Should two-parameter generalized complementary models for evaporation be simplified to single-parameter? A pairwise evaluation over grassland and forest sites

Models based on the complementary relationship for estimating evaporation typically incorporate two parameters, one for adjusting the relationship's shape and the other for formulating potential evaporation ($E_{po}$). In practical applications, single-parameter versions are often derived by fixing one of these parameters. But there is ongoing debate about which parameter to fix and under what conditions. To address these crucial questions in the application of generalized complementary models, we conducted a comprehensive comparison of the consequences arising from the simplification of three prominent two-parameter generalized complementary models (H2012 by Han et al. (2012), B2015 by Brutsaert (2015), and S2022 by Szilagyi et al. (2022)) to their respective single-parameter versions. This analysis utilized data from 24 grassland and 19 forest flux sites, showcasing varying land-atmosphere coupling dynamics. The results underscore the robustness of the two-parameter scheme in accommodating diverse land-atmosphere coupling. The choice of which parameter to fix depends on the land-atmosphere coupling strength. Under conditions where evaporation is closely coupled with the land surface, as observed over grasslands, fixing the $E_{po}$-related parameter while leaving the shape parameter for calibration (as in the simplification of H2012) preserves the dependence of the shape parameter on land surface wetness, albeit with an acceptable reduction in performance. In contrast, when evaporation is closely coupled to the outer atmosphere, as observed over forests, fixing the shape parameter but leaving the $E_{po}$-related parameter for calibration (as in the simplifications of B2015 and S2022) maintains the physical correlations between the $E_{po}$-related parameters and the major atmospheric factors, also with an acceptable reduction in performance. These findings provide valuable insights for the parameterization of complementary models, aiding in the selection of appropriate parameter-fixing strategies based on the prevailing land-atmosphere coupling conditions.