Natural integration of scalar ̄uxes from complex terrain

Large eddy simulations of turbulent ̄ow and transport in the atmospheric boundary layer were conducted over heterogeneous sources of heat and water vapor to identify the blending properties of the turbulent mixing in an unstably strati®ed boundary layer. The numerical simulations show that the concept of blending in the ABL is in fact a useful one, even under convective conditions, for a range of surface conditions. Since the transport eddies that are responsible for the blending have sizes that are constrained by the boundary layer depth, and since the vertical motion is so important under the unstable density strati®cation studied here, we see that when the length scales of the source variability on the land surface become signi®cantly greater than the ABL depth the blending is lost. In this case the source ®elds remain relatively uncoupled by the important eddy motion. However, for smaller surface length scales, the dynamic eddy motion couples the surface patches. Hence, there is good reason that the land surface exchange phenomenon would not be scale invariant over the entire range of scales. Because of the active role of temperature the e€ects of inhomogeneous surface sources of sensible heat persist higher into the ABL than do the e€ects of surface sources from more passive scalars, such as water vapor. Moreover, the mean ®elds of potential temperature and speci®c humidity blend at much lower heights than do the vertical turbulent ̄ux ®elds of these two scalars. We propose a useful measure of blending eciency for simulation studies and show how this bridges from the dynamics responsible for the blending to the horizontal homogeneity of scalar ̄ux ®elds at measurement heights in the ABL. Ó 1999 Elsevier Science Ltd. All rights reserved.