Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies |
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| Authors: | Jouko Launiainen |
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| Institution: | (1) Finnish Institute of Marine Research, Box 33, FIN-00931 Helsinki, Finland |
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| 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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