Observing global terrestrial water storage changes (TWSCs) from (inter-)seasonal to (multi-)decade time-scales is very important to understand the Earth as a system under natural and anthropogenic climate change. The primary goal of the Gravity Recovery And Climate Experiment (GRACE) satellite mission (2002–2017) and its follow-on mission (GRACE-FO, 2018–onward) is to provide time-variable gravity fields, which can be converted to TWSCs with $\sim 300$ km spatial resolution; however, the one year data gap between GRACE and GRACE-FO represents a critical discontinuity, which cannot be replaced by alternative data or model with the same quality. To fill this gap, we applied time-variable gravity fields (2013–onward) from the Swarm Earth explorer mission with low spatial resolution of $\sim 1500$ km. A novel iterative reconstruction approach was formulated based on the independent component analysis (ICA) that combines the GRACE and Swarm fields. The reconstructed TWSC fields of 2003–2018 were compared with a commonly applied reconstruction technique and GRACE-FO TWSC fields, whose results indicate a considerable noise reduction and long-term consistency improvement of the iterative ICA reconstruction technique. They were applied to evaluate trends and seasonal mass changes (of 2003–2018) within the world’s 33 largest river basins.

Although the knowledge of the gravity of the Earth has improved considerably with CHAMP, GRACE, and GOCE (see appendices for a list of abbreviations) satellite missions, the geophysical community has identified the need for the continued monitoring of the time-variable component with the purpose of estimating the hydrological and glaciological yearly cycles and long-term trends. Currently, the GRACE-FO satellites are the sole dedicated provider of these data, while previously the GRACE mission fulfilled that role for 15 years. There is a data gap spanning from July 2017 to May 2018 between the end of the GRACE mission and start the of GRACE-FO, while the Swarm satellites have collected gravimetric data with their GPS receivers since December 2013. We present high-quality gravity field models (GFMs) from Swarm data that constitute an alternative and independent source of gravimetric data, which could help alleviate the consequences of the 10-month gap between GRACE and GRACE-FO, as well as the short gaps in the existing GRACE and GRACE-FO monthly time series. The geodetic community has realized that the combination of different gravity field solutions is superior to any individual model and set up the Combination Service of Time-variable Gravity Fields (COST-G) under the umbrella of the International Gravity Field Service (IGFS), part of the International Association of Geodesy (IAG). We exploit this fact and deliver the highest-quality monthly GFMs, resulting from the combination of four different gravity field estimation approaches. All solutions are unconstrained and estimated independently from month to month. We tested the added value of including kinematic baselines (KBs) in our estimation of GFMs and conclude that there is no significant improvement. The non-gravitational accelerations measured by the accelerometer on board Swarm C were also included in our processing to determine if this would improve the quality of the GFMs, but we observed that is only the case when the amplitude of the non-gravitational accelerations is higher than during the current quiet period in solar activity. Using GRACE data for comparison, we demonstrate that the geophysical signal in the Swarm GFMs is largely restricted to spherical harmonic degrees below 12. A 750 km smoothing radius is suitable to retrieve the temporal variations in Earth's gravity field over land areas since mid-2015 with roughly 4 cm equivalent water height (EWH) agreement with respect to GRACE. Over ocean areas, we illustrate that a more intense smoothing with 3000 km radius is necessary to resolve large-scale gravity variations, which agree with GRACE roughly at the level of 1 cm EWH, while at these spatial scales the GRACE observes variations with amplitudes between 0.3 and 1 cm EWH. The agreement with GRACE and GRACE-FO over nine selected large basins under analysis is 0.91 cm, 0.76 cm yr⁻¹, and 0.79 in terms of temporal mean, trend, and correlation coefficient, respectively. The Swarm monthly models are distributed on a quarterly basis at ESA's Earth Swarm Data Access (at https://swarm-diss.eo.esa.int/, last access: 5 June 2020, follow Level2longterm and then EGF) and at the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/series/02_COST-G/Swarm, last access: 5 June 2020), as well as identified with the DOI https://doi.org/10.5880/ICGEM.2019.006 (Encarnacao et al., 2019).

We develop a high-resolution regional gravity field model by a combination of spherical harmonics, band-limited spherical radial basis functions (SRBFs) and the residual terrain model (RTM) technique. As the main input data set, we employ a dense terrestrial gravity database (3–6 stations km⁻²), which enables gravity field modelling up to very short spatial scales. The approach is based on the remove–compute–restore methodology in which all the parts of the signal that can be modelled are removed prior to the least-squares adjustment in order to smooth the input gravity data. To this end, we utilize degree-2159 spherical harmonic models and the RTM technique using topographic models at 2 arcsec resolution. The residual short-scale gravity signal is modelled via the band-limited Shannon SRBF expanded up to degree 21 600, which corresponds to a spatial resolution of 30 arcsec. The combined model is validated against GNSS/levelling-based height anomalies, independent surface gravity data, deflections of the vertical and terrestrial vertical gravity gradients achieving an accuracy of 2.7 cm, 0.53 mGal, 0.39 arcsec and 279 E in terms of the RMS error, respectively. A key aspect of the combined approach, especially in mountainous areas, is the quality of the RTM. We therefore compare the performance of two RTM techniques within the innermost zone, the tesseroids and the polyhedron. It is shown that the polyhedron-based approach should be preferred in rugged terrain if a high-quality RTM is required. In addition, we deal with the RTM computations at points located below the reference surface of the residual terrain which is known to be a rather delicate issue.

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).