Linear inverse models (LIMs) suitable for studies of atmospheric extratropical variability and predictability on longer than weekly time scales have been constructed for each season of the year, using atmospheric observations of the past 30 years. Notably, these empirical-dynamical models include tropical diabatic heating as a predicted model variable rather than as a forcing, and also include, in effect, the feedback of the extratropical weather systems on the more slowly varying circulation. The models are capable of reproducing both lagged covariance statistics from independent data and the development of individual streamfunction and tropical heating anomalies. In fact, week 2 predictions by the models have skill comparable to that of the NCEP MRF ensemble mean forecasts (forecasts are available at http://www.cdc.noaa.gov/lim). Theoretical predictability limits derived for the LIM suggest that the model has useful mean forecast skill at forecast lead times of between three and five weeks, depending upon both season and geographical region. Some initial atmospheric states which result in strong deterministic growth are associated with greater predictability because of a relatively high signal to noise ratio, although these states too have strong seasonal dependence. Our analysis further suggests that without inclusion of tropical heating, weekly averages may be predictable between about 1-2 weeks in the extratropics, but with tropical heating included, they may be predictable as far as 5-7 weeks ahead.

Sensitivity of streamfunction anomaly growth to both the strength and location of tropical diabatic heating anomalies is shown to shift from the central Pacific in winter to the West Pacific and Indian oceans in summer. Such optimal anomaly growth is related not only to ENSO but also to tropical intraseasonal variability. These results also have important implications for the development of persistent anomalies, such as North American heat waves and droughts.