DERIVATION OF THE RELATIONSHIP BETWEEN THE OBUKHOV STABILITY PARAMETER AND THE BULK RICHARDSON-NUMBER FOR FLUX-PROFILE STUDIES

Using the relationship between the bulk Richardson number R(z) and the Obukhov stability parameter z/L (L is the Obukhov length), formally o btained from the flux-profile relationships, methods to estimate z/L a re discussed. Generally, z/L can not be uniquely solved analytically f rom flux-profile relationships, and it may be defined using routine ob servations only by iteration. In this paper, relationships of z/L in t erms of R(z) obtained semianalytically were corrected for variable aer odynamic roughness z(0) and for aerodynamic-to-temperature roughness r atios z(0)/z(T), using the flux-profile iteration procedure. Assuming the so-called log-linear profiles to be valid for the near-neutral and moderately stable region (z/L < 1), a simple relationship is obtained . For the extension to strong stability, a simple series expansion, ba sed on utilisation of specified universal functions, is derived. For t he unstable region, a simple form based on utilisation of the Businger -Dyer type universal functions, is derived. The formulae yield good es timates for surfaces having an aerodynamic roughness of 10(-5) to 10(- 1) m, and an aerodynamic-to-temperature roughness ratio of z(0)/z(T) = 0.5 to 7.3. When applied to the universal functions, the formulae yie ld transfer coefficients and fluxes which are almost identical with th ose from the iteration procedure.