Linear inverse models (LIMs) suitable for studies of atmospheric variability on longer than weekly time scales have been constructed from the output of the GFDL R30 and NCAR CCM3 GCMs forced with observed annually-varying SSTs. Notably, these LIMs include tropical diabatic heating as a predicted model variable rather than as a pre-specified forcing, and also include, in effect, the feedback of the extratropical weather systems on the more slowly varying circulation. The LIMs can also provide a better linear representation of the dynamical system than a linearization of the GCM model equations.

The LIMs are capable of reproducing both lagged covariance statistics from independent GCM data and the development of individual streamfunction and tropical heating anomalies in the GCMs. Consequently, such LIMs provide a powerful diagnostic tool, since they allow a determination of the dynamical relationship between time-evolving tropical forcing and extratropical response in the GCM, and particularly can reveal structures leading to significant anomaly growth on different timescales. They also allow a better understanding of the dynamical chain in the GCM leading from tropical SST anomalies through tropical convection anomalies to extratropical circulation anomalies. This is an important diagnosis, since it is the tropical diabatic heating, and not the sea surface temperatures per se, that ultimately forces the extratropical response to ENSO in each model.

LIMs constructed from GCM output can also be compared to LIMs constructed from a 30-year observational dataset (Winkler et al., J. Climate, in press). Such a comparison produces a diagnosis of how and where the low-frequency dynamics of the real atmosphere are reproduced in the GCM, and how and where they are not. For example, extratropical circulation anomalies during Northern winter in the GFDL GCM are more sensitive to tropical forcing in the west Pacific, and less sensitive to forcing in the east Pacific, than is the case in nature. On the other hand, summertime results suggest that while tropical heating anomalies over southeast Asia affect North American circulation anomalies, they do not in the GCM.