A nonparametric approach to estimating terrestrial evaporation: Validation in eddy covariance sites

Terrestrial evaporation is essential to the global hydrological cycle and climate systems. It is a complicated energy and mass transfer process that involves radiation, conduction, diffusion, convection, and surface–atmosphere interactions. The energetic and diffusive controls on evaporation were combined in the contemporary theory (e.g. the Penman–Monteith equation), in which surface–atmosphere interfacial transfer coefficients were adopted and parameterized semi-empirically or empirically to achieve a solution to evaporation. The solution achieved through this parameterization leaves unsolvable uncertainty. Thus, the theory of evaporation remains diagnostic rather than predictive. Here we show that terrestrial evaporation can be predicted without parameterization. Terrestrial evaporation, as a mechanical and thermodynamic process, follows Hamiltonʹs principle in the macro-state. With surface temperature as a generalized coordinate of the Hamiltonian, and incorporating equilibrium evaporation, we present a nonparametric solution in a simple analytical form. We used observational data collected at 26 eddy covariance sites to test the effectiveness and the generality of the solution. Results showed good agreements between the estimated and the observed values, by an absolute difference of 10.3 ± 20.2 W m−2 for latent heat flux (evaporation) and −11.8 ± 21.0 W m−2 for sensible heat flux, for all the tested sites. Further examination demonstrated that the proposed approach achieved the performance compatible to the Penman–Monteith approach. We anticipate our analysis to be a starting point for more sophisticated investigation into the complex nature of terrestrial evaporation. Its simplicity should have potential value in applications, in addition to contributing to fundamental theory.