Climate Dynamics

, Volume 50, Issue 9–10, pp 3355–3374 | Cite as

On the link between mean state biases and prediction skill in the tropics: an atmospheric perspective

  • Ingo RichterEmail author
  • Takeshi Doi
  • Swadhin K. Behera
  • Noel Keenlyside


The present study examines how mean state biases in sea-surface temperature (SST), surface wind and precipitation affect model skill in reproducing surface wind and precipitation anomalies in the tropics. This is done using theoretical arguments, atmosphere-only experiments in the Coupled Model Intercomparison Project Phase 5, and customized sensitivity tests with the SINTEX-F general circulation model. Theoretical arguments suggest that under certain conditions the root mean square error (RMSE) of a variable can be related to its variance and its mean, which indicates a direct link between bias and skill. The anomaly correlation coefficient (ACC), on the other hand, is generally not related to either the mean state or its variance, as several examples document. Multi-model atmosphere-only experiments with prescribed SST warming suggest that both ACC and RMSE of surface wind and precipitation are rather insensitive to warming on the order of 4 K. When SST biases from a free-running control simulation are prescribed in SINTEX-F, the ACC of surface wind is almost unaffected in the equatorial Pacific and Atlantic, while that of precipitation decreases noticeably in some regions but also increases in others. The RMSE of both fields shows widespread deterioration. There is a tendency for warm SST biases to increase the signal-to-noise ratio and sometimes ACC as well. The results suggest that, in the context of atmosphere-only simulations, improving SST and precipitation biases does not necessarily improve the skill in reproducing anomalies of surface wind and precipitation.



The authors would like to thank Prof. Shang-Ping Xie for helpful comments on the manuscript. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison which provides coordinating support and led development of software infrastructure for CMIP, and the climate modeling groups for making available their model output. The authors thank the two anonymous reviewers for their constructive comments, which helped to improve the manuscript.


  1. Adler RF, Huffman GJ, Chang A, Ferraro R, Xie P, Janowiak J, Rudolf B, Schneider U, Curtis S, Bolvin D, Gruber A, Susskind J, Arkin P (2003) The version 2 global precipitation climatology project (GPCP) monthly precipitation analysis (1979–present). J Hydrometeor 4:1147–1167CrossRefGoogle Scholar
  2. An SI, Jin F-F (2004) Nonlinearity and Asymmetry of ENSO. J Clim 17:2399–2412CrossRefGoogle Scholar
  3. Barnston AG (1992) Correspondence among the correlation, RMSE, and Heidke forecast verification measures: refinement of the Heidke score. Weather Forecast 7:699–709CrossRefGoogle Scholar
  4. Bellenger H, Guilyardi E, Leloup J, Lengaigne M, Vialard J (2013) ENSO representation in climate models: from CMIP3 to CMIP5. Clim Dyn. doi: 10.1007/s00382-013-1783-z Google Scholar
  5. Bjerknes J (1969) Atmospheric teleconnections from the equatorial Pacific. Mon Weather Rev 97:163–172CrossRefGoogle Scholar
  6. Carton JA, Huang B (1994) Warm events in the tropical Atlantic. J Phys Oceanogr 24:888–903CrossRefGoogle Scholar
  7. Davey MK et al (2002) STOIC: a study of coupled model climatology and variability in topical ocean regions. Clim Dyn 18:403–420CrossRefGoogle Scholar
  8. de Szoeke SP, Xie S-P (2008) The tropical eastern Pacific seasonal cycle: assessment of errors and mechanisms in IPCC AR4 coupled ocean-atmosphere general circulation models. J Clim 21:2573–2590CrossRefGoogle Scholar
  9. Dee DP et al (2011) The ERA-interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137:553–597CrossRefGoogle Scholar
  10. DelSole T, Shukla J (2010) Model fidelity versus skill in seasonal forecasting. J Clim 23:4794–4806CrossRefGoogle Scholar
  11. DelSole T, Shukla J (2012) Climate models produce skillful predictions of Indian summer monsoon rainfall. Geophys Res Lett 39:L09703. doi: 10.1029/2012GL051279 CrossRefGoogle Scholar
  12. Deppenmeier A-L, Haarsma RJ, Hazeleger W (2016) The Bjerknes feedback in the tropical Atlantic in CMIP5 models. Clim Dyn 7:2691. doi: 10.1007/s00382-016-2992-z CrossRefGoogle Scholar
  13. Ding H, Keenlyside N, Latif M, Park W, Wahl S (2015a) The impact of mean state errors on equatorial Atlantic interannual variability in a climate model. J Geophys Res. Oceans. doi: 10.1002/2014JC010384 Google Scholar
  14. Ding H, Greatbatch RJ, Latif M, Park W (2015b) The impact of sea surface temperature bias on equatorial Atlantic interannual variability in partially coupled model experiments. Geophys Res Lett 42:5540–5546CrossRefGoogle Scholar
  15. Eade R, Smith D, Scaife A, Wallace E, Dunstone N, Hermanson L, Robinson N (2014) Do seasonal-to-decadal climate predictions underestimate the predictability of the real world? Geophys Res Lett 41:5620–5628. doi: 10.1002/2014GL061146 CrossRefGoogle Scholar
  16. Edwards PN (2000) A brief history of atmospheric general circulation modeling. In: Randall DA (ed) General circulation model development: past, present, and future. Academic Press, London, pp 67–90Google Scholar
  17. Frauen C, Dommenget D (2010) El Nino and La Nina amplitude asymmetry caused by atmospheric feedbacks. Geophys Res Lett 37:L18801CrossRefGoogle Scholar
  18. Graham NE, Barnett TP (1987) Sea surface temperature, surface wind divergence, and convection over tropical oceans. Science 238:657–659CrossRefGoogle Scholar
  19. Gualdi S, Navarra A, Guilyardi E, Delecluse P (2003) Assessment of the tropical Indo-Pacific climate in the SINTEX CGCM. Ann Geophys 46:1–26Google Scholar
  20. Gualdi S, Alessandri A, Navarra A (2005) Impact of atmospheric horizontal resolution on El Niño Southern Oscillation forecasts. Tellus 57A:357–374Google Scholar
  21. Guilyardi E (2006) El Nino-mean state-seasonal cycle interactions in a mutil-model ensemble. Clim Dyn 26:329–348CrossRefGoogle Scholar
  22. Held IM, Soden BJ (2006) Robust responses of the hydrological cycle to global warming. J Clim 19:5686–5699. doi: 10.1175/JCLI3990.1 CrossRefGoogle Scholar
  23. Horel JD, Wallace JM (1981) Planetary-scale atmospheric phenomena associated with the Southern Oscillation. Mon Weather Rev 109:813–829CrossRefGoogle Scholar
  24. Huang P, Xie SP, Hu K, Huang G, Huang R (2013) Patterns of the seasonal response of tropical rainfall to global warming. Nat Geosci 6:357–361CrossRefGoogle Scholar
  25. Hung MP, Lin JL, Wang W, Kim D, Shinoda T, Weaver SJ (2013) MJO and convectively coupled equatorial waves simulated by CMIP5 climate models. J Clim 26:6185–6214CrossRefGoogle Scholar
  26. Jin EK et al (2008) Current status of ENSO prediction skill in coupled ocean-atmosphere models. Clim Dyn 31:647–664CrossRefGoogle Scholar
  27. Kang IS, Lee JY, Park CK (2004) Potential predictability of summer mean precipitation in a dynamical seasonal prediction system with systematic error correction. J Clim 17:834–844CrossRefGoogle Scholar
  28. Kirtman B, Pirani A (2009) The state of the art of seasonal prediction outcomes and recommendations from the first world climate research program (WCRP) workshop on seasonal prediction. Bull Am Meteor Soc. doi: 10.1175/2008BAMS2707.1 Google Scholar
  29. Lee JY, Wang B, Kang IS, Shukla J et al (2010) How are seasonal prediction skills related to models’ performance on mean state and annual cycle? Clim Dyn 35:267–283CrossRefGoogle Scholar
  30. Li G, Xie S-P (2014) Tropical biases in CMIP5 multimodel ensemble: the excessive equatorial Pacific cold tongue and double ITCZ problems. J Clim 27:1765–1780CrossRefGoogle Scholar
  31. Lindzen RS, Nigam S (1987) On the role of the sea surface temperature gradients in forcing the low-level winds and convergence in the tropics. J Atmos Sci 44:2418–2436CrossRefGoogle Scholar
  32. Luo JJ, Masson S, Behera SK, Gualdi S, Navarra A, Yamagata T (2003) South Pacific origin of the decadal ENSO-like variation as simulated by a coupled GCM. Geophys Res Lett 30:2250. doi: 10.1029/2003GL018649 Google Scholar
  33. Luo JJ, Masson S, Behera SK, Shingu S, Yamagata T (2005) Seasonal climate predictability in a coupled AOGCM using a different approach for ensemble forecast. J Clim 18:4474–4497CrossRefGoogle Scholar
  34. Madec G, Delecluse P, Imbard M, Levy C (1998) OPA 8.1 ocean general circulation model reference manual. Tech. Rep. Note 11, LODYC/IPSL, Paris, FranceGoogle Scholar
  35. 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(9–10):2393–2409. doi: 10.1007/s00382-012-1599-2 CrossRefGoogle Scholar
  36. Manganello JV, Huang B (2009) The influence of systematic errors in the Southeast Pacific on ENSO variability and prediction in a coupled GCM. Clim Dyn 32:1015–1034CrossRefGoogle Scholar
  37. Nagura M, Sasaki W, Tozuka T, Luo J-J, Behera SK, Yamagata T (2013) Longitudinal biases in the Seychelles Dome simulated by 35 ocean-atmosphere coupled general circulation models. J Geophys Res Oceans 118:831–846. doi: 10.1029/2012JC008352 CrossRefGoogle Scholar
  38. Neelin JD, Battisti DS, Hirst AC, Jin F-F, Wakata Y, Yamagata T, Zebiak S (1998) ENSO theory. J Geophys Res 103:14261–14290CrossRefGoogle Scholar
  39. Power S, Delage F, Chung C, Kociuba G, Keay K (2013) Robust twenty-first-century projections of El Niño and related precipitation variability. Nature 502(7472):541–545CrossRefGoogle Scholar
  40. Reynolds RW, Rayner NA, Smith TM, Stokes DC, Wang W (2002) An improved in situ and satellite SST analysis for climate. J Clim 15:1609–1625CrossRefGoogle Scholar
  41. Richter I (2015) Climate model biases in the eastern tropical oceans: causes, impacts and ways forward. WIREs Clim Change 6:345–358CrossRefGoogle Scholar
  42. Richter I, Xie S-P (2008) On the origin of equatorial Atlantic biases in coupled general circulation models. Clim Dyn 31:587–598CrossRefGoogle Scholar
  43. Richter I, Xie S-P, Behera SK, Doi T, Masumoto Y (2014a) Equatorial Atlantic variability and its relation to mean state biases in CMIP5. Clim Dyn 42:171–188. doi: 10.1007/s00382-012-1624-5 CrossRefGoogle Scholar
  44. Richter I, Behera SK, Doi T, Taguchi B, Masumoto Y, Xie S-P (2014b) What controls equatorial Atlantic winds in boreal spring? Clim Dyn 43(11):3091–3104CrossRefGoogle Scholar
  45. Richter I, Chang P, Xu Z, Doi T, Kataoka T, Nagura M, Oettli P, de Szoeke S, Tozuka T (2016) An overview of coupled GCM performance in the tropics. In: Yamagata T, Behera SK (eds) Indo-Pacific climate variability and predictability, vol 8. World Scientific, SingaporeGoogle Scholar
  46. 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. Tech. Rep. No. 218, Max-Planck-Institut für Meteorologie, Hamburg, GermanyGoogle Scholar
  47. Sasaki W, Doi T, Richards KJ, Masumoto Y (2015) The influence of ENSO on the equatorial Atlantic precipitation through the Walker circulation in a CGCM. Clim Dyn 44:191–202CrossRefGoogle Scholar
  48. Scaife AA, Arribas A, Blockley E, Brookshaw A, Clark RT, Dunstone N, Eade R, Fereday D, Folland CK, Gordon M, Hermanson L, Knight JR, Lea DJ, MacLachlan C, Maidens A, Martin M, Peterson AK, Smith D, Vellinga M, Wallace E, Waters J, Williams A (2014) Skillful long-range prediction of European and North American winters. Geophys Res Lett 41:2014GL059. doi: 10.1002/2014gl059637 Google Scholar
  49. Sobel AH, Camargo SJ (2012) Projected future seasonal changes in tropical summer climate. J Clim 24:473–487CrossRefGoogle Scholar
  50. Spencer H, Sutton R, Slingo JM (2007) El Nino in a coupled climate model: sensitivity to changes in mean state induced by heat flux and wind stress corrections. J Clim 20:2273–2298CrossRefGoogle Scholar
  51. Sperber KR, Palmer TN (1996) Interannual tropical rainfall variability in general circulation model simulations associated with the atmospheric model intercomparison project. J Clim 9:2727–2750CrossRefGoogle Scholar
  52. Tompkins AM, Feudale L (2010) Seasonal ensemble predictions of West African Monsoon precipitation in the ECMWF system 3 with a focus on the AMMA special observing period in 2006. Weather Forecast 25:768–788CrossRefGoogle Scholar
  53. Valcke S, Terray L, Piacentini A (2000) The OASIS coupler user guide version 2.4. Tech. Rep. TR/CGMC/00–10, CERFACE, Toulouse, FranceGoogle Scholar
  54. Wang B, Ding QH, Fu XH, Kang IS, Jin K, Shukla J, Doblas-Reyes F (2005a) Fundamental challenge in simulation and prediction of summer monsoon rainfall. Geophys Res Lett 32:L15711CrossRefGoogle Scholar
  55. Wang B, Lee J-Y, Kang I-S, Shukla J, Park C-K, Kumar A., Schemm J, Cocke S, Kug J.-S, Luo J-J, Zhou T, Wang B, Fu X, Yun W-T, Alves O, Jin EK, Kinter J, Kirtman B, Krishnamurti T, Lau NC, Lau W, Liu P, Pegion P, Rosati T, Schubert S, Stern W, Suarez M, Yamagata T (2009) Advance and prospectus of seasonal prediction: assessment of the APCC/CliPAS 14-model ensemble retrospective seasonal prediction (1980–2004). Clim Dyn. doi: 10.1007/s00382-008-0460-0 Google Scholar
  56. Wu R, Kirtman B (2005) Roles of Indian and Pacific Ocean air–sea coupling in tropical atmospheric variability. Clim Dyn 25:155–170. doi: 10.1007/s00382-005-0003-x CrossRefGoogle Scholar
  57. Xie S-P, Carton JA (2004) Tropical Atlantic variability: Patterns, mechanisms, and impacts. In: Wang C, Xie S-P, Carton JA (eds) In Earth climate: the ocean-atmosphere interaction, Geophysical Monograph, 147. AGU, Washington D.C., pp 121–142Google Scholar
  58. Xie SP, Deser C, Vecchi G, Ma J, Teng H, Wittenberg A (2010) Global warming pattern formation: sea surface temperature and rainfall. J Clim 23:966–986CrossRefGoogle Scholar
  59. Zebiak SE (1986) Atmospheric convergence feedback in a simple model for El Niño. Mon Weather Rev 114:1263–1271CrossRefGoogle Scholar
  60. Zebiak SE, Cane A (1987) A model El Niño-Southern oscillation. Mon Weather Rev 115:2262–2278CrossRefGoogle Scholar
  61. Zhang C (1993) Large-scale variability of atmospheric deep convection in relation to sea surface temperature in the tropics. J Clim 6:1898–1913CrossRefGoogle Scholar
  62. Zheng XT, Xie S-P, Lu LH, Zhou ZQ (2016) Inter-model uncertainty in ENSO amplitude change tied to Pacific ocean warming pattern. J Clim. doi: 10.1175/JCLI-D-16-0039.1 (in press) Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Application LaboratoryJAMSTECYokohamaJapan
  2. 2.University of BergenBergenNorway

Personalised recommendations