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Caio A. S. Coelho

Is a group of forecasts better than one?. Caio A. S. Coelho. Department of Meteorology, University of Reading. Plan of talk. Introduction Combination in meteorology Bayesian combination Conclusion and future directions. The Pioneer of combination. Pierre-Simon Laplace (1749-1827). a.

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Caio A. S. Coelho

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

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

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

  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 ECMWF Meteo-France (MF) Max Planck Institut (MPI) DEMETER web page: http://www.ecmwf.int/research/demeter

  7. December Nino-3.4 raw forecasts

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

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

  10. Kharin and Zwierscombined forecasts

  11. The Bayesian approach 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 Y: Observed December Nino-3.4 index X: Ensemble mean forecast of Y for December Likelihood:p(X=x|Y) Posterior:p(Y|X=x) Example: Ensemble mean (X=x=27C) Prior:p(Y)

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

  13. Nino-3.4 index observational data Nino-3.4 index mean values: Jul: 27.1C Dec: 26.5C r: 0.87 July and December Reynolds OI V2 SST (1950-2001) R2 =0.76

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

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

  16. Skill and uncertainty measures 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

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