Fundamental Forcings of the Time Dependent Variations of the Southern Oscillation Index (SOI)

Inspired by the 11-year peaks in the autocorrelation functions of Seoul's rainfalls over a period of 234 years and rain and snow days for 385 years, we examined the time series of the SOI and its monthly Darwin and Tahiti surface pressure observations for a period of 146 years. The frequency components of the SOI signal and noise and both stations' pressure values are from solar activity, QBO, the annual cycle, the derived harmonics of the solar cycle, and the amplitude modulation of the annual cycle by QBO. The absence or weakness of the fundamental period and the dominance of the derived frequency peaks reveal the strong nonlinear response in pressure of the atmosphere to solar forcing and QBO. The fundamental and derived harmonics broaden their frequency band by spread-spectrum style modulation with the background noises. The analysis results confirm that the conventional El-Nino frequency band comprises periodicities originating directly and indirectly from the frequencies of the three driving forcings. We found no evidence of an intrinsic period or frequency possibly originating from the instability of the coupled ocean and atmosphere system.; Figure 1| ACF and FFT of the time series of the SOI signal and noise, Darwin and Tahiti pressure values, QBO. a and b, ACF and FFT of the SOI signal, c and d, for Darwin surface pressure, e and f, for Tahiti surface pressure, e and f, for the SOI noise, and g and h for the QBO time series. The blue and red vertical bars in the left-hand side column (a, c, e, g, i) denote the ACF peaks at lag values of 7 years and 11 years. In the right-hand side column (b, d, f, h, j), the red bars denote the harmonics with periods of 5.5 years (2nd bar from the left) and 3.7 years (the 3rd one from the left) derived from the solar cycle of an 11-year period. The left-most blue bar represents a 7-year period and the right-most blue bar shows the QBO position over the spectrum. The grey boxes mark the range of coefficients and amplitudes of pure stochastic processes at 95 % confidence level. The data for QBO cover 59 years in contrast with 146 years for the other parameters.