Time–Frequency Variability of ENSO and Stochastic Simulations

The time–frequency spectral structure of El Niño–Southern Oscillation (ENSO) time series holds much information about the physical dynamics of the ENSO system. The authors have analyzed changes of the spectrum with time of three ENSO indices: the conventional Southern Oscillation index (SOI), Niño3 sea surface temperatures, and a tropical Pacific rain index, over the period 1871–1995. Three methods of time–frequency analysis—windowed Fourier transform, wavelet analysis, and windowed Prony’s method—were used, and the results are in good agreement. The time–frequency spectra of all the series show strong multidecadal variations over the past century. In particular, there was reduced activity of ENSO in the 2–3-yr periodicity range during the period 1920–60, compared with both the earlier and later periods. The dominant frequencies in the spectra do not appear to be constrained to certain frequency bands, and there is no evidence that the ENSO system has fixed modes of oscillation. The qualitative behavior of the real SOI time series has been compared with that of time series simulated by an autoregressive stochastic process of order 3 and time series created by phase-randomizing the spectral components of the SOI. The decadal variability of the amplitude and time–frequency spectra was found to be very similar between the observed and simulated SOIs. This suggests that the decadal variability of ENSO can be well simulated by a stochastic model and that stochastic forcing may be an important component of ENSO dynamics.