Linking the Budyko framework with the complementary evaporation principle for proper consideration of surface energy availability

The widely-used Budyko framework synthesizes the competition between water and energy availability simply using climatological mean precipitation (P) and potential evaporation (PE). While PE within the Budyko framework is often regarded as the atmospheric evaporative demand (AED), AED can substantially differ from PE assuming ample water availability due to its responsive behavior to soil moisture. This could violate the independence assumption between P and PE underpinning the Budyko framework, potentially leading to ill-posed parameterization of land-surface properties. Here, we showed that the use of AED as PE in a Budyko equation could significantly disturb a global runoff sensitivity assessment to climatic and land-property changes. By linking a two-parameter Budyko equation and the complementary evaporation principle (CEP), we found that climatic changes play a more important role in altering runoff than a prior assessment would suggest. This study also suggests that linking the Budyko equation with CEP can isolate the responsiveness of AED to soil moisture, allowing more proper consideration of surface energy balance.