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Bayesian methods for combining climate forecasts

Bayesian methods for combining climate forecasts. David B. Stephenson, Sergio Pezzulli, Caio Coelho (*) Francisco J. Doblas-Reyes, Magdalena Balmaseda. Introduction Conditioning and Bayes’ theorem Results. (*): Department of Meteorology, The University of Reading. 1. Introduction.

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Bayesian methods for combining climate forecasts

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  1. Bayesian methods for combining climate forecasts David B. Stephenson, Sergio Pezzulli, Caio Coelho (*) Francisco J. Doblas-Reyes, Magdalena Balmaseda • Introduction • Conditioning and Bayes’ theorem • Results (*): Department of Meteorology, The University of Reading

  2. 1. Introduction

  3. Motivation • Empirical versus dynamical forecasts? • Why not combine both types of forecast in order to use ALL possible information? • Ensemble forecasts + probability model  probability forecasts • Use sample of ensemble forecasts to update historical (prior) probability information (post-forecast assimilation)

  4. El Nino – Southern Oscillation <1982/3 <1997/8 • Big El Nino events in 1982/3 and 1997/8 • La Nina/normal conditions since 1998 • El Nino event predicted for end of 2002 Jan 1997 Nov 1997 Mar 1998

  5. Recent sea temperature anomalies 16 Sep 2002 • ENSO forecasts from ECMWF, Reading Sep 2002-Feb 2003

  6. DATA Sea Surface Temperatures (SST) “at” location Nino 3.4 ( 5S - 5N , 170W - 120W ) December means of Nino 3.4: • Reynolds SST : 1950-2001 • ECMWF DEMETER ensemble forecasts: 1987-1999

  7. Some notation … • Observed Dec Nino-3.4 • Ensemble mean forecast • Ensemble standard deviation • Normal (Gaussian) probability forecasts:

  8. 2. Conditioning and Bayes theorem

  9. Probability density functions (distributions) Bi-dimensional or Joint distribution of X & Y Uni-dimensional

  10. Marginal distributions p(x*) = p(x*, y) dy Y x* X

  11. Conditional distributions p(x | y*) = p(x, y*) /p(y*) y*

  12. Conditional-chain Rule p(y) p(x|y) = p(x , y) =p(x) p(y|x) Bayes Theorem p(x|y) = p(x , y) / p(y)  p(x , y) =p(x) p(y|x)

  13. Thomas Bayes 1701-1761 An Essay towards Solving a Problem In the Doctrine of Chances. Philosophical Transactions of the Royal Society, 1763 The process of belief revision on any event W (the weather) consists in updating the probability of W when new information F (the forecast) becomes available p(W | F)p(W)p(F | W) p(W) = N( , 2) p(F | W) = N( + W , V)

  14. The Likelihood Model

  15. 3. Forecast results

  16. Empirical forecasts

  17. Coupled model forecasts  Note: many forecasts outside the 95% prediction interval!

  18. Combined forecast  Note: more forecasts within the 95% prediction interval!

  19. Mean likelihood model estimates • ensemble forecasts too cold on average (alpha>0) • ensemble forecast anomalies too small (beta<1) • ensemble forecast spread underestimates forecast uncertainty

  20. Forecast statistics and skill scores Note that the combined forecast has: • A large increase in MAE (and MSE) forecast skill • A realistic uncertainty estimate

  21. Conclusions and future directions • Bayesian combination can substantially improve the skill and uncertainty estimates of ENSO probability forecasts • Methodology will now be extended to deal with multi-model DEMETER forecasts • Similar approach could be developed to provide better probability forecasts at medium-range (Issues: non-normality, more forecasts, lagged priors, etc.).

  22. Coupled Model Ensemble Forecast

  23. Ensemble Forecast and Bias Correction Bias Corrected

  24. Climatology

  25. Climatology + Ensemble

  26. Coupled-Model Bias-Corrected Ensemble Forecast Climatology + Ensemble

  27. Coupled-Model Bias-Corrected Ensemble Forecast Empirical Regression Model + Ensemble

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