A Closed-Form Equation Linking Soil Moisture and Evaporation

Abstract

Estimating evaporation from surface soil moisture data poses a persistent challenge for modeling the hydrological cycle. Deriving a physics-based solution to convert single-probe soil moisture data into evaporation estimates has always been challenging. Such an equation would enhance hydrological models and remote sensing methods. In this study, we derive a closed-form analytical solution for Richards’ equation for water flux to translate single-depth single-time soil moisture data into evaporation rate. In addition, this solution links subsurface net water flux and soil moisture at each single soil depth. This solution is derived by estimating the soil moisture gradient from the temporal history of soil moisture at a single depth and assuming an exponential decay of soil moisture over time during drying periods. The proposed solution has demonstrated consistent results with HYDRUS-1D simulations for a range of soils and boundary conditions, as well as measured eddy covariance data. This model shows high performance in coarse- to fine-textured soils under free drainage and zero-flux boundary conditions. This work establishes a foundation for future research leveraging in situ and remote sensing soil moisture data to improve evaporation estimates at various spatial scales.

Prof. Dr. Kang Yu

Professor of Precision Agriculture

My research interests include precision crop farming, hyperspectral remote sensing, and AI in agriculture.