Bergman, J. W., and P. J. Rasch, 2002: Parameterizing vertically coherent cloud distributions. J. Atmos. Sci., 59, 2165-2182.
A parameterization for specifying subgrid-scale cloud distributions in atmospheric models is developed. The fractional area of a grid-scale column in which clouds from two levels overlap (i.e., the cloud overlap probability) is described in terms of the correlation between horizontal cloudiness functions in the two levels. Cloud distributions that are useful for radiative transfer and cloud microphysical calculations are then determined from cloud fraction at individual model levels and a decorrelation depth. All pair-wise overlap probabilities among cloudy levels are obtained from the cloudiness correlations. However, those probabilities can overconstrain the determination of the cloud distribution. It is found that cloud fraction in each level along with the overlap probabilities among nearest neighbor cloudy levels is sufficient to specify the full cloud distribution.
The parameterization has both practical and interpretative advantages over existing parameterizations. The parameterized cloud fields are consistent with physically meaningful distributions at arbitrary vertical resolution. In particular, bulk properties of the distribution, such as total cloud fraction and radiative fluxes calculated from it, approach asymptotic values as the vertical resolution increases. Those values are nearly obtained once the cloud distribution is resolved; that is, if the thickness of cloudy levels is less than one half of the decorrelation depth. Furthermore, the decorrelation depth can, in principle, be specified as a function of space and time, which allows one to construct a wide range of cloud distributions from any given vertical profile of cloud fraction.
The parameterization is combined with radiative transfer calculations to examine the sensitivity of radiative fluxes to changes of the decorrelation depth. Calculations using idealized cloud distributions display strong sensitivities (~50 W m-2) to changes of decorrelation depth. Those sensitivities arise primarily from the sensitivity of total cloud fraction to that parameter. Radiative fluxes calculated from a version of the National Center for Atmospheric Research Community Climate Model (CCM) show only a small sensitivity. The reason for this small sensitivity is traced to the propensity of CCM to produce overcast conditions within individual model levels. Thus, in order for the parameterization to be fully useful, it is necessary that other cloud parameterizations in the atmospheric model attain a threshold of realism.