Adding a Third Normal to CLUBB

Mr. Sven Bergmann
University of Wisconsin-Milwaukee

The Cloud Layers Unified By Binormals (CLUBB) model uses the sum of two normal probability density function (pdf) components to represent subgrid variability within a single grid layer of an atmospheric model. This binormal approach, while computationally efficient, restricts the model’s ability to capture the full spectrum of potential shapes encountered in real-world atmospheric data. This thesis proposes to introduce a third normal pdf component strategically positioned between the existing two, significantly enhancing the model’s representational flexibility. This trinormal representation allows for a wider range of grid-layer shapes while permitting analytic solutions for certain higher order moments. The core of this work lies in deriving the necessary mathematical transformations for incorporating the third normal pdf seamlessly into the CLUBB framework. This thesis lists all formulas, inputs, and outputs associated with the extended model as well as gives an outline
on how to check those equations. Additionally, it describes certain asymptotic behavior of the trinormal pdf under various parameter settings.

Advisor: Prof. Vince Larson

Committee Members:
Profs. Vince Larson, Peter Hinow, and David Spade