Implications of the temporal variations of geoid heights over South American vertical reference frames

Abstract

The temporal variations in a vertical reference frame depend on the variations in the reference surface (e.g., the geoid), and in the surface where the benchmarks are located. The mass redistribution on and beneath the Earth’s surface generates changes in the geoid, which is the reference surface for orthometric heights. To model the phenomena and processes that affect Earth’s gravity field, the maintenance of a high-precision global physical reference frame that considers its temporal variations is necessary. In this contribution, we estimate and analyze the impact of three geophysical signals, namely mega-earthquakes (Mw > 7.5), hydrological loadings, and glacial isostatic adjustment over the South American vertical reference frames based on the Gravity Recovery and Climate Experiment monthly solutions, glacial isostatic adjustment, and hydrological models. Our results reveal that long-term trends range from −0.5 to 0.3 mm/year, which implies possible height variations up to 10 mm over 20 years. These results point out the possibilities for maintaining modern vertical reference frames if variations in the trends (e.g., due to accelerations) are disregarded. The seasonal variations (from peak to peak), co-seismic deformation, and post-seismic deformation reach 31 mm, 3.8 mm, and 0.8 mm, respectively. According to wavelet analysis based on the independent components (IC) obtained from independent component analysis, it was observed that the predominant signal has one cycle per year. The first four ICs represent 94.4% of the geoid variability. The spatial patterns of the four modes indicated that geoid variations are concentrated in the Amazon, Tocantins, Parana, and Sao Francisco river basins. Temporal variations of the geoid in South America reach magnitudes that should be considered in the evolution of height systems to accomplish the requirements of a modern height system (accuracy on the order of 10 mm or better).

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. Amos, M., Heck, B., Kersley, B., Schone, T., Sanchez, L., Drewes, H., 2007. Conventions for the Definition and Realization of a Conventional Vertical Reference System (CVRS).

    Google Scholar 

  2. Barletta VR, Bordoni A (2009) Clearing observed PGR in GRACE data aimed at global viscosity inversion: Weighted Mass Trends technique. Geophys. Res. Lett. 36. https://doi.org/10.1029/2008GL036429

  3. Bettadpur S (2018) GRACE 327-742 (CSR-GR-12-xx) GRAVITY RECOVERY AND CLIMATE EXPERIMENT UTCSR Level-2 Processing Standards Document 742, 0–16.

  4. Bevis M, Brown A (2014) Trajectory models and reference frames for crustal motion geodesy. J. Geod. 88:283–311. https://doi.org/10.1007/s00190-013-0685-5

    Article  Google Scholar 

  5. Bottiglieri M, Falanga M, Tammaro U, Obrizzo F, De Martino P, Godano C, Pingue F (2007) Independent component analysis as a tool for ground deformation analysis. Geophys. J. Int. 168:1305–1310. https://doi.org/10.1111/j.1365-246X.2006.03264.x

    Article  Google Scholar 

  6. Cardoso JF, Souloumiac A (1993) Blind beamforming for non-Gaussian signals. IEE Proceedings, Part F Radar Signal Process. 140:362–370. https://doi.org/10.1049/ip-f-2.1993.0054

    Article  Google Scholar 

  7. Cazenave A, Chen J (2010) Time-variable gravity from space and present-day mass redistribution in the Earth system. Earth Planet. Sci. Lett. 298:263–274. https://doi.org/10.1016/j.epsl.2010.07.035

    Article  Google Scholar 

  8. Chen JL, Wilson CR, Tapley BD, Blankenship DD, Ivins ER (2007) Patagonia Icefield melting observed by Gravity Recovery and Climate Experiment (GRACE). Geophys. Res. Lett. 34:1–6. https://doi.org/10.1029/2007GL031871

    Article  Google Scholar 

  9. Chen JL, Wilson CR, Tapley BD (2010) The 2009 exceptional Amazon flood and interannual terrestrial water storage change observed by GRACE. Water Resour. Res. 46:1–10. https://doi.org/10.1029/2010WR009383

    Article  Google Scholar 

  10. Cheng M, Ries J (2017) The unexpected signal in GRACE estimates of C20. J. Geod. 91:897–914. https://doi.org/10.1007/s00190-016-0995-5

    Article  Google Scholar 

  11. Cheng M, Ries JC, Tapley BD (2011) Variations of the Earth’s figure axis from satellite laser ranging and GRACE. J. Geophys. Res. Solid Earth 116. https://doi.org/10.1029/2010JB000850

  12. Christopoulou EB, Skodras AN, Georgakilas AA (2002) Time series analysis of sunspot oscillations using the wavelet transform. 2002. In: 14th Int. Conf. Digit. Signal Process. Proceedings. DSP 2002 (Cat. No.02TH8628) 2, pp 893–896. https://doi.org/10.1109/ICDSP.2002.1028234

    Google Scholar 

  13. Ferreira VG, Montecino HD, Ndehedehe CE, del Rio RA, Cuevas A, de Freitas SRC (2019) Determining seasonal displacements of Earth’s crust in South America using observations from space-borne geodetic sensors and surface-loading models. Earth, Planets Sp. 71:1–16

    Article  Google Scholar 

  14. Flury J, Rummel R (2004) Future satellite gravimetry for geodesy. Earth, Moon Planets 94:13–29. https://doi.org/10.1007/s11038-005-3756-7

    Article  Google Scholar 

  15. Forootan E, Kusche J (2012) Separation of global time-variable gravity signals into maximally independent components. J. Geod. 86:477–497. https://doi.org/10.1007/s00190-011-0532-5

    Article  Google Scholar 

  16. Geruo A, Wahr J, Zhong S (2013) Computations of the viscoelastic response of a 3-D compressible earth to surface loading: An application to glacial isostatic adjustment in Antarctica and Canada. Geophys. J. Int. 192:557–572. https://doi.org/10.1093/gji/ggs030

    Article  Google Scholar 

  17. Godah W, Szelachowska M, Krynski J (2017) On the analysis of temporal geoid height variations obtained from GRACE-based GGMs over the area of Poland. Acta Geophys. 65:713–725. https://doi.org/10.1007/s11600-017-0064-3

    Article  Google Scholar 

  18. Heck B, Mälzer H (1983) Determination of vertical recent crustal movements by levelling and gravity data. Tectonophysics 97:251–264. https://doi.org/10.1016/0040-1951(83)90152-X

    Article  Google Scholar 

  19. Hoffmann F, Metzger S, Moreno M, Deng Z, Sippl C, Ortega-Culaciati F, Oncken O (2018) Characterizing afterslip and ground displacement rate increase following the 2014 Iquique-Pisagua M w 8.1 earthquake, Northern Chile. J. Geophys. Res. Solid Earth:1–22. https://doi.org/10.1002/2017JB014970

  20. IAG (2015) IAG Resolutions at the XXVI IUGG General Assembly 2015.

  21. Ihde J, Sánchez L, Barzaghi R, Drewes H, Foerste C, Gruber T, Liebsch G, Marti U, Pail R, Sideris M (2017) Definition and Proposed Realization of the International Height Reference System (IHRS). Surv. Geophys. 38:549–570. https://doi.org/10.1007/s10712-017-9409-3

    Article  Google Scholar 

  22. Jacob T, Wahr J, Gross R, Swenson SAG (2012) Estimating geoid height change in North America: Past, present and future. J. Geod. 86:337–358. https://doi.org/10.1007/s00190-011-0522-7

    Article  Google Scholar 

  23. Kleijer F, Kenselaar F, de Bruijne AJT, Molendijk RE (2002) Employing the strict kinematic model for the maintenance of a height reference frame based on conventional levellings. In: Vertical Reference Systems. Springer, Berlin, pp 119–124

    Google Scholar 

  24. Krynski J, Kloch-glowka G, Szelachowska M (2014) Analysis of Time Variations of the Gravity Field Over Europe Obtained from GRACE Data in Terms of Geoid Height and Mass Variation Variations of Earth Gravity Field. Earth Edge Sci. a Sustain. Pl 139:365–370. https://doi.org/10.1007/978-3-642-37222-3

    Article  Google Scholar 

  25. Kusche J (2007) Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models. J. Geod. 81:733–749. https://doi.org/10.1007/s00190-007-0143-3

    Article  Google Scholar 

  26. Liu B, Dai W, Peng W, Meng X (2015) Spatiotemporal analysis of GPS time series in vertical direction using independent component analysis. Earth, Planets Sp. 67. https://doi.org/10.1186/s40623-015-0357-1

  27. Marti U, Schlatter A (2002) The new height system in Switzerland, in: Vertical Reference Systems. Springer, Berlin, pp 50–55

    Google Scholar 

  28. Montecino HD, de Freitas SRC, Báez JC, Ferreira VG (2017) Effects on Chilean Vertical Reference Frame due to the Maule Earthquake co-seismic and post-seismic effects. J. Geodyn. 112:22–30. https://doi.org/10.1016/j.jog.2017.07.006

    Article  Google Scholar 

  29. Moreira DM, Calmant S, Perosanz F, Xavier L, Rotunno Filho OC, Seyler F, Monteiro AC (2016) Comparisons of observed and modeled elastic responses to hydrological loading in the Amazon basin. Geophys. Res. Lett. 43:9604–9610. https://doi.org/10.1002/2016GL070265

    Article  Google Scholar 

  30. Peltier WR (1994) Ice age paleotopography. Science 265:195–201. https://doi.org/10.1126/science.265.5169.195

    Article  Google Scholar 

  31. Plag H-P, Pearlman M (2009) Global geodetic observing system: meeting the requirements of a global society on a changing planet in 2020. Springer Science & Business Media

  32. Rangelova E, Fotopoulos G, Sideris MG (2010) Implementing a Dynamic Geoid as a Vertical Datum for Orthometric Heights in Canada. In: International Association of Geodesy Symposia, pp 295–302. https://doi.org/10.1007/978-3-642-10634-7_38

    Google Scholar 

  33. Rangelova E, Van Der Wal W, Sideris MG (2012) How Significant is the Dynamic Component of the North American Vertical Datum? J. Geod. Sci. 2:281–289. https://doi.org/10.2478/v10156-012-0005-7

    Article  Google Scholar 

  34. Rodell M, Houser PR, Jambor U, Gottschalck J, Mitchell K, Meng C-J, Arsenault K, Cosgrove B, Radakovich J, Bosilovich M, Entin JK, Walker JP, Lohmann D, Toll D, Rodell M, Houser PR, Jambor U, Gottschalck J, Mitchell K, Meng C-J, Arsenault K, Cosgrove B, Radakovich J, Bosilovich M, Entin JK, Walker JP, Lohmann D, Toll D (2004) The Global Land Data Assimilation System. Bull. Am. Meteorol. Soc. 85:381–394. https://doi.org/10.1175/BAMS-85-3-381

    Article  Google Scholar 

  35. Sánchez L, Sideris MG (2017) Vertical datum unification for the International Height Reference System (IHRS). Geophys. J. Int. 209:570–586. https://doi.org/10.1093/gji/ggx025

    Article  Google Scholar 

  36. Save H, Tapley BD, Bettadpur S (2018) GRACE RL06 reprocessing and results from CSR. Geophys. Res. Abstr. EGU Gen, Assem

    Google Scholar 

  37. Shrivastava MN, González G, Moreno M, Reddy C, Salazar P, Yáñez G, González J, de la Llera JC, Báez JC (2016) Coseismic and Afterslip of the Mw 8.3 Illapel Earthquake 2015 from Continuous GPS data. Geophys. Res. Lett. 43:10710–10719. https://doi.org/10.1002/2016GL070684.Received

    Article  Google Scholar 

  38. Sjöberg LE (1989) The Secular Change of Gravity and the Geoid in Fennoscandia. In: Earthquakes at North-Atlantic Passive Margins: Neotectonics and Postglacial Rebound. Springer Netherlands, Dordrecht, pp 125–139. https://doi.org/10.1007/978-94-009-2311-9_9

    Google Scholar 

  39. Sjöberg LE, Bagherbandi M (2017) Gravity Inversion and Integration. Springer, Berlin. https://doi.org/10.1007/978-3-319-50298-4

    Google Scholar 

  40. Sun W, Okubo S (2004) Coseismic deformations detectable by satellite gravity missions: A case study of Alaska (1964, 2002) and Hokkaido (2003) earthquakes in the spectral domain. J. Geophys. Res. B Solid Earth 109. https://doi.org/10.1029/2003JB02554

  41. Sun T, Ferreira VG, He X, Andam-Akorful SA (2016) Water availability of são francisco river basin based on a space-borne geodetic sensor. Water (Switzerland) 8:8. https://doi.org/10.3390/w8050213

    Article  Google Scholar 

  42. Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys. Res. Lett. 33. https://doi.org/10.1029/2005GL025285

  43. Swenson S, Chambers D, Wahr J (2008) Estimating geocenter variations from a combination of GRACE and ocean model output. J. Geophys. Res. Solid Earth 113. https://doi.org/10.1029/2007JB005338

  44. Tapley BD, Chambers DP, Bettadpur S, Ries JC (2003) Large scale ocean circulation from the GRACE GGM01 Geoid. Geophys. Res. Lett. 30. https://doi.org/10.1029/2003GL018622

  45. Tapley BD, Watkins MM, Flechtner F, Reigber C, Bettadpur S, Rodell M, Sasgen I, Famiglietti JS, Landerer FW, Chambers DP, Reager JT, Gardner AS, Save H, Ivins ER, Swenson SC, Boening C, Dahle C, Wiese DN, Dobslaw H, Tamisiea ME, Velicogna I (2019) Contributions of GRACE to understanding climate change. Nat. Clim. Chang. 9:358–369. https://doi.org/10.1038/s41558-019-0456-2

    Article  Google Scholar 

  46. Tushingham AM, Peltier WR (1991) Ice-3G: A new global model of Late Pleistocene deglaciation based upon geophysical predictions of post-glacial relative sea level change. J. Geophys. Res. 96:4497–4523. https://doi.org/10.1029/90JB01583

    Article  Google Scholar 

  47. Van Dam T, Wahr J, Milly PCD, Shmakin AB, Blewitt G, Lavallée D, Larson KM (2001) Crustal displacements due to continental water loading. Geophys. Res. Lett. 28:651–654. https://doi.org/10.1029/2000GL012120

    Article  Google Scholar 

  48. Vermeersen BLA (2004) Challenges from solid earth dynamics for satellite gravity field missions in the post-GOCE era. Earth, Moon Planets 94:31–40. https://doi.org/10.1007/s11038-004-6816-5

    Article  Google Scholar 

  49. Vigny C, Socquet A, Peyrat S, Ruegg J-C, Métois M, Madariaga R, Morvan S, Lancieri M, Lacassin R, Campos J, Carrizo D, Bejar-Pizarro M, Barrientos S, Armijo R, Aranda C, Valderas-Bermejo M-C, Ortega I, Bondoux F, Baize S, Lyon-Caen H, Pavez A, Vilotte JP, Bevis M, Brooks B, Smalley R, Parra H, Baez J-C, Blanco M, Cimbaro S, Kendrick E (2011) The 2010 Mw 8.8 Maule megathrust earthquake of Central Chile, monitored by GPS. Science 332:1417–1421. https://doi.org/10.1126/science.1204132

    Article  Google Scholar 

  50. Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earth’s gravity field: Hydrological and oceanic effects and their possible detection using GRACE. J. Geophys. Res. 103:30205–30229. https://doi.org/10.1029/98JB02844

    Article  Google Scholar 

  51. Wang G, Soler T (2015) Measuring Land Subsidence Using GPS : Ellipsoid Height versus Orthometric Height. J. Surv. Eng. 141:05014004. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000137

    Article  Google Scholar 

  52. Wang L, Shum CK, Simons FJ, Tapley B, Dai C (2012) Coseismic and postseismic deformation of the 2011 tohoku-oki earthquake constrained by GRACE gravimetry. Geophys. Res. Lett. 39. https://doi.org/10.1029/2012GL051104

  53. Zlotnicki V, Wahr J, Fukumori I, Song YT (2007) Antarctic circumpolar current transport variability during 2003-05 from GRACE. J. Phys. Oceanogr. 37:230–244. https://doi.org/10.1175/JPO3009.1

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank the CSR centers for providing monthly solutions of the gravity field. The GLDAS data used in this study were acquired as part of the mission of NASA’s Earth Science Division and were archived and distributed by the Goddard Earth Sciences (GES) Data and Information Services Center (DISC).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Henry D. Montecino Castro.

Additional information

Responsible Editor: Longjun Dong

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Castro, H.D.M., de Freitas, S.R.C. Implications of the temporal variations of geoid heights over South American vertical reference frames. Arab J Geosci 14, 185 (2021). https://doi.org/10.1007/s12517-021-06562-0

Download citation

Keywords

  • Temporal variations of the geoid
  • GRACE
  • South America
  • Vertical reference frames