Improving the representation of subgrid-scale variability of total water in the ECHAM6 GCM

Cloud cover is an important factor for global climate simulations (e.g. for radiation and precipitation). But due to their coarse resolution todays general circulation models (GCMs) typically neither resolve clouds nor the important related processes as e.g. convection. In order to provide a representation of subgrid-scale variability of moisture, cloud parameterizations are introduced into GCMs. For the approach of statistical schemes an underlying probability density function (PDF) of moisture describing the subgrid-scale variability is assumed. In this study three development steps to improve the representation of subgrid-scale variablity of total water are applied to the statistical scheme by Tompkins (2002). First, in cases of negative distribution minima an approximation of a truncated beta distribution by the general beta distribution is introduced. This avoids an additional evaporation of cloud water and by this improves the consistency with the cloud condensate contained in the model. As a second step, prognostic equations for the higher moments variance and skewness are implemented. These moments provide an easier physical interpretation than the previously used shape parameter and distribution width. Additionally, the range of possible skewness values is extended by allowing negative skewness. Both changes increase the flexibility and applicability of the scheme. In the third step a new parameterization for the contribution by convection to the time evolution of variance and skewness is introduced. By this, a stronger coupling to the convection parameterization is established. And these new source terms are formulated exclusively in the space of the moments, which provides an easier use of other distributions or closures. The three steps are implemented in the ECHAM6 GCM and the evaluation is done by using the measure of critical relative humidity (Quaas 2011). This meassure is based on the assumption of an uniform distribution of moisture, which is used to calculate the threshold of critical relative humidity from satellite and reanalysis data. The evaluation of the presented development steps within this meassure shows, that it is possible to reproduce a subgrid-scale variability close to observed values.