Some properties of the vertical structure matrices of the atmospheric models

Vertical discretization of the hydrostatic atmospheric models is considered. The matrices of the vertical structure are derived for three different vertical approximations: simplified vertical discretization, Charney-Phillips and Lorenz staggered grids. Analysis of the properties of these vertical structure matrices is performed using matrix factorization and results about total positivity. The well-posedness of initial value problem for vertically discretized equations is shown based on oscillatory properties of the vertical structure matrices.