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Article Type:
Research Article

Reduction of Density and Pressure Gradient Errors in Ocean Simulations

John K. DukowiczTheoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico

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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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