A PDF-Based Model for Boundary Layer Clouds. Part I: Method and Model Description

Abstract

A new cloudy boundary layer single-column model is presented. It is designed to be flexible enough to represent a variety of cloudiness regimes-such as cumulus, stratocumulus, and clear regimes-without the need for case-specific adjustments. The methodology behind the model is the so-called assumed probability density function (PDF) method. The parameterization differs from higher-order closure or mass-flux schemes in that it achieves closure by the use of a relatively sophisticated joint PDF of vertical velocity, temperature, and moisture. A family of PDFs is chosen that is flexible enough to represent various cloudiness regimes. A double Gaussian family proposed by previous works is used. Predictive equations for grid box means and a number of higherorder turbulent moments are advanced in time. These moments are in turn used to select a particular member from the family of PDFs, for each time step and grid box. Once a PDF member has been selected, the scheme integrates over the PDF to close higher-order moments, buoyancy terms, and diagnose cloud fraction and liquid water. Since all the diagnosed moments for a given grid box and time step are derived from the same unique joint PDF, they are guaranteed to be consistent with one another. A companion paper presents simulations produced by the single-column model.

Analytic upscaling of a local microphysics scheme. Part I: Derivation

“…The PDF that we use is predicted by the Cloud Layers Unified By Binormals (CLUBB) single-column model (SCM) (Golaz et al, 2002a(Golaz et al, , 2002b. CLUBB assumes that the PDF is a weighted mixture, or sum, of two multivariate normal/log-normal functions (see Eq.…”

“…A mixture PDF can take on a variety of skewed and unskewed shapes because its two components can vary independently, as depicted in Figure 1 of Golaz et al (2002a). In Golaz et al (2002a), the PDF, P(w, θ l , r t ), was a function only of liquid water potential temperature, θ l , total water mixing ratio, r t , and vertical velocity, w. We assume that θ l , r t , and w are each distributed as a normal mixture. Because subgrid variations in θ l and r t are small, perturbations in s may be approximated as a linear combination of perturbations in θ l and r t .…”

“…Unlike Golaz et al (2002a), this paper extends the PDF to include r r , N r , and cloud droplet concentration per mass of air, N c . It can be written P(w, θ l , r t , r r , N r , N c ).…”

Analytic upscaling of a local microphysics scheme. Part II: Simulations

“…The SCM we use is the Cloud Layers Unified By Binormals (CLUBB) model (Golaz et al, 2002a(Golaz et al, , 2002bLarson and Golaz, 2005). The SCM is a higher-order closure model that achieves closure by prediction of a PDF of subgrid variability.…”

“…The SCM is a higher-order closure model that achieves closure by prediction of a PDF of subgrid variability. In earlier work (Golaz et al, 2002a), the functional form of the PDF was assumed to be a mixture of two multivariate normal distributions. The PDF was a function of liquid water potential temperature θ l , total water mixing ratio r t , and vertical velocity w. The use of a multivariate PDF tightly integrates the dynamics, such as turbulence and updraughts/downdraughts, with the thermodynamics.…”