Sigmoid Generalized Complementary Equation for Evaporation Over Wet Surfaces: A Nonlinear Modification of the Priestley‐Taylor Equation

Abstract

The deviations of the Priestley‐Taylor (PT) coefficient from a fixed value around 1.26 indicate a nonlinear dependence of wet surface evaporation (E) on the equilibrium evaporation (Erad, which is the radiation term in Penman potential evaporation [EPen]). The linear PT equation with a fixed coefficient underestimates E for small Erad but overestimates E for large Erad, whereas the Penman equation with calibrated linear wind function has the opposite bias. In this study, the sigmoid generalized complementary (SGC) equation by Han and Tian (2018a), https://doi.org/10.1029/2017wr021755 was applied to estimate the wet surface evaporation by setting its asymmetric parameter to infinity. The SGC equation with one fixed parameter captures the nonlinear dependence of E on Erad over wet surfaces by including the aerodynamic component of EPen with a reference wind function, and amends the shortages of the linear PT and Penman equation. By using datasets over open water surfaces of lakes and ocean, wetlands, and paddy fields, the validation results indicate that the wet surface SGC equation performed better than the linear PT and Penman equations on evaporation estimation. The success of the wet surface SGC equation has implications for the extension of the complementary principle to consider varying aerodynamic conditions over wet surfaces.

On the Estimation of Potential Evaporation Under Wet and Dry Conditions

“…For example, assuming a standard meteorological station set in a hot, dry desert months after the last rainfall event, the observed meteorological variables (e.g., radiation, temperature and vapor pressure deficit, which are later put in a certain form of E P model to estimate E P ) under such conditions can be very different from those would be measured if the surface is adequately supplied with water. The difference between actual (dry or non‐potential) and hypothetical conditions (wet) has resulted in conceptual difficulties with the standard procedure of E P calculation and led many to investigate the E P concept (Aminzadeh et al., 2016; Brutsaert, 2015; Crago & Qualls, 2018; Han et al., 2021; Morton, 1983; Qualls & Crago, 2020; Szilagyi & Jozsa, 2008; Zhang & Brutsaert, 2021). As proposed by Brutsaert (2015), instead of being called “potential evaporation,” this specific term estimated based on meteorological observations under non‐potential conditions should be called “apparent potential evaporation” to reflect the difference, such as those measured by a “small” evaporation pan or estimated by the Penman equation in non‐potential environments.…”

Potential Evaporation and the Complementary Relationship

“…The CR provides a simple framework for estimating actual evaporation with basic meteorological observations. Over the years, the complementarity principle has evolved from a conceptual symmetric linear relationship (Bouchet, 1963) to a generalized asymmetric nonlinear relationship (Brutsaert, 2015; Brutsaert et al., 2020; S. Han & Tian, 2018; S. Han et al., 2021; Kim & Chun, 2021; Ma et al., 2021; Szilagyi et al., 2017). Nevertheless, the state‐of‐the‐art CR models still suffer from two main issues.…”

Abrupt Change of the Generalized Complementary Relationship of Evaporation Over Irrigated Double Cropping North China Plain With East Asian Monsoon

“…where 𝐴𝐴 𝐴𝐴0.5 is the corresponding x-value of 𝐴𝐴 𝐴𝐴= 0.5 , 𝐴𝐴 𝐴𝐴0.5 = 0.5+𝑏𝑏 −1 𝛼𝛼 HT (1+𝑏𝑏 −1 ) . Parameters 𝐴𝐴 𝐴𝐴HT and b represent the impacts of aerodynamic or atmospheric conditions (Han et al, 2021) and land surface properties (L. Wang et al, 2020), respectively, which endow the sigmoid function the capability of accounting for the effects of changing land and atmospheric conditions.…”