The long-term LOD seems to be the big mystery, and it also aligns to temperature variations.

Dickey, J.O.; Marcus, S.L.; de Viron, O. Air temperature and anthropogenic forcing: Insights from the solid Earth. J. Clim. 2011, 24, 569–574. http://journals.ametsoc.org/doi/full/10.1175/2010JCLI3500.1

There are some long tidal periodicities that may match according to this paper http://www.mdpi.com/2225-1154/5/4/83