1 seasonal forecasts and predictability masato sugi climate prediction division/jma
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Seasonal Forecasts and Predictability
Masato Sugi
Climate Prediction Division/JMA
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History of Seasonal Forecasts at JMA
1942 Statistical One-month and Three-month forecasts1943 Statistical Warm/Cold season forecasts
1996 Dynamical One month forecast1999 El Nino Outlook with Coupled Model2003 Dynamical Three month forecast Dynamical Warm/Cold season forecasts
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One month forecasts : AGCM with persistent SSTA
T106L40 GSM0103 26 member
Three month forecasts: AGCM with persistent SSTA
T63L40 GSM0103 31 member
Warm/Cold season forecasts: Two tier method
T63L40 GSM0103 31 member
using SSTA predicted CGCM02
Operational models for seasonal forecasts at JMA
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Seasonal Forecasts
Issuance time
Lead time Forecast period
Forecast range
Forecast range Lead time Forecast period
1 month 0 - 2 week 1 - 4 week
3 month 0 - 2 month 1 - 3 month
6 month 0 - 3 month 3 month
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Analysis of Variance (ANOVA)
nxxxx 21
n2
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122
2
2
2
ii r
: correlation between and
ir
Variance explained by the i-th component
Decomposition of meteorological variable:
If and are statistically independent, then
x ix
ix jx
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ns xxx
)()()( ns xVxVxV
)(
)(
xV
xVR s
Decomposition of observed variable
: predictable signal
: unpredictable noise
Potential predictability
: variance of signal
: variance of noise
sx
nx
)( sxV
)( nxV
Potential predictability gives the upper limit of forecast skill.
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n2
s2
noise variance
signal variance
2cclimatologicaltotal variance
Forecast lead time
Variance
ns xxx
)()()( ns xVxVxV
nsc222
sx : Predictable signal
nx : Unpredictable noise
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Predictable signal: - some low-frequency internal modes- externally forced slowly varying modes- decadal modes - trends due to global warming
Unpredictable noise: - high-frequency internal modes
- most low-frequency modes that have strong interaction with high-frequency modes
Predictable signal and unpredictable noise
In seasonal forecasts, most important predictable signal is SST forced variability.
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Ensemble forecasts
- starting from slightly different initial conditions
- with the same boundary condition (SST)
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yyyyy ns
)(1
1)()( yV
NyVyV s
)(
)(
)(
)(
yV
yV
xV
xVR ss
Estimating potential predictability R
from ensemble simulation
: simulated variable
: predictable signal
: unpredictable noise
: ensemble mean
: deviation from
potential predictability
sy
ny
y
y
y y
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Ensemble simulation experiment
- MRI-JMA98 AGCM T42L30
- GISST 1949 - 1998
- 6-member, 50-year simulation
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JJA
DJF
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n
0 sx
nsc222
cs r
cn r 21
model)(real),( RryxCor
model)(perfect),( RyxCor sxy
Forecast PDF
model)(perfect),( RyxCor
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33%33%33%
0
- 0.43c 0.43c
PBPN PA
Climatological PDF )exp(2
1),0,()( 2
2
cc
c
xxNxP
PA : probability of Above normal
PN : probability of Normal
PB : probability of Below normal
Three-Category Forecast
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Forecast PDF ))(
exp(2
1),,()( 2
2
n
s
n
ns
xxxxNxP
PA : probability of Above normal
PN : probability of Normal
PB : probability of Below normal
APBP NP
0.43c- 0.43c 0 xs
Probability of three categories
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))(),(),(()( sCsBsAsc xpxpxpMaxxp
Percent Correct (Pc) : percentage of correct forecast
Deterministic category forecast
Category of highest probability
Forecast category
sssscc dxxpxpp )()(
)|()()( snssF xxpxpxp Forecast PDF
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0.0 0.0 1.0 33 %0.01 0.1 0.995 36 0.04 0.2 0.980 390.09 0.3 0.954 420.1 0.316 0.949 430.16 0.4 0.917 460.2 0.447 0.894 470.25 0.5 0.866 490.3 0.548 0.837 510.36 0.6 0.800 540.4 0.632 0.775 550.49 0.7 0.714 580.5 0.707 0.707 590.6 0.775 0.632 630.64 0.8 0.600 650.7 0.837 0.548 680.8 0.894 0.447 730.81 0.9 0.436 740.9 0.949 0.316 82
2rR rs 21 rn cp
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Overall skill of seasonal forecasts for seasonal mean temperature over Japan
Percent correct of three category forecasts:
40~50%
This value corresponds to the correlation between ensemble mean and observation:
0.23~0.52
Even though the percent correct is 40~50%
probability forecast is still useful.
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For example, if percent correct is 47% , then correlation is 0.44, s = 0.44c , n = 0.90c .
Climatological PDF
Forecast PDF
If forecast ensemble mean Xs = 0.4 c , then
0.00
0.10
0.20
0.30
0.40
0.50
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If potential predictability is 50% , then correlation is 0.707, s = 0.707c , n = 0.707c .
Climatological PDF
Forecast PDF
If forecast ensemble mean Xs = 0.7 c , then
0.00
0.10
0.20
0.30
0.40
0.50
0.60
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Summary
• In seasonal forecasts , it is important to understand the predictability and intrinsic uncertainty.
• Potential predictability is generally high in the tropics but low in the extratropics.
• Although there is a large uncertainty in seasonal forecasts, the forecast probability information is still potentially useful.
• Application technology of probability forecast to agriculture, water management, health, energy, etc., need to be developed.
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Appendix
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)(
)(
yV
yV
V
VR ss
Estimation error in R due to model deficiency
RyVV
RyVV
RyVV
RyVV
ss
ss
)(
)(
)(
)(
underestimated
overestimated
overestimated
underestimated
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)(
)(
xV
xV
V
VR ss
A proposal for estimating model independent potential predictability
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nsm yyyy
smn yyy ,0
ess yxy
Ensemble mean
for large ensemble size
We further assume
then
nes yyxy
ns xxx
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)()()()(
)(),(
2
22
xVyVyVxV
xVyxCor
es
s
)()()()()1()( nnes xVyVyVxVxyV
ns xxx
nes yyxy
correlation
RMSE
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)()(,,0,1 nnsesse xVyVxyxyy
2
2
222
)(
)(
)()()(
)(),( R
xV
xV
xVxVxV
xVyxCor s
ns
s
)(2)( nxVxyV
0,0,0,0 nes yyy
undefinedCor
)()()()( ns xVxVxVxyV
Perfect model
Climatology forecast
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)()()()(
)(),(
2
22
xVyVyVxV
xVyxCor
nes
s
)()()()()1()( nnes xVyVyVxVxyV
)()(1
)( nnn yVyVN
yV
Ensemble mean nes yyxy
better skill because
RxV
xVyxCor s
)(
)(),(2
)()( nxVxyV
Perfect model
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)()()()(
)(),(
2
22
xVyVyVxV
xVyxCor
nes
s
)()()()()1()( nnes xVyVyVxVxyV
)()( ee yVyV
Multi model ensemble mean
nes yyxy
better skill when
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?)()( ee yVyV
Multi model ensemble mean
0),( ejeiij yyCove
)()( eeii yVyVV
If
and for all i
then )()(1
)( eee yVyVM
yV
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?)()( ee yVyV Multi model ensemble mean
0),( ejeiij yyCove
)( jiVV ji
if
but
then weighted average improves the skill
eiie ywM
y1
ii
i VVw
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Estimating from multi model ensemble simulations
0),( ejeiij yyCoveif
sii VyxCov ),(
sjj VyxCov ),(
sjiji VyyCov ),(
sji V,,
si Vand
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Summary
By using multi-model ensemble simulations we can estimate
1) model independent signal variance and potential predictability,
V
VRV s
s and
ii Vand
2) signal amplitude and model error variance for each model,
3) optimum weight for multi-model ensemble
ii
i VVw
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