The speedometer needle in a car shows how fast the wheels are spinning. The climate system also has rotation, but it is invisible: it happens in state space, where each point is a combination of ocean temperature, the depth of the warm layer, and other parameters. Probabilistic angular momentum acts like such a speedometer, showing how fast and in which direction the climate 'spins' between its states.
El Niño is a warm current that every few years changes weather across the planet. Scientists track it using two numbers: the sea surface temperature in a specific region of the Pacific Ocean and the depth at which water warms to 20 degrees. These two numbers can be thought of as coordinates of a point on a plane. Connecting the points over many months gives a trajectory that does not just wander but curls into loops. It is these loops that the new tool captures.
To measure the rotation, the authors took monthly El Niño data spanning 56 years and daily data for the Madden–Julian oscillation, another climate cycle that operates on timescales of weeks. For each time point, they computed a small rotation: where the point on the state plane moved in one step. Then they summed all these rotations and built a distribution. It turned out to be strongly asymmetric: the mean is noticeably different from zero, although the most probable value is zero. This is like a speedometer that often reads zero but sometimes the needle swings sharply to the right.
Before this work, it was unclear how to detect such hidden rotations in real data. Now climatologists have a speedometer that can be attached to any set of measurements. It has already been tested on a simple linear model, and predictions matched observations. This means the tool works and can be used to compare different climate models: if a model does not reproduce the probability rotation, it misses an important part of the physics.
The speedometer needle has come full circle: now we see that the climate does not just change; it moves in a circle, and that circle can be measured. The next step is to apply the same approach to other climate cycles, such as the North Atlantic Oscillation, and see what other hidden rotations appear there.
Probabilistic angular momentum has the same units as the diffusion coefficient: length squared divided by time. For El Niño, with its indices of temperature (°C) and depth (cm), the units become exotic: °C·cm/month.
The idea that climate oscillations are manifestations of hidden rotations in an abstract space echoes Isaac Asimov's novel 'The End of Eternity', where changes in reality are described as loops in a multidimensional state space.