Using multichannel singular spectrum analysis (MSSA) we decomposed climatic time series into principal components, and compared them with Earth rotation parameters. The global warming trends were initially subtracted. Similar quasi 60 and 20 year periodic oscillations have been found in the global mean Earth temperature anomaly (HadCRUT4) and global mean sea level (GMSL). Similar cycles were also found in Earth rotation variation. Over the last 160 years multi-decadal change of Earth's rotation velocity is correlated with the 60-year temperature anomaly, and Chandler wobble envelope reproduces the form of the 60-year oscillation noticed in GMSL. The quasi 20-year oscillation observed in GMSL is correlated with the Chandler wobble excitation. So, we assume that Earth's rotation and climate indexes are connected. Despite of all the clues hinting this connection, no sound conclusion can be done as far as ocean circulation modelling is not able to correctly catch angular momentum of the oscillatory modes.
Zotov, L., Bizouard, C., & Shum, C. K. (2016). A possible interrelation between Earth rotation and climatic variability at decadal time-scale. Geodesy and Geodynamics, 7(3), 216–222. https://doi.org/10.1016/j.geog.2016.05.005