Oceanography The Official Magazine of
The Oceanography Society
Volume 25 Issue 02

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Volume 25, No. 2
Pages 20 - 29


Global Modeling of Internal Tides Within an Eddying Ocean General Circulation Model

By Brian K. Arbic , James G. Richman, Jay F. Shriver , Patrick G. Timko , E. Joseph Metzger, and Alan J. Wallcraft  
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Article Abstract

Ocean tides, and the atmospherically forced oceanic general circulation and its associated mesoscale eddy field, have long been run separately in high-resolution global models. They are now being simulated concurrently in a high-resolution version of the HYbrid Coordinate Ocean Model (HYCOM). The incorporation of horizontally varying stratification with the addition of atmospheric forcing yields internal tides (internal waves of tidal frequency) in high-latitude, low-stratification regions that are qualitatively different from those in earlier global internal tide models, in which atmospheric forcing and horizontally variable stratification were absent. The internal tides in the new concurrent HYCOM simulations compare well with those measured in along-track satellite altimeter data. The new concurrent simulations demonstrate that the wavenumber spectrum of sea surface height—a measure of the energy contained in different length scales—is dominated in some locations by internal tides and in others by mesoscale eddies. Tidal kinetic energies in the new concurrent simulations compare well with those in current-meter observations, as long as sufficient spatial averaging is performed. The new concurrent simulations are being used in the planning of future-generation satellite altimeters, in the provision of boundary conditions for coastal ocean models, and in studies of ocean mixing.


Arbic, B.K., J.G. Richman, J.F. Shriver, P.G. Timko, E.J. Metzger, and A.J. Wallcraft. 2012. Global modeling of internal tides within an eddying ocean general circulation model. Oceanography 25(2):20–29, https://doi.org/10.5670/oceanog.2012.38.


Alford, M.H. 2003. Improved global maps and 54-year history of wind-work on ocean inertial motions. Geophysical Research Letters 30, 1424, https://doi.org/10.1029/2002GL016614.

Arbic, B.K., S.T. Garner, R.W. Hallberg, and H.L. Simmons. 2004. The accuracy of surface elevations in forward global barotropic and baroclinic tide models. Deep-Sea Research Part II 51:3,069–3,101, https://doi.org/10.1016/j.dsr2.2004.09.014.

Arbic, B.K., A.J. Wallcraft, and E.J. Metzger. 2010. Concurrent simulation of the eddying general circulation and tides in a global ocean model. Ocean Modelling 32:175–187, https://doi.org/10.1016/j.ocemod.2010.01.007.

Bell, T.H. 1975. Lee waves in stratified flows with simple harmonic time dependence. Journal of Fluid Dynamics 67:705–722, https://doi.org/10.1017/S0022112075000560.

Carter, G.S., O.B. Fringer, and E.D. Zaron. 2012. Regional models of internal tides. Oceanography 25(2):56–65, https://doi.org/10.5670/oceanog.2012.42.

Cartwright, D.E. 1999. Tides: A Scientific History. Cambridge University Press, Cambridge, 192 pp.

Chassignet, E.P., H.E. Hurlburt, O.M. Smedstad, G.R. Halliwell, P.J. Hogan, A.J. Wallcraft, R. Baraille, and R. Bleck. 2007. The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system. Journal of Marine Systems 65:60–83, https://doi.org/10.1016/j.jmarsys.2005.09.016.

Cox, C.S. 1958. Measurements of slopes of high frequency wind waves. Journal of Marine Research 16:199–225.

Cummings, J.A. 2005. Operational multivariate ocean data assimilation. Quarterly Journal of the Royal Meteorological Society 131: 3,583–3,604.

Egbert, G.D., A.F. Bennett, and M.G.G. Foreman. 1994. TOPEX/POSEIDON tides estimated using a global inverse model. Journal of Geophysical Research 99:24,821–24,852, https://doi.org/10.1029/94JC01894.

Egbert, G.D., and R.D. Ray. 2000. Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405:775–778, https://doi.org/10.1038/35015531.

Fu, L.-L., and A. Cazenave, eds. 2001. Satellite Altimetry and Earth Sciences: A Handbook of Techniques and Applications. Academic Press, San Diego, 463 pp.

Fu, L.-L., and R. Ferrari. 2008. Observing oceanic submesoscale processes from space. Eos, Transactions American Geophysical Union 89(48), 488, https://doi.org/10.1029/2008EO480003.

Garner, S.T. 2005. A topographic drag closure built on an analytical base flux. Journal of the Atmospheric Sciences 62:2,302–2,315, https://doi.org/10.1175/JAS3496.1.

Hecht, M.W., and H. Hasumi, eds. 2008. Ocean Modeling in an Eddying Regime. Geophysical Monograph 177, American Geophysical Union, Washington, DC, 409 pp, https://doi.org/10.1029/GM177.

Hendershott, M.C. 1972. The effects of solid earth deformation on global ocean tides. Geophysical Journal of the Royal Astronomical Society 29:389–402, https://doi.org/10.1111/j.1365-246X.1972.tb06167.x.

Hibiya, T., M. Nagasawa, and Y. Niwa. 2006. Global mapping of diapycnal diffusivity in the deep ocean based on the results of expendable current profiler (XCP) surveys. Geophysical Research Letters 33, L03611, https://doi.org/10.1029/2005GL025218.

Holloway, P.E., P.G. Chatwin, and P. Craig. 2001. Internal tide observations from the Australian North West Shelf in summer 1995. Journal of Physical Oceanography 31:1,182–1,199, https://doi.org/10.1175/1520-0485(2001)031<1182:ITOFTA>2.0.CO;2.

Hurlburt, H.E., and P.J. Hogan. 2000. Impact of 1/8° to 1/64° resolution on Gulf Stream model-data comparisons in basin-scale subtropical Atlantic Ocean models. Dynamics of Atmospheres and Oceans 32:283–329, https://doi.org/10.1016/S0377-0265(00)00050-6.

Hurlburt, H.E., E.J. Metzger, J.G. Richman, E.P. Chassignet, Y. Drillet, M.W. Hecht, O. Le Galloudec, J.F. Shriver, X. Xu, and L. Zamudio. 2010. Dynamical evaluation of ocean models using the Gulf Stream as an example. Pp. 545–609 in Operational Oceanography in the 21st Century. G.B. Brassington and A. Schiller, eds, Springer-Verlag, New York.

Kelly, S.M., and J.D. Nash. 2010. Internal-tide generation and destruction by shoaling internal tides. Geophysical Research Letters 37, L23611, https://doi.org/10.1029/2010GL045598.

Langmuir, I. 1938. Surface motion of water induced by wind. Science 87:119–123, https://doi.org/10.1126/science.87.2250.119.

Le Provost, C. 2001. Ocean tides. Pp. 267–303 in Satellite Altimetry and Earth Sciences: A Handbook of Techniques and Applications. Academic Press, San Diego.

Le Traon, P.-Y., P. Klein, and B.-L. Hua. 2008. Do altimeter wavenumber spectra agree with the interior or surface quasigeostrophic theory? Journal of Physical Oceanography 38:1,137–1,142, https://doi.org/10.1175/2007JPO3806.1.

Maltrud, M.E., and J.L. McClean. 2005. An eddy resolving global 1/10° simulation. Ocean Modelling 8:31–54, https://doi.org/10.1016/j.ocemod.2003.12.001.

Metzger, E.J., O.M. Smedstad, P.G. Thoppil, H.E. Hurlburt, D.S. Franklin, G. Peggion, J.F. Shriver, and A.J. Wallcraft. 2010. Validation Test Report for the Global Ocean Forecast System V3.0 – 1/12° HYCOM/NCODA: Phase II. Naval Research Laboratory, NRL/MR/7320—10-9236, 70 pp. Available online at: http://www7320.nrlssc.navy.mil/pubs/2010/metzger1-2010.pdf (accessed May 10, 2012).

Munk, W., and C. Wunsch. 1998. Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Research Part I 45:1,977–2,010, https://doi.org/10.1016/S0967-0637(98)00070-3.

Murray, R.J. 1996. Explicit generation of orthogonal grids for ocean models. Journal of Computational Physics 126(2):251–273, https://doi.org/10.1006/jcph.1996.0136.

Niwa, Y., and T. Hibiya. 2011. Estimation of baroclinic tide energy available for deep ocean mixing based on three-dimensional global numerical simulations. Journal of Oceanography 67:493–502, https://doi.org/10.1007/s10872-011-0052-1.

Padman, L., S. Howard, and R. Muench. 2006. Internal tide generation along the South Scotia Ridge. Deep-Sea Research Part II 53:157–171, https://doi.org/10.1016/j.dsr2.2005.07.011.

Parke, M.E., R.H. Stewart, D.L. Farless, and D.E. Cartwright. 1987. On the choice of orbits for an altimetric satellite to study ocean circulation and tides. Journal of Geophysical Research 92:11,693–11,707, https://doi.org/10.1029/JC092iC11p11693.

Pedlosky, J. 1987. Geophysical Fluid Dynamics. Springer-Verlag, Berlin, 710 pp.

Pedlosky, J. 1996. Ocean Circulation Theory. Springer-Verlag, Berlin, 453 pp.

Phillips, O.M. 1966. The Dynamics of the Upper Ocean. Cambridge University Press, New York, 269 pp.

Pond, S., and G.L. Pickard. 1983. Introductory Dynamical Oceanography, Second Edition. Pergamon Press, Oxford, 329 pp.

Ponte, R.M. 1993. Variability in a homogeneous global ocean forced by barometric pressure. Dynamics of Atmospheres and Oceans 18(3–4):209–234, https://doi.org/10.1016/0377-0265(93)90010-5.

Ray, R.D. 1998. Ocean self-attraction and loading in numerical tidal models. Marine Geodesy 21:181–191, https://doi.org/10.1080/01490419809388134.

Ray, R.D. 1999. A Global Ocean Tide Model From TOPEX/POSEIDON Altimetry: GOT99.2. National Aeronautics and Space Administration Technical Memorandum, NASA/TM-1999-209478, 58 pp.

Ray, R.D., and G.T. Mitchum. 1996. Surface manifestation of internal tides generated near Hawai’i. Geophysical Research Letters 23:2,101–2,104, https://doi.org/10.1029/96GL02050.

Ray, R.D., and G.T. Mitchum. 1997. Surface manifestation of internal tides in the deep ocean: Observations from altimetry and tide gauges. Progress in Oceanography 40:135–162, https://doi.org/10.1016/S0079-6611(97)00025-6.

Rosmond, T.E., J. Teixeira, M. Peng, T.F. Hogan, and R. Pauley. 2002. Navy Operational Global Atmospheric Prediction System (NOGAPS): Forcing for ocean models. Oceanography 15(1):99–108, https://doi.org/10.5670/oceanog.2002.40.

Schmitt, R.W. 2008. Salinity and the global water cycle. Oceanography 21(1):12–19, https://doi.org/10.5670/oceanog.2008.63.

Schmitz, W.J. Jr. 1996a. On the World Ocean Circulation: Volume I, Some Global Features/North Atlantic Circulation. Woods Hole Oceanographic Institution Technical Report WHOI-96-03, 140 pp.

Schmitz, W.J. Jr. 1996b. On the World Ocean Circulation: Volume II, The Pacific and Indian Oceans/A Global Update. Woods Hole Oceanographic Institution Technical Report WHOI-96-08, 237 pp.

Scott, R.B., B.K. Arbic, E.P. Chassignet, A.C. Coward, M. Maltrud, W.J. Merryfield, A. Srinivasan, and A. Varghese. 2010. Total kinetic energy in four global eddying ocean circulation models and over 5000 current meter records. Ocean Modelling 32:157–169, https://doi.org/10.1016/j.ocemod.2010.01.005.

Shum, C.K., P.L. Woodworth, O.B. Andersen, G.D. Egbert, O. Francis, C. King, S.M. Klosko, C. Le Provost, X. Li, J.-M. Molines, and others. 1997. Accuracy assessment of recent ocean tide models. Journal of Geophysical Research 102:25,173–25,194, https://doi.org/10.1029/97JC00445.

Siedler, G., J. Church, and J. Gould. 2001. Ocean Circulation and Climate: Observing and Modeling the Global Ocean. Academic Press, San Diego, 715 pp.

Simmons, H.L., R.W. Hallberg, and B.K. Arbic. 2004. Internal wave generation in a global baroclinic tide model. Deep-Sea Research Part II 51:3,043–3,068, https://doi.org/10.1016/j.dsr2.2004.09.015.

Simmons, H.L. 2008. Spectral modification and geographic redistribution of the semi-diurnal internal tide. Ocean Modelling 21:126–138, https://doi.org/10.1016/j.ocemod.2008.01.002.

Simmons, H.L., and M.H. Alford. 2012. Simulating the long-range swell of internal waves generated by ocean storms. Oceanography 25(2):30–41, https://doi.org/10.5670/oceanog.2012.39.

Stammer, D. 1997. Global characteristics of ocean variability estimated from regional TOPEX/Poseidon altimeter measurements. Journal of Physical Oceanography 27:1,743–1,769, https://doi.org/10.1175/1520-0485(1997)027<1743:GCOOVE>2.0.CO;2.

Thoppil, P.G., J.G. Richman, and P.J. Hogan. 2011. Energetics of a global ocean circulation model compared to observations. Geophysical Research Letters 38, L15607, https://doi.org/10.1029/2011GL048347.

Vallis, G.K. 2006. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press, Cambridge, 745 pp.

Wunsch, C. 1975. Internal tides in the ocean. Reviews of Geophysics 13:167–182, https://doi.org/10.1029/RG013i001p00167.

Xu, Y., and L.-L. Fu. 2011. Global variability of the wavenumber spectrum of oceanic mesoscale turbulence. Journal of Physical Oceanography 41:802–809, https://doi.org/10.1175/2010JPO4558.1.

Yu, L. 2007. Global variations in oceanic evaporation (1958–2005): The role of changing wind speed. Journal of Climate 20:5,376–5,390, https://doi.org/10.1175/2007JCLI1714.1.

Yu, L., and R.A. Weller. 2007. Objectively analyzed air-sea heat fluxes for the global ice-free oceans (1981–2005). Bulletin of the American Meteorological Society 88:527–539, https://doi.org/10.1175/BAMS-88-4-527.

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