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.
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
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
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
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
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
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
Farrell WE (1972) Deformation of the Earth by surface loads. Rev Geophys 10:761–797. doi:10.1029/RG010i003p00761
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
Gross RS (2000) The excitation of the Chandler wobble. Geophys Res Lett 27(15):2329–2332. doi:10.1029/2000GL011450
Gross RS (2007) Earth rotation variations—long period. In: Herring T, Schubert G (eds) Treatise on geophysics, vol 3. Elsevier, Oxford, pp 239–294
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
Haubrich R Jr, Munk W (1959) The pole tide. J Geophys Res 64(12):2373–2388. doi:10.1029/JZ064i012p02373
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
Leuliette EW, Willis JK (2011) Balancing the sea level budget. Oceanography 24(2):122–129. doi:10.5670/oceanog.2011.32
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
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
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
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
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
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
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
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
Wahr JM (1985) Deformation induced by polar motion. J Geophys Res 90(B11):9363–9368. doi:10.1029/JB090iB11p09363
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
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
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
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
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00190-015-0848-7