leaching-prone component of the hydrologic response,which chiefly determines the export of dissolved nutrients from soil, as a result ofinteractions between mobile/immobile phases along the pathways of runoff formation.The influence of temporal fluctuations of soil moisture on slow components of thecatchment-scale runoff is thus investigated by means of a stochastic framework, where theintermittency of rainfall is modeled by a marked Poisson process with exponentiallydistributed intensities. The probability distribution of the relevant runoff components andits moment-generating function are derived by coupling a stochastic description of soilmoisture dynamics with a suitably simplified flow model. New exact solutions areachieved in two different cases, namely, when (1) infiltration rates are assumedproportional 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 shallowsoils). In both cases, the derived probability density functions of slow components ofrunoff are well described by a Gamma distribution, whose shape is controlled by the ratiobetween the runoff frequency and the inverse of the mean residence time of subsurfaceflow. The framework developed allows one to link the probabilistic structure of slowcomponents of runoff with simple (pluviometric, soil, vegetation, and geomorphologic)macroscopic parameters, with implications for the ecohydrology of fluvial systems and fordrought prediction in ungauged basins. Comparisons with Monte Carlo simulations of amore detailed rainfall-runoff model to a real catchment located in northeastern Italysuggest the ability of the approach proposed to capture the main features of runoffprobability distributions in heterogeneous catchments.