An analytical model of evaporation efficiency for unsaturated soil surfaces with an arbitrary thickness

Analytical expressions of evaporative efficiency over bare soil (defined as the ratio of actual to potential soil evaporation) have been limited to soil layers with a fixed depth and/or to specific atmospheric conditions. To fill the gap, a new analytical model is developed for arbitrary soil thicknesses and varying boundary layer conditions. The soil evaporative efficiency is written [0.5 − 0.5 cos(πθL/θmax)] P with θL being the water content in the soil layer of thickness L, θmax the soil moisture at saturation and P a function of L and potential soil evaporation. This formulation predicts soil evaporative efficiency in both energy-driven and moisture-driven conditions, which correspond to P < 0.5 and P > 0.5 respectively. For P = 0.5, an equilibrium state is identified when retention forces in the soil compensate the evaporative demand above the soil surface. The approach is applied to in situ measurements of actual evaporation, potential evaporation and soil moisture at five different depths (5, 10, 30 and 60/100 cm) collected in summer at two sites in southwestern France. It is found that (i) soil evaporative efficiency cannot be considered as a function of soil moisture only, since it also depends on potential evaporation, (ii) retention forces in the soil increase in reaction to an increase of potential evaporation and (iii) the model is able to accurately predict soil evaporation process for soil layers with an arbitrary thickness up to 100 cm. This new model representation is expected to facilitate the coupling of land surface models with multi-sensor (multi-sensing-depth) remote sensing data.