Abstract
Abstract. 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 nonlinear functions. The original CR denotes that the actual evaporation (E) and “apparent” potential evaporation (Epa) depart from the potential evaporation (Ep0) 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 Epa and/or Ep0. Recently, the linear CR was generalized to a sigmoid function and a polynomial function. The sigmoid function does not involve the formulations of Epa and Ep0 but uses the Penman (1948) potential evaporation and its radiation component as inputs, whereas the polynomial function inherits Ep0 and Epa 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.
Highlights
The complementary principle provides a framework for estimating terrestrial land surface evaporation by adopting routinely observed meteorological variables and offers strong potential applications (Brutsaert and Stricker, 1979; McMahon et al, 2016; Morton, 1983)
We summarize the 56-year development of the complementary principle with a specific focus on its evolution from a symmetric linear complementary relationship (CR) to generalized nonlinear functions
Determining the parameters of the generalized complementary functions is urgent for the application of B2015 and H2017 to evaporation estimation, as well as the development of the generalized complementary principle
Summary
The complementary principle provides a framework for estimating terrestrial land surface evaporation by adopting routinely observed meteorological variables and offers strong potential applications (Brutsaert and Stricker, 1979; McMahon et al, 2016; Morton, 1983). The generalized complementary principle with earlier linear CRs as special cases has a more rigorous physical base (Brutsaert, 2015; Han and Tian, 2018b), and its methodology based on nonlinear functions is robust and effective. The generalized complementary principle has received much attention for its promising applications in estimating evaporation upon its proposal (Ai et al, 2017; Brutsaert et al, 2017, 2020; Han and Tian, 2018a; Liu et al, 2016; Szilagyi et al, 2016; Zhang et al, 2017). We compare the two types of generalized complementary functions and discuss their future development
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