Cloud Size Distributions from Many Different LES of Shallow Cumulus Convection

Any parameterization of cumulus clouds that is grounded in physics has to acknowledge the wide variety of cloud sizes and heights in any cloud field. Especially in modern, multi-plume based parameterizations such as ED-(MF)n, knowledge of the cloud size distribution under different circumstances is crucial. While the cloud size distributions (CSDs) have been studied many times before, it has proven hard to gain a physical understanding from them. In part, this is because of sample sizes that are too small to cover several decades of a logarithmic distribution, or because a CSD was built from many different cloud scenes, thus hiding variability in CSDs between different scenes. In this study, we use a large number of Large Eddy Simulations (LES) scenes to study this variability. We use 25m resolution, 25-50km domain simulations of a wide variety of cumulus fields to determine the variability in the cloud size distribution. Using a thorough statistical analysis we can distinguish between different distributions, such as double power laws, log normal and exponential distributions. We find that the CSD is not only set by atmospheric conditions, but is also sensitive to resolution and domain size. We find convincing evidence that a double power law is the best fit for most of cloud scenes. Not only horizontal cloud size is subject to a power law distribution, the same is true for the cloud height. Here, we find that the distribution shows a discontinuity around 150m above cloud base. Both the distribution of smaller and of larger clouds cannot be distinguished from a power law. The slope of this distribution is likely determined by the detrainment rate; the location of the discontinuity is likely related to the convective inhibition. Observations (e.g., airplaines, ceilometers) often yield a chord length distribution, not a cloud area distribution. Using LES fields, we developed an empirical conversion between these two. The conversion kernel from chord length to area is governed by a gamma function, with a mean and standard deviation that are a function of the chord length. For small chord lengths (<200m), standard deviation is relatively large, suggesting that little information about the cloud size is contained in them. We show that this conversion kernel gives good results for a wide range of chord lengths, and can therefore be used to retrieve cloud size distributions from 1D observations.