An analytical model for estimation of land surface net water flux from near-surface soil moisture observations

The accurate determination of land surface water fluxes at various spatiotemporal scales remains a challenge in hydrological sciences. It is intuitive that land surface net water flux (i.e., infiltration minus evapotranspiration) directly affects near-surface soil moisture. However, there exists no hydrological model suitable to calculate net water flux based on measured near-surface soil moisture data. This is a consequence of the mathematical structure of existing models that use 'boundary conditions' to determine 'internal conditions', whereas what is needed is a model amenable to use near-surface soil moisture data (an internal condition) to determine the surface water flux (a boundary condition). To pursue the idea of utilizing remotely-sensed or in situ (i.e., sensor networks) near surface soil moisture data for estimation of net water flux, we derived an analytical model via inversion of Warrick's 1975 analytical solution to the linearized Richards' equation for arbitrary time-varying surface flux boundary conditions. The applicability of the new analytical solution was evaluated based on actual water flux observations as well as HYDRUS-1D simulations for four vastly different sites in Arizona, California, Idaho, and Indiana. Our results demonstrate that the proposed model reasonably captures net water flux variations in natural settings, including layered and vegetated soils, especially at larger time scales (e.g., monthly). While the model works for a wide range of climatic conditions, the prediction accuracy is somewhat lower for extreme dry or wet conditions. A major advantage of the new model is that it does not require calibration, which provides an unprecedented opportunity for large scale estimation of land surface net water flux using remotely sensed near-surface soil moisture observations.