Reduced Descriptions of Coupled GFD Systems (Slow Manifolds in the Ocean and Atmosphere)

A distinctive difficulty in climate-system modeling, analysis and prediction is the presence of two or more time scales in the problem. The atmosphere and oceans each support slow Rossby and fast inertia-gravity waves, while the characteristic times of atmosphere, oceans, and ice sheets are about a factor of 10 apart. Thus the proper treatment, via slaved-variable and slow-manifold theory of time-scale disparity within each subsystem and between subsystems is of the essence. The workshop topics will include

(i) the connection between the slow manifold, averaged descriptions, the quasi-geostrophic approximation, and intermediate balanced models;

(ii) models of the coupled ocean-atmosphere system; and

(iii) slow-manifold theory. Tools such as asymptotics, averaging, center manifold, inertial manifold, attractors and their approximations are indispensable for dealing with these problems.

Keywords: coupling, ENSO, intermediate models