Enso seasonal synchronization theory

Abstract

One of the key characteristics of the El Ni˜no-Southern Oscillation (ENSO) phenomenon is its synchronization to the annual cycle. Current theories over two possible mechanisms to account for this synchronization: frequency locking of ENSO to periodic forcing by the annual cycle, or the effect of the seasonally varying background state of the equatorial Pacific on the coupled stability of the ocean-atmosphere system. Using a parametric recharge oscillator model of ENSO, we test which of these scenarios provides a better explanation for the observational characteristics of ENSO/annual cycle interactions. Analytical solutions obtained from the neutral case of the model show that the annual modulation of the growth rate parameter results directly in ENSO's seasonal variance, amplitude modulation, and 2:1 phase synchronization of ENSO to the annual cycle. The analytical solutions are shown to be applicable to numerical runs of the model in the neutral case, as well as the long-term behavior of the damped model excited by stochastic noise. The synchronization characteristics of the stochastically forced model agree with the observations, and are shown to account for the variety of ENSO synchronization in state of the art coupled general circulation model simulations. Additionally, the idealized model predicts spectral peaks at "combination tones" between ENSO and the annual cycle that exist in both the observations and many coupled models. These results are then compared with the predictions of the nonlinear frequency entrainment model for ENSO/annual cycle interactions. The oscillator model is extended to include periodic forcing by the annual cycle and a nonlinear saturation term, and the resulting system is shown to be equivalent to the periodically forced van der Pol oscillator. Results from experiments with the van der Pol oscillator demonstrate that the frequency locking scenario predicts the existence of a spectral peak at the biennial frequency corresponding to the observed 2:1 phase synchronization. Such a peak does not exist in the observed ENSO spectrum. Hence, we conclude that the seasonal modulation of the coupled stability of the equatorial Pacific ocean-atmosphere system is the mechanism responsible for the synchronization of ENSO events to the annual cycle.