Development and Validation of a Vertically Two-Dimensional Mesoscale Numerical Model.

In this thesis a vertical, two dimensional, grid-point mesoscale model is developed, using the equations of motion and thermodynamics in a dry flow. A non-dimensional vertical coordinate s is used. The hydrostatic assumption is made. To avoid the sensitivity of the continuity equation, several derived equations are used based on the first law of thermodynamics, the pressure tendency equation, and the top boundary condition, which was that the vertical motion was zero at the top boundary. These derived equations include the equation for prediction of density, Richardson's equation for vertical motion, and the pressure tendency at the top of the model. A simplified calculation of dry, subgrid convection is made to prevent instability. The equations are integrated using explicit finite differences with a time step of 2 minutes.