# SLR, GRACE and Swarm Gravity Field Determination and Combination
## 4 Conclusions  
Satellite laser ranging can contribute to the derivation of mass change estimates at the spatial scale of the Amazon basin, Greenland, or West Antarctica prior to the GRACE mission. SLR and high-low tracking of the Swarm satellites both may be used to bridge the gap between GRACE and GRACE-FO concerning the large scale mass loss in the polar regions of the Earth. When all individual gravity field results are truncated at the same spherical harmonic degree, the results can be compared directly. They match well for Greenland with a somewhat higher inter-annual variability of the SLR monthly mass estimates. Swarm can only be included in the comparison near the end of the life-time of the  
Figure 16: Monthly differences between GRACE and SLR (blue), Swarm (green) or combined mass estimates within Greenland. Missing values indicate gaps in the GRACE time-series.  
Figure 15: Monthly mass estimates within Greenland. All time-series truncated at degree 6 and with C\({}_{20}\) excluded.  
GRACE satellites. The seasonal variations visible in Swarm monthly mass estimates seem to be slightly over-estimated. On the other hand, the SLR derived mass loss within Greenland is larger than what can be extracted from GRACE observations between 2014 and 2017. After 2017, both SLR and Swarm results indicate moderate mass gain within Greenland.  
For a correct localization of mass change signal along the coast of West Antarctica, a spherical harmonic expansion up to degree 10 is desirable. This can be achieved by the regularization of SLR-only gravity field models or, preferably, by a combination with other LEO, e.g., Swarm data. A combination on the normal equation level, correctly taking into account all correlations between estimated and pre-eliminated parameters, is feasible as long as all satellite data is processed consistently. The best fit between a SLR/Swarm combination and GRACE for the period from January 2015 to August 2016, where both Swarm and GRACE observations of good quality are available, is achieved when SLR and Swarm normal equations are combined with almost equal weights.  
It is foreseen to continue the combination of SLR data, taking into account the contributions by different analysis centers, and the combination of SLR with Swarm and possibly also GRACE-FO on the normal equation level in the frame of the Combination Service for Time-variable Gravity field models (COST-G) [34; 52], the newly established product center of the International Gravity Field Service (IGFS) under the umbrella of the International Association of Geodesy (IAG).  
GRACE processing, derivation of mass trends, conceptualization and writing--U.M.; SLR processing and investigation--K.S.; determination of kinematic GRACE and Swarm orbits--D.A.; Swarm processing--C.D.; software development, supervision and funding--D.T.; supervision and project administration (SLR)--R.D.; supervision and project administration (GRACE, Swarm)--A.J.  
This research was partly funded by BKG \"Vertrag uber die Weiterentwicklung der Berner GNSS Software, 21.04.2017\" and by the ESA project Swarm-DISC, contract No. 4000109587/13/I-NB.  
We want to thank three anonymous reviewers for their invaluable comments.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} AC & Analysis Centre \\ AOD & Atmosphere and Ocean De-Aliasing \\ CMA & Celestial Mechanics Approach \\ GIA & Glacial Isostatic Adjustment \\ GPS & Global Positioning System \\ Gt & Gigatons (10\({}^{12}\) kg) \\ LEO & Low Earth Orbiter \\ NEQ & Normal Equation \\ PPP & Precise Point Positioning \\ RMS & Root Mean Square \\ SHC & Spherical Harmonic Coefficients \\ SLR & Satellite Laser Ranging \\ VCE & Variance Component Estimation \\ \end{tabular}