The influence of LRI observations on GRACE-FO gravity field models

Analysing the measurement data from both instruments produces a very similar picture of the monthly Earth gravity field, as can be seen in Fig. 1. The respective KBR and LRI gravity field solutions were filtered beforehand in order to reduce the dominant error structures caused by temporal aliasing and to visualise the actual mass change signals. Both measuring units therefore provide comparable gravity field data, reliably and independently of each other, which enables the continuous observation of mass changes on Earth. Despite the significantly higher measurement accuracy of the LRI compared to the KBR instrument, no significant differences can be detected, at least at the level of the globally spatially resolved Earth gravity field. The typical spatial error structures along the meridians (stripes in north-south direction) in the gravity field solutions are equally visible, albeit here in a reduced form due to the subsequent filtering. These error patterns are caused by temporal undersampling of geophysical gravity field signals due to periodic and non-periodic mass variations in the ocean and atmosphere. In principle, these should not be included in the final gravity field solution, as corresponding background models are used during data processing to reduce these short-wave signals, which have periods of only a few days or even hours, away from the target signal. However, these models are not error-free. The residual error is reflected in the form of temporal aliasing, e.g. by the aforementioned striping structures, in the resolved gravity field. This temporal aliasing is, in addition to the error of the accelerometers (measuring unit for determining the non-gravitational forces), the largest error influence in the monthly solutions of the Earth's gravity fields. The higher measurement accuracy of the LRI is dominated by these error influences and can therefore only be exploited to a limited extent with a single pair such as GRACE-FO.

However, when analyzing the estimated gravity field solutions in more detail, significant differences between KBR- and LRI-based models can also be identified. Fig. 2 shows the corresponding estimated gravity fields for January 2019 in the form of spherical harmonic coefficients in triangular form, separately for the sine (S) and cosine (C) coefficients for all degrees and orders up to 180 (corresponding to about 111 km spatial resolution). It is noticeable that the lower order coefficients in the LRI solution are better estimated than those in the KBR solution. This phenomenon increases with increasing degree. The advantage of the LRI over the KBR is therefore mainly in the area of the zonal and near-zonal coefficients, i.e. those around order 0. These coefficients reflect signals in the polar regions on Earth, and it can be assumed that the error components in this range are reduced by the LRI measurements. However, it must be emphasized again that this reduction is hardly or not at all visible in the final gravity field models of a single-pair solution, since the error components of the temporal aliasing described above are dominated by high-frequency geophysical signals. It therefore makes sense to continue developing improved background models of the oceanic tides and the transient dynamics in the atmosphere and ocean in addition to further improvements in sensor data analysis. Although the subsequent processing of the time-variable, monthly gravity field solution with digital filters leads to a significant reduction in error structures, it also reduces the spatial resolution and leads to the loss of the target signal in certain parts, which means that the high-frequency signal components are lost. As can be seen in Fig. 2, the LRI benefits from a higher spatial resolution of the time-variable monthly field, e.g. up to degree and order 180 instead of the usual order 96 (corresponds approximately to a spatial resolution of 208 km). It can therefore be assumed that in the case of the contribution to high-resolution static (i.e. averaged over many years) gravity fields by GRACE-FO, the high measurement accuracy of the LRI in the high frequency range can lead to visible improvements. This work is still pending, e.g. as part of the NEROGRAV research group.