A Parameterisation of the Effective Roughness Length over Inhomogeneous, Flat Terrain |
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Authors: | M. Baldauf F. Fiedler |
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Affiliation: | (1) Institut für Meteorologie und Klimaforschung, Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe, Germany |
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Abstract: | A parameterisation ofthe effective roughness length is presented for an arbitrary givenroughness distribution z0(x,y) over flat terrainat neutral stratification.Beyond pure averaging, it takes into account the spatial structure of the distribution, especially the influence of length scales, and inflow direction.To allow for interactions between different rough areas, Boussinesq-approximated equations with a turbulence closure of first order are considered and solved using perturbation theory.As a result, the logarithm of the effective roughness length isrepresented as a sum over the product of the Fourier transformation of log z0 and a so-called dynamic function, which describesthe response of the flow field to a single wavelength of z0.Although the numerical expenditure is larger than for simple averaging formulae,this method could be used by large-scale models to calculateeffective roughness lengths in every close-to-surface grid cell. |
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Keywords: | Effective roughness length Heterogeneous terrain Perturbation theory Prandtl boundary layer |
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