A nondimensional atlas for potential evaporation and the Bouchet–Morton complementary relationship: separating definition choices from land–atmosphere adjustment

Potential evaporation is central to hydrology, ecohydrology, and drought/climate-impact studies, yet “potential evaporation / evaporative demand” remains fragmented across definitions, implementations, and complementary relationship (CR) formulations. This fragmentation complicates intercomparison, obscures physical interpretation, and can lead to conflicting conclusions even when analyses use the same underlying data. Here I present a synthesis framework that unifies CR curve families and clarifies which aspects of inferred behavior arise from definitional choices versus land–atmosphere adjustment physics.

I recast CR theory in a nondimensional phase space defined by x ≡ E_p0/E_paand y ≡ E/E_pa, where E is actual evaporation, E_pa is “apparent potential” evaporation diagnosed from the drying environment, and E_p0 is a wet-environment benchmark. In this atlas, physically admissible behavior occupies a constrained region and diverse CR formulations become directly comparable. Remaining differences among curve families can be summarized with a small set of geometric descriptors (e.g., wet-limit slope, dry-end location, and curvature), enabling a compact “fingerprint” of CR behavior.

To prevent definitional artifacts from masquerading as physical inference, I introduce definition-consistency tests that isolate the impact of the wet benchmark choice on the x-axis mapping. I show that inconsistent wet-benchmark definitions can primarily induce horizontal remapping in x, biasing inferred asymmetry/curvature and thereby altering conclusions about coupling regimes. To interpret geometry physically, I connect atlas descriptors to a minimal coupled mixed-layer model that links curve shape to a small set of drivers controlling land–atmosphere feedback strength and adjustment timescales (e.g., ventilation and boundary-layer mixing).

Finally, I demonstrate the framework using eddy-covariance evaporation and meteorological time series from NEON sites, showing how inter-site differences emerge largely through differences in the distribution of x and in the curvature of the median y(x) response. The atlas provides a transparent pathway to compare, interpret, and select potential evaporation metrics for ecohydrological and hydroclimatic applications, while reconciling apparently divergent results across the CR literature.