Equilibrium Evaporation and the Convective Boundary Layer

Abstract

A theory is developed for surface energy exchanges in well-mixed, partlyopen systems, embracing fully open and fully closed systems as limits.Conservation equations for entropy and water vapour are converted intoan exact rate equation for the potential saturation deficit D in a well-mixed, partly open region. The main contributions to changes in D arise from (1) the flux of D at the surface, dependent on a conductance gq that is a weighted sum of the bulk aerodynamic and surface conductances; and (2) the ‘exchange’ flux of D with the external environment by entrainment or advection, dependent on a conductance ge that is identifiable with the entrainment velocity when the partly open region is a growing convective boundary layer (CBL). The system is fully open when ge/gq → ∞, and fully closed when ge/gq → 0. The equations determine the steady state surface energy balance (SEB) in a partly open system, the associated steady-state deficit, and the settling time scale needed to reach the steady state. The general result for the steady-state SEB corresponds to the equations of conventional combination theory for the SEB of a vegetated surface, with the surface-layer deficit replaced by the external deficit and with gq replaced by the series sum (gq-1 + ge-1)-1. In the fully open limit D is entirely externally prescribed, while in the fully closed limit, D is internally determined and the SEB approaches thermodynamic equilibrium energy partition. In the case of the CBL, the conductances gq and ge are themselves functions of D through short-term feedbacks, induced by entrainment in the case of ge and by both physiological and aerodynamic (thermal stability) processes in the case of gq. The effects of these feedbacks are evaluated. It is found that a steady-state CBL is physically achievable only over surfaces with at least moderate moisture availability; that entrainment has a significant accelerating effect on equilibration; that the settling time scale is well approximated by h/(gq + ge), where h is the CBL depth; and that this scale is short enough to allow a steady state to evolve within a semi-diurnal time scale only when h is around 500 m or less.