Persistent performance of the power-function complementary relationship in Earth system models under a warming scenario

This study presents a systematic evaluation of the power-function complementary relationship (CR) for estimating global terrestrial evapotranspiration (E) under a high-emission warming scenario. Three parameterization strategies for the exponent b—the polynomial method (b = 2), the combined CR-Budyko framework, and the isenthalpic index approach—were applied independently to atmospheric forcing from eighteen Earth System Models (ESMs) participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6) under the SSP5-8.5 pathway over 1980–2100. CR-based E was evaluated against ESM-simulated E at both the global and basin scales to assess the robustness of each parameterization approach across space and time. All three approaches demonstrated strong agreement with the reference E, maintaining basin-scale Nash–Sutcliffe efficiency > 0.88 and Pearson r > 0.95 throughout the study period, even under intensified warming. The polynomial method provided stable and globally neutral performance, with the smallest basin-scale bias across all periods. The CR-Budyko framework most closely reproduced tropical E during the historical period but exhibited growing overestimation under future warming. The isenthalpic index approach most faithfully tracked the global E anomaly trend and performed comparably to the polynomial method in warm and arid regions. The results suggest that the power-function CR provides a physically grounded, calibration-free framework for E assessment in CMIP6 ESMs under warming, while demonstrating that the choice of b parameterization strategy has meaningful implications for regional E estimation across diverse hydroclimatic regimes.