Chapter 15 - Numerical Models

15.3 Global Ocean Models

Several types of global models are widely used in oceanography. Most have grid points about one tenth of a degree apart, which is sufficient to resolve mesoscale eddies, such as those seen in Figures 11.10, 11.11, and 15.2, that have a diameter larger than two to three times the distance between grid points. Vertical resolution is typically around 30 vertical levels. Models include:

1. Realistic coasts and bottom features;
2. Heat and water fluxes though the surface;
3. Eddy dynamics; and
4. The meridional-overturning circulation.

Many assimilate satellite and float data using techniques described in §15.5. The models range in complexity from those that can run on desktop workstations to those that require the world's fastest computers.

All models must be be run to calculate one to two decades of variability before they can be used to simulate the ocean. This is called spin-up. Spin-up is needed because initial conditions for density, fluxes of momentum and heat through the sea-surface, and the equations of motion are not all consistent. Models are started from rest with values of density from the Levitus (1982) atlas and integrated for a decade using mean-annual wind stress, heat fluxes, and water flux. The model may be integrated for several more years using monthly wind stress, heat fluxes, and water fluxes.

The Bryan-Cox models led to the development of several widely used models which are providing impressive views of the global ocean circulation.

Geophysical Fluid Dynamics Laboratory Modular Ocean Model MOM
This is perhaps the most widely used model growing out of the original Bryan-Cox code. It consists 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, and it is in the public domain. The model is widely use for climate studies and for studying the ocean's circulation over a wide range of space and time scales (Pacanowski and Griffies, 1999).

Because MOM is used to investigate processes which cover a wide range of time and space scales, the code and manual are lengthy. However, it is far from necessary for the typical ocean modeler to become acquainted with all of its aspects. Indeed, MOM can be likened to a growing city with many different neighborhoods. Some of the neighborhoods communicate with one another, some are mutually incompatible, and others are basically independent. This diversity is quite a challenge to coordinate and support. Indeed, over the years certain "neighborhoods'' have been jettisoned or greatly renovated for various reasons.
From Pacanowski and Griffies (1999).

The model uses the momentum equations, equation of state, and the hydrostatic and Boussinesq approximations. Subgrid-scale motions are reduced by use of eddy viscosity. Version 4 of the model has improved numerical schemes, a free surface, realistic bottom features, and many types of mixing including horizontal mixing along surfaces of constant density. Plus, it can be coupled to atmospheric models.

Parallel Ocean Program Model POP
This model was produced by Smith and colleagues at Los Alamos National Laboratory (Maltrud et al, 1998) is another widely used model growing out of the original Bryan-Cox code. The model includes improved numerical algorithms, realistic coasts, islands, and unsmoothed bottom features. It has model has 1280 × 896 equally spaced grid points on a Mercator projection extending from 77°S to 77°N, and 20 levels in the vertical. Thus it has 2.2 × 10⁷ points giving a resolution of 0.28° × 0.28° cos θ, which varies from 0.28° (31.25 km) at the equator to 0.06° (6.5 km) at the highest latitudes. The average resolution is about 0.2°. The model was is forced by ECMWF wind stress and surface heat and water fluxes (Barnier et al, 1995).

Figure 15.1 Instantaneous, near-surface geostrophic currents in the Atlantic for October 1, 1995 calculated from the Parallel Ocean Program numerical model developed at the Los Alamos National Laboratory. The length of the vector is the mean speed in the upper 50m of the ocean. The direction is the mean direction of the current. From Richard Smith..

Hybrid Coordinate Ocean Model HYCOM
All the models just described use x, y, z coordinates. Such a coordinate system has both advantages and disadvantages. It can have high resolution in the surface mixed layer and in shallower regions. But it is less useful in the interior of the ocean. Below the mixed layer, mixing in the ocean is easy along surfaces of constant density, and difficult across such surfaces. A more natural coordinate system in the interior of the ocean uses x, y, ρ, where ρ is density. Such a model is called an isopycnal model. Essentially, ρ is replaced with z(ρ).Because isopycnal surfaces are surfaces of constant density, horizontal mixing is always on constant-density surfaces in this model.

The Hybrid Coordinate Ocean Model HYCOM model uses different vertical coordinates in different regions of the ocean, combining the best aspects of z-coordinate model and isopycnal-coordinate model (Bleck, 2002). The hybrid model has evolved from the Miami Isopycnic-Coordinate Ocean Model (figure 15.2). It is a primitive-equation model driven by wind stress and heat fluxes. It has realistic mixed layer and improved horizontal and vertical mixing schemes that include the influences of internal waves, shear instability, and double-diffusion (see §8.5). The model results from collaborative work among investigators at many oceanographic laboratories.

Figure 15.2 Output of Bleck’s Miami Isopycnal Coordinate Ocean Model MICOM. It is a high-resolution model of the Atlantic showing the Gulf Stream, its variability, and the circulation of the North Atlantic. From Bleck.

Regional Oceanic Modelling System ROMS
This is a regional model that can be imbedded in models of much larger regions. It is widely used for studying coastal current systems closely tied to flow further offshore, for example, the California Current. ROMS is a hydrostatic, primitive equation, terrain-following model using stretched vertical coordinates. The model is driven by surface fluxes of momentum, heat, and water. It has improved surface and bottom boundary layers (Shchepetkin and McWilliams, 2004).

Climate Models are used for studies of large-scale hydrographic structure, climate dynamics, and water-mass formation. These models are the same as the eddy-admitting, primitive equation models I have just described except the horizontal resolution is much coarser because they must simulate ocean processes for decades or centuries. As a result, they must have high dissipation for numerical stability, and they cannot simulate mesoscale eddies. Typical horizontal resolutions are 2° to 4°. The models tend, however, to have high vertical resolution necessary for describing the deep circulation important for climate.

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