# Comparison of Terrestrial Water Storage Changes Derived from GRACE/GRACE-FO and Swarm: A Case Study in the Amazon River Basin

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## Abstract

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## 1. Introduction

^{−1}, respectively. This suggests that Swarm TVG data have the potential to invert the large-scale Earth surface mass changes. The SH coefficients of TVGF derived from hl-SST data are up to a degree and order from ~10 to 15, and the corresponding spatial resolution is from ~1300 to 2000 km, which shows a big difference compared with that of GRACE (~350 km) [35]. Da Encarnação et al. [36,37] found that the maximum spatial resolution of the Swarm TVGF model is a degree of 12. However, most studies focus on the comparison of the numerical values of long-term trend changes derived from GRACE and Swarm. However, there are few studies on the comparison between the spatial distribution of long-term trend changes and the seasonal changes derived from GRACE and Swarm.

## 2. Study Area

## 3. Data and Methodologies

#### 3.1. GRACE/GRACE-FO Data

_{20}term was replaced by the corresponding data from Satellite laser ranging (SLR) because of the lower accuracy of the GRACE TVG model [14]. Secondly, the 1-degree errors of the TVG model caused by geocenter motion were corrected by using the results from Swenson et al. [6]. Thirdly, the effect of ice rebound was deducted from the TVGF model using the ICE-5G glacier isostatic adjustment (GIA) model. Finally, smooth-filtering processing using a 300 km fan filter [2] was used to reduce the observation noise of the GRACE data.

#### 3.2. Swarm Data

_{20}term was replaced by the corresponding data from SLR, the 1-degree errors of the TVG model were corrected and the effect of ice rebound was deducted by using the ICE-5G GIA model).

#### 3.3. Scale Factor Estimated from GLDAS

- (1)
- The time series of regional TWSC was calculated based on global GLDAS original gridded data;
- (2)
- An SH expansion of the original gridded data was performed and truncated to the same degree as the GRACE or Swarm models. These were processed by the same filtering method;
- (3)
- According to the processed SH coefficients, the TWSC time series was computed in regional areas;
- (4)
- The scale factor was calculated according to the time series obtained in step 3 and the original ones using the least squares rule.

#### 3.4. Data Analysis

#### 3.4.1. Degree-Error RMS

#### 3.4.2. Degree Correlation Analysis

#### 3.4.3. The Analysis of TWSC Time Series

## 4. Results

#### 4.1. Precision Evaluation of the Gravity Filed Model

_{20}coefficient is a negative value, due to its lower precision in Swarm models [14] (Figure 6). As seen in Figure 6, there is a big difference between the C

_{20}coefficients from Swarm, GRACE and SLR. However, the C

_{20}coefficients from GRACE and SLR are close. This explains why the correlation coefficient of the C

_{20}term is negative in Figure 5.

#### 4.2. Filter Results

#### 4.3. TWSC of Amazon River Basin

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Kornfeld, R.P.; Arnold, B.W.; Gross, M.A.; Dahya, N.T.; Klipstein, W.M.; Gath, F.P.; Bettadpur, S. GRACE-FO: The gravity recovery and climate experiment follow-on mission. J. Spacecr. Rockets
**2019**, 56, 931–951. [Google Scholar] [CrossRef] - Wahr, J.; Molenaar, M.; Bryan, F. Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. J. Geophys. Res.
**1998**, 103, 30205–30229. [Google Scholar] [CrossRef] - Li, Q.; Luo, Z.C.; Zhong, B.; Wang, H.H. Terretrial water storage change of the 2010 southwest China drought detected by GRACE temporal gravity filed. Chin. J. Geophys.
**2013**, 56, 1843–1849. (In Chinese) [Google Scholar] - Chen, J.L.; Wilson, C.R.; Blankenship, D.D.; Tapley, B.D. Antarctic mass rates from GRACE. Geophys. Res. Lett.
**2006**, 33, L11502. [Google Scholar] [CrossRef] [Green Version] - Luo, Z.C.; Li, Q.; Zhang, K.; Wang, H.H. Trend of mass changes in the Antarctic ice sheet recovered from the GRACE temporal gravity field. Sci. China Earth Sci.
**2012**, 55, 76–82. [Google Scholar] [CrossRef] - Swenson, S.; Chembers, D.; Wahr, J. Estimating geocenter variations from a combination of GRACE and ocean model output. J. Geophys. Res.
**2008**, 113, B08410. [Google Scholar] [CrossRef] [Green Version] - Chambers, D.; Wahr, J.; Nerem, R. Preliminary observations of global ocean mass variations with GRACE. Geophys. Res. Lett.
**2004**, 31, L13310. [Google Scholar] [CrossRef] [Green Version] - Han, S.C.; Sauber, J.; Riva, R. Contribution of satellite gravimetry to understanding seismic source processes of the 2011 Tohoku-Oki earthquake. Geophys. Res. Lett.
**2011**, 38, L24312. [Google Scholar] [CrossRef] - Han, S.C.; Riva, R.; Sauber, J.; Okal, E. Source parameter inversion for recent great earthquakes from a decade-long obervation of global gravity field. J. Geophys. Res.
**2013**, 118, 1240–1267. [Google Scholar] [CrossRef] [Green Version] - Zou, Z.B.; Luo, Z.C.; Wu, H.B.; Shen, C.Y.; Li, H. Gravity changes observed by GRACE before the Japan Mw9.0 Earthquake. Acta Geod. Cartogr. Sin.
**2012**, 41, 171–176. [Google Scholar] - Tapley, B.D.; Bettadpur, S.; Ries, J.C.; Thompson, P.F.; Watkins, M.M. GRACE measurements of mass variability in the Earth system. Science
**2004**, 305, 503–505. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Chen, M.K.; Shum, C.K.; Tapley, B.D. Determination of long-term changes in the Earth’s gravity field from satellite laser ranging observations. J. Geophys. Solid Earth
**1997**, 102, 22377–22390. [Google Scholar] [CrossRef] - Cheng, M.; Tapley, B.D. Seasonal variations in low degree zonal harmaonics of the Earth’s gravity field from satellite laser ranging observations. J. Geophys. Res. Solid Earth
**1999**, 104, 2667–2681. [Google Scholar] [CrossRef] - Cheng, M.; Tapley, B.D. Variations in the Earth’s oblatenness during the past 28 years. J. Geophys. Res. Solid Earth
**2004**, 109, B09402. [Google Scholar] [CrossRef] - Talpe, M.J.; Nerem, R.S.; Forootan, E.; Schmidt, M.; Lemoine, F.G.; Enderlin, E.M.; Landerer, F.W. Ice mass change in Greenland and Antarctica between 1993 and 2013 from satellite gravity measurements. J. Geod.
**2017**, 91, 1283–1298. [Google Scholar] [CrossRef] [Green Version] - Haberkorn, C.; Bloßfeld, M.; Bouman, J.; Fuchs, M.; Schmidt, M. Toward a consistent estimation of the earth’s gravity field by combining normal equation matrices from GRACE and SLR. In IAG 150 Year; Springer: Berlin, Germany, 2015; pp. 375–381. [Google Scholar]
- Olsen, N.; Friis-Christensen, E.; Floberhagen, R.; Alken, P.; Beggan, C.D.; Chulliat, A.; Doornbos, E.; da Encarnacan, J.T.; Hamilton, B.; Hulot, C.; et al. The Swarm Satellite Constellation Application and Research Facility (SCARF) and Swarm data products. Earth Planets Space
**2013**, 65, 1189–1200. [Google Scholar] [CrossRef] - ESA. Swarm-The Earth’s magnetic field and environment explorers. ESA Rep. SP
**2004**. [Google Scholar] - Zangerl, F.; Griesaucr, F.; Sust, M.; Montenbruck, O.; Buckert, B.; Garcia, A. SWARM GPS Precise Orbit Determination Receiver Initial In-Orbit Performance Evaluation. In Proceedings of the 27th International Technical Meeting of the Satellite Division of the Institute of Navigation, Tampa, FL, USA, 8–12 September 2014; pp. 1459–1468. [Google Scholar]
- Van den IJssel, J.; Encarnacao, J.; Doornbos, E.; Visser, P. Precise science orbit for the Swarm satellite constellation. Adv. Space Res.
**2015**, 56, 1042–1055. [Google Scholar] [CrossRef] - Prange, L. Global Gravity Field Determination Using the GPS Measurements Made Onboard the Low Earth Orbiting Satellite CHAMP; Schweizerische Geodätische kommission/Swiss Geodetic Commission: Zürich, Switzerland, 2010. [Google Scholar]
- Lin, T.J.; Hwang, C.; Tseng, T.P.; Chao, B.F. Low-degree gravity changes from GPS data of COSMIC and GRACE satellite missions. J. Geodyn.
**2012**, 53, 34–42. [Google Scholar] [CrossRef] - Baur, O. Greenland mass variation from time-variable gravity in the absence of GRACE. Geophys. Res. Lett.
**2013**, 40, 4289–4293. [Google Scholar] [CrossRef] - Weigelt, M.; van dam, T.; Baur, O.; Tourian, M.J.; Steffen, H.; Sosnica, K.; Jäggl, A.; Zehentner, N.; Mayer-Gürr, T.; Sneeuw, N. How well can the combination of hl-SST and SLR replace GRACE? A discussion from the point of view of applications. In Proceedings of the Grace Science Team Meeting 2014, Potsdam, Germany, 29 September–01 October 2014. [Google Scholar]
- Visser, P.N.A.M.; van der Wal, W.; Schrama, E.J.O.; van den IJssel, J.; Bouman, J. Assessment of observing time-variable gravity from GOCE GPS and accelerometer observations. J. Geod.
**2014**, 88, 1029–1046. [Google Scholar] [CrossRef] - Wang, Z.T.; Chao, N.F. Time-variable gravity signal in Greenland revealed by SWARM high-low Satellite-to-Satellite Tracking. Chin. J. Geophys.
**2014**, 57, 3117–3128. (In Chinese) [Google Scholar] - Wang, X.X.; Gerlach, C.; Rummel, R. Time-variable gravity field from satellite constellations using the energy integral. Geophys. J. Int.
**2012**, 190, 1507–1525. [Google Scholar] [CrossRef] [Green Version] - Bezděk, A.; Sebera, J.; Klokočník, J.; Kostelecky, J. Gravity field models from kinematic orbits of CHAMP, GRACE and GOCE satellites. Adv. Space Res.
**2014**, 53, 412–429. [Google Scholar] [CrossRef] - Bezděk, A.; Sebera, J.; Teixeira da Encarnação, J.; Klokocnik, J. Time-variable gravity fields derived from GPS tracking of Swarm. Geophys. J. Int.
**2016**, 205, 1665–1669. [Google Scholar] [CrossRef] [Green Version] - Beutle, G.; Jäggi, A.; Mervart, L.; Meyer, U. The celestial mechanics approach: Theoretical foundations. J. Geod.
**2010**, 84, 605–624. [Google Scholar] [CrossRef] [Green Version] - Jäggi, A.; Dahle, C.; Arnold, D.; Bock, H.; Meyer, U.; Beutler, G.; van den IJssel, J. Swarm kinematic orbits and gravity fields from 18 months of GPS data. Adv. Space Res.
**2016**, 57, 218–233. [Google Scholar] [CrossRef] - Ilk, K.H.; Mayer-Gürr, T.; Feuchtinger, M. Gravity Field Recovery by Analysis of Short Arcs of CHAMP//Earth Observation with CHAMP; Springer: Berlin/Heidelberg, Germany, 2005; pp. 127–132. [Google Scholar]
- Weigelt, M.; van Dam, T.; Jäggi, A.; Prange, L.; Tourian, M.J.; Keller, W.; Sneeuw, N. Time-variable gravity signal in Greenland revealed by high-low satellite-to-satellite tracking. J. Geophys. Res. Solid Earth
**2013**, 118, 3848–3859. [Google Scholar] [CrossRef] [Green Version] - Lück, C.; Kusche, J.; Rietbroek, R.; Löcher, A. Time-variable gravity fields and ocean mass change from 37 months of kinematic Swarm orbits. Solid Earth
**2018**, 9, 323–339. [Google Scholar] [CrossRef] [Green Version] - Wang, X.L. Study on Extraction Method and Application of Time-Variable Gravity Signal Detected by Satellite. Ph.D. Thesis, Wuhan University, Wuhan, China, 2019. [Google Scholar]
- Da Encarnação, T.J.; Arnold, D.; Bezděk, A.; Dahle, C.; Doornbos, E.; van den IJssel, J.; Jäggi, A.; Mayer-Gürr, T.; Sebera, J.; Visser, P.; et al. Gravity field models derived from Swarm GPS data. Earth Planets Space
**2016**, 68, 127. [Google Scholar] [CrossRef] [Green Version] - Da Encarnação, T.J.; Visser, P.; Arnold, D.; Bezděk, A.; Doornbos, E.; Ellmer, M.; Guo, J.Y.; van den IJssel, J.; Iorfida, E.; Jäggi, A.; et al. Description of the multi-approach gravity field models from Swarm GPS data. Earth Syst. Sci. Data
**2020**, 12, 1385–1417. [Google Scholar] [CrossRef] - Fan, Y.; Miguez-Macho, G. Potential groundwater contribution to Amazon evapotranspiration. Hydrol. Earth Syst. Sci.
**2009**, 14, 2039–2056. [Google Scholar] [CrossRef] [Green Version] - Latrubesse, E.M.; Arima, E.Y.; Dunne, T.; Park, E.; Baker, V.R.; d’Hort, F.M.; Wight, C.; Wittmann, F.; Zuanon, J.; Baker, P.A.; et al. Damming the rivers of the Amazon basin. Nature
**2017**, 546, 363–369. [Google Scholar] [CrossRef] - Malhi, Y.; Roberts, J.T.; Betts, R.A.; Killeen, T.J.; Li, W.; Nobre, C.A. Climate change, deforestaion, and the fate of the Amazon. Science
**2008**, 319, 169–172. [Google Scholar] [CrossRef] [Green Version] - Nobre, C.A.; Sellers, P.J.; Shukla, J. Amazonian deforestation and regional climate change. J. Clim.
**1991**, 4, 957–988. [Google Scholar] [CrossRef] [Green Version] - Chaudhari, S.; Pokhrel, Y.; Moran, E.; Miguez-Macho, G. Muti-decadal hydrologic change and variability in the Amazon River basin: Understanding terrestrial water storage variations and drought characteristics. Hydrol. Earth Syst. Sci.
**2019**, 23, 2841–2862. [Google Scholar] [CrossRef] [Green Version] - Swenson, S.; Wahr, J. Post-processing removal of correlated errors in GRACE data. Geophys. Res. Lett.
**2006**, 33, L08402. [Google Scholar] [CrossRef] - Jean, Y.; Meyer, U.; Jäggi, A. Combination of GRACE monthly gravity field solutions from different processing strategies. J. Geod.
**2018**, 92, 1313–1328. [Google Scholar] [CrossRef] [Green Version] - Rodell, M.; Houser, P.; Jambor, U.E.A.; Gottschalck, J.; Mitchell, K.; Meng, C.; Arsenault, K.; Cosgrove, B.; Radakovich, J.; Bosilovich, M. The global land data assimilation system. Bull. Am. Meteorol. Soc.
**2004**, 85, 381–394. [Google Scholar] [CrossRef] [Green Version] - Chen, J.L.; Wilson, C.R.; Famiglietti, J.S.; Rodell, M. Spatial sensitivity of the Gravity Recovery and Climate Experiment(GRACE) time-variable gravity observations. J. Geophys. Res. Solid Earth
**2006**, 111, 115–139. [Google Scholar] [CrossRef] [Green Version] - Zhou, X.H.; Xu, H.Z.; Wu, B.; Peng, B.B.; Lu, Y. Earth’s gravity field derived from GRACE satellite tracking data. Chin. J. Geophys.
**2006**, 49, 718–723. [Google Scholar] [CrossRef] - Zhang, Z.; Chao, B.; Chen, J.L.; Wilson, C. Terrestrial water storage anomalies of Yangtze River basin droughts observed by GRACE and Connections with ENSO. Glob. Planet Chang.
**2015**, 126, 35–45. [Google Scholar] [CrossRef] - Wang, X.L.; Luo, Z.C.; Zhong, B.; Wu, Y.H.; Huang, Z.K.; Zhou, H.; Li, Q. Separation and recovery of geophysical signals based on the Kalman filter with GRACE gravity data. Remote Sens.
**2019**, 11, 393. [Google Scholar] [CrossRef] [Green Version] - Zhang, Z.Z.; Chao, B.F.; Yang, L.; Hsu, H.T. An effective filtering for GRACE time-variable gravity: Fan filter. Geophys. Res. Lett.
**2009**, 36, L17311. [Google Scholar] [CrossRef] - Li, F.P.; Wang, Z.T.; Chao, N.F.; Feng, J.D.; Zhang, B.B.; Tian, K.J.; Han, Y.K. 2015–2016 drought event in the Amazon River Basin as measured by Swarm constellation. Geomat. Inf. Sci Wuhan Univ.
**2020**, 45, 595–603. [Google Scholar] - Chen, J.L.; Wilson, C.R.; Tapley, B.D.; Yang, Z.L.; Niu, G.Y. 2005 drought event in the Amazon River basin as measured by GRACE and estimated by climate models. J. Geophys. Res.
**2009**, 114, B05404. [Google Scholar] [CrossRef] - Panisset, J.S.; Libonati, R.; Gouveia, C.M.P.; Silva, F.M.; Franca, D.A.; Franca, J.R.A.; Peres, L.F. Contrasting patterns of the extreme drought episodes of 2005, 2010 and 2015 in the Amazon Basin. Int. J. Clinatol.
**2018**, 38, 1096–1104. [Google Scholar] [CrossRef] - Chen, J.L.; Wilson, C.R.; Tapley, B.D. The 2009 exceptional Amazon flood and interannual terretrial water storage observed by GRACE. Water Storage Res.
**2010**, 46, 439–445. [Google Scholar] - Nie, N.; Zhang, W.; Guo, H. 2010–2012 drougt and flood events in Amazon River Basin inferred by GRACE satellite observations. J. Appl. Remote Sens.
**2015**, 9, 096023. [Google Scholar] [CrossRef] - Zehentner, N.; Mayer-Gürr, T. Precise orbit determination based on raw GPS measurement. J. Geod.
**2016**, 90, 275–286. [Google Scholar] [CrossRef] [Green Version] - Guo, J.Y.; Shang, K.; Jekeli, C.; Shum, C.K. On the energy integral formulation of gravitational potential differences from satellite-to-satellite tracking. Celest. Mech. Dyn. Astr.
**2015**, 121, 415–429. [Google Scholar] [CrossRef] - Zhang, B.B. Precise Orbit Determination and the Earth Gravity Field Recovery by Acceleration Approach for Swarm. Ph.D. Thesis, Wuhan University, Wuhan, China, 2017. [Google Scholar]
- Jäggi, A.; Meyer, U.; Lasser, M.; Jenny, B.; Lopez, T.; Flechtner, F.; Dahle, C.; Förste, C.; Mayer-Gürr, T.; Kvas, A.; et al. International Combination Service for Time-variable Gravity Fields (COST-G)—Start of operational phase and future perspectives. In IAG Symposia; Springer: Berlin/Heidelberg, Germany, 2020. [Google Scholar] [CrossRef]
- Christopher, E.N.; Vagner, G.F. Assessing land water storage dynamics over South America. J. Hydrol.
**2020**, 580, 124339. [Google Scholar] - Forootan, E.; Schumacher, M.; Mehrnegar, N.; Bezděk, A.; Talpe, M.J.; Farzeneh, S.; Zhang, C.Y.; Zhang, Y.; Shum, C.K. An iterative ICA-based reconsyruction method to produce consisitent time-variable total water storage fields using GRACE and Swarm Satellite Data. Remote Sens.
**2020**, 12, 1639. [Google Scholar] [CrossRef]

**Figure 1.**Amazon River basin (the red curve is the basin boundary and the bold line is the main stream).

**Figure 2.**Internal coincidence accuracy of Gravity Recovery and Climate Experiment (GRACE) and Swarm models.

**Figure 4.**Degree-error root mean square (RMS) of the residual values of spherical harmonic (SH) coefficients of Swarm monthly gravity field relative to the GRACE model.

**Figure 5.**Degree correlation between Swarm and the GRACE models (left column is C coefficient results and right column is S coefficient results).

**Figure 7.**Monthly surface mass variation on March 2016 with unfiltered (

**top row**), 300 km fan filter (

**second row**), 500 km fan filter (

**third row**) and 700 km fan filter (

**bottom row**) from GRACE (

**left column**) and Swarm (

**right column**).

**Figure 8.**The terrestrial water storage change (TWSC) time series in the Amazon River basin calculated using GRACE (

**blue curve**) and Swarm (

**green curve**).

**Figure 9.**Long-term trends of TWSC in the Amazon River basin calculated by GRACE and Swarm. (

**a**) GRACE results; (

**b**) Swarm results.

Institute | AIUB | ASU | IfG | COST-G |
---|---|---|---|---|

Orbit | AIUB | ITSG | IfG | Combination |

Approach | Celestial mechanics | Acceleration | Short-arc | Combination |

Highest order | 70 | 40 | 40 | 40 |

Time span | 2014.01–2016.12 | 2013.12–2020.05 | 2013.11–2016.12 | 2013.12–2020.05 |

Download address | ftp://ftp.aiub.unibe.ch/GRAVITY/SWARM/ | http://www.asu.cas.cz/~bezdek/vyzkum/geopotencial/index.php | http://ftp.tugraz.at/outgoing/ITSG/tvgogo/gravityFieldModels | http://icgem.gfz-potsdam.de/series/02_COST-G/Swarm |

**Table 2.**Long-term trends and seasonal changes from Swarm and GRACE TVG field. AA and AP present the annual amplitude and annual phase, respectively.

Model | Time Span | Long-Term Trend (cm/a) | AA (cm) | AP (rad) |
---|---|---|---|---|

GRACE | 2013.12–2020.05 | −0.72 | 15.65 | −1.36 |

Swarm | −1.50 | 16.39 | −1.33 |

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**MDPI and ACS Style**

Cui, L.; Song, Z.; Luo, Z.; Zhong, B.; Wang, X.; Zou, Z.
Comparison of Terrestrial Water Storage Changes Derived from GRACE/GRACE-FO and Swarm: A Case Study in the Amazon River Basin. *Water* **2020**, *12*, 3128.
https://doi.org/10.3390/w12113128

**AMA Style**

Cui L, Song Z, Luo Z, Zhong B, Wang X, Zou Z.
Comparison of Terrestrial Water Storage Changes Derived from GRACE/GRACE-FO and Swarm: A Case Study in the Amazon River Basin. *Water*. 2020; 12(11):3128.
https://doi.org/10.3390/w12113128

**Chicago/Turabian Style**

Cui, Lilu, Zhe Song, Zhicai Luo, Bo Zhong, Xiaolong Wang, and Zhengbo Zou.
2020. "Comparison of Terrestrial Water Storage Changes Derived from GRACE/GRACE-FO and Swarm: A Case Study in the Amazon River Basin" *Water* 12, no. 11: 3128.
https://doi.org/10.3390/w12113128