Analysis of diagnostic climate model cloud parametrizations using large‐eddy simulations

Current climate models often predict fractional cloud cover on the basis of a diagnostic probability density function (PDF) describing the subgrid-scale variability of the total water specific humidity, qt, favouring schemes with limited complexity. Standard shapes are uniform or triangular PDFs, the widths of which are assumed to scale with the grid-box mean qt or the grid-box mean saturation specific humidity, qs. In this study, the qt variability is analysed from large-eddy simulations for two stratocumulus, two shallow cumulus, and one deep convective cases. We find that, in most cases, triangles are a better approximation to the simulated PDFs than uniform distributions. In 2 of the 24 slices examined, the actual distributions were so strongly skewed that the simple symmetric shapes could not capture the PDF at all. The distribution width for either shape scales acceptably well with both the mean values of qt and qs, the former being a slightly better choice. The qt variance is underestimated by the fitted PDFs, but overestimated by the existing parametrizations. While the cloud fraction is in general relatively well diagnosed from fitted or parametrized uniform or triangular PDFs, it fails to capture cases with small partial cloudiness, and in 10–30% of the cases misdiagnoses clouds in clear skies or vice versa. The results suggest choosing a parametrization with a triangular shape, where the distribution width would scale with the grid-box mean qt using a scaling factor of 0.076. However, this is subject to the caveat that the reference simulations examined here were partly for rather small domains and driven by idealised boundary conditions.