Modelliing evaporation from soil profiles

Evaporation is a significant part of the water cycle and the main process for water vapor exchange between Earth's surface and atmosphere. Evaporation from bare soil consists of two main stages: stage 1, with a relatively high and often steady evaporation rate that is controlled mainly by atmospheric conditions, and stage 2, with lower and exponentially decreasing evaporation rates that are limited by the diffusive nature of the vapor flow and the hydraulic properties of the drying medium. In dry or drought conditions that are characterized with long dry spells, stage 1 is short and during stage 2 water is depleted from the top near-surface soil, forming a dry soil layer (DSL), where water flows in vapor phase only. Measuring bare soil evaporation over larger areas is challenging due to the natural heterogeneity. These measurements become even more challenging under dry conditions, due to the equipment needed for capturing low fluxes under extremely high liquid water potentials and equivalent vapor pressures. Therefore, predictive tools are essential for estimation of soil evaporation. To date, modeling of this transient evaporation process is limited, mainly because it either requires sophisticated numerical models that account for its complexities or relies on analytical solutions that are too simplistic to capture its dynamics.
We present an analytical model that accounts for the main mechanisms of the evaporation process, but is relatively simple in its construction. The governing mechanisms during this dynamic process are captured by accounting for the hydraulic properties of the drying medium, the characteristic features of the medium that control water flow, the atmospheric forcing, and the partitioning between the liquid and vapor phases of the water within the drying profile. We validate this simplified approach using data from a numerical model and from evaporation experiments in different soil types, under various ambient conditions. In addition to depicting evaporation rates and the cumulative loss of water over time, we demonstrate the effect of soil hydraulic properties and their heterogeneity on the evaporation process. Additionally, we show how the model predicts the spatiotemporal partitioning between water (liquid and vapor) phases, with specific attention to the DSL that develops during longer periods of evaporation, with the corresponding downward migration of the evaporative front.