Every winter, the Pacific Ocean off the coast of Peru warms up, and every summer it cools down. This rhythm resembles a clock whose gears turn at different speeds at different times of the year. Old models missed this difference: they assumed the clock runs uniformly throughout the year. The new work adds a calendar to the clockwork, allowing us to see how the pace changes from month to month.

The scientists proposed two approaches. The first divides the year into segments and measures the gear speed in each, much like a watchmaker checking the timekeeping every hour rather than once a day. The second derives a formula linking the current gear speed to how quickly oscillations from a random jolt decay.

Tests on El Niño data showed the model captures the seasonal rhythm: the dynamics change smoothly, and the strength of random jolts has two peaks, in spring and autumn. This explains why El Niño tends to originate during these seasons. Now scientists can choose the right tool for the task, whether for precise motion description or for assessing random influences. Previously, it was unclear how to separate these contributions in seasonal data, but now the climate clockwork can be taken apart piece by piece.