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-dimensi onal (1-D) boundary-layer models, a convective boundary-layer filled with r adiatively active 'smoke' was simulated. The programme is sponsored by the Global Energy and Water Experiment Cloud Systems Study. Cloud-top-cooling r ates were chosen to be comparable with those observed in marine stratocumul us, 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 si mulations could only be a result of different numerical representations of fluid motion and subgrid-scale turbulence. At a workshop in De Bilt, The Ne therlands in August 1995, results from numerous groups around the world wer e compared with each other and with a previously investigated laboratory an alogue to the smoke cloud. The intercomparison results show that models must be run with higher vertic al resolution in the inversion than is customary at present, in order to ac curately simulate the entrainment rate into cloud-topped boundary-layers un der strong inversions. in three-dimensional (3-D) models using a vertical g rid spacing of 5-12.5 m, sufficient to resolve the horizontal variability o f inversion height, entrainment rates were 10-50% larger than the range con sistent with the laboratory experiments. With a larger vertical grid spacin g of 25 m, 1-D, 2-D and 3-D models all overestimated the entrainment rate b y more than 50%. 3-D models with monotone advection-schemes overestimated e ntrainment slightly more than those with non-monotone schemes, at least whe n 25 m vertical grid-spacing was used. However, results from non-monotone s chemes had several undesirable features associated with the generation of u ndershoots and overshoots, most notably spurious turbulent mixing above the smoke layer. The 1-D models tended to underestimate turbulent kinetic ener gy (TKE) but performed reasonably well given their simplicity. 2-D models p roduced too much entrainment and considerably overestimated TKE, compared w ith 3-D models with the same numerical formulation. Based on a simple scaling-argument, we propose that the minimum vertical gr id-spacing required to obtain an accurate entrainment-rate is of the order of the horizontal fluctuations in inversion height, which is proportional t o the layer-averaged TKE and inversely proportional to the inversion streng th.