In order to clarify whether entrainment processes are affected by surface heterogeneities, a series of LES runs for 1D stripe-like heat flux heterogeneities of different amplitude as well as different inversion strengths have been conducted. Usually, the entrainment rate is deduced from the temporal change of the boundary layer height (zi), which is often taken as the height where the sensible heat flux exhibits a minimum. However, this method may fail over heterogeneous terrain if the flux is calculated from deviations from the horizontal mean. For this reason zi has been calculated with a gradient method from local temperature profiles.
The simulation results show that the entrainment rate is considerably modified and increasing for increasing heat flux amplitudes, except for small heat flux amplitudes where the entrainment rate is found to be less than for the homogeneous control run. A secondary circulation develops in all cases, with a strong updraft over the middle of the stronger heated surface patch (warm patch) and a weaker downdraft over the less heated patch (cold patch). As a result of this circulation pattern, the local zi over the warm patch is higher than over the cold patch. The strength of this folding of the interfacial layer between mixed layer and free atmosphere, however, is strictly limited and reaches its critical value even for small heat flux amplitudes.
In order to study the responsible entrainment processes over heterogeneous terrain, we used a new approach: we calculated the local cooling rate by means of the flux divergence. The analysis shows a cooling of the free atmosphere and warming of the mixed layer due to entrainment of warm air and detrainment of cool air, respectively. The obtained cooling/warming rates coincide with the previously derived entrainment rate from zi. Furthermore, the results show a high cooling rate in the middle of the warm patch, but also a local maximum over the center of the cold patch. The latter is counterintuitive, but we show that this maximum is caused by a flow convergence over the cold patch. Moreover, we find that effects of lateral entrainment, wind shear caused by the secondary circulation and different turbulence regimes between the warm and the cold patch play an important role.