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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

22

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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13

14

15

16

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

27

)(

)(

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

11

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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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