Climate Dynamics

, Volume 53, Issue 5–6, pp 3373–3385 | Cite as

Improving the CPC’s ENSO Forecasts using Bayesian model averaging

  • Hanpei Zhang
  • Pao-Shin ChuEmail author
  • Luke He
  • David Unger


Statistical and dynamical model simulations have been commonly used separately in El Niño–Southern Oscillation (ENSO) prediction. Current models are imperfect representations of ENSO and each of them has strength and weakness for capturing different aspects in ENSO prediction. Thus, it is important to utilize the results from a variety of different models. The Bayesian model averaging (BMA) is an effective tool not only in describing uncertainties associated with each model simulation but also providing the forecast performance of different models. The BMA method was developed to combine the NCEP/CPC three statistical and one dynamical model forecasts of seasonal Ocean Niño Index (ONI) from 1982 to 2010. The BMA weights were derived directly from the predictive performance of the combined models. The highly efficient expectation–maximization (EM) algorithm was used to achieve numerical solutions. We show that the BMA method can be used to assess the performance of the individual models and assign greater weights to better performing models. The continuous ranked probability score is applied to evaluate the BMA probability forecasts. As an elaboration of the reliability diagram, the attributes diagram is used that includes the calibration function, refinement distribution, and reference lines. The combination of statistical and dynamical models is found to provide a more skillful prediction of ENSO than only using a suite of statistical models, a single bias-corrected dynamical model, or the equally weighted average forecasts from all four models. Probability forecasts of El Niño events based only on winter ONI values are reliable and exhibit sharpness. In contrast, an under-forecasting bias and less reliable forecasts are noted for La Niña.



This study was funded by the Hawaii State Climate Office through SOEST at the University of Hawaii at Manoa and the Climate Prediction Center of NCEP. We thank May Izumi for her editing service.


  1. Barnston AG, van den Dool HM, Zebiak SE, Barnett TP, Ji M, Rodenhuis DR, Cane MA, Leetmaa A, Graham NE, Ropelewski CF, Kousky VE, O’Lenic EA, Livezey RE (1994) Long-lead seasonal forecasts—where do we stand? Bull. Am Meteorol Soc 75:2097–2114CrossRefGoogle Scholar
  2. Barnston AG, Glantz MH, He Y (1999) Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997/98 El Nino episode and the 1998 La Nina onset. Bull Am Meteorol Soc 80:217–243CrossRefGoogle Scholar
  3. Barnston AG, Tippett MK, L’Heureux ML, Li S, DeWitt DG (2012) Skill of real-time seasonal ENSO model predictions during 2002–11: is our capability increasing? Bull Am Meteorol Soc 93:631–651CrossRefGoogle Scholar
  4. Barnston AG, Tippett MK (2013) Predictions of Nino3. 4 SST in CFSv1 and CFSv2: a diagnostic comparison. Clim Dyn 41:1615–1633CrossRefGoogle Scholar
  5. Bishop CH, Shanley KT (2008) Bayesian model averaging’s problematic treatment of extreme weather and a paradigm shift that fixes it. Mon Wea Rev 136:4641–4652CrossRefGoogle Scholar
  6. Chen D, Zebiak SE, Busalacchi AJ, Cane MA (1995) An improved procedure for EI Niño forecasting: implications for predictability. Science 269:1699–1702CrossRefGoogle Scholar
  7. Chu P-S, Zhao X (2011) Bayesian analysis for extreme climatic events: a review. Atmos Res 102:243–262CrossRefGoogle Scholar
  8. Coelho CAS, Pezzulli S, Balmaseda M, Doblas-Reyes FJ, Stephenson DB (2004) Forecast calibration and combination: a simple Bayesian approach for ENSO. J Climate 17:1504–1516CrossRefGoogle Scholar
  9. Fang M, Li X (2016) Application of Bayesian model averaging in the reconstruction of past climate change using PMIP3/CMIP5 multimodel ensemble simulations. J Clim 29:175–189CrossRefGoogle Scholar
  10. Faust J, Wright JH (2013) Forecasting inflation. In Handbook of economic forecasting (Vol. 2, pp. 2–56). ElsevierGoogle Scholar
  11. Glantz MH (2001) Currents of change: impacts of El Niño and La Niña on climate and society. Cambridge Univ. Press, CambridgeGoogle Scholar
  12. Gneiting T, Raftery AE, Westveld AH III, Goldman T, T (2005) Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation. Mon Wea Rev 133:1098–1118CrossRefGoogle Scholar
  13. He Y, Barnston AG (1996) Long-lead forecasts of seasonal precipitation in the tropical Pacific Islands Using CCA. J Climate 9:2020–2035CrossRefGoogle Scholar
  14. Hsu W-R, Murphy AH (1986) The attributes diagram A geometrical framework for assessing the quality of probability forecasts. Int J Forecast 2:285–293. CrossRefGoogle Scholar
  15. Kirtman BP, Min D (2009) Multimodel ensemble ENSO prediction with CCSM and CFS. Mon Wea Rev 137:2908–2930CrossRefGoogle Scholar
  16. Kirtman BP, Pirani A (2009) The state of the art of seasonal prediction: outcomes and recommendations from the First World Climate Research Program Workshop on seasonal prediction. Bull Am Meteorol Soc 90:455–458CrossRefGoogle Scholar
  17. Landsea CW, Knaff JA (2000) How much skill was there in forecasting the very strong 1997–98 El Niño? Bull Am Meteorol Soc 81:2107–2120CrossRefGoogle Scholar
  18. Madigan D, Raftery AE (1994) Model selection and accounting for model uncertainty in graphical models using OCCAM’s window. J Am Stat Assoc 89:1535–1546CrossRefGoogle Scholar
  19. McAvaney BJ, Coauthors (2001) Model evaluation. climate change 2001: the scientific basis. In: Houghton JT (ed) Cambridge Univ. Press, Cambridge, pp 471–523Google Scholar
  20. McPhaden MJ, Glantz MH (2006) ENSO as an integrating concept in earth science. Science 314:1740–1745CrossRefGoogle Scholar
  21. Min SK, Simonis D, Hense A (2007) Probabilistic climate change predictions applying Bayesian model averaging. Philos Trans R Soc Lond: Math Phys Eng Sci 365:2103–2116CrossRefGoogle Scholar
  22. Peng P, Kumar A, van den Dool H, Barnston AG (2002) An analysis of multimodel ensemble predictions for seasonal climate anomalies. J Geophys Res 107:D23, 4710. CrossRefGoogle Scholar
  23. Raftery AE, Gneiting T, Balabdaoui TF, Polakowski M (2005) Using Bayesian model averaging to calibrate forecast ensembles. Mon Wea Rev 133:1155–1174CrossRefGoogle Scholar
  24. Rasmusson EM, Wallace JM (1983) Meteorological aspects of the El Niño/Southern oscillation. Science 222:1195–1202. CrossRefGoogle Scholar
  25. Rings J, Vrugt JA, Schoups G, Huisman JA, Vereecken H (2012) Bayesian model averaging using particle filtering and Gaussian mixture modeling: theory, concepts, and simulation experiments. Water Resour Res 48(5)Google Scholar
  26. Saha S et al. (2014) The NCEP climate forecast system version 2. J Clim 27(6):2185–2208CrossRefGoogle Scholar
  27. Sarachik ES, Cane MA (2010) The El Niño-Southern oscillation phenomenon. Cambridge Univ. Press, p 384Google Scholar
  28. Schepen A, Wang QJ, Robertson DE (2014) Combining the strengths of statistical and dynamical modeling approaches for forecasting Australian seasonal rainfall. J Geophys Res (Atmospheres), 117(D20)Google Scholar
  29. Sloughter JM, Gneiting T, Raftery AE (2010) Probabilistic wind speed forecasting using ensembles and Bayesian model averaging. J Amer Stat Assoc 105:25–35CrossRefGoogle Scholar
  30. Tebaldi C, Smith RL, Nychka D, Mearns LO (2005) Quantifying uncertainty in projections of regional climate change: a Bayesian approach to the analysis of multimodel ensembles. J Climate 18:1524–1540CrossRefGoogle Scholar
  31. Tian X, Xie Z, Wang A, Yang X (2012) A new approach for Bayesian model averaging. Sci China Earth Sciences 55:1336–1344CrossRefGoogle Scholar
  32. Trenberth KE (1998) Development and forecasts of the 1997/98 El Niño: CLIVAR scientific issues. CLIVAR Exchanges 3:4–14Google Scholar
  33. Van den Dool HM (1994) Searching for analogues, how long must we wait? Tellus, 46A, 314–324CrossRefGoogle Scholar
  34. Vrugt JA, Robinson BA (2007) Treatment of uncertainty using ensemble methods: comparison of sequential data assimilation and Bayesian model averaging. Water Resour Res 43:W01411. CrossRefGoogle Scholar
  35. Wang QJ, Schepen A, Robertson DE (2012) Merging seasonal rainfall forecasts from multiple statistical models through Bayesian model averaging. J Climate 25:5524–5537CrossRefGoogle Scholar
  36. Wilks DS (2011) Statistical methods in the atmospheric sciences. Academic Press, 676 pp 334–340Google Scholar
  37. Xue Y, Leetmaa A (2000) Forecasts of tropical Pacific SST and sea level using a Markov model. Geophys Res Lett 27:2701–2704CrossRefGoogle Scholar
  38. Yu Z-P, Chu P-S, Schroeder T (1997) Predictive skills of seasonal to annual rainfall variations in the U.S. affiliated Pacific islands: Canonical correlation analysis and multivariate principal component regression approaches. J Clim 10:2586–2509CrossRefGoogle Scholar
  39. Zhang W, Villarini G, Slater L, Vecchi GA, Bradley AA (2017) Improved ENSO forecasting using bayesian updating and the North American multimodel ensemble (NMME). J Climate 30:9007–9025CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Atmospheric Sciences, School of Ocean and Earth Science and TechnologyUniversity of Hawaii at ManoaHonoluluUSA
  2. 2.Climate Prediction Center, NCEP, NOAACollege ParkUSA

Personalised recommendations