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Ocean general circulation model : ウィキペディア英語版
Ocean general circulation model
Ocean general circulation models (OGCMs) are a particular kind of general circulation model to descript physical and thermodynamical processes in oceans, they include all of the major influences on the oceanic general circulation. The oceanic general circulation is defined as the horizontal space scale and time scale larger than mesoscale (of order 100 km and 6 months). They depict oceans using a three-dimensional grid that include active thermodynamics and hence are most directly applicable to climate studies, hence they are the most advanced tools currently available for simulating the response of the global ocean system to increasing greenhouse gas concentrations.〔http://www.ipcc-data.org/guidelines/pages/gcm_guide.html〕 A hierarchy of OGCMs have been developed that include varying degrees of spatial coverage, resolution, geographical realism, process, etc.
==History==

The first generation of OGCMs assumed “rigid lid” to eliminate high-speed external gravity waves. According to CFL criteria without those fast waves, we can use a bigger time step, which is not so computationally expensive. But it also filtered those ocean tides and other waves having the speed of tsunamis. Within this assumption Bryan and co-worker Cox developed a 2D model, a 3D box model, and then a model of full circulation in GFDL, with variable density as well, for the world ocean with its complex coastline and bottom topography.〔K. Bryan, J. Comput. Phys. 4, 347 (1969)〕 The first application with specified global geometry was done in the early 1970s.〔M. D. Cox, in Numerical Models of Ocean Circulation (National Academy of Sciences, Washington, DC, 1975), pp. 107 120〕 Cox designed a 2° latitude-longitude grid with up to 12 vertical levels at each point.
With more and more research on ocean model, mesoscale phenomenon, e.g. most ocean currents have crossstream dimensions equal to Rossby radius of deformation, started to get more awareness. However, in order to analyze those eddies and currents in numerical models, we need grid spacing to be approximately 20 km in middle latitudes. Thanks to those faster computers and further filtering the equations in advance to remove internal gravity waves, those major currents and low-frequency eddies then can be resolved, one example is the three-layer quasi-geostrophic models designed by Holland.〔W. R. Holland, J. Phys. Oceanogr. 8, 363 (1978)〕 Meanwhile there are some model retaining internal gravity wave, for example one adiabatic layered model by O'Brien and his students, which did retain internal gravity waves so that equatorial and coastal problems involving these waves could be treated, led to an initial understanding of El Niño in terms of those waves.〔A. J. Busalacchi and J. J. O'Brien, ibid. 10, 1929 (1980)〕
In the late 1980s, simulations could finally be undertaken using the GFDL formulation with eddies marginally resolved over extensive domains and with observed winds and some atmospheric influence on density.〔http://www.mbari.org/staff/braccio/science/semtner.html Albert J. Semtner〕 Further more these simulation with high enough resolution such as the Southern Ocean south of latitude 25°,〔The FRAM Group, Eos 72, 169 (1991)〕 the North Atlantic,〔F. O. Bryan, C. W. Böning, W. R. Holland, J. Phys. Oceanogr. 25, 289 (1995)〕 and the World Ocean without the Arctic 〔A. J. Semtner and R. M Chervin, J. Geophys. Res. 97, 5493 (1992)〕 provided first side-by-side comparison with data.
Early in the 1990s, for those large scale and eddies resolvable models the computer requirement for the 2D ancillary problem associated with the rigid lid approximation was becoming excessive. Further more, in order to predict tidal effects or compare height data from satellites, methods were developed to predict the height and pressure of the ocean surface directly. For example, one method is to treat the free surface and the vertically averaged velocity using many small steps in time for each single step of the full 3D model.〔P. D. Killworth, D. Stainforth, D. J. Webb, S. M. Paterson, J. Phys. Oceanogr. 21, 1333 (1991)〕 Another method developed at Los Alamos National Laboratory solves the same 2D equations using an implicit method for the free surface.〔J. K. Dukowicz and R. D. Smith, J. Geophys. Res. 99, 7991 (1994)〕 Both methods are quite efficient.

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