El Nino Southern Oscillation and the annual cycle: Subharmonic frequency-locking and aperiodicity

An intermediate coupled model for the El Nino/Southern Oscillation (ENSO) phenomenon is used to examine the interaction of ENSO with the seasonal cycle and how this is related to the irregularity of ENSO time series. Under annual mean conditions, the mechanisms that give rise to an inherent ENSO frequency and spatial pattern are well understood in this model, When the annual cycle is included, the ENSO cycle tends to lock to rational multiples of the annual frequency. The role of such subharmonic frequency locking in the transition to chaos in ENSO models has recently been examined by Jin et al., Tziperman et al, and Chang et al. Here we fit this transition scenario into a broader perspective. We emphasize three main points: (1) Using Floquet theory, we show step by step the relation of the ENSO mode in the linearized annual average case to the linear and nonlinear cases with the seasonal cycle. The dynamics that determine the spatial pattern and the basic oscillation mechanism are the same, thus putting a decade of theory on the linear annual average case onto firmer ground. (2) The quasi-periodicity scenario for the transition to chaos fundamentally involves two parameters, one governing the amplitude of the ENSO cycle, the other the inherent period. Examining model behavior as a function of parameters reveals that at reasonable amplitude of the ENSO cycle, superstable frequency-locked regimes are more prevalent than chaotic regimes. (3) When stochastic forcing by atmospheric uncoupled variability-''weather noise''-is included, the resulting irregularity in frequency-locked regimes still carries the signature of the frequency-locked spectral peaks. Thus the role of subharmonic frequency-locked resonances is important whether or not irregularity is due to internal chaotic behavior or to weather noise.