Coupled stochastic dynamics of water table and soil moisture in bare soil conditions

The soil water content plays a fundamental role in a number of important environmental processes, including those involved in the water cycle, vegetation dynamics, soil biogeochemical cycles, and land-atmosphere interactions. Despite the recent efforts spent in the analytical modeling of the stochastic soil moisture dynamics in dryland ecosystems, the probabilistic characterization of the soil water balance in groundwater dependent environments is still missing, due to the complexity arising from the existence of shallow aquifers and capillary rise. This paper makes a first step in the direction of studying the stochastic soil water balance in groundwater dependent systems. An analytic probabilistic framework is developed for the modeling of soil moisture dynamics at the daily timescale for the case of bare soil conditions and in the presence of a shallow water table. This framework accounts for random rainfall occurrence, water table fluctuations, capillary rise, and soil evaporation. The stochastic soil water balance equation is analytically solved in the steady state, and the probability density functions of water table depth, soil moisture (as a function of depth), and evaporation are obtained and discussed for a variety of climate conditions and soil properties.