When a meteorologist talks about the chance of rain, they rely on the current state of the atmosphere: pressure, humidity, wind. Similarly, for rare climate events, such as a strong El Niño, the warm current off the coast of South America, one can build a probability map. On this map, each point corresponds to a specific state of the ocean and atmosphere, and the color shows the probability that an event will start from there.

But how do you build such a map? The direct way is to run many simulations from each point and count the fraction that lead to the event. That is very expensive. Instead, the scientists trained a neural network on pairs of initial state and outcome, and it learned to predict the probability. Tests on a simple model showed that the network makes only small errors.

It turns out that the map has four types of regions. In some, the probability is always 0 or 1, meaning the outcome is predetermined. In others, the probability changes smoothly, so forecasting is possible but not precise. And there are regions where the slightest change in the starting point flips the probability from 0 to 1. There, forecasting is practically impossible. Knowing where these regions are helps to honestly assess forecast uncertainty.