1. A Statistical Analysis on the Stratosphere-Troposphere Coupled Variability by Using Large Samples obtained from a Mechanistic Circulation Model Yoko NAITO & Shigeo YODEN Dept. of Geophysics, Kyoto Univ.

2. Outline  Check the model results with data observed in the real atmosphere  A statistical analysis with data obtained by a numerical experiment

3. 1.1 A statistical analysis by using large samples E1.0W1.0 1. Introduction  Frequency distributions of zonal-mean temperature (86N, 449hPa, 10800 days) in two runs: E1.0 and W1.0 ~1K Frequency (%) Naito, Taguchi and Yoden (2003) A parameter sweep experiment on the effects of the equatorial QBO on stratospheric sudden warming events [J.Atmos.Sci., 60, 1380— ] Temperature (K) Close to Gaussian; Heavily overlapped

4. 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 ) [T W ] : average of T W [T E ] : average of T E  W 2 : variance of T W  E 2 : variance of T E N W : sample size of T W N E : sample size of T E The difference is very significant

5. 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 EquatorialExtratropical Dynamical variability Stratospheric Sudden Warming (SSW) events

6. 1953 1963 1974 1985 19962004 1962 1973 1984 1995 year altitude 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)

7. 3. Numerical experiments 3.1 Naito, Taguchi and Yoden (2003)  Model Simplified 3-D global circulation model  Imposed “QBO-wind” forcing du  dt  ……  QBO  u  U QBO   QBO : relaxation coefficient ; U QBO : basic profile (confined in the equatorial lower stratosphere)  Long time integrations N W = N E = 10800 days Fixed external conditions

8. at 90 o N, 2.6hPa W1.0 E1.0 (K) 300 200 (K) 300 200 1000011000120001150010500 (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

9. 2. Numerical Experiments Temperature (K) Lag (day) 3.3 Composites of the polar temperature during SSWs A key day is defined here Z significance 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)

10. 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)

11. 4.2 Composite difference (Westerly minus Easterly) of the zonal-mean temperature (K) pressure (hPa) Maximal difference; ~4K ~2K latitude 50 hPa 250 hPa

12. 4.3 Statistical significance (%) of the composite difference latitude 98.30 % Most significant; 99.9985% pressure (hPa) Maximal difference; ~4K ~2K 50 hPa 250 hPa

13. ~2K ’ Close to Gaussian; Heavily overlapped 99.9985% significance 4.4 Frequency distribution of the polar temperature at the upper troposphere 90 o N, 250hPa Westerly Easterly

14. Concluding remarks  Proposal of a new experimental framework Long time integrations can be done with a 3-D global circulation model by changing a key external parameter. Statistical significance of the QBO effects on the extratropical variability is tested by the large sample method.  Possible application of this statistical method Effects of the other external causes can be tested by this statistical method. (ex. 11-year solar cycle, volcanic aerosols, El Nino/Southern Oscillation, and so on)

15. That’s all. Thank you for your attention.