Thermodynamic insights into the complementary relationship and novel estimation

Evaporation serves as a crucial link among the global water cycle, energy cycle, and carbon cycle. The Complementary Relationship (CR), initially proposed by Bouchet in 1963, has been widely accepted as a tool for estimating actual terrestrial evaporation rates. However, its physical foundation has long been subject to scrutiny. This study aims to explore the thermodynamic basis of the CR based on the path of isenthalps and to propose a novel method for estimating actual evaporation rates under different land surface conditions. By examining the changes of air masses in the temperature-vapor pressure state coordinates and employing a first-order approximation, an analytical expression of the complementary relationship in thermodynamics has been derived. The current results indicate that, according to the derived analytical expression, actual evaporation can be determined by the temperature and vapor pressure states at the initial and final positions, with the process of change characterized by the coefficients defined in this study. Notably, the model performs optimally when the land surface is relatively moist.