Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

Abstract. The Budyko framework posits that a catchment's long-term mean evapotranspiration (ET) is primarily governed by the availabilities of water and energy, represented precipitation (P) potential (PET), respectively. This assertion supported distinctive clustering pattern catchments take in space. Several semi-empirical, nonparametric curves have been shown to generally represent this but cannot explain deviations from central tendency. Parametric equations attempt generalize framework, through introduction catchment-specific parameter (n or w). Prevailing interpretations suggest explicit functional forms trajectories space for individual undergoing changes aridity index, PETP, while n w values catchment biophysical features; however, neither these arise derivation equations. In study, we reexamine, reinterpret, test two key assumptions current both theoretically empirically. our theoretical test, use model ET demonstrate can change without invoking landscape features are not required follow curve trajectories. Our empirical uses data 728 reference United Kingdom (UK) States (US) illustrate rarely transferable between across time catchments. nontransferability implies proxy variables ETP, rendering parametric underdetermined lacking predictive ability. Finally, show nonunique, suggesting their physical unfounded. Overall, conclude that, shape captures global behavior multiple catchments, specific arbitrary reflective dynamic