It is shown that a general representation of GCM column cloud fraction within probability density function (PDF)-based statistical cloud parameterizations can be obtained using statistical functions called copulas that encapsulate the dependence structure of rank statistics in a multivariate system. Using this theory, a new Gaussian copula formulation of GCM cloud overlap
is obtained. The copula approach provides complete flexibility in the choice of the marginal PDF of each layer’s moisture and temperature, and, compared with earlier approaches, including the “generalized overlap” approach, allows a far more general specification of the correlation between any pair of layers. It also allows easy addition of new layer variables, such as temperature, into the modeled gridcolumn statistics. As a preliminary test of this formulation, its ability to statistically describe a cloud resolving model simulation of a complex multi-layer case study, including both large-scale and convective clouds, is examined. The Gaussian copula cloud fraction is found to be significantly less biased than other common cloud overlap methods for this case study. Estimates
of several non-linear quantities are also improved with the Gaussian copula model: the variance of condensed water path and the fluxes of solar and thermal radiation at atmospheric column boundaries. This first paper, though limited to the simpler case of water clouds, addresses sub-gridscale variability in both moisture and temperature. This work is envisioned as a first step towards developing a generalized statistical framework for GCM cloud parameterization and for assimilating statistical information from
high-resolution satellite observations into GCMs and global analyses.