Bryan, Kirk (1929-)

The Bryan-Cox Code

Bryan started his research at the Geophysical Fluid Dynamics Laboratory in the 1960s. The laboratory was then located in Washington, D.C. (it has since transferred to Princeton University). With a team of colleagues, Bryan developed numerical schemes to calculate the equations of motion describing flow on a sphere. These schemes led to the “Bryan-Cox code,” used in many early simulations, which allowed the development of the Modular Ocean Model currently used by many numerical oceanographers and climate scientists.

The “Bryan-Cox code” was used to create the first simulation models that calculate realistic circulation of oceanic regions. The models are often very complex, and their output is difficult to interpret. The Bryan-Cox model calculated the three-dimensional flow in the ocean combining the continuity and momentum equation with the hydrostatic and Bouss-inesq approximations, and a simplified equation of state. These models are called primitive equation models because they use the most basic form of the equations of motion. The equation of state allows the model to calculate changes in density due to fluxes of heat and water through the sea surface, so the model includes thermodynamic processes.

The Bryan-Cox model used large horizontal and vertical viscosity and diffusion to eliminate turbulent eddies of diameters smaller than about 311 mi. (500km.). It also had complex coastlines, smoothed sea-floor features, and a rigid lid. The rigid lid was necessary for eliminating ocean-surface waves, such as tides and tsunamis, which move far too fast to be accounted for by the time steps used by all simulation models. Criticism of the model concerns the lid. Islands substantially slow the computation, and the sea-floor features must be smoothed to eliminate steep gradients.

The Geophysical Fluid Dynamics Laboratory Modular Ocean Model (MOM) is perhaps the most widely used model that grew out of the original Bryan-Cox code. It is made up of a large set of modules that can be configured to run on many different computers to model many different aspects of the circulation. The source code is open and free. The model is commonly used for climate studies and to assess the ocean's circulation over a wide range of space and time scales. The Parallel Ocean Program Model also grew out of the Bryan-Cox code.

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