Controlling factors of errors in the predicted annual and monthly evaporation from the Budyko framework

The Budyko framework (BF) has been used to predict evaporation (E) at annual or monthly time scales, but few studies have analyzed the errors in the predicted E in a systematic manner. This study develops an error-decomposition framework which expresses the errors in the BF-predicted annual and monthly E as a function of (1) the anomalies (i.e. deviations from the long-term mean) of precipitation (P), potential evapotranspiration (PET), runoff (R) and catchment water storage change (ΔS), (2) the (long-term) mean water storage change, and (3) the mean difference between the predicted and actual E. The error variance of BF-predicted E can be decomposed into the variance and covariance terms of P, PET, R and ΔS. The relative contribution of each of these controlling factors to the total error variance of E are evaluated at 14 major river basins in China with the mean annual aridity index ranging between 0.55 and 11.78. It is found that climatic factors (P and PET) and catchment responses (R and ΔS) play different roles in the errors of predicted E among diverse climates of 14 basins. Under the humid (energy-limited) condition, the variance and covariance terms of P, PET, R and ΔS are comparably important in the contribution to the prediction error variance of E. In contrast, under the arid (water-limited) condition the error variance of predicted E is dominated by the magnitude of ΔS anomalies. Results of this study suggest that the incorporation of ΔS into BF can improve the predictability of annual and monthly E more under the arid climates than humid climates.