Earth's climate resembles a choir, where each member sings their own part at their own pitch. Some voices hold low notes, like multi-year ocean temperature oscillations, while others produce rapid trills, like short atmospheric waves. The conductor needs to hear each one, but the voices overlap and the notes blend into a mush.

For a long time, sPCA suffered from two ailments. First, it was sensitive to noise, like a listener bothered by the hum of the hall. Second, if two modes had similar amplitudes, their eigenvectors mixed, and the physical picture was lost. The authors of the new study solved both problems. They estimated cross-spectral matrices using the Morlet wavelet, a wave pulse with a Gaussian envelope that localizes frequency well even on short segments. Then they added a key step: rotating the eigenvectors.

Rotation is like adjusting a microphone. If two voices are equally loud, you can turn the microphone to capture one singer more clearly. The tuning criterion is phase smoothness. For a propagating wave, the phase changes linearly from point to point, like a wave traveling through a stadium. If the phase is jagged, the axis is rotated incorrectly. The method, called rotated spectral PCA (rsPCA), minimizes the "jaggedness" of the phase and finds a position where each mode looks like a clean traveling wave.

On synthetic data with two waves traveling in opposite directions, the method worked brilliantly. Classical PCA required nine components to explain only a tenth of the variability, while rsPCA with its first two components explained 46% and 26% and accurately recovered both waves. Even when the waves had equal amplitudes and were hidden by 90% noise, the rotation separated them without error.

Then the method was applied to real sea surface temperature data from the Pacific Ocean for 1940–2018. At low frequencies, it isolated the El Niño mode with a period of 2–7 years, and its correlation with the Niño 3.4 index was 0.72. At subannual frequencies, the rotation helped disentangle several extratropical modes, including a wave in the South Pacific that moves westward at about 20 degrees of longitude per month, which is 0.4 meters per second. For comparison, that is the speed of a leisurely walk.

Previously, such modes merged into an indistinguishable hum, and forecasters could not tell which signal mattered for seasonal prediction. Now that the voices are separated, we can better diagnose climate models and look for teleconnections that were previously hidden. The method requires no parametric assumptions and is easy to implement, so it can be readily applied to other climate variables, such as geopotential height. The ocean's choir can finally be listened to voice by voice.