Estimation of upper bounds for the applicability of non-linear similarity functions for non-dimensional wind and temperature profiles in the surface layer in very stable conditions

Abstract

The computation of surface fluxes by Monin–Obukhov similarity theory with different linear/non-linear similarity functions for non-dimensional wind and temperature profiles becomes limited to specific ranges of ζ = z / L (where z is the height above ground and L is the Obukhov length) and bulk Richardson number ( Ri B ) under very stable conditions. A systematic mathematical analysis is carried out to estimate the upper bounds of ζ and Ri B for the extent of applicability of different non-linear similarity functions in the surface layer under these conditions. A generalized methodology is proposed on the basis of momentum drag coefficient ( C D ) and heat exchange coefficient ( C H ) and applied to various non-linear similarity functions available in the literature. A theoretically derived criterion for the applicability of each of the non-linear similarity function is evaluated with observations from Cooperative Atmosphere-Surface Exchange Study-99 and UK Meteorological Office’s Cardington datasets. The evaluation with both datasets for each non-linear similarity function confirms the validity of proposed theoretical results under very stable conditions.