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Self-Attraction and Loading of Oceanic Masses

  • Julian Kuhlmann
  • Maik Thomas
  • Harald Schuh
Living reference work entry

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Abstract

When attempting to simulate sea-level variations precisely, the gravitational potential of the moving water masses themselves and their capability of modifying the Earth’s shape have to be considered. Self-attraction and loading (SAL) describes said effects. We describe SAL theoretically, deriving equations that allow to compute SAL either with spherical harmonic functions or with a convolution integral, and show how the equations can be modified to reduce computational demands of the calculation. Key questions of past and ongoing research on the topic include a quantification of SAL at periods from days to years and generated by different processes, the possibility of dynamical feedbacks, and the question of how SAL can be adequately represented in various modeling applications. Gravitation being a body force of infinite range, investigations of SAL include a wide range of processes connected to mass redistribution. For instance, this includes the fast tidal variability, but also atmospherically induced ocean dynamics, or mass redistribution on land and in the atmosphere. Future research is expected to be focused on tidal applications and to consider SAL on longer time scales as an equilibrium response.

Keywords

Ocean Model Gravitational Potential Love Number Mass Redistribution Spherical Harmonic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. United States Department of Commerce. http://people.math.sfu.ca/~cbm/aands/
  2. Accad Y, Pekeris CL (1978) Solution of the tidal equations for the M_2 and S_2 tides in the world oceans from a knowledge of the tidal potential alone. Philos Trans R Soc A Math Phys Eng Sci 290(1368):235–266. doi:10.1098/rsta.1978.0083, http://rsta.royalsocietypublishing.org/content/290/1368/235
  3. Chambers DP, Wahr J, Nerem RS (2004) Preliminary observations of global ocean mass variations with GRACE. Geophys Res Lett 31(13):L13310. doi:10.1029/2004GL020461, http://www.agu.org/pubs/crossref/2004.../2004GL020461.shtml
  4. Egbert GD, Bennett AF, Foreman MGG (1994) TOPEX/POSEIDON tides estimated using a global inverse model. J Geophys Res 99(C12):24821. doi:10.1029/94JC01894, http://www.agu.org/pubs/crossref/1994/94JC01894.shtml
  5. Farrell WE (1972) Deformation of the Earth by surface loads. Rev Geophys Space Phys 10(3): 761–797CrossRefGoogle Scholar
  6. Farrell WE, Clark JA (1976) On postglacial sea level. Geophys J R Astron Soc 46(3):647–667. doi:10.1111/j.1365-246X.1976.tb01252.x, http://doi.wiley.com/10.1111/j.1365-246X.1976.tb01252.x
  7. Gordeev RG, Kagan BA, Polyakov EV (1977) The effects of loading and self-attraction on global ocean tides: the model and the results of a numerical experiment. J Phys Oceanogr 7(2):161–170. doi:10.1175/1520-0485(1977)007¡0161:TEOLAS¿2.0.CO;2, http://journals.ametsoc.org/doi/abs/10.1175/1520-0485%281977%29007%3C0161%3ATEOLAS%3E2.0.CO%3B2
  8. Hendershott MC (1972) The effects of solid Earth deformation on global ocean tides. Geophys J Int 29(4):389–402. doi:10.1111/j.1365-246X.1972.tb06167.x, http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.1972.tb06167.x
  9. Kendall RA, Mitrovica JX, Milne GA (2005) On post-glacial sea level – II. Numerical formulation and comparative results on spherically symmetric models. Geophys J Int 161: 679–706. doi:10.1111/j.1365-246X.2005.02553.x, http://doi.wiley.com/10.1111/j.1365-246X.2005.02553.x
  10. Klemann V, Thomas M, Schuh H (2013) Elastic and viscoelastic reaction of the lithosphere to loads. In: Freeden W, Zuhair Nashed M, Sonar T (eds) Handbook of geomathematics. Springer, Berlin/HeidelbergGoogle Scholar
  11. Kuhlmann J, Dobslaw H, Thomas M (2011) Improved modeling of sea level patterns by incorporating self-attraction and loading. J Geophys Res 116(C11):C11036. doi:10.1029/2011JC007399, http://www.agu.org/pubs/crossref/2011/2011JC007399.shtml
  12. Müller M (2007) A large spectrum of free oscillations of the world ocean including the full ocean loading and self-attraction effects. Phd thesis, Universität Hamburg. http://www.springerlink.com/content/978-3-540-85575-0
  13. Müller M (2008) Synthesis of forced oscillations, Part I: tidal dynamics and the influence of the loading and self-attraction effect. Ocean Model 20(3):207–222. doi:10.1016/j.ocemod.2007.09.001, http://linkinghub.elsevier.com/retrieve/pii/S1463500307001151
  14. Munk W, MacDonald GJF (1960) The rotation of the Earth – a geophysical discussion. Cambridge University Press, CambridgeGoogle Scholar
  15. Ray RD (1998) Ocean self-attraction and loading in numerical tidal models. Mar Geodesy 21(3):181–192. doi:10.1080/01490419809388134CrossRefGoogle Scholar
  16. Richter K, Riva R, Drange H (2013) Impact of self-attraction and loading effects induced by shelf mass loading on projected regional sea level rise. Geophys Res Lett 40(6):1144–1148. doi:10.1002/grl.50265, http://doi.wiley.com/10.1002/grl.50265
  17. Schmidt R, Schwintzer P, Flechtner F, Reigber C, Guntner A, Doll P, Ramillien G, Cazenave A, Petrovic S, Jochmann H (2006) GRACE observations of changes in continental water storage. Glob Planet Change 50(1–2):112–126. doi:10.1016/j.gloplacha.2004.11.018, http://linkinghub.elsevier.com/retrieve/pii/S0921818105000317
  18. Smirnow WI (1955) Lehrgang der Höheren Mathematik Teil III, 2. VEB Deutscher Verlag der Wissenschaften, BerlinzbMATHGoogle Scholar
  19. Stepanov VN, Hughes CW (2004) Parameterization of ocean self-attraction and loading in numerical models of the ocean circulation. J Geophys Res 109(C3):C03037. doi:10.1029/2003JC002034, http://www.agu.org/pubs/crossref/2004/2003JC002034.shtml
  20. Tamisiea ME, Hill EM, Ponte RM, Davis JL, Velicogna I, Vinogradova NT (2010) Impact of self-attraction and loading on the annual cycle in sea level. J Geophys Res 115(C7):C07004. doi:10.1029/2009JC005687, http://www.agu.org/pubs/crossref/2010/2009JC005687.shtml
  21. Vinogradova NT, Ponte RM, Tamisiea ME, Davis JL, Hill EM (2010) Effects of self-attraction and loading on annual variations of ocean bottom pressure. J Geophys Res 115(C6):C06025. doi:10.1029/2009JC005783, http://www.agu.org/pubs/crossref/2010/2009JC005783.shtml
  22. Vinogradova NT, Ponte RM, Tamisiea ME, Quinn KJ, Hill EM, Davis JL (2011) Self-attraction and loading effects on ocean mass redistribution at monthly and longer time scales. J Geophys Res 116(C8):C08041. doi:10.1029/2011JC007037, http://www.agu.org/pubs/crossref/2011/2011JC007037.shtml
  23. Wu P (2004) Using commercial finite element packages for the study of earth deformations, sea levels and the state of stress. Geophys J Int 158(2):401–408. doi:10.1111/j.1365-246X.2004.02338.x, http://gji.oxfordjournals.org/cgi/doi/10.1111/j.1365-246X.2004.02338.x
  24. Zahel W (1991) Modeling ocean tides with and without assimilating data. J Geophys Res 96(B12):20379. doi:10.1029/91JB00424, http://www.agu.org/pubs/crossref/1991/91JB00424.shtml

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Earth System Modelling, Helmholtz Centre Potsdam, GFZ German Research Centre for GeosciencesPotsdamGermany
  2. 2.FU BerlinBerlinGermany
  3. 3.TU BerlinBerlinGermany

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