The Impact of Land–Atmosphere Interactions on the Temporal Variability of Soil Moisture at the Regional Scale

This study examines the impact of the nonlinear dynamics of soil-moisture feedbacks to precipitation on the temporal variability of soil moisture at the regional scale. It is a modeling study in which the large-scale soil-water balance is first formulated as an ordinary differential equation and then recast as a stochastic differential equation by incorporating colored noise representing the high-frequency temporal variability and correlation of precipitation. The underlying model couples the atmospheric and surface-water balances and accounts for both precipitation recycling and precipitation-efficiency feedbacks, which arise from the surface energy balance. Based on the governing Fokker–Planck equation, three different analytical solutions (corresponding to differing forms and combinations of feedbacks) are derived for the steady-state probability density function of soil moisture. Using NCEP–NCAR reanalysis data, estimates of potential evapotranspiration, and long-term observations of precipitation, streamflow, and soil moisture, the model is parameterized for a 5° 5° region encompassing the state of Illinois. It is shown that precipitationefficiency feedbacks can be significant contributors to the variability of soil moisture at the regional scale. Precipitation recycling, on the other hand, increases the variability by a negligible amount. For all feedback cases, the probability density function is unimodal and nearly symmetric. The analysis concludes with an examination of the dependence of the shape of the probability density functions on spatial scale. It is shown that the associated increases in either the correlation time scale or the variance of the noise will produce a bimodal distribution when precipitation-efficiency feedbacks are included. However, the magnitudes of the necessary increases are of an unrealistic magnitude.