STABILITY DEPENDENCE OF HEIGHT SCALES AND EFFECTIVE ROUGHNESS LENGTHSOF MOMENTUM AND HEAT-TRANSFER OVER ROUGHNESS CHANGES

It is widely accepted that the correct formulation of an effective rou ghness length, defined as the area average of the roughness length in heterogeneous terrain, relies upon the appropriate determination of a height scale. At this height a meteorological quantity is approximatel y in equilibrium with local surface conditions and independent of hori zontal position. This research note determines explicitly the differen t height scales from the perturbation solutions of flow velocity and t emperature, as well as the fluxes of momentum and heat, in a stratifie d boundary layer. These solutions are derived from the asymptotic appr oximation theory and shown to capture major characteristics of momentu m and heat transfer over heterogeneous terrain with changes of the und erlying roughness lengths. The effective roughness lengths can then be computed by use of these height scales. The dependence of height scal es and effective roughness lengths upon stratification is also discuss ed briefly.