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Towards a unified understanding: the linkage of MaxEnt, ETRHEQ, and SFE Models in estimating evapotranspiration
  • Yi Wang,
  • Richard Michael Petrone,
  • Mazda Kompanizare
Yi Wang
University of Waterloo

Corresponding Author:[email protected]

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Richard Michael Petrone
University of Waterloo
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Mazda Kompanizare
University of Saskatchewan
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The maximum information entropy production model (MaxEnt), the relative humidity at equilibrium approach (ETRHEQ), and the Surface Flux Equilibrium model (SFE) are the three effective parsimonious models to estimate evapotranspiration. No attempts have been made to investigate their congruence, distinctions, or potential complementarity. Our mathematical analysis demonstrates that minimizing the dissipation function of energy fluxes in MaxEnt is equivalent to minimizing the vertical variance of RH in ETRHEQ. The effectiveness of both MaxEnt and ETRHEQ lies in the fact that far-from-equilibrium ecosystems progress toward a steady state (the SFE state) by minimizing dissipation. This tendency is manifested through the vertical variance of RH. The connection between MaxEnt, ETRHEQ, and SFE 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 MaxEnt and ETRHEQ share a common physical foundation, 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 hydrometeorological 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. Delving into the precise computation of dissipation and entropy production for energy fluxes at different temporal and spatial scales presents an appealing avenue for prospective research.
21 Dec 2023Submitted to ESS Open Archive
27 Dec 2023Published in ESS Open Archive