
COMPUTATIONAL REQUIREMENTS FOR OCEAN ASPECTS OF CLIMATE MODELING

Climate modeling has as its goals the understanding and prediction
of the ocean-atmosphere-ice system from the distant past to the long-
term future.  Improvements in oceanic physical understanding will have
major benefits for understanding in related fields such as geochemistry,
marine biology, marine geology, and global habitability.  The benefits
of accurate climate prediction, including an assessment of the limits
thereof, have potential economic value as large as a trillion dollars
when accumulated over the 21st century, on account of the major climatic
impacts on agriculture and energy usage.  As indicated here, the ocean
possesses a combination of very large computing requirements through
its small but important spatial scales and its climatically long time
scales; so that its computational needs easily rank in the PetaFLOPS
class of potential computing.

The primary length scale for geophysical fluids is the Rossby radius of
deformation, which is the distance internal gravity waves travel before
the earth's rotation impedes spreading of their energy from source areas.
Energy accumulates in steady or slowly varying flows with cross-stream
dimensions as small as the radius of deformation but with along-stream
dimensions (and importance) being of global scale.  Instabilities of
ocean currents, as well as many aspects of the thermohaline circulation,
occur at this length scale.

The proper treatment of both dynamic and thermodynamic processes in
geophysical models requires a grid size that is somewhat less than the
local radius of deformation.  Unfortunately, the oceanic radius of
deformation is only about 1/10 that of the atmosphere and typically
varies from about 100 km to 10 km between the tropics and high latitudes.
This means that grids of ocean models should have about 100 times as
many horizontal gridpoints as dynamically comparable atmospheric models;
and ocean grids should use spacings of small fractions of a degree.
Poleward decrease of the deformation radius suggests using mercator grids.
Recent experience with a global ocean model (POP) at 1/6-degree (average)
mercator grid size has recovered much, but not all, of the variability of
the strong unstable currents; and further experience with an Atlantic-only
model (MICOM) at 1/18-degree average grid size has shown that the Gulf
Stream's separation and its instabilities are properly simulated only when
the grid size is less than about 1/12 degree.  The latter is a target goal
for global ocean models.

An added demand in global ocean modeling is that integrations of 1000
years or longer are required to reach thermohaline equilibrium and thereby
to evaluate properly the models in a climatic context.  By contrast,
atmosphere-only models reach statistical equilibrium is well under
10 years.  The resulting net requirement for ocean-related computing,
both from more grid points and for longer integrations, is therefore a
factor of 10**4 in equilibrium simulations with well-resolved dynamics.
In the following table, the computational demands of progressively
better-resolution ocean simulations run to 1000-year equilibrium are
indicated.  In the likely event that many of these integrations are
conducted with interactive atmospheric and ice models for a complete
treatment of the physical climate system, the computer requirements
would be as much as a factor of two larger.



     POSSIBLE GLOBAL SIMULATIONS ON ADVANCED COMPUTERS
   with parallel ocean models (derived from the LANL/POP*)


Time Frame  Sust. Speed    Horizontal   Number of   Computer
(year);     in teraflops   (mercator)   Levels in   Time for
Needed      (10^12 oper-   Grid Size    vertical    thermohaline
Memory      ations/sec)    in degrees               equilibrium


2000        1.0            1/4 average  20          35 hours
4.0 GB                     (poor res.)

2005        10.            1/6 avg.     40          24 hrs.
18. GB                     (fair res.)

2010        100.           1/8 avg.     40          6 hrs.
32 GB                      (moderate)

2015        1000.          1/12 avg.    80          4 hrs.
144. GB                    (good res.)


Further experiments on a PetaFLOPS machine with terabyte memory:

turbulence (high res.)     1/24 avg.    160        64 hrs.

clim. variation (10K yrs)  1/12 avg.    160        640 hrs.

glacial climate (120K yrs) 1/12 avg.    80         480 hrs.


* (POP = Los Alamos Parallel Ocean Program of Smith, Malone, and
   Dukowicz; MICOM = Miami Isopycnal Coordinate Ocean Model of Bleck,
   O,Keefe, and Sawdey)




The above requirements are representative of the class of ocean
models used in climate applications.  Ocean models typically use
finite differencing of local space-time physics and hydrodynamics;
any many of the algorithms are newly revised with better scalability.
Models are capable of using massively parallel machines up to 1000
processors for present-day large problems, such as global domains
with 1/6-degree spacing and 20 levels.  Domain decomposition in the
horizontal leaves the vertical to be handled within each processor.
However, the nature of the problems requires memory accessability
across all three dimensions in approximately equal proportions.
As horizontal resolution is improved, the number of vertical levels
can be expected to increase comparably in order to treat thin cold
bottom currents that complete the cycle of poleward heat transport.
When the number of grid points increases in all three coordinate
directions, the computations should scale well up to 10,000 processors
for existing algorithms available in both POP and MICOM.  In addition,
development of more complex parameterizations, in order to treat more
accurately the vertical transfer processes, will automatically improve
scalability up to tens of thousands of processors.

Parameterizations will on occasion be usable in the horizontal to
accomplish some fraction of the transfers that are attributable to
mesoscale transients.  Validation of such parameterizations will
require runs of higher-resolution models, since observations are
inadequate for this task.  There remains the possibility that no
fully adequate parameterization will be found, since they have yet
to be found in the analogous atmospheric case.  Furthermore, an
assessment of the effect of oceanic turbulence on the nature of
climate variations will require very long simulations with high-
resolution models.  Thus, model integrations of the type indicated
in the above table will constitute a large fraction of the total
ocean computational effort in the future.

Many aspects of ocean modeling are similar to those of atmospheric
modeling in regard to memory usage, archiving strategy, software
requirements, and so forth.  The principal difference in the ocean
context is that ocean models will be run for much longer simulated
times at high resolution than has been possible in the past.  This
will make the memory needs grow less than speed needs; and it will
affect the archiving requirement in analogous fashion (as long-term
evolution requires limited results to be saved along the way).

In summary, the oceanic part of climate simulations imposes small
space scales and long time scales that dictate a need for PetaFLOPS
computing as soon as it can be developed.  Fortunately, the scientific
and practical benefits from improved understanding and predictive
capability will more than justify the fraction of the developmental
expense to produce such a machine for certain applications to climate.

