Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies

Abstract

Using the relationship between the bulk Richardson number Rz and the Obukhov stability parameter z/L (L is the Obukhov length), formally obtained from the flux-profile relationships, methods to estimate z/L are discussed. Generally, z/L can not be uniquely solved analytically from flux-profile relationships, and it may be defined using routine observations only by iteration. In this paper, relationships of z/L in terms of Rz obtained semianalytically were corrected for variable aerodynamic roughness z0 and for aerodynamic-to-temperature roughness ratios z0/zT, using the flux-profile iteration procedure. Assuming the so-called log-linear profiles to be valid for the nearneutral and moderately stable region (z/L<1), a simple relationship is obtained. For the extension to strong stability, a simple series expansion, based on utilisation of specified universal functions, is derived. For the unstable region, a simple form based on utilisation of the Businger-Dyer type universal functions, is derived. The formulae yield good estimates for surfaces having an aerodynamic roughness of 10-5 to 10-1 m, and an aerodynamic-to-temperature roughness ratio of z0/zT=0.5 to 7.3. When applied to the universal functions, the formulae yield transfer coefficients and fluxes which are almost identical with those from the iteration procedure. © 1995 Kluwer Academic Publishers.