Estimating the sensitivity of the Priestley–Taylor coefficient to air temperature and humidity

Abstract. The Priestley–Taylor (PT) coefficient (α) is generally set as a constant value or is fitted as an empirical function of environmental variables, and it can bias the evaporation estimation or hydrological projections under global warming. By using an atmospheric boundary layer model, this study derives a theoretical and parameter-free equation for estimating α as a function of air temperature (T) and specific humidity (Q). With observations from several waterbodies and non-water-limited land sites, we demonstrate that, in addition to estimating the value of α well, the derived expressions can also capture the sensitivity of α to T and Q, that is, dα/dT and dα/dQ. α is generally negatively associated with T and Q, in which regard T plays a more fundamental role in controlling α behaviors. Based on climate model data, we further show that this negative relationship between α and T is of great importance for long-term hydrological predictions. We also provide a lookup graph for practical and broad uses to directly find the values of dα/dT and dα/dQ under specific conditions. 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.