1. YODEN Shigeo Dept. of Geophysics, Kyoto Univ., JAPAN August 4, 2004; SPARC 2004 Victoria ＋ α － β for Colloquium on April 15, 2005 1.Introduction 2.Internal variability obtained in large ensemble experiments 3.Experiments on the QBO effects on the S-T coupled variability 4.Experiments on the spurious trends due to finite-length datasets 5.Concluding Remarks Large Ensemble Experiments on the Interannual Variability and Trends the Interannual Variability and Trends with a Stratosphere-Troposphere with a Stratosphere-Troposphere Coupled Model Coupled Model

2. 1. Introduction Causes of interannual variations of S-T coupled system (Yoden et al., 2002; JMSJ ) ENSO

3. Labitzke Diagram (Seasonal Variation of Histograms of the Monthly Mean Temperature; at 30 hPa) South Pole (NCEP) North Pole (NCEP) North Pole (Berlin) courtesy of Dr. Labitzke Length of the observed dataset is 50 at most 50 years. numerical experiments Only numerical experiments can supply much longer datasets to obtain statistically significant results, although they are not real but virtual.

4. The Earth Simulator R&D Center  Advancement of computers http://www.es.jamstec.go.jp/esc/jp/index.html ENIAC http://ei.cs.vt.edu/~history/ENIAC.Richey.HTML

5.  Hierarchy of numerical models Hoskins (1983; Quart.J.Roy.Meteor.Soc.) “Dynamical processes in the atmosphere and the use of models” OBSERVATIONS DYNAMICAL MODELS COMPLEX MEDIUM SIMPLE EVOLVING CONCEPTIAL MODELS A schematic illustration of the optimum situation for meteorological research

6.  Our research activity for these two decades LOM: Low-Order Model  Yoden (1987a,b,c) stratospheric sudden warmings (SSWs)  Yoden and Holton (1988) quasi-biennial oscillation (QBO)  Yoden (1990) seasonal march in NH and SH MCM: Mechanistic Circulation Model  Taguchi, Yamaga and Yoden (2001) SSWs in S-T coupled system  Taguchi and Yoden (2002a,b,c) internal S-T coupled variations  Naito, Taguchi and Yoden (2003) QBO effects on coupled variations  Nishizawa and Yoden (2005) spurious trends due to short dataset GCM: General Circulation Model  Yoden, Naito and Pawson (1996) SSWs in Berlin TSM GCM  Yoden, Yamaga, Pawson and Langematz (1999) a new Berlin GCM

7.  3D global MCM: Taguchi, Yamaga and Yoden (2001)  an atmospheric GCM  simplified physical processes parameter sweep experiments long-time integrations (max. 15,000 years) 2. Natural internal variability obtained in large ensemble experiments with an MCM

8.  Labitzke diagram for 1000-year integrations Taguchi and Yoden (2002b) reliable PDFs (mean, std. deviation, skewness,...) Monthly mean temperature (90N, 2.6 hPa)

9.  Use of reliable PDFs to evaluate the rarity of September 2002 in the SH Hio and Yoden (2005, JAS Special issue, 62-3, 567-580) 02 zonal-mean zonal wind (45S, 20hPa, Oct.1-15) (45-75S, 100hPa, Aug.16-Sep.30) upward EP flux

10. Monthly mean temperature (90N, 2.6 hPa) Frequency distribution [%] x -3 -2 -1 Mean +1 +2 +3 +4 +5. -U 45S,20hPa 4.2 4.2 58.3 20.8 8.3 0.0 4.2 0.0 0.0 Gaussian 2.1 13.6 34.1 34.1 13.6 2.1 0.1 3x10 -3 - T&Y(Feb.) 0.3 8.7 47.7 32.8 7.0 1.8 1.1 0.2 0.2

11. 3. Experiments on the QBO effects on the S-T coupled variability with an MCM  Perpetual winter integrations Naito, Taguchi and Yoden (2003, JAS, 60, 1380-1394) Naito and Yoden (2005)  “QBO forcing” in the zonal momentum eq.: : prescribed zonal mean zonal wind of a particular phase of the QBO  Assessment of the atmospheric response to a small (or finite) change in the external parameter by a statistical method.

12. 10,800-day mean fields of zonal-mean zonal wind [m/s] 75m/s50m/s 55m/s 45m/s

13. Time series of zonal-mean temperature [K] at φ=86N, p =2.6hPa for 2,000 days Total: 1,153 events

14.  Statistical significance QBO effects on the troposphere a large sample method  A standard normal variable:  The probability that Z reaches 40.6 for two samples of the same populations is quite small ( < 10 -27 ) E1.0W1.0 Frequency distributions of zonal-mean temperature [K] (86N, 449hPa, 10800 days)

15.  Observational fact Naito and Yoden (2005, SOLA, 1, 17-20) QBO effects on the polar troposphere W (2250 days) E (1800 days) Frequency distributions of zonal-mean T (90N, 200hPa, DJF for 1957-2002)

16. 4. Experiments on the spurious trends due to finite-length datasets with internal variability  Nishizawa and Yoden (2005, JGR in press) Linear trend  IPCC the 3rd report (2001)  Ramaswamy et al. (2001) Estimation of spurious trend  Weatherhead et al. (1998) Importance of variability with non-Gaussian PDF  SSWs  extreme weather events We do not know  PDF of spurious trend  significance of the estimated value

17.  Linear trend We assume a linear trend in a finite-length dataset with random variability  Spurious trend We estimate the linear trend by the least square method We define a spurious trend as N = 5 10 20 N = 50

18.  Moments of the spurious trend Mean of the spurious trend is 0 Standard deviation of the spurious trend is Skewness is also 0 Kurtosis is given by standard deviation of natural variability kurtosis of natural variability + Monte Carlo simulation with Weibull (1,1) distribution

19.  Probability density function (PDF) of the spurious trend When the natural variability is Gaussian distribution When it is non-Gaussian  Edgeworth expansion of the PDF  Cf. Edgeworth expansion of sample mean (e.g., Shao 2003)

20.  Cooling trend run 96 ensembles of 50-year integration with external linear trend  -0.25K/year around 1hPa Small STD Dev. Largest STD Dev.

21.  Application to the real atmosphere data 20-year data of NCEP/NCAR reanalysis application of the model statistics -0.1K/year -0.5K/year +0.1K/year t-test >99% >90%

22. Necessary length for 99% statistical significance [years] 87N 47N  How many years do we need to get statistically significant trend ? - 0.5K/decade in the stratosphere 0.05K/decade in the troposphere

23. 50-year data 20-year data [K/decade] [K/decade]  How small trend can we detect in finite length data with statistical significance ?

24. Recent advancement in computing facilities has enabled us to do some parameter sweep experiments with 3D MCMs Very long-time integrations give reliable PDFs (non-Gaussian, bimodal,.... ), which might be important for nonlinear perspectives in climate-change studies Atmospheric response to small change in an external parameter (e.g., QBO, solar cycle, …) can be statistically assessed by a large sample method 5. Concluding Remarks