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  • Bryden, H. L., 1973: New polynomials for thermal expansion, adiabatic temperature gradient and potential temperature of seawater. Deap-Sea Res, 20 , 401–408.

    • Search Google Scholar
    • Export Citation

  • Cox, M. D., 1984: A primitive equation three-dimensional model of the ocean. GFDL Ocean Group Tech. Rep. No. 1, NOAA/GFDL, Princeton University, 250 pp.

    • Search Google Scholar
    • Export Citation

  • Dewar, W. K., Y. Hsueh, T. J. McDougall, and D. Yuan, 1998: Calculation of pressure in ocean simulations. J. Phys. Oceanogr, 28 , 577–588.

    • Search Google Scholar
    • Export Citation

  • Dukowicz, J. K., and R. D. Smith, 1994: Implicit free-surface method for the Bryan–Cox–Semtner ocean model. J. Geophys. Res, 99 , 7991–8014.

    • Search Google Scholar
    • Export Citation

  • Fofonoff, N. P., and R. C. Millard Jr., . 1983: Algorithms for computation of fundamental properties of seawater. UNESCO Marine Science Tech. Paper 44, 55 pp.

    • Search Google Scholar
    • Export Citation

  • Jackett, D. R., and T. J. McDougall, 1995: Minimal adjustment of hydrographic profiles to achieve static stability. J. Atmos. Oceanic Technol, 12 , 381–389.

    • Search Google Scholar
    • Export Citation

  • Levitus, S., and T. P. Boyer, 1994b: World Ocean Atlas 1994, Vol. 4:. Temperature, NOAA Atlas NESDIS 4, U.S. Dept. of Commerce, 117 pp.

  • ——, Burgett, R., and T. P. Boyer, 1994a: World Ocean Atlas 1994, Vol. 3:. Salinity, NOAA Atlas NESDIS 3, U.S. Dept. of Commerce, 99 pp.

    • Search Google Scholar
    • Export Citation

  • Semtner, A. J,Jr, 1986: Finite-difference formulation of a World Ocean model. Advanced Physical Oceanographic Numerical Modelling, J. J. O'Brien, Ed., D. Reidel, 187–202.

    • Search Google Scholar
    • Export Citation

  • Sun, S., R. Bleck, C. Rooth, J. Dukowicz, E. Chassignet, and P. Killworth, 1999: Inclusion of thermobaricity in isopycnic-coordinate ocean models. J. Phys. Oceanogr, 29 , 2719–2729.

    • Search Google Scholar
    • Export Citation
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Reduction of Density and Pressure Gradient Errors in Ocean Simulations

John K. Dukowicz1
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  • 1 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
Print Publication:
01 Jul 2001
DOI:
https://doi.org/10.1175/1520-0485(2001)031<1915:RODAPG>2.0.CO;2
Page(s):
1915–1921
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Abstract

Existing ocean models often contain errors associated with the computation of the density and the associated pressure gradient. Boussinesq models approximate the pressure gradient force, ρ−1∇p, by ρ−10∇p, where ρ0 is a constant reference density. The error associated with this approximation can be as large as 5%. In addition, Cartesian and sigma-coordinate models usually compute density from an equation of state where its pressure dependence is replaced by a depth dependence through an approximate conversion of depth to pressure to avoid the solution of a nonlinear hydrostatic equation. The dynamic consequences of this approximation and the associated errors can be significant. Here it is shown that it is possible to derive an equivalent but “stiffer” equation of state by the use of modified density and pressure, ρ* and p*, obtained by eliminating the contribution of the pressure-dependent part of the adiabatic compressibility (about 90% of the total). By doing this, the errors associated with both approximations are reduced by an order of magnitude, while changes to the code or to the code structure are minimal.

Corresponding author address: Dr. John K. Dukowicz, Los Alamos National Laboratory, Theoretical Division, T-3 Fluid Dynamics, MS B216, Los Alamos, NM 87545. Email: duk@lanl.gov

Abstract

Existing ocean models often contain errors associated with the computation of the density and the associated pressure gradient. Boussinesq models approximate the pressure gradient force, ρ−1∇p, by ρ−10∇p, where ρ0 is a constant reference density. The error associated with this approximation can be as large as 5%. In addition, Cartesian and sigma-coordinate models usually compute density from an equation of state where its pressure dependence is replaced by a depth dependence through an approximate conversion of depth to pressure to avoid the solution of a nonlinear hydrostatic equation. The dynamic consequences of this approximation and the associated errors can be significant. Here it is shown that it is possible to derive an equivalent but “stiffer” equation of state by the use of modified density and pressure, ρ* and p*, obtained by eliminating the contribution of the pressure-dependent part of the adiabatic compressibility (about 90% of the total). By doing this, the errors associated with both approximations are reduced by an order of magnitude, while changes to the code or to the code structure are minimal.

Corresponding author address: Dr. John K. Dukowicz, Los Alamos National Laboratory, Theoretical Division, T-3 Fluid Dynamics, MS B216, Los Alamos, NM 87545. Email: duk@lanl.gov

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