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The Pan-Alpine gravity database 2020

This data publication is a new compilation of land gravity data expressing the Earth’s gravitational acceleration field on the broader area of the European Alps. The dataset is based on national databases from 10 countries, but surmounts any barriers related to national reference systems. The input to this dataset is the largest Alpine compilation of point-wise data on land ever, and also includes marine data in adjacent regions in the Mediterranean Sea. Following quality control, this represents a total of 349’938 terrestrial gravity points and about 700’000 marine stations. Only such a dataset allows to investigate the Alpine orogen from shallow (sedimentary) to large (mantle) depths, which is among the primary goals of the AlpArray science program. Broad effort to collect all existing, public and private, point-based gravity data in the area of interest: 2-23°E, 41-51°N. The final, published grids are shared with the community on a 4*4 km2 grid; the results on 2*2 km2 grid are available upon request and approval from the group. We developed and fine-tuned an approach in which all raw data could be processed in the same, homogeneous way. Outliers were discarded. Full details are given in the reference publication (Zahorec et al., 2020).

The gravity field model based on the second invariant of the GOCE gravitational gradient tensor: IGGT_R1

IGGT_R1 is a static gravity field model based on the second invariant of the GOCE gravitational gradient tensor, up to degree and order 240. Based on tensor theory, three invariants of the gravitational gradient tensor (IGGT) are independent of the gradiometer reference frame (GRF). Compared to traditional methods for calculation of gravity field models based on GOCE data, which are affected by errors in the attitude indicator, using IGGT and least squares method avoids the problem of inaccurate rotation matrices. IGGT_R1 is the first experiment to use this method to build a real gravity field model by using GOCE gravitational gradients.This new model has been developed by Wuhan University (WHU), GFZ German Research Centre for Geosciences (GFZ), Technical University of Berlin (TUB), Huazhong University of Science and Technology (HUST) and Zhengzhou Information Engineering University (IEU). More details about the gravity field model IGGT_R1 is given in our paper “The gravity field model IGGT_R1 based on the second invariant of the GOCE gravitational gradient tensor” (Lu et al., 2017, http://doi.org/10.1007/s00190-017-1089-8).This work is supported by the Chinese Scholarship Council (No. 201506270158), the Natural Science Foundation of China (Nos. 41104014, 41131067, 41374023, 41474019 and 41504013) and the Key Laboratory of Geospace Environment and Geodesy, Ministry Education, Wuhan University (No. 16-02-07).

Level-2a simulated gravity field solutions of ESA’s science support study to Mass change And Geosciences International Constellation (MAGIC) Phase A

The joint ESA/NASA Mass-change And Geosciences International Constellation (MAGIC) mission has the objective to extend time series from previous gravity missions, including an improvement of accuracy and spatio-temporal resolution. The long-term monitoring of Earth's gravity field carries information on mass-change induced by water cycle, climate change, and mass transport processes between atmosphere, cryosphere, oceans and solid Earth. The MAGIC mission will be composed of two satellite pairs flying in different orbit planes. The NASA/DLR--led first pair (P1) is expected to be in a near-polar orbit around 500 km of altitude; while the second ESA--led pair (P2) is expected to be in an inclined orbit of 65--70 degrees at approximately 400 km altitude. The ESA--led pair P2 Next Generation Gravity Mission (NGGM) shall be launched after P1 in a staggered manner to form the MAGIC constellation. The addition of an inclined pair shall lead to reduction of temporal aliasing effects and consequently of reliance on de-aliasing models and post-processing. The main novelty of the MAGIC constellation is the delivery of mass-change products at higher spatial resolution, temporal (i.e. sub--weekly) resolution, shorter latency, and higher accuracy than GRACE and GRACE-FO. This will pave the way to new science applications and operational services. The performances of different MAGIC mission scenarios for different application areas in the field of geosciences were analysed in the frame of the initial ESA Science Support activities for MAGIC. The data sets provided here are the Level-2a simulated gravity field solutions of MAGIC scenarios and the related reference signal that were used for these analyses. The .gfc files in the folders monthly (31-day solutions) and weekly (7-day solutions) contain the estimated (HIS) coefficients (Cnm, Snm) as well as the formal errors (SigCnm, SigSnm) of the different MAGIC scenarios. In order to compute the coefficient errors, the reference/true HIS coefficients contained in the folder HIS_reference_fields need to be subtracted from the estimated HIS coefficients. The data sets provided here comprise the Level-2a simulated gravity field solutions of MAGIC scenarios and the related reference signal (based on Dobslaw et al. 2014; 2015) that were used for the above analyses.

Using real polar terrestrial gravimetry data to overcome the polar gap problem of GOCE - the gravity field model IGGT_R1C

With the successful completion of ESA's PolarGAP campaign, terrestrial gravimetry data (gravity anomalies) are now available for both polar regions. Therefore, it is now possible to overcome the GOCE polar gap by using real gravimetry data instead of some regularization methods. But terrestrial gravimetry data needs to become filtered to remove the high-frequency gravity information beyond spher. harm. degree e.g. 240 to avoid disturbing spectral leakage in the satellite-only gravity field models. For the gravity anomalies from the Arctic, we use existing global gravity field models (e.g., EGM2008) for this filtering. But for the gravity anomalies from Antarctica, we use local gravity field models based on a point mass modeling method to remove the high-frequency gravity information. After that, the boundary-value condition from Molodensky's theory is used to build the observation equations for the gravity anomalies. Finally, variance component estimation is applied to combine the normal equations from the gravity anomalies, from the GOCE GGs (e.g., IGGT_R1), from GRACE (e.g., ITSG-Grace2014s) and for Kaula's rule of thumb (higher degree/order parts) to build a global gravity field model IGGT_R1C without disturbing impact of the GOCE polar gap. This new model has been developed by German Research Centre for Geosciences (GFZ), Technical University of Berlin (TUB), Wuhan University (WHU) and Huazhong University of Science and Technology (HUST).Parametersstatic model modelname IGGT_R1Cproduct_type gravity_fieldearth_gravity_constant 0.3986004415E+15radius 0.6378136460E+07max_degree 240norm fully_normalizedtide_system tide_freeerrors formal

WHU-GRACE-GPD01s: Monthly gravity field models derived from GRACE intersatellite geopotential differences

The WHU-GRACE-GPD01s models are the latest monthly gravity field solutions recovered from GRACE intersatellite geopotential difference (GPD) data processed at the School of Geodesy and Geomatics, Wuhan University, China. The intersatellite GPDs are estimated from GRACE Level-1B (RL03) data based on the improved energy balance equation and remove-compute-restore (RCR) technique, and the background models are consistent with GRACE Level-2 processing standards document (RL06). Further details are presented in Zhong et al. (2020, 2022). The WHU-GRACE-GPD01s models include two sets of GRACE monthly solutions: one is the unconstrained monthly solutions with the maximum degree and order of 60, the other is the constrained monthly solutions up to the maximum degree and order 96 with Kaula regularization constraint, and the optimal regularization parameter is determined using variance component estimation (VCE). This work is supported by the National Natural Science Foundation of China (No. 41974015, 41474019, 42061134007) and the Project Supported by the Special Fund of Hubei Luojia Laboratory (Grant No. 220100004).

Python Package Regional TWS Uncertainty

Python tool box, which allows the user to calculate mean TWS time series, their uncertainties, and regional covariance matrices for arbitrary regions. This tool box has been used to produce the results presented in Boergens et al. (2021) based on the TWS data of Boergens and Kvas (2021).

International Combination Service for Time-variable Gravity Fields (COST-G) Monthly GRACE/GRACE-FO RL02 Series

Second release of combined monthly gravity fields of the GRACE and GRACE-FO satellite missions in spherical harmonic representation (Level-2 product) generated by the Combination Service for Time-variable Gravity Fields (COST-G; Jäggi et al., 2020), a product center for time-variable gravity fields of IAG's International Gravity Field Service (IGFS). COST-G RL02 is a combination of gravity field time series provided by the following analysis centers (ACs) and partner analysis centers (PCs) of COST-G: ACs: - GFZ Helmholtz Centre for Geosciences: GFZ RL06 (GRACE), GFZ RL06.3 (GRACE-FO) - Graz University of Technology, Institute of Geodesy: ITSG-Grace2018 (GRACE), ITSG-Grace_op (GRACE-FO) - Centre National d’Etudes Spatiales, Groupe de Recherche de Geodesie Spatiale: CNES_GRGS_RL05_CHOL (GRACE & GRACE-FO) - Astronomical Institute University of Bern: AIUB-RL03 (GRACE), AIUB-GRACE-FO_rl02op (GRACE-FO) - Leibniz Universität Hannover: LUH-GRACE-2020 (GRACE), LUH-GRACE-FO-2020 (GRACE-FO) - Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences: APM-SYSU (GRACE) - HuaZhong University of Science and Technology: HUST-Grace2024 (GRACE & GRACE-FO) - Southern University of Science and Technology, Department of Earth and Space Sciences: SUSTech2025 (GRACE) - Tongji University, College of Surveying and Geo-informatics: Tongji-Grace2022 (GRACE) PCs: - Center for Space Research at University of Texas: CSR RL06 (GRACE), CSR RL06.3 (GRACE-FO) - NASA Jet Propulsion Laboratory: JPL RL06 (GRACE), JPL RL06.3 (GRACE-FO) --------------------------------------------------------------------------------------------- Version History: 4 July 2025: Release of Version 2.1. This is an update of Version 2.0 of the same data set including the following changes: Replacement of Tongji-Grace-Costg (nonofficial release) by Tongji-Grace2022; replacement of HUST-Grace2023 (nonofficial release) by HUST-Grace2024 (currently also not yet officially released); use of GFZ RL06.3, CSR RL06.3, JPL RL06.3 and CNES_GRGS_RL05_CHOL for the entire GRACE-FO period. 25 April 2025: Initial release of the data (Version 2.0).

CNES/GRGS RL04 Earth gravity field models, from GRACE and SLR data

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/

Post-processed GRACE/GRACE-FO Geopotential GSM Coefficients GFZ RL06 (Level-2B Product)

Post-processed GRACE/GRACE-FO spherical harmonic coefficients of GFZ RL06 Level-2 GSM products representing an estimate of Earth's gravity field variations during the specified timespan. Post-processing steps comprise: (1) subtraction of a long-term mean field; (2) optionally, decorrelation and smoothing with VDK filter (anisotropic filter taking the actual error covariance information of the underlying GSM coefficients into account, see Horvath et al. (2018)); (3) replacement of coefficients C20, C30 (only for the months within the period from 2016/11 through 2017/06), C21 and S21 (only for the months within the period from 2002/04 through 2017/06) and its formal standard deviations by values estimated from a combination of GRACE/GRACE-FO and Satellite Laser Ranging (SLR); (4) subtraction of linear trend caused by Glacial Isostatic Adjustment (GIA) as provided by a numerical model; (5) insertion of geocenter coefficients (C10, C11, S11); and (6) removal of estimated aliased signal of the S2 tide (161 days period). These coefficients represent signals caused by water mass redistribution over the continents and in the oceans. These post-processed GRACE/GRACE-FO GSM products are denoted as Level-2B products. There are multiple variants of Level-2B products available that differ by the characteristics of the anisotropic filter applied. These variants are distinguishable by the following strings in the product file names: - 'NFIL': Level-2B product is not filtered - 'VDK1': Level-2B product is filtered with VDK1 - 'VDK2': Level-2B product is filtered with VDK2 - 'VDK3': Level-2B product is filtered with VDK3 - 'VDK4': Level-2B product is filtered with VDK4 - 'VDK5': Level-2B product is filtered with VDK5 - 'VDK6': Level-2B product is filtered with VDK6 - 'VDK7': Level-2B product is filtered with VDK7 - 'VDK8': Level-2B product is filtered with VDK8 The individual auxiliary data sets and models used during the post-processing steps mentioned above are provided as well (in the aux_data folder): - 'GRAVIS-2B_2002095-2020091_GFZOP_0600_NFIL_0004.gz': Long-term mean field calculated as unweighted average of the 183 available GFZ RL06 GSM products in the period from 2002/04 up to and including 2020/03. - 'GRAVIS-2B_GFZOP_GRACE+SLR_LOW_DEGREES_0004.dat': time series of coefficients C20, C30, C21 and S21 estimated from a combination of GRACE/GRACE-FO and SLR - 'GRAVIS-2B_GIA_ICE-6G_D_VM5a_0004.gz': Model from Peltier et al. (2018) for subtraction of linear trend caused by GIA - 'GRAVIS-2B_GFZOP_GEOCENTER_0004.dat': Time series with geocenter coefficients estimated from GFZ RL06 Further information about the Level-2B products and the auxiliary data is provided in the header of the corresponding data files. --------------------------------------------------------------------------------------------- Version History: 16 January 2025: Release of Version 0004. This is an update of Version 0003 of the same data set (see changelog). 21 April 2023: Release of Version 0003. This is an update of Version 0002 of the same data set (see changelog). 09 June 2020: Release of Version 0002. This is an update of Version 0001 of the same data set (see changelog). All changes and updates are documented in the changelog available via the data download section. Previously released versions of this data set are available in the "old_versions" subfolder in the data download folder.

Post-processed GRACE/GRACE-FO Geopotential GSM Coefficients COST-G RL01 (Level-2B Product)

Post-processed GRACE/GRACE-FO spherical harmonic coefficients of COST-G RL01 Level-2 GSM products representing an estimate of Earth's gravity field variations during the specified timespan. Post-processing steps comprise: (1) subtraction of a long-term mean field; (2) optionally, decorrelation and smoothing with VDK filter (anisotropic filter taking the actual error covariance information of the underlying GSM coefficients into account, see Horvath et al. (2018)); (3) replacement of coefficients C20 and C30 (only for the months within the period from 2016/11 through 2017/06) and its formal standard deviations by values estimated from a combination of GRACE/GRACE-FO and Satellite Laser Ranging (SLR); (4) subtraction of linear trend caused by Glacial Isostatic Adjustment (GIA) as provided by a numerical model; (5) insertion of geocenter coefficients (C10, C11, S11); and (6) removal of estimated aliased signal of the S2 tide (161 days period). These coefficients represent signals caused by water mass redistribution over the continents and in the oceans. These post-processed GRACE/GRACE-FO GSM products are denoted as Level-2B products. There are multiple variants of Level-2B products available that differ by the characteristics of the anisotropic filter applied. These variants are distinguishable by the following strings in the product file names: - 'NFIL': Level-2B product is not filtered - 'VDK1': Level-2B product is filtered with VDK1 - 'VDK2': Level-2B product is filtered with VDK2 - 'VDK3': Level-2B product is filtered with VDK3 - 'VDK4': Level-2B product is filtered with VDK4 - 'VDK5': Level-2B product is filtered with VDK5 - 'VDK6': Level-2B product is filtered with VDK6 - 'VDK7': Level-2B product is filtered with VDK7 - 'VDK8': Level-2B product is filtered with VDK8 The individual auxiliary data sets and models used during the post-processing steps mentioned above are provided as well (in the aux_data folder): - 'GRAVIS-2B_2002095-2020091_GFZOP_0600_NFIL_0003.gz': Long-term mean field calculated as unweighted average of the 183 available GFZ RL06 GSM products in the period from 2002/04 up to and including 2020/03. - 'GRAVIS-2B_COSTG_GRACE+SLR_LOW_DEGREES_0003.dat': time series of coefficients C20, C30, C21 and S21 estimated from a combination of GRACE/GRACE-FO and SLR - 'GRAVIS-2B_GIA_ICE-6G_D_VM5a_0003.gz': Model from Peltier et al. (2018) for subtraction of linear trend caused by GIA - 'GRAVIS-2B_COSTG_GEOCENTER_0003.dat': Time series with geocenter coefficients estimated from COST-G RL01 Further information about the Level-2B products and the auxiliary data is provided in the header of the corresponding data files. --------------------------------------------------------------------------------------------- Version History: 21 April 2023: Release of Version 0003. This is an update of Version 0002 of the same data set (see changelog). 15 June 2020: Initial release of the data. Note that the initial version number is 0002 in order to reflect the consistent data processing of this data set and Version 0002 of the data set Dahle & Murböck (2019, https://doi.org/10.5880/GFZ.GRAVIS_06_L2B). All changes and updates are documented in the changelog available via the data download section. Previously released versions of this data set are available in the "old_versions" subfolder of the data download folder.

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