The slow manifold of the atmosphere, as defined by Lorenz, is a lower-dimensional invariant manifold that is devoid of high-frequency gravity waves. The existence of such an invariant slow manifold in primitive equation (PE) models is still questionable. However, some parts of the PE model’s attractors consist of solutions that are very close to superbalance states (i.e., without gravity waves). This study investigates the predictability of such PE models. The local predictability of the model in regions of approximate balanced states is compared with that in regions of states with gravity waves. The growth of errors on time scales of gravity waves and Rossby waves is also studied. The relation between the local predictability and the unstable manifolds of the model is examined.

The concept of slow manifold is extended to systems that have two (or more) separate scales of motion, such as the interacting ocean-atmosphere system. This study also investigates the local predictability of a low-order model representing coupled ocean-atmosphere system using the ideas and results obtained from the PE model. The interaction of fast and slow growth of errors and the idea of projecting the system onto a “slow climate manifold” are also investigated.