We thank members of the Ocean, Climate, and Prediction Groups at GFDL for testing this scheme, and earlier versions, in various model configurations. In particular, we thank Jeff Anderson, Bob Hallberg, Matt Harrison, George Mellor, Thomas Neumann, Young-Gyu Park, Igor Polyakov, Tony Rosati, Torsten Seifert, Mike Spelman, Eli Tziperman, David Webb, Mike Winton, and Bruce Wyman for enjoyable conversations and useful suggestions. Bob Hallberg and Igor Polyakov deserve special thanks for extensive suggestions and useful critiques. Comments from the anonymous reviewers are also greatly appreciated. We thank Jerry Mahlman, the director of GFDL, for his support and encouragement.
Barnier, B., 1998: Forcing the oceans. Ocean Modeling and Parameterization, E. P. Chassignet and J. Verron, Eds., NATO Advanced Study Institute, Kluwer Academic, 45–80.
Beron-Vera, F. J., J. Ochoa, and P. Ripa, 1999: A note on boundary conditions for salt and freshwater balances. Ocean Modelling,1, 111–118.
Bleck, R., and L. T. Smith, 1990: A wind-driven isopycnic coordinate model of the north and equatorial Atlantic Ocean. 1. Model development and supporting experiments. J. Geophys. Res.,95 (C3), 3273–3285.
Blumberg, A. F., and G. L. Mellor, 1987: A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Coastal Ocean Models, N. Heaps, Ed., Coastal and Estuarine Sciences, Vol. 4, Amer. Geophys. Union, 1–16.
Bryan, F. O., 1987: Parameter sensitivity of primitive equation ocean general circulation models. J. Phys. Oceanogr.,17, 970–985.
Bryan, K., 1969: A numerical method for the study of the circulation of the world ocean. J. Comput. Phys.,4, 347–376.
——, 1984: Accelerating the convergence to equilibrium of ocean-climate models. J. Phys. Oceanogr.,14, 666–673.
——, and M. D. Cox, 1972: An approximate equation of state for numerical models of the ocean circulation. J. Phys. Oceanogr.,2, 510–514.
Cox, M. D., 1984: A primitive equation, 3-dimensional model of the ocean. GFDL Ocean Group Tech. Rep. 1, 143 pp.
——, and K. Bryan, 1984: A numerical model of the ventilated thermocline. J. Phys. Oceanogr.,14, 674–687.
Culler, D. E., and J. P. Singh, 1998: Parallel Computer Architecture:A Hardware/Software Approach. Morgan Kaufmann, 1100 pp.
Danabasoglu, G., J. C. McWilliams, and W. G. Large, 1996: Approach to equilibrium in accelerated global oceanic models. J. Climate,9, 1092–1110.
Dewar, W. K., and R. X. Huang, 1996: On the forced flow of salty water in a loop. Phys. Fluids,8, 954–970.
——, Y. Hsueh, T. J. McDougall, and D. Yuan, 1998: Calculation of pressure in ocean simulations. J. Phys. Oceanogr.,28, 577–588.
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.
——, ——, and R. C. Malone, 1993: A reformulation and implementation of the Bryan–Cox–Semtner ocean model on the connection machine. J. Atmos. Oceanic Technol.,10, 195–208.
Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.
Gordon, C., C. Cooper, C. A. Senior, H. Banks, J. M. Gregory, T. C. Johns, J. F. B. Mitchell, and R. A. Wood, 2000: The simulation of SST, sea ice extents and ocean heat transports in a version of the Hadley Centre coupled model without flux adjustments. Climate Dyn.,16, 147–168.
Griffies, S. M., and R. W. Hallberg, 2000: Biharmonic friction with a Smagorinsky viscosity for use in large-scale eddy-permitting ocean models. Mon. Wea. Rev.,128, 2935–2946.
Guyon, M., G. Madec, F. X. Roux, M. Imbard, C. Herbaut, and P. Fronier, 1999: Parallelization of the OPA ocean model. Calculateurs Paralleles,11, 499–517.
Hallberg, R., 1995: Some aspects of the circulation in ocean basins with isopycnals intersecting the sloping boundaries. Ph.D. thesis, University of Washington, Seattle, WA, 244 pp.
——, 1997: Stable split time stepping schemes for large-scale ocean modeling. J. Comput. Phys.,135, 54–65.
Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. John Wiley, 477 pp.
Higdon, R. L., and A. F. Bennett, 1996: Stability analysis of operator splitting for large-scale ocean modeling. J. Comput. Phys.,123, 311–329.
——, and R. A. de Szoeke, 1997: Barotropic–baroclinic time splitting for ocean circulation modeling. J. Comput. Phys.,135, 30–53.
Holland, W. R., J. C. Chow, and F. O. Bryan, 1998: Application of a third-order upwind scheme in the NCAR ocean model. J. Climate,11, 1487–1493.
Huang, R. X., 1993: Real freshwater flux as a natural boundary condition for the salinity balance and thermohaline circulation forced by evaporation and precipitation. J. Phys. Oceanogr.,23, 2428–2446.
Jackett, D. R., and T. J. McDougall, 1995: Minimal adjustment of hydrographic profiles to achieve static stablilty. J. Atmos. Oceanic Technol.,12, 381–389.
Killworth, P. D., 1987: Topographic instabilities in level model OGCM’s. Ocean Modelling (unpublished manuscript), 75, 9–12.
——, and N. R. Edwards, 1999: A turbulent bottom boundary layer code for use in numerical models. J. Phys. Oceanogr.,29, 1221–1238.
——, J. M. Smith, and A. E. Gill, 1984: Speeding up ocean circulation models. Ocean Modelling (unpublished manuscript), 56, 1–5.
——, D. Stainforth, D. J. Webb, and S. M. Paterson, 1991: The development of a free-surface Bryan–Cox–Semtner ocean model. J. Phys. Oceanogr.,21, 1333–1348.
Large, W. G., and S. Pond, 1981: Open ocean flux measurements in moderate to strong winds. J. Phys. Oceanogr.,11, 324–336.
Leonard, B. P., 1979: A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng.,19, 59–98.
Levitus, S., 1982: Climatological Atlas of the World Ocean. NOAA Prof. Paper 13, U.S. Government Printing Office, Washington, DC, 173 pp.
Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997:A finite-volume, incompressible Navier–Stokes model for studies of the ocean on parallel computers. J. Geophys. Res.,102, 5753–5766.
Mellor, G. L., 1996: User’s guide for a three-dimensional, primitive equation, numerical ocean model. Program in Atmospheric and Oceanic Studies, Princeton University, Princeton, NJ, 40 pp. [Available from Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ 08542.].
Pacanowski, R. C., and A. Gnanadesikan, 1998: Transient response in a z-level ocean model that resolves topography with partial cells. Mon. Wea. Rev.,126, 3248–3270.
——, and S. M. Griffies, 2000: The MOM 3.1 manual. NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, NJ, 680 pp.
——, K. Dixon, and A. Rosati, 1991: The GFDL modular ocean model user guide. GFDL Ocean Group Tech. Rep. 2, Geophysical Fluid Dynamics Laboratory, Princeton, NJ, 16 pp.
Redler, R., K. Ketelsen, J. Dengg, and C. W. Böning, 1998: A high-resolution numerical model for the circulation of the Atlantic Ocean. Proceedings of the Fourth European CRAY-SGI MPP Workshop, H. Lederer and F. Hertweck, Eds., Max-Planck-Institut für Plasmaphysik, 95–108.
Roullet, G., and G. Magec, 2000: Salt conservation, free surface and varying volume. A new formulation for Ocean GCMs. J. Geophys. Res.,105, 23 927–23 947.
Semtner, A. J., Jr., 1974: An oceanic general circulation model with bottom topography. Numerical Simulation of Weather and Climate, Tech. Rep. 9, Department of Meteorology, University of California, Los Angeles.
Smith, R. D., J. K. Dukowicz, and R. C. Malone, 1992: Parallel ocean general circulation modeling. Physica D,60, 38–61.
Webb, D. J., 1995: The vertical advection of momentum in Bryan–Cox–Semtner ocean general circulation models. J. Phys. Oceanogr.,25, 3186–3195.
——, 1996: An ocean model code for array processor computers. Comput. Geophys.,22, 569–578.
——, A. C. Coward, B. A. de Cuevas, and C. S. Gwilliam, 1997: A multiprocessor ocean general circulation model using message passing. J. Atmos. Oceanic Technol.,14, 175–183.
——, B. A. de Cuevas, and A. C. Coward, 1998: The first main run of the OCCAM global ocean model. Southampton Oceanography Centre Internal Doc. 34, 44 pp.
Wolff, J.-O., E. Maier-Reimer, and S. Legutke, 1997: The Hamburg Ocean Primitive Equation Model HOPE. DKRZ Tech. Rep. 13, 98 pp.