A Semi-Analytical Approach for Parametrization of the Obukhov Stability Parameter in the Unstable Atmospheric Surface Layer.

A semi-analytical scheme is proposed to parametrize the Obukhov stability parameter $$\zeta $$ (= $$z/L$$ ; $$z$$ is the height above the ground and $$L$$ is the Obukhov length) in terms of the bulk Richardson number ( $$R_{iB}$$ ) in unstable conditions within the framework of Monin-Obukhov similarity (MOS) theory. The scheme involves, (i) a solution of a cubic equation in $$\zeta $$ whose coefficients depend on the gradient Richardson number ( $$R_{i}$$ ), and (ii) a relationship between $$R_{i}$$ and $$R_{iB}$$ . The proposed scheme is applicable for a wide range (i) $$-5\le R_{iB}\le 0$$ , (ii) $$0\le \hbox {ln}(z_{0}/z_{h})\le 29.0$$ , and (iii) $$10\le z/z_{0}\le 10^{5}$$ and performs relatively better than all other schemes in terms of accuracy in computation of surface-layer transfer coefficients. The absolute errors in computing the transfer coefficients do not exceed 7 %. The analysis presented here is found to be valid for different $$\gamma _{m}$$ and $$\gamma _{h}$$ appearing in the expressions of the similarity functions $$\varphi _{m}$$ and $$\varphi _{h}$$ (representing non-dimensional wind and temperature profiles), so long as the ratio of $$\gamma _{m}$$ to $$\gamma _{h} \ge 1$$ . The improved scheme can be easily employed in atmospheric modelling for a comprehensive range of $$R_{iB}$$ and a variety of surfaces. [ABSTRACT FROM AUTHOR]