42
Kirk Bryan
models is to link theory and observation, but models cannot be thought of as a substitute for either theory or data. A very concrete scientific achievement of models is
the ability to diagnose the thermohaline circulation from data, and to predict how it
might change under different climate conditions. The ability of models to simulate
the complicated tropical air–sea interaction of the El Ni˜ no phenomenon has led to
many theories, which are still being tested (Chang et al., 2005). It is through models
that we can already see in a quantitative way that the World Ocean plays the dominate
role in climate change and climate variability on longer time-scales.
REFERENCES
Arakawa, A., 1966. Computational design for long-term numerical integration of the equations of fluid
flow: Two-dimensional incompressible flow. Part I. J. Comput. Phys., 1, 119–143.
Bleck, R., and D. Boudra, 1981. Initial testing of a numerical ocean circulation model using a hybrid
(quasi-isopycnic) vertical coordinate. J. Phys. Oceanogr. 11, 755–770.
Blumberg, A. F., and G. L. Mellor, 1987. A description of a three-dimensional coastal ocean circulation
model. Three-Dimensional Coastal Ocean Models, Vol. 4, N. Heaps, ed., American Geophysical
Union, Washington, DC, 208 pp.
Bryan, F., 1986. Maintenance and variability of the thermohaline circulation. Geophysical Fluid Dynamics
Program Thesis, Princeton University.
Bryan, F., and W. R. Holland, 1989. A high resolution simulation of the wind and thermohaline-driven
circulation in the North Atlantic Ocean. Proceedings of the ’Aha Huliko’a Hawaiian Workshop,
January 17–20, 1989.
Bryan, K., 1963. A numerical investigation of a nonlinear model of a wind-driven ocean. J. Atmos. Sci.
20, 594–606.
Bryan, K., 1969. A numerical method for the study of the circulation of the world ocean. J. Comput. Phys.
4, 347–376, reprinted with corrections, J. Comput. Phys. 30 th Anniversary Volume 1997.
Bryan, K., 1991. Michael Cox (1941–1989): His pioneering contributions to ocean circulation modeling.
J. Phys. Oceanogr. 21, 1259–1270.
Bryan, K., and M. D. Cox, 1967. A numerical investigation of the oceanic general circulation. Tellus 19,
54–80.
Bryan, K., and M. D. Cox, 1968a. A nonlinear model of an ocean driven by wind and differential heating:
Part I. Description of the three-dimensional velocity and density fields. J. Atmos. Sci. 25, 945–967.
Bryan, K., and M. D. Cox, 1968b. A nonlinear model of an ocean driven by wind and differential heating:
Part II. An analysis of the heat, vorticity, and energy balance. J. Atmos. Sci. 25, 968–978.
Bryan, K., and L. J. Lewis, 1979. A water mass model of the world ocean. J. Geophys. Res. 84, 2503–2517.
Bryan, K., and M. J. Spelman, 1985. The ocean’s response to a CO 2 -induced warming. J. Geophys. Res.
90, 11, 679–11,688.
Bryan, K., S. Manabe, and M. J. Spelman, 1988. Interhemispheric asymmetry in the transient response of
a coupled ocean–atmosphere model to a CO 2 forcing. J. Phys. Oceanogr. 18, 851–867.
Chang, P., T. Yamagata, P. Schopf, S. K. Behera, J. Carton, W. S. Kessler, G. Meyers, T. Qu, F. Schott,
S. Sheytye, and S.-P. Xie, 2005. Climate fluctuations of tropical coupled system—the role of ocean
dynamics. J. Climate (submitted).
Cox, M. D., 1970. A mathematical model of the Indian Ocean. Deep-Sea Res. 17, 47–75.
Cox, M. D., 1984. A primitive equation, 3-dimensional model of the ocean. GFDL Ocean Group Technical
Report No. 1, Geophysical Fluid Dynamics Laboratory, Princeton, NJ.
Cox, M. D., 1987. Isopycnal diffusion in a z-coordinate ocean model. Ocean Modeling 74, 1–5.
Kirk Bryan
models is to link theory and observation, but models cannot be thought of as a substitute for either theory or data. A very concrete scientific achievement of models is
the ability to diagnose the thermohaline circulation from data, and to predict how it
might change under different climate conditions. The ability of models to simulate
the complicated tropical air–sea interaction of the El Ni˜ no phenomenon has led to
many theories, which are still being tested (Chang et al., 2005). It is through models
that we can already see in a quantitative way that the World Ocean plays the dominate
role in climate change and climate variability on longer time-scales.
REFERENCES
Arakawa, A., 1966. Computational design for long-term numerical integration of the equations of fluid
flow: Two-dimensional incompressible flow. Part I. J. Comput. Phys., 1, 119–143.
Bleck, R., and D. Boudra, 1981. Initial testing of a numerical ocean circulation model using a hybrid
(quasi-isopycnic) vertical coordinate. J. Phys. Oceanogr. 11, 755–770.
Blumberg, A. F., and G. L. Mellor, 1987. A description of a three-dimensional coastal ocean circulation
model. Three-Dimensional Coastal Ocean Models, Vol. 4, N. Heaps, ed., American Geophysical
Union, Washington, DC, 208 pp.
Bryan, F., 1986. Maintenance and variability of the thermohaline circulation. Geophysical Fluid Dynamics
Program Thesis, Princeton University.
Bryan, F., and W. R. Holland, 1989. A high resolution simulation of the wind and thermohaline-driven
circulation in the North Atlantic Ocean. Proceedings of the ’Aha Huliko’a Hawaiian Workshop,
January 17–20, 1989.
Bryan, K., 1963. A numerical investigation of a nonlinear model of a wind-driven ocean. J. Atmos. Sci.
20, 594–606.
Bryan, K., 1969. A numerical method for the study of the circulation of the world ocean. J. Comput. Phys.
4, 347–376, reprinted with corrections, J. Comput. Phys. 30 th Anniversary Volume 1997.
Bryan, K., 1991. Michael Cox (1941–1989): His pioneering contributions to ocean circulation modeling.
J. Phys. Oceanogr. 21, 1259–1270.
Bryan, K., and M. D. Cox, 1967. A numerical investigation of the oceanic general circulation. Tellus 19,
54–80.
Bryan, K., and M. D. Cox, 1968a. A nonlinear model of an ocean driven by wind and differential heating:
Part I. Description of the three-dimensional velocity and density fields. J. Atmos. Sci. 25, 945–967.
Bryan, K., and M. D. Cox, 1968b. A nonlinear model of an ocean driven by wind and differential heating:
Part II. An analysis of the heat, vorticity, and energy balance. J. Atmos. Sci. 25, 968–978.
Bryan, K., and L. J. Lewis, 1979. A water mass model of the world ocean. J. Geophys. Res. 84, 2503–2517.
Bryan, K., and M. J. Spelman, 1985. The ocean’s response to a CO 2 -induced warming. J. Geophys. Res.
90, 11, 679–11,688.
Bryan, K., S. Manabe, and M. J. Spelman, 1988. Interhemispheric asymmetry in the transient response of
a coupled ocean–atmosphere model to a CO 2 forcing. J. Phys. Oceanogr. 18, 851–867.
Chang, P., T. Yamagata, P. Schopf, S. K. Behera, J. Carton, W. S. Kessler, G. Meyers, T. Qu, F. Schott,
S. Sheytye, and S.-P. Xie, 2005. Climate fluctuations of tropical coupled system—the role of ocean
dynamics. J. Climate (submitted).
Cox, M. D., 1970. A mathematical model of the Indian Ocean. Deep-Sea Res. 17, 47–75.
Cox, M. D., 1984. A primitive equation, 3-dimensional model of the ocean. GFDL Ocean Group Technical
Report No. 1, Geophysical Fluid Dynamics Laboratory, Princeton, NJ.
Cox, M. D., 1987. Isopycnal diffusion in a z-coordinate ocean model. Ocean Modeling 74, 1–5.