Linking the complementary evaporation relationship with the Budyko framework for ungauged areas in Australia

Abstract

Abstract. While the calibration-free complementary relationship (CR) has performed excellently in predicting terrestrial evapotranspiration (ETa), how to determine the Priestley–Taylor coefficient (αe) is a remaining question. In this work, we evaluated this highly utilizable method, which only requires atmospheric data, with in situ flux observations and basin-scale water-balance estimates (ETwb) in Australia, proposing how to constrain it with a traditional Budyko equation for ungauged locations. We found that the CR method with a constant αe transferred from fractional wet areas performed poorly in reproducing the mean annual ETwb in unregulated river basins, and it underperformed advanced physical, machine-learning, and land surface models in closing grid-scale water balance. This problem was remedied by linking the CR method with a traditional Budyko equation that allowed for an upscaling of the optimal αe from gauged basins to ungauged locations. The combined CR–Budyko framework enabled us to reflect climate conditions in αe, leading to more plausible ETa estimates in ungauged areas. The spatially varying αe conditioned by local climates enabled the CR method to outperform the three ETa models in reproducing the grid-scale ETwb across the Australian continent. We argued here that the polynomial CR with a constant αe could result in biased ETa, and it can be constrained by a traditional Budyko equation for improvement.