Modeling the Continental-Scale Dynamics of the Coupled Land-Surface and Atmospheric Water Balances with a Stochastic Differential Equation

Using a stochastic differential equation (SDE) approach, we examine the dynamics of the continental-scale water balance in the central United States. Whitenoise and colored-noise versions of the model are developed based on analysis of atmospheric data from the National Center for Environmental Prediction (NCEP) reanalysis project and long-term records of precipitation and soil moisture. Improved correspondence to observations is also achieved by inclusion of terms in the SDE representing both hydrodynamic and thermodynamic soil-moisture feedbacks. We show that temporally correlated (i.e., colored) atmospheric moisture flux removes the bimodality of the soil moisture probability distribution and that our colored-noise formulation successfully captures the water balance dynamics in the study region despite the absence of multiple soil moisture states. Specifically, the improved model reproduces both the autocorrelation structure and the inter-annual variability in the observations.