Towards understanding the intrinsic variations of the Priestley-Taylor coefficient based on a theoretical derivation

Abstract. Priestley-Taylor (PT) coefficient (α) is generally set as a constant value or fitted as an empirical function of environmental variables, and it can bias the evaporation estimation or hydrological projections. This study derives a theoretical equation for α using an atmospheric boundary layer model, which shows that α is a function of air temperature (T) and specific humidity (Q). More importantly, the derived expressions can well estimate the sensitivity of α to T and Q, that is, dα/dT and dα/dQ, compared to water surface observations. α is generally negatively associated with T and Q, and its changes are fundamentally controlled by T and modulated by Q. Based on climate model data, it is shown that the variation of α to T (negative association) is of great importance for long-term hydrological predictions. For practical and broad uses, a lookup graph is also provided to directly find the dα/dT and dα/dQ values. Overall, the derived expression gives a physically clear and straightforward approach to quantify changes in α, which is essential for PT-based hydrological simulation and projections.