TECHNICAL REPORTS OF THE METEOROLOGICAL RESEARCH INSTITUTE No.80 2017

Chapter 1

OGCMs and MRI.COM
This chapter outlines the ocean general circulation models (OGCM) and the status of MRI.COM.

1.1 What do OGCMs cover?
OGCMs have been supposed to simulate relatively large-scale phenomena such as global-scale thermohaline circulations,basin-scale wind-driven circulations, and mesoscale eddies (Figure 1.1). Small-scale processes that are either unresolved
or neglected might be incorporated in some forms of subgrid-scale (SGS) parameterizations. The current basin or global
scale OGCMs may cover phenomena from thermohaline circulations to mesoscale eddies, but it is still almost impossible toconduct a simulation long enough to achieve a quasi-steady state of a thermohaline circulation with a horizontal resolution(∼ several km) that is suﬃciently high to resolve mesoscale eddies, even with the present computation resources. For
these reasons, the standard practice in the ocean model community is to use a low horizontal resolution (a few hundredkilometers) model to study global thermohaline circulations and to use a limited-domain model to study an eddying
ocean. Some research projects seek to conduct a several-hundred-year integration of a high resolution model that resolves
mesoscale eddies using enormous resources, but such a resource is not available to everyone.
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PRQWK\U\U\U \UFigure1.1 Various oceanic phenomena in terms of their space and time scales and coverage of the ocean generalcirculation model. the figure of oceanic phenomena is adopted from von Storch and Zwiers (2001), but somephenomena are added.

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TECHNICAL REPORTS OF THE METEOROLOGICAL RESEARCH INSTITUTE No.80 2017
1.2 Classification of OGCMs
In recent years, the OGCMs are used to directly simulate some of the previously unresolved small scale phenomena.
These include submesoscale currents (McWilliams, 2016) and the generation of internal gravity waves due to the interactions of tides and mesoscale currents with topographic features. Because large scale features such as mesoscale eddies,boundary currents, and oceanic fronts are prerequisite for the spontaneous emergence of these fine-scale features, anapproach of embedding (nesting) subdomains with refined grids in a basin scale model is often taken. Use of a common
OGCM code is preferable in these approaches.

1.2 Classification of OGCMs
Most OGCMs used by ocean research scientists and by operational centers for forecasting climate and oceanic statesnumerically solve almost the same set of equations for the Boussinesq and hydrostatic ocean. The fundamental equations
consist of the momentum equation for continuous fluid, the advection-diﬀusion equation for temperature and salinity, theequation of state of sea water, and the mass conservation equation, collectively called primitive equations (Chapter 2).
If necessary, equations for additional processes such as surface mixed-layer physics, sea ice, and bottom boundary layer
physics are added.
Most OGCMs applied to ocean-climate studies adopt the finite diﬀerence or finite volume method on structured meshto discretize the equations. Recently, the finite element method on horizontally unstructured mesh is also applied to bothcoastal ocean simulation and global ocean simulation (e.g., Chen et al., 2011; Danilov, 2013). MRI.COM takes the former
approach. The spectral approach widely used by atmospheric models would have diﬃculty treating lands that completely
block ocean circulation in the zonal direction, and thus this approach is not usually adopted in general-purpose oceanmodels.
Ocean models adopting horizontally structured mesh are classified by how they discretize the vertical direction. The
choice of the vertical coordinate leads to fundamental diﬀerences among the models. There are three classes: zcoordinate models or z-models adopting depth as the vertical coordinate, σ-coordinate or terrain following models
adopting fractional depth between the sea surface and the sea floor as the vertical coordinate, and ρ-coordinate orisopycnal models adopting isentropic surfaces (iso-potential density surfaces) as the vertical coordinate. Each class has
its advantages and disadvantages and recent eﬀorts are directed toward adopting generalized vertical coordinates, i.e.,
remedying each model’s disadvantages by using advantages of other classes. Readers are referred to the book by Griﬃes(2004) for more general discussion about OGCMs.

1.2.1

Z -coordinate models ( z -models)The first z-coordinate general circulation model was developed by Dr. Kirk Bryan and his colleagues at the GeophysicalFluid Dynamics Laboratory (GFDL) in the 1960’s (e.g., Bryan, 1969). This model is sometimes referred to as the BryanCox-Semtner model or GFDL model. The z-models utilize the character of the ocean that the local pressure is expressed
as a function of depth by zero-order approximation, which makes implementing the equation of state straightforward.
Implementation of bottom topography and drawing of results are also straightforward. The models of this class aremost widely used in the community because of their versatility. Such models were first used as components of coupledatmosphere-ocean models.
The descendant of the GFDL model is called the Modular Ocean Model (MOM; Griﬃes, 2012) and is one of the mostwidely used z-models. Massachusetts Institute of Technology general circulation model (MITgcm; Marshall et al., 1997)
and Nucleus for European Modelling of the Ocean (NEMO; Madec and the NEMO team, 2008) are also widely used.
Most climate centers participating in climate model intercomparison projects use the z-coordinate models; MRI.COM
also adopts z-coordinate. In Japan, the Center for Climate System Research Ocean Component Model (COCO) at theUniversity of Tokyo (Hasumi, 2006) and the Research Institute of Applied Mechanics Ocean Model (RIAMOM) are alsoin this class.
The major disadvantages of this class of models are as follows:• The vertical resolution in shallow seas and near the sea floor tends to be low and the processes that arise near thecoast and the sea floor tend to be poorly reproduced.
• Numerical inaccuracy in the tracer transport algorithm immediately leads to spurious diapycnal mixing of thetransported properties, while the diapycnal mixing is supposed to be very small in the ideal ocean interior.
The first disadvantage is expected to be remedied by the σ-models and the second by the ρ-models. However, z-model’sdisadvantages are not completely overcome; these substitutes have their own diﬃculties.

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TECHNICAL REPORTS OF THE METEOROLOGICAL RESEARCH INSTITUTE No.80 2017
Chapter 1

OGCMs and MRI.COM

1.2.2 Sigma-coordinate models (σ -models)The first sigma-coordinate model was developed by Dr. George Mellor and his colleagues at Princeton University. Since
the number of vertical grid points is invariable throughout the model domain, σ-models are widely used for coastal oceansimulations.
Two major sigma-models are widely used in the community: The Princeton Ocean Model (POM; Mellor, 2004) andthe Regional Ocean Modeling System (ROMS; Shchepetkin and McWilliams, 2003; 2005).
The major disadvantages of this class of models are as follows:• An accurate representation of the horizontal pressure gradient is diﬃcult near steeply sloping bottom topography.
• The lateral mixing along the same vertical layer near the continental slope region might lead to mixing of theshoreward light water and the seaward dense water.
These problems might prohibit using σ-models in long-term integrations of the global ocean.

1.2.3 Isopycnal-coordinate models ( ρ-models)The first isopycnal-coordinate model was developed by Dr. Rainer Bleck at the University of Miami. The development of
this class of models is based on the fact that sea water moves along isopycnal surfaces in the interior. Thus, the characterof a water mass is well maintained in the ocean interior. Since many theoretical studies of physical oceanography use
an isopycnal-coordinate framework, the ρ-models have the great advantage of providing good correspondence betweentheory and numerical models.
A major ρ-model widely used in the community is the Miami Isopycnic Coordinate Ocean Model (MICOM; Bleck andBoudra, 1986) developed at the University of Miami.
The major disadvantages of this class of models are as follows:• Implementation of surface mixed layer models into a ρ-model is in itself inappropriate.
• Since the density levels are prescribed, this class of models might not be appropriate for studying a drastic climatechange that could lead to great variations in density of major water masses.
The Hybrid Coordinate Ocean Model (HYCOM; Bleck et al., 2002) has been developed in an eﬀort to remedy some ofthese disadvantages.

1.3 About MRI.COMMRI.COM is a z-coordinate model and uses the finite volume method on structured mesh to discretize the governingequations. The horizontal grid arrangement is Arakawa’s B-grid (Arakawa, 1972). Coast lines are defined by theperiphery of the grid cell centered by the velocity point, i.e., the lines connecting the tracer points. This arrangement issuitable for the discrete expressions for the side boundary conditions for velocity, and transport through a narrow passage
can be achieved with a single grid cell.
The program structure of MRI.COM is presented along with a typical computational cost of each process in Figure 1.2.
Though the program code should ideally use MKS units, MRI.COM basically uses cgs units for historical reasons. The
sea ice model, the mixed-layer model, some surface bulk formulae, and biogeochemical models are coded in MKS units
and converted into cgs units before their outputs are used by the main part. Details are described in each chapter.

1.4 Future of OGCMs and MRI.COMAs OGCMs acquire scientific and numerical integrity, they expand the area of their usage and begin to fulfill social as well
as scientific needs. The developer of an OGCM thus has the responsibility to ensure its scientific and numerical integrity
and to acknowledge its limitations. Feedback from users of various fields and continuous eﬀorts to overcome limitations
will certainly improve the OGCMs.
The advance of OGCMs has kept pace with that of super-computers. The mainstream of super computing is shiftingfrom vector computation to massively parallel computation with distributed memory. To rewrite the current vector-friendly
program codes to adapt to this shift is immediately needed for some OGCMs. With increasing computing power, everhigher resolution simulations will be achieved. The result will be more strongly aﬀected by how subgrid-scale processes
are parameterized and thus subgrid-scale schemes should be selected carefully.
To continue to stand as a multi-purpose model, an OGCM should be easily coupled with other component models and–3–

TECHNICAL REPORTS OF THE METEOROLOGICAL RESEARCH INSTITUTE No.80 2017
1.4 Future of OGCMs and MRI.COM[program ﬁle name]exchange withatmosphere

initialization[time.F90, gridm.F90, gridg.F90, topo.F90]

chap 21

typical cost
4%
11%

surface ﬂuxes

bulk formulasea icechap 14chap 17[surﬄux.F90][bulk.F90][ice̲main̲cat.F90, etc.]

1%

continuity equation(determine vertical transport)

chap 5[continuity.F90]

6%equation of motion(baroclinic component)

chap 7[clinic.F90]

11%equation of motion(barotropic component)

chap 6[surface.F90][surface̲integ.F90][surface̲bcli.F90]

29%

advection of tracers

chap 8chap 13[tracer.F90][som̲adv.F90]

22%

diﬀusion of tracers(isopycnal and diapycnal)

chap 9chap 10[trcimp.F90][ipcoef.F90][ipycmix.F90]

2%calculation of density
stability check and adjustment

chap 4chap 10[density.F90][stratiﬁcation.F90][cnvajs.F90]

2%

preparation for the next time step chap 19[rewrit.F90][surface.F90]

12%

mixed layer model
determine vertical mixing coeﬀ.

chap 15[my25.F90][nkoblm.F90][gls.F90]

1%

output to ﬁleswith speciﬁed intervals

chap 21[history.F90]

termination

Figure1.2 Structure and typical computational cost of components of MRI.COM. Note that the sum of computationalcosts does not become 100% owing to round-oﬀ at each component.

data assimilation schemes. Other component models include wave, river, iceberg, and ice-shelf models. In the interaction
with these models, physical quantities should be exchanged by following conservative lows. Having an interface touniversal couplers and an adjoint code should be mandatory for such a multi-purpose OGCM.
These are the main subjects for developing MRI.COM in the coming years.

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