Coupled ocean-atmosphere models exhibit a variety of forms of tropical interannual variability that may be understood as different flow regimes of the coupled system. The parameter dependence of the primary bifurcation is examined in a “stripped-down” version of the Zebiak and Cane model using the equatorial band approximation for the sea surface temperature (SST) equation as by Neelin. In Part I of this three-part series, numerical results are obtained for a conventional semispectral version; Parts II and III use an integral formulation to generate analytical results in simplifying limits. In the uncoupled case and in the fast-wave limit (where oceanic adjustment occurs fast compared to SST time scales), distinct sets of modes occur that are primarily related to the time scales of SST change (SST modes) and of oceanic adjustment (ocean-dynamics modes). Elsewhere in the parameter space, the leading modes are best characterized as mixed SST/ocean-dynamics modes; in particular, the continuous surfaces in parameter space formed by the eigenvalues of each type of mode can join.
A regime in the fast-wave limit in which the most unstable mode is purely growing, with SST anomalies in the eastern Pacific, proves to be a useful starting point for describing these mergers. This mode is linked to several oscillatory regimes by surfaces of degeneracy in the parameter space, at which two degrees of freedom merge. Within the fast-wave limit, changes in parameters controlling the strength of the surface layer or the atmospheric structure produce continuous transition of the stationary mode to propagating modes. Away from the fast-wave limit, the stationary mode persists at strong coupling even when time scales of ocean dynamics become important. On the weaker coupling side, the stationary mode joins to an oscillatory mode with mixed properties, with a standing oscillation in SST whose growth and spatial form may be understood from the SST mode at the fast-wave limit but whose period depends on subsurface oceanic dynamics. The oceanic dynamics, however, is only remotely related to that of the uncoupled problem. In fact, this standing-oscillatory mixed mode is insensitive to low-coupling complications involving connections to a sequence of uncoupled ocean modes at different parameter values, most of which are members of a discretized scattering spectrum. The implication that realistic coupled regimes are best understood from strong rather than weak coupling is pursued in Parts II and III. The interpretation of the standing-oscillatory regime as a stationary SST mode perturbed by wave dynamics gives a rigorous basis to the original physical interpretation of a simple model of Suarez and Schopf. However, viewing the connected modes as different regimes of a mixed SST/ocean-dynamics mode allows other simple models to be interpreted as alternate approximations to the same eigensurface; it also makes clear why varying degrees of propagating and standing oscillation can coexist in the same coupled mode.