Small-scale and mesoscale variability of scalars in cloudy boundary layers: One-dimensional probability density functions

A key to parameterization of subgrid-scale processes is the probability den sity function (PDF) of conserved scalars. If the appropriate PDF is known, then grid box average cloud fraction, liquid water content, temperature, an d autoconversion can be diagnosed. Despite the fundamental role of PDFs in parameterization, there have been few observational studies of conserved-sc alar PDFs in clouds. The present work analyzes PDFs from boundary layers co ntaining stratocumulus, cumulus, and cumulus-rising-into-stratocumulus clou ds. Using observational aircraft data, the authors test eight different paramet erizations of PDFs, including double delta function, gamma function, Gaussi an, and double Gaussian shapes. The Gaussian parameterization, which depend s on two parameters, fits most observed PDFs well but fails for large-scale PDFs of cumulus legs. In contrast, three-parameter parameterizations appea r to be sufficiently general to model PDFs from a variety of cloudy boundar y layers. If a numerical model ignores subgrid variability, the model has biases in d iagnoses of grid box average liquid water content, temperature, and Kessler autoconversion, relative to the values it would obtain if subgrid variabil ity were taken into account. The magnitude of such biases is assessed using observational data. The biases can be largely eliminated by three-paramete r PDF parameterizations. Prior authors have suggested that boundary layer PDFs from short segments a re approximately Gaussian. The present authors find that the hypothesis tha t PDFs of total specific water content are Gaussian can almost always be re jected for segments as small as 1 km.