Analytical solution of surface layer similarity equations

Abstract

Turbulent exchange between the surface and the atmosphere strongly depends on the stability of the surface layer. If surface radiometric temperature, rather than aerodynamic temperature, is used to parameterize the surface turbulent fluxes, the solution of the stability parameter is related to the thermal roughness length zT, which is generally not identical to the aerodynamic roughness length ZO. This note derives the exact solution of the stability parameter equation for a stable surface layer and proposes an approximate analytical solution for an unstable surface layer. The solution can improve the computational efficiency of flux parameterization and is applicable in a wide range of Z/ZO (50-104) and ZO/ZT (from less than 1 to greater than 104).