Every few years, the water off the coast of Peru becomes warmer than usual. This phenomenon is called El Niño, and it can change weather across the entire planet: droughts in some places, floods in others. Forecasting a strong El Niño six months ahead is very difficult because the ocean behaves like a capricious mechanism: small random wind gusts can steer it in different directions.

Scientists built a simple ocean model and added random wind bursts to it. Then, for each possible ocean state, they calculated the probability of a strong El Niño. It turned out that there are regions where the probability changes smoothly, and forecasts can be made confidently. But there are also regions where the slightest shift in the initial state changes the probability abruptly: today it is 10 percent, and a little to the right, it is already 90. There, forecasting is impossible, even if we know the ocean state exactly.

This is like a compass that points clearly in some places, but in others the needle trembles at the slightest breath of air. Previously, it was unclear how to assess where forecasts are reliable and where they are not. Now scientists know how to find these regions and can apply the method to real climate models to warn about heat waves and other rare events.