Description of a Global Shallow Water Model Based on the Spectral TransformMethod

摘要

The most common formulation of the equations of motion for simulating large-scaleatmospheric flow, otherwise known as the meteorological primitive equations, includes the vertical dependence of the atmospheric state variables. Many of the mathematical and computational properties of these equations, however, are embodied in a simpler 2-dimensional system of equations that govern the behavior of a rotating, homogeneous, incompressible and hydrostatic fluid with a finite free surface height. This system of equations is equivalently referred to as either the one-level primitive equations, the divergent barotropic system of equations, or the shallow water equations. The shallow water equations provide a useful framework for the analysis of the dynamics of large-scale atmospheric flow (e.g., the geostrophic adjustment process), as well as the analysis of innovative numerical methods that might be applied to the solution of baroclinic formulations of the primitive equations. The purpose of the technical note is to document a global shallow water equation model based on the spectral transform method. The technical note includes a derivation of the governing system along with a detailed discussion of the spectral transform algorithm as applied to the shallow water system in spherical geometry, including the use of semi-implicit time differencing. Finally, a complete application code, including graphics and post analysis packages is briefly described. It is the authors' expectation that the availability of these modeling tools, coupled with the description provided in the technical report, will be the benefit to both the education and research community.