A Parameterisation of the Effective Roughness Length over Inhomogeneous, Flat Terrain

Authors: Baldauf M.¹; Fiedler F.¹

Source: Boundary-Layer Meteorology, Volume 106, Number 2, February 2003 , pp. 189-216(28)

Publisher: Springer

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Abstract:

A parameterisation of the effective roughness length is presented for an arbitrary given roughness distribution z₀(x,y) over flat terrain at 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 is represented as a sum over the product of the Fourier transformation of log z₀ and a so-called dynamic function, which describes the 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 calculate effective roughness lengths in every close-to-surface grid cell.

Keywords: Effective roughness length; Heterogeneous terrain; Perturbation theory; Prandtl boundary layer

Language: English

Document Type: Research article

Affiliations: 1: Institut für Meteorologie und Klimaforschung, Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe, Germany

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