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

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