Anomally models based on a spectral general circulation model (GCM) are formulated and applied to study of low-frequency atmospheric variability in the extratropics, and long-range forecasting research. A steady linear version of the anomaly model is treated by a matrix method. This model consists of nine vertical levels, 15 wave rhomboidal truncation, primitive equation system, and a fixed basic state, which is three-dimensionally variable. The matrix to be handled is extremely large, but can be solved using Krylov's technique. The solutions represent various teleconnection patterns known in the observed atmosphere. The sensitivity of the response of this anomaly model to zonally variability of the temporally fixed basic fields and to the geographical position of tropical heatings is investigated. The solutions of the steady linear anomaly model are compared with those of the original GCM, revealing that there are a few similarities among the solutions, but considerable discrepancies are also evident. A time-dependent nonlinear anomaly model is applied to further investigate the discrepancy. It appears that transient are crucial for explaining the disagreement, although the study with the time-dependent anomaly model is preliminary.
A noteworthy aspect of the overall approach is that the anomaly models are derived, with only small modifications, from the full GCM, and therefore, their relationship can be readily investigated. It is concluded that the steady linear model may be used as a diagnostic tool for investigating the characteristics of the full GCM and the dynamics of a particular state of the atmosphere. However, caution is needed when there is a significant role played by transient eddies, and in the treatment of tropical Rayleigh friction.