An Analytical Formulation of the Monin–Obukhov Stability Parameter in the Atmospheric Surface Layer Under Unstable Conditions

Abstract

A non-iterative analytical scheme is developed for unstable stratification that parametrizes the Monin–Obukhov stability parameter $$\zeta $$ ( $${=}z{/}L$$ , where z is the height above the ground and L is the Obukhov length) in terms of bulk Richardson number ( $$Ri_B$$ ) within the framework of Businger–Dyer type similarity functions. The proposed scheme is valid for a wide range of roughness lengths of heat and momentum. The absolute relative error in the transfer coefficients of heat and momentum is found to be less than 1.5% as compared to those obtained from an iterative scheme for Businger–Dyer type similarity functions. An attempt has been made to extend this scheme to incorporate the similarity functions having a theoretically consistent free convection limit. Further, the performance of the scheme is evaluated using observational data from two different sites. The proposed scheme is simple, non-iterative and relatively more accurate compared to the schemes reported in the literature and can be used as a potential alternative to iterative schemes used in numerical models of the atmosphere.