Replacing GRACE/GRACE-FO With Satellite Laser Ranging: Impacts on Antarctic Ice Sheet Mass Change
Abstract
Satellite laser ranging (SLR) observations have long been relied upon for measuring changes in Earth's dynamic oblateness, . This major component of Earth's time-variable gravity field is not well observed by the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions, leading to the common practice of replacing their values with those obtained by SLR. The coefficient, which has a large impact on the recovered Antarctic Ice Sheet mass changes, is shown here to be poorly observed by GRACE/GRACE-FO when either mission is operating without two fully functional accelerometers. The GRACE spacecraft pair operated nominally until October 2016 when one accelerometer was powered off due to battery limitations, while GRACE-FO is currently excluding one accelerometer from the data processing due to elevated noise levels. Beginning with the launch of Laser Relativity Satellite in 2012, SLR-derived values are suitable for replacing any problematic GRACE/GRACE-FO estimates, enabling the accurate recovery of Antarctic Ice Sheet mass changes, among others.
Key Points
- GRACE and GRACE-FO estimates are inaccurate when operating in single accelerometer mode
- Satellite laser ranging provides high-quality estimates after the launch of LARES in 2012
- Recovery of Antarctic Ice Sheet mass changes with GRACE-FO requires the satellite laser ranging
1 Introduction
The Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions have revolutionized our ability to monitor important geophysical mass change and transport processes in the hydrosphere, cryosphere, ocean, and solid Earth at monthly intervals to a spatial resolution of 300–500 km (Luthcke et al., 2013; Wahr et al., 2006). As the length of the data record grows, the time-variable gravity (TVG) and mass change products afforded by these missions are vital for improving our understanding of long-term changes to the Earth's large ice sheets and climate. The accurate recovery of changes to the Antarctic Ice Sheet (AIS) is of utmost importance, as the ice contained therein has the potential to substantially impact sea level rise in the coming decades and centuries (Shepherd et al., 2018). Continued monitoring of AIS mass change is among the key priorities identified in the two recent Decadal Surveys on Earth Science and Applications from Space (National Academies of Sciences & Engineering, 2018; National Research Council, 2007) and is an essential goal for the GRACE-FO mission.
Built on GRACE heritage, the GRACE-FO mission consists of a polar satellite pair, where the precise inter-satellite ranging system is paramount for observing the TVG signals. Each individual spacecraft is also equipped with an on-board accelerometer that provides accurate measurements of the non-gravitational forces acting on each satellite, such as drag, solar radiation pressure, and attitude control, in order to separate their effects from the gravitational perturbations on satellite motion. In other words, the accelerometers are critical to the mission design and required to achieve the required inter-satellite ranging measurement capabilities. The accelerometers on each GRACE spacecraft operated nominally until October 2016 when the GRACE-B accelerometer was turned off for six out of the seven final GRACE solution months (May 2017 excepted) in order to reduce the power load on the diminished battery. In an effort to mitigate the loss of this accelerometer, the Level-1B team at the Jet Propulsion Laboratory (JPL) developed a sophisticated algorithm to “transplant” the GRACE-A accelerometer measurements onto GRACE-B, taking into account the flight time, orientation, and satellite-specific thrusting events (Bandikova et al., 2019). Overall, this approach has been highly successful at extending the valuable data record of the GRACE mission by facilitating the production of monthly gravity solutions from November 2016 through June 2017 (the inter-satellite ranging system was turned off for September and part of October 2016). Shortly after its launch, one of the GRACE-FO accelerometers (GRACE-D) was observed to have elevated noise levels relative to the other (GRACE-C). As of the initial Level 2 data release through August 2019, the GRACE-FO products are currently determined using the same general accelerometer transplant approach as was used during the final months of the GRACE mission, with some adjustments to account for differences in the attitude control system (McCullough et al., 2019). As the accelerometer on GRACE-D still measures real accelerations, albeit with higher noise, the GRACE-FO Science Data System team continues to explore the optimal calibration methods to use the GRACE-D accelerometer observations and augment the “full transplant” with local accelerometer measurements (so-called hybrid transplant) for estimating improved monthly gravity solutions.
Below, we present analysis of the GRACE and GRACE-FO RL06 Level 2 spherical harmonics and show that estimates of are less reliable when either mission is operating in single accelerometer mode. We also show that beginning with the launch of the Laser Relativity Satellite (LARES), a dedicated satellite laser ranging (SLR) satellite of the Italian Space Agency, is well observed by estimating low-degree TVG fields with SLR measurements. We then demonstrate the impact of replacing the problematic GRACE/GRACE-FO values with those obtained from SLR on estimates of AIS mass change, which highlights the importance of the recommended replacement procedure for the proper scientific application of the Level 2 products. This recommended procedure mimics the commonly applied approach of replacing GRACE/GRACE-FO estimates with those obtained from SLR (Cheng & Ries, 2017; Loomis et al., 2019a).
2 Data and Methods
The GRACE and GRACE-FO analysis presented here applies the RL06 Level 2 spherical harmonic products provided by the Science Data System processing centers at JPL, the Center for Space Research (CSR) at University of Texas, and the German Research Centre for Geosciences (GFZ). We primarily utilize the JPL solution, but the general results hold regardless of which product is used. In addition to the correction mentioned above, and the correction that is the focus of this paper, the GRACE/GRACE-FO products also need to be corrected for the offset between the Earth center of mass and center of figure. We have applied this geocenter correction using the appropriate Technical Note 13 (TN-13) file provided by the project for each Level 2 product. In order to provide an estimate of ice mass changes in the AIS, we also need to remove a model of the secular solid Earth signal caused by glacial isostatic adjustment (GIA), for which we use IJ05_R2 (Ivins et al., 2013) to be consistent with (Shepherd et al., 2012, 2018). The selected model assumes a lithosphere thickness of 65 km with upper and lower mantle viscosities of and Pa s, respectively. To extract the time series of mass change from the corrected monthly spherical harmonics, we apply an averaging kernel of the ice sheet following the method of Swenson and Wahr (2002). Our selected AIS kernel (expanded and smoothed to 200 km with a scale factor of 1.14) approximately reproduces the time series of the JPL RL06 mascon solution (Watkins et al., 2015). A primary benefit of the mascons is the significant mitigation of signal leakage from the ice sheets into the surrounding ocean, and so, they are a useful aid for designing an AIS kernel that also mitigates signal leakage.
In addition to the loss of the GRACE-B accelerometer data for six out of seven GRACE solutions after August 2016, we also note that August 2016 could potentially be problematic for recovering the very low degree terms (i.e., ) due to the intermittent data for that month. The reduced power load near the end of the GRACE mission limited the capability of the observing system for certain beta angles (the angle between the orbit plane and the Earth-Sun vector). For the daily arcs included in the GRACE August 2016 solution, the inter-satellite ranging observations are only available for about a half-revolution ( 45 min) at a time, resulting in only 52% of possible data collected, as compared to the more than 95% that was collected for the majority of the mission (see Figure 1). As discussed below, this month corresponds to larger disagreement between the SLR and some GRACE solutions than normal, and we speculate that it could be due to the intermittent nature of the inter-satellite ranging data.
The processing and estimation details of the NASA GSFC SLR low-degree TVG solution are described by a series of previous studies (Lemoine et al., 2006; Loomis et al., 2019a; Zelensky et al., 2014). The most recent work of Loomis et al. (2019a) was primarily focused on the improved recovery of and its impact on important geophysical signals. Following the work of Cheng and Ries (2017), Loomis et al. (2019a) estimates TVG spherical harmonic coefficients plus using the following set of five SLR satellites: LAGEOS-1 (1976–present), LAGEOS-2 (1992–present), Starlette (1975–present), Stella (1993–present), and AJISAI (1986–present). See Pearlman et al. (2019) for a thorough summary of these SLR satellites. The sensitivity of various combinations of SLR satellites to the low-degree spherical harmonic coefficients is analyzed by Sośnica et al. (2015), with a significant increase in sensitivity observed when LARES (2012–present) is added to the solution set and a marginal increase with the addition of Larets (2003–present) and BLITS (2009–2013). Sośnica et al. (2015) state that the LARES contribution is vital due to its combination of low area-to-mass ratio, low altitude, and unique inclination of 69.5°. Following their analysis and the importance of accurate recovery, the five-satellite SLR product presented in Loomis et al. (2019a) has been replaced with a seven-satellite solution that now includes LARES and Larets. This new product applies the same relative weighting to each satellite as Sośnica et al. (2015) and uses 7-day data processing arcs for all satellites. Both the weights and arc length are slight departures from Loomis et al. (2019a), which used 28-day arcs for LAGEOS-1/2 and weighted the five satellites according to Cheng and Ries (2017). The analysis of Loomis et al. (2019a) shows that these design choices have a minor effect on the estimates, while the choice of background TVG model is far more consequential. Following that work, we continue to apply a TVG model derived from the dual accelerometer span of GRACE data in the processing of SLR data and subsequent estimation of the and TVG spherical harmonic coefficients. The use of 7-day arcs for all satellites facilitates 28-day sliding window solutions with weekly sampling, which allows us to more closely match the GRACE/GRACE-FO solution windows. Each “weekly” solution combines four sets of 7-day normal equations. The resulting time series is then averaged within each GRACE/GRACE-FO month to produce the and values provided operationally as Technical Note 14 (TN-14), where values are only provided after the launch of LARES in 2012. The results of Loomis et al. (2019a) suggest that shortening the SLR arcs to exactly match the GRACE/GRACE-FO solution windows (e.g., 31 1-day arcs for January 2019) will adversely affect the recovery of , which is why we have adopted the sliding window solution approach utilizing 7-day arcs. The solution is relatively insensitive to the LARES data weight, as modifying it by two orders of magnitude only affects the agreement with the dual accelerometer GRACE by 2%.
Lastly, we note that the SLR data processing applies the same atmospheric and ocean de-aliasing product RL06 AOD1B (Flechtner, 2007) used for processing the GRACE and GRACE-FO data so that the SLR-derived spherical harmonic coefficients are consistent with the RL06 GSM products. Both the and values from TN-14 are applied in the analysis below.
3 Results and Discussion
The time series of values from JPL RL06 GRACE/GRACE-FO and the GSFC 7-satellite SLR solution are shown in Figure 2, with excellent agreement observed between the GRACE and SLR values when GRACE is operating with both accelerometers. The “ ” indicates that the mean of all TN-14 values has been removed from both time series. From March 2012 to July 2016, which corresponds to the common span of LARES and dual accelerometer GRACE data, the RMS of the differences between the SLR and GRACE estimates is regardless of which GRACE product is used. Over the single accelerometer GRACE/GRACE-FO months, the RMS differences increase substantially to , , and for JPL, CSR, and GFZ, respectively. We also note that the RMS of the differences between the five-satellite (not shown) and the recommended seven-satellite solution is , clearly demonstrating the importance of the additional satellites (especially LARES) for recovering with SLR.
As discussed above, the GRACE estimates for August 2016 could potentially be problematic given the intermittent data coverage throughout that month. JPL, CSR, and GFZ report absolute differences to SLR of , , and , respectively. It is not clear why the CSR value for that particular month is in better agreement with SLR, but given the excellent agreement between SLR and all GRACE solutions for March 2012–July 2016, it seems sensible to suggest that the GFZ and JPL values for August 2016 also be considered for replacement.
As additional validation of the new seven-satellite SLR solution, we examine a number of key signal statistics for the span March 2012–July 2016, which are summarized in Table 1. First, we present the best-fit annual signals for and and note that this span is too short to recover statistically significant trend estimates (i.e., the uncertainties are larger than the estimates). The comparison is included to highlight the good agreement between the five-satellite solution, which was the focus of Loomis et al. (2019a), and the seven-satellite solution presented here. Annual fits for the GRACE are not reported due to their unrealistic values (Cheng & Ries, 2017). Similarly, we do not report annual fits for the unrealistic five-satellite solution. For the comparison, we report that the seven-satellite SLR agrees with all GRACE solutions within 2- model fit uncertainties for both annual amplitude and phase.
| amplitude | phase | amplitude | phase | |
|---|---|---|---|---|
| Solution | ( ) | (°) | ( ) | (°) |
| GRACE JPL | — | — | 7.6 1.3 | 97.4 9.2 |
| GRACE CSR | — | — | 8.4 1.3 | 97.3 7.9 |
| GRACE GFZ | — | — | 7.5 1.4 | 103.2 9.5 |
| SLR five-satellite | 5.0 1.4 | 81.3 15.5 | — | — |
| SLR seven-satellite | 4.7 1.3 | 75.9 15.6 | 7.0 1.8 | 89.4 13.3 |
- Note. Annual signal parameters are not reported for the inaccurate GRACE and SLR five-satellite . The SLR five-satellite solution corresponds to Loomis et al. (2019a), while the SLR seven-satellite and solutions are distributed as TN-14. The amplitude, , and phase, , are defined as ), where is 1 January.
As discussed in Sośnica et al. (2015), Cheng and Ries (2017), and Loomis et al. (2019a), high correlations between spherical harmonic coefficients in the formal error covariance matrix could negatively impact the observability and quality of the parameter estimates. Sośnica et al. (2015) noted the very high formal error correlations between the and coefficients, reporting values of when LARES is excluded from the solution and when LARES is included. We observe similar values of when using the same data weights as Sośnica et al. (2015) but observe an extreme sensitivity of to the assigned LARES data weight, with virtually no effect on the estimated or time series. This result demonstrates that the data errors that map into the estimates via the generalized inverse (see, e.g., Menke, 2015, equation 2.4.2) are significantly reduced for LARES, which is expected due to its very low area-to-mass ratio and corresponding reduction in non-gravitational errors (Sośnica, 2014). The formal 1- uncertainties for both and are reduced by a factor of 3 when LARES is added to the solution, and the SLR estimates agree well with GRACE/GRACE-FO for both the dual and single accelerometer months (RMS of the differences is ).
Now that we have established the reliability of the seven-satellite SLR estimates and the degraded quality of single accelerometer GRACE/GRACE-FO estimates, we quantify the effect of the recommended replacement approach on measuring AIS mass changes. Note that we have focused on AIS due to the extreme impact of estimates on its recovered mass variability, but the improved SLR values do have non-negligible impacts on other geographic regions as well. Figure 3 presents the AIS mass change time series computed with the original and replaced values, along with a simplistic prediction of mass anomalies determined by fitting a regression model to GRACE data over January 2007–July 2016 and extrapolating the model through the latest GRACE-FO solution of August 2019 (the regression model includes a bias, trend, annual, and semiannual, and the fit begins in 2007 due to the significant change in the trend that occurred around 2007–2008; Shepherd et al., 2018). We can then analyze the agreement between the regression model predictions and the monthly estimates with and without replacement as a simple assessment of solution reliability. For comparison, we first report that the RMS of the monthly estimate differences to the regression model over the span January 2007–July 2016 is 140 Gt. Now considering the model prediction span of August 2016–August 2019, we determine RMS values of 236 Gt with replacement and 353 Gt without. Examining the GIA-corrected mass trends and the 2- model fit uncertainties, we compute a GRACE value of Gt year over the span January 2007–July 2016, while trends of and Gt year are obtained over August 2016–August 2019 with and without replacement, respectively. Over the full span of both missions, April 2002–August 2019, we determine a -corrected AIS mass trend of Gt year . As shown in Figure 3, the SLR replacement has little impact on AIS mass change when GRACE is in dual accelerometer mode, and those differences only modify the computed trend by 6 Gt year for March 2012–July 2016 and 1 Gt year for the full span.
In addition to the model fit uncertainties, the GIA model and GRACE signal leakage errors must also be considered to determine realistic trend uncertainties. Ivins et al. (2013) report a 1- error of 13 Gt year , while Loomis et al. (2019b) report a 2- GRACE AIS signal leakage error of 7 Gt year . We define the total trend uncertainties as the root sum square of the model fit, GIA, and leakage errors, resulting in final -corrected trend estimates and 2- uncertainties of , , and Gt year for January 2007–July 2016, August 2016–August 2019, and the full mission span, respectively. If the ICE-6G_D GIA model (Peltier et al., 2018) is applied instead of IJ05_R2, all reported trends would change by Gt year .
4 Conclusions
The TVG products of GRACE and GRACE-FO, in conjunction with SLR-derived estimates of , continue to advance our knowledge and understanding of mass change in the Earth system. Here, we have demonstrated that the GRACE and GRACE-FO estimates are degraded when measurements of non-gravitational accelerations from only one accelerometer are used in the data processing, which is currently the case for all GRACE and GRACE-FO monthly solutions after October 2016 except May 2017. The exact relationship between the transplant accelerometer data and the degraded estimates is still under investigation, and it is conceivable that advances in the transplant product for both missions could mitigate the issue. Fortunately, we do have an immediate solution, as we have demonstrated that is well recovered by SLR when LARES data are included in the low-degree TVG solution. The 2012 launch of LARES provides a sufficient span of time (March 2012–July 2016) to successfully validate the SLR estimates to the high-quality, dual accelerometer GRACE products. Therefore, we recommend that all single accelerometer GRACE/GRACE-FO estimates be replaced with those obtained by the seven-satellite SLR solution presented here and provided as TN-14. We also suggest that users consider replacing the August 2016 values due to the intermittent nature of the inter-satellite ranging data throughout that month.
We have analyzed the impact of the recommended replacement procedure on the recovered mass change time series of the AIS. Noting the fairly consistent signal trend beginning around 2007–2008, we report a GRACE trend of Gt year over the dual accelerometer span of January 2007–July 2016 (2- uncertainties include model fit, GIA, and leakage errors). Without the replacement procedure, the estimated GRACE/GRACE-FO mass trend for August 2016–August 2019 is Gt year , while the recommended approach yields a value of Gt year . This result highlights the major impact replacement has on the scientific analysis of the results; specifically, the extended corrected data set reveals a similar rate of mass loss as the prior decade, whereas the uncorrected data set would erroneously report a 45% reduction in the rate of mass loss in recent years.
Acknowledgments
This work was funded by NASA through the GRACE-FO Science Data System. GRACE and GRACE-FO Level 2 spherical harmonics and the Technical Notes TN-13 and TN-14 are all distributed via PO.DAAC (https://podaac.jpl.nasa.gov). SLR normal point data are obtained from CDDIS, a global data center for the International Laser Ranging Service (ILRS; https://cddis.nasa.gov). The NASA GSFC SLR products also are available at https://neptune.gsfc.nasa.gov/slr_tvg/. We acknowledge the excellent work of the entire Science Data System team for GRACE and GRACE-FO. We also acknowledge the expertise of our colleagues F. G. Lemoine, N. P. Zelensky, and D. S. Chinn, whose prior work was foundational to the NASA GSFC SLR data processing capabilities. NASA GSFC colleague T. J. Sabaka provided valuable feedback during the revision of the manuscript. A portion of this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
