G4.1

Next Generation Gravity Missions are expected to enhance our knowledge of mass transport processes in the Earth system, establishing their products applicable to new scientific fields and serving societal needs. Compared to the current situation (GRACE Follow-On), a significant step forward to increase spatial and temporal resolution can only be achieved by new mission concepts, complemented by improved instrumentation and tailored processing strategies.

In extensive numerical closed-loop mission simulations studies, different mission concepts have been studied in detail, with emphasis on orbit design and resulting spatial-temporal ground track pattern, enhances processing and parameterization strategies, and improved post-processing/filtering strategies. Promising candidates for a next-generation gravity mission are double-pair and multi-pair constellations of GRACE/GRACE-FO-type satellites, as they are currently jointly studied by ESA and NASA. An alternative concept is high-precision ranging between high- and low-flying satellites. Since such a constellation observes mainly the radial component of gravity-induced orbit perturbations, the error structure is close to isotropic, which significantly reduces artefacts of along-track ranging formations. This high-low concept was proposed as ESA Earth Explorer 10 mission MOBILE and is currently further studies under the name MARVEL by the French space agency. Additionally, we evaluate the potential of a hybridization of electro-static and cold-atom accelerometers in order to improve the accelerometer performance in the low-frequency range.

In this contribution, based on full-fledged numerical closed-loop simulations with realistic error assumptions regarding their key payload, different mission constellations (in-line single-pair, Bender double-pair, multi-pairs, precise high-low tracking) are assessed and compared. Their overall performance, dealiasing potential, and recovery performance of short-periodic gravity signals are analyzed, in view of their capabilities to retrieve gravity field information with short latencies to be used for societally relevant service applications, such as water management, groundwater monitoring, and forecasting of droughts and floods.

How to cite: Pail, R.: Future Gravity Mission Concepts for Sustained Observation of Mass Transport in the Earth System, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9447, https://doi.org/10.5194/egusphere-egu21-9447, 2021.

Advances in atom interferometry have led to quantum gravity gradiometer instruments, which have further led to spaceborne mission concepts utilizing this technology to measure Earth’s gravity field and its time variations. The mass changes inferred from gravity change measurements lead to greater understanding of the dynamical Earth system, as demonstrated by GRACE and GRACE Follow-On missions.

We report the results from a sensitivity and performance assessment study with quantum gradiometers used in two configurations – first as a single-axis gradiometer with a GNSS receiver; and second in a novel hybrid configuration combining cross-track quantum gravity gradiometer and an inter-satellite tracking system. The relative advantages of the two configurations are assessed in terms of their susceptibility to system errors (such as tracking, pointing, or measurement errors), and to modeling errors due to aliasing from rapid time- variations of gravity (so-called “de-aliasing errors”). We evaluate and discuss the impact of de-aliasing errors on gravity fields resulting from the study. We conclude with a specification of the key measurement error thresholds for a notional hybrid gravity field mapping mission.

Part of the research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004).

Acknowledgement: UTCSR effort was funded by JPL grant 1656926. Use of resources at the Texas Advanced Computing Center is gratefully acknowledged. 

How to cite: Rosen, M., Bettadpur, S., Chiow, S., and Yu, N.: Hybrid Architectures with Quantum Gravity Gradiometry and Satellite-to-Satellite Tracking for Spaceborne Mass Change Measurements - A Sensitivity and Performance Analysis, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6730, https://doi.org/10.5194/egusphere-egu21-6730, 2021.

The American/German missions Gravity Recovery and Climate Experiment (GRACE) and the GRACE Follow-On (GRACE-FO) and the European mission (Swarm) play an important role in study of the Earth's gravity field with unprecedented high-precision and high-resolution measurements. The aim of this study is to use Swarm data to fill-in the data-gap between GRACE and GRACE-FO missions from July 2017 to May 2018, and evaluate the new datasets in Africa. We used the available data from the triple GRACE processing centers CSR, GFZ and JPL, in addition to the Swarm TVGF data provided by the Czech Academy of Sciences (ASU) and the International Combination Service for Time-variable Gravity (COST-G). The GRCAE and Swarm date have been tested in the frequency and space domains. For the frequency domain, the data assessed in two different levels: the potential degree variances and the harmonic coefficients themselves. The results show consistency between GRACE/GRACE-FO and Swarm for all processing centers. In the space domain, a comparison between GRACE/GRACE-FO and Swarm for the TWS, gravity anomaly, and the potential/geoid have been carried out. For the TWS, an artificial gap (AG) - simulating the gap between GRACE and GRACE-FO – has been artificially made in the GRACE data from July 2015 to May 2016. The GRACE AG has been filled by the two sets of the Swarm data for CSR, GFZ and JPL. The results indicated that the best agreement has been achieved between GRACE-CSR and Swarm COST-G. For the gravity anomaly and the potential/geoid, a better agreement between GRACE and Swarm data has been concluded. Eventually, we chose Swarm COST-G data to fill-in the gap between GRACE and GRACE-FO CSR in order to be used, among others, to estimate the TWS in Africa for the period from April 2002 to October 2020. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants Nos. 42030105, 41721003, 41804012, 41631072, and 41874023.

How to cite: Mohasseb, H., Abd-Elmotaal, H. A., and Shen, W.: Validation of Using SWARM to Fill-in the GRACE/GRACE-FO Gap: Case Study in Africa, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2723, https://doi.org/10.5194/egusphere-egu21-2723, 2021.

Atom Interferometers as inertial sensors were getting quite some interest in the last decade. Several attempts have been made to combine the two sensors (i.e. classical inertial measurement units IMU and cold atom interferometers), mainly with the goal to use the atom interferometer as main sensor, and support it with different conventional sensors in order to suppress noise and achieve maximum sensitivity and long-term stability.
We present a quite promising combination of both sensors in an error state extended Kalman Filter framework aimed especially on further improving the performance of a conventional high end IMU. While the full potential of the cold atom interferometer is not yet entirely exploited in this combination, first simulations in terrestrial applications with small and even larger change of inertial forces show an increase of the navigation solution precision by a factor of 20 and more.

How to cite: Tennstedt, B., Weddig, N., and Schön, S.: A hybrid CAI/IMU solution for higher navigation performance, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9776, https://doi.org/10.5194/egusphere-egu21-9776, 2021.

Atom gravimeters based on atom interferometry offer new measurement capabilities, by combining high sensitivities and accuracies at the best level of a few tens of nm.s⁻² with the possibility to perform continuous measurements. Being absolute meters, their scale factor is accurately determined and do not need calibration. Because of their high sensitivity and low drift, superconducting gravimeters are the key instruments for the continuous monitoring of gravity variations. Nevertheless, being relative meters, they need to be calibrated.

We revisit a 2015 one month long common view measurement of an absolute cold atom gravimeter (CAG) and a relative iGrav superconducting gravimeter, which we use to investigate the CAG long term stability and calibrate the iGrav scale factor. The initial measurement has already been presented at EGU 2016. Here finalized, we present how it allowed us to push the CAG long-term stability down to the level of 0.5 nm.s⁻². We investigate the impact of the duration of the measurement on the uncertainty in the determination of the correlation factor and show that it is limited to about 3‰ by the coloured noise of our cold atom gravimeter. A 3-days long measurement session with an additional FG5X absolute gravimeter allows us to directly compare the calibration results obtained with two different absolute meters. Based on our analysis, we expect that with an improvement of its long term stability, the CAG will allow to calibrate the iGrav scale factor to better than the per mille level (1σ level of confidence) after only one-day of concurrent measurements during maximum tidal amplitudes.

How to cite: Merlet, S., Gillot, P., Cheng, B., Karcher, R., Imanaliev, A., Timmen, L., and Pereira Dos Santos, F.: Calibration of a superconducting gravimeter with an absolute atom gravimeter, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10963, https://doi.org/10.5194/egusphere-egu21-10963, 2021.

A height definition in terms of geopotential numbers offers a variety of advantages. Moreover, from the theoretical point of view, such a definition is considered more fundamental. 

We know, however, that relativistic gravity (here General Relativity) requires to reformulate the basic geodetic notions and to develop a consistent theoretical framework, relativistic geodesy, to yield an undoubtedly correct interpretation of measurement results.

The new framework of chronometric geodesy that builds on the comparison of clocks offers fundamental insight into the spacetime geometry if a solid theoretical formulation of observables is underlying modern high-precision measurements. Here we approach a genuine relativistic definition of the concept of height. Based on the relativistic generalization of geopotential numbers, a definition of chronometric height is suggested, which reduces to the well-known notions in the weak-field limit.

How to cite: Philipp, D.: Chronometric Height: a relativistic height definition by generalizing geopotential numbers, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9889, https://doi.org/10.5194/egusphere-egu21-9889, 2021.

We propose a new approach for testing the gravitational redshift based on frequency signals transmission between a spacecraft and a ground station. By a combination of one uplink signal and two downlink signals, the gravitational redshift can be tested at about 6.5×10^-6 level for a GNSS satellite (the signals’ frequencies are about 1.2~1.6 GHz), and about 2.2×10^-6 level for the International Space Station (the signals’ frequencies are up to 14.7 GHz), under the assumption that the clock accuracy is about 10^-17 level. For better desinged cases the accuracy of gravitational redshift test can be improved to several parts in 10^-8 level (the signals’ frequencies are about 8~12 GHz). Compared to the scheme of Gravity Probe-A (GP-A) experiment conducted in1976, the new approach does not require any onboard signal transponders, and the frequency values of the three links can be quite arbitrarily given. As the hardware requirement is reduced, a number of spacecrafts could be chosen as candidates for a gravitational redshift experiment. This approach could also be used in gravitational potential determination, which has prospective applications in geodesy. This study is supported by National Natural Science Foundation of China (NSFC) (grant Nos. 42030105, 41721003, 41631072, 41874023, 41804012), Space Station Project (2020)228, and Natural Science Foundation of Hubei Province(grant No. 2019CFB611).

How to cite: Shen, Z., Shen, W.-B., He, L., Zhang, T., and Cai, Z.: An improved approach for testing gravitational redshift via spacecraft based three frequency links combination, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1942, https://doi.org/10.5194/egusphere-egu21-1942, 2021.

The GRACE mission, now continued as the GRACE-FO mission, has provided an unprecedented quantification of large-scale changes in the water cycle.
Meanwhile, stationary optical clocks show fractional instabilities below 10^-18 when averaged over an hour, and continue to be improved in terms of precision and accuracy, uptime, and transportability. The frequency of a clock is affected by the gravitational redshift, and thus depends on the local geopotential; a relative frequency change of 10^-18 corresponds to a geoid height change of about 1 cm. This effect could be exploited for sensing temporal geopotential changes via a network of clocks distributed at the Earth's surface. 
Here, we concentrate on how the measurements of an ensemble of optical clocks connected accross Europe via optical fibre links could be used to validate and complement gravity field solutions from GRACE-FO and potential future gravity missions.
Through simulations it is shown how hydrology (water storage) and atmosphere (dry and wet air mass) variations over Europe could be observed with clock comparisons in a future network. We assume different scenarios for clock and GNSS uncertainties, where we deem the latter to be nessecary to separate local height changes from the mass redistribution signals. Our findings suggest that even under conservative assumptions -- a clock error of 10^-18 and vertical height control error of 1.4 mm for daily measurements -- hydrological signals at the annual time scale and atmospheric signals down to the weekly time scale could be observed.
However, the requirements to an optical clock network used for validation of GRACE-FO and future gravity missions are higher than that, which is demonstrated along with the according spatial resolutions.

How to cite: Schröder, S., Stellmer, S., and Kusche, J.: Potential and scientific requirements of optical clock networks for validating satellite gravity missions, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10912, https://doi.org/10.5194/egusphere-egu21-10912, 2021.

According to Einstein’s general relativity theory (GRT), a clock at a position with higher potential runs faster than a clock at a position with lower potential. Hence, inversely, one can determine the gravity potential (geopotential) and orthometric height based on precise clocks. If a clock with an accuracy of 10^-18 is used, the geopotential difference between two points can be determined with an accuracy of centimeters level. With the rapid development of science and technology, optical clocks achieve 10^-18 stability, which opens up opportunity for scientists to practically determine geopotential as well as orthometric height using optical clocks. One of the challenges of classical geodesic in the long time has been the unification of local hight systems. To complete this task is very difficult because each country has a regional high system. This problem can be solved if using a clock network, which overcomes the weaknesses of the spirit leveling method. Here we provide a formulation to establish a model of a network using optical clocks linked together by optical fibers for the purpose of determining the geopotential and establishing a unified world hight system at centimeter accuracy level. This study is supported by National Natural Science Foundation of China (NSFC) (grant Nos. 41721003, 42030105, 41631072, 41874023, 41804012), and Space Station Project (2020)228.

Key words: GRT, optical clocks network, frequency transfer, geopotential, orthometric height

How to cite: Hoang, A. T. and Shen, W.: Optic-fiber gravity frequency transfer network, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7739, https://doi.org/10.5194/egusphere-egu21-7739, 2021.

High-performance clock networks are considered as a novel tool in geodesy. Today the latest generation of optical clocks approaches a fractional frequency uncertainty of 1.0x10^-18, which corresponds to about 1.0 cm in height or 0.1 m²/s² in geopotential. The connected clocks are thus promising to enable “relativistic geodesy” in practice: Gravity potential (or height) differences can be inferred through the ultra-precise comparison of clocks’ frequencies.

In this study, we will investigate the possibility of high-performance clock networks for detecting time-variable gravity signals. In the past two decades, the satellite gravity mission GRACE, now continued by its follow-on mission, has significantly improved our knowledge on the Earth’s gravity field, especially on its changes over time. However, the results are limited in terms of spatial resolution (about a few hundreds of kilometers) and temporal resolution (standard is one month). Terrestrial clock networks can be used to observe point-wise gravity potential values at locations of interest. By continuously tracking of changes w.r.t. a reference clock, time-series of gravity potential values are obtained, which reveal the gravity variations at these locations. To elaborate this idea, we will address the following research questions:

• Are clock measurements with the accuracy of 10^-18 sensitive enough to time-variable gravity signals? Or what is the requirement on the clock’s performance for detecting time-variable gravity signals?
• Which kinds of time-variable signals can be “seen” by clocks, the long-term trends (yearly), seasonal variations or short-term changes (weekly/daily)?
• In which regions might clock networks be sensitive to time-variable gravity signals, in Amazon, Greenland or also in Europe?
• An “absolute” reference clock is required for a network that should be least affected by gravity variations. Where should it be placed?

We gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2123 “QuantumFrontiers” (Project-ID: 390837967). This work is also funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 434617780 – SFB 1464.

How to cite: Wu, H. and Müller, J.: Clock networks and their sensibility to time-variable gravity signals, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-10744, https://doi.org/10.5194/egusphere-egu21-10744, 2021.

VLBI technique plays important role in both astronomy and geodesy due its fantastic ability to determine the position of celestial bodies and the length of baseline on Earth. Moreover it also presents excellent work on time comparisons between atomic clocks located in remote positions where optical fiber links are not accessible. Due to its high reliability and stability, the information of Earth’s gravity field can be extracted from VLBI time comparisons in the framework of general relativity. In this study, we provide a formulation to determine the gravity potential difference by VLBI time comparisons. In fact the precision of the estimated gravity potential depends on the performance of participated clocks and the accuracy of time comparison technique. Thus we present simulation experiments using clocks with 10^-16@1d stability and broadband VLBI observation and determine gravity potential difference within a VLBI network around world with 10 m²/s² precision which is equivalent to 1 m in height. The results could be greatly improved using optical atomic clocks with much higher stabilities. Furthermore it can be applied to height transfer across oceans and unifying the height system. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, and Space Station Project (2020)228.

How to cite: Wu, Y. and Shen, W.-B.: Determining gravity potential difference via VLBI time comparisons, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1927, https://doi.org/10.5194/egusphere-egu21-1927, 2021.

The Earth’s gravity potential (geopotential) field plays an important role in geodesy, for instance, it is the basis for defining the geoid and the International Height Reference System (IHRS). In chronometric geodesy, the main challenge for directly measuring geopotential differences between two stations lies in that a reliable link for time comparison is needed. Currently, most satellite links for time comparison are dealt with in the microwave domain, for which the ionospheric and tropospheric effects are major error sources that greatly influence the signal propagation compared to optical space links. Recently, accurate laser time transfer links between satellite and ground stations have already been planned and confirmed, such as Laser Time Transfer (LTT, China) on BeiDou satellites and Tiangong II / China's space station (CSS), Time Transfer by Laser Link (T2L2, French) on Jason-2 mission and European Laser Timing (ELT, Europe) on Atomic Clock Ensemble in Space (ACES). Therefore, in this study, we propose an approach for determining the geopotential difference between two ground atomic clocks based on the Two-way Laser Time Transfer (TWLTT) technique via a space station as a bridge, which could have potential applications in geoscience. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, Space Station Project (2020)228, and the Natural Science Foundation of Hubei Province of China under Grant 2019CFB611.

How to cite: Ruby, A., Shen, W.-B., Shaker, A., Ashry, M., Pengfei, Z., Rui, X., Shen, Z., and Xu, W.: Geopotential Determination Between Ultra-Stable Distant Clocks Based on Two-Way Space Laser Time Transfer Links, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1378, https://doi.org/10.5194/egusphere-egu21-1378, 2021.

Due to the influence of pseudo-range noise, traditional GNSS common view method is difficult to improve the accuracy of time-frequency transfer. GNSS carrier phase precise point positioning (PPP) time-frequency transfer has become a research hotspot because of its high accuracy. In this paper, a time-frequency transfer model of GNSS carrier phase single difference (SD) and Integer Single Difference (ISD) between any two ground stations is studied. In order to solve the problem that the SD ambiguity cannot be fixed due to the influence of the phase biases at the receivers, a method of SD ambiguity fixing is proposed, that is the SD ambiguity is fixed with the constraint of the fixed double difference ambiguity among several stations and satellites. Here taking four time-frequency links between pairs of ground stations, BRUX-OPMT (262.3km), BRUX-PTBB (454.6km), BRUX-WTZR (637.7km) and BRUX-CEBR (1331.6km) as examples, the multi-GNSS time-frequency transfer experiment of SD, ISD and PPP method is carried out. The results show that the SD and PPP time-frequency transfer accuracy is equivalent, the stability of ISD is improved compared with SD, and the difference RMS between epochs is less than 10 ps. High precision carrier phase SD, ISD and PPP technology can be applied to the study of determining the gravity potential based on time-frequency measurements. This study is supported by the National Natural Science Foundations of China (NSFC) under Grants 42030105, 41721003, 41804012, 41631072, 41874023, Space Station Project (2020)228, and the Natural Science Foundation of Hubei Province of China under Grant 2019CFB611.

How to cite: Xu, W., Shen, W.-B., Cai, C., Ning, A., and Shen, Z.: GNSS Carrier Phase Integer Single Difference Times and Frequency Transfer Accuracy Evaluation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1894, https://doi.org/10.5194/egusphere-egu21-1894, 2021.