Linear predictions and diagnosis of time-averages in a two-level model

We study the exact anomaly model of a simple two-level GCM. Linear predictions made from the initial state and a posteriori forcings are described. From the initial state alone, a linear barotropic model is superior to dependent persistence forecasts. Even greater dependent and independent skill is obtained from a linear baroclinic model, especially at short time scales. Inclusion of an empirical linear prediction for surface temperature provides only a marginal improvement, despite the significant effect that the surface temperature field has a posteriori on the atmospheric anomalies. This marginal improvement is related to the skill of the linear model in predicting the surface temperature which is the same as for predicting the atmospheric anomalies. Inclusion of an empirical parameterization for the transient eddies provides a significant improvement to the linear models. This parameterization method is also used to parameterize the baroclinic forcings in a barotropic model. The heavily parameterized barotropic model shows a significant improvement, and is comparable to the parameterized linear baroclinic model, especially for long term forecasts.