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
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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
1. Introduction
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
The Earth Simulator
R&D Center
ENIAC
http://ei.cs.vt.edu/~history/ENIAC.Richey.HTML
http://www.es.jamstec.go.jp/esc/jp/index.html
EVOLVING
CONCEPTIAL MODELS
OBSERVATIONS
DYNAMICAL MODELS
COMPLEX MEDIUM SIMPLE
“Dynamical processes in the atmosphere and the use of models”
A schematic illustration of the optimum situation for meteorological research
2. Natural internal variability obtained in large ensemble experiments with an MCM
Monthly mean temperature (90N, 2.6 hPa)
zonal-mean zonal wind
(45S, 20hPa, Oct.1-15)
02
upward EP flux
(45-75S, 100hPa, Aug.16-Sep.30)
to evaluate the rarity of September 2002 in the SH
Frequency distribution [%]
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
: prescribed zonal mean zonal wind of
a particular phase of the QBO
to a small (or finite) change in the external parameter
by a statistical method.
50m/s
75m/s
55m/s
45m/s
45m/s
Total: 1,153 events
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)
4. Experiments on the spurious trends due to finite-length datasets with internal variability
with non-Gaussian PDF
value
in a finite-length dataset with random variability
by the least square method
N = 5 10 20
N = 50
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)
Small STD Dev. Largest STD Dev.
-0.1K/year
-0.5K/year
+0.1K/year
t-test
>99%
>90%
to get statistically significant trend ?
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]
has enabled us to do
some parameter sweep experiments with 3D MCMs