The unexpected signal in GRACE estimates of $C_{20}$

Abstract

For science applications of the gravity recovery and climate experiment (GRACE) monthly solutions, the GRACE estimates of $C_{20}$ (or $J_{2}$) are typically replaced by the value determined from satellite laser ranging (SLR) due to an unexpectedly strong, clearly non-geophysical, variation at a period of $\sim$160 days. This signal has sometimes been referred to as a tide-like variation since the period is close to the perturbation period on the GRACE orbits due to the spherical harmonic coefficient pair $C_{22}/S_{22}$ of S2 ocean tide. Errors in the S2 tide model used in GRACE data processing could produce a significant perturbation to the GRACE orbits, but it cannot contribute to the $\sim$160-day signal appearing in $C_{20}$. Since the dominant contribution to the GRACE estimate of $C_{20}$ is from the global positioning system tracking data, a time series of 138 monthly solutions up to degree and order 10 ($10\times 10$) were derived along with estimates of ocean tide parameters up to degree 6 for eight major tides. The results show that the $\sim$160-day signal remains in the $C_{20}$ time series. Consequently, the anomalous signal in GRACE $C_{20}$ cannot be attributed to aliasing from the errors in the S2 tide. A preliminary analysis of the cross-track forces acting on GRACE and the cross-track component of the accelerometer data suggests that a temperature-dependent systematic error in the accelerometer data could be a cause. Because a wide variety of science applications relies on the replacement values for $C_{20}$, it is essential that the SLR estimates are as reliable as possible. An ongoing concern has been the influence of higher degree even zonal terms on the SLR estimates of $C_{20}$, since only $C_{20}$ and $C_{40}$ are currently estimated. To investigate whether a better separation between $C_{20}$ and the higher-degree terms could be achieved, several combinations of additional SLR satellites were investigated. In addition, a series of monthly gravity field solutions ($60\times 60$) were estimated from a combination of GRACE and SLR data. The results indicate that the combination of GRACE and SLR data might benefit the resonant orders in the GRACE-derived gravity fields, but it appears to degrade the recovery of the $C_{20}$ variations. In fact, the results suggest that the poorer recovery of $C_{40}$ by GRACE, where the annual variation is significantly underestimated, may be affecting the estimates of $C_{20}$. Consequently, it appears appropriate to continue using the SLR-based estimates of $C_{20}$, and possibly also $C_{40}$, to augment the existing GRACE mission.