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 !