A review of the complementary principle of evaporation: from the original linear relationship to generalized nonlinear functions

The complementary principle is an important methodology for estimating actual evaporation by using routinely observed meteorological variables. This review summaries its 56-year development, focusing on how related studies have shifted from adopting a symmetric linear complementary relationship (CR) to employing generalized non-linear functions. The original CR denotes that the actual evaporation (E) and apparent potential evaporation (E-pa) depart from the potential evaporation (E-p0) complementarily when the land surface dries from a completely wet environment with constant available energy. The CR was then extended to an asymmetric linear relationship, and the linear nature was retained through properly formulating E-pa and/or E-p0. Recently, the linear CR was generalized to a sigmoid function and a polynomial function. The sigmoid function does not involve the formulations of E-pa and E-p0 but uses the Penman (1948) potential evaporation and its radiation component as inputs, whereas the polynomial function inherits E-p0 and Ep a as inputs and requires proper formulations for application. The generalized complementary principle has a more rigorous physical base and offers a great potential in advancing evaporation estimation. Future studies may cover several topics, including the boundary conditions in wet environments, the parameterization and application over different regions of the world, and integration with other approaches for further development.