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Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data


How and where the ocean tides dissipate their energy are long-standing questions1 that have consequences ranging from the history of the Moon2 to the mixing of the oceans3. Historically, the principal sink of tidal energy has been thought to be bottom friction in shallow seas4,5. There has long been suggestive evidence6,7, however, that tidal dissipation also occurs in the open ocean through the scattering by ocean-bottom topography of surface tides into internal waves, but estimates of the magnitude of this possible sink have varied widely3,8,9,10,11. Here we use satellite altimeter data from Topex/Poseidon to map empirically the tidal energy dissipation. We show that approximately 1012 watts—that is, 1 TW, representing 25–30% of the total dissipation—occurs in the deep ocean, generally near areas of rough topography. Of the estimated 2 TW of mixing energy required to maintain the large-scale thermohaline circulation of the ocean12, one-half could therefore be provided by the tides, with the other half coming from action13 on the surface of the ocean.

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Figure 1: Estimates of M2 tidal energy dissipation.
Figure 2: Area-integrated dissipation for selected shallow seas and deep-ocean areas.

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  1. Munk, W. H. & MacDonald, G. J. F. The Rotation of the Earth: A Geophysical Discussion (Cambridge Univ. Press, 1960 ).

    MATH  Google Scholar 

  2. Hansen, K. S. Secular effects of oceanic tidal dissipation on the moon's orbit and the earth's rotation. Rev. Geophys. Space Phys. 20, 457–480 (1982).

    Article  ADS  Google Scholar 

  3. Munk, W. H. Once again: once again–tidal friction. Prog. Oceanogr. 40, 7–36 (1997).

    Article  ADS  Google Scholar 

  4. Taylor, G. I. Tidal friction in the Irish Sea. Phil. Trans. R. Soc. Lond. A 220, 1–33 (1919).

    Article  ADS  Google Scholar 

  5. Jeffreys, H. Tidal friction in shallow seas. Phil. Trans. R. Soc. Lond. A 221, 239–264 (1920).

    Article  ADS  Google Scholar 

  6. Munk, W. H. Abyssal recipes. Deep-Sea Res. 13, 707– 730 (1966).

    Google Scholar 

  7. Bell, T. H. Topographically induced internal waves in the open ocean. J. Geophys. Res. 80, 320–327 ( 1975).

    Article  ADS  Google Scholar 

  8. Morozov, E. G. Semidiurnal internal wave global field. Deep-Sea Res. 42, 135–148 (1995).

    Article  Google Scholar 

  9. Wunsch, C. Internal tides in the ocean. Rev. Geophys. Space Phys. 13, 167–182 (1975).

    Article  ADS  Google Scholar 

  10. Baines, P. G. On internal tide generation models. Deep-Sea Res. 29 , 307–338 (1982).

    Article  ADS  Google Scholar 

  11. Sjöberg, B. & Stigebrandt, A. Computations of the geographical distribution of the energy flux to mixing processes via internal tides and the associated vertical circulation in the ocean. Deep-Sea Res. 39, 269–291 (1992).

    Article  ADS  Google Scholar 

  12. Munk, W. H. & Wunsch, C. Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Res. 45, 1977–2010 (1998).

    Article  Google Scholar 

  13. Wunsch, C. The work done by the wind on the ocean circulation. J. Phys. Oceanogr. 28, 2331–2339 ( 1998).

    Article  ADS  Google Scholar 

  14. Gregg, M. C. Scaling turbulent dissipation in the thermocline. J. Geophys. Res. 94, 9686–9698 ( 1989).

    Article  ADS  Google Scholar 

  15. Ledwell, J. R., Watson, A. J. & Law, C. S. Evidence for slow mixing across the pycnocline from an open ocean tracer release experiment. Nature 364 , 701–703 (1993).

    Article  ADS  CAS  Google Scholar 

  16. Armi, L. Some evidence for boundary mixing in the deep sea. J. Geophys. Res. 83, 1971–1979 ( 1978).

    Article  ADS  Google Scholar 

  17. Polzin, K. L., Toole, J. M., Ledwell, J. R. & Schmitt, R. W. Spatial variability of turbulent mixing in the abyssal ocean. Science 276, 93–96 ( 1997).

    Article  CAS  Google Scholar 

  18. Samelson, R. M. Large scale circulation with locally enhanced vertical mixing. J. Phys. Oceanogr. 28, 712–726 (1998).

    Article  ADS  Google Scholar 

  19. Shum, C. K. et al. Accuracy assessment of recent ocean tide models. J. Geophys. Res. 102, 25173–25194 (1997).

    Article  ADS  Google Scholar 

  20. Cartwright, D. E. & Ray, R. D. Energetics of global ocean tides from Geosat altimetry. J. Geophys. Res. 96, 16897–16912 (1991).

    Article  ADS  Google Scholar 

  21. Hendershott, M. C. in The Sea (eds Goldberg, E. et al.) 47– 95 (Wiley, New York, 1977).

    Google Scholar 

  22. Ray, R. D. Ocean self-attraction and loading in numerical tidal models. Mar. Geodesy 21, 181–192 ( 1998).

    Article  Google Scholar 

  23. Le Provost, C. L. & Lyard, F. Energetics of the barotropic ocean tides: An estimate of bottom friction dissipation from a hydrodynamic model. Prog. Oceanogr. 40, 37–52 (1997).

    Article  ADS  Google Scholar 

  24. Egbert, G. D. Tidal data inversion: interpolation and inference. Prog. Oceanogr. 40, 81–108 ( 1997).

    Article  Google Scholar 

  25. Egbert, G. D., Bennett, A. F. & Foreman, M. G. G. TOPEX/POSEIDON tides estimated using a global inverse model. J. Geophys. Res. 99, 24821 –24852 (1994).

    Article  ADS  Google Scholar 

  26. Ray, R. D. A Global Ocean Tide Model from TOPEX/POSEIDON Altimetry: GOT99.2 (NASA/TM-1999-209478, Goddard Space Flight Center, Greenbelt, Maryland 1999).

    Google Scholar 

  27. Ray, R. D. Inversion of oceanic tidal currents from measured elevations. J. Mar. Sys. (submitted).

  28. Dushaw, B. D. et al. A TOPEX/POSEIDON global tidal model (TPXO.2) and barotropic tidal currents determined from long range acoustic transmissions. Prog. Oceanogr. 40, 337–369 (1998).

    Article  ADS  Google Scholar 

  29. Ray, R. D., Eanes, R. J. & Chao, B. F. Detection of tidal dissipation in the solid Earth by satellite tracking and altimetry. Nature 381, 595–597 (1996).

    Article  ADS  CAS  Google Scholar 

  30. Ray, R. D. & Mitchum, G. T. Surface manifestation of internal tides in the deep ocean: observations from altimetry and island gauges. Prog. Oceanogr. 40, 135–162 (1997).

    Article  ADS  Google Scholar 

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We thank W. Munk for discussions. This work was supported by the US National Science Foundation (G.D.E.) and the US National Aeronautics and Space Administration (R.D.R.).

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Egbert, G., Ray, R. Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405, 775–778 (2000).

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