Climate Dynamics

, Volume 47, Issue 12, pp 3901–3915 | Cite as

Improved ensemble-mean forecasting of ENSO events by a zero-mean stochastic error model of an intermediate coupled model



How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño–Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-year hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism.


Model-error perturbation ENSO prediction Ensemble-mean dynamics Nonlinear heating 


  1. Alves O, Balmaseda M, Anderson D, Stockdale T (2004) Sensitivity of dynamical seasonal forecasts to ocean initial conditions. Q J R Meteorol Soc 130:647–668CrossRefGoogle Scholar
  2. An SI, Jin FF (2004) Nonlinearity and asymmetry of ENSO. J Clim 17(12):2399–2412CrossRefGoogle Scholar
  3. Ashok K, Yamagata T (2009) Climate change: the El Niño with a difference. Nature 461:481–484CrossRefGoogle Scholar
  4. Ashok K, Behera SK, Rao SA, Weng H, Yamagata T (2007) El Niño Modoki and its possible teleconnection. J Geophys Res 112:C11007. doi:10.1029/2006JC003798 CrossRefGoogle Scholar
  5. Barnston AG, Tippett MK, L’Heureux ML, Li S, DeWitt DG (2012) Skill of real-time seasonal ENSO model predictions during 2002–2011: is our capability increasing? Bull Am Meteorol Soc 93:63–651CrossRefGoogle Scholar
  6. Batstone C, Hendon HH (2005) Characteristics of stochastic variability associated with ENSO and the role of the MJO. J Clim 18:1773–1789CrossRefGoogle Scholar
  7. Battisti DS, Hirst AC (1989) Interannual variability in the tropical atmosphere/ocean system: influence of the basic state, ocean geometry and nonlinearity. J Atmos Sci 46:1687–1712CrossRefGoogle Scholar
  8. Bjerknes J (1969) Atmospheric teleconnections from the equatorial Pacific. Mon Weather Rev 97:163–172CrossRefGoogle Scholar
  9. Blanke B, Neelin JD, Gutzler D (1997) Estimating the effect of stochastic wind stress forcing on ENSO irregularity. J Clim 10:1473–1486CrossRefGoogle Scholar
  10. Buizza R, Palmer TN (1998) Impact of ensemble size on ensemble prediction. Mon Weather Rev 126(9):2503–2518CrossRefGoogle Scholar
  11. Capotondi A, Wittenberg AT, Newman M, Di Lorenzo E, Yu JY, Braconnot P, Cole J, Dewitte B, Giese B, Guilyardi E, Jin FF, Karnauskas K, Kirtman B, Lee T, Schneider N, Xue Y, Yeh SW (2015) Understanding ENSO diversity. Bull Am Meteorol Soc 96:921–938CrossRefGoogle Scholar
  12. Chang CC, Yang SC, Keppenne C (2014) Applications of the mean recentering scheme to improve typhoon track prediction: a case study of typhoon Nanmadol (2011). J Meteor Soc Jpn 92:559–584CrossRefGoogle Scholar
  13. Ding H, Keenlyside N, Latif M (2012) Impact of the equatorial Atlantic on the El Niño Southern Oscillation. Clim Dyn 38(9):1965–1972CrossRefGoogle Scholar
  14. Duan WS, Zhang R (2010) Is model parameter error related to a significant spring predictability barrier for El Niño events? Results from a theoretical model. Adv Atmos Sci 27(5):1003–1013CrossRefGoogle Scholar
  15. Duan WS, Zhao P (2015) Revealing the most disturbing tendency error of Zebiak–Cane model associated with El Niño predictions by nonlinear forcing singular vector approach. Clim Dyn 44:2351–2367CrossRefGoogle Scholar
  16. Feng LS, Zheng F, Zhu J, Liu HW (2015) The role of stochastic model error perturbations in predicting the 2011/12 double-dip La Niña. SOLA 11:65–69CrossRefGoogle Scholar
  17. Gebbie G, Eisenman I, Wittenberg A, Tziperman E (2007) Modulation of westerly wind bursts by sea surface temperature: a semi-stochastic feedback for ENSO. J Atmos Sci 64:3281–3295CrossRefGoogle Scholar
  18. Gill AE (1980) Some simple solutions for heat-induced tropical circulation. Q J R Meteorol Soc 106:447–462CrossRefGoogle Scholar
  19. Guilyardi E, Wittenberg A, Fedorov A, Collins M, Wang C, Capotondi A, van Oldenborgh GJ, Stockdale T (2009) Understanding El Niño in ocean–atmosphere general circulation models: progress and challenges. Bull Am Meteorol Soc 90:325–340CrossRefGoogle Scholar
  20. Hendon HH, Wheeler MC, Zhang C (2007) Seasonal dependence of the MJO–ENSO relationship. J Clim 20:531–543CrossRefGoogle Scholar
  21. Izumo T, Vialard J, Lengaigne M, de Boyer Montégut C, Behera SK, Luo JJ, Cravatte S, Masson S, Yamagata T (2010) Influence of the Indian Ocean Dipole on following year’s El Niño. Nat Geosci 3:168–172CrossRefGoogle Scholar
  22. Ji M, Leetmaa A (1997) Impact of data assimilation on ocean initialization and El Niño prediction. Mon Weather Rev 125:742–753CrossRefGoogle Scholar
  23. Ji M, Reynolds RW, Behringer DW (2000) Use of TOPEX/Poseidon sea level data for ocean analyses and ENSO prediction: some early results. J Clim 13:216–231CrossRefGoogle Scholar
  24. Jin FF, An S, Timmermann A, Zhao J (2003) Strong El Niño events and nonlinear dynamical heating. Geophys Res Lett 30(3):1120. doi:10.1029/2002GL016356 CrossRefGoogle Scholar
  25. Jin FF, Lin L, Timmermann A, Zhao J (2007) Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing. Geophys Res Lett 34:L03807. doi:10.1029/2006GL027372 Google Scholar
  26. Jin EK, James L, Kinter III, Wang B, Park C-K, Kang I-S, Kirtman BP, Kug J-S, Kumar A, Luo JJ, Schemm J, Shukla J, Yamagata T (2008) Current status of ENSO prediction skill in coupled ocean–atmosphere models. Clim Dyn 31(6):647–664CrossRefGoogle Scholar
  27. Kalnay E (2003) Atmospheric modeling, data assimilation, and predictability. Cambridge University Press, CambridgeGoogle Scholar
  28. Kalnay E, Kanamitsu M, Kistler R et al (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77:437–471CrossRefGoogle Scholar
  29. Karspeck AR, Kaplan A, Cane MA (2006) Predictability loss in an intermediate ENSO model due to initial error and atmospheric noise. J Clim 19(15):3572–3588. doi:10.1175/JCLI3818.1 CrossRefGoogle Scholar
  30. Keenlyside N, Kleeman R (2002) Annual cycle of equatorial zonal currents in the Pacific. J Geophys Res 107:3093. doi:10.1029/2000JC000711 CrossRefGoogle Scholar
  31. Keenlyside N, Latif M, Botzet M, Jungclaus J, Schulzweida U (2005) A coupled method for initialising ENSO forecasts using SST. Tellus A 57:340–356CrossRefGoogle Scholar
  32. Keenlyside N, Ding H, Latif M (2013) Potential of equatorial Atlantic variability to enhance El Niño prediction. Geophys Res Lett 40:2278–2283. doi:10.1002/grl.50362 CrossRefGoogle Scholar
  33. Kirtman BP (2003) The COLA anomaly coupled model: ensemble ENSO prediction. Mon Weather Rev 131:2324–2341CrossRefGoogle Scholar
  34. Kirtman BP, Shukla J, Balmaseda M, Graham N, Penland C, Xue Y, Zebiak SE (2002) Current status of ENSO forecast skill: a report to the climate variability and predictability (CLIVAR) working group on seasonal to interannual prediction. WCRP Informal Report No. 23/01, 31 ppGoogle Scholar
  35. Kleeman R (2008) Limits, variability, and general behavior of statistical predictability of the midlatitude atmosphere. J Atmos Sci 65:263–275CrossRefGoogle Scholar
  36. Kleeman R, Moore AM (1997) A theory for the limitations of ENSO predictability due to stochastic atmospheric transients. J Atmos Sci 54:753–767CrossRefGoogle Scholar
  37. Kleeman R, Moore AM (1999) New method for determining the reliability of dynamical ENSO predictions. Mon Weather Rev 127:694–705CrossRefGoogle Scholar
  38. Klein SA, Hartmann DL (1993) The seasonal cycle of low stratiform clouds. J Clim 6:1587–1606CrossRefGoogle Scholar
  39. Kug JS, Li T, An SI et al (2006) Role of the ENSO–Indian Ocean coupling on ENSO variability in a coupled GCM. Geophys Res Lett 33:L09710. doi:10.1029/2005GL024916 CrossRefGoogle Scholar
  40. Latif M, Anderson D, Barnett T et al (1998) A review of the predictability and prediction of ENSO. J Geophys Res Oceans 103(C7):14375–14393CrossRefGoogle Scholar
  41. Levitus S (1982) Climatological atlas of the world ocean. NOAA Prof. Paper 13, 173 pp and 17 microficheGoogle Scholar
  42. Lin JL (2007) The double-ITCZ Problem in IPCC AR4 coupled GCMs: ocean–atmosphere feedback analysis. J Clim 20:4497–4525CrossRefGoogle Scholar
  43. Lukas R, Lindstrom E (1991) The mixed layer of the western equatorial Pacific Ocean. J Geophys Res 96:3343–3357CrossRefGoogle Scholar
  44. Luo JJ, Masson S, Behera SK, Shingu S, Yamagata T (2005) Seasonal climate predictability in a coupled OAGCM using a different approach for ensemble forecasts. J Clim 18:4474–4497CrossRefGoogle Scholar
  45. Luo JJ, Masson S, Behera SK, Yamagata T (2008) Extended ENSO predictions using a fully coupled ocean–atmosphere model. J Clim 21:84–93CrossRefGoogle Scholar
  46. Luo JJ, Zhang RC, Behera SK et al (2010) Interaction between El Niño and extreme Indian Ocean dipole. J Clim 23:726–742CrossRefGoogle Scholar
  47. Luo JJ, Yuan CX, Sasaki W et al (2015) Current status of intraseasonal–seasonal-to-interannual prediction of the Indo-Pacific climate. In: Yamagata T, Behera S (eds) Chapter 3 in The Indo-Pacific climate variability and predictability, Asia-Pacific weather and climate book series, vol 7. The World Scientific Publisher, SingaporeGoogle Scholar
  48. Madden R, Julian P (1972) Description of global-scale circulation cells in the tropics with a 40–50 day period. J Atmos Sci 29:1109–1123CrossRefGoogle Scholar
  49. Magnusson L, Alonso-Balmaseda M, Corti S, Molteni F, Stockdale T (2013) Evaluation of forecast strategies for seasonal and decadal forecasts in presence of systematic model errors. Clim Dyn 41:2393–2409CrossRefGoogle Scholar
  50. Mantua NJ, Battisti DS (1995) Aperiodic variability in the Zebiak-Cane coupled ocean-atmosphere model: air-sea interactions in the western equatorial Pacific. J Clim 8:2897–2927CrossRefGoogle Scholar
  51. Mason SJ, Mimmack GM (2002) Comparison of some statistical methods of probabilistic forecasting of ENSO. J Clim 15:8–29CrossRefGoogle Scholar
  52. McCreary JP (1981) A linear stratified ocean model of the equatorial undercurrent. Philos Trans R Soc London 298:603–635CrossRefGoogle Scholar
  53. McPhaden MJ, Yu X (1999) Equatorial waves and the 1997–98 El Nino. Geophys Res Lett 26:2961–2964CrossRefGoogle Scholar
  54. McPhaden MJ, Zebiak SE, Glantz MH (2006) ENSO as an integrating concept in earth science. Science 314:1739–1745CrossRefGoogle Scholar
  55. Monterey G, Levitus S (1997) Seasonal variability of mixed layer depth for the world ocean. Technical report NOAA, Silver Spring, MDGoogle Scholar
  56. Moore AM, Kleeman R (1996) The dynamics of error growth and predictability in a coupled model of ENSO. Q J R Meteorol Soc 122:1405–1446CrossRefGoogle Scholar
  57. Moore AM, Kleeman R (1999) Stochastic forcing of ENSO by the intraseasonal oscillation. J Clim 12:1199–1220CrossRefGoogle Scholar
  58. Mueller JA, Veron F (2010) Bulk formulation of the heat and water vapor fluxes at the air–sea interface, including nonmolecular contributions. J Atmos Sci 67:234–247CrossRefGoogle Scholar
  59. Palmer TN, Andersen U, Cantelaube P et al (2004) Development of a European multi-model ensemble system for seasonal to inter-annual prediction (DEMETER). Bull Am Meteorol Soc 85(6):853–872CrossRefGoogle Scholar
  60. Penland C (2003) A stochastic approach to nonlinear dynamics: a review (Electronic supplement to ‘Noise out of chaos and why it won’t go away’). Bull Am Meteorol Soc 84:925. doi:10.1175/BAMS-84-7-Penland CrossRefGoogle Scholar
  61. Peters ME, Bretherton CS (2005) A simplified model of the Walker circulation with an interactive ocean mixed layer and cloud-radiative feedbacks. J Clim 18:4216–4234CrossRefGoogle Scholar
  62. Picaut J, Hackert E, Busalacchi AJ, Murtugudde R, Lagerloef GSE (2002) Mechanisms of the 1997–1998 El Niño-La Niña, as inferred from space-based observations. J Geophys Res. doi:10.1029/2001JC000850 Google Scholar
  63. Ramanathan V, Collins W (1991) Thermodynamic regulation of ocean warming by cirrus clouds deduced from observations of the 1987 El Niño. Nature 351:27–32CrossRefGoogle Scholar
  64. Rasmusson EM, Carpenter TH (1982) Variations in tropical sea surface temperature and surface wind fields associated with the Southern Oscillation/El Niño. Mon Weather Rev 110:354–384CrossRefGoogle Scholar
  65. Roads JO (1987) Predictability in the extended range. J Atmos Sci 44:1228–1251CrossRefGoogle Scholar
  66. Rodriguez-Fonseca B, Polo I, Garcia-Serrano J, Losada T, Mohino E, Mechoso CR, Kucharski F (2009) Are Atlantic Niños enhancing Pacific ENSO events in recent decades? Geophys Res Lett 36(20):L20705CrossRefGoogle Scholar
  67. Roeckner E, Arpe K, Bengtsson L, Christoph M, Claussen M, Dümenil L, Esch M, Giorgetta M, Schlese U, Schulzweida U (1996) The atmospheric general circulation model ECHAM-4: model description and simulation of present-day climate. Max-Planck Institute for Meteorology, Hamburg, p 90, Report No. 218Google Scholar
  68. Rosati A, Miyakoda K, Gudgel R (1997) The impact of ocean initial conditions on ENSO forecasting with a coupled model. Mon Weather Rev 125:754–772CrossRefGoogle Scholar
  69. Saha S, Nadiga S, Thiaw C et al (2006) The NCEP climate forecast system. J Clim 19(15):3483–3517CrossRefGoogle Scholar
  70. Saji NH, Goswami BN, Vinayachandran PN, Yamagata T (1999) A dipole mode in the tropical Indian Ocean. Nature 401:360–363Google Scholar
  71. Shutts G (2004) A stochastic kinetic-energy backscatter algorithm for use in ensemble prediction systems. Tech Memo 449, ECMW, ReadingGoogle Scholar
  72. Smith TM, Reynolds RW, Peterson TC, Lawrimore J (2008) Improvements to NOAA’s historical merged land–ocean surface temperature analysis (1880–2006). J Clim 21:2283–2296CrossRefGoogle Scholar
  73. Suarez MJ, Schopf PS (1988) A delayed action oscillator for ENSO. J Atmos Sci 45(21):3283–3287CrossRefGoogle Scholar
  74. Tang Y, Yu B (2008) MJO and its relationship to ENSO. J Geophys Res 113:D14106. doi:10.1029/2007JD009230 CrossRefGoogle Scholar
  75. Tippett MK, Barnston AG (2008) Skill of multimodel ENSO probability forecasts. Mon Weather Rev 136:3933–3946CrossRefGoogle Scholar
  76. Tsyrulnikov MD (2005) Stochastic modelling of model errors: a simulation study. Q J R Meteorol Soc 131:3345–3371. doi:10.1256/qj.05.19 CrossRefGoogle Scholar
  77. Tziperman E, Stone L, Cane M, Jarosh H (1994) El Nino chaos: overlapping of resonances between the seasonal cycle and the Pacific ocean–atmosphere oscillator. Science 264:72–74CrossRefGoogle Scholar
  78. Tziperman E, Zebiak S, Cane MA (1997) Mechanisms of seasonal–ENSO interaction. J Atmos Sci 54:61–71CrossRefGoogle Scholar
  79. Vimont D, Wallace JM, Battisti DS (2001) Footprinting: a seasonal connection between the mid-latitudes and tropics. Geophys Res Lett 28:3923–3926CrossRefGoogle Scholar
  80. Wang L, Yang HJ (2014) The role of atmospheric teleconnection in the subtropical thermal forcing on the equatorial Pacific. Adv Atmos Sci 31(4):985–994CrossRefGoogle Scholar
  81. Wilks Daniel (2014) Probabilistic canonical correlation analysis forecasts, with application to tropical Pacific sea-surface temperatures. Int J Climatol 34(5):1405–1413CrossRefGoogle Scholar
  82. Williams PD (2005) Modelling climate change: the role of unresolved processes. Philos Trans R Soc Math Phys Eng Sci 363(1837):2931–2946CrossRefGoogle Scholar
  83. Wyrtki K (1975) El Niño—the dynamic response of the equatorial Pacific Ocean to atmospheric forcing. J Phys Oceanogr 5:572–584CrossRefGoogle Scholar
  84. Yang SC, Rienecker M, Keppenne C (2010) The impact of ocean data assimilation on seasonal-to-interannual forecasts: a case study of the 2006 El Niño event. J Clim 23:4080–4095CrossRefGoogle Scholar
  85. Yu Y, Mu M, Duan WS (2012) Does model parameter error cause a significant “spring predictability barrier” for El Niño events in the Zebiak–Cane model? J Clim 25(4):1263–1277CrossRefGoogle Scholar
  86. Zavala-Garay J, Moore AM, Kleeman R (2004) Influence of stochastic forcing on ENSO prediction. J Geophys Res Oceans (1978–2012) 109:C11007. doi:10.1029/2004JC002406
  87. Zavala-Garay J, Zhang C, Moore AM, Kleeman R (2005) The linear response of ENSO to the Madden–Julian oscillation. J Clim 18:2441–2459CrossRefGoogle Scholar
  88. Zebiak SE, Cane MA (1987) A model El Niño-Southern Oscillation. Mon Weather Rev 115:2262–2278CrossRefGoogle Scholar
  89. Zhang C, Gottschalck J (2002) SST anomalies of ENSO and the Madden–Julian oscillation in the equatorial Pacific. J Clim 15:2429–2445CrossRefGoogle Scholar
  90. Zhang RH, Zebiak SE, Kleeman R, Keenlyside N (2003) A new intermediate coupled model for El Niño simulation and prediction. Geophys Res Lett. doi:10.1029/2003GL018010 Google Scholar
  91. Zhang RH, Zebiak SE, Kleeman R, Keenlyside N (2005) Retrospective El Niño forecast using an improved intermediate coupled model. Mon Weather Rev 133:2777–2802CrossRefGoogle Scholar
  92. Zhang W, Chen QL, Zheng F (2015) Bias corrections of the heat flux damping process to improve the simulation of ENSO post-2000. SOLA 11:181–185CrossRefGoogle Scholar
  93. Zheng F, Zhang RH (2012) Effects of interannual salinity variability and freshwater flux forcing on the development of the 2007/08 La Niña event diagnosed from Argo and satellite data. Dyn Atmos Oceans 57:45–57CrossRefGoogle Scholar
  94. Zheng F, Zhang RH (2015) Interannually varying salinity effects on ENSO in the tropical Pacific: a diagnostic analysis from Argo. Ocean Dyn 65(5):691–705CrossRefGoogle Scholar
  95. Zheng F, Zhu J (2008) Balanced multivariate model errors of an intermediate coupled model for ensemble Kalman filter data assimilation. J Geophys Res 113:C07002. doi:10.1029/2007JC004621 Google Scholar
  96. Zheng F, Zhu J (2010a) Spring predictability barrier of ENSO events from the perspective of an ensemble prediction system. Glob Planet Change 72:108–117CrossRefGoogle Scholar
  97. Zheng F, Zhu J (2010b) Coupled assimilation for an intermediated coupled ENSO prediction model. Ocean Dyn 60:1061–1073CrossRefGoogle Scholar
  98. Zheng F, Zhu J (2015) Roles of initial ocean surface and subsurface states on successfully predicting 2006–2007 El Niño with an intermediate coupled model. Ocean Sci 11:187–194CrossRefGoogle Scholar
  99. Zheng F, Zhu J, Zhang RH, Zhou GQ (2006) Ensemble hindcasts of SST anomalies in the tropical Pacific using an intermediate coupled model. Geophys Res Lett 33:L19604. doi:10.1029/2006GL026994 CrossRefGoogle Scholar
  100. Zheng F, Zhu J, Zhang RH (2007) The impact of altimetry data on ENSO ensemble initializations and predictions. Geophys Res Lett 34:L13611. doi:10.1029/2007GL030451 Google Scholar
  101. Zheng F, Wang H, Zhu J (2009a) ENSO ensemble prediction: initial condition perturbations vs. model perturbations. Chin Sci Bull 54(14):2516–2523CrossRefGoogle Scholar
  102. Zheng F, Zhu J, Wang H, Zhang RH (2009b) Ensemble hindcasts of ENSO events over the past 120 years using a large number of ensembles. Adv Atmos Sci 26(2):359–372CrossRefGoogle Scholar
  103. Zheng F, Zhang RH, Zhu J (2014) Effects of interannual salinity variability on the barrier layer in the western-central equatorial Pacific: a diagnostic analysis from Argo. Adv Atmos Sci 31(3):532–542CrossRefGoogle Scholar
  104. Zhu J, Huang B, Marx L, Kinter JL III, Balmaseda MA, Zhang RH, Hu ZZ (2012) Ensemble ENSO hindcasts initialized from multiple ocean analyses. Geophys Res Lett 39:L09602. doi:10.1029/2012GL051503 CrossRefGoogle Scholar
  105. Zhu J, Huang B, Balmaseda MA, Kinter JL III, Peng P, Hu ZZ, Marx L (2013) Improved reliability of ENSO hindcasts with multi-ocean analyses ensemble initialization. Clim Dyn 41(7–8):1941–1954CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.International Center for Climate and Environment Science (ICCES), Institute of Atmospheric PhysicsChinese Academy of SciencesBeijingChina

Personalised recommendations