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

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 1950-2001

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()

1. Estimating the prior p()

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

Likelihood Model

Likelihood Model Perfect forecast

3. Use Bayes theorem to get posterior pdf

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

a) Climatology forecast

b) Ensemble forecast

c) Bayesian with uniform prior

d) Bayesian full

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

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

Conclusions Bayesian approach: improved MSE and MAE improved skill in ~15% more realistic uncertainty estimate e-mail: c.a.d.s.coelho@reading.ac.uk http://www.met.rdg.ac.uk/~swr01cac

Probabilistic Forecast = pr(An | For) ECMWF, Reading, 24. 7. 2002 COAPEC project : November 2002-2004 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?

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

Joint and Conditional distributions y* x* p(x | y*) = p(x, y*) /p(y*)

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

Future plans Non Normality Multi Model Forecasts System 2 data More informative prior Non Normality Multi Model Forecasts System 2 data sergio@met.reading.ac.uk

Joint and Conditional distributions y* p(x | y*) = p(x, y*) /p(y*)

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