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The ability to predict terrestrial evapotranspiration (E) is limited by the complexity of rate-limiting pathways as water moves through the soil, vegetation (roots, xylem, stomata), canopy air space, and the atmospheric boundary layer. The impossibility of specifying the numerous parameters required to model this process in full spatial detail has necessitated spatially upscaled models that depend on effective parameters such as the surface vapor conductance (C-surf). C-surf accounts for the biophysical and hydrological effects on diffusion through the soil and vegetation substrate. This approach, however, requires either site-specific calibration of C-surf to measured E, or further parameterization based on metrics such as leaf area, senescence state, stomatal conductance, soil texture, soil moisture, and water table depth. Here, we show that this key, rate-limiting, parameter can be estimated from an emergent relationship between the diurnal cycle of the relative humidity profile and E. The relation is that the vertical variance of the relative humidity profile is less than would occur for increased or decreased evaporation rates, suggesting that land-atmosphere feedback processes minimize this variance. It is found to hold over a wide range of climate conditions (arid-humid) and limiting factors (soil moisture, leaf area, energy). With this relation, estimates of E and C-surf can be obtained globally from widely available meteorological measurements, many of which have been archived since the early 1900s. In conjunction with precipitation and stream flow, long-term E estimates provide insights and empirical constraints on projected accelerations of the hydrologic cycle.