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

Abstract

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.

Sensitivity Analysis of the Maximum Entropy Production Method to Model Evaporation in Boreal and Temperate Forests

“…R n and VPD were positively correlated at all sites during the peak of the growing season (0.40 ≤ R ≤ 0.55) and the ratio λE/R n allows a better assessment of the relationship between evaporation and atmospheric humidity. Our analysis demonstrates the ability of the MEP model to capture VPD limitations on transpiration, consistent with the complementary principle of evaporation (Bouchet, 1963; Brutsaert, 2015; Han & Tian, 2020) and recent empirical studies. Using flux tower data, Novick et al.…”

A Graphical Interpretation of the Rescaled Complementary Relationship for Evapotranspiration

“…In the advection‐aridity approach (Brutsaert & Stricker, 1979), LE p is taken to be LE pen Equation and LE w is taken to be LE PT . While these definitions are widely accepted (e.g., Brutsaert, 2015), multiple authors have noted various shortcomings with the symmetric CR Equation , including Brutsaert and Parlange (1998), Brutsaert et al., (2020), Han & Tian (2017, 2020), Hobbins et al. (2004), Kahler and Brutsaert (2006), Lhomme and Guillioni (2006, 2010), and Pettijohn and Salvucci (2009).…”

“…(2016). The “generalized complementary principle” (GCP) developed by Brutsaert (2015) has been a highly cited CR formulation (e.g., Brutsaert et al., 2017, 2020; R. Crago & Qualls, 2018; R. Crago et al., 2016; Han & Tian, 2020; Szilagyi et al., 2016b; Zhang et al., 2017). To determine whether the proposed model is an improvement over the GCP, we will apply both methods to multiple years of data from seven sites in Australia and discuss the results and implications.…”

“…Crago & Qualls, 2018;R. Crago et al, 2016;Han & Tian, 2020;Szilagyi et al, 2016b;Zhang et al, 2017). To determine whether the proposed model is an improvement over the GCP, we will apply both methods to multiple years of data from seven sites in Australia and discuss the results and implications.…”

Determinants of the Asymmetric Parameter in the Generalized Complementary Principle of Evaporation

“…These functions are mainly applied at longer time scales (i.e., annual) with water balance data. At monthly and daily scales, the Penman‐Monteith (PM) equation (Monteith, 1965) and complementary principle (Bouchet, 1963) are commonly used in estimating actual evaporation, especially when the precipitation information cannot represent the local water availability condition (Han & Tian, 2020). The PM equation is considered an accurate expression to estimate E and is widely used (Allen et al, 1998; Q. Fu et al, 2016; Neitsch et al, 2011; Otto‐Bliesner et al, 2016; van Beek et al, 2011), but it requires the input of canopy resistance ( r c ), which is a vegetation‐specific parameter.…”