Applications and Challenges of GRACE and GRACE Follow-On Satellite Gravimetry

Time-variable gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions have opened up a new avenue of opportunities for studying large-scale mass redistribution and transport in the Earth system. Over the past 19 years, GRACE/GRACE-FO time-variable gravity measurements have been widely used to study mass variations in different components of the Earth system, including the hydrosphere, ocean, cryosphere, and solid Earth, and significantly improved our understanding of long-term variability of the climate system. We carry out a comprehensive review of GRACE/GRACE-FO satellite gravimetry, time-variable gravity fields, data processing methods, and major applications in several different fields, including terrestrial water storage change, global ocean mass variation, ice sheets and glaciers mass balance, and deformation of the solid Earth. We discuss in detail several major challenges we need to face when using GRACE/GRACE-FO time-variable gravity measurements to study mass changes, and how we should address them. We also discuss the potential of satellite gravimetry in detecting gravitational changes that are believed to originate from the deep Earth. The extended record of GRACE/GRACE-FO gravity series, with expected continuous improvements in the coming years, will lead to a broader range of applications and improve our understanding of both climate change and the Earth system.

Time-Variable Gravity Field from the Combination of HLSST and SLR

The Earth’s time-variable gravity field is of great significance to study mass change within the Earth’s system. Since 2002, the NASA-DLR Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE follow-on mission provide observations of monthly changes in the Earth gravity field with unprecedented accuracy and resolution by employing low-low satellite-to-satellite tracking (LLSST) measurements. In addition to LLSST, monthly gravity field models can be acquired from satellite laser ranging (SLR) and high-low satellite-to-satellite tracking (HLSST). The monthly gravity field solutions HLSST+SLR were derived by combining HLSST observations of low earth orbiting (LEO) satellites with SLR observations of geodetic satellites. Bandpass filtering was applied to the harmonic coefficients of HLSST+SLR solutions to reduce noise. In this study, we analyzed the performance of the monthly HLSST+SLR solutions in the spectral and spatial domains. The results show that: (1) the accuracies of HLSST+SLR solutions are comparable to those from GRACE for coefficients below degree 10, and significantly improved compared to those of SLR-only and HLSST-only solutions; (2) the effective spatial resolution could reach 1000 km, corresponding to the spherical harmonic coefficient degree 20, which is higher than that of the HLSST-only solutions. Compared with the GRACE solutions, the global mass redistribution features and magnitudes can be well identified from HLSST+SLR solutions at the spatial resolution of 1000 km, although with much noise. In the applications of regional mass recovery, the seasonal variations over the Amazon Basin and the long-term trend over Greenland derived from HLSST+SLR solutions truncated to degree 20 agree well with those from GRACE solutions without truncation, and the RMS of mass variations is 282 Gt over the Amazon Basin and 192 Gt in Greenland. We conclude that HLSST+SLR can be an alternative option to estimate temporal changes in the Earth gravity field, although with far less spatial resolution and lower accuracy than that offered by GRACE. This approach can monitor the large-scale mass transport during the data gaps between the GRACE and the GRACE follow-on missions.

Evaluation of GRACE/GRACE Follow-On Time-Variable Gravity Field Models for Earthquake Detection above Mw8.0s in Spectral Domain

This study compares the Gravity Recovery And Climate Experiment (GRACE)/GRACE Follow-On (GFO) errors with the coseismic gravity variations generated by earthquakes above Mw8.0s that occurred during April 2002~June 2017 and evaluates the influence of monthly model errors on the coseismic signal detection. The results show that the precision of GFO monthly models is approximately 38% higher than that of the GRACE monthly model and all the detected earthquakes have signal-to-noise ratio (SNR) larger than 1.8. The study concludes that the precision of the time-variable gravity fields should be improved by at least one order in order to detect all the coseismic gravity signals of earthquakes with M ≥ 8.0. By comparing the spectral intensity distribution of the GFO stack errors and the 2019 Mw8.0 Peru earthquake, it is found that the precision of the current GFO monthly model meets the requirement to detect the coseismic signal of the earthquake. However, due to the limited time length of the observations and the interference of the hydrological signal, the coseismic signals are, in practice, difficult to extract currently.

Muscle in Variable Gravity: “I Do Not Know Where I Am, But I Know What to Do”

Purpose: Fascicle and sarcomere lengths are important predictors of muscle mechanical performance. However, their regulation during stretch-shortening cycle (SSC) activities in usual and challenging conditions is poorly understood. In this study, we aimed to investigate muscle fascicle and sarcomere behavior during drop jumps (a common SSC activity) in conditions of variable gravity.Methods: Fifteen volunteers performed repeated drop jumps in 1 g, hypo-gravity (0 to 1 g), and hyper-gravity (1 to 2 g) during a parabolic flight. Gastrocnemius medialis (GM) electromyographic activity and fascicle length (Lf) were measured at drop-off, ground contact (GC), minimum ankle joint angle (MAJ), and push-off. GM sarcomere number was estimated by dividing Lf, measured by ultrasound at rest, by published data on GM sarcomere length, and measured in vivo at the same joint angle. Changes in sarcomere length were estimated by dividing GM Lf in each jump phase by sarcomere number calculated individually. The sarcomere force-generating capacity in each jump phase was estimated from the sarcomere length-tension relationship previously reported in the literature.Results: The results showed that, regardless of the gravity level, GM sarcomeres operated in the ascending portion of their length-tension relationship in all the jump phases. Interestingly, although in hypo-gravity and hyper-gravity during the braking phase (GC-MAJ) GM fascicles and sarcomeres experienced a stretch (as opposed to the quasi-isometric behavior in 1 g), at MAJ they reached similar lengths as in 1 g, allowing sarcomeres to develop about the 70% of their maximum force.Conclusion: The observed fascicle behavior during drop jumping seems useful for anchoring the tendon, enabling storage of elastic energy and its release in the subsequent push-off phase for effectively re-bouncing in all gravity levels, suggesting that an innate neuromuscular wisdom enables to perform SSC movements also in challenging conditions.

Some Reflections On Sparrow's Work On Similarity Solutions for Laminar Film Condensation On a Vertical Plate

In this contribution in honor of Late Prof. E. M. Sparrow, we reflect on the pioneering work of Sparrow and Gregg on the development of similarity solutions for laminar film condensation on a vertical plate. Dhir and Lienhard using this work as a basis developed a generalized solution for isothermal curved surfaces on which gravitational acceleration varied along the surface and for variable gravity situations. Subsequently non-isothermal surfaces were also considered. These studies were publisher earlier in the J. Heat Transfer.

Earth’s Time-Variable Gravity from GRACE Follow-On K-Band Range-Rates and Pseudo-Observed Orbits

During its science phase from 2002–2017, the low-low satellite-to-satellite tracking mission Gravity Field Recovery And Climate Experiment (GRACE) provided an insight into Earth’s time-variable gravity (TVG). The unprecedented quality of gravity field solutions from GRACE sensor data improved the understanding of mass changes in Earth’s system considerably. Monthly gravity field solutions as the main products of the GRACE mission, published by several analysis centers (ACs) from Europe, USA and China, became indispensable products for quantifying terrestrial water storage, ice sheet mass balance and sea level change. The successor mission GRACE Follow-On (GRACE-FO) was launched in May 2018 and proceeds observing Earth’s TVG. The Institute of Geodesy (IfE) at Leibniz University Hannover (LUH) is one of the most recent ACs. The purpose of this article is to give a detailed insight into the gravity field recovery processing strategy applied at LUH; to compare the obtained gravity field results to the gravity field solutions of other established ACs; and to compare the GRACE-FO performance to that of the preceding GRACE mission in terms of post-fit residuals. We use the in-house-developed MATLAB-based GRACE-SIGMA software to compute unconstrained solutions based on the generalized orbit determination of 3 h arcs. K-band range-rates (KBRR) and kinematic orbits are used as (pseudo)-observations. A comparison of the obtained solutions to the results of the GRACE-FO Science Data System (SDS) and Combination Service for Time-variable Gravity Fields (COST-G) ACs, reveals a competitive quality of our solutions. While the spectral and spatial noise levels slightly differ, the signal content of the solutions is similar among all ACs. The carried out comparison of GRACE and GRACE-FO KBRR post-fit residuals highlights an improvement of the GRACE-FO K-band ranging system performance. The overall amplitude of GRACE-FO post-fit residuals is about three times smaller, compared to GRACE. GRACE-FO post-fit residuals show less systematics, compared to GRACE. Nevertheless, the power spectral density of GRACE-FO and GRACE post-fit residuals is dominated by similar spikes located at multiples of the orbital and daily frequencies. To our knowledge, the detailed origin of these spikes and their influence on the gravity field recovery quality were not addressed in any study so far and therefore deserve further attention in the future. Presented results are based on 29 monthly gravity field solutions from June 2018 until December 2020. The regularly updated LUH-GRACE-FO-2020 time series of monthly gravity field solutions can be found on the website of the International Centre for Global Earth Models (ICGEM) and in LUH’s research data repository. These operationally published products complement the time series of the already established ACs and allow for a continuous and independent assessment of mass changes in Earth’s system.