Revisiting the thermodynamic derivation of the Penman-Monteith Equation

Abstract. The Penman‑Monteith (PM) equation is the most commonly used method for determining latent heat fluxes (λE) from vegetated land surfaces and is regarded as a best practice for calculating evapotranspiration. It is based on a general energy balance approach, in which evaporation is derived indirectly by approximating the sensible heat flux (SH). The temperature difference between the surface and the near-surface air, which drives SH and is required to compute the heat flux, is eliminated from the associated system of equations by introducing the slope of the saturation vapor pressure curve at the air temperature (s_Ta). However, in the PM equation this slope does not describe, in the original sense, a change in the thermodynamic state of a system; rather, it represents the ratio of a spatial heat and a constructed moisture potential difference between the surface and the near-surface air. In the thermodynamic derivation of the PM equation by Monteith (1965), this apparent physical inaccuracy is resolved by describing the evaporation process not anymore through classical flux‑gradient relationships but through the thermodynamic state change of the near‑surface air. This derivation, however, is based on the assumption that the sensible heat flux from the surface heats the air mass into which evaporation occurs. This heat input increases the saturation vapor pressure of the near-surface air, allowing the partitioning of SH and λE according to s_Ta. For vegetated surfaces this assumption does not hold, because the phase transition during transpiration occurs into the air inside the leaf and not into the air close to the surface, into which the sensible heat flux takes place. For the air inside a leaf, however, the sensible heat flux into the atmosphere does not constitute an energy input but rather an energy sink; therefore Monteith’s (1965) thermodynamic concept cannot be transferred to vegetated surfaces. Thus, the use of s_Ta to partition the available energy at the surface can only be physically justified for water saturated, unvegetated surfaces and the PM equation should therefore be applied only under such conditions.