A trail in the sand stretches across the entire beach. The animal passed here at night, and from its footprints you can reconstruct not only its size but also its gait: where it sped up, where it slowed down, how it shifted its weight. That is essentially what researchers did with El Niño. Rather than building a giant model of the ocean and atmosphere, they took the 135-year trail of this climate phenomenon, a series of 1620 monthly values of the MEI.ext index, and tried to read from it the equation of motion.
First, they cleaned the trail of small debris: they filtered out fast fluctuations with periods shorter than a year, leaving only the slow stride that retains 95% of the signal's energy. Then they represented each moment in time as a point in a five-dimensional space, where the coordinates are five values of the series shifted relative to one another. And here something unexpected emerged: the system's trajectory, which would have been expected to wander throughout this space, actually hugs a plane. As if the animal that left the trail moved not randomly but along an invisible path.
Once this equation was extracted and trained on just the first 486 points (40.5 years), it began predicting the remaining 94.5 years with remarkable accuracy. At 6 months ahead, the correlation between forecast and reality reaches 0.96, whereas the best current climate models achieve about 0.86. And a useful forecast, when correlation exceeds 0.6, persists for up to 10.5 months. Strong events, deviating from the norm by more than one standard deviation, are predicted even more reliably.
The spring predictability barrier is especially important. Every spring, the quality of El Niño forecasts drops sharply, and this has plagued meteorologists for decades. In the new model, the barrier is greatly weakened: the maximum improvement over a linear model occurs precisely in the spring months. It turns out that the shortcoming of physical models was not complexity but their failure to account for deterministic nonlinearity that can be extracted directly from the data.
The trail in the sand turned out to be not just an imprint but an encrypted gait. And now that the equation has been read, El Niño forecasts can be made in seconds on an ordinary computer, not a supercomputer. This is not a replacement for physical models but a cheap and independent aid for agriculture, water management, and energy. After all, if you know the animal's gait, you can predict where it will head next.
The model is trained on just 486 points (40.5 years of data) but forecasts 94.5 years ahead. Moreover, the computational cost of forecasting is practically zero, unlike the supercomputer calculations of physical models.