Introduction

The representation of atmospheric flow fields by means of spherical functions has a long history. Haurwitz (1940) represented the movement of Rossby waves by means of spherical functions. The development of the spectral method for the numerical integration of the equations of atmospheric motion goes back to Silberman (1954), who integrated the barotropic vorticity equation in spherical geometry. The spectral method attracted the attention of others and studies were performed, for example, by Lorenz (1960), Platzman (1960), Kubota et al. (1961), Baer and Platzman (1961), and Elsaesser (1966). Lorenz demonstrated that, for nondivergent barotropic flow, the truncated spectral equations have some important properties. Just like the exact differential equations, they preserve the mean squared vorticity, called enstrophy, and the mean kinetic energy. Platzman pointed out that this very desirable property automatically eliminated nonlinear instability, which at that time was a substantial difficulty in grid-point models. The early work made use of the so-called interaction coefficients to handle nonlinearity. This cumbersome procedure was replaced by the efficient transform technique for solving the spectral equations, which was devised independently by Orszag (1970) and by Eliasen et al. (1970). In compressed form the essential information on spectral modeling is given by Haltiner and Williams (1980). Much valuable information about spectral techniques – which is usually not readily available – can be extracted from the “gray” literature. We refer to an excellent report by Eliasen et al. (1970). Finally, we refer the reader to an excellent article on “Global modelling of atmospheric flow by spectral methods”, by Bourke et al. (1977).