Clarifying the Distinction between Steric and Baroclinic Sea Surface Height

Edward D. Zaron aOregon State University, Corvallis, Oregon

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https://orcid.org/0000-0002-7799-2883
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Richard D. Ray bNASA Goddard Space Flight Center, Greenbelt, Maryland

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Abstract

One of the most fundamental uses of ocean models is for the prediction of sea level. Vertical integration of the hydrostatic equation leads to the partitioning of sea level in terms of atmospheric pressure, steric height, and bottom pressure. In an effort to validate the baroclinic wave dynamics of numerical ocean models, some researchers have compared the steric height from models with the sea level anomaly derived from satellite altimetry. The use of steric height in these comparisons captures the qualitative aspects of the baroclinic waves, but it neglects a nonnegligible contribution from bottom pressure. A more accurate evaluation of baroclinic wave dynamics using sea level would involve projecting the pressure field onto orthogonal barotropic and baroclinic components to isolate the baroclinic sea level anomaly. This note illustrates the quantitative difference between steric height and baroclinic sea level, which amounts to approximately a 20% bias of steric height over baroclinic sea level, depending on location.

Significance Statement

The bottom pressure variability associated with superinertial internal waves is not negligible, but it has been neglected in a recent series of ocean model validation studies. Baroclinic surface pressure, and its associated sea level anomaly, should be used instead of steric height for model–data comparisons of baroclinic sea level variability.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Edward D. Zaron, edward.d.zaron@oregonstate.edu

Abstract

One of the most fundamental uses of ocean models is for the prediction of sea level. Vertical integration of the hydrostatic equation leads to the partitioning of sea level in terms of atmospheric pressure, steric height, and bottom pressure. In an effort to validate the baroclinic wave dynamics of numerical ocean models, some researchers have compared the steric height from models with the sea level anomaly derived from satellite altimetry. The use of steric height in these comparisons captures the qualitative aspects of the baroclinic waves, but it neglects a nonnegligible contribution from bottom pressure. A more accurate evaluation of baroclinic wave dynamics using sea level would involve projecting the pressure field onto orthogonal barotropic and baroclinic components to isolate the baroclinic sea level anomaly. This note illustrates the quantitative difference between steric height and baroclinic sea level, which amounts to approximately a 20% bias of steric height over baroclinic sea level, depending on location.

Significance Statement

The bottom pressure variability associated with superinertial internal waves is not negligible, but it has been neglected in a recent series of ocean model validation studies. Baroclinic surface pressure, and its associated sea level anomaly, should be used instead of steric height for model–data comparisons of baroclinic sea level variability.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Edward D. Zaron, edward.d.zaron@oregonstate.edu
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  • Arbic, B. K., 2022: Incorporating tides and internal gravity waves within global ocean general circulation models: A review. Prog. Oceanogr., 206, 102824, https://doi.org/10.1016/j.pocean.2022.102824.

    • Search Google Scholar
    • Export Citation
  • 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 Modell., 32, 175187, https://doi.org/10.1016/j.ocemod.2010.01.007.

    • Search Google Scholar
    • Export Citation
  • 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, 2029, https://doi.org/10.5670/oceanog.2012.38.

    • Search Google Scholar
    • Export Citation
  • Baker-Yeboah, S., D. R. Watts, and D. A. Byrne, 2009: Measurements of sea surface height variability in the eastern South Atlantic from pressure sensor–equipped inverted echo sounders: Baroclinic and barotropic components. J. Atmos. Oceanic Technol., 26, 25932609, https://doi.org/10.1175/2009JTECHO659.1.

    • Search Google Scholar
    • Export Citation
  • Buijsman, M. C., B. K. Arbic, J. A. M. Green, R. W. Helber, J. G. Richman, J. F. Shriver, P. G. Timko, and A. Wallcraft, 2015: Optimizing internal wave drag in a forward barotropic model with semidiurnal tides. Ocean Modell., 85, 4255, https://doi.org/10.1016/j.ocemod.2014.11.003.

    • Search Google Scholar
    • Export Citation
  • Buijsman, M. C., and Coauthors, 2016: Impact of parameterized internal wave drag on the semidiurnal energy balance in a global ocean circulation model. J. Phys. Oceanogr., 46, 13991419, https://doi.org/10.1175/JPO-D-15-0074.1.

    • Search Google Scholar
    • Export Citation
  • Carrère, L., C. Le Provost, and F. Lyard, 2004: On the statistical stability of the M2 barotropic and baroclinic tidal characteristics from along-track TOPEX/Poseidon satellite altimetry analysis. J. Geophys. Res., 109, C03033, https://doi.org/10.1029/2003JC001873.

    • Search Google Scholar
    • Export Citation
  • Carrère, L., and Coauthors, 2021: Accuracy assessment of global internal-tide models using satellite altimetry. Ocean Sci., 17, 147180, https://doi.org/10.5194/os-17-147-2021.

    • Search Google Scholar
    • Export Citation
  • de Souza, J. M. A. C., S. H. Suanda, P. P. Couto, R. O. Smith, C. Kerry, and M. Roughan, 2023: Moana Ocean hindcast—A >25-year simulation for New Zealand waters using the Regional Ocean Modeling System (ROMS) v3.9 model. Geosci. Model Dev., 16, 211231, https://doi.org/10.5194/gmd-16-211-2023.

    • Search Google Scholar
    • Export Citation
  • Dushaw, B. D., P. F. Worcester, and M. A. Dzieciuch, 2011: On the predictability of mode-1 internal tides. Deep-Sea Res. I, 58, 677698, https://doi.org/10.1016/j.dsr.2011.04.002.

    • Search Google Scholar
    • Export Citation
  • Egbert, G. D., and S. Y. Erofeeva, 2002: Efficient inverse modeling of barotropic ocean tides. J. Atmos. Oceanic Technol., 19, 183204, https://doi.org/10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., and P. P. Niiler, 1973: The theory of seasonal variability in the ocean. Deep-Sea Res., 20, 141177, https://doi.org/10.1016/0011-7471(73)90049-1.

    • Search Google Scholar
    • Export Citation
  • Gregory, J. M., and Coauthors, 2019: Concepts and terminology for sea level: Mean, variability and change, both local and global. Surv. Geophys., 40, 12511289, https://doi.org/10.1007/s10712-019-09525-z.

    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., 2016: The vertical mode decomposition of surface and internal tides in the presence of a free surface and arbitrary topography. J. Phys. Oceanogr., 46, 37773788, https://doi.org/10.1175/JPO-D-16-0131.1.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., L. K. Rosenfeld, G. S. Carter, and M. C. Gregg, 2002: Internal waves in Monterey submarine canyon. J. Phys. Oceanogr., 32, 18901913, https://doi.org/10.1175/1520-0485(2002)032<1890:IWIMSC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lahaye, N., and S. G. Llewellyn Smith, 2020: Modal analysis of internal wave propagation and scattering over large-amplitude topography. J. Phys. Oceanogr., 50, 305321, https://doi.org/10.1175/JPO-D-19-0005.1.

    • Search Google Scholar
    • Export Citation
  • Locarnini, R. A., and Coauthors, 2018: Temperature. Vol. 1, World Ocean Atlas 2018, NOAA Atlas NESDIS 81, 52 pp.

  • Nelson, A. D., B. K. Arbic, E. D. Zaron, A. C. Savage, J. G. Richman, M. C. Buijsman, and J. F. Shriver, 2019: Toward realistic nonstationarity of semidiurnal baroclinic tide in hydrodynamic models. J. Geophys. Res. Oceans, 124, 66326642, https://doi.org/10.1029/2018JC014737.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1979: Geophysical Fluid Dynamics. Springer-Verlag, 624 pp.

  • Ray, R. D., and G. D. Egbert, 2017: Tides and satellite altimetry. Satellite Altimetry over Oceans and Land Surfaces, D. Stammer and A. Cazenave, Eds., CRC Press, 427–458.

  • Savage, A. C., and Coauthors, 2017: Frequency content of sea surface height variability from internal gravity waves to mesoscale eddies. J. Geophys. Res. Oceans, 122, 25192538, https://doi.org/10.1002/2016JC012331.

    • Search Google Scholar
    • Export Citation
  • Schindelegger, M., D. P. Kotzian, R. D. Ray, J. A. M. Green, and S. Stolzenberger, 2022: Interannual changes in tidal conversion modulate M2 amplitudes in the Gulf of Maine. Geophys. Res. Lett., 49, e2022GL101671, https://doi.org/10.1029/2022GL101671.

    • Search Google Scholar
    • Export Citation
  • Shriver, J. F., B. K. Arbic, J. G. Richman, R. D. Ray, E. J. Metzger, A. J. Wallcraft, and P. G. Timko, 2012: An evaluation of the barotropic and internal tides in a high-resolution global ocean circulation model. J. Geophys. Res., 117, C10024, https://doi.org/10.1029/2012JC008170.

    • Search Google Scholar
    • Export Citation
  • Talley, L. D., G. L. Pickard, W. J. Emery, and J. H. Swift, 2011: Descriptive Physical Oceanography: An Introduction. 6th ed. Academic Press, 560 pp.

  • Wang, J., L.-L. Fu, B. Qiu, D. Menemenlis, J. T. Farrar, Y. Chao, A. F. Thompson, and M. M. Flexas, 2018: An observing system simulation experiment for the calibration and validation of the surface water ocean topography sea surface height measurement using in situ platforms. J. Atmos. Oceanic Technol., 35, 281297, https://doi.org/10.1175/JTECH-D-17-0076.1.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 2013: Baroclinic motions and energetics as measured by altimeters. J. Atmos. Oceanic Technol., 30, 140150, https://doi.org/10.1175/JTECH-D-12-00035.1.

    • Search Google Scholar
    • Export Citation
  • Zaron, E. D., 2019: Predictability of non-phase-locked baroclinic tides in the Caribbean Sea. Ocean Sci., 15, 12871305, https://doi.org/10.5194/os-15-1287-2019.

    • Search Google Scholar
    • Export Citation
  • Zaron, E. D., R. C. Musgrave, and G. D. Egbert, 2022: Baroclinic tidal energetics inferred from satellite altimetry. J. Phys. Oceanogr., 52, 10151032, https://doi.org/10.1175/JPO-D-21-0096.1.

    • Search Google Scholar
    • Export Citation
  • Zhao, Z., M. H. Alford, J. A. MacKinnon, and R. Pinkel, 2010: Long-range propagation of the semidiurnal internal tide from the Hawaiian Ridge. J. Phys. Oceanogr., 40, 713736, https://doi.org/10.1175/2009JPO4207.1.

    • Search Google Scholar
    • Export Citation
  • Zilberman, N. V., M. A. Merrifield, G. S. Carter, D. S. Luther, M. D. Levine, and T. J. Boyd, 2011: Incoherent nature of M2 internal tides at the Hawaiian Ridge. J. Phys. Oceanogr., 41, 20212036, https://doi.org/10.1175/JPO-D-10-05009.1.

    • Search Google Scholar
    • Export Citation
  • Zweng, M. M., and Coauthors, 2018: Salinity. Vol. 2, World Ocean Atlas 2018, NOAA Atlas NESDIS 82, 50 pp.

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