Advancing Evaporation Estimation in Ungauged Alpine Basins: From Spatiotemporal Trade-offs to Distributed Parameterization of Complementary Relationship Models

Estimating terrestrial evaporation (E) accurately is critical for understanding hydrological cycles and managing water resources, particularly in ungauged alpine basins. The complementary relationship (CR) principle, which requires only routine meteorological inputs, offers a promising approach for large-scale E estimation. We systematically evaluated the spatiotemporal performance of four fixed-parameter CR models (AA, PGCR, EGCR, SGCR) in the source region of the Yellow River. Our analysis revealed inherent trade-offs between their temporal and spatial accuracy: optimizing for time series degraded spatial distribution, and vice versa. A key finding was that models with spatially and temporally distributed parameters (CFCR and BGCR) significantly outperformed fixed-parameter models by better capturing heterogeneity, with parameter αₑ showing the strongest sensitivity. Building on this, we extended the CR framework (specifically the BGCR model) to the highly heterogeneous Upper Indus Basin (UIB). The results show that applying a uniform Budyko parameter (w) introduces significant spatial bias. We therefore developed novel distributed parameterization schemes in which w is dynamically estimated using basin characteristics—specifically the precipitation seasonality index (SI) and albedo. The dual-variable scheme (BGCR-2) reduced the root-mean-square error by 16.1% compared to the uniform scheme and outperformed benchmark products such as ERA5-E. Our work demonstrates that moving from fixed to dynamically parameterized CR models is essential for achieving reliable E estimates across scales, offering a transferable approach for improving hydrological modeling and water resource assessment in ungauged regions worldwide.