Evaporation and advection II: evaporation downwind of a boundary separating regions having different surface resistances and available energies

Using the model and methods developed in Part I of this study, it is shown that steady‐state evaporation, downwind of a sharp boundary separating uniform regions with constant but different surface resistances and available energies, can be written as\documentclass{article}\pagestyle{empty}\begin{document}$$ E\; = \;(S/(S + Y))\;(Rn\; - \;G)\; + \;(S/(S\; + \;Y))\;(1/r_s [r_s (Rn\; - \;G)\; - \;r_s (Rn\; - \;G)]\Phi _x $$\end{document}where ϕ x is a dimensionless ‘exchange function’ that decreases from unity to zero as distance increases downwind of the boundary. The symbols have their conventional meanings and the primes signify upwind values. The form of ϕ x depends on the profiles of wind speed and effective diffusivity, and on the downwind surface resistance and temperature via the parameter γr s /(s+γ) . Empirical expressions for ϕ x are obtained from a known solution of the atmospheric diffusion equations assuming power law forms of the wind speed and effective diffusivity profiles and from a simple model assuming perfect vertical mixing and constant wind speed beneath an impermeable inversion base. These may give some indication of the form and magnitude of ϕ x at small and at large distances respectively.