An analytical model for soil-atmosphere feedback

Soil-atmosphere feedback is a key for understanding the hydrological cycle and the direction of potential system changes. This paper presents an analytical framework to study the interplay between soil and atmospheric moisture, using as input only the boundary conditions at the upstream end of trajectory, assuming advective moisture transport with average wind speed along this trajectory and vertical moisture exchange with the soil compartment of uniform vertical properties. Precipitation, evaporation from interception and runoff are assumed to depend through simple functional relationships on the soil moisture or the atmospheric moisture. Evaporation from soil moisture (including transpiration) depends on both state variables, which introduces a nonlinear relationship between the two compartments. This nonlinear relationship can explain some apparently paradoxical phenomena such as a local decrease of precipitation accompanied by a runoff increase. The solutions of the resulting water balance equations correspond to two different spatial moisture regimes showing either an increasing or a decreasing atmospheric moisture content along a trajectory starting at the coast, depending on boundary conditions and parameters. The paper discusses how different model parameters (e.g. time scales of precipitation, evaporation or runoff) influence these regimes and how they can create regime switches. Such an analysis has potential to anticipate the range of possible land use and climate changes or to interpret the results of complex land-atmosphere interaction models. Based on derived analytical expressions for the Horton index, the Budyko curve and a precipitation recycling ratio, the analytical framework opens new perspectives for the classification of hydrological systems.