An analysis for the extent of applicability of the Webb's formulation for non-dimensional wind and temperature profiles in the surface layer in weak wind stable conditions

The linear functional forms of universal similarity functions (Φm and Φh) are commonly used to compute the surface layer fluxes. The applicability of these forms is limited [Sharan, M., Rama Krishna, T.V.B.P.S. and Aditi: 2003a, ‘On the bulk Richardson number and flux-profile relations in an atmospheric surface layer under weak wind stable conditions’, Atmos. Environ. 37, 3681–3691.] to RiB < Prtγ / β2 where RiB is bulk Richardson number, Prt is turbulent Prandtl number and β and γ are constants appearing in the linear forms of Φm and Φh. Values of RiB larger than Prtγ / β2 are often observed in the observational studies especially in weak wind stable conditions. Thus, a mathematical analysis is carried out to estimate the upper bound of RiB and stability parameter z / L (where z is the height above the ground and L is Obukhov length) for the applicability of a non-linear functional form of the similarity function proposed by Webb [Webb, E.K.: 1970, ‘Profile relationships: the log-linear range, and extension to strong stability’, Quart. J. Roy. Meteorol. Soc. 96, 67–90.] in stable conditions. The upper bounds are estimated by analyzing the behaviour of momentum drag coefficient in weak wind stable conditions. It is shown that Webb's formulation is applicable in the surface layer as long as z / L ≤ z / z0 and RiB≤(z/z0−1)[(1+β)ln(z/z0)]−1 (where z0 is roughness length).