Representation of 3D heterogeneous cloud fields using copulas: Theory for water clouds

Abstract

AbstractIt is shown that a general representation of GCM column cloud fraction within probability density function (PDF)‐based statistical cloud parametrizations 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 modelled grid‐column 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 nonlinear 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 subgrid‐scale variability in both moisture and temperature. This work is envisaged as a first step towards developing a generalized statistical framework for GCM cloud parametrization and for assimilating statistical information from high‐resolution satellite observations into GCMs and global analyses. Copyright © 2008 Royal Meteorological Society