1. Caio A. S. Coelho, S. Pezzulli, M. Balmaseda (*), F. J. Doblas-Reyes (*) and D. B. Stephenson Forecast calibration and combination: A simple Bayesian approach Department of Meteorology, University of Reading and ECMWF (*) Aim: To create reliable probability forecasts from ensembles of predictions

2. Empirical forecasts of Niño-3.4 Well-calibrated: Most observations in the 95% prediction interval (P.I.) 95% P.I.

3. ECMWF coupled model ensemble forecasts  Observations not within the 95% prediction interval!  Coupled model forecasts need calibration http://www.ecmwf.int/research/demeter m=9 DEMETER: 5-month lead

4. Conceptual framework Data Assimilation “Forecast Assimilation”

5. Prior: Univariate X and Y Posterior: Likelihood: Bayes’ theorem:

6. Modelling the likelihood p(X|Y) y

7. Combined forecasts  Note: most observations within the 95% prediction interval!

8. All forecasts ForecastMAE (  C) Skill Score (%) Uncert. (  C) Climatolog y 1.1601.19 Empirical0.53550.61 Coupled0.57510.33 Combined0.31740.32 Skill Score = [1- MAE/MAE(climatology)]*100% Empirical Coupled Combined

9. Prior: Likelihood: Posterior: Multivariate X and Y bias Matrices

10. Equatorial Pacific SST anomalies ForecastBrier Score (B) BSS (%) Climatology0.250 Multi-model0.1924 FA 80-010.1731 SST anomalies: Y (°C) Forecast probabilities: p DEMETER: 7 coupled models 6-month lead Climatology: BSS = [1- B/B(clim.)]*100%

11. South American DJF rainfall anomalies Obs Multi-model Bayesian combined (mm/day) DEMETER: 7 coupled models 1-month lead Start: Nov -> DJF ENSO composites: 1980-2001 El Ni ñ o 82/83 86/87 87/88 90/91 91/92 92/93 93/94 94/95 97/98 La Ni ñ a 83/84 84/85 88/89 95/96 98/99 99/00 00/01 r=0.58 r=0.94 r=0.39r=0.79

12. Conclusions Forecast Assimilation: improves the skill of probability forecasts can be extended to deal with multi-model spatial forecasts improves the skill of seasonal precipitation forecasts in South America Three publications available at http://www.met.rdg.ac.uk/~swr01cac e-mail: c.a.d.s.coelho@reading.ac.uk