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

摘要

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 <= R-iB <= 0, (ii) 0 <= ln(z(0)/z(h)) <= 29.0, and (iii) 10 <= z/z(0) <= 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 phi(m) and phi(h) (representing non-dimensional wind and temperature profiles), so long as the ratio of gamma(m) to gamma(h) >= 1. The improved scheme can be easily employed in atmospheric modelling for a comprehensive range of R-iB and a variety of surfaces