Variation of Earth's Oblateness J2 on Interannual-to-Decadal Timescales

The Earth's oblateness varies slightly due to a host of physical processes that involve large-scale meridional N-S mass redistributions in the Earth. We analyze these minute, broadband signals in the observed Delta J(2) data series for 1976-2019 (43 years). We first remove the near-quadratic variation (due to the glacial isostatic adjustment plus the accelerating land ice melting) and the seasonal terms (due to seasonality of the surface geophysical fluids) by least squares regression. Then we examine via cross-correlation function and cross-coherence spectrum the relationships of the remaining interannual-to-decadal Delta J(2) with various climate oscillations in terms of their respective indices. We elucidate the contributions of the Antarctic Oscillation and Arctic Oscillation (for timescales shorter than 5 years), Pacific Decadal Oscillation (for timescales longer than 5 years), and the absence thereof in El Nino-Southern Oscillation and Atlantic Multidecadal Oscillation. Removal of their contributions from Delta J(2) reveals two remaining, nonclimatic long-period signals: An 18.61-year tidal signal calls for an augmentation in the in-phase value and a reduction of the out-of-phase value in the theoretical models per International Earth rotation and Reference systems Service (IERS), while a more detailed quantitative study awaits future, longer data. An additional 10.5-year signal is found to be correlated with the solar cycle, but the origin of this apparent correlation is uncertain presently.