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1 Seasonal Forecasts and Predictability Masato Sugi Climate Prediction Division/JMA

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2 History of Seasonal Forecasts at JMA 1942 Statistical One-month and Three-month forecasts 1943 Statistical Warm/Cold season forecasts 1996 Dynamical One month forecast 1999 El Nino Outlook with Coupled Model 2003 Dynamical Three month forecast Dynamical Warm/Cold season forecasts

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3 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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4 Seasona l Forecasts Issuance time Lead time Forecast period Forecast range Forecast rangeLead timeForecast period 1 month0 - 2 week1 - 4 week 3 month0 - 2 month1 - 3 month 6 month0 - 3 month3 month

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5 Analysis of Variance (ANOVA) : correlation between and Variance explained by the i-th component Decomposition of meteorological variable: If and are statistically independent, then

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6 Decomposition of observed variable : predictable signal : unpredictable noise Potential predictability : variance of signal : variance of noise Potential predictability gives the upper limit of forecast skill.

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7 noise variance signal variance climatological total variance Forecast lead time Variance : Predictable signal : Unpredictable noise

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8 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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9 Ensemble forecasts - starting from slightly different initial conditions - with the same boundary condition (SST)

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10 Estimating potential predictability R from ensemble simulation : simulated variable : predictable signal : unpredictable noise : ensemble mean : deviation from potential predictability

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11 Ensemble simulation experiment - MRI-JMA98 AGCM T42L30 - GISST 1949 - 1998 - 6-member, 50-year simulation

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16 JJA DJF

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17 Forecast PDF

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18 33% 0 - 0.43 c 0.43 c PBPB PNPN PAPA Climatological PDF P A : probability of Above normal P N : probability of Normal P B : probability of Below normal Three-Category Forecast

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19 Forecast PDF P A : probability of Above normal P N : probability of Normal P B : probability of Below normal 0.43 c - 0.43 c 0 xsxs Probability of three categories

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20 Percent Correct (Pc) : percentage of correct forecast Deterministic category forecast Category of highest probability Forecast category Forecast PDF

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21 0.00.01.033 % 0.010.10.99536 0.040.20.98039 0.090.30.95442 0.10.3160.94943 0.160.40.91746 0.20.4470.89447 0.250.50.86649 0.30.5480.83751 0.360.60.80054 0.40.6320.77555 0.490.70.71458 0.5 0.7070.70759 0.6 0.7750.63263 0.640.80.60065 0.70.8370.54868 0.80.8940.44773 0.810.90.43674 0.90.9490.31682

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22 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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23 For example, if percent correct is 47%, then correlation is 0.44, s = 0.44 c, n = 0.90 c. Climatological PDF Forecast PDF If forecast ensemble mean Xs = 0.4 c, then

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24 If potential predictability is 50%, then correlation is 0.707, s = 0.707 c, n = 0.707 c. Climatological PDF Forecast PDF If forecast ensemble mean Xs = 0.7 c, then

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25 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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26 Appendix

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27 Estimation error in R due to model deficiency underestimated overestimated underestimated

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28 A proposal for estimating model independent potential predictability

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29 Ensemble mean for large ensemble size We further assume then

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30 correlation RMSE

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31 Perfect model Climatology forecast

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32 Ensemble mean better skill because Perfect model

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33 Multi model ensemble mean better skill when

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34 Multi model ensemble mean If and for all i then

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35 Multi model ensemble mean if but then weighted average improves the skill

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36 Estimating from multi model ensemble simulations if

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37 Summary By using multi-model ensemble simulations we can estimate 1) model independent signal variance and potential predictability, 2) signal amplitude and model error variance for each model, 3) optimum weight for multi-model ensemble

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