On the analytical solutions of flux-profile relationships for the atmospheric surface layer

Abstract

Analytical solutions of surface layer similarity equations are presented for the nondimensional profile functional forms suggested by Businger et al. For stable atmospheric conditions, exact analytical solutions of the Monin-Obukhov stability parameters ζ=z/L, in terms of gradient Richardson number (Ri) and bulk Richardson number (Rib), respectively, are obtained. For unstable atmospheric conditions, an exact solution of the same in terms of Ri is found. An approximate relationship between ζ and Rib for an unstable surface layer, based on the solution of ζ in terms of Ri, is suggested. The proposed analytical solutions can replace costly numerical iterative methods as well as some of the ad hoc parameterizations used for estimating surface fluxes and related turbulence characteristics. -Author