Date of Award

May 2016

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Vincent E. Larson

Committee Members

Vincent E. Larson, Clark Evans, Jonathan Kahl, Kyle Swanson, Peter Hinow


Hydrometeors, Integrals, Microphysics, Multivariate, Parameterization, Probability Density Function


The subgrid-scale representation of hydrometeor fields is important for calculating microphysical process rates. In order to represent subgrid-scale variability, the Cloud Layers Unified By Binormals (CLUBB) parameterization uses a multivariate Probability Density Function (PDF). In addition to vertical velocity, temperature, and moisture fields, the PDF includes hydrometeor fields. Previously, each hydrometeor field was assumed to follow a multivariate single lognormal distribution. Now, in order to better represent the distribution of hydrometeors, two new multivariate PDFs are formulated and introduced in part one of this two-part project.

The new PDFs represent hydrometeors using either a delta-lognormal or a delta-double-lognormal shape. The two new PDF distributions, plus the previous single lognormal shape, are compared to histograms of data taken from Large-Eddy Simulations (LES) of a precipitating cumulus case, a drizzling stratocumulus case, and a deep convective case. Finally, the warm microphysical process rates produced by the different hydrometeor PDFs are compared to the same process rates produced by the LES.

Microphysics processes have feedback effects on moisture and heat content. Not only do these processes influence mean values, but also variability and fluxes of moisture and heat content. For example, evaporation of rain below cloud base may produce cold pools. This evaporative cooling may increase the variability in temperature in the below-cloud layer. Likewise, rain production in the moistest part of cloud tends to decrease variability in cloud water. These effects are usually not included in most coarse-resolution weather and climate models, or else are crudely parameterized.

In part two of this two-part project, the microphysical effects on moisture and heat content are parameterized using the PDF method. This approach is based on predictive, horizontally-averaged equations for the variances, covariances, and fluxes of moisture and heat content. These higher-order moment equations contain microphysical source terms. Using a simple warm-rain microphysics scheme, the microphysics terms can be calculated by integrating analytically over the multivariate PDF.

A LES of a precipitating cumulus case indicates that microphysical terms are dominant in some budgets. The analytic integrals for the microphysics terms are implemented in the CLUBB model. Interactive single-column simulations agree qualitatively with the LES.