How well does a power law fit to a diabatic boundary-layer wind profile?

Two types of wind profile laws are frequently used for the atmospheric surface-layer: the theoretically derived logarithmic profile with corrections for non-neutral thermal stratification and the empirically derived power law. Due to its mathematical simplicity the power law is widely used. This study investigates in which situations the power law is a good approximation to the logarithmic profile. In extension to existing studies not only the slope of the logarithmic and the power law profiles but also the curvatures should coincide. The roughness and stratification conditions for which such a coincidence is possible are calculated analytically. For neutral and unstable conditions slope and curvature of a power law profile cannot coincide with that of the logarithmic profile. This can only happen under certain circumstances in a stably stratified flow. The practical result of this sudy is that the power law offers a goo fit to the logarithmic profile for slightly stable conditions and for very smooth surfaces only. Thus the power law profile provides a good description of the wind profile over the sea but not over rough terrain.