A Statistical Analysis on the

Stratosphere-Troposphere Coupled Variability

by Using Large Samplesobtained from a Mechanistic Circulation

Model

Yoko NAITO & Shigeo YODEN

Dept. of Geophysics, Kyoto Univ.

Outline

Check the model results with data observed in

the real atmosphere

A statistical analysis with data obtained by

a numerical experiment

1.1 A statistical analysis by using large samples

E1.0 W1.0

1. Introduction

Frequency distributions of zonal-mean temperature (86N, 449hPa, 10800 days) in two runs: E1.0 and W1.0

~1K

Frequ

en

cy (

%)

Naito, Taguchi and Yoden (2003)

A parameter sweep experiment

on the effects of the equatorial

QBO on stratospheric suddenwarming events

[J.Atmos.Sci., 60, 1380— ]

Temperature (K)

Close to Gaussian;Heavily overlapped

1.2 Testing the difference between two averages The large sample method A standard normal variable Z : The probability that Z reaches 40.6 for two

samples of the same populations is very small ( < 10-27 )

2 2

2 2

226.8 225.840.6

1.87 1.75

10800 10800

W E

W E

W E

T TZ

N N

[TW] : average of TW

[TE] : average of TE

W2 : variance of TW

E2 : variance of TE

NW : sample size of TW

NE : sample size of TE

The difference is very significant

2. QBO effects on the extratropical stratosphere and troposphere

(Yoden et al., 2002; JMSJ )2.1 The S-T coupled variability and its possible causes

EquatorialEquatorial ExtratropicalExtratropicalDynamical variability StratosphericStratospheric

Sudden WarmingSudden Warming(SSW) events(SSW) events

1953

1963

1974

1985

1996 2004

1962

1973

1984

1995

yearalt

itu

de

32(km)

18

Westerly

Easterly

Westerly

Easterly

2.2 QBO: Quasi-Biennial Oscillation

(data provided by Naujokat)

Zonal wind over the Equator in the lower stratosphere (m/s)

3. Numerical experiments3.1 Naito, Taguchi and Yoden (2003)

Model Simplified 3-D global circulation model

Imposed “QBO-wind” forcing

du dt ……QBOuUQBO

QBO : relaxation coefficient ; UQBO : basic

profile

(confined in the equatorial lower stratosphere)

Long time integrations • NW = NE = 10800 days

• Fixed external conditions

at 90oN, 2.6hPa

W1.0

E1.0

(K)300

200

(K)300

20010000 11000 120001150010500

(day)

3.2 The polar temperature and SSW events

… key day of a SSW event

Obtained time series of the temperature

SSW: Stratospheric Sudden Warming events 57 events in the W1.0 run 168 events in the E1.0 run cf. observed major warmings in the past 46 years: 7 events in the Westerly phase 13 events in the Easterly phase

2. Numerical Experiments

Tem

pera

ture

(K

)

Lag (day)

3.3 Composites of the polar temperature during SSWs

A key day isdefined here

Zsignificance

• Lower stratosphere - most significant (> 99.99999% at Lag ~ 4 days)• Mid-troposphere - still significant (> 99.9999% at Lag ~ 12 days)

W1.0 ( 57 events) E1.0 (168 events)

4. Real atmosphere

4.1 Data and method of the analysis

NCEP/NCAR Reanalysis Data

- Winter months (Dec,Jan,Feb) during 1958—2003

2316 days in the Westerly, 1834 days in the Easterly

Independence of the serial data

- N is replaced by an effective sample size N’ N /

0

0 : an effective sampling time (day)

(of the order of months in the stratosphere,

of the order of weeks in the troposphere)

4.2 Composite difference (Westerly minus Easterly) of the zonal-mean temperature (K)

pre

ssu

re (

hPa)

Maximal differenc

e;

~4K

~2K

latitude

50 hPa

250 hPa

4.3 Statistical significance (%) of the composite difference

latitudelatitude

98.30 %

Most significant;

99.9985%

pre

ssu

re (

hPa)

Maximal differenc

e;

~4K

~2K

50 hPa

250 hPa

~2K

’

Close to Gaussian; Heavily overlapped

99.9985% significan

ce

4.4 Frequency distribution of the polar temperature at the upper troposphere90oN, 250hPa

Westerly

Easterly

Concluding remarksProposal of a new experimental framework • Long time integrations can be done

with a 3-D global circulation modelby changing a key external parameter.

• Statistical significance of the QBO effectson the extratropical variability is testedby the large sample method.

Possible application of this statistical method

• Effects of the other external causescan be tested by this statistical method.(ex. 11-year solar cycle, volcanic aerosols, El Nino/Southern Oscillation, and so on)

That’s all.Thank you for your attention.