Skip to main content

Advertisement

Log in

Revisiting the pole tide for and from satellite altimetry

  • Original Article
  • Published:
Journal of Geodesy Aims and scope Submit manuscript

Abstract

Satellite altimeter sea surface height observations include the geocentric displacements caused by the pole tide, namely the response of the solid Earth and oceans to polar motion. Most users of these data remove these effects using a model that was developed more than 20 years ago. We describe two improvements to the pole tide model for satellite altimeter measurements. Firstly, we recommend an approach that improves the model for the response of the oceans by including the effects of self-gravitation, loading, and mass conservation. Our recommended approach also specifically includes the previously ignored displacement of the solid Earth due to the load of the ocean response, and includes the effects of geocenter motion. Altogether, this improvement amplifies the modeled geocentric pole tide by 15 %, or up to 2 mm of sea surface height displacement. We validate this improvement using two decades of satellite altimeter measurements. Secondly, we recommend that the altimetry pole tide model exclude geocentric sea surface displacements resulting from the long-term drift in polar motion. The response to this particular component of polar motion requires a more rigorous approach than is used by conventional models. We show that erroneously including the response to this component of polar motion in the pole tide model impacts interpretation of regional sea level rise by \(\pm \)0.25 mm/year.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

Similar content being viewed by others

References

  • A G, Wahr J, Zhong S (2012) 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. doi:10.1093/gji/ggs030

  • Agnew DC, Farrell WE (1978) Self-consistent equilibrium ocean tides. Geophys J R Astron Soc 55:171–181. doi:10.1111/j,1365-246X.1978.tb04755.x

    Article  Google Scholar 

  • Argus DF, Gross RS (2004) An estimate of motion between the spin axis and the hotspots over the past century. Geophys Res Lett 31. doi:10.1029/2004GL019657

  • Beckley BD, Ray RD, Lemoine FG, Zelensky NP, Yang X, Desai S, Brown S, Mitchum G, Ricko M (2014) Maintaining the accuracy of a sea surface height climate data record from multi-mission altimeter data. Fall Meeting of the American Geophysical Union, San Francisco, CA, December 15–19

  • Beckley BD, Ray R, Holmes S, Zelensky N, Lemoine F, Yang X, Brown S, Desai S, Mitchum G, Hausman J (2013) Integrated multi-mission ocean altimeter data for climate research TOPEX/Poseidon, Jason-1, and OSTM/Jason-2 user’s handbook, PO.DAAC, CA, USA. doi:10.5067/ALTCY-TJ122

  • Beckley BD, Zelensky NP, Holmes SA, Lemoine FG, Ray RD, Mitchum GT, Desai SD, Brown ST (2010) Assessment of the Jason-2 extension to the TOPEX/Poseidon, Jason-1 sea-surface height time series for global mean sea level monitoring. Mar Geod 33(S1):447–471. doi:10.1080/01490419.2010.491029

  • Blewitt G (2003) Self-consistency in reference frames, geocenter definition, and surface loading of the solid Earth. J Geophys Res 108 (B2). doi:10.1029/2002JB002082

  • Carton JA, Wahr JM (1986) Modeling the pole tide and its effect on the Earth’s rotation. Geophys J R Astron Soc 84:121–138. doi:10.1111/j.1365-246X.1986.tb04348.x

    Article  Google Scholar 

  • Cartwright DE, Edden AC (1973) Corrected tables of tidal harmonics. Geophys J R Astron Soc 33:253–264. doi:10.1111/j.1365-246X.1973.tb03420.x

    Article  Google Scholar 

  • Cartwright DE, Taylor RJ (1971) New computations of the tide-generating potential. Geophys J R Astron Soc 23:45–73. doi:10.1111/j.1365-246X.1971.tb01803.x

    Article  Google Scholar 

  • Chao BF, Chung W-Y (2012) Amplitude and phase variations of Earth’s Chandler wobble under continual excitation. J Geodyn 62. doi:10.1016/j.jog.2011.11.009

  • Desai SD (2002) Observing the pole tide with satellite altimetry. J Geophys Res 107(C11):3186. doi:10.1029/2001JC001224

  • Desai SD, Ray RD (2014) Consideration of tidal variations in the geocenter on satellite altimeter observations of ocean tides. Geophys Res Lett 41:2454–2459. doi:10.1002/2014GL059614

  • Egbert GD, Erofeeva SY (2002) Efficient inverse modeling of barotropic ocean tides. J Atmos Oceanic Technol 19:183–204. doi:10.1175/1520-0426

    Article  Google Scholar 

  • Ekman M, Stigebrandt A (1990) Secular change of the seasonal variation in sea level and of the pole tide in the Baltic Sea. J Geophys Res 95(C4):5379–5383. doi:10.1029/JC095iC04p05379

    Article  Google Scholar 

  • Farrell WE (1972) Deformation of the Earth by surface loads. Rev Geophys 10:761–797. doi:10.1029/RG010i003p00761

    Article  Google Scholar 

  • Fu L-L, Christensen EJ, Yamarone CA Jr, Lefebvre M, M énard Y, Dorrer M, Escudier P (1994) TOPEX/POSEIDON mission overview. J Geophys Res 99(C12):24369–24381. doi:10.1029/94JC01761

    Article  Google Scholar 

  • Gross RS (2000) The excitation of the Chandler wobble. Geophys Res Lett 27(15):2329–2332. doi:10.1029/2000GL011450

    Article  Google Scholar 

  • Gross RS (2007) Earth rotation variations—long period. In: Herring T, Schubert G (eds) Treatise on geophysics, vol 3. Elsevier, Oxford, pp 239–294

    Chapter  Google Scholar 

  • Guo JY, Li YB, Huang Y, Deng HT, Xu SQ, Ning JS (2004) Green’s function of the deformation of the Earth as a result of atmospheric loading. Geophys J Int 159:53–68. doi:10.1111/j.1365-246X.2004.02410.x

    Article  Google Scholar 

  • Haubrich R Jr, Munk W (1959) The pole tide. J Geophys Res 64(12):2373–2388. doi:10.1029/JZ064i012p02373

    Article  Google Scholar 

  • Kang K, Wahr J, Heflin M, Desai S (2014) Stacking global GPS verticals and horizontals to solve for the fortnightly and monthly body tides: implications for mantle inelasticity. J Geophys Res Solid Earth 120:1787–1803. doi:10.1002/2014JB011572

  • Lambin J, Morrow R, Fu L-L, Willis JK, Bonekamp H, Lillibridge J, Perbos J, Zaouche G, Vaze P, Bannoura W, Parisot F, Thouvenot E, Coutin-Faye S, Lindstrom E, Mignogno M (2010) The OSTM/Jason-2 mission. Mar Geod 33(S1):4–25. doi:10.1080/01490419.2010.491030

    Article  Google Scholar 

  • Leuliette EW, Willis JK (2011) Balancing the sea level budget. Oceanography 24(2):122–129. doi:10.5670/oceanog.2011.32

    Article  Google Scholar 

  • Masters D, Nerem RS, Choe C, Leuliette E, Beckley B, White N, Ablain M (2012) Comparison of global mean sea level time series fro TOPEX/Poseidon, Jason-1, and Jason-2. Mar Geod 35(Sup1):20–41. doi:10.1080/01490419.2012.717862

    Article  Google Scholar 

  • Ménard Y, Fu L-L, Escudier P, Parisot F, Perbos J, Vincent P, Desai S, Haines B, Kunstmann G (2003) The Jason-1 mission. Mar Geod 26(3–4):131–146. doi:10.1080/714044514

    Article  Google Scholar 

  • Munk WH, Macdonald GJF (1960) The rotation of the Earth: a geophysical discussion. Cambridge University Press, New York

  • O’Connor WP, Chao BF, Zheng D, Au AY (2000) Wind stress forcing of the North Sea “pole tide”. Geophys J Int 142(2):620–630. doi:10.1046/j.1365-246x.2000.00184.x

  • Petit G, Luzum B (2010) IERS conventions 2010, international Earth rotation and reference systems service, Verlag des Bundesamts für Kartographie und Geodäsie. Tech, Note 36

  • Poma A (2000) The Markowitz wobble. In: Dick S, McCarthy D, Luzum B (eds) Polar motion: historical and scientific problems. ASP conference series, vol 208

  • Ray RD (2013) Precise comparisons of bottom-pressue and altimetric ocean tides. J Geophys Res Oceans 118:4570–4584. doi:10.102/jgrc.20336

    Article  Google Scholar 

  • Ray RD, Erofeeva SY (2014) Long-period tidal variations in the length of day. J Geophys Res Solid Earth 119:1498–1509. doi:10.1002/2013JB010830

    Article  Google Scholar 

  • Tamisiea ME (2011) Ongoing glacial isostatic contributions to observations of sea level change. Geophys J Int 186:1036–1044. doi:10.1111/j.1365-246X.2011.05116.x

    Article  Google Scholar 

  • Trupin A, Wahr J (1990) Spectroscopic analysis of global tide gauge sea level data. Geophys J Int 100(3):441–453. doi:10.1111/j.1365.246X.1990.tb00697.x

    Article  Google Scholar 

  • Tsimplis MN, Flather RA, Vassie JM (1994) The North Sea pole tide described through a tide-surge numerical model. Geophys Res Lett 21(6):449–452. doi:10.1029/94GL00181

    Article  Google Scholar 

  • Wahr JM (1981) Body tides on an elliptical, rotating, elastic and oceanless earth. Geophys J R Astron Soc 64:677–704. doi:10.1111/j.1365-246X.1981.tb02690.x

    Article  Google Scholar 

  • Wahr JM (1985) Deformation induced by polar motion. J Geophys Res 90(B11):9363–9368. doi:10.1029/JB090iB11p09363

    Article  Google Scholar 

  • Wahr J, Nerem RS, Ries J, Bettadpur S (2015) The pole tide and its effect on GRACE time-variable gravity measurements: implications for estimates of surface mass variations. J Geophys Res Solid Earth 120:4597–4615. doi:10.1002/2015JB011986

    Article  Google Scholar 

  • Wunsch C (1974) Dynamics of the pole tide and the damping of the Chandler wobble. Geophys J Int 39(3):539–550. doi:10.1111/j.1365-246X.1974.tb05471.x

    Article  Google Scholar 

  • Xie L, Dickman SR (1996) Tide gauge data analysis of the pole tide in the North Sea. Geophys J Int 126(3):863–870. doi:10.1111/j.1365-246X.1996.tb04708.x

    Article  Google Scholar 

Download references

Acknowledgments

SDD performed the work described in this paper at the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics and Space Administration. Work at the University of Colorado was partially supported by NASA GRACE funding, and by NASA’s ‘Making Earth Science Data Records for Use in Research Environments (MEaSUREs) Program. We thank G. Egbert and S. Erofeeva for providing the TPXO8 ocean tide model. The IERS is acknowledged for providing the EOPC04 polar motion time series. We thank two anonymous reviewers for their useful feedback.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shailen Desai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Desai, S., Wahr, J. & Beckley, B. Revisiting the pole tide for and from satellite altimetry. J Geod 89, 1233–1243 (2015). https://doi.org/10.1007/s00190-015-0848-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00190-015-0848-7

Keywords

Navigation