Appraisal of Budyko formula in calculating long‐term water balance in humid watersheds of southern China

Abstract

AbstractThe Budyko formula for estimating the long‐term average annual evaporation is applied to calculate the long‐term water balance in 29 humid watersheds of southern China. As a result of overestimation of evaporation, the long‐term average annual runoff is underestimated, with the Nash‐Sutcliffe efficiency (NSE) at just − 17%. A one‐variable linear regression model is employed to find that the Budyko scatter and the relative errors of Budyko runoff and evaporation estimates are all closely related to the long‐term aridity index. Through combining the original Budyko formula with the different linear regression models for estimating the Budyko estimation errors, three forms of revised Budyko equation for estimating the long‐term average annual runoff are derived, with all their NSE values to be around 66%. After calibration, both one‐parameter Turc‐Pike and one‐parameter Fu equations lead to the NSE value of 60% in estimating long‐term average annual runoff. Two conclusions are made, with the first one being that, the nonparametric Budyko formula, although very intuitive and very simple, does not apply well in calculating long‐term water balance in 29 humid watersheds in southern China. The second one is that, the parametric evaporation formulae, with locally optimized parameter values, can achieve better accuracy in estimating long‐term average annual evaporation and runoff than the nonparametric Budyko evaporation formula. Copyright © 2011 John Wiley & Sons, Ltd.