An analytical generalization of Budyko framework with physical accounts of climate seasonality and water storage capacity

Abstract. The Budyko framework is an effective and widely used method for describing long-term water balance in large catchments. However, it only considers the limits of water and energy in evaporation (E), and ignores the impacts of climate seasonality and water storage capacity (Sc), resulting in errors for Mediterranean climate and catchments with small Sc. Here we combined the Ponce-Shetty model with Budyko hypothesis, and analytically generalized Budyko framework with physical accounts of climate seasonality and Sc. Precipitation (P), potential evaporation (PE), and Sc are used to represent the limits of water, energy, and space for E, respectively. Our results show that previous Budyko-type equations can be treated as special cases of generalized Budyko-type equations with uniform P and PE and infinite Sc. The new generalized equations capture the observed decrease in E due to asynchronous P and PE and small Sc, and perform better than the Budyko-type equations with varying parameters in the contiguous United States with fewer parameters. Overall, our generalization of Budyko framework improves the robustness and accuracy for estimating mean annual E with the aid of physical interpretation, and will facilitate water balance assessment at regional to global scales.