OCEAN MODELING ON 
THE CONNECTION 
MACHINE

Global climate modeling is one of the 
Grand Challenges of computational sci-
ence. The dynamics of the oceans 
greatly influence the global climate sys-
tem because the ocean and atmosphere 
are strongly coupled by fluxes of mois-
ture, energy, and momentum. The 
atmosphere is conditioned by the ocean 
on all time scales ranging through daily, 
seasonal, and climatological periods. 
The ocean is, in turn, conditioned by 
the atmosphere, but its response time is 
much longer, and this inertia tends to 
smooth out high-frequency fluctuations 
in the atmosphere. Oceanic general cir-
culation models are, therefore, essential 
components of numerical models 
designed to address issues associated 
with long-term global climate change.

Modeling ocean dynamics is less com-
plicated physically but more demand-
ing computationally than modeling 
atmospheric dynamics. Longer integra-
tions at finer resolution are required 
because of the much broader range of 
temporal and spatial scales that encom-
pass the relevant dynamics in the 
ocean. The next generation of mas-
sively parallel machines will provide 
the computational resources needed for 
long simulations of oceanic circulation 
at high resolution. 

In order to take advantage of this 
emerging computer power, we have 
implemented a global ocean model on 
the CM as part of the DOE CHAMMP 
program.

 The model solves the 3D primitive 
equations for stratified fluid flow with 
realistic coastal and ocean-bottom 
topography. The code was rewritten for 
the CM based on the Cray version of 
the Semtner-Chervin ocean model, and 
the data structure was reorganized for 
greater computational efficiency on the 
parallel architecture. The performance 
of the CM code is about the same as 
that of the Cray code, which is highly 
vectorized and parallelized to run on 
multiprocessor Crays. 

 Some of the algorithms in the Cray 
code, particularly the barotropic 
streamfunction solver, did not parallel-
ize well on the CM, and we have devel-
oped more efficient algorithms which 
are appropriate for the parallel architec-
ture. In particular, we have imple-
mented a new numerical formulation of 
the barotropic equations, which 
involves the surface-pressure field 
rather than the streamfunction. This 
method is more efficient for both paral-
lel and vector computers. It has the 
advantage of being able to include any 
number of islands in the coastal topog-
raphy at no extra computational cost; 
and it uses a numerical algorithm, 
which is much more stable than the 
original method in the presence of 
steep and rapidly varying bottom 
topography. In addition, we have 
developed a new parallel precondition-
ing method, based on the idea of a local 
symmetric approximate-inverse opera-
tor, which is used in a conjugate gradi-
ent algorithm for the solution of the 
barotropic equations. This precondi-
tioner is very effective in accelerating 
convergence to a solution. The combi-
nation of these techniques substantially 
improves the performance of the code. 
On a half-degree by half-degree grid 
with 20 vertical levels, the surface-pres-
sure version of the barotropic solver 
with 80 islands is about four times 
faster than that of the streamfunction 
solver with three islands, and the full 
code runs more than twice as fast.

 This new implementation of the ocean 
model provides an efficient tool for glo-
bal ocean modeling on parallel 
machines that support Fortran 90. Fur-
thermore, the new surface-pressure for-
mulation of the model should improve 
performance on any parallel or vector 
supercomputer, while allowing for 
more detailed coastal and bottom 
topography in the computational grid. 
With this model we intend to perform 
decade-long simulations by develop-
ing full-scale production capabilities on 
the CM-200 and by running problems 
at modestly high resolution (1/2o to 1/
3o). Then, when the next-generation 
CM-5 becomes available, we will carry 
out higher resolution calculations (1/4o 
and higher) in order to study scientific 
issues such as the global thermohaline 
circulation and the resolution depen-
dence of physical parameterizations. 
Eventually, the model will be coupled 
to a massively parallel atmospheric 
GCM to investigate issues associated 
with ocean-atmosphere coupling.


 Barotropic currents and sea-surface 
temperature after a 4-year simulation 
on a 1/2 deg. x 1/2 deg. grid with 20 depth lev-
els. This calculation includes surface 
forcing with climatological annually 
averaged wind-stress fields, and inte-
rior forcing toward observed tempera-
ture and salinity. The movie sequence 
shows the magnitude of the vertically 
integrated velocity field, where red 
indicates stronger currents, blue 
weaker currents. Western boundary currents in the 
North Atlantic and North Pacific corre-
spond to the Gulf Stream and the 
Kuroshio Current off the coast of 
Japan. Note the strong, wind-driven 
Antarctic Circumpolar Current; its 
detailed course and dynamics are 
largely determined by the bottom 
topography.

Acknowledgement:  Rick Smith, LANL, T-3