Seasonal Forecasts and Predictability

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

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 CoupledModel 2003 Dynamical Three month forecast Dynamical Warm/Cold season forecasts

3. Operational models for seasonal forecasts at JMA 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

4. Seasonal Forecasts Issuance time Forecast period Lead time 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

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

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

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

8. Predictable signal and unpredictable noise • 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 In seasonal forecasts, most important predictable signal is SST forced variability.

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

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

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

16. JJA DJF

17. Forecast PDF

18. PN PA PB 33% 33% 33% 0.43c - 0.43c 0 Three-Category Forecast Climatological PDF PA : probability of Above normal PN : probability of Normal PB : probability of Below normal

19. Probability of three categories Forecast PDF xs - 0.43c 0 0.43c PA : probability of Above normal PN : probability of Normal PB : probability of Below normal

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

21. 0.0 0.0 1.0 33 % • 0.01 0.1 0.995 36 • 0.04 0.2 0.980 39 • 0.09 0.3 0.954 42 • 0.1 0.316 0.949 43 • 0.16 0.4 0.917 46 • 0.2 0.447 0.894 47 • 0.25 0.5 0.866 49 • 0.3 0.548 0.837 51 • 0.36 0.6 0.800 54 • 0.4 0.632 0.775 55 • 0.49 0.7 0.714 58 • 0.5 0.707 0.707 59 • 0.6 0.775 0.632 63 • 0.64 0.8 0.600 65 • 0.7 0.837 0.548 68 0.8 0.894 0.447 73 0.81 0.9 0.436 74 • 0.9 0.949 0.316 82

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.

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

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

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.

26. Appendix

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

28. A proposal for estimating model independent potential predictability

29. Ensemble mean for large ensemble size We further assume then

30. correlation RMSE

31. Perfect model Climatology forecast

32. Ensemble mean better skill because Perfect model

33. Multi model ensemble mean better skill when

34. Multi model ensemble mean If and for all i then

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

36. Estimating from multi model ensemble simulations if

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