ALBERT

Description: The CNES/GRGS RL04 Earth gravity models are a set of gravity field solutions based on GRACE and SLR data, provided at different time samplings: (A) CNES/GRGS RL04 time series (A/1) A monthly GRACE+SLR time series of gravity field models (A/2) A 10-day GRACE+SLR time series of gravity field models (B) A mean gravity model EIGEN-GRGS.RL04.MEAN-FIELD, computed from the monthly RL04 GRACE+SLR time series and from GOCE data. (A) CNES/GRGS RL04 time series DATA: The data from the Star Camera Assembly (SCA), Accelerometer (ACC), K-Band Ranging (KBR) and GPS receiver are used. The KBR data is processed in the form of the relative velocity between the spacecrafts: K-Band Range-Rate (KBRR). In addition to the data from GRACE, the data from 5 SLR satellites are also used (Lageos, Lageos-2, Starlette, Stella and Ajisai), in order to provide an accurate and consistent description of the very low degrees of the gravity field (mainly degrees 1 and 2). The version of the GRACE data used for RL04 is L1B-v2 for the ACC and GPS data, L1B-v3 for the SCA and KBR data. INVERSION METHOD: By contrast with the GRACE solutions in spherical harmonics provided by other groups, the CNES/GRGS solutions are not obtained by a simple Cholesky inversion. The normal matrices are first diagonalized, ordered by decreasing order of the Eigen values and only the best defined sets of linear combinations of the spherical harmonics are solved. More details can be found here: https://grace.obs-mip.fr/variable-models-grace-lageos/grace-solutions-release-04/rl04-products-description/ (B) EIGEN-GRGS.RL04.MEAN-FIELD mean model EIGEN-GRGS.RL04.MEAN-FIELD is a mean model of Earth's gravity field spherical harmonics coefficients, based on the RL04 version of the CNES/GRGS time series of monthly gravity field determinations from GRACE & SLR data. EIGEN-GRGS.RL04.MEAN-FIELD is complete to degree and order 300. Between degrees 1 and 90, it contains time-variable gravity (TVG) coefficients ; above degree 90, it is a static field. EIGEN-GRGS.RL04.MEAN-FIELD is based on GOCE-DIR5 for the part between degree 91 and 300. The TVG coefficients between degrees 1 and 90 are obtained from a regression on the GRGS-RL04-v1 monthly time series of solutions (2002/09 – 2016/06). For degrees 1 and 2 this TVG part is temporally extended to 1993/01-2019/02 through the use of a GRGS SLR-only solution based on the data of 5 SLR satellites (Lageos, Lageos-2, Starlette, Stella, Ajisai). Outside of the measurements period (1993/01-2019/02 for degrees 1 and 2, 2002/09-2016/06 for degrees 3 to 90), the gravity field is extrapolated in the following way: - for degrees 1 and 2, before 1993/01 : average slope based on historical SLR data, mean annual and semi-annual periodic signals based on their average value between 1993 and 2019 - for degrees 1 and 2, after 2019/02 : average slope & mean annual and semi-annual periodic signals (based on their average value between 1993 and 2019) - for degrees 3 to 90, before 2002/09 : zero-slope extrapolation, mean annual and semi-annual periodic signals based on their average value between 2002 and 2016 - for degrees 3 to 90, after 2016/06 : average slope & mean annual and semi-annual periodic signals (based on their average value between 1993 and 2019) More details can be found here: https://grace.obs-mip.fr/variable-models-grace-lageos/mean-fields/release-04/

Description: The striking improvements in long- to medium-wavelengths gravity field recovery achieved with GPS-CHAMP and GPS-GRACE high-low and GRACE K-band range low-low satellite-to-satellite tracking prompted us to combine the satellite data with surface data from altimetry over the oceans and gravimetry over the continents to generate a new, high resolution global gravity field model: EIGEN-CG01C. The model is complete to degree/order 360 in terms of spherical harmonics and resolves half-wavelengths of 55 km in the geoid and gravity anomaly fields. A special band-limited combination method has been applied in order to preserve the high accuracy from the satellite data in the lower frequency band of the geopotential and to allow for a smooth transition to the high-frequency band, dominated by the surface data. Compared to pre-CHAMP/GRACE global high-resolution gravity field models, the accuracy was improved by one order of magnitude to 4 cm and 0.5 mgal in terms of geoid heights and gravity anomalies, respectively, at a spatial resolution of 200 km half-wavelength. The overall accuracy at degree/order 360 is estimated to be 20 cm and 5 mgal, respectively, and benefits significantly from recently released new gravity anomaly compilations over the polar regions. In general, the accuracy over the oceans is better than over the continents reflecting the higher quality of the available surface data.

Description: With the release of the combined GRACE monthly gravity field time-series COST-G RL01 the Combination Service for Time-variable Gravity fields (COST-G) of the International Association of Geodesy (IAG) became operational in July 2019. We present the COST-G RL01 time-series and provide validation in terms of orbit fit, ice mass trends, lake altimetry and sea level budget. We identify weak points in the combined monthly gravity fields and discuss possible improvements of the combination strategy for future combinations. While COST-G RL01 is based on sets of re-processed GRACE monthly gravity fields, COST-G also provides combinations of monthly Swarm high-low satellite-to-satellite tracking (hl-SST) gravity fields on an operational basis with a latency of 3 months. Combinations of GRACE-FO monthly gravity fields are in the process of operationalization. We provide a status report and first results of GRACE-FO combinations. Combined GRACE, Swarm and GRACE-FO gravity fields complement each other to provide a long-term time-series of mass variation in the system Earth.

Description: Operationally combined monthly gravity fields of the GRACE-FO satellite mission in spherical harmonic representation (Level-2 product) generated by the Combination Service for Time-variable Gravity Fields (COST-G; Jäggi et al. (2020):http://dx.doi.org/10.1007/1345_2020_109), a product center for time-variable gravity fields of IAG's International Gravity Field Service (IGFS). COST-G_GRACE-FO_RL01_OP is a combination of AIUB-GRACE-FO_op, GFZ-RL06 (GFO), GRGS-RL05 (unconstrained solution), ITSG-Grace_op, LUH-GRACE-FO, CSR-RL06 (GFO) and JPL-RL06 (GFO). The original time-series were provided by the analysis centers (ACs) and partner analysis centers (PCs) of COST-G.

Description: In the framework of the COmbination Service for Time-variable Gravity fields (COST-G) gravity field solutions from different analysis centres are combined to provide a consolidated solution of improved quality and robustness to the user. As in many other satellite-related sciences, the correct application of background models plays a crucial role in gravity field determination. Therefore, we publish a set of data of various commonly used forces in orbit and gravity field modelling (Earth's gravity field, tides etc.) evaluated along a one day orbit arc of GRACE, together with auxiliary data to enable easy comparisons. The benchmark data is compiled with the GROOPS software by the Institute of Geodesy (IfG) at Graz University of Technology. It is intended to be used as a reference data set and provides the opportunity to test the implementation of these models at various institutions involved in orbit and gravity field determination from satellite tracking data. In view of the COST-G GRACE and GRACE Follow-On gravity field combinations, we document the outcome of the comparison of the background force models for the Bernese GNSS software from AIUB (Astronomical Institute, University of Bern), the EPOS software of the German Research Centre for Geosciences (GFZ), the GINS software, developed and maintained by the Groupe de Recherche de Géodésie Spatiale (GRGS), the GRACE-SIGMA software of the Leibniz University of Hannover (LUH) and the GRASP software also developed at LUH. We consider differences in the force modelling for GRACE (-FO) which are one order of magnitude smaller than the accelerometer noise of about 10−10 m s−2 to be negligible and formulate this as a benchmark for new analysis centres, which are interested to contribute to the COST-G initiative.

Description: The recently completely recalibrated and reprocessed Gravity Field and Steady-State Ocean Circulation Explorer(GOCE) gravity gradient data were used by GFZ and CNES/GRGS to generate a new gravity field model viathe direct approach (DIR-R6). This work was done on behalf of the European Space Agency (ESA) within theconsortium of the GOCE High Level Processing Facility (GOCE-HPF).DIR-R6 is a satellite-only global gravity field model in terms of spherical harmonics to maximum degree andorder 300. It has been inferred by the combination of GOCE gravity gradient data with data from Satellite LaserRanging (SLR) tracking (LAGEOS 1/2, Stella, Starlette, Ajisai and LARES) and Gravity Recovery and ClimateExperiment (GRACE). Due to the instrumental behavior of the GOCE satellite gradiometer, the gravity gradientobservation equations must be preprocessed and filtered. Here, within the direct numerical method, the filteringhas been done using a low pass filter with a cut-off period of 8 seconds. The GOCE GPS-SST data are only usedto geolocate the gradients. The low-to-medium degree spherical harmonic coefficients of the gravity field aredetermined using GRACE GPS-SST and KBR data as well as SLR data from GFZ’s release 6 models. All dataare combined at normal equation level, which are solved using Cholesky decomposition. We applied the sphericalcap regularization to stabilize the low-order spherical harmonic coefficients for the polar gaps in the GOCE data.Furthermore, Kaula regularization is used at the high degrees. .When compared to the previous gravity field models based on GOCE data, for instance to the earlier releases ofESA’s GOCE models, DIR-R6 is more accurate, especially in its medium to high resolution. This is demonstratedamong others by GPS/leveling, orbit determination tests and an oceanographic evaluation.

Description: In the framework of the COmbination Service of Time-variable Gravity fields (COST-G) gravity field solutions from different analysis centres are combined to provide a consolidated solution of improved quality to the user. As in many other satellite-related sciences, the correct application of background models plays a crucial role in gravity field determination. Therefore, we publish a set of data of various commonly used forces in orbit and gravity field modelling (gravity field, tides etc.) evaluated along a one day orbit arc of GRACE, together with some additional data to enable easy comparisons. The benchmark data is compiled with the GROOPS software by the Institute of Geodesy (IfG) at Graz University of Technology. It is intended to be used as a reference and provides the opportunity to test the implementation of these models at various analysis centres. In view of the COST-G GRACE (-FO) gravity field combinations, we show the outcome of such a background force field software validation for the GRACE-SIGMA software of the Leibniz University of Hannover (LUH), the GRGS GINS software, EPOS of the German Research Centre for Geosciences (GFZ) and the Bernese GNSS software from AIUB (Astronomical Institute, University of Bern). We consider differences in the force modelling for GRACE (-FO) of one order of magnitude less than the accelerometer noise to be negligible, and make an attempt to quantify and explain differences exceeding this threshold.

Description: We present 10-day water mass solutions estimated from both GRACE and GRACE-FO KBR Range (KBRR) residuals for continental hydrology using GINS software developed by the CNES/GRGS group. The inter-satellite velocity residuals have been converted into along-track differences of potential using the energy balance approach. Maps of equivalent water height are obtained by inversion of these potential differences onto juxtaposed surface elements over the region of interest, or better, time coefficients of designed orthogonal Slepian functions. This latter band-limited representation offers the advantage of reducing drastically the number of parameters to be fitted. Shannon number of 60 for the regional Slepian representation is usually considered for GRACE-type data for basins of arbitrary shapes. The regional solutions are validated by comparison with series of existing Level-2 solutions produced by (official) centers once the contribution of the missing long-wavelength part of the time-varying field, i.e. low degree harmonic coefficients such as C〈sub〉20〈/sub〉, is simply added for completion. The patterns shown in the regional solutions reveal strong seasonal variations of water mass in the large tropical basins, e.g. Amazon and Congo, as well as important trends corresponding to regional droughts and continuous melting of the ice sheets that contributes to sea level rise.