GRACE era variability in the Earth’s oblateness: A comparison of estimates from six different sources

We study fluctuations in the degree-2 zonal spherical harmonic coefficient of the Earth's gravity potential, $C_{20}$, over the period 2003-2015. This coefficient is related to the Earth's oblateness and studying its temporal variations, $\Delta C_{20}$, can be used to monitor large-scale mass movements between high and low latitude regions. We examine $\Delta C_{20}$ inferred from six different sources, including satellite laser ranging (SLR), GRACE and global geophysical fluids models. We further include estimates that we derive from measured variations in the length-of-day (LOD), from the inversion of global crustal displacements as measured by GPS, as well as from the combination of GRACE and the output of an ocean model as described by \cite{sunetal2016}. We apply a sequence of trend- and seasonal moving average filters to the different time series in order to decompose them into an interannual, a seasonal and an intraseasonal component. We then perform a comparison analysis for each component, and we further estimate the noise level contained in the different series using an extended version of the three-cornered-hat method. For the seasonal component, we generally obtain a very good agreement between the different sources, and except for the LOD-derived series, we find that over 90\% of the variance in the seasonal components can be explained by the sum of an annual and semiannual oscillation of constant amplitudes and phases, indicating that the seasonal pattern is stable over the considered time period. High consistency between the different estimates is also observed for the intraseasonal component, except for the solution from GRACE, which is known to be affected by a strong tide-like alias with a period of about 161 days. Estimated interannual components from the different sources are generally in agreement with each other, although estimates from GRACE and LOD present some discrepancies. Slight deviations are further observed for the estimate from the geophysical models, likely to be related to the omission of polar ice and groundwater changes in the model combination we use. On the other hand, these processes do not seem to play an important role at seasonal and shorter time scales, as the sum of modelled atmospheric, oceanic and hydrological effects effectively explains the observed $C_{20}$ variations at those scales. We generally obtain very good results for the solution from SLR, and we confirm that this well-established technique accurately tracks changes in $C_{20}$. Good agreement is further observed for the estimate from the GPS inversion, showing that this indirect method is successful in capturing fluctuations in $C_{20}$ on scales ranging from intra- to interannual. Obtaining accurate estimates from LOD, however, remains a challenging task and more reliable models of atmospheric wind fields are needed in order to obtain high-quality $\Delta C_{20}$, in particular at the seasonal scale. The combination of GRACE data and the output of an ocean model appears to be a promising approach, particularly since corresponding $\Delta C_{20}$ is not affected by tide-like aliases, and generally gives better results than the solution from GRACE, which still seems to be of rather poor quality.