The Entropy of Climate Swings ✛

You can sit on a seesaw and pump your legs, or you can just tip from one side to the other. The Pacific Ocean does both. Every few years, warm water off the coast of Peru gives way to cooler water, and rainfall patterns, winds, and entire ecosystems across half the planet reshuffle. These shifts are called El Niño and La Niña, together known as ENSO: Earth's climate seesaw.

For a long time, climatologists tracked the seesaw using a single number: the atmospheric pressure difference between Tahiti and Darwin, Australia. When pressure rises in Darwin and falls in Tahiti, the index goes negative, and El Niño sets in. When the opposite happens, it's La Niña. This index, the SOI, has been recorded daily from 1991 to 2023, yielding 11,744 data points. The author of the new study decided to ask not "when will the seesaw tip," but "how unusual is the very swing from one side to the other?"

To calculate the entropy of a transition, the author first extracted a slow background from the daily SOI values: the annual cycle, the Madden–Julian oscillation, and five other rhythms. He described the remainder as a random walk in which the strength of random kicks depends on the current state, much as gusts of wind rock a swing harder once it's already moving. Then, for each of the 11 transitions between phases, he compared the probability of the forward path with that of the reverse path. If the forward path is much more likely than the reverse, entropy increases sharply, and the transition can be called extreme.

It turns out that nearly all transitions are ordinary. Only one, from the strong La Niña of 1999–2000 to the moderate El Niño of 2002–2003, deviated from the mean by four standard deviations. That's like the seesaw suddenly looping the loop, but even such a loop fits within the rules of the game: all transitions satisfied the probabilistic version of the second law of thermodynamics. In other words, the climate seesaw doesn't squeak.

Previously, it was unclear whether fluctuation theorems could be applied to climate indices at all, and whether ENSO transitions are extreme events. Now it's clear that almost all of them are statistically ordinary, with only one approaching the threshold. The method can be extended to multivariate indicators: sea surface temperature, outgoing radiation, precipitation. Then entropy analysis would no longer depend on a single number and would reveal which components of the system truly carry information about the phase transition. For now, the seesaw swings without squeaking, and that in itself is news.