1. Caio A. S. Coelho, S. Pezzulli, M. Balmaseda (*), F. J. Doblas-Reyes (*) and D. B. Stephenson Bayesian combination of ENSO forecasts Department of Meteorology, University of Reading and ECMWF (*) Aim Coupled forecasts Empirical forecasts Bayesian combination Conclusion and future directions Plan of talk

2. Aim Improve ENSO probability forecasts by using Bayesian approach to combine historical information with coupled model ensemble forecasts

3. ECMWF coupled model forecasts  Note: observations not within the 95% prediction interval! Nino-3 index DEMETER: 1987-98 9 members Jul -> Dec 5 months lead DEMETER web page: http://www.ecmwf.int/research/demeter R 2 =0.90

4. July and December Reynolds OI V2 SST (1950-2001) Nino-3 index observational data Nino-3 index mean values: Jul: 25.5  C Dec: 25.0  C r: 0.83 R 2 =0.69

5. Empirical persistence forecasts R 2 =0.79  Larger 95% prediction interval  More observations within the 95% prediction interval

6.  : Observed December Nino-3 index X: Ensemble mean forecast of  for December Thomas Bayes ( 1701-1761) The process of belief revision on any event  consists in updating the probability of  when new information X becomes available The Bayesian approach Example: Ensemble mean (X=x=27  C) Likelihood:p(X=x|  ) Prior:p(  ) Posterior:p(  |X=x)

7. Modelling the likelihood p(X=x|  )  =8.55  C  =0.67  =9.88 R 2 =0.95

8. Combined forecasts  Note: more observations within the 95% prediction interval! R 2 =0.90

9. All forecasts ForecastMAE (  C) Skill Score (%) Uncert. (  C) Climatolog y 1.0801.23 Empirical0.50530.72 Raw0.53510.33 Combined0.35680.39 Skill Score = [1- MAE/MAE(climatology)]*100% R 2 =0.79 R 2 =0.90

10. Conclusions and future directions Bayesian combination improves the skill and uncertainty estimates of ENSO probability forecasts Methodology is now being extended to deal with multi-model DEMETER forecasts Extend method for South America rainfall forecasts e-mail: c.a.d.s.coelho@reading.ac.uk http://www.met.rdg.ac.uk/~swr01cac

11. Example: December 2002 forecasts Nino-3.4 Forecast Forecast + 1.96 std.dev (95% P.I) 1) Climatology 26.47 + 2.33  C 2) Empirical 27.82 + 1.14  C 3) Raw 27.13 + 0.54  C 4) Bias-corrected 27.56 + 0.54  C 5) Combined 28.13 + 0.71  C  Note: Best accuracy and reliability obtained through the combined forecast Observed Nino-3.4 value = 28.10  C