Normal Modes of a Global Nonhydrostatic Atmospheric Model

Abstract

Abstract Anticipating use of a very high resolution global atmospheric model for numerical weather prediction in the future without a traditional hydrostatic assumption, this article describes a unified method to obtain the normal modes of a nonhydrostatic, compressible, and baroclinic global atmospheric model. A system of linearized equations is set up with respect to an atmosphere at rest. An eigenvalue–eigenfunction problem is formulated, consisting of horizontal and vertical structure equations with suitable boundary conditions. The wave frequency and the separation parameter, referred to as “equivalent height,” appear in both the horizontal and vertical equations. Hence, these two equations must be solved as a coupled problem. Numerical results are presented for an isothermal atmosphere. Since the solutions of the horizontal structure equation can only be obtained numerically, the coupled problem is solved by an iteration method. In the primitive-equation (hydrostatic) models, there are two kinds of ...