It is of great interest to numerous geophysical studies that the time series of global gravity field models derived from Gravity Recovery and Climate Experiment (GRACE) data remains uninterrupted after the end of this mission. With this in mind, some institutes have been spending efforts to estimate gravity field models from alternative sources of gravimetric data. This study focuses on the gravity field solutions estimated from Swarm global positioning system (GPS) data, produced by the Astronomical Institute of the University of Bern, the Astronomical Institute (ASU, Czech Academy of Sciences) and Institute of Geodesy (IfG, Graz University of Technology). The three sets of solutions are based on different approaches, namely the celestial mechanics approach, the acceleration approach and the short-arc approach, respectively. We derive the maximum spatial resolution of the time-varying gravity signal in the Swarm gravity field models to be degree 12, in comparison with the more accurate models obtained from K-band ranging data of GRACE. We demonstrate that the combination of the GPS-driven models produced with the three different approaches improves the accuracy in all analysed monthly solutions, with respect to any of them. In other words, the combined gravity field model consistently benefits from the individual strengths of each separate solution. The improved accuracy of the combined model is expected to bring benefits to the geophysical studies during the period when no dedicated gravimetric mission is operational.@en

Since 2002 Gravity Recovery and Climate Experiment (GRACE) provides monthly gravity fields from K-band ranging (KBR) between two GRACE satellites. These KBR gravity monthlies have enabled the global observation of time-varying Earth mass signal at a regional scale (about 400 km resolution). Apart from KBR, monthly gravity solutions can be computed from onboard GPS data. The newly reprocessed GPS monthlies from 13 yr of GRACE data are shown to yield correct time-variable gravity signal (seasonality, trends, interannual variations) at a spatial resolution of 1300 km (harmonic degree 15). We show that GPS fields from new Swarm mission are of similar quality as GRACE GPS monthlies. Thus, Swarm GPS monthlies represent new and independent source of information on time-variable gravity, and, although with lower resolution and accuracy, they can be used for its monitoring, particularly if GRACE KBR/GPS data become unavailable before GRACE Follow-On is launched (2017 August).@en

Several alternative gravity forward modelling methodologies and associated numerical codes with their own advantages and limitations are available for the solid Earth community. With upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets, it is vital to understand the opportunities and limitations of the various approaches. In this paper, we discuss the four widely used techniques: global spherical harmonics (GSH), tesseroid integration (TESS), triangle integration (TRI), and hexahedral integration (HEX). A constant density shell benchmark shows that all four codes can produce similar precise gravitational potential fields. Two additional shell tests were conducted with more complicated density structures: laterally varying density structures and a crust-mantle interface density. The differences between the four codes were all below 1.5% of the modelled gravity signal suitable for reproducing satellite-acquired gravity data. TESS and GSH produced the most similar potential fields (<0.3 %). To examine the usability of the forward modelling codes for realistic geological structures, we use the global lithosphere model WINTERC-G that was constrained, among other data, by satellite gravity field data computed using a spectral forward modelling approach. This spectral code was benchmarked against the GSH, and it was confirmed that both approaches produce a similar gravity solution with negligible differences between them. In the comparison of the different WINTERC-G-based gravity solutions, again GSH and TESS performed best. Only short-wavelength noise is present between the spectral and tesseroid forward modelling approaches, likely related to the different way in which the spherical harmonic analysis of the varying boundaries of the mass layer is performed. The spherical harmonic basis functions produce small differences compared to the tesseroid elements, especially at sharp interfaces, which introduces mostly short-wavelength differences. Nevertheless, both approaches (GSH and TESS) result in accurate solutions of the potential field with reasonable computational resources. Differences below 0.5% are obtained, resulting in residuals of 0.076 mGal standard deviation at 250 km height. The biggest issue for TRI is the characteristic pattern in the residuals that is related to the grid layout. Increasing the resolution and filtering allow for the removal of most of this erroneous pattern, but at the expense of higher computational loads with respect to the other codes. The other spatial forward modelling scheme, HEX, has more difficulty in reproducing similar gravity field solutions compared to GSH and TESS. These particular approaches need to go to higher resolutions, resulting in enormous computation efforts. The hexahedron-based code performs less than optimal in the forward modelling of the gravity signature, especially with a laterally varying density interface. Care must be taken with any forward modelling software as the approximation of the geometry of the WINTERC-G model may deteriorate the gravity field solution.@en