Constraining the power-function complementary relationship with a steady-state Budyko equation for predicting terrestrial evapotranspiration globally

Abstract

The power-function complementary relationship (CR) represents the latest advancement in definitive CR models, offering enhanced predictions of terrestrial evapotranspiration (E), all while elucidating the physical interpretations of its associated parameters. In this study, we introduced practical approaches to integrate the traditional Budyko framework into the novel CR model for global-scale E prediction. Under a steady-state assumption, the power-function CR was equated with the Turc-Mezentsev equation, thereby introducing an additional constraint for determining key parameters. We presented two illustrative cases where the aridity index and land-specific parameter constrain the exponent and the Priestley-Taylor coefficient of the CR, respectively. Compared to its calibration-free counterpart, the CR model constrained by the Budyko framework demonstrated improved performance in capturing spatial and temporal variations of E in point locations, mesoscale catchments, and large river basins. This improvement was not only from considering long-term precipitation partitioning, but also from the ability of the combined framework to rectify biases in input data. While the calibration-free methods exhibited poorer performance, they hold potential for superior results with higher-quality forcing inputs. By merging the Turc-Mezentsev equation with the power-function CR, this study provides insights into refining E predictions, accounting for climatic conditions and input data quality.