There are at present within the field of ocean general circulation modeling four classes of numerical models which have achieved a significant level of community management and involvement, including shared community development, regular user interaction, and ready availability of software and documentation via the World Wide Web. These four classes are loosely characterized by their respective approaches to spatial discretization (finite difference, finite element, finite volume) and vertical coordinate treatment (geopotential, isopycnic, sigma, hybrid).
The earliest class of ocean models, and still the most widely applied, was pioneered by Kirk Bryan and his colleagues at GFDL utilizing low-order finite difference techniques applied to the oceanic primitive equations written in geopotential (z-based) coordinates. At present, variations on this first OGCM are in place at Harvard (Harvard Ocean Prediction System, HOPS), GFDL (Modular Ocean Model, MOM (MOM), the Los Alamos National Lab (Parallel Ocean Program, POP), the National Center for Atmospheric Research (NCAR Community Ocean Model, NCOM), and other institutions. A set of geopotential models based upon a structured, finite volume disctretization has also been developed at MIT (MITgcm).
During the 1970's, two competing approaches to vertical discretization and coordinate treatment made their way into ocean modeling. These alternatives were based respectively on vertical discretization in immiscible layers ("layered" models) and on terrain-following vertical coordinates ("sigma" coordinate models). In keeping with 1970's-style thinking on algorithms, both these model classes used (and, by and large, continue to use) low-order finite difference schemes similar to those employed in the geopotential coordinate models.
Today, several examples of layered and sigma-coordinate models exist. The former category includes models designed and built at the Naval Research Lab (the Navy Layered Ocean Model NLOM), the University of Miami (the Miami Isopycnic Coordinate Ocean Model, MICOM), GFDL (the Hallberg Isopycnic Model, HIM), and others. In the latter are models from Princeton (the Princeton Ocean Model, POM), and Rutgers University and UCLA (the Regional Ocean Modeling System, ROMS), to name the two most widely used in this class.
More recently, OGCM's have been constructed which make use of more advanced, and less traditional, algorithmic approaches. Most importantly, models have been developed based upon Galerkin finite element schemes -- e.g., the triangular finite element code QUODDY (Dartmouth University) and the spectral finite element code SEOM (Rutgers). These differ most fundamentally from earlier models in the numerical algorithms used to solve the equations of motion, and their use of unstructured (as opposed to structured) horizontal grids. Recently, finite volume methods have also been adopted to achieve unstructured gridding (FVCOM).
In recent years, the usage of terrain-following coordinates (sigma, hybrid)
ocean models has increased tremendously in a wide range of successful
applications. This has led to improvements of the numerical algorithms
for time-stepping, advection, pressure gradient, and subgrid-scale
parameterizations. Early in 2000, a new initiative was started, under the
sponsorship of ONR Ocean, Atmosphere, and Space Research Division, to develop the next
generation terrain-following ocean community model for scientific and
operational applications. The new model, named TOMS (Terrain-following
Ocean Modeling System), incorporates the state-of-art knowledge in
physics, numerics and advanced data assimilation. The purpose of this
web site is to facilitate the development and testing of TOMS and to
provide forum to ocean community at large.