ENSO dynamics: low-dimensional-chaotic or 1 stochastic?

We apply a test for deterministic, low-dimensional, and nonlinear dynamics to the Niño 3 time series for the El Niño Southern Oscillation (ENSO). The test is positive if the time series includes the seasonal variation, but negative if it onlyrepresents the anomaly, i.e., the deviation from the seasonal cycle. The results indicate that deterministic, low-dimensional, and nonlinear dynamics in ENSO is associated with the seasonal cycle, and that the dynamics determining the inter-annual timing and strength of El Niño/La Niña episodes is high-dimensional/stochastic. Application of stochastic forcing to a time-delay equation for equatorial-wave dynamics can reproduce stochastic dynamics and other important aspects of ENSO. Without such stochastic forcing this model yields deterministic, low-dimensional dynamics. With stochastic forcing our test still yields such dynamics if the seasonal cycle is retained, but does not if the annual cycle is subtracted before the test is applied. The model results illustrate that the seasonal variability can be governed by low-dimensional nonlinear dynamics, while the inter-annual variability associated with ENSO is dominated by the stochastic forcing.