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

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

3. ECMWF coupled model forecasts
Nino-3 index
DEMETER:
9 members
Jul -> Dec
5 months lead
R2 =0.90
 Note: observations not within the 95% prediction interval!
DEMETER web page:

4. Nino-3 index observational data
mean values:
Jul: 25.5C
Dec: 25.0C
r: 0.83
July and December Reynolds OI V2 SST ( )
R2 =0.69

5. Empirical persistence forecasts
Larger 95% prediction interval
More observations within the 95% prediction interval

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

7. Modelling the likelihood p(X=x|)
=8.55 C
=0.67
=9.88
R2=0.95

8. Combined forecasts
R2 =0.90
 Note: more observations within the 95% prediction interval!

9. All forecasts R2 =0.90 R2 =0.79 R2 =0.90 Forecast MAE (C) Skill Score
(%)
Uncert.
Climatology
1.08
1.23
Empirical
0.50 53
0.72
Raw
0.53 51
0.33
Combined
0.35 68
0.39
Skill Score = [1- MAE/MAE(climatology)]*100%

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

11. Example: December 2002 forecasts
Observed Nino-3.4 value = 28.10C
Nino-3.4
Forecast
Forecast std.dev
(95% P.I)
1) Climatology C
2) Empirical C
3) Raw C
4) Bias-corrected C
5) Combined C
Note: Best accuracy and reliability obtained through the
combined forecast