Derivation of the Penman–Monteith Equation with the Thermodynamic Approach. I: A Review and Theoretical Development

Abstract

A review of the derivation of the Penman–Monteith equation, with the thermodynamic approach of Monteith, is presented. Evapotranspiration (henceforth referred to simply as evaporation) is described as a process consisting of a pair of formal thermodynamic subprocesses (adiabatic cooling and diabatic heating) that leads to changes in the energy states of the ambient air in ways that are readily quantifiable. The Penman–Monteith equation is derived in two steps. As an initial approximation, first a form of the equation that models evaporation into a quiescent ambient air, from a wet source/sink surface, is developed based on thermodynamic equations of state applied to a suitably defined system. In a subsequent step, resistance parameters are introduced into the basic equations, accounting for the dynamic effects of wind-surface interactions and those of (bulk) canopy system effects on evaporation, leading to the Penman–Monteith equation. Although less compact than the conventional approach, the thermodynamic approach to the derivation of the Penman–Monteith equation exhibits a benefit of revealing key assumptions and concepts that are not explicit in the conventional approach. The initial step of the thermodynamic formulation accentuates the notion that the Penman–Monteith equation is fundamentally a description of the process of vapor and heat transfer between a wet source/sink surface and a stationary ambient air. The subsequent step, on the other hand, emphasizes the fact that wind and crop effects on evaporation are taken into account in an approximate sense. The thermodynamic approach also shows that evaporation is essentially a process driven by energy supply and as such, each term of the Penman–Monteith equation represents a separate heat source for evaporation. Furthermore, the approach reveals some useful mathematical/physical attributes of the key parameters of the Penman–Monteith equation. The derivation here emphasizes basic assumptions and mathematical/physical interpretations of results and fills conceptual gaps left from the original discussion. The resultant equations for latent heat flux, sensible heat flux, and the final air temperature represent a coupled set. Thus, numerical solutions to this system of equations are presented and evaluated in a companion manuscript.