Surface Flux Equilibrium Theory Explains an Empirical Estimate of Water‐Limited Daily Evapotranspiration

Abstract

Abstract Evapotranspiration (ET) plays a central role in the water, energy, and carbon cycles but is difficult to model and estimate due to its dependence on the heterogeneous land surface. Recent studies suggest that standard weather station atmospheric observations alone may be sufficient to estimate ET. This is surprising since ET over land is often strongly constrained by the land surface, for instance, by water limitation. While these studies have been empirically successful, a physical explanation for why this is possible has been lacking. Here, we provide a physical explanation for why one of these approaches—the ET from Relative Humidity at Equilibrium (ETRHEQ) method—works, using a simple model of a steady‐state idealized atmospheric boundary layer. We show that, across a wide range of plausible parameter values, this model reproduces ETRHEQ, suggesting that it contains the essential physics that lead to ETRHEQ. We derive a closed‐form expression for ETRHEQ at steady state and use it to show that ETRHEQ can be explained in terms of the near‐surface relative humidity (RH) budget of the idealized model: in particular, it is equivalent to assuming a balance between surface moistening and heating terms in the RH budget. Negative feedbacks between surface fluxes (constrained by the surface energy budget) and atmospheric temperature and humidity mean that these terms typically balance, explaining the empirical success of ETRHEQ over a wide range of conditions. We define this state—in which the moistening and heating terms balance in the RH budget—as “surface flux equilibrium.”

Keywords

• evapotranspiration
• land‐atmosphere coupling
• boundary layer meteorology
• hydrometeorology
• water stress