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Discussion papers
https://doi.org/10.5194/hess-2019-545
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2019-545
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: review article 25 Nov 2019

Submitted as: review article | 25 Nov 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Complementary principle of evaporation: From original linear relationship to generalized nonlinear functions

Songjun Han1 and Fuqiang Tian2 Songjun Han and Fuqiang Tian
  • 1State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
  • 2State Key Laboratory of Hydro-science and Engineering, Tsinghua University, Beijing 100084, China

Abstract. The complementary principle is an important methodology for estimating evaporation. Throughout the 56-year development, related studies have shifted from adopting a symmetric linear complementary relationship (CR) to employing generalized nonlinear functions. Studies based on the linear CR have been maintained for a long time by rationally formulating the potential (Epo) and apparent potential evaporation (Ep) and/or employing an asymmetric parameter. These works have also advanced two types of generalized nonlinear complementary functions by invoking the boundary conditions. The first type inherits the concepts of three types of evaporation yet still requires the prognostic modelling of Epo. Polynomial functions are derived and tested for this type of function. Meanwhile, the second type does not involve Epo, yet requires a diagnostic modelling of actual evaporation by using the radiation and aerodynamic components of the Penman (1948) equation as inputs. A sigmoid function is derived by satisfying the boundary conditions based on physical considerations. The generalized nonlinear functional approach has improved the understandings on the complementary principle, and shows potential in advancing the evaporation research. Further studies may cover several topics including boundary conditions, analytical forms, parameterization, and application.

Songjun Han and Fuqiang Tian
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Songjun Han and Fuqiang Tian
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Short summary
The complementary principle is an important methodology for estimating evaporation. Throughout the 56-year development, related studies have shifted from adopting a symmetric linear complementary relationship (CR) to employing generalized nonlinear functions. We also compare the the polynomial and sigmoid types of generalized complementary functions, and discuss their future development.
The complementary principle is an important methodology for estimating evaporation. Throughout...
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