An intercomparison of radiatively driven entrainment and turbulence in a smoke cloud, as simulated by different numerical models

As part of a programme of intercomparison of eddy-resolving and one-dimensional (1-D) boundary-layer models, a convective boundary-layer filled with radiatively active 'smoke' was simulated. The programme is sponsored by the Global Energy and Water Experiment Cloud Systems Study. Cloud-top-cooling rates were chosen to be comparable with those observed in marine stratocumulus, while avoiding evaporative feedbacks on entrainment and turbulence that are also important in liquid-water clouds. The radiative-cooling rate had a specified dependence on the smoke profile, so that differences between simulations could only be a result of different numerical representations of fluid motion and subgrid-scale turbulence. At a workshop in De Bilt, The Netherlands in August 1995, results from numerous groups around the world were compared with each other and with a previously investigated laboratory analogue to the smoke cloud. The intercomparison results show that models must be run with higher vertical resolution in the inversion than is customary at present, in order to accurately simulate the entrainment rate into cloud-topped boundary-layers under strong inversions. In three-dimensional (3-D) models using a vertical grid spacing of 5-12.5 m, sufficient to resolve the horizontal variability of inversion height, entrainment rates were 10-50% larger than the range consistent with the laboratory experiments. With a larger vertical grid spacing of 25 m, 1-D, 2-D and 3-D models all overestimated the entrainment rate by more than 50%. 3-D models with monotone advection-schemes overestimated entrainment slightly more than those with non-monotone schemes, at least when 25 m vertical grid-spacing was used. However, results from non-monotone schemes had several undesirable features associated with the generation of undershoots and overshoots, most notably spurious turbulent mixing above the smoke layer. The 1-D models tended to underestimate turbulent kinetic energy (TKE) but performed reasonably well given their simplicity. 2-D models produced too much entrainment and considerably overestimated TKE, compared with 3-D models with the same numerical formulation. Based on a simple scaling-argument, we propose that the minimum vertical grid-spacing required to obtain an accurate entrainment-rate is of the order of the horizontal fluctuations in inversion height, which is proportional to the layer-averaged TKE and inversely proportional to the inversion strength.