Physical Interpretation of the Complementary Relationship for Evapotranspiration

The complementary relationship (CR) between actual evapotranspiration (ET) and apparent potential evapotranspiration (PETa) is widely adopted as a simple yet powerful approach for ET estimation over land. However, most existing CR formulations remain empirical, largely due to a lack of clear physical interpretation of its key parameter. In this study, we show that the CR naturally emerges from the surface energy balance and clarify the physical meaning of its parameter: the wet Bowen ratio, defined as the Bowen ratio when the surface becomes saturated. Fundamentally, the CR originates from the partitioning of available energy: ET is directly linked to the latent heat flux, while PETa is proportional to the sensible heat flux. Additionally, the CR can be interpreted as the atmospheric response (encapsulated by PETa) to ET dynamics across wet and dry conditions. In contrast, ET exhibits a positive relationship with the energy-based potential evapotranspiration (PETe), which controls and drives ET over land. This physically grounded relationship among ET, PETa, and PETe advances our understanding of the spatial and temporal variations in ET, as well as its critical role in land-atmosphere interactions, thereby facilitating the practical application of the CR for ET estimation across diverse environments.