This work is motivated by the question: how much complexity is appropriate for a cloud parameterization used in general circulation models (GCM). To approach this question, cloud parameterizations across the complexity range are explored using general circulation models and theoretical Monte-Carlo simulations. Their results are compared with high-resolution satellite observations and simulations that resolve the GCM subgrid-scale variability explicitly. A process-orientated evaluation is facilitated by GCM forecast simulations which reproduce the synoptic state. For this purpose novel methods were develop to a) conceptually relate the underlying saturation deficit probability density function (PDF) with its saturated cloudy part, b) analytically compute the vertical integrated liquid water path (LWP) variability, c) diagnose the relevant PDF-moments from cloud parameterizations, d) derive high-resolution LWP from satellite observations and e) deduce the LWP statistics by aggregating the LWP onto boxes equivalent to the GCM grid size. On this basis, this work shows that it is possible to evaluate the sub-grid scale variability of cloud parameterizations in terms of cloud variables. Differences among the PDF types increase with complexity, in particular the more advanced cloud parameterizations can make use of their double Gaussian PDF in conditions, where cumulus convection forms a separate mode with respect to the remainder of the grid-box. Therefore, it is concluded that the difference between unimodal and bimodal PDFs is more important, than the shape within each mode. However, the simulations and their evaluation reveals that the advanced parameterizations do not take full advantage of their abilities and their statistical relationships are broadly similar to less complex PDF shapes, while the results from observations and cloud resolving simulations indicate even more complex distributions. Therefore, this work suggests that the use of less complex PDF shapes might yield a better trade-off. With increasing model resolution initial weaknesses of simpler, e.g. unimodal PDFs, will be diminished. While cloud schemes for coarse-resolved models need to parameterize multiple cloud regimes per grid-box, higher spatial resolution of future GCMs will separate them better, so that the unimodal approximation improves.

This work is motivated by the question: how much complexity is appropriate for a cloud parameterization used in general circulation models (GCM). To approach this question, cloud parameterizations across the complexity range are explored using general circulation models and theoretical Monte-Carlo simulations. Their results are compared with high-resolution satellite observations and simulations that resolve the GCM subgrid-scale variability explicitly. A process-orientated evaluation is facilitated by GCM forecast simulations which reproduce the synoptic state. For this purpose novel methods were develop to a) conceptually relate the underlying saturation deficit probability density function (PDF) with its saturated cloudy part, b) analytically compute the vertical integrated liquid water path (LWP) variability, c) diagnose the relevant PDF-moments from cloud parameterizations, d) derive high-resolution LWP from satellite observations and e) deduce the LWP statistics by aggregating the LWP onto boxes equivalent to the GCM grid size. On this basis, this work shows that it is possible to evaluate the sub-grid scale variability of cloud parameterizations in terms of cloud variables. Differences among the PDF types increase with complexity, in particular the more advanced cloud parameterizations can make use of their double Gaussian PDF in conditions, where cumulus convection forms a separate mode with respect to the remainder of the grid-box. Therefore, it is concluded that the difference between unimodal and bimodal PDFs is more important, than the shape within each mode. However, the simulations and their evaluation reveals that the advanced parameterizations do not take full advantage of their abilities and their statistical relationships are broadly similar to less complex PDF shapes, while the results from observations and cloud resolving simulations indicate even more complex distributions. Therefore, this work suggests that the use of less complex PDF shapes might yield a better trade-off. With increasing model resolution initial weaknesses of simpler, e.g. unimodal PDFs, will be diminished. While cloud schemes for coarse-resolved models need to parameterize multiple cloud regimes per grid-box, higher spatial resolution of future GCMs will separate them better, so that the unimodal approximation improves.