Prediction of the weighted-mean soil water diffusivity in supporting the falling rate stage of evaporation

Abstract

Daily soil evaporation from drying soil can be described as isothermal linear diffusion process, resulting in a simple equation for estimating soil evaporation rate. However, determining soil water diffusivity and subsequently the crucial parameter of weighted-mean diffusivity, essential for estimating soil evaporation rate, is challenging and time-consuming. In this paper, the soil water diffusivity was re-evaluated by considering the effect of film flow, a phenomenon often overlooked but recently argued by Wang et al. (2019, https://doi.org/10.1029/2019WR025003) as the dominant process in the falling rate stage of evaporation. Theoretical derivation reveals a universal relationship between soil water diffusivity and matric potential, independent of soil types. Additionally, soil water diffusivity can be expressed in the form of an exponential function, a form commonly assumed empirically in the literature. Testing with various datasets suggests that the theoretically derived soil water diffusivity generally agrees closely with observations for matric potentials less than about −1 m, wherein the diffusivity accounting for capillary flow shows significant underestimation. Furthermore, a simple function is derived for estimating the weighted-mean diffusivity, enabling a direct estimation of soil evaporation rates in the falling rate stage. Testing with various data sets of different soil types and ambient conditions generally demonstrates close agreements between the estimated soil evaporation rates and observations, indicating that the developed method provides a robust estimation of the weighted-mean soil water diffusivity. When the initial matric potential of the linear diffusion process of drying is higher than about −1 m, which usually occurs under very high atmospheric demand conditions or for very coarse-textured soils, however, the effects of capillary flow were found to be important and need consideration. The effects of vapor diffusion were also discussed and found to have a negligible impact on the estimation of weighted-mean soil water diffusivity.