Performance of Non-Linear Evaporation Complementary Relationships: A Global Basin-Scale Intercomparison

Long-term catchment water balance is generally described as precipitation (P) equaling the sum of runoff (Q) and evaporation (E). While P and Q are reliably observed, accurately observing or estimating E remains a great challenge. The generalized complementary relationship (GCR), as the latest development of the complementary principle, addresses this by describing land-atmosphere interactions through various functions, including sigmoid (denoted as H18), polynomial (B15), exponential (G21), and power (S2, S1, and S0), offering a promising approach for long-term watershed evaporation estimation. Evaluating the performance of these different functions is key to enhance estimation accuracy and support better hydrological modeling at the catchment scale. The modeling performance and parameters of six typical GCR functions are investigated in global 2112 catchments. Results indicated that all non-linear GCR functions can  well estimate multi-year average evaporation, with a determination coefficient (R²) of 0.93 ± 0.06. Performance and parameters exhibit obvious spatial variability, which depend on catchment attributes to a certain extent. Specifically, model performance demonstrates higher linear correlation with net radiation, water vapor pressure deficit, and normalized difference vegetation index (NDVI); whereas parameters are more strongly linked to aridity index (AI), NDVI. All six GCR-based functions perform well in catchments with moderate humidity by properly calibrating shape and complementary parameters, but some (i.e., H18, G21, S0, and S1) have limitations or become inapplicable under extremely wet or dry conditions.