Revisiting a Two‐Parameter Budyko Equation With the Complementary Evaporation Principle for Proper Consideration of Surface Energy Balance

Abstract

AbstractThe Budyko framework, widely regarded as a simple and convenient tool to synthesize catchment water balance, is often employed with the atmospheric evaporative potential (Ep) that responds to water availability over a land surface. In this study, we demonstrated how the responsiveness of Ep to soil moisture deficiency affects outcomes from a conventional Budyko equation. We combined a two‐parameter Budyko equation with the state‐of‐the‐art complementary relationship (CR) of evaporation (E), and analytically showed that the two‐parameter Budyko equation corrects Ep to the wet environment E (Ew) of the CR. Using the Budyko equation combined with the CR, we assessed runoff sensitivity to climatic and land surface changes. Results showed that the CR could become a constraint for calibrating the implicit parameter of the Budyko equation. When compared to the Turc‐Mezentsev equation with Ep, the shape parameters of the two‐parameter Budyko equation increased to regenerate an ensemble of global E data sets. Correcting Ep to Ew via the Budyko equation with CR reduced runoff elasticities to land property changes, suggesting that climatic changes are more important to changes in runoff than a prior sensitivity assessment would suggest. This study also suggests that the two‐parameter Budyko equation isolates the effect of the Ep adjustment from the shape parameter, allowing it to more properly account for surface energy availability.