Towards a unified understanding: the linkage of MaxEnt, ETRHEQ, and SFE
Models in estimating evapotranspiration
Abstract
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.