The present study is designed to provide both a method whereby the details of the nonlinear exchange process which occurs in the atmosphere may be considered in a simplified form, and also to indicate from some calculations the complexity of those exchanges.

In this study, the RAMS@CSU cloud-resolving mesoscale forecast model is run in a real-time configuration with a sophisticated microphysical package and multiple nested grids, in which the smallest grid has increased vertical resolution in the lower boundary layer. Using this configuration, two specific fog events are simulated in 3-D using initialization data with a horizontal resolution of 40 km.

A generalization of the two-dimensional spectral forecast equations is suggested, whereby the atmospheric flow field in horizontal and vertical directions is represented in terms of orthogonal functions, which are eigenfunctions of certain differential operators in the three-dimensional equations. The technique is applied to the quasi-geostrophic potential vorticity equation.