Assessing the Complementary Role of Surface Flux Equilibrium (SFE) Theory and Maximum Entropy Production (MEP) Principle in the Estimation of Actual Evapotranspiration

Although evapotranspiration (ET) from the land is a key variable in Earth system models, the accurate estimation of ET based on physical principles remains challenging. Parameters used in current ET models are largely empirically based, which could be problematic under rapidly changing climatic conditions. Here, we propose a physically based ET model that estimates ET based on the surface flux equilibrium (SFE) theory and the maximum entropy production (MEP) principle. We derive an expression for aerodynamic resistance based on the MEP principle, then propose a novel ET model that integrates the SFE model and the MEP principle. The proposed model, which is referred to as the SFE-MEP model, becomes equivalent to the MEP state in non-equilibrium conditions when turbulent mixing is weak and the land surface is dry. Under conditions meeting land-atmosphere equilibrium, the SFE-MEP model is similar to ET estimation based on the SFE model. This blended nature of the SFE-MEP ET model allows accurate ET estimation for most inland regions by overcoming the ET overestimation issue of the SFE model in dry conditions. As a result, the SFE-MEP model significantly improves the performance of SFE ET estimation, particularly for arid regions. The proposed model and its high accuracy of ET estimation enable novel insight into various Earth system models as it does not require any empirical parameters and only uses readily obtainable meteorological variables including reference height air temperature, relative humidity, available energy, and radiometric surface temperature.