Ocean general circulation model

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.[2] The first application with specified global geometry was done in the early 1970s.[3] 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 cross-stream 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.[4] 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.[5]

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.[6] Furthermore these simulations with high enough resolution such as the Southern Ocean south of latitude 25°,[7] the North Atlantic,[8] and the World Ocean without the Arctic [9] 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. Furthermore, 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.[10] Another method developed at Los Alamos National Laboratory solves the same 2D equations using an implicit method for the free surface.[11] Both methods are quite efficient.

OGCMs have many important applications: dynamical coupling with the atmosphere, sea ice, and land run-off that in reality jointly determine the oceanic boundary fluxes; transpire of biogeochemical materials; interpretation of the paleoclimate record;climate prediction for both natural variability and anthropogenic chafes; data assimilation and fisheries and other biospheric management.[12] OGCMs play a critical role in Earth system model. They maintain the thermal balance as they transport energy from tropical to the polar latitudes. To analyze the feedback between ocean and atmosphere we need ocean model, which can initiate and amplify climate change on many different time scales, for instance, the interannual variability of El Niño [13] and the potential modification of the major patterns for oceanic heat transport as a result of increasing greenhouse gases.[14] Oceans are a kind of undersampled nature fluid system, so by using OGCMs we can fill in those data blank and improve understanding of basic processes and their interconnectedness, as well as to help interpret sparse observations. Even though, simpler models can be used to estimate climate response, only OGCM can be used conjunction with atmospheric general circulation model to estimate global climate change.[15]

ocean parameterization scheme family tree

Molecular friction rarely upsets the dominant balances (geostrophic and hydrostatic) in the ocean. With kinematic viscosities of v=10⁻⁶m ² s⁻¹ the Ekman number is several orders of magnitude smaller than unity; therefore, molecular frictional forces are certainly negligible for large-scale oceanic motions. A similar argument holds for the tracer equations, where the molecular thermodiffusivity and salt diffusivity lead to Reynolds number of negligible magnitude, which means the molecular diffusive time scales are much longer than advective time scale. So we can thus safely conclude that the direct effects of molecular processes are insignificant for large-scale. Yet the molecular friction is essential somewhere. The point is that large-scale motions in the ocean interacted with other scales by the nonlinearities in primitive equation. We can show that by Reynolds approach, which will leads to the closure problem. That means new variables arise at each level in the Reynolds averaging procedure. This leads to the need of parameterization scheme to account for those sub grid scale effects.

Here is a schematic “family tree” of subgridscale (SGS) mixing schemes. Although there is a considerable degree of overlap and interrelatedness among the huge variety of schemes in use today, several branch points maybe defined. Most importantly, the approaches for lateral and vertical subgridscale closure vary considerably. Filters and higher-order operators are used to remove small-scale noise that is numerically necessary. Those special dynamical parameterizations (topographic stress, eddy thickness diffusion and convection) are becoming available for certain processes. In the vertical, the surface mixed layer (sml) has historically received special attention because of its important role in air-sea exchange. Now there are so many schemes can be chose from: Price-Weller-Pinkel, Pacanowksi and Philander, bulk, Mellor-Yamada and KPP (k-profile parameterization) schemes.

Adaptive (non-constant) mixing length schemes are widely used for parameterization of both lateral and vertical mixing. In the horizontal, parameterizations dependent on the rates of stress and strain (Smagroinsky), grid spacing and Reynolds number (Re) have been advocated. In the vertical, vertical mixing as a function stability frequency (N^2) and/or Richardson number are historically prevalent. The rotated mixing tensors scheme is the one considering the angle of the principle direction of mixing, as for in the main thermocline, mixing along isopycnals dominates diapycnal mixing. Therefore the principle direction of mixing is neither strictly vertical nor purely horizontal, but a spatially variable mixture of the two.

OGCMs and AGCMs have much in common, such as, the equations of motion and the numerical techniques. However, OGCMs have some unique features. For example, the atmosphere is forced thermally throughout its volume, the ocean is forced both thermally and mechanically primarily at its surface, in addition, the geometry of ocean basins is very complex. The boundary conditions are totally different. For ocean models, we need to consider those narrow but important boundary layers on nearly all bounding surfaces as well as within the oceanic interior. These boundary conditions on ocean flows are difficult to define and to parameterize, which results in a high computationally demand.

Ocean modeling is also strongly constrained by the existence in much of the world's oceans of mesoscale eddies with time and space scales, respectively, of weeks to months and tens to hundreds of kilometers. Dynamically, these nearly geostrophic turbulent eddies are the oceanographic counterparts of the atmospheric synoptic scale. Nevertheless, there are important differences. First, ocean eddies are not perturbations on an energetic mean flow. They may play an important role in the poleward transport of heat. Second, they are relatively small in horizontal extent so that ocean climate models, which must have the same overall exterior dimensions as AGCMs, may require as much as 20 times the resolution as AGCM if the eddies are to be explicitly resolved.

Most of the difference between OGCMs and AGCMs is that the data are sparser for OGCMs. Also, the data are not only sparse but also nonuniform and indirect.

We can classify ocean models according to different standards. For example, according to vertical ordinates we have geo-potential, isopycnal and topography-following models. According to horizontal discretizations we have unstaggered or staggered grids. According to methods of approximation we have finite difference and finite element models. There are three basic types of OGCMs:

1. Idealized geometry models: Models with idealized basin geometry have been used extensively in ocean modeling and have played a major role in the development of new modeling methodologies. They use a simplified geometry, offering a basin itself, while the distribution of winds and buoyancy force are generally chosen as simple functions of latitude.
2. Basin-scale models: To compare OGCM results with observations we need realistic basin information instead of idealized data. However, if we only pay attention to local observation data, we don't need to run whole global simulation, and by doing that we can save a lot of computational resources.
3. Global models: This kind of model is the most computationally costly one. More experiments are needed as a preliminary step in constructing coupled Earth system models.

• List of ocean circulation models
• General circulation model (GCM)
• Climate model