Every few years, the Pacific Ocean seems to take a deep breath: warm water spreads from Indonesia toward South America, and weather patterns across the globe go haywire. This phenomenon is called El Niño. Scientists record its pulse using numbers: the pressure difference between two islands and the water temperature at a specific location. Records have been kept for 66 years for one index and 147 years for another.
Previously, it was thought that deviations from the average rhythm were random noise, like static on a radio. But when scientists looked closely at the records, they found that strong pulses occur much more often than such a model predicts. The probability of an event with an amplitude twice the threshold drops not by a factor of hundreds, but only by a factor of 23. It is as if, in a calm sea, a wave as tall as a house rolled in every week. Moreover, the ocean remembers its past states: today's temperature depends on what happened several years ago. The memory does not fade even on long timescales.
This is why forecasts often fail: models do not account for this long memory and frequent strong events. If new data are incorporated into them, forecasts will become more accurate, and we will be better prepared for droughts, floods, and other consequences. The ocean does not breathe like a metronome, but like a jazz drummer who remembers every beat.
The power-law tail exponent μ = 4.52 for SOI means that an event with amplitude twice the threshold occurs roughly 23 times less often than an event at the threshold amplitude. That is much slower than the Gaussian distribution predicts.