Long-term observation of Earth’s temporal gravity field with enhanced temporal and spatial resolution is a major objective for future satellite gravity missions. Improving the performance of the accelerometers present in such missions is one of the main paths to explore. In this context, we propose to study an original concept of a hybrid accelerometer associating a state-of-the-art electrostatic accelerometer (EA) and a promising quantum sensor based on cold atom interferometry. To assess the performance potential of such an instrument, numerical simulations were performed to determine its impact in terms of gravity field retrieval. Taking advantage of the long-term stability of the cold atom interferometer (CAI), it is shown that the reduced drift of the hybrid sensor could lead to improved gravity field retrieval. Nevertheless, this gain vanishes once temporal variations of the gravity field and related aliasing effects are taken into account. Improved de-aliasing models or some specific satellite constellations are then required to maximize the impact of the accelerometer performance gain. To evaluate the achievable acceleration performance in-orbit, a numerical simulator of the hybrid accelerometer was developed and preliminary results are given. The instrument simulator was in part validated by reproducing the performance achieved with a hybrid lab prototype operating on the ground. The problem of satellite rotation impact on the CAI was also investigated both with instrument performance simulations and experimental demonstrations. It is shown that the proposed configuration, where the EA’s proof-mass acts as the reference mirror for the CAI, seems a promising approach to allow the mitigation of satellite rotation. To evaluate the feasibility of such an instrument for space applications, a preliminary design is elaborated along with a preliminary error, mass, volume, and electrical power consumption budget.

Ocean tide (OT) background models (BMs) used for a priori de-aliasing of GRACE/GRACE-FO observations feature distinct spatial uncertainties (primarily in coastal proximity and in latitudes above ±60°), and therefore pose one of the largest contributors to the overall retrieval error. The retrieval performance can be expected to increase if this underlying spatial error distribution is stochastically modelled and incorporated into the data processing chain. In this contribution, we derive realistic error variance-covariance matrices (VCM) based on a set of five state-of-the-art OT models. The additional value of using such VCMs is assessed through numerical closed-loop simulations, where they are rigorously propagated from model to observation level. Further, different approximations of the resulting VCM of observations are assumed, that is full, block-diagonal and diagonal, in order to evaluate the trade-off between computational efficiency and accuracy. It is asserted that correctly weighting the OT BM error can improve the gravity retrieval performance by up to three orders of magnitude, provided no further error contributors are considered. In comparison, the overall gain in retrieval performance is reduced to 75 per cent once instrument noise is taken into account. Here, it is shown that simultaneously modelling the OT BM and the instrument errors is critical, as each effect induces different types of correlations between observations, and exclusively considering covariance information based on the sensor noise may degrade the solution. We further demonstrate that the additional benefit of incorporating OT error VCMs is primarily limited by the de-aliasing performance for non-tidal mass variations of atmosphere (A) and oceans (O). This emphasizes the necessity of best-possible AO-de-aliasing (e.g. through optimized processing techniques and/or improved BMs) in order to optimally exploit the OT BM weighting.

SUMMARY: Temporal aliasing errors resulting from the undersampling of non-tidal atmospheric as well as oceanic mass variations constitute the largest limitation towards the retrieval of monthly gravity solutions based on GRACE and GRACE-FO satellite gravity missions. Their mitigation is thus a primary goal of current research. Unfortunately, the two-step co-parametrization approach proposed for application in Bender-type gravity retrieval scenario in Wiese et al. yields no added value for a single satellite pair. A detailed study of this parametrization strategy is carried out and it is shown that the reason for this is the flawed central assumption of the proposed method, that is that signals of different spatial wavelengths can be perfectly captured and separated with respect to their temporal extent. Based on this finding, we derive a multi-step self-de-aliasing approach (DMD) which aims to rectify the shortcoming of the Wiese et al. method specifically for the single-pair case while retaining its independence from background-model-based de-aliasing of non-tidal atmosphere and ocean (AO) signal components. The functionality and added value of this novel approach is validated within a set of numerical closed-loop simulations as well as in real GRACE and GRACE-FO data processing. The simulation results show that the DMD may improve the gravity retrieval performance in the high-degree spectrum by more than one order of magnitude if one aims to retrieve the full AOHIS (i.e. atmosphere, ocean, hydrology, ice, solid earth) signal, and by at least a factor 5 if a priori AO de-aliasing is applied. Simultaneously, the DMD is shown to degrade the retrieval of the low degrees, but it is also demonstrated that this issue can be mitigated by introducing a constraint into the processing scheme. The simulation results are widely confirmed by results obtained from applying the DMD to real GRACE/GRACE-FO data of the test years 2007, 2014 and 2019. The applicability of the DMD is further shown for Bender-type gravity retrieval. It is demonstrated that in case of a double-pair-based gravity retrieval this approach is at least equivalent to the Wiese et al. method.

The Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided global long-term observations of mass transport in the Earth system with applications in numerous geophysical fields. In this paper, we targeted the in-orbit performance of the GRACE key instruments, the ACCelerometers (ACC) and the MicroWave ranging Instrument (MWI). For the ACC data, we followed a transplant approach analyzing the residual accelerations from transplanted accelerations of one of the two satellites to the other. For the MWI data, we analyzed the post-fit residuals of the monthly GFZ GRACE RL06 solutions with a focus on stationarity. Based on the analyses for the two test years 2007 and 2014, we derived stochastic models for the two instruments and a combined ACC+MWI stochastic model. While all three ACC axes showed worse performance than their preflight specifications, in 2007, a better ACC performance than in 2014 was observed by a factor of 3.6 due to switched-off satellite thermal control. The GRACE MWI noise showed white noise behavior for frequencies above 10 mHz around the level of $1.5\times {10}^{-6} \mathrm{m}/\sqrt{\mathrm{Hz}}$. In the combined ACC+MWI noise model, the ACC part dominated the frequencies below 10 mHz, while the MWI part dominated above 10 mHz. We applied the combined ACC+MWI stochastic models for 2007 and 2014 to the monthly GFZ GRACE RL06 processing. This improved the formal errors and resulted in a comparable noise level of the estimated gravity field parameters. Furthermore, the need for co-estimating empirical parameters was reduced.

The imperfections of geophysical background models (BM) widely applied in GRACE/GRACE-FO data processing pose one of the primary limitations towards the gravity field retrieval performance. With regard to ocean tide (OT) models, it could be shown that incorporating prior knowledge on the spatial distribution of uncertainties in terms of error variance–co-variance matrices (VCMs) has the potential to reduce temporal aliasing in designated spectral bands. It is therefore reasonable to assume that the same approach can be beneficial for the mitigation of aliasing related to errors within models representing the non-tidal atmospheric and oceanic (AO) contributions. Unlike in the case of OT, however, the uncertainties of the AO components feature variations not only in space, but also in time. In this contribution, we propose a method for the derivation of stationary and non-stationary error VCMs on the basis of the AOe07 time series, as well as the methodology for their respective application in the data processing chain on the basis of error propagation. The added value of these error VCMs is assessed in a series of numerical closed-loop simulations for a GRACE-type mission scenario. The impact of these error VCMs is studied with respect to their spatial resolution as well as the extent of correlation between model samples, and also in combination with the stochastic information of other error sources (OT, sensor noise). It is shown that in a best-case scenario, the combined stochastic modelling of BM errors can reduce the retrieval error by 35% on average when applying stationary error information for AO, and by 60% when applying non-stationary error VCMs. In a more realistic scenario where a mismatch between the observed and stochastically modelled error is introduced, the improvements are in comparison smaller, but nevertheless constitute 10 and 18%, respectively. It is also shown that the joint stochastic modelling of all error sources is crucial to improve the gravity solution, while applying stochastic modelling only for individual contributors may even degrade the performance. Additionally, it is demonstrated that the inclusion of BM error models is applicable for a double-pair-based gravity retrieval in the same manner.