# Ocean General Circulation Models

September 17, 2012, 8:13 pm
 Topics: More

Western North Atlantic surface temperature map, with the Gulf Stream in red. Source: NASA

Ocean general circulation models (OGCMs) are computer programs that evolve the ocean's three-dimensional state forward in time. This layer contains over 95% of the atmosphere’s mass and virtually all of its water vapor, and it produces nearly all weather, although current research suggests possible interactions between this layer and higher atmospheric levels[1]. Because of the disparity between scales of horizontal and vertical motions governing global and regional climate, the two motions are treated differently by model algorithms. The resulting set of equations is often referred to as the primitive equations.[2]

## Overview of models

 This article draws content from CCSP, 2008: Climate Models: An Assessment of Strengths and Limitations. A Report by the U.S. Climate Change Science Program

Ocean general circulation models (OGCMs) solve the primitive equations for global incompressible fluid flow analogous to the ideal-gas primitive equations solved by atmospheric GCMs. In climate models, OGCMs are coupled to the atmosphere and ice models through the exchange of heat, salinity, and momentum at the boundary among components. Like the atmosphere, the ocean’s horizontal dimensions are much larger than its vertical dimension, resulting in separation between processes that control horizontal and vertical fluxes. With continents, enclosed basins, narrow straits, and submarine basins and ridges, the ocean has a more complex three-dimensional boundary than does the atmosphere. Furthermore, the thermodynamics of seawater are very different from those of air, so that an empirical equation of state must be used in place of the ideal gas law.

## Vertical discretization

An important distinction among ocean models is the choice of vertical discretization. Many models use vertical levels that are fixed distances below the surface (Z-level models) based on the early efforts of Bryan and Cox (1967) and Bryan (1969a, b). The General Fluid Dynamics Laboratory (GFDL) and Community Climate System Model (CCSM) ocean components fall into this category (Griffies et al. 2005; Maltrud et al. 1998). Two Goddard Institute for Space Studies (GISS) models (R and AOM) use a variant of this approach in which mass rather than height is used as the vertical coordinate (Russell, Miller, and Rind 1995; Russell et al. 2000). A more fundamental alternative uses density as a vertical coordinate. Motivating this choice is the desire to control as precisely as possible the exchange of heat between layers of differing density, which is very small in much of the ocean yet centrally important for simulation of climate. The GISS EH model utilizes a hybrid scheme that transitions from a Z-coordinate near the surface to density layers in the ocean interior (Sun and Bleck 2001; Bleck 2002; Sun and Hansen 2003).

## Horizontal grids

Horizontal grids used by most ocean models in the CMIP3 archive are comparable to or somewhat finer than grids in the atmospheric models to which they are coupled, typically on the order of 100 km (~ 1º spacing in latitude and longitude) for most of Earth. In many OGCMs the north-south resolution is enhanced within 5º latitude of the equator to improve the ability to simulate important equatorial processes.

OGCM grids usually are designed to avoid coordinate singularities caused by the convergence of meridians at the poles. For example, the CCSM OGCM grid is rotated to place its North Pole over a continent, while the GFDL models use a grid with three poles, all of which are placed over land (Murray 1996). Such a grid results in having all ocean grid points at numerically viable locations.

## Near ocean surface mixing

Processes that control ocean mixing near the surface are complex and take place on small scales (order of centimeters). To parameterize turbulent mixing near the surface, the current generation of OGCMs uses several different approaches (Large, McWilliams, and Doney 1994) similar to those developed for atmospheric near-surface turbulence. Within the ocean’s stratified, adiabatic interior, vertical mixing takes place on scales from meters to kilometers (Fig. 2.1); the smaller scales also must be parameterized in ocean components.

Ocean mixing contributes to its heat uptake and stratification, which in turn affects circulation patterns over time scales of decades and longer. Experts generally feel (e.g., Schopf et al. 2003) that subgrid-scale mixing parameterizations in OGCMs contribute significantly to uncertainty in estimates of the ocean’s contribution to climate change.

Very energetic eddy motions occur in the ocean on the scale of a few tens of kilometers. These so-called mesoscale eddies are not present in the ocean simulations of CMIP3 climate models.

## Use in climate models

Ocean models used for climate simulation cannot afford the computational cost of explicitly resolving ocean mesoscale eddies. Instead, they must parameterize mixing by the eddies. Treatment of these mesoscale eddy effects is an important factor distinguishing one ocean model from another. Most real ocean mixing is along rather than across surfaces of constant density. Development of parameterizations that account for this essential feature of mesoscale eddy mixing (Gent and McWilliams 1990; Griffies 1998) is a major advance in recent ocean and climate modeling. Inclusion of higher-resolution, mesoscale eddy–resolving ocean models in future climate models would reduce uncertainties associated with these parameterizations.

Other mixing processes that may be important in the ocean include tidal mixing and turbulence generated by interactions with the ocean’s bottom, both of which are included in some models. Lee, Rosati, and Spellman (2006) describe some effects of tidal mixing in a climate model. Some OGCMs also explicitly treat the bottom boundary and sill overflows (Beckman and Dosher 1997; Roberts and Wood 1997; Griffies et al. 2005). Furthermore, sunlight penetration into the ocean is controlled by chlorophyll distributions (e.g., Paulson and Simpson 1977; Morel and Antoine 1994; Ohlmann 2003), and the depth of penetration can affect surface temperatures. All U.S. CMIP3 models include some treatment of this effect, but they prescribe rather than attempt to simulate the upper ocean biology controlling water opacity. Finally, the inclusion of fresh water input by rivers is essential to close the global hydrological cycle; it affects ocean mixing locally and is handled by models in a variety of ways.

The relatively crude resolution of OGCMs used in climate models results in isolation of the smaller seas from large ocean basins. This requires models to perform ad hoc exchanges of water between the isolated seas and the ocean to simulate what in nature involves a channel or strait. (The Strait of Gibraltar is an excellent example.) Various modeling groups have chosen different methods to handle water mixing between smaller seas and larger ocean basins.

OGCM components of climate models are often evaluated in isolation—analogous to the evaluation of AGCMs with prescribed ocean and seaice boundary conditions—in addition to being evaluated as components of fully coupled ocean-atmosphere GCMs. (Results of full AOGCM evaluation are discussed in Chapter 5.) Evaluation of ocean models in isolation requires input of boundary conditions at the airsea interface. To compare simulations with observed data, boundary conditions or surface forcing are from the same period as the data. These surface fluxes also have uncertainties and, as a result, the evaluation of OGCMs with specified sea-surface boundary conditions.

## References

• CCSP, 2008: Climate Models: An Assessment of Strengths and Limitations. A Report by the U.S. Climate Change Science Program and the Subcommittee on Global Change Research [Bader D.C., C. Covey, W.J. Gutowski Jr., I.M. Held, K.E. Kunkel, R.L. Miller, R.T. Tokmakian and M.H. Zhang (Authors)]. Department of Energy, Office of Biological and Environmental Research, Washington, D.C., USA, 124 pp.
• Wolff J-O, Maier-Reimer E, Legutke S (1997) The Hamburg Ocean Primitive Equation Model HOPE. DKRZ report 13, Hamburg, Germany,
•  Maier-Reimer E, Mikolajewicz U (1992) The Hamburg Large Scale Geostrophic Ocean General Circulation Model (Cycle 1). DKRZ report 2, Hamburg, Germany
• Oberhuber JM (1993) Simulation of the Atlantic circulation with a coupled sea ice-mixed layer-isopycnal general circulation model, part I: model description. Journal of Physical Oceanography, 23, 808–829
•  Oberhuber JM (1993) The OPYC Ocean General Circulation Model. DKRZ report 7, Hamburg, Germany,
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