• Blumberg, A. F., , and Mellor G. L. , 1987: A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Coastal Ocean Models, N. Heaps, Ed., Vol. 4, Coastal and Estuarine Sciences, Amer. Geophys. Union, 1–16.

    • Search Google Scholar
    • Export Citation
  • Chen, C., , and Beardsley R. C. , 1998: Tidal mixing and cross-frontal particle exchange over a finite amplitude asymmetric bank: A model study of Georges Bank. J. Mar. Res., 56 , 11631201.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Foldvik, A., , Middleton J. H. , , and Foster T. D. , 1990: The tides of the southern Weddell Sea. Deep-Sea Res., 37 , 13451362.

  • Foreman, M. G. G., 1978: Manual for tidal current analysis and prediction. Pacific Marine Science Rep. 78-6, Institute of Ocean Sciences, Patricia Bay, Sidney, BC, Canada, 70 pp.

    • Search Google Scholar
    • Export Citation
  • Furevik, T., , and Foldvik A. , 1996: Stability at M2 critical latitude in the Barents Sea. J. Geophys. Res., 101 , 88238837.

  • Holloway, P. E., 1996: A numerical model of internal tides with application to the Australian northwest shelf. J. Phys. Oceanogr., 26 , 2137.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kleim, N., , and Pietrzak J. D. , 1999: On the pressure gradient error in sigma coordinate ocean models: A comparison with a laboratory experiment. J. Geophys. Res., 104 , 29 78129 799.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kundu, P., 1990: Fluid Mechanics. Academic Press, 668 pp.

  • Mellor, G. L., 1991: An equation of state for numerical modeling of oceans and estuaries. J. Atmos. Oceanic Technol., 8 , 609611.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • ——,. 1998: User's guide for a three-dimensional, primitive equation, numerical ocean model. Report of the Atmospheric and Ocean Sciences Program, Princeton University, Princeton, NJ, 41 pp. [Available online at http://www.aos.princeton.edu/WWWPUBLIC/htdocs.pom].

    • Search Google Scholar
    • Export Citation
  • ——, Ezer, T., , and Oey L-Y. , 1994: The pressure gradient conundrum of sigma coordinate models. J. Atmos. Oceanic Technol., 11 , 11261134.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • ——, Oey, L-Y., , and Ezer T. , 1998: Sigma coordinate pressure gradient errors and the seamount problem. J. Atmos. Oceanic Technol., 15 , 11221131.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Middleton, J. H., , and Denniss T. , 1993: The propagation of tides near the critical latitude. Geophys. Astrophys. Fluid Dyn., 68 , 113.

  • ——, and Foster, T. D., 1977: Tidal currents in the central Weddell Sea. Deep-Sea Res., 24 , 11951202.

  • ——, ——, and Foldvik, A., 1982: Low-frequency currents and continental shelf waves in the southern Weddell Sea. J. Phys. Oceanogr., 12 , 618634.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Robertson, R., 1999: Mixing and heat flux mechanisms in the upper ocean in the Weddell Sea. Ph.D. thesis, Oregon State University, 173 pp.

    • Search Google Scholar
    • Export Citation
  • ——,. 2001a: Internal tides and baroclinicity in the southern Weddell Sea. Part I: Model description. J. Geophys. Res., in press.

  • ——,. 2001b: Internal tides and baroclinicity in the southern Weddell Sea. Part II: Effects of the critical latitude and stratification. J. Geophys. Res., in press.

    • Search Google Scholar
    • Export Citation
  • —— Padman, L., , and Egbert G. D. , 1998: Tides in the Weddell Sea. Ocean, Ice and Atmosphere: Interactions at the Antarctic Continental Margin. Antarctic Research Series, S. S. Jacobs and R. F. Weiss, Eds., Vol. 75, Amer. Geophys. Union, 341–369.

    • Search Google Scholar
    • Export Citation
  • Woodgate, R. A., , Schröder M. , , and Østerhus S. , 1998: Moorings from the Filchner Trough and the Ronne Ice Shelf Front: Preliminary results, H. Oerter, Ed., Filchner-Ronne Ice Shelf Program,. Alfred-Wegener Institute Rep. 12, 85–90.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 133 133 93
PDF Downloads 30 30 3

A Correction to the Baroclinic Pressure Gradient Term in the Princeton Ocean Model

View More View Less
  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

An error in the calculation of the baroclinic pressure gradient term in the Princeton Ocean Model (POM) was identified while modeling the M2 tidal current near its critical latitude in the southern Weddell Sea. The error arises from the present calculation of density, which involves the subtraction of a background density profile from the density field calculated at each internal time step. The small displacement of sigma surface depths relative to the surface, as surface elevation changes, causes a slight error in the calculation of the vertical and horizontal gradients of potential density. The error is largest at the seabed over rapidly changing bathymetry such as the continental slope. The baroclinic pressure gradient error is typically much smaller than the Coriolis term in the momentum equations and, therefore, usually unimportant. Close to the critical latitude, however, near-resonance between the error and Coriolis terms can cause an energetic and spatially complex spurious inertial mode to develop. The error is significant when modeling tides near their critical latitudes, and will contribute to the error in the baroclinic pressure gradient in other simulations. Two methods were suggested for fixing this problem. The preferred method was tested by applying the new form of POM to the southern Weddell Sea. The new results are consistent with both current meter data and predictions of linear internal wave theory.

Current affiliation: Alfred-Wegener-Institut, Bremerhaven, Germany.

Current affiliation: Earth and Space Research, Seattle, Washington.

Corresponding author address: Dr. Robin Robertson, Alfred-Wegener-Institut, Postfach 12 01 61, D-27515 Bremerhaven, Germany. Email: rrobertson@ldeo.columbia.edu or rrobertson@awi-bremerhaven.de

Abstract

An error in the calculation of the baroclinic pressure gradient term in the Princeton Ocean Model (POM) was identified while modeling the M2 tidal current near its critical latitude in the southern Weddell Sea. The error arises from the present calculation of density, which involves the subtraction of a background density profile from the density field calculated at each internal time step. The small displacement of sigma surface depths relative to the surface, as surface elevation changes, causes a slight error in the calculation of the vertical and horizontal gradients of potential density. The error is largest at the seabed over rapidly changing bathymetry such as the continental slope. The baroclinic pressure gradient error is typically much smaller than the Coriolis term in the momentum equations and, therefore, usually unimportant. Close to the critical latitude, however, near-resonance between the error and Coriolis terms can cause an energetic and spatially complex spurious inertial mode to develop. The error is significant when modeling tides near their critical latitudes, and will contribute to the error in the baroclinic pressure gradient in other simulations. Two methods were suggested for fixing this problem. The preferred method was tested by applying the new form of POM to the southern Weddell Sea. The new results are consistent with both current meter data and predictions of linear internal wave theory.

Current affiliation: Alfred-Wegener-Institut, Bremerhaven, Germany.

Current affiliation: Earth and Space Research, Seattle, Washington.

Corresponding author address: Dr. Robin Robertson, Alfred-Wegener-Institut, Postfach 12 01 61, D-27515 Bremerhaven, Germany. Email: rrobertson@ldeo.columbia.edu or rrobertson@awi-bremerhaven.de

Save