<s>
Ocean	O
general	B-Application
circulation	I-Application
models	I-Application
(	O
OGCMs	B-Application
)	O
are	O
a	O
particular	O
kind	O
of	O
general	B-Application
circulation	I-Application
model	I-Application
to	O
describe	O
physical	O
and	O
thermodynamical	O
processes	O
in	O
oceans	O
.	O
</s>
<s>
A	O
hierarchy	O
of	O
OGCMs	B-Application
have	O
been	O
developed	O
that	O
include	O
varying	O
degrees	O
of	O
spatial	O
coverage	O
,	O
resolution	O
,	O
geographical	O
realism	O
,	O
process	O
detail	O
,	O
etc	O
.	O
</s>
<s>
The	O
first	O
generation	O
of	O
OGCMs	B-Application
assumed	O
“	O
rigid	O
lid	O
”	O
to	O
eliminate	O
high-speed	O
external	O
gravity	O
waves	O
.	O
</s>
<s>
But	O
it	O
also	O
filtered	O
those	O
ocean	O
tides	O
and	O
other	O
waves	O
having	O
the	O
speed	O
of	O
tsunamis	B-Application
.	O
</s>
<s>
However	O
,	O
in	O
order	O
to	O
analyze	O
those	O
eddies	B-Operating_System
and	O
currents	O
in	O
numerical	O
models	O
,	O
we	O
need	O
grid	O
spacing	O
to	O
be	O
approximately	O
20km	O
in	O
middle	O
latitudes	O
.	O
</s>
<s>
Thanks	O
to	O
those	O
faster	O
computers	O
and	O
further	O
filtering	O
the	O
equations	O
in	O
advance	O
to	O
remove	O
internal	O
gravity	O
waves	O
,	O
those	O
major	O
currents	O
and	O
low-frequency	O
eddies	B-Operating_System
then	O
can	O
be	O
resolved	O
,	O
one	O
example	O
is	O
the	O
three-layer	O
quasi-geostrophic	O
models	O
designed	O
by	O
Holland	O
.	O
</s>
<s>
In	O
the	O
late	O
1980s	O
,	O
simulations	O
could	O
finally	O
be	O
undertaken	O
using	O
the	O
GFDL	O
formulation	O
with	O
eddies	B-Operating_System
marginally	O
resolved	O
over	O
extensive	O
domains	O
and	O
with	O
observed	O
winds	O
and	O
some	O
atmospheric	O
influence	O
on	O
density	O
.	O
</s>
<s>
Early	O
in	O
the	O
1990s	O
,	O
for	O
those	O
large-scale	O
and	O
eddies	B-Operating_System
resolvable	O
models	O
,	O
the	O
computer	O
requirement	O
for	O
the	O
2D	O
ancillary	O
problem	O
associated	O
with	O
the	O
rigid	O
lid	O
approximation	O
was	O
becoming	O
excessive	O
.	O
</s>
<s>
OGCMs	B-Application
have	O
many	O
important	O
applications	O
:	O
dynamical	O
coupling	O
with	O
the	O
atmosphere	O
,	O
sea	O
ice	O
,	O
and	O
land	O
run-off	O
that	O
in	O
reality	O
jointly	O
determine	O
the	O
oceanic	O
boundary	O
fluxes	O
;	O
transpire	O
of	O
biogeochemical	O
materials	O
;	O
interpretation	O
of	O
the	O
paleoclimate	O
record	O
;	O
climate	O
prediction	O
for	O
both	O
natural	O
variability	O
and	O
anthropogenic	O
chafes	O
;	O
data	O
assimilation	O
and	O
fisheries	O
and	O
other	O
biospheric	O
management	O
.	O
</s>
<s>
OGCMs	B-Application
play	O
a	O
critical	O
role	O
in	O
Earth	B-Application
system	I-Application
model	I-Application
.	O
</s>
<s>
Oceans	O
are	O
a	O
kind	O
of	O
undersampled	O
nature	O
fluid	O
system	O
,	O
so	O
by	O
using	O
OGCMs	B-Application
we	O
can	O
fill	O
in	O
those	O
data	O
blank	O
and	O
improve	O
understanding	O
of	O
basic	O
processes	O
and	O
their	O
interconnectedness	O
,	O
as	O
well	O
as	O
to	O
help	O
interpret	O
sparse	O
observations	O
.	O
</s>
<s>
Even	O
though	O
,	O
simpler	O
models	O
can	O
be	O
used	O
to	O
estimate	O
climate	O
response	O
,	O
only	O
OGCM	B-Application
can	O
be	O
used	O
conjunction	O
with	O
atmospheric	O
general	B-Application
circulation	I-Application
model	I-Application
to	O
estimate	O
global	O
climate	O
change	O
.	O
</s>
<s>
There	O
are	O
different	O
types	O
grid	O
types	O
that	O
can	O
be	O
used	O
by	O
OGCMs	B-Application
.	O
</s>
<s>
Finite	B-Algorithm
differences	I-Algorithm
grids	O
are	O
the	O
most	O
common	O
grid	O
types	O
for	O
OGCMs	B-Application
.	O
</s>
<s>
For	O
the	O
grids	O
,	O
the	O
Arakawa	B-Application
Grids	I-Application
are	O
often	O
used	O
.	O
</s>
<s>
This	O
was	O
only	O
used	O
in	O
some	O
of	O
the	O
earliest	O
OGCMs	B-Application
.	O
</s>
<s>
It	O
is	O
also	O
possible	O
to	O
have	O
a	O
so-called	O
nested	B-Application
grid	I-Application
model	I-Application
.	O
</s>
<s>
A	O
nested	B-Application
grid	I-Application
model	I-Application
is	O
an	O
adaptation	O
of	O
the	O
finite	B-Algorithm
differences	I-Algorithm
grid	O
in	O
which	O
some	O
parts	O
have	O
a	O
higher	O
density	O
of	O
grid	O
points	O
.	O
</s>
<s>
Sometimes	O
models	O
use	O
a	O
finite	B-Application
element	I-Application
grid	I-Application
.	O
</s>
<s>
The	O
big	O
advantage	O
of	O
finite	B-Application
element	I-Application
grids	O
is	O
that	O
it	O
allows	O
flexible	O
resolution	O
throughout	O
the	O
domain	O
of	O
the	O
model	O
.	O
</s>
<s>
The	O
spectral	O
grids	O
are	O
the	O
least	O
used	O
grids	O
for	O
OGCMs	B-Application
,	O
while	O
being	O
widely	O
used	O
in	O
atmospheric	O
general	B-Application
circulation	I-Application
models	I-Application
.	O
</s>
<s>
The	O
vertical	O
grids	O
used	O
for	O
ocean	O
general	B-Application
circulation	I-Application
models	I-Application
are	O
often	O
different	O
from	O
their	O
atmospheric	O
counterparts	O
.	O
</s>
<s>
OGCMs	B-Application
require	O
a	O
long	O
spin-up	O
time	O
to	O
be	O
able	O
to	O
realistically	O
represent	O
the	O
studied	O
basins	O
.	O
</s>
<s>
For	O
OGCMs	B-Application
of	O
a	O
global	O
scale	O
it	O
is	O
often	O
a	O
challenge	O
to	O
reach	O
this	O
state	O
.	O
</s>
<s>
There	O
have	O
been	O
many	O
attempts	O
to	O
decrease	O
the	O
spin-up	O
time	O
of	O
OGCMs	B-Application
.	O
</s>
<s>
To	O
accelerate	B-Algorithm
the	I-Algorithm
convergence	I-Algorithm
of	O
a	O
model	O
,	O
several	O
methods	O
have	O
been	O
proposed	O
.	O
</s>
<s>
A	O
third	O
proposed	O
method	O
is	O
the	O
jacobian	O
–	O
free	O
Newton	B-Algorithm
–	I-Algorithm
Krylov	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
This	O
method	O
uses	O
the	O
matrix-vector	O
products	O
obtained	O
from	O
an	O
explicit	O
OGCM	B-Application
's	O
jacobian	O
.	O
</s>
<s>
The	O
method	O
can	O
be	O
applied	O
to	O
many	O
existing	O
explicit	O
OGCMs	B-Application
and	O
can	O
significantly	O
speed	O
up	O
the	O
spin-up	O
time	O
.	O
</s>
<s>
OGCMs	B-Application
and	O
AGCMs	B-Application
have	O
much	O
in	O
common	O
,	O
such	O
as	O
,	O
the	O
equations	O
of	O
motion	O
and	O
the	O
numerical	O
techniques	O
.	O
</s>
<s>
However	O
,	O
OGCMs	B-Application
have	O
some	O
unique	O
features	O
.	O
</s>
<s>
Ocean	O
modeling	O
is	O
also	O
strongly	O
constrained	O
by	O
the	O
existence	O
in	O
much	O
of	O
the	O
world	O
's	O
oceans	O
of	O
mesoscale	O
eddies	B-Operating_System
with	O
time	O
and	O
space	O
scales	O
,	O
respectively	O
,	O
of	O
weeks	O
to	O
months	O
and	O
tens	O
to	O
hundreds	O
of	O
kilometers	O
.	O
</s>
<s>
Dynamically	O
,	O
these	O
nearly	O
geostrophic	O
turbulent	O
eddies	B-Operating_System
are	O
the	O
oceanographic	O
counterparts	O
of	O
the	O
atmospheric	O
synoptic	O
scale	O
.	O
</s>
<s>
First	O
,	O
ocean	O
eddies	B-Operating_System
are	O
not	O
perturbations	O
on	O
an	O
energetic	O
mean	O
flow	O
.	O
</s>
<s>
Second	O
,	O
they	O
are	O
relatively	O
small	O
in	O
horizontal	O
extent	O
so	O
that	O
ocean	O
climate	B-Application
models	I-Application
,	O
which	O
must	O
have	O
the	O
same	O
overall	O
exterior	O
dimensions	O
as	O
AGCMs	B-Application
,	O
may	O
require	O
as	O
much	O
as	O
20	O
times	O
the	O
resolution	O
as	O
AGCM	B-Application
if	O
the	O
eddies	B-Operating_System
are	O
to	O
be	O
explicitly	O
resolved	O
.	O
</s>
<s>
There	O
also	O
are	O
more	O
constraints	O
on	O
the	O
OGCM	B-Application
's	O
due	O
to	O
lacking	O
data	O
for	O
the	O
ocean	O
.	O
</s>
<s>
According	O
to	O
horizontal	O
discretizations	O
we	O
have	O
unstaggered	O
or	O
staggered	B-Application
grids	I-Application
.	O
</s>
<s>
According	O
to	O
methods	O
of	O
approximation	O
we	O
have	O
finite	O
difference	O
and	O
finite	B-Application
element	I-Application
models	O
.	O
</s>
<s>
There	O
are	O
three	O
basic	O
types	O
of	O
OGCMs	B-Application
:	O
</s>
<s>
Basin-scale	O
models	O
:	O
To	O
compare	O
OGCM	B-Application
results	O
with	O
observations	O
we	O
need	O
realistic	O
basin	O
information	O
instead	O
of	O
idealized	O
data	O
.	O
</s>
