Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

[摘要] The Budyko framework posits that a catchment's long-termmean evapotranspiration (ET) is primarily governed bythe availabilities of water and energy, represented by long-term meanprecipitation ( P ) and potential evapotranspiration(PET), respectively. This assertion is supported bythe distinctive clustering pattern that catchments take in Budyko space.Several semi-empirical, nonparametric curves have been shown to generallyrepresent this clustering pattern but cannot explain deviations from thecentral tendency. Parametric Budyko equations attempt to generalize thenonparametric framework, through the introduction of a catchment-specificparameter ( n or w ) . Prevailing interpretations of Budyko curves suggestthat the explicit functional forms represent trajectories through Budykospace for individual catchments undergoing changes in the aridity index, PET P , while the n and w values representcatchment biophysical features; however, neither of these interpretationsarise from the derivation of the Budyko equations. In this study, wereexamine, reinterpret, and test these two key assumptions of the currentBudyko framework both theoretically and empirically. In our theoreticaltest, we use a biophysical model for ET to demonstrate that n and w values can change without invoking changes in landscape biophysicalfeatures and that catchments are not required to follow Budyko curvetrajectories. Our empirical test uses data from 728 reference catchments inthe United Kingdom (UK) and United States (US) to illustrate that catchments rarelyfollow Budyko curve trajectories and that n and w are not transferablebetween catchments or across time for individual catchments. Thisnontransferability implies that n and w are proxy variables for ET P , rendering the parametric Budyko equationsunderdetermined and lacking predictive ability. Finally, we show that theparametric Budyko equations are nonunique, suggesting their physicalinterpretations are unfounded. Overall, we conclude that, while the shape ofBudyko curves generally captures the global behavior of multiple catchments,their specific functional forms are arbitrary and not reflective of thedynamic behavior of individual catchments.

[学科分类] 妇产科学