# SLR, GRACE and Swarm Gravity Field Determination and Combination
###### Abstract  
Satellite gravimetry allows for determining large scale mass transport in the system Earth and to quantify ice mass change in polar regions. We provide, evaluate and compare a long time-series of monthly gravity field solutions derived either by satellite laser ranging (SLR) to geodetic satellites, by GPS and K-band observations of the GRACE mission, or by GPS observations of the three Swarm satellites. While GRACE provides gravity signal at the highest spatial resolution, SLR sheds light on mass transport in polar regions at larger scales also in the pre- and post-GRACE era. To bridge the gap between GRACE and GRACE Follow-On, we also derive monthly gravity fields using Swarm data and perform a combination with SLR. To correctly take all correlations into account, this combination is performed on the normal equation level. Validating the Swarm/SLR combination against GRACE during the overlapping period January 2015 to June 2016, the best fit is achieved when down-weighting Swarm compared to the weights determined by variance component estimation. While between 2014 and 2017 SLR alone slightly overestimates mass loss in Greenland compared to GRACE, the combined gravity fields match significantly better in the overlapping time period and the RMS of the differences is reduced by almost 100 Gt. After 2017, both SLR and Swarm indicate moderate mass gain in Greenland. satellite gravimetry; ice mass change; GRACE; SLR; swarm; normal equation combination 2019 11 956 10.3390/rs11080956 10.  
lower orbit altitude, the Laser Relativity Satellite (LARES) as the youngest member of the SLR family, which also provide information about temporal variations of the Earth gravity field at the lowest degrees of the spherical harmonic spectrum. The geodetic SLR satellites are optimal for gravimetry by their spherical geometry and their favorable area-to-mass ratio that minimizes the effect of surface forces [9]. For studies of temporal gravity field variations derived by SLR in the pre-GRACE era, see [PERSON] et al. [10], [PERSON] et al. [11] and [PERSON] and [PERSON] [12]. For a focus on variations in Earth oblateness, where GRACE results are unreliable [13], compare [PERSON] and [PERSON] [14] [PERSON] and [PERSON] [15] and [PERSON] et al. [16]. In addition, other Earth observing satellites at orbits below 1500 km altitude, so-called low Earth orbiters (LEOs), which are equipped with GPS receivers for precise orbit determination, may serve for deriving the mass distribution of the Earth and its temporal variations at low to medium resolution [17]. Due to the time-period covered and their low orbit altitude, the three satellites of the Swarm mission [18] are well suited to bridge the gap between GRACE and GRACE-FO. We present a long-term series covering 1995-2018 of low resolution monthly gravity field coefficients derived at the Astronomical Institute of the University of Bern (AIUB) from a combined orbit determination of LAGEOS and the geodetic SLR satellites in low Earth orbits [19]. The derived gravity fields are compared to time-series of GRACE solutions spanning 2003-2016, which were also determined at AIUB [20]. Finally, also the GPS-derived Swarm kinematic orbits that are routinely computed at AIUB [21] are exploited to derive monthly gravity fields for the time-period 2014-2018. Due to the different orbital altitudes and ground track patterns of the satellites, and due to the different observation techniques used, the gravity fields derived differ in their spherical harmonic and corresponding spatial resolution [22]. The truncation of the spherical harmonic expansion of the gravity field leads to spatial leakage that has to be taken into account when comparing the results (e.g., [4; 23; 24; 25; 26]). Furthermore, the high-resolution GRACE gravity fields commonly are smoothed to suppress noise in the high-degree coefficients (e.g., [27; 28; 29]).