A. Spectral analyses

The source of initial conditions for all integration carried out with the COLA GCM is a global gridded analysis of the atmospheric state. Such an analysis is usually taken from the operational products provided by the NCEP (Kanamitsu, 1989; Kanamitsu et al., 1990) or the European Centre for Medium Range Weather Forecasts (ECMWF; Bengtsson et al., 1982; Anderson et al., 1991; Trenberth, 1992). Several centers (NCEP, GSFC, ECMWF, GFDL, and COLA) have reassimilated observational data taken from previous periods (Kalnay et al. 1996; Paolino et al., 1994; Gibson et al., 1997; Schubert et al., 1993), and some of these reanalyses have been used for some COLA GCM integrations. In any case, a basic requirement for integrating the COLA GCM is to start from a global, spectral analysis based on a global gridded analysis. It is beyond the scope of this document to include a description of the assimilation systems used to produce these analyses.

B. Nonlinear normal mode initialization

Gridded global analyses, by the nature of the assumptions which are employed to make such analyses, may include finite amplitude gravity waves which are almost certainly unresolved and which are certainly beyond accurate reach of the current observing system. For example, spurious gravity wave noise is introduced into the analyses because the several polar orbiting satellite passes, which are made in a given six hour data assimilation period, are assumed to be valid at the time of the analysis, so that a given observation may be aliased by as much as three hours. Because the COLA GCM dynamics can support such gravity waves, it is important to reduce or eliminate the spurious signals introduced by the assimilation process. The method employed to eliminate the noise is called nonlinear normal mode initialization (NNMI - Machenauer, 1977; Baer and Tribbia, 1977). The application of NNMI in the COLA GCM closely follows that described in MRF88. In the following section, the manner in which the heating tendencies are included is described.

C. Inclusion of heating

In developing the separable primitive equations for NNMI purposes, both the terms which are nonlinear in deviations from the resting basic state and those which force the thermodynamic equation (heating) are maintained on the right hand side. Implicitly, then, while iterating in the Machenauer (1977) scheme, both the nonlinearity and heating could be included in the forcing function. This is carried out in practice by integrating the COLA GCM several time steps (using uninitialized analyses as initial conditions) to compute a mean heating rate. This heating rate is included on the right hand side in each iteration of the NNMI scheme, as in MRF88. The effect of the inclusion is to allow a more realistic divergent circulation in the tropics (largely driven by heating) to be represented in the initial conditions.