Accurate estimation of terrestrial evaporation is crucial for advancing our understanding of the hydrological cycle and supporting sustainable water resource management. However, current evaporation models often face significant uncertainties due to their reliance on complex meteorological inputs (e.g., precipitation) and intricate parameterizations of vegetation and soil processes. Here we introduce a physically-based, calibration-free complementary relationship (CR) model that requires only routine meteorological variables-radiation, temperature, humidity, and wind speed-thereby eliminating the need for detailed surface data. The CR model is rigorously evaluated against water balance-derived evaporation estimates across 62 major catchments worldwide, demonstrating superior performance in both magnitude and trend compared to existing evaporation products, including 10 global datasets derived from remote sensing models, land surface models, and reanalysis methods, particularly in arid regions with sparse vegetation cover. Furthermore, when driven by reanalysis datasets, the CR model's evaporation estimates outperform the direct evaporation outputs from these datasets. Using the CR model, we generate monthly global terrestrial evaporation estimates for the period 2001-2022, yielding a mean annual evaporation rate of 552 +/- 5.5 mm yr- 1 (67.7 +/- 0.7 x 103 km3 yr- 1, excluding Antarctica and Greenland) and a global terrestrial evaporation trend of 0.94 +/- 0.34 mm yr- 2. Our results highlight the robustness of the CR model in estimating evaporation across global terrestrial environments, offering a straightforward yet effective approach for understanding hydrological responses to climate change and informing water resource management strategies.