The ocean shifts its currents, and each current remembers the past in its own way. One responds to what happened two months ago, another to what happened seven months back. But here's the catch: observations are made once a month, and the delay may not be a whole number. If a warm wave crosses the ocean in two and a half months, the records only have marks for 'two' and 'three.' Standard models can't look between them, so they make mistakes.
The new model allows delays to be fractional. If it needs the value from two and a half months ago, it takes the average of the records from two and three months. It's like recalling midweek from a diary that only notes Mondays and Fridays: you fill in the missing piece. Meanwhile, the hidden regime switches according to a probabilistic rule, like a current that changes direction under a random wind.
The algorithm works in two steps. First, it guesses which regime the ocean was in at each moment; then it adjusts parameters to make the data fit better. Fractional delays are found by brute force: the algorithm tries different values and keeps those that make the model more accurate. On El Niño data spanning 860 months, the two-regime model found delays of 2.386 and 7.301 months. This means the ocean, in different states, remembers the past with different depths, and now we can measure that depth.
El Niño literally means 'the boy' in Spanish, named by Peruvian fishermen who noticed warm water around Christmas. The delay in El Niño models reflects the time it takes for a warm water wave to cross the Pacific Ocean.