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:
 Realistic coasts and bottom features;
 Heat and water fluxes
though the surface;
 Eddy dynamics; and
 The meridionaloverturning 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 spinup.
Spinup is needed because initial conditions for density, fluxes of momentum
and heat through the seasurface, 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 meanannual 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 BryanCox 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 BryanCox 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. Subgridscale
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 BryanCox 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 × 10^{7}
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, nearsurface 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 constantdensity
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
zcoordinate model and isopycnalcoordinate model (Bleck, 2002). The hybrid
model has evolved from the Miami IsopycnicCoordinate Ocean Model (figure 15.2).
It is a primitiveequation 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 doublediffusion
(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 highresolution 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, terrainfollowing 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 largescale
hydrographic structure, climate dynamics, and watermass formation. These models
are the same as the eddyadmitting, 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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