1. ECMWF Seasonal Forecast Group Meeting: 24 July 2002
Bayesian improvement of ENSO forecasts
PhD Student: Caio Coelho (*)
Supervisors: Dr. David B. Stephenson(*)
Dr. Francisco J. Doblas-Reyes (ECMWF)
Dr. Sergio Pezzulli (*)
(*): Deptartment of Meteorology, University of Reading

2. Aim: To improve probabilistic Nino-3 SST forecasts
Data: • December mean Nino-3 index
• ECMWF – DEMETER Oct 1986-Apr 1997
• 9 ensemble forecasts 4 times/yr
• August -> December (5 months lead)
Climatology: Reynolds OI SST

3. Example: Ensemble mean (X=x=27C)
: Observable Nino-3 index in December
X: forecast of  for December
Likelihood:p(X=x|)
Posterior:p(|X=x)
Prior:p()

4. 1. Estimating the prior p()

5. 2. Modelling the likelihood p(X=x|)
p(X=x|)=f()
Weighted regression
=0.71
=7.55 C
=9.85
X(t)=ensemble mean
V(t)=ensemble variance

6. Likelihood Model

7. Likelihood Model
Perfect forecast

8. 3. Use Bayes theorem to get posterior pdf

9. All forecasts a) Climatology b) DEMETER c) Bayesian – U. prior
d) Bayesian full

10. a) Climatology forecast

11. b) Ensemble forecast

12. c) Bayesian with uniform prior

13. d) Bayesian full

14. Skill Score = [1- MAE/MAE(climatology)]*100
Verification Scores
Forecast
MSE
[C]2
MAE
[C]
Skill Score (MAE)
Uncertainty
a) Climatology
1.01
0.80
0 %
1.23
b) DEMETER
0.32
0.49
38 %
0.34
c) Bayes (U.prior)
0.23
0.43
46 %
0.50
d) Bayes full
0.22
0.38
53 %
0.46
Skill Score = [1- MAE/MAE(climatology)]*100

15. Skill-Spread relationship
Skill=|X--|
Skill=spread
Linear fit
Spread=

16. Conclusions
Bayesian approach:
improved MSE and MAE
improved skill in ~15%
more realistic uncertainty estimate

17. Probabilistic Forecast = pr(An | For)
ECMWF, Reading,
COAPEC project : November
Quantifying the economic value of coupled
ocean-atmosphere model ensemble forecasts
for decision-making within the UK energy industry
S.Pezzulli, D.B.Stephenson, A.O.’Neill, R.Sutton, P-P. Mathieu
S. Majithia (NGC)
T. Palmer (ECMWF)
Probabilistic Forecast = pr(An | For)
Joint and conditional probabilities
Hints for discussion?

18. Joint and Marginal distributions
p(x*) =  p(x*, y) dy y* x*
p(y*) =  p(x, y*) dx

19. Joint and Conditional distributionsy* x*
p(x | y*) = p(x, y*) /p(y*)

20. p() p(x|) = p(,x) = p(x) p(|x) prior Likelihood 1 … n (1 , x1)
(m , xm)

21. Future plans Non Normality Multi Model Forecasts System 2 data
More informative prior
Non Normality
Multi Model Forecasts
System 2 data

22. Joint and Conditional distributionsy*
p(x | y*) = p(x, y*) /p(y*)

23. Joint and Marginal distributions
p(x*) =  p(x*, y) dy y* x*
p(y*) =  p(x, y*) dx