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, AZ Jan. 15, 2009. Introduction. Evidence for OA interaction: ENSO. NOAA / PMEL / TAO. Introduction. Evidence for OA interaction: MJO. - PowerPoint PPT PresentationTRANSCRIPT
Ocean-Atmosphere coupling on different spatio-temporal scales
Lei Zhou
Raghu Murtugudde
16th Conference on Air-Sea Interaction, Phoenix, AZJan. 15, 2009
Introduction• Evidence for OA interaction: ENSO
NOAA / PMEL / TAO
Introduction• Evidence for OA interaction: MJO
Image courtesy of Science/AAAS
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.
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.
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.
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
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
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
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.
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
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
From the real part, the following condition must be satisfied
)6(0
2 222
22
0
222
4
rkc
lk
H
rk
ck
c
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
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
Inverse of the imaginary part of the unstable solution, with the unit of day
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
Inverse of the imaginary part of one solution, with the unit of day
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
Thanks !