At the Astronomical Institute of the University of Bern, we study gravity field determination from GRACE Follow-On satellite-to-satellite tracking using the inter-satellite link (KBR and LRI) and kinematic positions of the satellites as observations. The kinematic positions are obtained from a precise point positioning, where the carrier phase ambiguities are fixed to integer values. We use a simplified
stochastic model based on epoch-wise covariance information, which may be efficiently derived in the kinematic point positioning process, and extend this model by an empirical noise model derived from the residuals of a reduced-dynamic orbit fit of the kinematic positions to correctly characterise their stochastic behaviour. In addition, we use empirical covariances of range-rate residuals to characterise
the inter-satellite link noise. We investigate the interplay between the empirical noise model and the stochastic parameters of our Celestial Mechanics Approach (CMA) for gravity field determination.
We validate the performance of our gravity field determination by analysing the residuals of combined orbits calculated using both kinematic positions and K-band data, and by analysing the quality of co-
estimated gravity field solutions.
Furthermore, we provide an update about on-going investigation regarding GRACE Follow-On at the
AIUB.

How to cite: Lasser, M., Meyer, U., Arnold, D., and Jäggi, A.: Time-variable gravity field determination from GRACE Follow-On data at the AIUB, GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 8–10 Oct 2024, GSTM2024-85, https://doi.org/10.5194/gstm2024-85, 2024.

Since December 2019, CNES is producing its fifth release of GRACE and GRACE-FO time-variable gravity solutions. This presentation will provide an update on the evolution of processing since last year and on the prospect of a new reprocessing in 2025, based on the new FES2022 barotropic tide model that recently became available and on the update of the TUGO ocean dealiasing model by the LEGOS/CLS team.

Furthermore, in order to characterize as objectively as possible the quality of the time-variable gravity field solutions produced by the different groups involved in the GRACE/GRACE-FO processing, a software for detecting defects in the solutions by supervised artificial intelligence methods was developed for CNES by the company Magellium. A description of the algorithms used (Random Forest and Convolutional Neural Network) will be presented, as well as the performance indices obtained for the CNES solution and, we hope, for a set of other solutions.

How to cite: Lemoine, J.-M., Bourgogne, S., Bruinsma, S., Vaujour, T., Pfeffer, J., and Thenoz, C.: Evaluation of CNES RL05 by AI and prospects for a sixth re-iteration, GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 8–10 Oct 2024, GSTM2024-84, https://doi.org/10.5194/gstm2024-84, 2024.

The benefit of combining long spans of GRACE data for enhancing the spatial resolution of the mean field and regression model parameters (e.g., trend and annual) has been demonstrated for years with the series of GOCO spherical harmonic gravity models (and others). More recently, our group has been applying the same general approach to the estimation of regularized regression mascons, with a particular focus on enhancing the spatial resolution of the recovered mass trends. Initial studies estimated the global trends over the full span of GRACE and GRACE-FO data, but recently we have been working to exploit the same approach over multiple time intervals within the data record, to capture mass change information over shorter intervals while also leveraging the higher spatial resolution afforded by the stacking of normal equations over many months. This approach was recently applied towards the quantification and classification of terrestrial water storage changes in the Great Basin in the Western U.S. (Hall et al., 2024). In this presentation, we provide a summary of this recent study, and discuss the challenges associated with estimating, comparing, and assessing uncertainties for high-resolution regression mascons over multiple time intervals.

How to cite: Loomis, B., Hall, D., DiGirolamo, N., Sabaka, T., Rachlin, K., and Croteau, M.: Optimization and assessment of high-resolution regression mascons for multiple time intervals within the GRACE/GRACE-FO record, GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 8–10 Oct 2024, GSTM2024-18, https://doi.org/10.5194/gstm2024-18, 2024.

The GRACE-FO mission is equipped with two ranging instruments, namely a laser ranging interferometer (LRI) and a microwave instrument (MWI), which are used to measure the distance variations between the two spacecraft (GF1 and GF2). Despite the LRI's role as a technology demonstrator in the current mission, the successor mission, GRACE-C, will exclusively utilise the LRI due to its nanometre-level accuracy in range measurements.

As a consequence of the high level of accuracy achieved, many more features can be observed at high frequencies compared to the MWI range. The range variations have, in general, a gravitational signal, which rolls off quickly above 10 mHz, and non-gravitational signals stemming from atmospheric drag and thruster firings. However, additional spontaneous and sudden range changes are observed (above the gravity-signal band) in LRI and the accelerometer, which we have designated as 'momentum transfer event' (MTE) candidates. When such events turn out to transfer considerable momentum (confirmed MTE), we attribute them to external factors, such as impacts by meteoroids or space debris. However, some events seem to produce no net Δv change but are like vibrations that we attribute to internal structural changes, as previously observed in the GRACE mission (Nadir radiator foil, Kornfeld et al., 2019).

The raw ranging phase, φ_LRI, is utilised to detect the MTE candidates, from which the range and range acceleration are calculated. A filter has been constructed using the algorithm created by Bähre (2023) in order to facilitate the calculation of the precise change in range rate (Δv_LRI). By applying a specific threshold to the Δv_LRI data, it is possible to identify instances where momentum transfer or vibrations could have occurred between each spacecraft. Moreover, the correlation between the range accelerations of these events and the change in momentum recorded by the accelerometer (ACC) data is analysed. This process detected over 150 events per satellite between June 2018 and July 2023.

In order to improve the detection algorithm, the filter is characterised by simulating different event types while varying the filter parameters. This parametric study facilitated the selection of optimal filter parameters that enable effective detection and accurate Δv estimation.  

We then apply the filter to GRACE-FO LRI data, classify the detected events in LRI data according to their correlation with accelerometer data, and present the event statistics. Subsequently, the classifications are examined to ascertain whether the events occur when specific surfaces of the satellite are illuminated by the sun.

As was the case with the effects identified in GRACE data, which informed the development of GRACE-FO, detecting and analysing the effects observed in LRI data are essential for understanding their underlying causes and preventing their recurrence in future missions like GRACE-C and NGGM.

How to cite: Bekal, P., Müller, V., Misfeldt, M., Müller, L., Sudha, R. K., and Heinzel, G.: Momentum Transfer Events: Detection and Analysis in LRI Data, GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 8–10 Oct 2024, GSTM2024-48, https://doi.org/10.5194/gstm2024-48, 2024.

Although the Laser Ranging Interferometer (LRI) on GRACE Follow-On has a higher precision than the K/Ka-Band Ranging (KBR) system, special circumstances lead to the decision to operate the satellites in nadir pointing mode and, starting in July 2023, in wide deadband mode to improve the quality of the accelerometer transplants and reduce propellant consumption. During these periods, the LRI is unable to record ranging data due to its narrow pointing requirements. However, the LRI will be the primary and only ranging instrument on future missions, and it is important to understand its data and optimize the data processing.

Therefore, we have continued to (re-)analyze the raw telemetry from the LRI and have advanced the data processing, resulting in alternative LRI1B datasets that we are making publicly available. These data products include the Tilt-to-Length Coupling Correction (aka Antenna Offset Correction in KBR), an alternative calculation of the Light Time Correction, different models for a time-dependent absolute laser frequency, consideration of relativistic effects acting on the spacecraft proper time when converting the phase to a range, and also a quality flag to mark special events such as sun blinding periods.

We have recently produced a new LRI1B v54 release that includes all available LRI data (June 2018 to June 2023) and a dataset with a sampling rate of 0.2 Hz, the same as the KBR sampling, to facilitate comparisons. We will present an analysis of the differences between LRI1B v54 and KBR1B v04 in the spectral, geographic, and time domains to support ongoing investigations into why the ocean RMS values of the monthly gravity fields from LRI are often slightly higher than those from KBR.

In addition, Duwe et al. [2024] recently showed that the post-fit residuals of LRI1B v04 exhibit some artifacts of the order of +/- 2.5 nm/s², visible when the residuals are high-pass filtered. We were able to confirm most of these features with the LRI1B v04 data, but could not observe them in our internally derived alternative product, LRI1B v54. We further show that the spurious signatures appear even without gravity field recovery by comparing LRI1B v04 and v54 at the level of the raw biased range (or range rate), i.e. without applying correction terms for light-time and antenna offset. We also show that the effects are most likely not present in the LRI1A v04 phase data, leading to the conclusion that these artifacts arise in the v04 Level1a to Level1b processing of SDS.

All of our data products are publicly available at https://www.aei.mpg.de/grace-fo-ranging-datasets.

_{Duwe et al [2024]: Residual Patterns in GRACE Follow-On Laser Ranging Interferometry Post-Fit Range Rate Residuals, Advances in Space Research, https://doi.org/10.1016/j.asr.2024.03.035.}

How to cite: Müller, L., Müller, V., Yan, Y., Misfeldt, M., Bekal, P., and Heinzel, G.: Recent Analyses with Alternative LRI1B Datasets of AEI, GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 8–10 Oct 2024, GSTM2024-70, https://doi.org/10.5194/gstm2024-70, 2024.

The GRACE Follow-On (GRACE-FO) mission features a unique setup with two independent inter-satellite ranging systems that operate simultaneously. In addition to the K-Band Ranging System (KBR), the GRACE-FO satellites are equipped with an experimental Laser Ranging Interferometer (LRI), offering significantly higher measurement precision than the KBR. The availability of these two concurrent ranging systems enables cross-calibration between the instruments and helps to partially distinguish ranging noise from other sources, such as noise from the accelerometer measurements.

A stochastic model is presented here taking the cross-correlation of the two ranging observation types into account by using variance component estimation to determine the noise covariance function. With this method, the KBR, LRI, and accelerometer noise can be partially separated. This modeling approach results in formal errors of the spherical harmonic coefficients that align well with empirical estimates which is crucial for a combination with other data types and uncertainty propagation. Gravity field solutions from the combined least-squares adjustment using LRI and KBR will be compared to KBR-only solutions. 

Monthly gravity field solutions up degree and order 120 only benefit slightly from the incorporation of the LRI data, however when determining gravity field solutions to a higher degree (200) a significant improvement can be seen. This is especially beneficial for the upcoming combined gravity field model GOCO, which is planned to be published in 2025.

How to cite: Öhlinger, F. and Mayer-Gürr, T.: Towards a new release of the combined global gravity field model GOCO: Contribution of GRACE-FO LRI data, GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 8–10 Oct 2024, GSTM2024-58, https://doi.org/10.5194/gstm2024-58, 2024.

Satellite Laser Ranging (SLR) to spherical geodetic satellites is used for recovering the Earth’s gravitational product GM, geocenter motion, and low-degree zonal spherical harmonics, especially C₂₀ and C₃₀. However, the orbital parameters of all geodetic satellites launched after 1992 were not optimized toward the gravity field recovery to maximize their sensitivity to specific gravity field parameters. Instead, the minimization of the potential errors of confirming general relativistic effects, such as the Lense-Thirring, was the main trigger in the selection of orbital parameters.

The diversity of orbital parameters in the current SLR constellation is limited. Most of the geodetic satellites have similar inclination angles: LAGEOS-2, Starlette, and Ajisai about 50°; LARES-1 and LARES-2 about 70°; Stella, Westpac, Larets—in the near sun-synchronous orbit with the inclination of 98°. The inclination angle of LAGEOS-1 is complementary to that of LARES-2 forming the butterfly configuration. The geodetic satellites cover only 60° out of 180° possible inclination angle ranges, i.e., only 33%. Moreover, the orbital heights classify satellites into consistent groups: the LAGEOS-1, LAGEOS-2, and LARES-2 orbit at a height of 5800 km; LARES-1 and Ajisai have a height of about 1500 km; whereas Starlette, Stella, and Westpac have the perigees at the height of about 800 km. Therefore, the gravity field recovery and decorrelation of some gravity field parameters by a diversity of orbital parameters is deficient in the current constellation of geodetic satellites.

We employ the Kaula theorem of gravitational perturbations caused by gravity field coefficients to find the best possible orbital parameters for a future geodetic satellite to maximize orbit sensitivity in terms of the recovery of low-degree gravity field harmonics, geocenter, and GM. We use the maximization of the secular rates of the ascending nodes as the measure of the even-zonal harmonics’ recovery and the maximum of periodic perturbations of the orbital eccentricity vector for the odd-zonal harmonics. We found that the best inclination for a future geodetic satellite is 35°–45° or 135°–145° with a height of about 1500–1700 km to recover C₂₀ and C₃₀. For the optimum heights, we consider three factors emerging from the (1) sensitivity of the satellite to a degree-specific gravity field coefficient, (2) the number of satellite revolutions within a pre-defined period, and (3) observability of a satellite from the perspective of ground stations. For a better geocenter recovery and derivation of the standard gravitational product, the preferable height is 2300–3500 km. We found that none of the existing geodetic satellites have, unfortunately, the optimum inclination angle and height for deriving GM, geocenter, and C₂₀ because there are no spherical geodetic satellites at the heights between 1500 (Ajisai and LARES-1) and 5800 km (LAGEOS-1/2, LARES-2).

How to cite: Sośnica, K., Gałdyn, F., Nowak, A., Najder, J., and Zajdel, R.: What are the best inclination angles and satellite heights for recovering geocenter, C20, C30, and other low-degree harmonics?, GRACE/GRACE-FO Science Team Meeting, Potsdam, Germany, 8–10 Oct 2024, GSTM2024-3, https://doi.org/10.5194/gstm2024-3, 2024.