An Optimal Transport Framework for Water‐Energy Coupling in Soil‐Vegetation‐Atmosphere Continuum

Abstract The coupling between soil moisture (SM) and evapotranspiration (ET) governs key dynamics of Earth's climate and biosphere productivity. Yet, prevailing statistical models fall short of capturing the physics of water–energy exchange across diverse hydroclimates. In this study, we introduce an optimal transport framework based on the hypothesis that hydroclimates regulate SM–ET coupling near a quasi‐optimum state. This state is characterized by least action principle, defined by dynamic convolution between the water potential gradient () driving land‐to‐atmosphere moisture flux and the time weighted mass flux (referred as the SM‐ET coupling metric, ). Global validation of this framework using decadal (2010–2019) SM and ET remote sensing data reveals widespread convergence toward the least action state across hydroclimatic zones, supporting the notion of emergent climatic regulation in SM–ET coupling. As a corollary to the proposed hypothesis, we estimate two emergent properties of the SM–ET coupling: active root zone depth supporting ET, and the characteristic transit timescales over which SM is lost to atmosphere. Our root depth estimates show strong correspondence with in situ measurements (correlation >0.86) across biomes, underscoring the framework's physical realism. Notably, dynamic transit times are also validated against isotope measurements and findings suggest that SM perturbations often cycle back into the atmosphere within 3–7 days, calling into question traditional metrics of bulk residence time, that often overestimates the actual turnover. Overall, this framework provides a physically grounded way to study water–energy interactions across diverse environments.