Martin Lasser

Groundwater is one of the most important freshwater resources for ecosystems and mankind. Because of its fundamental role in the Earth's water and energy cycles, groundwater has been declared an essential climate variable by GCOS, the Global Climate Observing System. Similar to other subsurface states and fluxes, groundwater is difficult to monitor at the global scale, with sufficient spatial coverage and over climate-relevant time scales. The Global Gravity-based Groundwater Product (G3P) is a global observation-based data set of large-scale groundwater storage variations. G3P capitalizes on the unique capability of GRACE and GRACE-FO satellite gravimetry as the only remote sensing technology to monitor subsurface mass variations. In a mass balance approach, satellite-based, in situ observation-based and model-based water storage variations of snow water equivalent, root-zone soil moisture, glacier mass, and surface water storage are subtracted from GRACE/-FO terrestrial water storage anomalies to result in monthly variations of groundwater storage. For this combination, the individual compartmental storage data are spatially filtered to be consistent with the spatial resolution of terrestrial water storage from satellite gravimetry. The G3P data set presented here covers the period 2002 to 2023 with monthly resolution on a 0.5° global grid and includes propagated uncertainty information. We describe the details of the G3P data processing chain and of each contributing data stream including their uncertainties and limitations, provide examples of spatial and temporal groundwater storage variations represented by the G3P data set, and present exemplary evaluation results against in situ groundwater observations for three large aquifer systems. The latter show moderate to high temporal correlation of aquifer-average G3P groundwater storage and in situ groundwater level variations on seasonal and interannual time scales. G3P is a prototype for an operational global groundwater service, under development as a cross-cutting extension of the existing portfolio of the Copernicus Climate Change Service C3S. The G3P data set is available via GFZ Data Services at https://doi.org/10.5880/g3p.2024.001 (Güntner et al., 2024).

So far, the operational combination of the monthly GRACE, or GRACE-FO gravity field solutions by the Combination Service of Time-variable Gravity fields (COST-G) has been performed on the solution level. The originally foreseen combination on the normal equation (NEQ) level suffered from the very diverse and not realistic formal uncertainties, which hampered the application of Variance Component Estimation (VCE) and made the use of empirical weighting factors mandatory. Meanwhile, empirical noise models that enable the determination of realistic formal uncertainties are available from several GRACE-FO analysis centers. Experimental NEQ-combinations confirmed the applicability of VCE for the GRACE-FO combination and also the combination with SLR turned out to be feasible without the use of empirical weighting factors. The combination of the future GRACE-C and NGGM missions on the NEQ-level is a prerequisite to generate gravity field solutions of the MAGIC constellation. Consequently, the combination of NEQs from different Analysis Centers (ACs), including also SLR, will be the goal of future COST-G releases, but relies on the cooperation of the ACs to provide their NEQs and to apply realistic noise models.

At the Astronomical Institute of the University of Bern (AIUB) the Celestial Mechanics Approach for the analysis of satellite orbital motion is currently employed for two space geodetic techniques, namely GNSS and Satellite Laser Ranging (SLR). Both are not only used for station network analyses but also for precise orbit determination (GNSS) and validation (SLR) of Low Earth Orbiting (LEO) satellites. In addition, GNSS-based LEO orbits and SLR observations to the spherical geodetic satellites are used in Earth gravity field recovery. Taking GRACE Follow-On as an example, we present temporal gravity field results, where we derive dynamic and reduced-dynamic orbits together with gravity field parameters from GPS carrier phase observations and combine them with SLR observations to the satellites. Hence, using the satellites as a space tie with respect to the gravity field. We validate our results by comparing them with solutions of superior quality derived from the operational GRACE Follow-On data processing at the AIUB, which include the K-band range-rate data, and we investigate the quality of the co-estimated orbits.

Inter-satellite ranging by space gravimetry missions, such as from the Gravity Recovery And Climate Experiment (GRACE) mission and its successor mission GRACE Follow-On, has been established to observe mass variations in the Earth system from space globally. A complex processing chain is needed to invert the instrument data (Level-1) of space gravimetry missions into global gravity field products, either represented as a spherical harmonic series expansion (Level-2) or further processed gridded products dedicated to use for various scientific applications (Level-3), and combine them with products from other remote sensing satellite missions or assimilate them into geophysical process models (Level-4). The complexity arises from the need to use multiple background models and apply numerous corrections. Consequently, providing uncertainties for the various products is challenging. Not only is inter-satellite ranging data needed in this processing chain, but also other satellite observations, such as GPS, and geophysical background models, e.g., for de-aliasing of high-frequency signals or signal separation in the Level-3 data sets. These observations and model data sets are contributing with their specific uncertainties to the overall uncertainty budget of the final gravity fields. As long as the uncertainties of the models cannot be fully accounted for, a formal uncertainty propagation remains insufficient. Thus, an empirical error assessment remains the only reliable way of uncertainty assessment at the moment. Finally, a further source of error is signal leakage, which is related to the signal attenuation at satellite altitude and may be aggravated by spatial filtering of the Level-3 products. A comprehensive review of the current status of the uncertainty modeling of mass variation products through the whole processing chain is missing and thus is addressed in this article.

Groundwater is one of the most important freshwater resources for ecosystems and mankind. Because of its fundamental role in the Earth's water and energy cycles, groundwater has been declared an essential climate variable by GCOS, the Global Climate Observing System. Similar to other subsurface states and fluxes, groundwater is difficult to monitor at the global scale, with sufficient spatial coverage and over climate-relevant time scales. The Global Gravity-based Groundwater Product (G3P) is a global observation-based data set of large-scale groundwater storage variations. G3P capitalizes on the unique capability of GRACE and GRACE-FO satellite gravimetry as the only remote sensing technology to monitor subsurface mass variations. In a mass balance approach, satellite-based, in situ observation-based and model-based water storage variations of snow water equivalent, root-zone soil moisture, glacier mass, and surface water storage are subtracted from GRACE/-FO terrestrial water storage anomalies to result in monthly variations of groundwater storage. For this combination, the individual compartmental storage data are spatially filtered to be consistent with the spatial resolution of terrestrial water storage from satellite gravimetry. The G3P data set presented here covers the period 2002 to 2023 with monthly resolution on a 0.5° global grid and includes propagated uncertainty information. We describe the details of the G3P data processing chain and of each contributing data stream, provide examples of spatial and temporal groundwater storage variations represented by the G3P data set, and present exemplary evaluation results against in situ groundwater observations for three large aquifer systems. G3P is a prototype for an operational global groundwater service, under development as a cross-cutting extension of the existing portfolio of the Copernicus Climate Change Service C3S. The G3P data set is available via GFZ Data Services at https://doi.org/10.5880/G3P.2024.001 (Güntner et al., 2024).

Groundwater is one of the most important freshwater resources for ecosystems and mankind. Because of its fundamental role in the Earth's water and energy cycles, groundwater has been declared an essential climate variable by GCOS, the Global Climate Observing System. Similar to other subsurface states and fluxes, groundwater is difficult to monitor at the global scale, with sufficient spatial coverage and over climate-relevant time scales. The Global Gravity-based Groundwater Product (G3P) is a global observation-based data set of large-scale groundwater storage variations. G3P capitalizes on the unique capability of GRACE and GRACE-FO satellite gravimetry as the only remote sensing technology to monitor subsurface mass variations. In a mass balance approach, satellite-based, in situ observation-based and model-based water storage variations of snow water equivalent, root-zone soil moisture, glacier mass, and surface water storage are subtracted from GRACE/-FO terrestrial water storage anomalies to result in monthly variations of groundwater storage. For this combination, the individual compartmental storage data are spatially filtered to be consistent with the spatial resolution of terrestrial water storage from satellite gravimetry. The G3P data set presented here covers the period 2002 to 2023 with monthly resolution on a 0.5° global grid and includes propagated uncertainty information. We describe the details of the G3P data processing chain and of each contributing data stream, provide examples of spatial and temporal groundwater storage variations represented by the G3P data set, and present exemplary evaluation results against in situ groundwater observations for three large aquifer systems. G3P is a prototype for an operational global groundwater service, under development as a cross-cutting extension of the existing portfolio of the Copernicus Climate Change Service C3S. The G3P data set is available via GFZ Data Services at https://doi.org/10.5880/G3P.2024.001 (Güntner et al., 2024).

Groundwater is one of the most important freshwater resources for ecosystems and mankind. Because of its fundamental role in the Earth's water and energy cycles, groundwater has been declared an essential climate variable by GCOS, the Global Climate Observing System. Similar to other subsurface states and fluxes, groundwater is difficult to monitor at the global scale, with sufficient spatial coverage and over climate-relevant time scales. The Global Gravity-based Groundwater Product (G3P) is a global observation-based data set of large-scale groundwater storage variations. G3P capitalizes on the unique capability of GRACE and GRACE-FO satellite gravimetry as the only remote sensing technology to monitor subsurface mass variations. In a mass balance approach, satellite-based, in situ observation-based and model-based water storage variations of snow water equivalent, root-zone soil moisture, glacier mass, and surface water storage are subtracted from GRACE/-FO terrestrial water storage anomalies to result in monthly variations of groundwater storage. For this combination, the individual compartmental storage data are spatially filtered to be consistent with the spatial resolution of terrestrial water storage from satellite gravimetry. The G3P data set presented here covers the period 2002 to 2023 with monthly resolution on a 0.5° global grid and includes propagated uncertainty information. We describe the details of the G3P data processing chain and of each contributing data stream, provide examples of spatial and temporal groundwater storage variations represented by the G3P data set, and present exemplary evaluation results against in situ groundwater observations for three large aquifer systems. G3P is a prototype for an operational global groundwater service, under development as a cross-cutting extension of the existing portfolio of the Copernicus Climate Change Service C3S. The G3P data set is available via GFZ Data Services at https://doi.org/10.5880/G3P.2024.001 (Güntner et al., 2024).

The very original motivation of the Combination Service for Time-variable Gravity fields (COST-G) has been a combination of monthly gravity fields computed by different Analysis Centres (ACs) on Normal EQuation (NEQ) level, thus, taking all formal correlations arising with the orbit and instrumentparameters directly into account. However, already early experiments within the EGSIEM project, where a prototype of the combinationservice was developed, showed that the use of different nuisance parameters - set up to absorb observation and background model deficiencies - by each of the ACs leads to diverse formal uncertainty estimates of the spherical harmonic coefficients representing the Earth’s gravity field. Though formally possible, a combination on NEQ-level yielded degraded results. Even more, this rendered an automated combination process, applying Variance Component Estimation (VCE) on NEQ-level to derive relative weights for the individual AC’s contributions, impossible. Meanwhile, realistic uncertainty information is available for the majority of background models, and empirical noise modelling techniques leading to realistic uncertainty estimates are well established among the ACs processing the GRACE Follow-On data. In preparation for ESA’s Next Generation Gravity Mission (NGGM), where the combination of gravity field solutions from different ACs and a contribution from Satellite Laser Ranging (SLR) to stabilise the very low degree spherical harmonic coefficients is foreseen on NEQ-level, the combination strategy has been revisited with GRACE-FO NEQs of AIUB (rl03op), GFZ (preliminary RL07) and TUG (ITSG-Grace_operational) NEQs, as well as LAGEOS 1 and 2 and LARES 2 SLR-NEQs from AIUB and CNES, with very promising results, which we show in this contribution.In this context, we also introduce the updated operational gravity field solution time series from the AIUB and investigate its impact on the COST-G combination. Background modelling has been revisited and the uncertainty characterisation has been improved by additionally co-estimating daily spherical harmonic coefficients constrained with AOe07 variance-covariance information.

Since mid-2018, the satellite pair of the gravimetry satellite mission called Gravity Recovery And Climate Experiment Follow-on (GRACE-FO) has been providing observations to determine the time-variable Earth’s gravity field with high temporal and spatial resolution. However, some of the low-degree Earth’s gravity field coefficients can better be determined by using Satellite Laser Ranging (SLR) observations to spherical geodetic satellites. Consequently, individual Earth’s gravity field coefficients may be replaced in the GRACE-FO products, or alternatively, the parameter estimation of the Earth’s gravity field can be performed using multi-technique combinations.The Variance Component Estimation (VCE) is a well-established and widely adopted technique in satellite geodesy. As an example, VCE is used for combining observations from different geodetic space techniques or even to or from individual satellites to estimate precise geodetic parameters, e.g., to derive an international terrestrial reference frame.In this study, applications of the VCE method, implemented in a development version of the Bernese GNSS software, are assessed for improved and more automated gravity field parameter determination. The primary focus is on the use of the VCE method for data quality assessments and to strengthen the orbit parametrization. In GRACE-FO data processing, reduced-dynamic orbits, where the usual orbit parameter set is extended with regular Piece-Wise Accelerations (PCAs), are used. In case of SLR data, the strong correlation between the gravity field coefficients and some of the dynamic orbit parameters prevents certain orbit parameters from being estimated but to compensate for this, stochastic pulses are set up. Both PCAs and the stochastic pulses need to be constrained in a way, that they can account for mis-modelings but preserve the sensitivity to the gravity field signal. It is shown that these constraints can be computed directly from VCE rather than determined empirically.

In recent years, the use of non-scientific low Earth orbiting (LEO) satellites for gravity field determination has been increasingly explored. In principle, the same methods as for non-dedicated scientific missions are applied by analysing the satellites’ orbital perturbations to gain information about the Earth’s gravity field. With currently over 100 CubeSats in orbit, the Spire commercial constellation provides a huge amount of GNSS tracking data in the same timeframe as scientific missions. This can be exploited to increase the spatio-temporal resolution of estimated gravity field solutions. Although the data quality is limited, previous analyses using data from a 2020 ESA Announcement of Opportunity project have shown that a combined processing of Spire CubeSats can achieve monthly gravity field solutions of similar quality as non-dedicated scientific missions. In our work, we make use of both the Spire data from 2020 and a new dataset from 2023 provided by EUMETSAT. At the Astronomical Institute of the University of Bern, non-gravitational forces acting on the satellite have so far not been explicitly modelled when determining the gravity field, but instead absorbed by pseudo-stochastic parameters such as piecewise constant accelerations. As these forces are prominent for CubeSats due to their low altitude and their large area-to-mass ratio, this study explores how the estimation of the orbits and gravity field solutions improves when explicitly modelling these forces. To achieve this, we determine kinematic orbit positions from Spire CubeSat GNSS phase and code data and introduce them as pseudo-observations in an orbit and gravity field recovery step, where dedicated non-gravitational force modelling is applied using macro-model information provided by Spire. The combination of the different Spire satellites is performed at the normal equation level using a least-squares approach.