Analytical solution of surface layer similarity equations

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 tu rbulent fluxes, the solution of the stability parameter is related to the t hermal roughness length z(T), which is generally not identical to the aerod ynamic roughness length z(o). This note derives the exact solution of the s tability parameter equation for a stable surface layer and proposes an appr oximate analytical solution for an unstable surface layer. The solution can improve the computational efficiency of flux parameterization and is appli cable in a wide range of z/z(o) (50-10(4)) and z(o)/z(T) (from less than 1 to greater than 10(4)).