A parameterisation of the effective roughness length over inhomogeneous, flat terrain

A parameterisation of the effective roughness length is presented for an arbitrary given roughness distribution z(0)(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 z(0) and a so-called dynamic function, which describes the response of the flow field to a single wavelength of z(0). 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.