On the mechanism of eastward-propagation ofsuper cloud clusters (SCCs) over the equator 

– Impact of precipitation activitieson climate of East Asia –

ICMCS-V_061101

Masanori YOSHIZAKI and Tomoe NASUNO(IORGC/JAMSTEC)

Topics1. Simple model: linear, 4-layer model with constant N and no basic wind2. Extension of simple model using a NICAM output (Diabatic heating: positive-only wave CISK)

Thanks to Drs. T. Nasuno and M. Sato for providing NICAM data

History and motivations

・ Hayashi ･ Sumi (1986) found an eastward- propagating mode around the equator in the aqua-planet numerical experiment.・ Eastward-propagating super cloud clusters （ SCCs) were obtained by satellite data, too. (e.g., Nakazawa ， Murakami ， Takayabu et al.)

Many theories to explain the mechanisms of eastward-propagating modes:

1) Atmospheric instability ・ Moisture convergence・ Surface evaporation2) Atmospheric response to independent

forcing・ Tropical intraseasonal stationary forcing・ Tropical stochastic forcing・ Lateral forcing Zhang (2003)

day

East

Westward propagating

Eastward propagating

Nakazawa

Which mechanisms are working?

Atmospheric instability, or atmospheric response to independent forcing?

Intraseasonal variation >>> MJO (Madden-Julian Oscillation)

・ Atmosphere with constant N and no basic wind,・ Equatorial-beta plane system (βE),・ 4 layers in the vertical,・ Linear system,・ Heating: positive-only wave-CISK,・ Large second-order horizontal diffusion.

Yoshizaki (1991a,1991b): a simple model of S ＣＣ s

　　　　 0 　　　　　　：ｗ B < 0 　Q=　　　　ｗ B ・ f(z) 　：ｗ B > 0

.0

,

),,(0

,

,

2

2

z

w

y

v

x

u

bQNwt

b

zd

dgNgbb

z

vuyyt

v

uvyxt

u

HH

HH

HH

Model:* Horizontal direction: Grid* Vertical direction: Mode expansion

Height

QNw

t

b 2

ｗ B

bottom

Model top

Q /N2 10

Total QEach modes

of Q

* Vertical mode expansion

Height Combination of two modesOnly 1st mode

ｗ B

* Two heating profiles were considered:

* Top-heavy heating profile can be expressed as a combination of positive 1st mode and negative 2nd mode

η1 = 1.5, η2=0.0

η1=1.5, η2=-1.5

Height

ｗ B

η1 = 1.5, η2=0.0

η1=1.5, η2=-1.5

Time

along the equator

Convective mode moves

westward in βE .

Eastward-propagating mode grows faster than westward-

propagating mode in βE .

→ Changes of vertical heating profiles induce different characteristic features of propagation!

* In this model, it is assumed that diabatic heating is greater than adibatic cooling due to upward motion in some layers.

However, is the ‘>’ case right, observationally or numerically?; Disturbance driven by convection for the ‘>’ case, or neutral wave in the stable stratification for the ‘<‘ case.

Further study could not be pursued in 1990’s, however, because there was no step to check above-mentioned features.

Recently, numerical outputs using a global NH model (NICAM)were available.

22 NwQQNwt

b

>>> Which mechanisms are working? Atmospheric instability , or atmospheric response to independent forcing?

Snapshot of ‘NICAM’ precipitation- Aqua planet -

NICAM: Nonhydrostatic ICosahedral Atmospheric Model = Global cloud-resolving nonhydrostatic model

40000 km / 30 days～ 15.4 m / s

SCC

7 km resolution

2S – 2N average

x - t distribution of diabatic heating

)10( 14

sK

tC

qLQ

p

v )(K

)1.0( 1sm

w

)( 1sm

u

Qzd

dw

(1) Comparison of Q (diabatic heating) and adiabatic cooling due to upward motion

(2) Comparison of Q (diabatic heating) and adiabatic cooling due to upward motion

)10( 14 sKzd

dwQD

Disturbances driven by convection ( or atmospheric instability )

D is positive in some layers in the vertical direction.

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0

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312

312

3122

z

w

y

v

x

u

rQz

wNLx

ut

gz

p

vrvuyy

pvNL

x

vu

t

v

uruvyx

puNL

z

uw

x

uu

t

u

HH

HH

HH

Governing equations

* 54 vertical grid model is used.* Parameter ε: 0 or 1 ε1 : Linear or nonlinear (NL) ε2 : With or without basic eastward wind ε3 : Including or excluding Rayleigh damping (function of z)

Positive only wave-CISK

X - time section of vertical motions at the height of 3.7 km along the equator

Blue ： upward motion

Red : downward motion

Full model: ε1=ε2=ε3 = 1 η=60

Tim

e (d

ay)

X (10,000 km)

Vertical section

Horizontal section

16 days~ 29 m / s

Yoshizaki (1991a,1991b)* Linear * No zonal wind* Constant N* 4 layers in the vertical * Mode expansion in the vertical * Combination of 1st and 2nd modes

Present calculation* Nonlinear* Zonal wind* Variable N* 54 layers in the vertical* Grid in the vertical * Diabatic heating simulated by NICAM

θ

Heating

Full model : Basic wind u + N + positive-only wave-CISK + Rayleigh damping

Rayleigh damping is working well.

Z

X

Vertical pattern of simulated SCC ｓ　

Conclusions1) Diabatic heating is larger than adiabatic cooling due to upward motion in some vertical layers: SCCs appeared in NICAM is disturbances driven by convection. Then, SCCs are excited due to atmospheric instability.2) The simple model is extended using the NICAM output.3) When positive-only wave-CISK is applied as diabatic heating, eastward-propagating disturbances appear as a dominant mode.4) MJO (or SCC) is responsible for the formation of tropical cyclones affecting East Asia. Thus, this study is important.

Further studies1) This vertical grid model should extend to a vertical mode model, to confirm results obtained by a simple vertical mode.2) Rayleigh damping is important to eliminate the reflection of vertically propagating gravity waves. The differences between inclusion/exclusion of Rayleigh damping should be studied.3) Multi-scale horizontal feature is not simulated due to selection rule of convection.

Horizontal pattern of simulated SCC ｓ

Height

Case of two vertical modes

Case of one vertical mode

ｗ B

Two heating profiles were considered:

* Top-heavy heating profile can be expressed as a combination of positive 1st mode and negative 2nd mode

η1 = 1.5, η2=0.0 η1=1.5, η2=-1.5

Time

along the equator

→ Changes of vertical profiles of heating induce different characteristic features of propagation!

Why does the difference of heating profiles produce different features?

Case of one vertical mode

(η1>1)

Only convective mode excited

η1 = 1.5, η2=0.0Similarly to an usual convection, disturbances with no propagation are excited

Convective mode growswithout propagation in no βE.

Convective mode moves westward in βE .

Why does the difference of heating profiles produce different features?

Case of two vertical modes

(η1>1, η2<0)

Convective and oscillation modes excited simultaneously

Oscillation mode can be separatedinto EP and WP modes.

EP mode grows faster than WP mode in βE .

Growth rate

Horizontal wavenumberSmall Large

Horizontal diffusion = 0

Growth rate

Horizontal wavenumberSmall Large

Small horizontal diffusion

Growth rate

Horizontal wavenumberSmall Large

Large horizontal diffusion

Selection rule of convection

In the linear atmosphere system, there are two independent modes;(1) neutral wave modes and (2) exponentially growing modes.

(1) Gravity wave, Kelvin wave, Rossby wave and so on: When forced, a selection rule does not work: All waves stimulated by forcing are evenly excited and appear following a dispersion relation.

(2) Baroclinic waves, Benard convection, shear instability and so on: Modes with maximum growth rate grow fastest and a selection rule works.

In this model, a positive-only wave-CISK works like usual convectionand disturbances with maximum growth rate are infinitesimally small without horizontal diffusion (and viscosity).>>>> A large horizontal diffusion is included to get modes with horizontal scales of 1000 km. >>>> No multi-scale horizontal structure!

)0u(

02

X - time section of vertical motions at the height of 3.7 km along the equator

Blue ： upward motion

Red : downward motion

Full model: ε1=ε2=ε3 = 1 η=60

Tim

e (d

ay)

X (10,000 km)

.0

,')(

,1

0

,'1

)(

,'1

)(

312

312

3122

z

w

y

v

x

u

rQz

wNLx

ut

gz

p

vrvuyy

pvNL

x

vu

t

v

uruvyx

puNL

z

uw

x

uu

t

u

HH

HH

HH

Governing equations

Parameter ε: 0 or 1*ε1 : Linear or nonlinear (NL)*ε2 : With or without basic eastward wind *ε3 : Including or excluding Rayleigh damping (function of z)

Height

Case of two vertical modes

Case of one vertical mode

ｗ B

η1 = 1.5, η2=0.0

η1=1.5, η2=-1.5

Time

along the equator

→ Changes of vertical profiles of heating induce different characteristic features of propagation!

Convective mode moves

westward in βE .

Eastward-propagating mode grows faster than westward-

propagating mode in βE .