On the relation between the ENSO cycle, its irregularity and decadal variation

The El Niño - Southern Oscillation (ENSO) climate variation is characterised by three major features: cyclical behavior, irregularity and a decadal component. A highly idealized stochastic model for ENSO is presented with properties illustrating all three of these features. The model describes the evolution of the two phases of ENSO as a damped linear oscillator with additive white noise forcing.

These phases can be thought of as corresponding to the time evolution of the real and imaginary part of the Principal Oscillation Pattern (POP) of Pacific sea surface temperature (SST) or sea level pressure (SLP). The real part corresponds to the mature phase of ENSO and the imaginary parts can be viewed as precursors. The physical relationship between the imaginary parts of SLP and SST POPs are investigated. The model allows for correlations between the phase forcings and can induce one of the phases to have a much higher spectral signature in the low frequency range. This has implications on decadal variability.

All parameters of the model including the stochastic forcing statistics and period and decay time are estimated from observational data. The theoretical spectrum of a linear system with additive stochastic noise is fitted to the observed power spectra. We find that the period of the oscillation is well restrained even when using only one phase. However, useful estimates of the forcing statistics and decay time can only be obtained when utilizing spectra for both phases of the oscillation in the spectral fit. Model generated time series show irregular oscillations with the period comparable to observations.