LETTERS. Warming of the Antarctic ice-sheet surface since the 1957 International Geophysical Year

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1 Vol Jnury 2009 doi: /nture07669 LETTERS Wrming of the Antrctic ice-sheet surfce since the 1957 Interntionl Geophysicl Yer Eric J. Steig 1, Dvid P. Schneider 2, Scott D. Rutherford 3, Michel E. Mnn 4, Josefino C. Comiso 5 & Drew T. Shindell 6 Assessments of Antrctic temperture chnge hve emphsized the contrst etween strong wrming of the Antrctic Peninsul nd slight cooling of the Antrctic continentl interior in recent decdes 1. This pttern of temperture chnge hs een ttriuted to the incresed strength of the circumpolr westerlies, lrgely in response to chnges in strtospheric ozone 2. This picture, however, is sustntilly incomplete owing to the sprseness nd short durtion of the oservtions. Here we show tht significnt wrming extends well eyond the Antrctic Peninsul to cover most of West Antrctic, n re of wrming much lrger thn previously reported. West Antrctic wrming exceeds 0.1 6C per decde over the pst 50 yers, nd is strongest in winter nd spring. Although this is prtly offset y utumn cooling in Est Antrctic, the continent-wide verge ner-surfce temperture trend is positive. Simultions using generl circultion model reproduce the essentil fetures of the sptil pttern nd the long-term trend, nd we suggest tht neither cn e ttriuted directly to increses in the strength of the westerlies. Insted, regionl chnges in tmospheric circultion nd ssocited chnges in se surfce temperture nd se ice re required to explin the enhnced wrming in West Antrctic. Recent chnges in Antrctic ice-sheet surfce tempertures pper enigmtic when compred with glol verge temperture trends. Although the Antrctic Peninsul is one of the most rpidly wrming loctions on Erth, wether sttions on the Antrctic continent generlly show insignificnt trends in recent decdes 1. However, ll ut two of the continuous records from wether sttions re ner the cost, providing little direct informtion on conditions in the continentl interior. The widely used wether forecst renlysis dt re known to hve errors owing to inconsistent ssimiltion skill in the stellite nd pre-stellite ers 3. In this Letter, we use sttisticl climte-field-reconstruction techniques to otin 50-yer-long, sptilly complete estimte of monthly Antrctic temperture nomlies. In essence, we use the sptil covrince structure of the surfce temperture field to guide interpoltion of the sprse ut relile 50-yer-long records of 2-m temperture from occupied wether sttions. Although it hs een suggested tht such interpoltion is unrelile owing to the distnces involved 1, lrge sptil scles re not inherently prolemtic if there is high sptil coherence, s is the cse in continentl Antrctic 4. Previous reconstructions of Antrctic ner-surfce tempertures hve yielded inconsistent results, prticulrly over West Antrctic, where records re few nd discontinuous 5 7. We improve upon this erlier work in severl wys. We use two independent estimtes of the sptil covrince of temperture cross the Antrctic ice sheet: surfce temperture mesurements from stellite therml infrred (T IR ) c e r or RE Figure 1 Verifiction nd upper-limit clirtion sttistics clculted for ech grid point from the comprison of reconstructed nd originl stellitederived monthly temperture nomlies., Clirtion r, ;, clirtion r, ; c, verifiction r, ; d, verifiction r, ; e, verifiction RE, ; f, verifiction RE, Wrm colours in e nd f (RE scores greter thn zero) show where results re more ccurte thn the climtologicl men temperture. Men grid-point verifiction results re RE , CE nd r Crosses show loctions of occupied wether sttions. d f 1 Deprtment of Erth nd Spce Sciences nd Quternry Reserch Center, University of Wshington, Settle, Wshington 98195, USA. 2 Ntionl Center for Atmospheric Reserch, Boulder, Colordo 80307, USA. 3 Deprtment of Environmentl Science, Roger Willims University, Bristol, Rhode Islnd, USA. 4 Deprtment of Meteorology, nd Erth nd Environmentl Systems Institute, Pennsylvni Stte University, University Prk, Pennsylvni 16802, USA. 5 NASA Lortory for Hydrospheric nd Biospheric Sciences, NASA Goddrd Spce Flight Center, Greenelt, Mrylnd 20771, USA. 6 NASA Goddrd Institute for Spce Studies nd Center for Climte Systems Reserch, Columi University, New York, New York 10025, USA. 459

2 LETTERS NATURE Vol Jnury 2009 oservtions 8, nd up-to-dte utomtic wether sttion (AWS) mesurements of ner-surfce ir temperture. We use method 9,10 dpted from the regulrized expecttion mximiztion lgorithm 11 (RegEM) for estimting missing dt points in climte fields. RegEM is n itertive lgorithm similr to principl-component nlysis, used s dt-dptive optimiztion of sttisticl weights for the wether sttion dt. Unlike simple distnce-weighting 5,6 or similr 7 clcultions, ppliction of RegEM tkes into ccount temporl chnges in the sptil covrince pttern, which depend on the reltive importnce of differing influences on Antrctic temperture t given time. Furthermore, the itertive nture of RegEM llows it to e used with discontinuous time series, permitting us to tke full dvntge of the dt ville from occupied wether sttions. We ssess reconstruction skill using reduction-of-error (RE) nd coefficient-of-efficiency (CE) scores s well s conventionl correltion (r) scores. Such verifiction metrics re lcking in previous Antrctic temperture reconstructions 5 7, ut re required for demonstrting skill reltive to the climtologicl men nd re therefore criticl for confidence in the clcultion of temporl trends 10. Skill metrics for our T IR -sed reconstruction from split clirtion nd verifiction experiments re significnt (.99% confidence) t ll grid points except in some restricted res, mostly on the estern side of the Antrctic Peninsul (Fig. 1). Results from our AWS-sed reconstruction gree well with those from the T IR dt (Fig. 2). This is importnt ecuse the infrred dt re strictly mesure of cler-sky temperture 8 nd ecuse surfce temperture differs from ir temperture 2 3 m ove the surfce, s mesured t occupied sttions or t AWSs. Trends in cloudiness or in the strength of the ner-surfce inversion could oth produce spurious trends in the temperture reconstruction. The greement etween the reconstructions, however, rules out either potentil is s significnt. Furthermore, detrending of the T IR dt efore reconstruction demonstrtes tht the results do not depend strongly on trends in sid dt (Supplementry Informtion). Our reconstructions show more significnt temperture chnge in Antrctic (Fig. 2), nd different pttern for tht chnge thn reported in some previous reconstructions 5,7 (Fig. 3). We find tht West Antrctic wrmed etween 1957 nd 2006 t rte of uc per decde (95% confidence intervl). Thus, the re of wrming is much lrger thn the region of the Antrctic Peninsul. The peninsul wrming verges uc per decde. We lso find significnt wrming in Est Antrctic t uc per decde ( ). The continent-wide trend is uc per decde. In the reconstruction sed on detrended T IR dt, wrming in West Antrctic remins significnt t greter thn 99% confidence, nd the continent-wide men trend remins t 0.08 uc per decde, lthough it is no longer demonstrly different from zero (95% confidence). This is in good greement with ref. 6, which reported verge continent-wide wrming of uc per decde ( ) nd shows overll wrming in West Antrctic, lthough sttisticl significnce could not e demonstrted owing to the shorter length nd greter vrince of the reconstruction. We emphsize tht, in generl, c d e f Temperture nomly ( C) Yer Figure 2 Reconstructed nnul men Antrctic temperture nomlies, Jnury 1957 to Decemer 2006., Est Antrctic;, West Antrctic. Solid lck lines show results from reconstruction using infrred stellite dt, verged over ll grid points for ech region. Dshed lines show the verge of reconstructed AWS dt in ech region. Stright red lines show verge trends of the T IR reconstruction. Verifiction results for the continentl men of the T IR reconstruction re RE , CE nd r Grey shding, 95% confidence limits Temperture trend ( C per decde) Figure 3 Sptil pttern of temperture trends (degrees Celsius per decde) from reconstruction using infrred (T IR ) stellite dt., Men nnul trends for ;, Men nnul trends for , to fcilitte comprison with ref. 2. c f, Sesonl trends for : winter (June, July, August; c); spring (Septemer, Octoer, Novemer; d); summer (Decemer, Jnury, Ferury; e); utumn (Mrch, April, My; f). Blck lines enclose those res tht hve sttisticlly significnt trends t 95% confidence (two-tiled t-test). Where it would otherwise e uncler, (not significnt) refers to res of insignificnt trends. Red circles nd djcent numers in show the loctions of the South Pole nd Vostok wether sttions nd their respective trends (degrees Celsius per decde) during the sme time intervl s the reconstruction ( ). Blck circles in show the loctions of Siple nd Byrd Sttions, nd the djcent numers show their respective trends 13 for

3 NATURE Vol Jnury 2009 LETTERS detrending of predictnd dt lowers the qulity of reconstructions y removing sptil covrince informtion 10. The detrended reconstruction therefore represents conservtive lower ound on trend mgnitude. Although ref. 7 concluded tht recent temperture trends in West Antrctic re sttisticlly insignificnt, the results were strongly influenced y the pucity of dt from tht region. When the complete set of West Antrctic AWS dt is included, the trends ecome positive nd sttisticlly significnt, in excellent greement with our results 12. Independent dt provide dditionl evidence tht wrming hs een significnt in West Antrctic. At Siple Sttion (76u S, 84u W) nd Byrd Sttion (80u S, 120u W), short intervls of dt from AWSs were spliced with 37-GHz (microwve) stellite oservtions, which re not ffected y clouds, to otin continuous records from 1979 to 1997 (ref. 13). The results show men trends of uc per decde nd uc per decde t Siple nd Byrd, respectively 13.Our reconstruction yields uc per decde nd uc per decde over the sme intervl. In our full 50-yer reconstruction, the trends re significnt, lthough smller, t oth Byrd ( uc per decde) nd Siple ( uc per decde). Furthermore, the sesonl chrcteristics of these dt 13 gree well with those from our reconstructions, with the gretest mount of wrming in ustrl spring nd winter (Fig. 3). Independent nlyses of tropospheric temperture trends hve lso found spring nd winter wrming to e gretest in West Antrctic 14,15. The sptil nd sesonl chrcteristics of our temperture reconstruction hve importnt implictions for understnding recent Antrctic climte chnge. Severl studies hve emphsized wrmingpeninsul, cooling-continent pttern tht is ttriuted to chnges in tmospheric circultion ssocited with the southern nnulr mode (SAM) 2,16. Cooling over much of Est Antrctic did occur in recent decdes, ut ws strongest during the short time intervl considered in erlier studies ( ; Fig. 3). Virtully ll res wrmed etween 1957 nd,1980. Our reconstruction differs from the results of modelling experiments tht tie Antrctic surfce temperture chnge to strtospheric ozone loss through chnges in the SAM In such simultions, the lrgest negtive temperture nomlies in Est Antrctic occur in summer, wheres in our reconstruction, Est Antrctic cooling is restricted to utumn (Fig. 3). The simultions show wrming in ustrl summer nd utumn, restricted to the peninsul, wheres in our reconstruction the gretest wrming is in winter nd spring, nd in continentl West Antrctic s well s on the peninsul. The well-known increses in temperture on the Antrctic Peninsul re strongly ssocited with chnges in se ice 19. Similrly, negtive nomlies in se-ice extent 20 nd the length of the se-ice seson 21 in the Amundsen Bellingshusen Se my e relted to the wrming trends we oserve in djcent West Antrctic. To explore this, we exmined model output from the NASA Goddrd Institute for Spce Studies (GISS) ModelE tmosphere-only nd coupled generl circultion models, which were run with multiple ocenic nd tmospheric oundry conditions until the end of 2003 (ref. 22). A slightly erlier tmospheric version of GISS ModelE hs een used in simultions of circultion nomlies ssocited with polr strtospheric ozone depletion 17. When driven y oserved se-surfce-temperture (SST) nd se-ice oundry conditions 23, the model reproduces mny of the sic fetures of our reconstruction, with wrming over most of the continent nd persistent in West Antrctic (Fig. 4). SST nd se-ice chnges lone produced wek cooling over prts of Est Antrctic during the 1980s nd 1990s. The detils of the comprisons oviously depend on the ccurcy of the SST nd se-ice oservtions (the ltter re not generlly considered relile efore 1979), nd multi-decdl internl vriility in the model is sustntil. However, it is noteworthy tht oth in the reconstruction nd in the model results, the rte of wrming is greter in continentl West Antrctic, prticulrly in spring nd winter, thn either on the peninsul or in Est Antrctic. In GISS ModelE, this is relted to SST chnges nd the loction of seice nomlies, prticulrly during the ltter period ( ), when they re strongly zonlly symmetric, with significnt losses in the West Antrctic sector ut smll gins round the rest of the continent (Fig. 4e). Rditive forcings lone re indequte to ccount for the oservtions (Supplementry Informtion). The net impct of SST, se ice, nd rditive forcings on Antrctic tempertures in GISS ModelE is in generl greement with our reconstruction. The sme model, when run in coupled mode (tht is, with dynmic ocen) fils to reproduce the strong trends oserved in West Antrctic nd the peninsul. The prole cuse of this discrepncy, common to other coupled models 24, is indequte representtion of se-ice nomlies nd their ssocited higher-order modes of Model oundry conditions Oservtions SST, se ice SST, se ice, forcings c d Se ice e f g h Se-ice chnge (%) Temperture trend ( C per decde) Figure 4 Comprison of reconstructed nd modelled men nnul temperture trends (degrees Celsius per decde) for the periods nd d, ; e h, , e, Reconstructed surfce temperture nd oserved 25-yer chnge in seice frctionl re 23., f, Surfce ir temperture from five-memer GISS ModelE tmosphere-only ensemle simultions with oserved se-surfcetemperture nd se-ice oundry conditions. c, g, Four-memer ensemle with the sme oundry conditions plus tmospheric forcings (chnges in tmospheric concentrtions of rditively ctive species, including ozone). d, h, Difference etween simultions with the sme forcings ut oserved versus climtologicl se ice, to isolte the effect of se ice lone. 461

4 LETTERS NATURE Vol Jnury 2009 tmospheric circultion. In this context, it is importnt tht the pttern of oserved temperture trends closely resemles the pttern of temperture nomlies ssocited with the zonl wve-3 pttern in tmospheric circultion 4. This circultion regime is efficient for the exchnge of ir etween the ocen nd the Antrctic continentl interior, nd is ssocited with tmospheric circultion nomlies in the Amundsen Bellingshusen Se, known to precede winter se-ice nomlies 25. Forced coupled models, including GISS ModelE, generlly show positive shift in the SAM nd n ssocited increse in the circumpolr westerlies over recent decdes, in good greement with oservtions 26. Oservtions lso suggest is towrds the positive phse in the wve-3 pttern 25 since out 1979, which is not reproduced in the coupled models. Using oserved SST nd se ice, GISS ModelE does produce sustntil shifts in the wve-3 circultion. Under those model conditions, greter cyclonic flow in the Amundsen Se region rings wrm, moist ir to West Antrctic, countering the effect of the enhnced circumpolr westerlies. An outstnding question in Antrctic climtology hs een whether the strong wrming of the peninsul hs lso occurred in continentl West Antrctic 19. Our results indicte tht this is indeed the cse, t lest over the lst 50 yers. Moreover, ice-core nlyses indicte verge wrming of West Antrctic over the entire twentieth century 27. Although the influence of ozone-relted chnges in the SAM hs een emphsized in recent studies of Antrctic temperture trends, the sptil nd sesonl ptterns of the oserved temperture trends indicte tht higher-order modes of tmospheric circultion, ssocited with regionl se-ice chnges, hve hd lrger role in West Antrctic. Men surfce temperture trends in oth West nd Est Antrctic re positive for , nd the men continentl wrming is comprle to tht for the Southern Hemisphere s whole 28. This wrming trend is difficult to explin without the rditive forcing ssocited with incresing greenhouse-gs concentrtions. However, the future trjectory of Antrctic temperture chnge lso depends on the extent to which chnges in tmospheric composition (whether from greenhouse gses or strtospheric ozone) ffect Southern Hemisphere se ice nd regionl tmospheric circultion ptterns. Improved representtion in models of coupled tmosphere/se-ice dynmics will e criticl for forecsting Antrctic temperture chnge. METHODS SUMMARY We use ner-surfce ir temperture dt from 42 occupied sttions nd 65 AWSs from the READER (Reference Antrctic Dt for Environmentl Reserch) dt set 1. We use pssive infrred rightness mesurements (T IR ) of surfce temperture from the Advnced Very High Resolution Rdiometer 8, stellite of the US Ntionl Ocenic nd Atmospheric Administrtion. We use the RegEM lgorithm 9 11 to comine the dt from occupied wether sttions with the T IR nd AWS dt in seprte reconstructions of the ner-surfce Antrctic temperture field. Split clirtion/verifiction tests re performed y withholding prend post-1995 T IR nd AWS dt in seprte RegEM clcultions. Clirtion nd verifiction sttistics re clculted for ech grid point from the comprison of the reconstructed time series nd the originl temperture time series. We show RE nd correltion r vlues in Fig. 1. CE verifiction vlues yield results indistinguishle from RE in our study nd re reported in Supplementry Informtion. Significnce levels of the clirtion/verifiction sttistics re sed on Monte Crlo simultions of red noise s the null hypothesis. In Fig. 2, the 95% confidence intervl is the unexplined vrince, 2s, where s 2 error 5 s2 dt (1 2 r2 ver ), s2 dt is the temporl vrince in the originl stellite temperture dt nd rver 2 is the verifiction frctionl resolved vrince. Significnce levels of trends re clculted using two-tiled t-test, with the numer of degrees of freedom djusted for utocorreltion. In reporting trends for different res, we define West Antrctic s 72u 90u S, 60u 180u W; Est Antrctic s 65u 90u S, u E; nd the Antrctic Peninsul s westerly longitudes north of 72u S. Full Methods nd ny ssocited references re ville in the online version of the pper t Received 14 Jnury; ccepted 1 Decemer Turner, J. et l. Antrctic climte chnge during the lst 50 yers. Int. J. Climtol. 25, (2005). 2. Thompson, D. W. J. & Solomon, S. Interprettion of recent Southern Hemisphere climte chnge. Science 296, (2002). 3. Bromwich, D. H. & Fogt, R. L. Strong trends in the skill of the ERA-40 nd NCEP- NCAR Renlyses in the high nd midltitudes of the southern hemisphere, J. Clim. 17, (2004). 4. Schneider, D. P., Steig, E. J. & Comiso, J. Recent climte vriility in Antrctic from stellite-derived temperture dt. J. Clim. 17, (2004). 5. Dorn, P. T. et l. Antrctic climte cooling nd terrestril ecosystem response. Nture 415, (2002). 6. Chpmn, W. L. & Wlsh, J. E. A synthesis of Antrctic tempertures. J. Clim. 20, (2007). 7. Monghn, A. J., Bromwich, D. H., Chpmn, W. & Comiso, J. C. Recent vriility nd trends of Antrctic ner-surfce temperture. J. Geophys. Res. 113, doi:1029/ 2007JD (2008). 8. Comiso, J. C. Vriility nd trends in Antrctic surfce tempertures from in situ nd stellite infrred mesurements. J. Clim. 13, (2000). 9. Rutherford, S. et l. Proxy-sed Northern Hemisphere surfce temperture reconstructions: Sensitivity to methodology, predictor network, trget seson nd trget domin. J. Clim. 18, (2005). 10. Mnn, M. E., Rutherford, S., Whl, E. & Ammnn, C. Roustness of proxy-sed climte field reconstruction methods. J. Geophys. Res. 112, doi: / 2006JD (2007). 11. Schneider, T. Anlysis of incomplete climte dt: Estimtion of men vlues nd covrince mtrices nd imputtion of missing vlues. J. Clim. 14, (2001). 12. Bromwich, D. H., Monghn, A. J. & Colwell, S. R. Surfce nd Mid-tropospheric Climte Chnge in Antrctic. Eos 89 (Fll meeting), str. C41A-0497 (2008). 13. Shumn, C. A. & Sterns, C. R. Decdl-length composite inlnd West Antrctic temperture records. J. Clim. 14, (2001). 14. Johnson, C. M. & Fu, Q. Antrctic tmospheric temperture trend ptterns from stellite oservtions. Geophys. Res. Lett. 34, doi:1029/2006gl (2007). 15. Turner, J. et l. Significnt wrming of the Antrctic winter troposphere. Science 311, (2006). 16. Gillett, N. P. & Thompson, D. W. J. Simultion of recent Southern Hemisphere climte chnge. Science 302, (2003). 17. Shindell, D. T. & Schmidt, G. A. Southern Hemisphere climte response to ozone chnges nd greenhouse gs increses. Geophys. Res. Lett. 31, doi: / 2004GL (2004). 18. Keeley, S. P. E. et l. Is Antrctic climte most sensitive to ozone depletion in the middle or lower strtosphere? Geophys. Res. Lett. 34, doi: /2007gl (2007). 19. Vughn, D. G. et l. Recent rpid regionl climte wrming on the Antrctic Peninsul. Clim. Chnge 60, (2003). 20. Kwok, R. & Comiso, J. C. Southern Ocen climte nd se ice nomlies ssocited with the Southern Oscilltion. J. Clim. 15, (2002). 21. Prkinson, C. L. Trends in the length of the Southern Ocen se ice seson, Ann. Glciol. 34, (2002). 22. Hnsen, J. et l. Climte simultions for with GISS Model E. Clim. Dyn. 29, (2007). 23. Ryner, N. A. et l. Glol nlyses of se surfce temperture, se ice nd night mrine ir tempertures since the lte nineteenth century. J. Geophys. Res. 108, doi: /2002jd (2003). 24. Connolley, W. M. & Brcegirdle, T. J. An Antrctic ssessment of IPCC AR4 coupled models. Geophys. Res. Lett. 34, doi: /2007gl (2007). 25. Hollnd, M. M. & Rphel, M. Twentieth century simultion of the Southern Hemisphere in coupled models. Prt II: Se ice conditions nd vriility. Clim. Dyn. 26, (2006). 26. Miller, R. L., Schmidt, G. A. & Shindell, D. T. Forced nnulr vritions in the 20th Century Intergovernmentl Pnel on Climte Chnge Fourth Assessment Report models. J. Geophys. Res. 111, doi: /2005jd (2006). 27. Schneider, D. P. & Steig, E. J. Ice cores record significnt 1940s Antrctic wrmth relted to tropicl climte vriility. Proc. Ntl Acd. Sci. USA 105, (2008). 28. Jones, P. D. & Moerg, A. Hemispheric nd lrge-scle surfce ir temperture vritions: Anextensive revision nd nupdte to J. Clim. 16, (2003). Supplementry Informtion is linked to the online version of the pper t Acknowledgements E.J.S. nd D.P.S. were supported y the US Ntionl Science Foundtion, grnt numers OPP nd OPP , s prt of the US ITASE progrmme. M.E.M. ws supported y the US Ntionl Science Foundtion, grnt numer OPP We thnk D. Winerenner, A. Monghn, D. Bromwich, J. Turner, P. Myewski, T. Scmos, E. Brd nd O. Bellier. Author Contriutions E.J.S., D.P.S., S.D.R. nd M.E.M. mde the reconstruction nd sttisticl clcultions. J.C.C. performed the cloud-msking clcultions nd provided the updted stellite dt set. D.T.S. provided the generl circultion model output nd guided its interprettion. E.J.S. wrote the pper. All uthors discussed the results nd commented on the mnuscript. Author Informtion Reprints nd permissions informtion is ville t Correspondence nd requests for mterils should e ddressed to E.J.S. (steig@ess.wshington.edu). 462

5 doi: /nture07669 METHODS Dt. We use the READER wether sttion tempertures from the British Antrctic Survey 1. Twenty-seven of the 42 occupied sttions hve t lest 50%- complete monthly verge dt from 1957 to present. Dt from 65 AWSs re ville, ut re discontinuous nd dte from 1980 t the erliest. In ddition, dt from only 24 of the AWSs re more thn 50% complete for We use pssive infrred rightness mesurements (T IR ) from the Advnced Very High Resolution Rdiometer, which re continuous eginning Jnury 1982 nd constitute the most sptilly complete Antrctic temperture dt set. The T IR dt re ised towrds cler-sky conditions, owing to the opcity of clouds in the infrred nd. Cloud msking is proly the lrgest source of error in the retrievl of T IR dt from rw stellite spectrl informtion. We hve updted the dt throughout 2006, using n enhnced cloud-msking technique to give etter fidelity with existing occupied nd utomtic wether sttion dt. We mke use of the cloud msking in ref. 8 ut impose n dditionl restriction tht requires tht dily nomlies e within threshold of 610 uc of climtology, conservtive technique tht will tend to dmp extreme vlues nd, hence, minimize trends 29. Vlues tht fll outside the threshold re removed. Clcultions. We use the RegEM lgorithm 11, developed for sprse dt infilling, to comine the occupied wether sttion dt with the T IR nd AWS dt in seprte reconstructions of the Antrctic temperture field. RegEM uses n itertive clcultion tht converges on reconstructed fields tht re most consistent with the covrince informtion present oth in the predictor dt (in this cse the wether sttions) nd the predictnd dt (the stellite oservtions or AWS dt). We use n dpttion of RegEM in which only smll numer, k,of significnt eigenvectors re used 10. Additionlly, we use truncted totl-lestsqures (TTLS) clcultion 30 tht minimizes oth the vector nd the mtrix A in the liner regression model Ax 5. (In this cse A is the spce-time dt mtrix, is the principl component time series to e reconstructed nd x represents the sttisticl weights.) Using RegEM with TTLS provides more roust results for climte field reconstruction thn the ridge-regression method originlly suggested in ref. 11 for dt infilling prolems, when there re lrge differences in dt vilility etween the clirtion nd reconstruction intervls 10. For completeness, we compre results from RegEM with those from conventionl principl-component nlysis (Supplementry Informtion). Monthly verge surfce temperture nomlies were otined from the T IR dt for the domin covering ll lnd res nd ice shelves on the Antrctic continent, t 50 km 3 50 km resolution 4. The monthly nomlies re efficiently chrcterized y smll numer of sptil weighting ptterns nd corresponding time series (principl components) tht descrie the vrying contriution of ech pttern. The results re reproducile using single-seson, nnul verge nd split-decde-length susets of the dt 4. The first three principl components re sttisticlly seprle nd cn e meningfully relted to importnt dynmicl fetures of high-ltitude Southern Hemisphere tmospheric circultion, s defined independently y extrpolr instrumentl dt. The first principl component is significntly correlted with the SAM index (the first principl component of se-level-pressure or 500-hP geopotentil heights for 20u S 90u S), nd the second principl component reflects the zonl wve-3 pttern, which contriutes to the Antrctic dipole pttern of se-ice nomlies in the Ross Se nd Weddell Se sectors 4,8. The first two principl components of T IR lone explin.50% of the monthly nd nnul temperture vriilities 4. Monthly nomlies from microwve dt (not ffected y clouds) yield virtully identicl results 4. Principl component nlysis of the wether sttion dt produces results similr to those of the stellite dt nlysis, yielding three seprle principl components. We therefore used the RegEM lgorithm with cut-off prmeter k 5 3. A disdvntge of excluding higher-order terms (k. 3) is tht this fils to fully cpture the vrince in the Antrctic Peninsul region. We ccept this trdeoff ecuse the Peninsul is lredy the est-oserved region of the Antrctic. Sttistics. We otined clirtion/verifiction sttistics y withholding the first nd lst 12.5 yers of the 25-yer T IR dt in seprte RegEM clcultions. We similrly split the AWS dt into pre- nd post-1995 dt. Confidence levels re sed on Monte Crlo simultions of red noise s the null hypothesis. For ech grid point, 1,000 red noise series were generted to hve the sme men, vrince nd lg-1 utocorreltion coefficient s the ctul time series over the clirtion period. Additionl vlidtion of the T IR -sed reconstruction ws otined y using the 15 occupied wether sttions with the most complete dt, reserving the other 27 for verifiction. Verifiction metrics t these sites re consistently significnt t.99% confidence, with the exception of some sites t the tip of the Antrctic Peninsul nd the three sites north of 55u S (Supplementry Informtion). We report verifiction sttistics s well s upper-ound clirtion-intervl sttistics. The ltter represent the mximum level of explined vrince tht could e expected in the reconstruction, given how much dt vrince is resolved over the clirtion intervl. We rely primrily on the RE sttistic; the lterntive verifiction sttistic, CE, yields indistinguishle results in our study (Supplementry Informtion). For completeness, we lso report correltion r vlues, ut with the recognition tht r is deficient skill metric ecuse it does not penlize the poor prediction of either mens or vrinces Reynolds, R. W. et l. An improved in situ nd stellite SST nlysis for climte. J. Clim. 15, (2002). 30. Fierro, R. D., Golu, G. H., Hnsen, P. C. & O Lery, D. P. Regulriztion y truncted totl lest squres. SIAM J. Sci. Comput. 18, (1997).

6 CORRECTIO & AMENDMENTS NATUREjVol 460j6 August 2009 CORRIGENDUM doi: /nture08286 Wrming of the Antrctic ice-sheet surfce since the 1957 Interntionl Geophysicl Yer Eric J. Steig, Dvid P. Schneider, Scott D. Rutherford, Michel E. Mnn, Josefino C. Comiso & Drew T. Shindell Nture 457, (2009) In this Letter, we reported trends on reconstructed temperture histories for different res of the Antrctic continent. The confidence levels on the trends, s given in the text, did not tke into ccount the reduced degrees of freedom in the time series due to utocorreltion. We report in Tle 1 the corrected vlues, sed on two-tiled t-test, with the numer of degrees of freedom djusted for utocorreltion, using N effective 5 N(1 2 r)/(1 1 r), in which N is the smple size nd r is the lg-1 utocorreltion coefficient of the residuls of the detrended time series. The medin of r is 0.27, resulting in reduction in the degrees of freedom from N to N effective for the monthly time series. We lso include results of further clcultion tht tkes into ccount oth the vrince nd the uncertinty in the reconstructed tempertures. We performed Monte-Crlo simultions of the reconstructed tempertures using Gussin distriution with vrince equl to the unresolved vrince from the split clirtion/verifiction tests descried in the pper. Confidence ounds were otined y detrending ech simultion nd otining the lg-1 utocorreltion coefficient nd vrince of the residuls; rndom reliztion of Gussin noise hving the sme lg-1 utocorreltion coefficient nd vrince ws then dded to the trend, nd new trend ws clculted. The 2.5th nd 97.5th percentiles of the 10,000 simulted trends give the 95% confidence ounds. For the cse of zero unresolved vrince, this clcultion converges on the sme vlue s the two-tiled t-test, ove. The 95% confidence minimum trend vlue is given y the 5th percentile vlues of the simulted trends, lst row of Tle 1. The corrected confidence levels do not chnge the ssessed significnce of trends, nor ny of the primry conclusions of the pper. We lso note tht there is typogrphicl error in Supplementry Tle 1: the correct loction of Automtic Wether Sttion Hrry is 83.0u S, 238.6u E. The position of this sttion on the mps in the pper is correct. Tle 1 Corrected confidence levels on men decdl temperture trends West Antrctic Est Antrctic Antrctic Peninsul All Antrctic Trend (uc per decde) % CI of trend in men reconstruction 95% CI of trend, ccounting for unresolved vrince in men reconstruction Minimum trend (95% confidence, ccounting for unresolved vrince in men reconstruction) The confidence levels re shown over the period for the reported surfce tempertures sed on stellite dt. CI, confidence intervl. 766