1. Caio A. S. Coelho Is a group of forecasts better than one? Department of Meteorology, University of Reading Introduction Combination in meteorology Bayesian combination Conclusion and future directions Plan of talk

2. Pierre-Simon Laplace (1749-1827) The Pioneer of combination a p Laplace (1818): Combination of two estimators slope residual

3. + numerical = methods Have combined forecasts better skill than individual forecasts? In modern times… Forecasts from

4. Forecast combination literature Trenkler and Gotu (2000): ~600 publications (1970-2000) Widely applied in Economics and Meteorology Overlap of methods in these areas Combined forecasts are better than individual forecasts

5. Some issues What is the best method for combining? Is it worth combining unbiased forecasts with biased forecasts?

6. DEMETER coupled model forecasts Nino-3.4 index (Y) Period: 1987-99 9 members Jul -> Dec 5 months lead DEMETER web page: http://www.ecmwf.int/research/demeter ECMWF Meteo-France (MF) Max Planck Institut (MPI)

7. December Nino-3.4 raw forecasts

8. Forecast combination in meteorology Linear combination of M ensemble mean forecasts X constants models ensemble mean combined forecast

9. Bias-removed multimodel ensemble mean forecast (Uem) Regression-improved multimodel ensemble mean forecast(Rem) Regression-improved multimodel forecast (Rall) Combination methods used in meteorology Kharin and Zwiers (2002) How to estimate w o and w i ?

10. Kharin and Zwiers combined forecasts

11. Y: Observed December Nino-3.4 index X: Ensemble mean forecast of Y for December Thomas Bayes ( 1701-1761) The process of belief revision on any event Y consists in updating the probability of Y when new information X becomes available The Bayesian approach Example: Ensemble mean (X=x=27  C) Likelihood:p(X=x|Y) Prior:p(Y) Posterior:p(Y|X=x)

12. Prior: Likelihood: Posterior: calibration Bayesian multimodel forecast (B) bias

13. July and December Reynolds OI V2 SST (1950-2001) Nino-3.4 index observational data Nino-3.4 index mean values: Jul: 27.1  C Dec: 26.5  C r: 0.87 R 2 =0.76

14. All combined forecasts Uem Rall Rem B Why are Rall and B so similar?

15. Combined forecasts in Bayesian notation ForecastLikelihoodPrior Uem Rem Rall B B prior Rem and Rall prior Bayesian combination Prior: Likelihood:

16. Skill and uncertainty measures ForecastMSE (  C) 2 Skill Score (%) Uncert. (  C) 2 Climatology1.9801.20 ECMWF (raw)1.64180.49 ECMWF (bias-removed)0.18910.49 ECMWF (regression-improved)0.22890.47 MF (raw)0.27860.39 MF (bias-removed)0.22890.39 MF (regression-improved)0.20900.46 MPI (raw)15.24-6690.49 MPI (bias-removed)1.52230.49 MPI (regression-improved)1.06460.86 Uem0.25881.79 Rem0.46770.56 Rall0.12940.38 B0.11940.23 Skill Score = [1- MSE/MSE(climatology)]*100%

17. Conclusions and future directions Forecast can be combined in several different ways Combined forecasts have better skill than individual forecasts Rall and B had best skill for Nino- 3.4 example Inclusion of very biased forecast has not deteriorated combination Extend method for South America rainfall forecasts