Higher precision estimates of regional polar warming by ensemble regression of climate model projections

Abstract

This study presents projections of twenty-first century wintertime surface temperature changes over the high-latitude regions based on the third Coupled Model Inter-comparison Project (CMIP3) multi-model ensemble. The state-dependence of the climate change response on the present day mean state is captured using a simple yet robust ensemble linear regression model. The ensemble regression approach gives different and more precise estimated mean responses compared to the ensemble mean approach. Over the Arctic in January, ensemble regression gives less warming than the ensemble mean along the boundary between sea ice and open ocean (sea ice edge). Most notably, the results show 3 °C less warming over the Barents Sea (~7 °C compared to ~10 °C). In addition, the ensemble regression method gives projections that are 30 % more precise over the Sea of Okhostk, Bering Sea and Labrador Sea. For the Antarctic in winter (July) the ensemble regression method gives 2 °C more warming over the Southern Ocean close to the Greenwich Meridian (~7 °C compared to ~5 °C). Projection uncertainty was almost half that of the ensemble mean uncertainty over the Southern Ocean between 30° W to 90° E and 30 % less over the northern Antarctic Peninsula. The ensemble regression model avoids the need for explicit ad hoc weighting of models and exploits the whole ensemble to objectively identify overly influential outlier models. Bootstrap resampling shows that maximum precision over the Southern Ocean can be obtained with ensembles having as few as only six climate models.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Notes

  1. 1.

    In this paper the word prediction is used in the statistical sense to signify the expectation of the response variable for a given explanatory variable obtained using a regression model. It does not necessarily refer to future forecasts.

References

  1. Abe M, Shiogama H, Nozawa T, Emori S (2011) Estimation of future surface temperature changes constrained using the future-present correlated modes in inter-model variability of CMIP3 multimodel simulations. J Geophys Res Atmos 116:D18104. doi:10.1029/2010jd015111

    Article  Google Scholar 

  2. Arzel O, Fichefet T, Goosse H (2006) Sea ice evolution over the 20th and 21st centuries as simulated by current AOGCMs. Ocean Model 12:401–415. doi:10.1016/j.ocemod.2005.08.002

    Article  Google Scholar 

  3. Boe JL, Hall A, Qu X (2009) September sea-ice cover in the Arctic Ocean projected to vanish by 2100. Nat Geosci 2(5):341–343. doi:10.1038/ngeo467

    Article  Google Scholar 

  4. Bracegirdle TJ, Connolley WM, Turner J (2008) Antarctic climate change over the twenty first century. J Geophys Res Atmos 113(D3). doi:10.1029/2007jd008933

  5. Brodeau L, Barnier B, Treguier AM, Penduff T, Gulev S (2010) An ERA40-based atmospheric forcing for global ocean circulation models. Ocean Model 31(3–4):88–104. doi:10.1016/j.ocemod.2009.10.005

    Article  Google Scholar 

  6. Bromwich DH, Fogt RL (2004) Strong trends in the skill of the ERA-40 and NCEP-NCAR reanalyses in the high and midlatitudes of the Southern Hemisphere, 1958–2001. J Clim 17(23):4603–4619. doi:10.1175/3241.1

    Article  Google Scholar 

  7. Bromwich DH, Fogt RL, Hodges KI, Walsh JE (2007) A tropospheric assessment of the ERA-40, NCEP, and JRA-25 global reanalyses in the polar regions. J Geophys Res Atmos 112(D10):D10111. doi:10.1029/2006jd007859

  8. Chapman WL, Walsh JE (2007) A synthesis of Antarctic temperatures. J Clim 20(16):4096–4117. doi:10.1175/jcli4236.1

    Article  Google Scholar 

  9. Christensen JH, Hewitson B, Busuioc A, Chen A, Gao X, Held I, Jones R, Kolli RK, Kwon W-T, Laprise R, Rueda VM, Mearns L, Menéndez CG, Räisänen J, Rinke A, Sarr A, Whetton P (2007) Regional climate projections. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL (eds) Climate change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. C. U. Press, Cambridge

    Google Scholar 

  10. Connolley WM, Bracegirdle TJ (2007) An antarctic assessment of IPCC AR4 coupled models. Geophys Res Lett 34(22). doi:10.1029/2007gl031648

  11. Dee DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, van de Berg L, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ, Haimberger L, Healy SB, Hersbach H, Holm EV, Isaksen L, Kallberg P, Kohler M, Matricardi M, McNally AP, Monge-Sanz BM, Morcrette JJ, Park BK, Peubey C, de Rosnay P, Tavolato C, Thepaut JN, Vitart F (2011) The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q J R Meteorol Soc 137(656):553–597. doi:10.1002/qj.828

    Article  Google Scholar 

  12. Draper NR, Smith H (1998) Applied regression analysis, 3rd edn. Wiley, New York

    Google Scholar 

  13. Giorgi F, Coppola E (2010) Does the model regional bias affect the projected regional climate change? An analysis of global model projections. Clim Chang 100(3–4):787–795. doi:10.1007/s10584-010-9864-z

    Article  Google Scholar 

  14. Giorgi F, Mearns LO (2002) Calculation of average, uncertainty range, and reliability of regional climate changes from AOGCM simulations via the “reliability ensemble averaging” (REA) method. J Clim 15:1141–1158

    Article  Google Scholar 

  15. Greene AM, Goddard L, Lall U (2006) Probabilistic multimodel regional temperature change projections. J Clim 19(17):4326–4343

    Article  Google Scholar 

  16. Hall A, Qu X (2006) Using the current seasonal cycle to constrain snow albedo feedback in future climate change. Geophys Res Lett 33:L03502. doi:10.1029/2005GL025127

    Article  Google Scholar 

  17. Hines KM, Bromwich DH, Marshall GJ (2000) Artificial surface pressure trends in the NCEP/NCAR reanalysis over the Southern Ocean and Antarctica. J Clim 12:3940–3952. doi:10.1175/1520-0442(2000)013<3940:ASPTIT>2.0.CO;2

    Article  Google Scholar 

  18. Ho CK, Stephenson DB, Collins M, Ferro CAT, Brown SJ (2012) Calibration strategies: a source of additional uncertainty in climate change projections. Bull Am Meteorol Soc 93(1):21–26. doi:10.1175/2011bams3110.1

    Article  Google Scholar 

  19. Hoaglin DC, Kempthorne PJ (1986) Influential observations, high leverage points, and outliers in linear regression: comment. Stat Sci 1(3):408–412

    Article  Google Scholar 

  20. Holland MM, Bitz CM (2003) Polar amplification of climate change in coupled models. Clim Dyn 21:221–232

    Article  Google Scholar 

  21. Kidston J, Gerber EP (2010) Intermodel variability of the poleward shift of the austral jet stream in the CMIP3 integrations linked to biases in 20th century climatology. Geophys Res Lett 37. doi:10.1029/2010gl042873

  22. Knutti R, Furrer R, Tebaldi C, Cermak J, Meehl GA (2010) Challenges in combining projections from multiple climate models. J Clim 23(10):2739–2758. doi:10.1175/2009jcli3361.1

    Article  Google Scholar 

  23. Kolstad EW, Bracegirdle TJ (2008) Marine cold-air outbreaks in the future: an assessment of IPCC AR4 model results for the Northern Hemisphere. Clim Dyn 30(7–8):871–885. doi:10.1007/s00382-007-0331-0

    Article  Google Scholar 

  24. Mahlstein I, Knutti R (2011) Ocean heat transport as a cause for model uncertainty in projected arctic warming. J Clim 24(5):1451–1460. doi:10.1175/2010jcli3713.1

    Article  Google Scholar 

  25. Marshall GJ, Harangozo SA (2000) An appraisal of NCEP/NCAR reanalysis MSLP viability for climate studies in the South Pacific. Geophys Res Lett 27:3057–3060

    Article  Google Scholar 

  26. Marshall GJ, Orr A, van Lipzig NPM, King JC (2006) The impact of a changing Southern Hemisphere Annular Mode on Antarctic Peninsula summer temperatures. J Clim 19(20):5388–5404

    Article  Google Scholar 

  27. Murphy JM, Sexton DMH, Barnett DN, Jones GS, Webb MJ, Collins M, Stainforth DA (2004) Quantification of modelling uncertainties in a large ensemble of climate change simulations. Nat 430:768–772. doi:10.1038/nature02771

    Article  Google Scholar 

  28. Overland JE, Wang MY (2007) Future regional Arctic sea ice declines. Geophys Res Lett 34. doi:10.1029/2007GL030808

  29. Pritchard HD, Arthern RJ, Vaughan DG, Edwards LA (2009) Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets. Nat 461(7266):971–975. doi:10.1038/nature08471

    Article  Google Scholar 

  30. Raisanen J (2007) How reliable are climate models? Tellus 59A:2–29. doi:10.1111/j.1600-0870.2006.00211.x

    Google Scholar 

  31. Raisanen J, Ruokolainen L, Ylhaisi J (2010) Weighting of model results for improving best estimates of climate change. Clim Dyn 35(2–3):407–422. doi:10.1007/s00382-009-0659-8

    Article  Google Scholar 

  32. Renwick JA (2004) Trends in the Southern Hemisphere polar vortex in NCEP and ECMWF reanalyses. Geophys Res Lett 31:L027209. doi:10.1029/2003GL019302

    Article  Google Scholar 

  33. Shindell D, Faluvegi G (2009) Climate response to regional radiative forcing during the twentieth century. Nat Geosci 2(4):294–300. doi:10.1038/ngeo473

    Article  Google Scholar 

  34. Steig EJ, Schneider DP, Rutherford SD, Mann ME, Comiso JC, Shindell DT (2009) Warming of the Antarctic ice-sheet surface since the 1957 International Geophysical Year. Nat 457(7228):459–462

    Article  Google Scholar 

  35. Sterl A (2004) On the (in)homogeneity of reanalysis products. J Clim 17(19):3866–3873

    Article  Google Scholar 

  36. Stroeve J, Holland MM, Meier W, Scambos T, Serreze M (2007) Arctic sea ice decline: faster than forecast. Geophys Res Lett 34(9). doi:10.1029/2007gl029703

  37. Tebaldi C, Rl Smith, Nychka D, Mearns LO (2005) Quantifying uncertainty in projections of regional climate change: a bayesian approach to the analysis of multimodel ensembles. J Clim 18:1524–1540. doi:10.1175/JCLI3363.1

    Article  Google Scholar 

  38. Thomas ER, Dennis PF, Bracegirdle TJ, Franzke C (2009) Ice core evidence for significant 100-year regional warming on the Antarctic Peninsula. Geophys Res Lett 36:L20704. doi:10.1029/2009gl040104

    Article  Google Scholar 

  39. Tjernstrom M, Graversen RG (2009) The vertical structure of the lower Arctic troposphere analysed from observations and the ERA-40 reanalysis. Q J R Meteorol Soc 135(639):431–443. doi:10.1002/qj.380

    Article  Google Scholar 

  40. Walsh JE, Chapman WL, Romanovsky V, Christensen JH, Stendel M (2008) Global climate model performance over Alaska and Greenland. J Clim 21(23):6156–6174. doi:10.1175/2008jcli2163.1

    Article  Google Scholar 

  41. Wang M, Overland JE, Kattsov V, Walsh JE, Zhang X, Pavlova T (2007) Intrinsic versus forced variation in coupled climate model simulations over the arctic during the twentieth century. J Clim 20(6):1093–1107

    Article  Google Scholar 

  42. Watterson IG, Whetton PH (2011) Distributions of decadal means of temperature and precipitation change under global warming. J Geophys Res Atmos 116:D07101. doi:10.1029/2010jd014502

    Article  Google Scholar 

  43. Weigel AP, Knutti R, Liniger MA, Appenzeller C (2010) Risks of model weighting in multimodel climate projections. J Clim 23(15):4175–4191. doi:10.1175/2010jcli3594.1

    Article  Google Scholar 

  44. Whetton P, Macadam I, Bathols J, O’Grady J (2007) Assessment of the use of current climate patterns to evaluate regional enhanced greenhouse response patterns of climate models. Geophys Res Lett 34(14). doi:10.1029/2007gl030025

  45. Zahn M, von Storch H (2010) Decreased frequency of North Atlantic polar lows associated with future climate warming. Nat 467(7313):309–312. doi:10.1038/nature09388

    Article  Google Scholar 

  46. Zhang XD (2010) Sensitivity of arctic summer sea ice coverage to global warming forcing: towards reducing uncertainty in arctic climate change projections. Tellus Ser A Dyn Meteorol Oceanogr 62A(3):220–227. doi:10.1111/j.1600-0870.2010.00441.x

    Google Scholar 

Download references

Acknowledgments

This study is part of the British Antarctic Survey Polar Science for Planet Earth Programme. It was funded by the Natural Environment Research Council. Two anonymous authors are thanked for their useful comments, which helped to significantly improve the manuscript. We acknowledge the modeling groups for making their simulations available for analysis, the Program for Climate Model Diagnosis and Inter-comparison (PCMDI) for collecting and archiving the CMIP3 model output, and the WCRP’s Working Group on Coupled Modelling (WGCM) for organizing the model data analysis activity. The WCRP CMIP3 multimodel data set is supported by the Office of Science, U.S. Department of Energy. The European Centre for Medium Range Weather Forecasting are thanked for providing the ERA-40 and ERA-Interim datasets.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Thomas J. Bracegirdle.

Appendix: Influential items in regression

Appendix: Influential items in regression

The regression model in (2) can be written in matrix form as \( {\mathbf{Y}} = {\mathbf{X}}b + {\mathbf{\varepsilon }} \). Y is a column vector of n climate model simulations of the climate response, X is the design matrix with n rows and 2 columns: the first column is filled with ones and the second column contains the present day values \( (x_{1} , \ldots ,x_{n} )^{\prime} \) from each climate model. For quadratic regression, a third column with \( (x_{1}^{2} , \ldots ,x_{n}^{2} )^{\prime} \) is added to X. ε is a column vector of n residuals.

The regression model parameters are given by the two row column vector \( b = (\mu ,\beta )^{\prime} \), which is estimated to be \( {\hat{\mathbf{b}}} = ({\mathbf{X}}^{{\mathbf{'}}} {\mathbf{X}})^{ - 1} {\mathbf{X}}^{{\mathbf{'}}} {\mathbf{Y}} \) using ordinary least squares estimation (Draper and Smith (1998), p 125). The estimated values of climate model responses are then given by \( {\hat{\mathbf{Y}}} = {\mathbf{X}}\hat{b} = {\mathbf{X}}(({\mathbf{X}}^{{\mathbf{'}}} {\mathbf{X}})^{ - 1} {\mathbf{X}}^{{\mathbf{'}}} {\mathbf{Y}}) = {\mathbf{HY}} \), where \( {\mathbf{H}} = ({\mathbf{X}}^{{\mathbf{'}}} {\mathbf{X}})^{ - 1} {\mathbf{X}}^{{\mathbf{'}}} \) is known as the ‘hat matrix’ (Draper and Smith (1998), p205). The ith diagonal element of the hat matrix H ii is called the leverage of the ith item, and helps to quantify how influential each item is on the overall fit (in our case, the items are the climate model simulations). Items having large leverage are known as influential items. One rule of thumb for labelling cases as “high leverage” is if the leverage exceeds 3p/n where p is the number of predictor variables and n is the sample size (Hoaglin and Kempthorne 1986). Influential items can unduly modify regression estimates especially if they are also outlier points with large residuals.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bracegirdle, T.J., Stephenson, D.B. Higher precision estimates of regional polar warming by ensemble regression of climate model projections. Clim Dyn 39, 2805–2821 (2012). https://doi.org/10.1007/s00382-012-1330-3

Download citation

Keywords

  • CMIP3
  • CMIP5
  • Climate model
  • Arctic
  • Antarctic
  • Regional climate
  • Weighting
  • Observational constraint
  • Southern Ocean
  • Sea ice edge
  • Polar climate