In the 1920s, British meteorologist Gilbert Walker, trying to forecast monsoons in India, noticed a strange connection: when air pressure rises over the eastern Pacific, it falls over the western Pacific, and vice versa. It was as if a giant air pendulum were swinging along the equator. Today, that pendulum is known as the Walker circulation, and it governs the alternation between El Niño and La Niña, the warm and cold phases of Earth's climate system.

For a long time, it remained a mystery why this pendulum does not swing evenly like a metronome but instead stalls in one position or another for years. Mathematicians studied the equations describing air movement over the tropics and found an answer: the system has two stable wells. Imagine a ball at the bottom of a hollow: it rests quietly until pushed. Similarly, the atmosphere can remain in an El Niño or La Niña state for years, as if stuck in one of the wells.

The transition between phases is not gradual but abrupt. In mathematics, such an event is called a saddle-node bifurcation: the two wells approach each other, merge, and the ball suddenly rolls into the remaining one. This is why El Niño and La Niña do not appear on a schedule but sporadically, every two to seven years. The trigger can be any disturbance, from a random gust of wind to a change in ocean temperature.

The authors did not merely simulate the atmosphere numerically; they rigorously proved that such two wells exist in the equations. This changes the view of El Niño: previously considered an oscillation, it is now seen as a system with two stable states. The practical benefit is that knowing the shape of the wells allows better predictions of when a transition will start and which phase will follow.

The pendulum that Walker noticed turned out to be not a simple one but one with two hollows. Now that the shape of these hollows is clear, scientists can better understand why the climate over the Pacific lingers in heat or coolness, and when to expect the next switch.