Ocean-Atmosphere coupling on different spatio-temporal scales
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Transcript of Ocean-Atmosphere coupling on different spatio-temporal scales
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Ocean-Atmosphere coupling on different spatio-temporal scales
Lei Zhou
Raghu Murtugudde
16th Conference on Air-Sea Interaction, Phoenix, AZJan. 15, 2009
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Introduction• Evidence for OA interaction: ENSO
NOAA / PMEL / TAO
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Introduction• Evidence for OA interaction: MJO
Image courtesy of Science/AAAS
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Introduction
• Implicit assumption a priori:
The spatial and temporal scales in the ocean and the atmosphere should be similar.
• Some inconsistent evidence:– MJO-induced Kelvin waves have a period of
~70 days, which is longer than that of MJOs– Intraseasonal SSTAs in the Indian Ocean are ~
hundreds km, while MJOs are ~ thousands km.
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Introduction
• So, any other possibilities?
• Assumption:– The ocean and the atmosphere can interact with
each other on different spatial and temporal scales.
– Scale similarity is not necessary for the ocean-atmosphere coupling.
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Review of uncoupled system
• Conclusion first:– No unstable waves in the linear uncoupled
system;– Thus, the unstable waves shown below in the
coupled system are only attributable to the air-sea interactions.
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For the barotropic, tropical ocean, the linear inviscid governing equations with no atmospheric forcing are adopted from Gill (1982)
The ocean:
),1(1
),1(
),1(
ctHy
v
x
u
by
gyut
v
ax
gyvt
u
Review of uncoupled system
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The atmosphere:For the barotropic atmosphere in the tropics, the governing equations without oceanic feedbacks are applied following Anderson and McCreary (1985),
),2(
),2(
),2(
2c
c
Pr
y
V
x
U
brVy
PyU
t
V
arUx
PyV
t
U
Review of uncoupled system
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Coupled System
,1
,
,0
tHy
v
x
u
ygyu
t
v
Hxgyv
t
u x
,
,
,
22 c
Q
c
Pr
y
V
x
U
rVy
PyU
t
V
rUx
PyV
t
U
The ocean The atmosphere
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With the same processes as above, we obtain
)3(
2
0
2
2
2
32
3
yx
U
Hx
v
t
v
t
v
c
y
tc
v
)4(2222
22
TQx
Ur
tr
c
x
Uyr
t
Assumptions used to obtain the above equations:
Meridional winds V are neglected
;Ux ;TQ mT
x
T
x
T
sf
g
xf
gv
Linear approximation
The following results are not sensitive to the parameters.
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Two Possibilities
• In order to solve the coupled equations, we need to assume wavelike solutions
– If the spatial and temporal scales are the same in the ocean and the atmosphere
– If the spatial and temporal scale are NOT the same in the ocean and the atmosphere
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Scales are the same …
The wavelike solutions of the form tkxiec
yvv
2exp
2
0
and tlykxieUU 0 are assumed.
)5(
.2
,
022
0222
022222
00
02
2
3
TlkUrkcr
kUyrkcik
UH
klTkk
ck
c
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From the real part, the following condition must be satisfied
)6(0
2 222
22
0
222
4
rkc
lk
H
rk
ck
c
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Scales are different …
Representing the wave properties in the ocean with a subscript o, and the wave properties in the atmosphere with a subscript a, Eq. (5) is re-written as
)7(
.2
,
022
0222
022222
00
2
02
2
3
TlkUrkcr
kUyrkcik
UH
kTkk
ck
c
ooaaa
aaa
aoooo
o
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In order to have non-trivial solutions, the following condition has to be satisfied
).8(0
),8(02
22222
22
2220
22
3
byrkc
ak
lk
rkcH
krk
ck
c
aa
o
oo
aa
aooo
o
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Inverse of the imaginary part of the unstable solution, with the unit of day
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Substituting 22222 yrkc aa into
02
22
2220
22
3
o
oo
aa
aooo
o
k
lk
rkcH
krk
ck
c
we have
)9(0
22
3
22
0
223
oooo
oo
o
aaa
kc
kc
lk
kH
kryr
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Inverse of the imaginary part of one solution, with the unit of day
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The oscillations with different temporal and spatial scales can interact with each other and lead to instabilities in both the ocean and the atmosphere in a linear framework.
Conclusion
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Thanks !