MODES OF INTERANNUAL TROPICAL OCEAN-ATMOSPHERE INTERACTION - A UNIFIED VIEW .3. ANALYTICAL RESULTS IN FULLY COUPLED CASES

The parameter-space dependence of the eigenmodes of the coupled tropic al ocean-atmosphere system, linearized about a climatological basic st ate, is further examined in a stripped-down intermediate coupled model using the formulation derived in Part II of this study to permit anal ytical treatment for a finite ocean basin. Part II examined the limit of weak coupling and showed the rapid transition to the mixed SST/ocea n dynamics modes of Part I, where it was argued that realistically cou pled modes are best understood from strong coupling. Here cases with o rder unity and larger coupling are explored to provide analytical prot otypes 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 poss ible, as well as for the transition from the well-separated case to mi xed 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 r ange of parameters; these are focused on because of their close relati on to the mixed SST/ ocean-dynamics modes with standing SST oscillatio ns and subsurface memory. The latter can be thought of as stationary S ST modes perturbed by wave dynamics. The east basin trapping exhibited by these modes can be produced even in a zonally homogeneous basic st ate as the result of east-west asymmetry due to beta in both atmospher e and ocean. An important new case is the strong-coupling limit where strongly growing modes dominated by coupled processes are examined. Th ese depend on both SST and ocean-dynamics time scales. but equatorial oceanic wave dynamics in the conventional sense is secondary to couple d processes in the basin interior. Because of this, these strongly gro wing modes are directly connected to SST modes in the fast-wave limit: extrapolating from the strong-coupling limit toward the fast-wave lim it, and vice versa, permits this eigensurface to be pieced together qu alitatively. 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 foun d in Part I and suggests that they must be a very robust feature of th e coupled system.