Does the Budyko curve reflect a maximum-power state of hydrological systems? A backward analysis

摘要

Almost all catchments plot within a small envelope around the Budyko curve.This apparent behaviour suggests that organizing principles may play a rolein the evolution of catchments. In this paper we applied the thermodynamicprinciple of maximum power as the organizing principle.In a top-down approach we derived mathematical formulations of the relationbetween relative wetness and gradients driving run-off and evaporation for asimple one-box model. We did this in an inverse manner such that, when theconductances are optimized with the maximum-power principle, the steady-statebehaviour of the model leads exactly to a point on the asymptotes of theBudyko curve. Subsequently, we added dynamics in forcing and actualevaporation, causing the Budyko curve to deviate from the asymptotes.Despite the simplicity of the model, catchment observations comparereasonably well with the Budyko curves subject to observed dynamics inrainfall and actual evaporation. Thus by constraining the model that has been optimized with themaximum-power principle with the asymptotes of the Budyko curve, wewere able to derive more realistic values of the aridity and evaporationindex without any parameter calibration.Future work should focus on better representing the boundary conditions ofreal catchments and eventually adding more complexity to the model.