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The behavior of the Cane-Zebiak ENSO prediction model is analyzed as a function of model parameters measuring the strength of coupling between the model ocean and atmosphere and the amplitude of the back-ground seasonal cycle specified in the model. As either of these two parameters is increased, the model undergoes a transition from periodic to chaotic behavior according to the universal quasi-periodicity route to chaos. Thus, the irregularity of model ENSO events and their partial locking to the seasonal cycle can both be explained as low-order chaotic behavior driven by the seasonal cycle. The chaos is due to irregular jumping of the Pacific natural ocean-atmosphere oscillator between different nonlinear resonances with the seasonal forcing. periodic seasonal forcing seems to be the main factor determining the chaotic behavior of the model. However, the full irregularity of model ENSO events is only explained by considering additional factors, possibly including the nonlinear interaction of different delay oscillator modes related to the different model ocean Rossby modes.
Tziperman et al. (Wed,) studied this question.