A minimal probabilistic model for soil moisture in seasonally dry climates

In seasonally dry climates, a distinct rainy season is followed by a pronounced dry season during which rainfall often makes a negligible contribution to soil moisture. Using stochastic analytical models of soil moisture to represent the effects of this seasonal change has been hindered by the need to mathematically represent the stochastic influence of wet season climate on dry season soil water dynamics. This study presents a simple process-based stochastic model for soil moisture dynamics, which explicitly models interseasonal transient dynamics while accounting for carry over soil moisture storage between the wet and dry seasons, and allows a derivation of an analytical expression for the dry season mean first passage time below a soil moisture threshold. Such crossing times pose controls on both vegetation productivity and water stress during dry summers. The new model, along with an existing model that incorporates nonzero dry season rainfall but not variability in the soil moisture condition at the start of the dry season, are tested against data from the Tonzi Ranch Ameriflux site. Both models predict first passage times well for high soil moisture thresholds, but the new model improves prediction at lower thresholds. The annual soil moisture probability distribution function (PDF) from the new model also compares well with observations.