https://doi.org/10.1029/2023WR036910

Wang, Y., Petrone, R.M., Kompanizare, M. (2024) Towards a unified understanding: the linkage of MaxEnt, ETRHEQ, and SFE Models in estimating evapotranspiration, Water Resources Research, https://doi.org/10.1029/2023WR036910

The maximum information entropy production model (MaxEnt), the relative humidity at equilibrium approach (ETRHEQ), and the Surface Flux Equilibrium model (SFE) are three recently developed models to estimate evapotranspiration. Although the connection between ETRHEQ and SFE is evident, no attempts have been made to investigate the congruence, distinctions, or potential complementarity between the two models and MaxEnt. Our mathematical analysis demonstrates that minimizing the vertical variance of RH in ETRHEQ is equivalent to minimizing the dissipation function of energy fluxes in MaxEnt, under the assumption of the same eddy diffusivity of heat and water vapor and with a specific expression for the ratio between the thermal inertia terms for H and LE. The connection between ETRHEQ, SFE, and MaxEnt is independent of Monin-Obukhov similarity theory (MOST)’s extremum solution, and MOST's extreme solution can be viewed as equivalent to introducing a constant correction factor to account for atmospheric stability. While ETRHEQ and MaxEnt can be united within a single hydrometeorological framework, they diverge in their approaches to modeling evapotranspiration, particularly in how they address the roles of vegetation and land surface heterogeneity. More importantly, the unified framework suggests that turbulence fluxes within the atmospheric boundary layer adhere to the principles of maximum information entropy production. The way in which dissipation, along with its associated entropy production, is established using information entropy theory deviates from traditional thermodynamic entropy formulations. Exploring the connection between thermodynamic and information entropy and developing proper formulations of dissipation for energy fluxes presents an appealing avenue for prospective research.

This paper seeks to establish a common theory for explaining the effectiveness of the maximum information entropy production model (MaxEnt), the relative humidity at equilibrium approach (ETRHEQ), and the Surface Flux Equilibrium model (SFE) in estimating evapotranspiration over a wide range of conditions. It uncovers that under reasonable assumptions, ETRHEQ’s method in terms of minimizing the vertical variance in relative humidity is equivalent to MaxEnt’s approach to minimizing dissipation. The united theory suggests that the movement of air and energy in the lower atmosphere follows the principles of maximum information entropy production, a concept that is a bit different from traditional ideas of entropy in thermodynamics. Looking into how thermodynamic entropy and information entropy are connected and figuring out the right way to calculate dissipation and entropy production for energy flux could lead to new insights in atmospheric science and land-atmosphere interactions.