Earth's climate is like a choir, where each member sings their own part. Some oscillations are slow, like multi-year changes in ocean temperature; others are fast, like short atmospheric waves. Scientists need to hear each voice, but the voices overlap, and the notes blend into a mush.

Previously, this method was sensitive to noise, like a listener bothered by the hum of the hall. And if two oscillations had equal strength, they couldn't be separated. The authors of the new work solved both problems. They used a special wave pulse that picks out frequencies well even in short segments, and then added a rotation of the analysis axes. This rotation is like adjusting a microphone: if two voices sound equally loud, you can turn the microphone so it picks up one singer more clearly.

The rotation is done so that the wave phase becomes flat. For a traveling wave, the phase changes smoothly, like a wave moving across a stadium. If the phase comes out jagged, the axis is turned incorrectly. The new method, called rotated spectral PCA, finds a position where each mode looks like a clean traveling wave. On synthetic data with two waves traveling in opposite directions, the method accurately recovered both waves, even when they had equal strength and were hidden by noise.

The method was then applied to real data of Pacific Ocean surface temperature from 1940 to 2018. At low frequencies, it isolated the El Niño mode with a period of 2–7 years, and its match with the known index was 0.72. At higher frequencies, the rotation helped separate several modes, including a wave in the South Pacific that moves westward at about 0.4 meters per second. For comparison, that is the speed of a leisurely walk. Previously, such modes blended into an indistinguishable hum, but now they can be listened to individually.