An improved method for the estimation of surface roughness of obstacle arrays

The Lettau (1969, Journal of Applied Meteorology 8, 828–832) relationship has been used for almost three decades by meteorologists and wind-tunnel engineers to estimate surface roughness from the geometry of regular arrays of roughness elements. However, Lettau’s relationship is limited to low roughness element densities. It does not account for the nonlinear decrease of the roughness length at high roughness densities, nor does it account for drag differences caused by different obstacle shapes or layouts. In this paper an improvement upon the Lettau relationship is derived starting from fundamental principles, based on certain assumptions about the velocity profile. The improved model includes the obstacle drag coefficient explicitly, and accounts for the peak in the z0 versus area density curve.