Change of Surface Roughness and Planetary Boundary Layer

The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found to compare quite well with recent numerical results from higher-order closure models, it is found that, even at a downwind distance such that the internal boundary layer has grown to the full height of the planetary boundary layers, the surface stress still considerably exceeds the equilibrium value