A parameterization for the horizontal subgrid-scale variability of water vapor and cloud condensate is introduced, which is used to diagnose cloud fraction in the spirit of statistically based cloud cover parameterizations. High-resolution cloud- resolving model data from tropical deep convective scenarios were used to justify the choice of probability density function (PDF). The PDF selected has the advantage of being bounded above and below, avoiding the complications of negative or infinite water mixing ratios, and can give both negatively and positively skewed functions as well as symmetric Gaussian-like bell-shaped curves, without discrete transitions, and is mathematically straightforward to implement. A development from previous statistical parameterizations is that the new scheme is prognostic, with processes such as deep convection, turbulence, and microphysics directly affecting the distribution of higher-order moments of variance and skewness. The scheme is able to represent the growth and decay of cirrus cloud decks and also the creation of cloud in clear sky or breakup of an overcast cloud deck by boundary layer turbulence. After introducing the mathematical framework, results using the parameterization in a climate model are shown to illustrate its behavior. The parameterization is shown to reduce cloud cover biases almost globally, with a marked improvement in the stratocumulus regions in the eastern Pacific and Atlantic Oceans
