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August 4, 2004; SPARC 2004 Victoria ＋α－β for Colloquium on April 15, 2005

Large Ensemble Experiments on

the Interannual Variability and Trends

with a Stratosphere-Troposphere

Coupled Model

YODEN Shigeo

Dept. of Geophysics, Kyoto Univ., JAPAN

- Introduction
- Internal variability obtained in large ensemble experiments
- Experiments on the QBO effects on the S-T coupled variability
- Experiments on the spurious trends due to finite-length datasets
- Concluding Remarks

Causes of interannual variations

of S-T coupled system

ENSO

(Yoden et al., 2002; JMSJ )

Labitzke Diagram (Seasonal Variation of Histograms

of the Monthly Mean Temperature; at 30 hPa)

Only numerical experiments

can supply much longer datasets

to obtain statistically significant results,

although they are not real but virtual.

Length of the observed dataset is

at most 50 years.

North Pole

(Berlin)

South Pole

(NCEP)

North Pole

(NCEP)

courtesy of

Dr. Labitzke

R&D Center

ENIAC

http://ei.cs.vt.edu/~history/ENIAC.Richey.HTML

http://www.es.jamstec.go.jp/esc/jp/index.html

- Advancement of computers

CONCEPTIAL MODELS

OBSERVATIONS

DYNAMICAL MODELS

COMPLEX MEDIUM SIMPLE

- Hierarchy of numerical models
- Hoskins (1983; Quart.J.Roy.Meteor.Soc.)

“Dynamical processes in the atmosphere and the use of models”

A schematic illustration of the optimum situation for meteorological research

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

2. Natural internal variability obtained in large ensemble experiments with an MCM

- 3D global MCM:
- Taguchi, Yamaga and Yoden (2001)
- an atmospheric GCM
- simplified physical processes
- parameter sweep experiments
- long-time integrations (max. 15,000 years)

Monthly mean temperature (90N, 2.6 hPa)

Labitzke diagram for 1000-year integrations- Taguchi and Yoden (2002b)
- reliable PDFs
- (mean,
- std. deviation,
- skewness, ...)

(45S, 20hPa, Oct.1-15)

02

upward EP flux

(45-75S, 100hPa, Aug.16-Sep.30)

- 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)

x-3 -2 -1 Mean +1 +2 +3 +4 +5 .

-U45S,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

Monthly mean temperature (90N, 2.6 hPa)

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.

Time series of zonal-mean temperature [K]at φ=86N, p=2.6hPa for 2,000 days

Total: 1,153 events

- QBO effects on the troposphere
- a large sample method
- A standard normal variable:
- The probability thatZ reaches 40.6 for two samples

of the same populationsis quite small ( < 10-27 )

Frequency distributions of

zonal-mean temperature [K]

(86N, 449hPa, 10800 days)

E1.0

W1.0

Frequency distributions of zonal-mean T

(90N, 200hPa, DJF for 1957-2002)

W (2250 days)

E (1800 days)

- Observational fact
- Naito and Yoden (2005, SOLA, 1, 17-20)
- QBO effects on the polar troposphere

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

- 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

- 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

+ Monte Carlo simulation

with Weibull (1,1) distribution

kurtosis of

natural variability

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)

Cooling trend run

- 96 ensembles of 50-year integration
- with external linear trend
- -0.25K/year around 1hPa

Small STD Dev. Largest STD Dev.

-0.5K/year

+0.1K/year

t-test

>99%

>90%

- Application to the real atmosphere data
- 20-year data of NCEP/NCAR reanalysis
- application of the model statistics

to get statistically significant trend ?

- - 0.5K/decade in the stratosphere
- 0.05K/decade in the troposphere

Necessary length for 99% statistical significance [years]

87N 47N

in finite length data with statistical significance ?

50-year data 20-year data

[K/decade] [K/decade]

5. Concluding Remarks

- 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

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