EL-NINO SOUTHERN OSCILLATION AND THE ANNUAL CYCLE - SUBHARMONIC FREQUENCY-LOCKING AND APERIODICITY

An intermediate coupled model for the El Nino/Southern Oscillation (EN SO) phenomenon is used to examine the interaction of ENSO with the sea sonal cycle and how this is related to the irregularity of ENSO time s eries. 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 model s has recently been examined by Jin et al., Tziperman et al, and Chang et al. Here we fit this transition scenario into a broader perspectiv e.We emphasize three main points: (1) Using Floquet theory, we show st ep by step the relation of the ENSO mode in the linearized annual aver age case to the linear and nonlinear cases with the seasonal cycle. Th e dynamics that determine the spatial pattern and the basic oscillatio n mechanism are the same, thus putting a decade of theory on the linea r annual average case onto firmer ground. (2) The quasi-periodicity sc enario for the transition to chaos fundamentally involves two paramete rs, one governing the amplitude of the ENSO cycle, the other the inher ent period. Examining model behavior as a function of parameters revea ls that at reasonable amplitude of the ENSO cycle, superstable frequen cy-locked regimes are more prevalent than chaotic regimes. (3) When st ochastic 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. Th us the role of subharmonic frequency-locked resonances is important wh ether or not irregularity is due to internal chaotic behavior or to we ather noise.