Abstract
Using the relationship between the bulk Richardson numberR z and the Obukhov stability parameterz/L (L is the Obukhov length), formally obtained from the flux-profile relationships, methods to estimatez/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 ofz/L in terms ofR z obtained semianalytically were corrected for variable aerodynamic roughnessz 0 and for aerodynamic-to-temperature roughness ratiosz 0/z T, 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 ofz 0/z T=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.
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Launiainen, J. Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies. Boundary-Layer Meteorol 76, 165–179 (1995). https://doi.org/10.1007/BF00710895
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DOI: https://doi.org/10.1007/BF00710895