Combination theory and equilibrium evaporation

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Abstract

This paper is an analysis of equilibrium evaporation and its role in the energy balance of a terrestrial surface, as described by combination theory. Three themes are covered: first, a brief historical review identifies multiple definitions of the concept of equilibrium evaporation. Second, these are formalized by developing the basic principles of combination theory with minimum approximation. Several measures are utilized to do this: linearization is avoided, radiative and storage coupling are incorporated systematically, and actual and linearized saturation deficits are distinguished. The formalism is used to analyse several algebraically defined states and limits for the surface energy balance. Third, the thermodynamic foundation of equilibrium evaporation is analysed by studying surface-atmosphere feedbacks in arbitrary closed and open evaporating systems. It is shown that under steady energy supply any closed evaporating system evolves towards a quasi-steady state in which the Bowen ratio takes the equilibrium value 1/εv, where εv is the ratio of the latent- and sensible-heat contents of saturated air with temperature, evaluated at the volume-averaged temperature in the closed system. This applies whether the system is well-mixed or imperfectly mixed, and whatever the internal distribution of surface fluxes and surface and aerodynamic resistances. In contrast, open systems cannot reach such an equilibrium. This evolutionary definition of equilibrium evaporation differs from an alternative algebraic definition, the fully decoupled limit. The differences between the two definitions are identified, and the evolutionary definition is shown to be more fundamental. Thus, the correct temperature for evaluating ε in determining equilibrium evaporation is the volume-averaged temperature in a closed region, which in the case of a convective boundary layer is well approximated by the mixed-layer temperature.

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