Modes of Interannual Tropical Ocean–Atmosphere Interaction—a Unified View. Part III: Analytical Results in Fully Coupled Cases

Abstract

The parameter-space dependence of the eigenmodes of the coupled tropical ocean-atmosphere system, linearized about a climatological basic state, is further examined in a stripped-down intermediate coupled model using the formulation derived in Part II of this study to permit analytical treatment for a finite ocean basin. Part II examined the limit of weak coupling and showed the rapid transition to the mixed SST/ocean dynamics modes of Part I, where it was argued that realistically coupled modes are best understood from strong coupling. Here cases with order unity and larger coupling are explored to provide analytical prototypes for the fully coupled case from a system that explicitly treats spatial structure in a finite basin. The coupled dynamics is explored for several regions of parameter space where simplifications are possible, as well as for the transition from the well-separated case to mixed modes. The case of surface-layer processes only provides a simple example of westward-propagating SST modes. Extensive results are given for SST modes in the fast-wave limit. In addition to propagating SST modes, stationary, purely growing SST modes exist over a significant range of parameters; these are focused on because of their close relation to the mixed SST/ocean-dynamics modes with standing SST oscillations and subsurface memory. The latter can be thought of as stationary SST modes perturbed by wave dynamics. The east basin trapping exhibited by these modes can be produced oven in a zonally homogeneous basic state as the result of east-west asymmetry due to ? in both atmosphere and ocean. An important new case is the strong-coupling limit where strongly growing modes dominated by coupled processes are examined. These depend on both SST and ocean-dynamics time scales, but equatorial oceanic wave dynamics in the conventional sense is secondary to coupled processes in the basin interior. Because of this, these strongly growing modes are directly connected to SST modes in the fast-wave limit: extrapolating from the strong-coupling limit toward the fast-wave limit, and vice versa, permits this eigensurface to be pieced together qualitatively. Purely growing modes in the strong-coupling limit can be traced all the way from the fast-wave limit to its converse, the fast-SST limit. This, and the relation of the strongly coupled modes to the SST modes, serves to explain the connection of the eigensurfaces found in Part I and suggests that they must be a very robust feature of the coupled system.