A'J ABSTRACT OF TH
Shenq - .ei
in
Analysis
General
by
Ocean
Models
Circulation
Redacted for Privacy
Abstract aoproved:
'oung - June
Han
simulated
stress
wind
Surface
192
1,
and
Stress
Wind
Science
of
July
presented on
Surface
of
Sinulated
Circulations
Master
for the degree of
Lee
Atmospheric Sciences
Title:
THFSIS OF
two-level
OSU
ov
cieneral circulation model is analyzed in terms
atmospheric
It
of its spatial aid temooral cnaracteristics,
shown
is
that the main features of the annual mean field in Morthern
are
Eemisphere
corresponlina
deirees
20
to
10
observational
too
south
of
The oatterns in
positions.
the Southern Hemisphere, however, are dell simulated.
The
mean fields reveal a distinct seasonal variability
monthly
which
the
deoendent
highly
Is
on
Spectral
latitude.
and
cross-soectral analysis of the 3-year time series Show that
eastward
travelina
time
synootic
dominate the variability.
disturbances
scale
The long oerlod disturbances are
symmetric and have no oreferred directions of
The ocean clrcuiations
version
of
the
OSU
simulated
six-layer
by
the
oropaaation.
barotropic
ocean general circulation
model using simulated wind stress are found to
he
larciely
controlje1
by
variabilities
the
of
stress curl f1el.
i1r
the
corresoni1ni
nass
The sesorl
trarisDort
are
larqer than that of the circulation driven by observed wind
stress due to the stroner variability of the curl field of
the
sj'iulated
Planetary waves with westward
wind stress,
phase orooaaation and eastward
constitute
a
najor
cart
rouo velocity are likely to
ot t'e resoonse of a barotrooic
'odel to the fluctuatinq winds.
SURPACE ItNO
ANAIJYSIS 3
srss
AND OCEAM CIRCUIJ&TIOMS SIMUEATED
BY
GENERAL
CIRCULATIOi
MODELS
bY
SKENG-EI LEE
A THESIS
submitted to
Oreon State University
in oartial fu1fi11ent of
the requirenents for the
degree of
Master of Science
Corn'nenCernent June 19R3
APPROVED:
Redacted for Privacy
Ass1stn'Pr&?essor of the Deortient of
Atmoso!eric
Sciences
in chre of njor
Redacted for Privacy
(Acting for U. L. Gates)
Chairin of the DepartTent of Atrnosoheric
Redacted for Privacy
Dean of
Date thesis is
resented
Typed by Shu-Chinq Ru for
July
1,
19R2
S,enc-Wei tee
Sciences
C KNOW L ED G M E 1 T
xoress ny crt1tude to
I woUli 11ce to
for
qtij'ance
his
Dr. Y.-J. Hr
and assistance in this research, and to
Dr. S. K. Esbensen for his valuable comments on some of the
material.
expert
helo
I
also sincerely thank
in
most
of
the
r. W. R. McKie for his
comouter
constructive review of the manuscript.
oroqrarnmjncj
and
TABLE OF' CDNTE'!TS
1.
INTRODUCTflN
2.
DESCRIPTION oF' THE AGCM SIMULATED WIND STRESS
FIELDS AND THE COMPARISON WITH OBSERVED FIELDS
Calculation of surface wind stress in
2.1.
the AGCM
3-year mean wind stress fIelds
2.2.
Vectors
2.2.1
2.2.2 Zonal-corrponent
MeridIonal-component
2.2.3
2.2.4 Curl
Root mean square wind stress
2.2.5
Seasonal Variations
2.3.
Vectors
2.3.1
Curl
2.3.2
I
5
7
11
12
15
18
25
28
32
32
43
SPECTRAL ANALYSIS OF' THE SIMULATED WIND STRESS
Autosoectral analysis
3.1.
Algorithm and method of calculatIon
3.1.1
Autospectra of simulated wind stress
3.1.2
Cross-soectral analysis
3.2.
AlgorIthm and method of calculation
3.2.1
Cross-spectra of selected fields
3.2.2
51
51
51
BAROTROPIC OCEAN EXPERIMENT
The ocean circulation driven by the
4.1.
AGCM simulated wind stress
Seasonal variation of simulated ocean
4,2.
transport
80
5.
SUMMARY
99
6.
RIBIJIOGRAP4Y
3.
4.
56
67
67
71
82
103
(IST OF' F'IURF'S
Daqe
F'iqure
2.1.
SchematIc representation of the OSfJ AGCM's
vertical structure.
22.
Annual mean observed wind stress vectorS,
13
2,3.
3-year mean A(C'-sImulated wind stress vectors.
14
2.4.
Zonal-co,00nent of the 3-year mean AGCMsimulated wind stress.
16
2.5,
Zonal-conoonent of the annual mean observed
wind stress.
17
2.6.
Zonal means of the simulated and observed
zonal-conponent of the wind stress.
19
2.7.
As is ft. 2.4 except for meridional component.
20
2.8.
As 1r fI. 2.5 except for meridional component.
22
2.9.
As in fiq, 2,6 except for meridional component.
24
2.10.
3-year mean ACM-simulate1 wind stress curl,
26
2.11.
Annual mean observed wind stress curl.
27
2.12.
Zonal means of the simulated and ohserved
wind stress curl.
29
2.13.
Root mean square observed wind stress over
(a) 4ortr Pacific (b) Iorth Atlantic Oceans.
(after Willebrand (1978))
30
2.14.
Root mean square simulated wind stress over
qiobal oceans,
31
2,15.
onthly variation of zonal mean of observed
zonal-co'noonent of the wind stress.
33
&
2.16a. Mean observed wind stress vectors for January.
34
2.16b, As in fiq. 216a except for July.
35
2.17.
As in fiq. 2.15 exceot for simulated wind
stress.
37
2.lRa, Mean simulated Mind stress vectors for
2.18b.
ti,ree Ja,uarles.
38
As in fii. 2.18a excert for Aoril,
39
2.lBc. As in fLi. 2.lRa exceot for July.
40
2.181. As in fi. 2.18a except for October.
41
2.19a. Mean observed Mind stress curl for January.
44
2.19b. As in fi. 2.19a except for July.
45
2.20a. Mean simulated Mind stress curl for
46
three Januartes.
2,20b. As in fi. 2.20a exceot for Aoril.
2.20c,
As in fj. 2,20a exceot for July.
2.20d. As in fij. 2.20a exceot tor October.
3.1.
48
49
r.onqituiinal1y averaqeci autosoectra over the
orth Pacific Jcen at 42J (J:34)
3.2.
47
57
LongItudinally averaged spectra of horizontal
stress at 5 latitudes over the 'orth Pacific
59
Ocean.
(1:55, J26).
3,3.
Autospectra at (90, 10!')
3.4.
Autospectra at 4 points over the South Pacific
61
Ocean.
63
3.5,
Autospectra at (160, 42M) (1:69, J:34),
65
3.6.
Longitudinally averaged autospectra of zonalcomoonent Mind stress for the summer and winter
3.7.
3.8.
over the 'lorth Pacific Ocean at 4214.
66
Coherence nd ohase spectra of stress comoonents
for two ooints at (170, 3014) and (160, 3014)
with a east-west separation of 963 Km.
72
As in fii. 3.7 except for two ooints at (170,
3014) and (150, 3014) with an east-west
seoaratton of 1926 Km.
3.9.
74
As in fIg. 3.7 except for two points at (160,
3014) and (160!, 3414) with an south-north
seoaration of 445 (rn,
76
3.10.
3.11.
4.1.
As in f1. 3.7 except for two points at (160!,
341) and (160!, 421) with ar south-north
seoaration of 80 Km.
79
Coherence and onase spectra of zona]. comoonent
wind stress for two points at (.175W, 581) and
(175!, 58N) with an east-west separation of
589 Km.
79
Annual mean streamfunction of the mass transoort
of the oceanic circulation driven b the ACCM
simulated surface wind stress.
94
4.2.
Streamfurictlon of the nass tranoort at day 90
of the oceanic circulation driven by observed
surface wind stress.
4.3a.
4onthly mean streamfunction of the simulated
transoort for January.
90
4.3b.
As in fii. 4.3a exceot for April.
91
4.3c.
As in f13. 4.3a exceot for July.
92
4.3d,
As in fi. 4,3a exceot for Octooer.
93
4.4a.
rirne-lonitude olot of the strearnfunction
alona 344 (J32) for day 190-240 of the
4,4b.
simulation.
97
As in fi. 4.4a exceot for day 300-360.
98
STRESS
ANALYSIS DF SURFACE AIND
AND OCEAN CIRCULATIONS SIMULATED
BY
GENERAL
1.
CIRCULATION
INTRODUCTION
The ocean has long been
Due
Imoortant
an
as
recognized
climate.
earth's
the
in
cofrDonent
'4ODEtS
large
the
to
coverage of the earth's surface and the high specific
water,
of
ocean
the
acts
as
It
heat
and
of
with the atmosphere and the ooleard transoort of
moisture
yonder Hear and Oort (1973)
energy by the ocean currents.
transports
oceanic
the
that
comparable overall imoortance
Thus,
reservoir.
exchange
influences the climate through Its
found
heat
a
heat
as
are
atmospheric
least
at
of
transports.
it is necessary to take into account the hydrosphere
as well as
climate.
the
The
ocean-atmosphere
for
atmosohere
first
model
better
exoeriment
was
done
by
modeling
of
the
coupled
using
a
UCflabe
(1969)
ho
performed a series of controlled experiments to investigate
the problem of ocean-atmosphere interaction.
et
al.
(1975)
carried
out a subsequent experiment with
realistic global qeogreohy and found
the role of oceans.
Later, Manabe
further
evidence
of
The Climatic Research Institute at DSIJ has recently
been devotinq much effort to couol.e a ne 6-level ocean
general circulation model (0GC) to the extstin 2-level
atmosPheric oeneral circulation rnode1(PGCM). Schiesinqer
and Gates (1981) examined the role of the ocean in the
qiobal climate in a series of five
simulations usini the OSU AGCM with different surface
and Gates studied the oerformance of OSU
-far
conditions.
maintenance
of
JGCM first by a hornoqeneous
Nir1ddrIven
ocean
exoeriment
(1982a), then by a baroclinic ocean exoer1nent In which the
ocean is driven by thernohaline forclnq as well as wind
third exoeriment which combined the
forcin (1982b).
OGCM with a mixed layer and sea-ice model is now in
oroqress. The couoled AGCM-OGCM model will then be used In
climate experiments. The main urpose of this study is to
A
examine
the
behavior
of
the
AGCM simulated wind stress
in the coupled model, is to be exoitcitly used hV
the OGCM as one of the major forcinq fields from the
4h1ch
overlyinci atmosohere.
Surface wind stress is
an
important
factor in the
It reoresents the orincipal.
mechanism for the dissipation of atmospheric kinetic enerqy
(Gates, 1979). It also contributes to the ocean the major
part of eneray for maintaininci the semi-oerrnanent currents
Sverdrup (1947)
and the corresoonding mass transoort.
atmosphere-ocean
system,
3
Showed that the mass transport for most of the ocean can be
approximated from a knowledge of wind stress alone. Later,
Bryan (1963) demonstrated, with a numerical model of a
barotrooic ocean, the sensitivity of nass transoort to the
wind stress field. Therefore, in order to get better
simulation of the ocean current and the associated mass and
energy transport, a reasonally good set of wind stress data
is greatly in need.
The first systematic comoutatlon of the
was
made
by
Scripps
wind
stress
Institute of 3ceanography in 194R.
iidaka (195R) later extended the comoltation to three malor
Both computations used only the mean speed
which,
in each direction category of the wind rose
to Hellerman (1965), would significantly
according
10-30%,
underestimate the wind stress magnitude by
world
oceans.
(1967) revised Hidaka's calculation by utilizing
wind roses with both direction ni speed frequencies,
More recently, Han and Lee (191) cornoiled a new set of
monthly mean stress data over the global ocean using
The
clirnatological monthly mean wind data.
uDdated
calculated stress data extended to high-latitude oceans and
revealed many features which were not resolved in earlier
Hellerrnan
anal vses.
Once the wind
stress field is established, it is
ri
desirable
its space-time variability Which might
row
to
contribute to the strong variability as which Is treguently
observed
the
In
Several spectra of wind soeed at
ocean.
certain stations in the surface layer have been documented.
are at stations on the Oregon coast (Erye et al.,
Examples
1972), on the troolcal Pacific island
Pairnyra
(Fiwang,
at weathershio P on NE Pacific (Fissel, 197F), etc.
1970),
ijlebrand (1978) analyzed
wind
of
Including
parameters,
surface
over Northern Jceans and found that eastwari
stress,
ropagatIna disturbances with period shorter than
days
10
dominate the atmospheric variability.
distributution
In the following, the spatial
of
the
3-year mean wind stress and stress curl fields simulated by
the OSU AcCM are reviewed.
are
seasonal
Their
These fields are comoared against the
also discussed.
observational fields whenever available.
wi].l
with
deal
space-time
the
simulated wind stress.
spectral
analysis
variabilities
are
characteristics
Results of
shown.
The next
the
In
auto-
model
driven
by
those
observed
variabilities of the simulated
also discussed.
the
cross-
and
OGCA
with
Streamfunction fields of ocean
mass transoort are compared with
same
of
the last chapter, the
simulated wind stress is actually tested on the
homogeneous stratification.
chapter
wind
simulated
stress.
streanfunction
by
the
Seasonal
fields
are
S
SIMU[ATD WIND STRESS
DESCRIPTIO1 or THE AGC
2.
FIELDS AMD THE CD!PARISDN WIT1 OBSERVED FIELDS
this
In
by
qenerated
the
chapter,
the
surface
0511 AGCM will be described in detail in
terms of mean field and temporal variations.
is
a
field
stress
wind
The JSU AGCM
primitive equation model for the troposohere.
It is
system
with
formulated
in
the 0
vertical
coordinate
a-defined as
a-=( P-P1.) / (Ps-P1)
where P is the pressure, PS
surface
structure
divided
and
top
is
of
the
sletched
in
pressures
P,the
and
model atmosohere.
Fl.2.1.
is level with a- = 1/2.
with a- equals
The interface between the layers
The tropopause corresponds to
0 and the surface is always :iven by 0 = 1.
boundary condition 0
earth's
is
At the center of
each layer are the reference levels 1 and 3
1/4 and 3/4 resoectively,
The vertical-
atmosohere
The
into two layers with equal mass.
the
at
da/dt
=
0
is
cr
=
The kinematic
applied
at
surface and the too of the model atmosphere,
the
The
primary dependent variables in the model are the horizontal
velocity V, temoerature I', and specific humidity q for both
layers, toqether with the surface pressure parameter
Ps-P, ).
The reader is referred to sates _et al,
IF (=
(1971),
Upper
teve%
LeJeI2.°'2
- Level 3,
3/4
layer
1
2.1.
Eatth
surface
reOte!tatt0n of tre OSU AGCM'S
vertt1 structutP
fter sateS et
(1971))
7
(1979)
Gates and Schlesinger (1977), Schlesinger and Gates
for
detailed
The horizontal, grid size
and numerical methods,
lonqitude
of the model's ohysica]. aspects
lescriotion
A B-scheme grid structure is
and 4jr latitude.
adopted in which the horizontal velocity is
oolnt
carried
at
a
that is stagaered one-halt grid length latitudinally
and longitudinally from the coint
variables
where
T,
q,
are carried.
lrand the ge000tential
2.1
5'in
J.s
CalculatIon of Surtace 4tnd Stress in the AGCM
wind
Surface
momentum)
serves
?
stress
as
turbulent
flux
of
of the frictional force In the
oart
lower layer of the AGCM.
(or
It is parameterized by
the
bulk
aerodynamic method
=
where
P4CDV;VS
(2.1.1)
P4 is the surface air
density,
Vs'
the
effective
-
surface wind soeed and Vs the vector surface wind.
The surface wind is extrapolated from the
vector
wind
at
level 3 and level 1 according to the formulae:
Vs = o.7V4 =
0.7(4
V3
(2.1.2)
and the effective wind soeed is given bY
Vs
ax (Vs I
,
6 )
(2.1.3)
R
where G is the gustiness oaraneter (: 2 'n/sec).
coefficient C
drag
Is qlvei, by
Zs
L2(1+3 5000)
CD
The
overno water surfaces
vnr[(I+o.o7(VsL2.5JxIO3 over water surfaces
(2. 1.4)
where Zs Is the surface elevation In meters.
The drag coefficient has been
evaluating
surface
the
wind
parameter
uncertain
an
in
It is knowh to be
stress,
affected by the surface Nind soeed and stability condition.
The
latter
estimation
shown
was
of
monthly
1981).
Reynold,
The
mean
little
very
nave
to
wind
stress
effect
(sbensen
on
and
formulation of the drag coefficient
over water surface In the ACCM Is suggested b
Deacon
and
Webb (1962), and is linearly dependent on wind soeed,
The numerical values of Cp over ocean for various wind
soeeds
are
tabulated
in Table 2.1.
Also included in the
's used h
table, as a comarison, are the C
(1981) (hereafter referred to as HL) and
Han and
Lee
illebrand (1978).
HL took the values for the neutral stability condition from
the
CD
table
given
by Bunker (1976).
from the formulae olven by
4Illebrand calculated
arratt (1977):
-&
= (0.75 +' ô.067 fVs
10
,,
(2.1.5)
Three esti!nates of the cirg coeffic1ert (10
Table 2.1
ACM
ind soeei (rfl/SQC)
a a a ----------------- -
fl
)
arratt
Buncer
a ------------------- flea aaaaaaa
o
-
5
1.00 - 1.35
1.20
0.75 - 1.09
5
- 10
1.35 - 1.70
1.54
1.09 - 1.42
10
- 15
1.70 - 2.05
1.87
1.42 - 1.76
15
- 20
2.05 - 2.40
2.16
1.76 - 2.09
20 - 25
2.40 - 2.50
2.40
2.09 - 2.43
25 - 30
2.50
2.60
2.43 - 2.76
- 35
2.50
2.90
2.76 - 3.10
35 - 40
2.50
3.00
3.10 - 3.43
40 - 50
2.50
3.20
3.43 - 4.10
>50
2.50
3.40
30
a a fi a a a a a a a flaflaa a a
a a a
As can been see, for wind see1 lower than
value
bY
Carratt's
formulae
other two are co,parable.
TI/sec.
the value in
is
25
m/sec,
the
is the sna].lest whereas the
For wind soeerl larger
than
25
GCM was held constant while the other
two continued increasir.
SDeel
>4.10
The large lifference at
higher
not inportant because Such speed Is rarely found
near the surface.
The source-sInk ter!ns in the governing equations
(and
hence the surface wind stress) are evaluated at every sixth
to
time step, that is,
values
once
the ieendent variable.
of
using
hour,
every
latest
the
The wind stress values
were saved every six hours.
Since the observed stress fields recently analyzed
HI
will, be heavily used as the verification of the
(1981)
AGCM's
bY
simulated
stress,
review
briefly
will
e
the
algorithm and data source of their calculation,
data
The primary surface wind
for
used
the
stress
calculation were obtained from the National Climatic Center
.
(MCC).
These data are defined 3fl a 5X5
each
for
rid
of
the
a
subsouare
MarSden
12 calendar months, and reoresent
observed climatoloqical surface winds available up to 1974.
The zonal and meridional comoonent of the wind
at
each
grid
oolnt,
directjon-soeed soace, were computed for
over
average
weighted
a
stress
each
of
the
12
calendar months from the formulae:
(2.1.6)
/
FCiUjCo5i)/flj
=
I-)
where
is the
unnormaliZed
frequency
(probability
of
ii
of wind soeed Uij
occurrence)
j!j is the observed wind In
;
soeed category I and direction category 1;
for direction 1;
f)
Is the air density,
The NCC data set orovides
In
only
wind
mean
the
soeed
and
eight directions (11, NE, E,.,,IW) olus total
standard deviation of the speed.
of
angle
C,is the surface drag coefficient for the
soeed category I and
frequency
the
soeed
for
each
ausstan
A
found
distribution
to
Ive a
lata-soarse
areas,
directionwas
satisfactory estimation of the wind stress.
Seciai care
was
taken
high latitudes.
mainly
in
stress
field
calculated
geostrophically
computed
in
the
This involved a merairtg of the
from
the
ICC
data
with
the
wind stress field, and a spatial
smoothing which removed the possible discontinuity
due
to
the merging.
2.2 3-YEAR MEAJ !IEfDS
We will look at the mean fields of the vectors,
zonal
and meridional components, curl and root mean square of the
simulated wind stress in this section.
the
averages
sImulation.
of
the
The mean fields are
6 hourly fields over three years of
12
2.2.1 Vectors
annual
Fig, 2.2 srows the zilobal distributions of the
stress vector.
observed
mean
the eastern oart of tne
Hemisphere,
and
basins.
the
In
'Jorthern
westerly stress turns c].occwiSe below SON
the
counterclocKwise
southern
ocean
The main gyres are found in
boundary
50M
above
westerlies
the
of
at 3GM in both
is
The northern boundary, however, is at 55'J
oceans.
Pacific
and
equatorward
and
35S
of
in
countercloccwlse
near Antarctica.
clockwise
the
Southern
the
In
stress
Nesterly
the
Hemisphere,
Atlantic.
the
in
6071
The
oceans.
both
in
The
boundaries between westerlies and easterlies are at 30S and
70S.
Fl;. 2.3 shows
vectors.
stress
the
In
distribution
north
the
of
Pacific,
simulated
the
wind
stress is
estwar1 almost everywhere exceot between 4071 and 2071.
cyclonic
gvre
is
found
centered at (175E, 45N) whIch is
about 15 degree south of the observed gyre.
anticyclortic
gyre
defined
and
anticyclonic
In the
gyres
are
exceot that they are 20 and 10 degrees south
of the corresoondinq those that are
means
observed
The
near Morth America Is not seen.
north Atlantic, the cyclonic
well
The
observed.
This
also
that the westerly stress belt is 10 degree narrower.
As shown in fig. 2.2, the annual mean
observed
stress
is
WI.
a...
/ / . / /111?
.
11/11/1/
a-
,,,pr,
4r,d,,,III..
11
/
/
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Annual mean observed wind stress Vectors,
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pa.
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an
P1g.
in
2.3.
au
sin
sis
is.
issu
sasu
asu
MU
SU
S
3-year mean AGCM-simulated wind stress vectors.
I-
15
southwesterly
and weak northwesterly over the North Indian
3cean desoite
the
throuh
November
dominating
!hile the simulated flel.-1 shows
4oril.
northeastely
strong
fairly
this
from
stress
northeasterly
1omtnatini
stress
northwesterly
and
This will be discussed in a later
area.
oart of this Chaoter.
me
fairly
over
Jistrioutlon
well
the
Southern
They
part of the ocean are clearly seen near 305.
east
degrees
simulated
of
observed
the
northward
stress
qyres.
3lon
is
yres on the eastern
The cyclonic
simulated.
Hernisohere
tne
are
1.0
Conseguentiv, the
west
coast
nf
continents is confined to a relatively narrow band.
2.2.2
Zonal component
F'ig, 2.4 shows the global distribution
North
Indian 3cean.
zonal
the
The region between
component of the simulated wind stress,
20M and 30S is dominated b
of
westward stress except
in
the
The oattern is similar to that of the
observed field (fIg. 2.5).
The magnitude Is smaller on the
average, except for eastern Dart of te south Pacific where
a center is found to have a value of 1.2 dyne cm2
,
while the center at aporoximately the same location on
the
observed
field
is 1.0 dyne cm
.
South of 30S, the
UN
?SN
?SN
..:
-1-i-.
.:::::.:
I
-..:
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L
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2
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is
1I
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3.5
4'i
___,.
_-i:-
7" -1. 1I:
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-
7.5
I
31u
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9
3Sf
tij. 2.4.
9.1
9Sf
I
tast
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19.1
I
uS
I
lilu
I
hIM
I
I
1
1
NM
flu
3SM
I
III
Zonal-conponent of the 3-year mean A(CM-simulated wind.
Contour interval is 0.2 dyne/cm2.
The zero lines are
dashed and negative values are stloled.
a'
SON
0N
/)r
\
10$
10$
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50$
705
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0
30E
Fig. 2,5,
SIE
OlE
uSE
ISlE
II
1SSU
1*IU
OSU
SIM
SM
I
As in Fig.2.4 except for annual mean observed wind stress.
30$
iR
eastward stress dominates most of the area with
observed
f1el,
zonat
the
mean
south-shift of the main qyres.
fjq, 2.6.
in
oceans
northern
over
distribution
shown
curve
magnitude
the
but
of
This can be clearly sen
stress is much smaller.
eastward
from
the
to
similar
The pattern is also
fr1ca.
of South
the tb
near
center
maximum
a
The
reflects
again
the
bounds
Fhe north and south
of positive area are 1R and 6 degres south of those of the
observed field.
at
The maximum values of the centers
located
30P4) and (53W, 30) are 0,5 and 0.7 dyne cm
(165E,
compared to 0.9 and 1.3 dyne cm2 for the observation.
south-shift
is
also
Illustrated
by the phase difference
stress
In
high
latitude of Iorth f4emisohere Is
relatively strong comoarel to the observation.
value
dyne cm
-2
center
the
at
dominating
The
'between the two curves shown in fIg. 2.6.
westward
The
of
the
Sea
Berinq
while no value over 0.4 dyne cm
-2
The maximum
is
Is
found
1.2
over
that area In the observed field.
2.2.3
'erjdIonal component
FIg. 2.7 shOws the meridional component (Tv)
simulated
stress.
wind
In
the
Positive values are found north of 15M
over
the
Pacific
the Atlantic.
Morthern
and
of
the
Hemisohere,
east
of
170F
and almost everywhere north of 15N over
Jegat1ve values are mainly on
the
western
80
_____- ØeGER VEO ZØNM.. -CøMPENT
S IPIULATEU Z04.JAL -CØMPØPIEN
70
30
w
IC
10
-to
-30.
-50.
-70.
-90.
i
I
I
-2.0
Fig. 2.6.
-1.5
-1.0
-0.6
0.0
0.5
1.0
1.5
I OYNE/CMN2 J
MAGNITU
Zonal means of the sirnlated (solid lines) nri observed
(dashed lines) zonal-component of the wind stress.
2.0
74.J]
.yJ
r-J
LL
)
f
\
,.:
(
(t
uN
(
:/
/
:
till
a
:
__-
-.----..---
.
4 f/V.
SiS
Sill
/
I
ç
/Y / 1,S.s
,
__7..
:( [l
I
Ut
I
2.7.
SIC
1
liii
/
o
:.
I
SIC
1$.
ISIW
ils
alu
NM
31M
S
As Is F'Ig. 2.4 except for meridional component.
31C
21
long the east coasts of the Asian and
The southern boundary
nts).
area
positive
absolute
The
olace.
same
south
values
observed
the
of
The northern boundary, however,
(fjq, 2.8),
the
deorees
15
is
is
are
general
in
summer
southwesterly
generally oosltive due to the strong
However, the simulated field has a negatIve value
monsoon.
is one of the largest negative values.
dyne cm2 which
Southern
-0.4
The center has a value of
everywhere in tnis region.
the
154.
of
Jcean, the annual mean of observed t y Is
Indian
the
about
at
s].iahtly laroer than observed in the region north
In
the
of
northward
Hemisphere,
stresses
found
are
mainly over the eastern part of the ocean basins.
In
They are
confined in a smaller area with a value larger than that of
the
observation.
maximum found over the Pacific is
The
oth cases have a
The contrast is small over the Atlantic.
dyne cm2
maximum of
1.0
northward
stress
observation.
the
against
4
In
.
weaker
much
is
maximum
of
the
0.5
observed 1.1 dyne cm
Indian
than
dyne crn
-2
instead
field.
However,
because
oriented.
the
of
northward
the
stresses
stress
difference
in
this
in
Ocean,
that
is
of
the
the
compared
The central oart of
the Pacific between lOS and 30S is dominated
stress
dyne cm2
0.58
observed
compared to the
0.90 dyne cri2
as
by
southward
in the observed
magnitude
Is
small
area are mainly east-west
High latitudes are dominated mainly by
westward
50N
3SN
23e
I"
dY
c
.S.N
KO/
::(_ro.}. 1
VEx A
/
:
(1
:
p
IØN
0.
'
1
SOS
eu
1.
s
F1j. 2.8.
As In rig, 2.5 except for merjjonaj component,
23
is almost zonai.
The distribution of observed
stress.
with well defined centers located south
southeast of Africa.
-0.69 dyne cm2
zonal distribution.
the
-0.4 dyne cm
over
value
means of both cases.
cannot
we
see
The simulated maqnitudes are much
has
Dnly a very small area
smaller than the observations.
a
and
The values at these centers can reach
In tne simulated field,
.
Australia
of
-2
Fii. 2.9 shows the zonal.
.
As in tne zonal component,
the
that
simulated wind stress field suffers phase difference in the
north hemisphere and a maznitu1e difference in the Southern
Hemisphere when compared to the observed field.
The wind stress is calculated from the
therefore
surface
wind,
oositioning errors of the rain gyres in the
the
Northern Hemisohere must result directly from the errors in
the
A comoarison between AGCM simulated wind
wind fields.
and observed wind at the surface, 800mb
400mb
(1977).
occur
C 0 =
1/4
)
was
qiven
by
3/4 ),
C
Schlesinoer
and
and Gates
The maximum soeed of the simulated westerlies
did
equatorward to the observed positions at all levels.
The difference is especially evident in July.
However, the
maximum soeed of simulated wind is larqer than the observed
wind,
stress
This contradicts the
fields,
comparison
between
two
wind
This could be due to the exclusion of land
ooints in the present study.
Also,
the
comparisons
made aqatost observational data trom different sources.
were
90
- BSERVED MER!DI2NAL-CØMPØPEWT
SIMULATED PIER IDIaNAL-CØMPØNENT
70
50
30
w
o
tO
I_J
-to
-30
-50
-70
-90
-0.5
-0.4
-0.3
-0.2
-0. t
MANTUDE
Fjz. 2.9.
0.1
0.0
I
0.2
0.3
0.4
OYN'CM*M2
As in Fig. 2.6 except for meriiional component,
Curl
2.2.4
crucial
The curl of wind stress is
in
decldir
liagnitude of nass transoort of the ocean by
direction
and
currents.
The relation between the transoort and the
M=(
'
0
x\
Y " 212C0560
,'
fdpvdz
current:
ocean
is
net
the
(2.2.1)
meridional
transoort
d is e1ual to or ireater than the 1eoth
curl
('Jeative)
(southward) Sverdrup transport.
distribution of the oserve
by
t
raiient becomes zero.
which the horizontal oressure
Positive
curl
Sverdruo (1947):
was first derived b
where M.,
the
corresoonis
northward
to
Ei. 2.11 shows the qiobal
The
annual mean stress curl.
curl, is aooroxlnated as the circulation per area within 5X5
1eree boxes whose centers are the corners of
1ecree
shows
E't. 2.10
subscuares.
distribution of the stnulated curl field.
Hefflisohere,
arsden
the
In the
5X5
olobal
orthern
values are found between 27N and SON
oosltive
(6O
in Atlantic).
The observed maximum centers alonc 60M
are
reoroduced
about
at
magnitudes are smaller,
of
the
the
sane
locations except the
As expected from the
distribution
zona]. component of the stress, the zero lines also
shift south to those of the observation.
The northern zero
geM
9ON
7SN
7IN
EON
SOH
30N
30,4
ION
ION
10$
I'S
30$
3e5
50$
SOS
70$
70$
,u
00$
30
S
35L
FIg, 2.10.
H(
0O
ia.
ISSE
105
15aI
ia.0
oe
cow
S
3$E
Contour
3-year mean AGCM-slmu:Iated wind stress curl.
.
The zero lines are
Interval Is 0.5 X 10
dyne/cm
dashed and the negative values are stippled.
0'
SON
s. .--..-.
d!Z3i-
70N
SON
:::IA
(
(%s.
t4(--_fl.I
,.".:.:
.
30N
1d
ION
los
( (O.52s1
t,7J 'r0.c-
30S
C)
(
c
SOS
'.5
.
.
.
los
9051
30W
0
30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W
Fig. 2.11.
0
30E
In Fig, 2.10 except for annual mean observed wind stress
curl. (after ian and Lee (1981))
s
p.J
28
line shifts iS leqrees, and the southern zero line shifts S
Southern femIsohere, the oattern a'irees
observations
to
In the
narrower than that of 'he observed field,
much
be
reilon
This causes the negatIve
ierees to the South.
zutte well with the
The
in the area between the e'uator and SOS.
observed centers over te Indian ocean are also seen on the
simulated field, exceot the value over the Pacific Ocean is
smaller
io8
1.5
unit
In
tourtd
ge cannot find the zonal distribution as
observed
the simulated
described
ooserved
and
curl,
clearly
are
features
The
fIelds.
We may
here.
illustrated
notice that there seems to be a constant latitudinal
between
shift
the
zonal
phase
mean curves of the curl and the
This
zonal stress comoortent.
variation
in
FIg. 2.12 shows the zona]. means of
field.
above
of
The distribution beyond 50S Is sbmewhat
dyne cm3 ).
noisy,
the
observed
against
(1.0
is
because
meridional
the
of the zonal wind stress is the dominant term of
the curl's magnitude.
2.2,5
Root mean square
The root mean square (rms) wind stress field gives the
spatial
distribution
of
the
energy density.
shows the rms observed surface wind stress over
Fig,
2.13
the
orth
Pacific and Atlantic Oceans, as given bY Wlllebrartd (1978).
He used four years of observational
data
up
to
1976
to
- Z2NAI.. MEAN ØBBERVED CUI..)
ZØNAL MEAN &XMULATW CURtI
.1.0
-0.5
0.5
0.0
MAGNITUDE
1.0
IIOMN-Ø DYNE.'CM3)
ai means of te simulated (solid lines) and observed
ished lines) wind stress curl.
2.0
calculate the surface wind stress and rms stress.
_15
35
.
(a)
25-
(b)
20
4W
60W
Eli.
2.13.
mear souare observed wind stress over
lant1c ice;
ta) North Pacific (b) Jorth
Root
after
value
The tyoical.
0W
1llebrad (1978))
between
Varies
1
and
dyne cm2
3
Maxima are found southwest of the Aleutian islands near 45N
in the Pacific and east of r4ewfounilanl
The
Atlantic.
qlob-1.
is
ienerally less than
found
value bein
oceans,
the
cornoticated.
position
The value
structure
the
of
1
the
30N
and
dyne cm2 , with the minimum
eivator.
the
found
norther
the
In
distribution
The minimum center is
here
in
between
Is a lItte
to
e
at
the
ft haopens to be a maximum in the observed
This is due to the soutnard shift of the
field,
yre
near
5O
distrioution of rms simulated wind
stress is ShoWn in fL, 2,14,
30S
near
cyclonic
In cne North 'Pacific lcean as we mentioned in section
2.2.1.
replaced
The observed
by
the
storm
track
semi-oeranent
(laroe
Aleutian
rms
value)
15
Low (small rms
NH
711$
-I
5.1$
31M2
/
111$
0
C3.
1
rJJ_LL
0
- .-__ / \>\1JLJ
-=:-. ..-'-
(
311
__-.J
:.
791
k'
I
5.1
,2
I-.______
3I
r'1. 2.14.
ss
vu
(J
_____
LIU
.3"
''--S..,---
sn
c\?%'II
,
Tr
us
ui
uas
s
s
3s
I
Ni
Root ilean square sirnilateri wind stress over olohal oceans.
rontour 1ntervl is 0.2 dyne/cm
The lines of
1
dyne/cm
are dashed.
.
32
are
In the Pacific, maxima
value) in the simulated field.
located in the Bering Sea and east of Janan with values 2.8
and 2.1
dyne
Pacific
is
cm2
,
larger
value
The
respectively.
the
over
that over the rktlantic where the
than
maximum value is found to be 1.8 dyne cm2 at locations
in
Morth Sea and east of New Fnqand,
2.3
Seasonal Variations
2.3.1 Vectors
the
First, we briefly zllscrlbe the seasonal chanae of
observed
wind stress field.
of zonal stress
strongly
reveals
deoenzJent
a
rhe study of the monthly mean
with
where a weak
southern
The
almost
all
exceotlons
semi-annual
latitudes
around
semi-annual variation, with
oredorninates,
rrom
mode
for
in the northern high latitudes
variation
505
predominates
maxima
in
are
with the
in
soring
and
fall,
the distributions of the monthly mean
shown in figs.
annual variations,
and
where distinct
603,
and
observed vector field for the 12 'nonths (only
July
1.s
on latitude as seen in fig. 2.15.
annual variation is the oredoninant
latitudes
which
variation
seasonal
January
and
2.16a,o). we can clearly see the
The most consoicuous one is
associated
sian monsoon as seen in the Indian Ocean and west
Pacific Ocean.
The northeasterly
stress
orevails
during
33
2. CI,
12.SS
72.SN
32.5S
52.SN
I .0
0. C
-1.0
2. C
1.0
0.0
-t .0
32.SN
2. 0
52.5S
t.0
D.0
-t.c
72.5S
2. 0
12.SN
1.0
0.
-t.c
J.Nt
1A1'R1
rig. 2.15.
'JIJL1
1øTtDc.0 JArJ
1JLtJL1 'øOt.0
Monthly variation of zonal mean of observel
zonal-conponent of the wind stress. Units
are iyne/cm'
I
I
l-
1! d'I/i
,,,,,
.w1I!l,Z--.-¼
79N
I/.d'// -'\t
1..-
/ /
/
/
.
--.
:
\
L..
rc
/L (
O
'
rOS i
....--../... j , ......,
34
3I
SIN
S's
l's
3.5
31S
5.5
S's
1SS
71$
-+115
91$ 431u
I
31E
lIE
91C
5105
ISlE
ill
151W
111W
91W
514J
30U
trig. 2.16a. Mean observed wind stress vectors for January.
(after Han and Lee (1981))
S
3S
71M
-
-
'
1.-.'tri
.av
k i
-
1$ ri
-"i
\ 1
I
1
1
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I
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,,
i*.,-
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F
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7 V------.-----.--.-.-.---ve
/ Fff
1N
1/IL!\ ,/1\--'
-.----.
tIs
I
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c
J, J
J/'/1\\\\
I -.-...-.-..---.,
31S
/ -.-. /_____------_, -__, ...
-.--.-.--.---.-.---.-.-.
--- .--.- -----.
'.
- -
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,s
'.
1-.-.-.-.--.-.-....-..--.'- -i..
---- --..-,--.-.-..-.--.-.--
'--",'. 'i
71$
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.. '.*.,._..__._.'.,_.,_-._._,
I ' \ '-.-..v'I /
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7.5
,,_._._.-_.-_.__- __.-.-_-_\.'
_._*_.___._.___.._._._
91$
1
1
3S
S
35E
$lC
NE
1SE
ISlE
ill
151W
1IW
91W
51W
31W
6
31C
F1, 2,16b, As In E1g, 2.16a except for July.
'I'
16
November
through
become southwesterly in
their
maximum
until October.
anti
Atlantic
reach
southwesterlies
rhe
gay.
its direction to
rDverses
intensity in July anti then qradually weaken
Pacific
The anticyclonie qvre in the North
experience
also
time while the
then
pril,
counteroerts
dramatic fluctuations with
the
in
Southern
fe!n1sphere
aooear to be semi-permanent.
tine
2.17 shOws the
Fig.
variability
of
zonal stress at latitudes close to those in Fi7.
simulated
2.15.
As
in the observed field, the annual variation is the dominant
mode
latitudes.
most
for
the
In
interestin'
the
Hemisphere.
The
similar to that of the observation at most
Is
However, some distinct
latitudes.
found
Southern
the
only at high latitudes in
variability
Semi-annual variation is found
can
inconsistences
latitudes of both hemispheres.
high
It is
to note that at 50N, the oattern is similar
observed
one
be
to
except the sIan is completely reversed.
This is due mainly to the southward shift of
the
westerly
stress as described in the orevious section.
FIgS.
2.18a-d show the distributions of the simulated
In the
vector fields of January, April, July, and October.
Northern
Hemisohere,
variation
occurs
orevious
section.
the
most
consoicuous
seasonal
the Indian Ocean as mentioned In a
over
In
the
simulated
field,
the
37
2. C
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2.18d. As in Fig. 2.18a except tor October.
35W
I
35$
42
stresses
northeasterly
winter
in
turn
ra'ivally
counterclockwise to northwesterlies as the season roes into
summer,
never
but
This
observed field.
vectors
stress
have
to
caused
has
observed
those of the
southwesterlies as found In the
reach
and
area.
this
over
stress
observed
the
the
icean,
Atlantic
the
anticyclonic qyre is found only durinc3
its center near 231.
ustralia, the nearly
east of
turn
variation with time.
little
clockwise
to
become
zonal
of
Zealand
Mew
in
season
summer
the
In the Indian Ocean and
stresses
cyclonic
June.
show
ocean
in
northward in July.
this northward flow, a distinct
east
The
In the Southern Hemisohere, the
anticyclonic gyres in the eastern Dart of
very
In
micrates
also
yre
cyclonlc
45N in winter to about 35N In summer.'
from
southward
with
field,
found to be well shaoei throughout the year.
never
in
The simulated anticyclonic
3O4 in July.
at
the
yre charvies Its nositlon from
ivre, which is the dominatino 'node In the
is
In
The center of the cell Is found at 45N
month to month.
January,
wind
nean
annual.
almost 0000site direction to
an
flcean, the cyclonic
Pacific
toe
cell
January
Because of
is
formed
It lasts throuhout the
southern winter and aradually fades as the northward stress
turns
back
to
zona].
aqain.
stress field In the Southern
accordance
with
the
Northern Hemisphere.
It Is obvious that the wind
Hemisphere
behaves
more
In
observed field with time than In the
43
2.3.2
Curl
By examing the monthly mean observed curl fields (only
January
2.19a,b), one finds
are shown In figs.
July
and
again
that the most dramatic seasonal variation occurs
the
monsoon
Asian
where a large negative value in
area,
the
summer can change to a weak positive value in
In
the
rteoative
and
the
throughout
year,
remains
values
in
direction
of
relatively
weaker
than
Variation is found only in
The
magnitude.
strength
in
transport during the year.
the
southern oceans, te'nooral fluctuation of
are
unchanged
almost
the maanitude does chanae from
but
season to season, indicating a variation
not
those
in
oattern
the
northern
not
but
the
but
in
curl
stress
the
oceans.
in
the
tine variations in te tropical ocean are
snail, yet it is significant because of the raPid
of
winter.
and Atlantic Dceans, the boundary between
Pacific
positive
in
response
ocean to the wind stress due to the small Coriolis
Parameter.
Pigs.
January
2.20a-d show
the
simulated
curl
July,
and
Dctober.
In
Aorll,
fields
the
riorthern
Hemisohere, the curl in January is generally positive
changes
for
over
to negative in
Ocean
and
gradually
summer.
However,
the
negative
compared
to the observation, due to the model's failure in
the
Indian
value
remains
small,
SON
I
I
I
I
I
I
I
I
I
I
70N
50N
30N
ç
..::'k(::
4'
\ E' 2
'
,
()
."
iON
(4?
á!4J%
-m
'-'
0.5
05
los
'00
'05
30S
1.0
-
505
TOS
90S1
30W
0
30E 6O
90E 120E 150E 180 150W 120W 90W 60W 30W
fl
Contour
Fig. 2.19a, Mean observed wind stress curl tor January.
The zero lines are
dyne/cm3
interval is 0.5 X 10
dashed and the negative values are stippled.
(after Han and Lee (1981))
.
30E
90N
.. ::::::::::::::::::::::'
i::::
.:::::::i
,.çk
70N
50N-'
A: ,°2:
I:h:llii
I
30N
iON
coE'
.:.::Nao-:L,---
3,'(
.--.
)
:.:O..:
:..'.::
F
30S
' r'-'''::'
__s_-_
05
'
50S
i.....
0 0.5.
-?:
'
.1
.::('--
los
90S
30W
0
30E 60E 90E 120E 150E 180 150W 120W 90W 60W 30W
Fj, 2.19b, As in Fig, 2.19a except for July.
0
30E
iI
nu
C)1., ri1J42
3."
,
)
t.N
1J./,
.
.
.
.
'(L
7
..
.
r&
O....
:.:..
.
/
..:
.
"i:
B..
I
i
30w
0
3
SOC
OBE
1205
I
I
ISSE
1$,
1SG
I
I2SU
9
Fig. 2.20a. Mean simulated wind stress curl for
Also see Flq. 2.19a,
three Januaries.
Sw
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N
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HE
95E
1
I
2eE
ISU
180
I
tHU
I
125W
I
90W
L1KfSI
-1N
I
6I
Fig. 2,20c. As in rig. 2.20a exceDt for July.
30W
0
35E
SN
PON
7N
;t4
30N
31N
I SN
ISM
1G5
tis
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I
31E
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Fig. 2.20d. As in Fig. 2.20a exceot for October.
0
50
tniian
Ocean.
Pacific
the
In
to
curl
South
the
to
from
In the Southern Hemisohere,
fields
over
the
Atlantic and east oart of the
Pacific ocean have little variation with
Indian
the
summer as a result of the seasonal mlqratlon of
the main iyre over the oceans.
the
over
and Atlantic oceans, the
oositive area shifts aout 10 deqrees
winter
monsoon
siimrnr
the
simulatinri the strenqth of
Ocean,
Over
time.
the
neative recilon oetween 105 and 305 in
the
January shifts about 15 learees to the north
July
in
and
the maximum value reaches -2.0 cooare1 to -1.0 in January.
distinct.
In the west Pacific Ocean, the variation Is also
The
sign
of
the
curl
is
seasons channes from summer
reversed almost everywhere as
to
(southern)
This
winter.
results from the chare of flow Pattern due to the bulldina
uo of the cyclonic cell east
of
Iew
Zealand
In
winter.
sjqnjflcant variation can be found at the southern
Another
tip of Africa, where the magnitude of the curl becomes very
lare
in
winter.
As
in
the
observed fields, the time
variability in the troolcal area is small both In magnitude
and
pattern.
me
large
values
near
the
northern and
southern boundaries are statistically unstable due
to
the
relatively short period of saroling, and hence they will be
smoothed out when
averages
period of simulation,
are
taken
over
longer
time
51
SPECTRAL A4ALYSIS OF SIMULATED WIND STRESS
3,
In the last chaPter the spatial characteristics ot the
simulated
AGCM
wind
in terms of mean fields and
stress,
root mean square fields, have been reviewed.
We
will
the temporal. characteristics of the wind stress by
examine
means of sPectral analysis of the 3-year time series.
allows
technique
total variance at
periods
conoutation
In
this
study,
from 12 hours to one year are resolved in
ranqing
quantities
selected
This
the contribution to the
of
frequencies.
various
The cross soectra between pairs
the autospectral analysis.
of
are
also
calculated.
This will
the examination of the relationshto between oairs
allo
now
quantities
information
at
various
about
the
of
frequencies, and will also provide
spatial
scales
and
directional
oroperties of disturbances.
3.1
Autosr'ectral analysis
3.1.1
Algorithm and method of calculation
The raw time series consists of 4380 data points
a
uniform time interval of 6 hours.
segments of six-month length
calculated
each.
with
It Is divided into ii
The
autospectrurn
s
for each seqment accordini to the definition In
Jenicins and Watts (1968, hereafter referred to as JW).
The
52
soectrl estimates are tnen averaqel over the it sementS.
For a stochst1c orocess x(t), -t/2<1<T/2, The
samole
spectrum Cxx(f) lefinel for a continuous range of frequency
)
can be exDressel as
2
C(f) = T (x(f)t
(3.1.1)
where X(f) is the Fourier trarsform of x(t)
T/2
X(f)=+J-T/2
X(t)e
2ft
dt
(3.1.2)
(3.1.1) then becomes
1/2
C(f) --
12u'ft
x(t)e
J-T/2
,
jztif'
/
x(t)e.
dt
11/2
By deftninq a pair of new vartaoles
u:t-t'
vt',
(3.1.3)
b ec o me s
T
(3.1.4)
Cx(f)=Jcxx(u)e_124u
where cxx(u) is the samole auto-covariance
function
(ACP)
and is comouted as
1 °
Cxx(U) =
(T-1t41
t4 H (X('t)_)(xCt+tuI)_)dt OIU(T
Jo
(3.1.5)
53
Thus the sar'ole soèctrurn is the Fourier
transform
of
the
By taklnq the inverse transform of (3.1.4), we
samole ACE.
ciet
°°
(3.1.6)
The sample soectrum Is able to tell how
Power)
distributed over frequencies.
is
the
variance
It Is lesired to
produce a soectrum that has smaller variance than
yet preserves the total oower.
Cxx(f),
spectrum
the
raw
This can
orocedure whIch Is commonly
be achieved thrDuqh a smoothir
done
(or
by introducinq a laci window on the ACE.
The smoothed
spectrum Is of the form
C(f)
du
Cxx(U)e.
du (3.1,7)
satisfies
some
-a
-
here w(u) is the laci
properties:
-
..ztfu
W(L4)C(U)e
window
w(0)
(1)
= 1,
which
basic
(2) an even function, and (3)
w(u)= 0 for fu> r,
Jow t&ce the Inverse transform of (3.1.7) and let u=0
o)
I
C(f)4f W(0)ccx(0)
i-co
By use of prooerty (1), we qet
Cxx(0)=jC*(f)dfCx(0)JCxx(f)df
(3.1.8)
hence the total cower (variance of the time series) remains
invariant.
oractice,
In
w(u)O for (UI>
'4
can reclace orooerty (3) by
we
< T), and the ACF needs to be computed
('4
only uo to maximum lag '4.
The behavior of the spectrum is largely controlled
the selection of '4.
If we choose a small
the soectrum will be made small,
look
smoother.
'width
C
width
spectral
window,
main
the
of
and
lobe
eoual
is
the
thus
a smaller
However,
the variance of
soectrum
the
2/M)
corresponding
which
imolles
smoothing over a wide range of treguency, so that the
(difference
between
The most commonly used lag windows
spectrum) may be large.
are
Bartlett,
Tuey
(cosine),
reader should refer to J
(1972)
for
details
or
Parzen windows,
Otnes
and
The
nochson
of the characteristics of these
Parzen
estimator
the smallest variance, and tre Tulcey estimator has the
Lowest bias.
of
(1968)
and
In general, for a given '4, the
windows.
has
more
bias
estimator and the true
soectrum
the
will
means a larger base
'4
of
to
'4
b
the
e choose Tucey
preference
of
its
inlow in this study
because
low-bias characteristic,
The
algebraic exoresslon for the Tuey window is
W(u)
=
o.(IcoS) IIM
to
IuI>M
(3.1.9)
55
and the corresponiinq sDectral window is
can
The variance of the sioothed soectrum
(75M/T)%
unsiioothed
the
of
be
reduced
to
In this Study, we
soectru'n.
choose M to be 25 days, theretore, the variance is
reduced
to about 10% of that of the raw sDectr']m.
Equation (3.1.7) can be written in discrete form for a
batch of discrete tyoc data
f)=
2t{co)+ 2Z cc((tQW(K)cos(2lTfKAt)j
(3 1.11)
Ic*
where
t
calculate
is
the
of frequency, i.e.
Then
interval.,
r
equals
M/t.
We
only over the oosittve half of the ranqe
Cxx(f)
function,
ttre
0<f<i/24t
the
value
since
Cxx(t)
is
an
even
is doubled as is necessary to
preserve the transfori, relation between sample soectrum an
sample ACF.
In (3.1.11) cxx('c) is calculated as
N-K
(XtX)(Xt+KX)
C,oc(p)=
Of(N-1 (3.1.12)
t=I
where N = T/At, which is the total number of data
oolnts;
and the lag window (Tuey) is
W()=
K>L
(3.1.13)
si
The
confidence
95%
interval
estimated
also
Is
by
calculatinq the lower and uooer limits of the Interval:
V
(IO5)
J1
((I_0.95)
where
the
is
)
'
degrees
estimator,
spectra].
window.
and
is
randoi
the
is
of
freedom
(3.1.14)
smoothed
to 2.667N/L for Tukey
equal
distributed
variable
chi-squared, with probability
the
for
as
Taking the logarithm of
.
(3.1,14), we oet
log C(f)* log
log C(f)+tog5
,ç(i_.95)
2.
expressions
The second parts in both
hence
frequency,
confidence
the
scale,
of
olot the soectrum on logarithmic
we
if
indeoendent
are
interval
is
constant
for
all
frequencies and can be indicated by a single vertical bar,
3.1.2 Autospectra of the simulated wind stress
fig.
In
3.1
wind
meridional
longitudinally
increase
maximum
the
the
of
The
SQectra
have
been
and
averaged
over S points from 140E to 120W in order to
statistical
resolvable
stability.
frequencies
The
are
(4ygujst frequency) which correspond to
365
zonal
components over the 4orth Pacific
stress
are shown.
¶Jcean at 42
autosoectra
the
days and 12 hours respectively.
minimum
and
2Nt
and
Deriods
of
Fhe soectra are lower
'57
I
$
.0
-------'N:\
.5
0
U
N
a.
0..0
I
I
N
1
*
U
'3$
2 -1. 0
0
-I. S
p.-
U
'3$
a.
ZØNAL CØMPØNENT
U)
-2. 0
(0
(0
PIERIOIØNIu.. COMPOt.4NT
(3$
p..
10
-2. S
-3. 0
4
-3. 5
-3.0
-2.5
p
p
-2.0
-1.5
-2.0
LØG FREQUENCY
F'ji. 3.1.
-0.5
ICPO)
0.0
0.5
Conqitudinafly averaqed autospectra over
the Morth Pacific Ocean at 42N (J34),
The 95% confidence interval Is indicated
br the vertical, bars,
1.0
)2
than 10 ('dyne/cm2
/pd vlrtuauv everywhere with a sharp
drop at 0.28 cpd which corresooids to synootic scale of 3.6
iays.
a
The 'drop of power is almost linear with frequency on
scale,
log-log
significant
No
The soectrum of observed
frecuency.
(Willebrand,
oea
is found at any
wind
stress
at
1978) shows a much flatter shape with a sharp
The power is mucr larger than that of the
droo at 0.3 cod,
This is
stress, especially at high frequencies,
simulated
probably due to the inability
meso-scale
43I
simulating
coarse-resolution model.
Also,
moving
fast
disturbances
scale
small
or
of
43N
heopens
by
be
to
a
the
latitude of maximum ooserved rns stress in constrast to the
minimum rms stress in simulated fields.
soectrum
The
of
the zona]. comoonent is larger than the meridional comoonent
only for frequencies lower than 0.035 cod (28 days).
is
true for most latitudes in the North Pacific.
the stress soectra for
the
observed
This
However,
component
zonal
is
larger for all freauencies.
3.2 displays the wind stress
rig,
at
five
different
are similar except
frequencies
is
at
62N
where
much more rapid.
stress field (fig
nultiole-center
latitudes from 26
the
magnitude
in
the
The shaoes
to 62N.
decrease
at
high
The structure of the rms
2.13) is reflected here.
nature
soectra
rns field
Due
,
judoe which latitude has the maximum averaged
to
the
it is hard to
enemy,
but
S9
2. C
i.E
N
-
a
a.
(I
z
N*
*
E
U
U
0.0
z
a
< -0_s
I-
LI
U
a.
w
J
30 LT 26
-J. 32
-J 34
01
Id
LAT. 34
LAT 42
Ilb
-l.5
-2. 0
3.0
-5-.-L5-L0 -.s
FREOtJENCY
F'i, 3.2.
.s
ICPO)
tonq1tudina11.y averaced spectra of horilatitudes over the
zontal stress 3t
North Pacific Ocean.
.0
it is clear that the northern latitudes have large energies
than the southern latitudes.
case
in
higher
at
iroos
s3ectra
rhe
latitudes.
lower
the
2N are larger than those
3.2. the spectra at 54P4 and
fIg.
at
Tnls Indeed Is
frequencies have virtually no difference for all latitudes.
rhe sPectra of selected oints over the North Atlantic
Ocean
reveals
those
on
very similar shape and energy level with
a
about
Pacific.
the
the soectrun over the North tnciian ocean exhibits
owever,
spectra
illustrates
3.3
Pig.
pattern.
different
a very
over
latituies
same
the
a oolnt at (90E, iON), just east of Sri Lanka.
of
As exoected fron the rms stress field, the enerqy level
very
the
80th
especially for the neridional component.
low,
Is
Components show a significant Deak at the diurnal frequency
day).
(one
troolcal
the
In
atrnosohere,
iependinq
islands
the
lands,
and
atmosoheric
geographical
the
on
Parameters
(Houze et al., 191).
attributed
to
diurnal
are
Jver
mechanisms
possible
variability is evident due to several
location,
Over
variations
many
controlled by land-sea breeze
the
ooen
oceans,
they
are
day-night differences in the radiative
the
surrounding
or near
of
heating profiles between the thick cloud covered
the
diurnal
a
area
and
clear air areas (McBride and Gray, 1980).
may
Atmospheric
tide
variability
althouah
also
contribute
to
it Is relatively weak,
the
diurnal
In the AGCM,
61
U
0
a.
o
N
I.
B
1.
0
0.
S
o. 0
-
g
I
N
I
*
\
r
U
'S
lii
z -t. 0
>.
0
-1. S
I-
U
Id
a.
ZNAL CØMPØNENT
'A
-2.
'A
U,
Id
---MERIOINAL CØMPØNENT
-2. :
-3.
-3.
-3.0
-2.6
-2.0
-1.5
-1.0
LØG FREQUENCY
Flcj. 3.3.
Autosoectra
-0.6
ICPDI
0.0
0.5
t (90E, iON) (I55, J:26),
1.0
62
characterlstics
the cloud effect and the diurnally varying
ocean point Is the existence of cloud.
ootnt
selected
(l75,
Pacific
not
does
be
the
fowever, the effect
because
out
ruled
the
is surrounded oy large land mass, besides,
another point
at
6S)
such
Show
the
a
center
strong
of
eguatorlal.
peak
at diurnal
'jg. 3,4 shows the soectra of horizontal stress
frequency.
'iagnItude
cannot
contrast
of land-sea
over
frequency
diurnal
at
resoonsible for the peak
echantsm
The nost likely
of solar radiation are included.
four ooints in the South Pacific alon
at
The energy level increases with latitude
except
175'.
385,
at
just east of New Zealand.
lthouah the data period is only 3 years, it is
oossible
oeaks of longer nerlod C at least to
resolve
to
the annual cycle) if there exists one.
we
still
ror
ourpose,
this
have to use a much narrower window, i.e., larger M,
To
averaae
of
avoid large cornouting tine, we first take
the
every four consecutive data to get a time series of one day
interval.
be
365
Then choose the maximum lag for Tukey window
days.
By
doing
this, the degrees of freedom is
largely reduced, hence a wider 95% confidence
expected.
One
point
arid
interval
is
in the west Pacific Ocean on 42N is
selected for this analysis.
iagnjtude
to
The
soectra
of
both components are calculated.
the
stress
n average
over frequency bands of different lengths is done for every
63
2. 0
1.
1.0
0
-
0.
LI
N
*
0.0
N
*
*
I) -0.5
hi
z
a
-1
0
I(-I
hi
a -*.s
J. 10
-,J 14
U)
U)
U)
lii
LAT 545
LAT JBS
LATE Z2S
-.J 1$
--J 2
LA!.
-2.0
-1.5
65
-2.0
-2.5
-3. 0-1--
-3.0
-2.5
-- I
-0.5
-1.0
FREQUENCY
3.4.
Autosoectra at 4
Pacific Ocean.
0.0
0.5
ICPO)
ojnts over the South
.0
64
Spectrum estimate In order to ootain equidistant spacing on
a logarithmic scale and to eliminate the wiggles at
3.5, annual oeas are found
s shown in fjg
frequencies.
cornoonent
meridional
The
uncertainty.
though
co'nOonent,
in the stress magnitude and Zonal
great
higher
wIth
not
does
exhibit a significant annual oe&c, however it has a neaK at
and the behavior of this
dynamics
The
cycle.
half-year
The arrival :ycle is stronger In
fluctuation are riot clear.
This reveals the
magnitude than In the comoorients.
stress
Since
1978).
wlllebrand,
tne
of
nonstattonary criaracter
wind
simulated
the
field
magnitude
stress
only
positive quantity, the annual cycle is distinct
Is
C
a
when
fluctuation of the comoonent stress is much stronger in one
we
the
repeat
verify
To
season than in another six months later.
this,
procedure used in obtaining the spectra jn
tjg, 3.1, except that the soectra are not averaged over all
the
segments
11
months oerlod in
but
the
over
year.
those containing the same six
'our
winter
o'ier
5
oojnts
The
summer
for
The energy level
all
for
Those
frequencies.
soectra for the other two seasons (not shown here) are
somewhat in between.
over
longitudinally.
and summer are shown In fig. 3.6.
Is higher in winter than In
obtained
Again, the spectra
roughly reoresenting the four seasons.
are averaged
are
spectra
all
seasons
illebrand oointel out that averaging
would
distort the spectra shape in the
oresence of nonstationarity.
However,
If
all
the
other
65
2. 0
1.0
0.
a
1)
0.0
N
*
*
'.5
I-
Li
w
Q.
U,
-STRESS MA(3NITLJDE
-2. 0
ZØNAL CØMPNEMT
U,
U,
MERLDIZNAL CØMPØNENT
La
I-
-2.5
-3.0
-3.5-F
-3.5
t-
-3.0
-2.5
-2.0
-1.5
-
-1.0
FREQUENCY
Ft, 3,5.
-0.5
0.0
0.
(CPO)
Autospectra at (160, 42M) (1=69, J=34).
.0
6!,
a. U
t.
S
I. o
0.
0
a.
U
N
0. o
\\
I
N
*
0.
I
U
Id
z -i.
o
0
1.
S
I-
U
U
a.
SUiIMER
4
-
9
---------WTNTER
10
-
3
(a
-2. 0
Cl)
(a
Id
IU)
S
-3. 0
-3. S
-3.0
I
-2.5
F1, 3.6.
-2.0
-1.0
-0.5
LG FREQUENCY
ICPO)
-1.5
0.0
0.5
1.0
Longjtujna11y averaqed autospectra of
zoh1-co'nporent 4ind stress for the swnmer
1nter over the 4orth Pacific 'Dcean
and
at 42M.
such
characteristics,
the shaoe, remiln unchanied for
as
nd
all seasons, as in the oresent analysis
averaing
the
atmosphere,
ouli
and will
justified
e
real
the
In
increase the statistical stability.
Cross-soectral analysis
3.2.
3.2.1
lqorithm and '4thod of calculation
The sample cross soectrun is defined as
C42f) = TXI*(f)X2(f)
for
two
time
wnere
-r/2<t<T/2,
conjugate.
series
and
x1 (t)
x2 Ct)
astertsc
the
(3.2.1)
In
denotes
ranoe
the
the
comdex
similar steps as in section 3.1., we qet
B
(T
C12(f) =
-121rIU
(3.2.2)
c,2(u)e
I
i-T
where c12 (u) is the sample CrOSS covariance function (CCF')
and is defined as
Tf2-U
(X1(t)-
C42(u)=
=-I
1)(X1(t.u)-Xa)ctt,
(x1(t)_1)(X(kiu)-
IUI >T
1)cjt,-TUO
o
=
The inverse transform of (3.2.2) Is written as
(QO
C12(u) =
I
-r
(3.2.3)
121rfU
C42(f)e.
(3.2.4)
Since C12 (f) is a coolex function, it can be written as
C12f) = R42(f) -
(3.2.5)
G12(f)
where R12 (f) is an even function and
G,.
(f)
is
an
odd
The samPle amolttuie and ohase spectra are then
function.
defined as
+ G(f)
A2'+)
(3.2.6)
tQr(-Gl2(f)/Rl2(f))
F12(f) =
F'roni (3.2.4) and (3.2.5), we qet
Ci2(u)JRiz(f)COS(2flft4)df +5 c2(f)si n(214u)4f
(3.2.7)
the first and second terms on the rtqht hand side reoresent
the
even
oart
respectively.
r
Cu)
and
odd oart q12 Cu) of the CCP,
They can be obtained by
definition
the
of
CCF:
2(u)
=(C;2(u)+Caa(_u))=JRia(-f)COs(21T-1u)f
-
g12(U)
By takjn
C12.(-i.0)
JG12(f)sin(21rfu)df
the inverse transform of the last two
equations,
we can calculate the value of R12 (f) and C12 U) as
R12f)
Jz(U)COS(21fU)dLA
(3.2.9)
G12(f)
912(u)Sin(2i$u)4U
Thus the anolitude and phase soectrun can
be
obtained
by
estimates,
introduce the la windo W(U)as a seibt1nq function,
qet
To
(3.2.6).
srnoothel
a
soectra].
we
JT5(21rfu)d
R12(f)
(3.2.10)
%(U)W(I.4)SIfl(2lTcU)dU
G12(f)
rd ohaSe Soectra are then
The smoothed ampliturle
by
reolacinq
(3.2.10).
R
It is
and
,
in
(3.2.6) 4ith
often more convenient
to
I2
obtained
inzi G12 in
calculate
the
sauared coherency soectrum defined as
(3.2.11)
K12(f) =
where C
U)
C22
(f) are the frequency soectra for
series x1 Ct) and
the previous section.
time
x1 (t)
resoectively as descrIbed In
discrete farm of the above equations for
estirnatini the smoothed cross soectra are similar to those
for autospectre, hence they are not described here.
The
JW showed that art estimator 112. U) which takes the
inverse hyperbolic tanqent value of coherency
121 will
have a variance which is controlled only by the s'noothlnq
factor (variance ratio) of the inoosed window, and is
relatively jncieoendent of frequency. qence, the confidence
K
interval can
be
reoresertted
b
a constant interval on the Y
7°
will
this
The coherency soectra to he shown in
scale.
be
in
scale.
Y
The
5%
sectinn
interval is
confidence
a vertical, bar.
calculated and illustrated b
frequency
certain
(f) at a
E'or squared coherency
t, we have
Y z U)
.L
arctanh J K,2 U)J
2
fttKaI(3212)
1-
and the 100(1- c)% confidence interval, is
/.
Yz(f) ± 2 (1 --a-)
2 42T
where + 7(1 -
)
(3.2.13)
is the range
which
in
the
100(1- a
chance that a random variable with normal distribution will
is 1.96 for
fall, the value of
I/IT
the
is
phase
of
95%.
for a specified w1ndo, and Is
variance ratj
O.75M/T for Tuky
probability
a
window.
The
Interval
confidence
for
soectral, estimates depends on the coherency estjmate
and the deqrees of freedom of
used a diaqram
rovjded in J
a certain frequency.
represented b
of
soectra
estimate,
We
to determine the interval, for
Several Intervals are calculated
and
vertical bars at corresoondinq freauertcies.
The raw ttie series are
seqments
the
12-month
divided
each.
rhe
Into
cross
S
overlappinq
soectra
are
n averaqe over all
senments
is made for squared coherency and phase soectrum,
F'inallv,
calculated for each sement.
71
and
the confidence intervals are evaluated for Y estimator
ohase spectrum.
3.2.2 Cross soectra of MInd stress components
the
perform
to
soectral analysis.
cross
the
often hard to Interoret
spectrum
cross
orovides
one-field
the
cross
The
a certain oatr of quantities.
for
prsented
are
that
soectra
However, It Is
that
information
series
time
There are many ootions for selecttnq two
here
are
tn-noint,
The "one-field" Is eithe.r
tyoe of correlations.
the zonal. or meridional co"oonent of wind stress.
Ca) Two ooints of east-west seoaration
Two ooints, at lonItuies 160E (t69) and hOE (1=71),
on
latitude
are
30
shown
are
In
coherences
The
east-west distance of 953 Km.
differences
They are separated b
selected.
fIg. 3,7,
arid
an
phase
The coherences for
zonal stress are very high for lower frequencies.
There Is
a distinct peak at 0.28 cod (3.6 days) which corresoonds to
the
time
synoptic
scale.
The
overall
coherence
for
meridional stress is low except between 0.16 cod (6.3 days)
and
0,33
frequencies
cod
(3
days).
The
low
coherence
at
htoh
could be either due to noise of any kind or to
the destructive interference amnonq different wavenumber
in
72
'B'
2'
6'
Id
to
I
Q.
-6
-12
-18
2.0
1.8
1.6
'.4
1.2
1.0
0.6
0.4
0.2
0.0
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
LØG FREQUENCY
rig. 3.7.
-0.5
0.0
0.5
1.0
ICPO)
Coherence and phase soectra of stress
comoonent for two points at (170E, 30N)
and (160E, 30N) with a east-west seoaration of 963 (rn.
The Y is the inverse
hyperbolic tanrlent of the coherence. See
text for detail.
73
a
process
sucgested
The latter was
broad wavenumoer bandwidth,
of
tllebrand
by
of
the
disturbance
from
analysis
his
in
ooservational data.
If there is a net prooagation of
one
ootnt
spatial
occur.
Otherwise,
respect
to
another,
to
phase spectrum of
symmetric
is
with
that connectes the two ooints.
The
indicates
the
stress
both
co'noonents
ohases
The
asymmetry.
east-west
chase difference will
disturbance
the
line
the
a
a
nearly
re
for
-190
about
to
It decreases
periods longer than 15 days,
zero
The negative ohase value
0.53 cpd (1.5 days).
degrees
at
means a
lag
of
the
first
calculation)
to
the
second point, hence indicating a net
eastward oropagation,
meridional
The la
at
for
the
comonent indicating the association of smaller
wavelength fluctuations.
value
this
in
distinct
more
is
point
(east
ooint
positive
to
The sudden increase
higher frequencies is due to the use of a single
branch Ot the multivalued arctan function in a comPuter and
should be recognized as continuously decreasing,
Fig. 3.8 shows the results
above
exceot
doubled.
the
The
between
distance
coherency
estimates
apoarently
components
are
estimates.
However,
it
of
is
lower
same
the
the
process
as
3oints
is
two
for
both
than
the
interesting
to
stress
orevious
note
that
.74
too.
120.
60.
Iii
(I)
I
0.
a.
-60.
-*20.
-180.
Itt
I It tt ,ittj t1
I
U
1.8
1.4
1.2
1.0
0.0
0.5
0.4
0.2
0.0
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
L0G FREOUENCY
Eig. 3.8,
-0.5
0.0
0.5
1.0
ICPO)
As. In F1Q, 3,1 except for two Points at
(17O, 30N) and (1SOC,30N) with an east
west seoaration of 1926 Km0
75
meridional stress is i1.rnoSt uncorrelated for
the
although
most frequencies,
cod
0.16
at
peak
the
clearly
still
exists, but with lower coherence.
(b) Two ooints with south-north seoaration
seoaratei
The same analysis for two points along 160E
by
a south-north distance of 445 Km are shown in fig. 3.9.
when
The stress components act differently
found
also
ohertomena,
(wjllebrand, 1973), can
states
which
theory,
entire
the
almost
larger coherence for
This
in
that
points
two
the
Period (4 days).
for
all
are
except at the
difference
is
h
the
turbulence
correlated at the synoptic
Indicatina symmetric structure with
are
synootic
The coherences
from fins,
of
the
generally low for higher frequencies
scale
of
3-5
jays.
phase
The
slightly negative between oeriods of 6 days
and 30 hours, Indicating a southward propagation.
see
zero
The ortase dIfference Is essentially
frequencies,
comoonent
atmosphere
The meridional components
respect to south-north wavenunber.
zonal
real
loogituilnal correlation
tme
well
hand.
frequency
the
predicted
he
exceeds the lateral correlation.
at
with
The meridional comoonent now has the
case.
orevious
the
comoarel
e
can
3.7 an 3.9 that no matter what orientation
the calculation is based on, the zonal component is
more 'red' than the meridional co'noonent.
always
76
-so.
ZNAL CI1PNENT
-120.
- MERrOZONAL COMPONENT
-180.
2.0
i.EJ
1.6
'.4
1.2
I.0'
0.8
0.6
0.4
ZONAL. COr
P4ENT
- MERIOOP4.t.. CeI8NENT
0.2
0.0 is-. i-i
-4.0
i-s
-3.5
us
-3.0
s-Ft-i $1) I it I( Iii, Iii., 1'
-0.6
-1.0
-1.5
-2.0
-2.6
LØG FREQUENCY
Pig. 3,9,
0.0
0.6
1.0
ICPOJ
As in Pig, 3,7 excePt for two points at
(l'6O, 30N) and (16O, 34N) with a southnorth separatIon of 445 cm.
77
F'lg.
3.10 Shows the results of the same orocess
with
fr
both
(890
distance
doubled
co'noonents
decrease
frequencies
of
The
Km).
Yet the
frequencies of the zonal component.
synoptic
oertoi
sane
the
soacing
scale
for
3.7,
cornoonent,
disturbances
the
at
oeaI
the
By
e firtd that for about
between 2 ooints, the coherence is much
zonal
larger for the
lower
at
the zonal comPonent still exists.
in
3.10 with fig.
comparing fjq,
and
comoonent
higher
at
esoeclally
rapidly,
meridional
the
coherences
is
indicating
larger
spatial
the
in its east-west
direction than in its south-north direction.
In an attenot to resolve the signal of longer oeriods,
we
again
modify the original time series as we dii in the
1/8 of
autospectral analysis, eccept the size is reduced to
its original size by tainq te average of 8 data in a two-
365
days
of the window is chosen to
The maximum la
day oeriod.
(or r:183).
rwo points at 175W and 175E on 58I,
seoarated by east-west distance of S89
The
spectrum
of
frequencies
K!n,
are
zonal stress is shown in fjq
overall coherence is high.
low
be
The most distinct oea
corresponds
to
the
3.11.
The
at
the
annual cycle.
phase is generally small, indicatina a symmetric
of low frequency disturbances.
selected.
The
structure
7
too.
120.
60.
Ia
ID
I
0.
a.
A
I
-60.
1'
-120.
'I
PP4ENT
ZONAL
- PIERIOIONAL COIIPONENT
- too.
t-, il
itt-It ill ttlll St ijii.iti ii 1111111 lIt
i-I-I--i-
2.0
I.e
1.6
1.4
1.2
l.a
0.0
0.6
0.4
ZØNAL C0NENT
- PREO10NAL. C2PNT
0.2
0.0
P.O
-3.6
-3.0
-2.6
-2.0
-1.51 -1.0
LØG FREOUENCY
Fig. 3.10.
-0.6
0.0
0.6
1.0
ICPO)
As in Fig. 3.7 exceot for two oolnts at
(1'60E, 34fl artd (160F, 42w) with a southnorth separation of 90 Kt,i,
79
teo.
20.
60.
U
U)
I
0.
-50.
- 20.
- lea.
2.4
2.2
2.0
I.e
1.6
1.4
1.2
l.0
o.a
0.6
0.4
0.2
0.0
-4.0
-3.5
-3.0
-2.6
-2.0
-1.6
-1.0
LØG FREQUENCY
3.11.
-0.6
0.0
0.5
1.0
ICPO)
Coherence and ohase spectra of zonal
comoorient wind stress for two points at
(175w, 5N) arid (175E, 58) with a east
west seoaration of 59 Km.
RO
ExPRIMEM'r
BR3TR3PIC QCA
4,
The large Scale ocean circulation Is primarily
by
atmospheric
the atmosphere.
stress and the exchange of heat with
Certain processes in the earth's hvrologlc
affect
that
cycle
wind
driven
the
such
salinity,
evaporation.
as
Imøortant
an
precipitation and river runoff nay also play
In recent years, numerical modeling techniques have
role.
study
become Increasingly useful for the
ocean
scale
numerical modeling for the ocean
those
from
for
te
orinciples of the
basic
The
circulations.
atmosphere.
different
much
not
are
large
these
of
primary
However,
difficulties exist due to currently limited knowledge about
processes,
process.
In spite of the
coarse-grid
with
reproduction of 'nany
features,
Indicating
difficulties,
ocean
lobal
of
that
some
models
observed
the
turbulent
subgrld-scale
the
e.g.
oceanic
experiments
ocean
good
show
do
large-scale
the coarse-resolution model is
capable of simulating some large-scale processes.
The homogeneous wind-driven oceanic circulation
has
been
shown to be successful in describing the general
characteristics of the horizontal circulation.
ocean,
model
the
most
striking
feature
Intensification of the circulation.
is
In the real.
the
western
The pattern exists
in
each ocean although the basin differs in shape, topography,
stratification and pattern
stress.
wind
of
that tre ocean circulation is governed by a set of
suggest
simple
the factors which vary among ocean basins.
of
those
The homogeneous model is able to expose
constraints
rorthermore, when the model
elementary way.
most
the
relatively
are
which
constraints
nowerful
Vet
independent
in
might
This
fails to Predict some feature well, the physical cause
be
related to the absence of stratification or to
roughly
any simolification made
wind-driven
model
Of
many
including
the
roles
friction,
has
factors
In
the
in
t000graphy,
on
the
The
model.
h,mogeneous
been extensively used to study the
-effect,
bottom
works
previous
can
general
ocean
effects,
nonlinear
good
etc.
circulation,
bottom
review
of
ocean circulation Is
homogeneous
given bY Welander (1975), although only
analytical
models
are included.
In this chapter, the barotrooic
six-layer
OCCM
version
euatton
The OSU-OGCM is
at
global
boundary
each
model
OSIJ
a
model in which the ocean is vertically
divided up to six layers of unequal mass depending
depth
the
Is tested, in which the ocean is driven by
the AGCM simulated surface wind stress.
primitive
of
ocean point.
extends
from
on
the
The horizontal domain of the
74r4
to
725.
The
northern
follows the edges of the continental shelf of the
composite landmass of the Morth and South America,
!urope,
The southern boundary follows the edge of
frica and Asia.
shelf
continental
the
combined
rAustralia
with
longitude
Han
streamfunction
and Antarctica are
Guinea,
rid size is 5
degrees
Gates
and
the
of
A descriotion of the governing
GCM.
Drocedures, and the numerical methods
solution
oy
is given
Zealani,
4ew
4 degrees in latitude which matches the
and
resolution of the OSU
equations,
Iew
The horizontal
treated as islands.
in
Antarctica.
of
mass
(1982a).
The
annual
transoort
and
the seasonal
variabilities of the strearnfunction fields
mean
discussed.
are
are also comoared against those oenerated by the same
They
model using observed wind stress.
The circulation driven by AGCM simulated wind stress
4.1.
In this experiment, the density of sea water is
as
constant
a
throughout
The heat and
the integration.
salinity fluxes prescribed at the uooer boundary
tacen
originally
diffusivity
cm
8
2
/sec
and
cm2 /sec
X
heat
in
,
and
1 gm/cm
salt.
and
topography
bottom
The
zero.
from
the
Gates
vertical
and
is
included,
Ielson
direction
fixed
eot
are
was
and
The
(1975).
given
is
as
I
horizontal
direction
is
for
momentum and 2 X 1O
cm2 /sec
for
The
reference
fixed
as
that
in
the
density
is
the specific heat of water is 1 cal/qm/deq C.
R3
We will refer to the experiment with time-varying AGC
stress
Case
as
In Case A the OCCM used a new set of
A.
AGCM simulated wind stress data every
from
the
rest,
year.
system
streamfunction
pattern
is
Starting
hours.
integrated for one simulated
was
mean
annual
The
wind
of
shown
in
transport
mass
total
jq. 4.2
fig. 4.1.
shows the streamfunction of simulated mass transport of the
exoeriment
the observed annual mean wind stress
hich
in
was used as the constant forcing (Han and 'ates, 192).
will
refer
to
We
the latter exoeriment as Case B hereafter.
The integration in Case B was carried out for
90
lays
to
obtain a steady state.
The streamfunction fields shown in figs. 4.1
are
similar
quite
term
in
Both
many of the
show
the
present model is relatively small
compared to the lateral friction due to the
diffusivity.
4.2
The nonlinear effect of the momentum
familiar ocean gyres.
advection
general.
In
and
Hence,
the
use
laroc
of
mean circulation driven b
varying forcing field should be very close to
that
the
driven
by constant mean forcing field.
In
clearly
Northern
the
in both
seen
are different.
20 N
which
is
Hemisphere,
clockwise
are
ase A and Case 3, but the oositions
The maximum transport is
10
qyres
degrees
found
to
be
South to that of Case B.
on
The
9.14
SIN
4j-*l
rj\
5.14
(__
3114
.3.14
Li
31$
JJ
I
,II
J
I
I
-91$
-
C..
3U
rig, 4.1.
ICE
E
lasE
I
I
I
ISlE
IC.
15511
iasis
U
I
uu
aIM
I
Arnu3l mean streamtunction of the mass transport ot the
oceanic circulation driven by the AGCM simulated surface
Contour interval is 4 Sv. The zero lines
wind stress.
are dashed and the nejative values are stippled.
3CC
90N
70N
50N
(4
30N
ION
LJ!U1
'Os
L
I
30S
50S
70S
9051
30W
I
0
Fig. 4.2.
30E 60E 90E120E 150E 180 150WI20W 90W 60W 30W
0
30E
streamfunction of the mass tranport at day 90 of the
oceanic circulation driven by observed surface wind stress.
Also see Fig, 4.1.
'I'
maximum
only to the latitudes of
boundary
western
the
all
the SUbtrOptca]. gyres intensify
with
associated
currents
that
oredicts
thenry
linear
curl,
stress
wind
and
subsequently return to the interior asbroad and relatively
slow currents.
positioning
error
figs 2.11.
The
circulation
Is
about
transoort
30 Sv (1 Sv
agreement
reasonable
tø12 cm3 /sec) in the
with
the
oWever,
80th Cases,
Case B.
geostrophic
observed
could
discrepancy
thermohaline
be
transport
due
circulation
to
and
Gates.
1982).
underestimate
tne
the Gulf stream.
The
qreatl.y
of
the
lack
Sv,
which
internal
of
By
viscous
coarse-arid
enhanced
Is
is comparable with the transoort of the
observed
florida Current (29 Sv), but still lower than the
transport of 75 Sv in the vicinity of Cape Hateras.
Pacific ocean, the
circulation is 3
model
the thermohaline
including
forcing (Han ani Gates, 1982b), the transoort
27
Ocean
Atlantic
and/or a nonlinear recirculatlon
which cannot be simulated bV a
to
geostrophic
observed
the
still
but
stream) is 12 Sv, which is smaller than the 15 Sv In
(Gulf
(Han
clockwise
the
of
The transoort in
transport of 40 Sv.
deiree
10
This Is smaller than In Case 8,
Pacific ocean.
in
maximum
the
zonal mean curls as shown in
the
from
exoect
could
we
i1ence,
north-south
extent
of
the
In the
clockwise
degrees comoarerl to 40 degrees in Case B.
This is the result of te existence of a broad
and
strong
counterclockwise subarctic qyre to the north. The transport
reach
could
circulation
in
Case
transport
the
while
Sv
18
nd rather weaK.
gyre in the Iorth Atlantic Ocean Is broad
In
is
agreement with that of Case B,
remarkable
Antarctica
present case.
transport.
of
Differences are found only in the maqnituie
The
circulation
observed
In the Southern Hemisphere, the
pattern
The subarctic
in less than 4 Sv,
S
same
tre
of
Current is much weaker In the
Circumpolar
Drake
the
The total mass transoort throucib
The
Passage is less than 4 Sv comoarel to in Sv In Case B.
difference results directly from the smaller curl value
the
AGCM simulated wind stress (fig. 2.12).
It is hard to
lack
judge tne accuracy of the oresent estimate due to the
of
direct
measurement
magnitudes in
numerical
transport
both
studies.
is
mainly
are
much
Han
and
cates
barocljrticity and topography.
hlch excludes the
smaller
cases
affected
baroclinic
However, the
transport.
this
of
by
other
than
found
(1982b)
effect
joint
the
of
the
of
In the barotropic experiment
the
effect,
transoort
is
largely controlled by the value of eddy ditfusivity because
the wind stress torque is mainly balanced
friction
a
in the Antarctica region.
bV
the
lateral
The oresent model uses
therefore
greatly
The clockwise subtropical gyres in the South
Atlantic
relatively
large
diffusivity
and
suppresses the transport,
98
and
Pacific Oceans aree well with those In Case 8.
South
Both cases fail to simulate
which
return bouniarv flow of toe South
Doleward
the
is
Pacific
Subtropical
current
oasses
Australia
Ocean
Indian
into
flows
and
model
the
Instead,
circulation.
Australia.
through a narrow channel between Irdo-Ch1na and
The
current,
Australia
East
the
total mass transoort through the channel is about
latter
Sv
agrees
In Case A cornoarel to 10 Sv In Case B.
The
with the observational estimate made b
Godfrey and Goldlng
(1981).
In the South Indian Ocean
transport
Sv,
less
is
circulation
not correctly
than
maximum
28
Sv
corresoonding
the
of
The associated Aquihas current is
in Case B.
simulated.
branching
without
the
,
the counterclockwise circulation is about 20
of
which
Case
for
It
returns
around the southern tl
interior
the
to
of Africa as is
found in Case B and the observation.
The
tropical
controlled,
circulatIon
therefore,
it
is
inertially
largely
is poorly simulated due to the
lack of inertial effect in the model.
The only tiiscernable
found in the eastern part of the
tropical
circulation
Pacific.
The maximu!n transoort is 9 Sv in Case
about
Sv
6
in
Case
is
B.
Both
observational estimate of 40 Sv.
are
much
A
and
is
less than the
89
Seasonal Variation of the Simulated Dcean Trnsoort
4.2.
seen
s can be
last
the
in
cnaoter,
ny cycle neriod
atmospheric forcing on the ocean can be of
However, most of the variance
between hours and years.
the
forcing
to
atmospheric
the
can
be
with
disturbances
less
is
than
one
oerlod
year,
the
the
inertial
traooed
the
simulated
ocean
barotropic model would be
temporal
(18
quite
oeriod
response can
of
penetrate to the ocean floor and is independent
Hence,
oeriods
traoped near the ocean surface.
strongly
when the forcing period is away from
and
ocean
Willebrand (1980) found the
longer than one year, or close to the inertial
hours),
of
field (wind stress) is explained in the ranze
ot one day to 300 days.
response
imposed
th
depth.
by
the
present
significant
due
to
response
the
characteristics of the AGCM sinulated wind stress
field.
Figs. 4.3a-d display the monthly mean stream functions
of
January,
seasons.
Aoril,
July
and
representing four
October
In the Northern Hemisphere, the cyclonic
yre
in
5
degrees to the south of its
winter position in the summer.
This results from the south
the
shift
Pacific
in
the
shifts
about
curl field.
The mean mass transport bV the
associated Kuroshio current Is
other
months.
However,
larger
in
Ppril
than
in
a more careful check of selected
7
sGl
30N
3$t4
10$
1 GS
1$5
3*5
3.5
'$5
'.5
705
7.5
I
I
I
3$IJ
0
3$E
Fig. 4.3a.
60
N(
1*SE
I
hOC
I
15$
I
ISSId
I
I
IUIJ
'.I
'.44
3
I
S
30E
Monthly mean strearnfunction of the simulated transPort for
The zero lines are
Contour interval is 5 Sv.
January.
dashed and the negative values are stippled,
0
0
E-fl
:::
N
J
rH r-')L..........
t'--.,
'R <_
105JS H
H
r1
L1.0
30$
pZ'
c/,-'
SOS
I
705
-1
.
(>
:
1
I
.
gas
la.s
1
30U
S
3G
SOC
OQE
Fig. 4.3b,
ISOC
IU
ISOIJ
iasw
OSU
OGU
3GW
S
AS in Fig,, 4.3a exceot for April,
'0
7014
SM
3M
:::
r
1014
Hi'
las
iss
30$
305
30W
0
30E
60E
90&
lilE
4.3c.
15$E
As ir
ISO
1SIU
SOW
30W
0
30
F'Iq. 4.3a except for July,
0
90N
get,'
Ll:...:%FIJ - ?SH
70N
1
7
*
(v'..
3s$
GN -1
I
4c
J1e5
I
- I, --
I
I
3gU
a
30E
GIE
t'ig.
I
eE
4.,3d.
JrL_1
?SS
t-. .s
I
iae
ISSE
IN
IS$W
ia.0
9W
61U
As in Fig. 4,3a exceDt for October,
30M
$
f 6'
daily fields reveals a maximal transoort
minimum
and
E'ebruary
v
rhe inrU3l
ctoher.
of 2() Sv in
1te
i.n
co!noarel to 24 Sv in Case
variability is 40 Sv in Case
B
in which maximum and ,inimurn transoortoccir in January and
Seotember, rasoe:tively.
from winter to summer.
The northward maSS transport by the
and
A minimum
aqrees well in ohase with that of
variability
annual
July.
in
value of 8 Sv is found in late Seote'noer but not
The
late
in
low in early July.
relatively
is
Sv
30
of
ulf Stream Current reaches a maximum
January
southward
moves
also
yre
The 4tlantic subtropical
Case 8, but not in rranitude.
seasonal variation
The most interesttr
the
Ocean.
Indian
North
in
strenqth of the
the
Althouzth
found
is
summer monsoon is not adequately simulated by the AGCM, the
ocean's
response
observed.
January
reverses
also
maximum
The
with
the
a
value
annual
circulation
reverses
qradually
counterclockwise in
current
weak
the
clockwise
The
pronounced.
winter
to
its
summer.
Its
oattern
rhe
the
In
become
associated
Somali
season
with
transoort
occurs
of 8 Sv (1.7 Sv In Case
maximum northward transoort is about 24 Sv in
aqrees well with that in Case 8.
Is
to
direction
direction
southward
variation
)
July,
as
in
and the
which
95
the
The subarctic circulation does not chanqe much in
while it varies significantly with tine In
Ocean
Atlantic
The naxImu
the Pacific Ocean.
wIth
January
In
The
agn1tude of about 20 Sv.
averaged
an
occurs
transport
nass
utnimum is found in su!nuer Tonths 1ith a iean value of less
than 8 Sv.
noves
circulation
counterclockwise
subtropical
the
Heiisphere,
Southern
the
In
toward the eluator as
January.
the seasons change fron July (southern winter) to
The
annual
variation
tne
of
sinulatel transoort of the
larer
Brazil current is 12 Sv, which is
simulated in Case B.
than
the
4
v
The maxinu!n of 24 Sv occurs in August
and the minimum is in January.
In the Pacific Ocean, the transoort of the return flow
just
east
of
does
Zealand
'Jew
not
change much in the
monthly mean fields, however, very raojd fluctuation can be
seen
from
response of
the selected daily fields, indicating the rapid
the
model
to
and
January intensifies
progresses
to July.
weak
A
variation
is
fairly
shifts
westward
as
the
season
rhls is also observed in Case B.
simulated transoort of the
current
field.
forcing
gyre occupying the western equatorial Pacific in
clockwise
little
the
the
in magnitude.
weak
in
Indian
Ocean
gyre
The
shows
The Antactica circumpolar
January.
It
gradually
96
intensifies until July, and then we&els very rapidly.
along
streamfunction
the
Westward
increases
the
of
order
barotrooic
found
cm/sec.
experiment
similar
velocity
anolitule
in
(rouos
of
Willebrand
part
of
amolitude
with
the wind stress
of
wave
(1980),
varying
with
characteristics
In
moving
trains
who
did
a
wind stress forcing,
the
zonal
simulated
field but with a smaller ohase soeed (3-5 rn/sec).
Therefore, the waves with westward
eastward
The
rn/sec.
also be identified with a oroup speed of the
can
70-80
indicates
This Increase is almost synchronous
fluctuation (fig. 2.17).
eastward
9-10
order
increase
seasonal
isolines
the
of
late October to late February as discussed
from
in this section.
the
tIlt
orooagation virtually everywhere, with the
ohase
phase soeeds
34N CJ32) for t.o 60-lay oeriods of
The
simulation.
the
of
Figs. 4.4a,b show the time-longitude sections
rouo
the
velocity
response
fluctuating winds.
are
of
a
ohase
propagation
and
liIely to constitute a main
barotrooic
model
to
the
-.
.-..
......-. ...
:
_________J
eae
-III
Fj, 4,4a.
-1b
Time-longitude plot of the strearutunction 1on 34N (J32)
Contour interval is
for day 180-240 of the simulation.
10 Sv. The zero lines are dashed and the neat1ve values
The abscissa Is tre lonqitude (deqree)
are stipoled.
and the ordinate Is tne time (day).
\
7i
Fig. 4,4b.
-iii
i
_____
-iS.
-141
-131
The heavy dashei
As ir Fig. 4,4a except tor 1ay 300-360.
lines correspond to an eastward group velocity of 75cm/sec.
SUMMARY
5.
OSU
Surface wind stress, as simulated by the
AGCM
has been analyzed.
2-level
The nalor findings are summarized
as follows:
Cl)
the
shifts
3-year mean vector fields reveal oosttlon
qvres
main
the northern oceans comPared with the
in
observations.
The cyclonic gyre In the
approximately
15
deqrees
Ocean
is
too far south compared with the
about
are
to 20 degrees south of the
10
southern
The distribution over the
observed.
Ocean
Pacific
The cyclonic and anticyclonic gyres over
oberved oosltlon.
Atlantic
of
oceans
is,
we1. simulated.
(2)
Magnitudes
(3)
bears
generally
fields,
I.e.
Hemisohere
and
stress
are
esoecially
distinct
emisphere.
vertical
The
wind
mean
The difference is
co!noonents fields.
in the Southern
3-year
than the obervations as revealed in the
smaller
generally
the
of
component
of
the
wind
stress
cur].
characteristics
as the stress
oositioning
differences
In
the
Morthern
magnitude
differences
In
the
Southern
the
same
Hemisphere.
(4)
The root mean square wind stress field shows that the
maximum time variability occurs In the northern oceans near
the northern boundary and western part of the oceans.
(5)
Seasonal
variablity
is
strongly
dependent
on
100
Annual
latitude.
Semi-annual variation is found only at
the
latitudes
high
In
The most distinct annual cycle
1emisohere.
southern
latitudes.
most
dominates
variation
simulated
over Indian ocean monsoon area Is missing in the
field.
similar
Autosoectral analysis of wind stress shows a
(6)
shaDe
Soectral
to
the
of
that
a frequency corresoondinq tO the synoptic time
at
frequency
4o slqntflcant oeak Is found at any
scale.
droos
It
sPectrum is oenerally white at low frequencies.
sharoly
The
stress.
observed
for
However, a distinct diurnal cycle
extratropical latitudes.
is found In the tropical area.
The annual oea)c Is resolvable
(2)
than
stress magnitude
reveals
The
wIndow,
spectral
the
The fluctuations are stronger
field.
comoonents,
stress
winter
In
which
of the stress
characteristics
nonstationary
the
narrower
a
Is much more dominant in the
peak
In
using
ôy
than
in
summer.
(8)
Cross-spectral
disturbances
oropaqating
the
variability
Disturbances
symmetric.
as
to
shows
analysis
is
the
eastward
the
that
synoptic time scale dominate
of
found
In
meridional
the
real
direction
1.ow frequency disturbances are
also
atmosphere.
are
rather
symmetric
and have no preferred oropaaatiort directions.
An exoeriment
using
a
homoaeneouS
ocean
which
Is
101
driven
AGCM simulated wind stress has been carried Out
bY
version
using a barotrooic
of
cCCM.
six-layer
OSIJ
We
found:
(1)
The oositions of the major circulations
controlled bY the wind stress cur). field.
are
largely
Thus, the annual.
mean circulations in the Northern Hemisohere driven by AGCM
wind stress reveal a southward shut comoared to
simulated
The
that driven bY observed wind stress.
the
Southern
aaree
Hemisphere
well.
circulations
in
with that driven by
observed wind stress.
(2)
The annual vari3bilities of
most
oceans
the
transoort
mass
in
for the oresent study are larger than that of
This is probably due to the
the observed wind stress case.
stronger seasonal variability of the simulated wind field.
(3)
the
ohase
Planetary waves with westward
speed
9-10
of
70'80 cm/sec are
rn/sec
likely
Drooagation
at
and eastward group velocity of
the
be
to
major
part
of
the
response of the barotrooic model to the fluctuating winds.
The overall performance of the simulated
is
satisfactory.
positioning error of the
the
However,
main gyre in the northern oceans must be improved
of
its
further
important
diagnostic
variabilities
effects
study
on
of
stress
wind
the
the
ocean
soatla].
in
transport
and
view
A
temporal
of the wind stress curl. is needed due to its
imoortance in modifying the ocean resoonse Reetmaa, 1978).
102
A
cross-sectra1.
arlvs1s beteer the ocean resoorse
the atnosoher1c forc1r, e.q.
lnd
stress
curl,
should
the
the strearn'function
also
e
done
in
order
quantitatively unierstnd the resoonse of the model to
forcing.
rd
to
the
t03
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The