From cloud overlap to PDF overlap

Abstract

In many applications, large-scale numerical models of the atmosphere must represent small-scale variability in clouds and water content. In particular, radiative-transfer calculations need to know 'cloud overlap': that is, whether or not cloud patches at different altitudes overlap each other in the horizontal. Furthermore, it is important to know the overlap of horizontal variability in water content, or 'PDF overlap' (where PDF denotes 'probability density function'). One approach to modelling PDF overlap is to stochastically generate profiles of water content that collectively have the desired statistical properties of the cloud field. Such approaches usually draw sample profiles using the Monte Carlo method and the independent-column approximation. This paper proposes a new stochastic generator of cloud profiles. The primary novel advantage of our algorithm is that it can model correlations among multiple fields, such as water content and temperature. The algorithm is based on a simplified mixture of multiple normals (i.e. a sum of several Gaussians), which we call a 'peg-hat' PDF because its normals are arranged like hats on pegs. The algorithm represents an entire vertical grid column by a single high-dimensional sample point. The peg-hat PDF is tested using large-eddy simulations of boundary-layer clouds: namely, a cumulus case, a case involving cumulus clouds rising into broken stratocumulus, and a marine stratocumulus case. For calculations of the histogram of liquid-water path, the peg-hat PDF outperforms a single-normal PDF for cumulus clouds, which are often skewed. The peg-hat and single-normal PDFs perform comparably for stratocumulus. Copyright © 2007 Royal Meteorological Society.