Potential evapotranspiration depends on precipitation and runoff in a catchment at the mean annual scale

As a proxy for atmospheric evaporative demand, potential evapotranspiration (EP) is usually estimated by meteorologic elements such as radiation, temperature, and vapor pressure. We investigate the controlling factors of EP from the perspective of catchment water balance. Through analyzing the relationships and constraint conditions of the variables in the Budyko framework and the generalized proportionality hypothesis (GPH), we demonstrate that the mean annual EP depends on precipitation (P) and runoff (Q) and the information of EP is contained in the water balance process. Further, we propose the Budyko-based and GPH-based hydrological approaches for EP estimation and obtain the hydrological EP for the MOPEX catchments. Significant linear relationships exist between the hydrological EP and the commonly used meteorological EP, i.e., the Penman EP (EP-Pen), Priestley-Taylor EP (EP-PT), and Hargreaves-Samani EP (EP-HS). Specifically, four hydrological EP are more consistent with EP-Pen among three meteorological EP, and the Budyko-based hydrological EP are more closely related to meteorological EP than the GPH-based one. This study enriches the EP estimation methods and provides new insight into the catchment water balance from the connection between EP and hydrologic elements. (Supported by Project 41971049 of NSFC).