Characteristics of potential evapotranspiration and its estimation from hydrological observation in the Budyko framework

Abstract. Potential evapotranspiration (E_P) is one of input variables in the Budyko framework, yet the diverse estimation methods cause discrepancies in its values. This raises a question about whether there exists a kind of E_P specially satisfying the Budyko framework. Based on the relationships among variables in the Budyko models and the deterministic value of E_P with known mean annual precipitation and runoff, we uncover the characteristics of E_P and its estimation method from hydrological observation in the Budyko framework. Accordingly, we introduce the concept of Budyko E_P. The non-parametric and parametric Budyko equations correspond to the reference and the adjustable Budyko E_P, respectively. For the Model Parameter Estimation Experiment catchments, the reference Budyko E_P is higher in the central and southern contiguous United States and lower in the northeastern and northwestern regions. The linear conversion functions are established from the meteorological E_P to the reference and optimized adjustable Budyko E_P separately. When estimating actual evapotranspiration (E) by Budyko models with the same data resources, employing two conversion functions with the meteorological E_P reduces the mean absolute error of E estimation by 33 % and 35 %, respectively, compared to using the optimized Budyko model parameter with the meteorological E_P. Further investigation suggests that the complementary relationship for evapotranspiration is one factor affecting the expression of the region-specific conversion function. Future in-depth exploration of the spatiotemporal differences in conversion functions will advance E estimation and the applications of Budyko E_P.