LETTERS. Improved estimates of upper-ocean warming and multi-decadal sea-level rise

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1 Vol June 28 doi:1.138/nture78 Improved estimtes of upper-ocen wrming nd multi-decdl se-level rise Cti M. Domingues 1, John A. Church 1,2, Neil J. White 1,2, Peter J. Gleckler 3, Susn E. Wijffels 1, Pul M. Brker 1 & Jeff R. Dunn 1 Chnges in the climte system s energy udget re predominntly reveled in ocen tempertures 1,2 nd the ssocited therml expnsion contriution to se-level rise 2. Climte models, however, do not reproduce the lrge decdl vriility in glolly verged ocen het content inferred from the sprse oservtionl dtse 3,4, even when volcnic nd other vrile climte forcings re included. The sum of the oserved contriutions hs lso not dequtely explined the overll multi-decdl rise 2. Here we report improved estimtes of ner-glol ocen het content nd therml expnsion for the upper 3 m nd 7 m of the ocen for , using sttisticl techniques tht llow for sprse dt coverge 5 7 nd pplying recent corrections 8 to reduce systemtic ises in the most common ocen temperture oservtions 9. Our ocen wrming nd therml expnsion trends for re out 5 per cent lrger thn erlier estimtes ut out 4 per cent smller for , which is consistent with the recognition tht previously estimted rtes for the 199s hd positive is s result of instrumentl errors 8 1. On verge, the decdl vriility of the climte models with volcnic forcing now grees pproximtely with the oservtions, ut the modelled multi-decdl trends re smller thn oserved. We dd our oservtionl estimte of upper-ocen therml expnsion to other contriutions to se-level rise nd find tht the sum of contriutions from 1961 to 23 is out mm yr 21, in good greement with our updted estimte of ner-glol men se-level rise (using techniques estlished in erlier studies 6,7 ) of mm yr 21. To estimte ocen het content nd ssocited thermosteric selevel chnges from 195 to 23 (see Methods), we use temperture dt 11 from reversing thermometers (whole period), expendle thy-thermogrphs (XBTs; since the lte 196s), modern nd more ccurte conductivity temperture depth (CTD) mesurements from reserch ships (since the 198s) nd Argo flots (mostly from 21). XBTs, providing more thn 5% of the dt, mesure temperture from free-flling expendle proes t depths estimted from the elpsed time since relese t the surfce. Significnt systemtic ises in XBT tempertures 9 re ssocited primrily with errors in the estimted depth of oservtions, proly result of sutle differences in the mnufcture of the XBTs 8. We use recent timevrile XBT fll-rte correction 8 to minimize these ises. To recover the lrge-scle ptterns from sprse temperture dt, we use reduced-spce optiml interpoltion technique 5. This pproch helps overcome the low is in previous estimtes of trends in het content 1,12 nd se level 12,13, prticulrly in the Southern Hemisphere 3,14, nd provides rigorous error estimtes (see Methods). Ner-glolly verged nomlies of ocen het content in the upper 7 m nd 1 m (plotted s three-yer running mens) nd se surfce temperture now trck ech other t multi-decdl timescles (Fig. 1). These glol verges ll show slight increse from 195 to out 196, 15-yer period to the mid-197s of zero or slightly negtive trend nd, fter the climte shift, stedy rise to the end of the record. This pttern is lso oserved in thermosteric se level (Fig. 2). Including time-vrile error estimtes, the liner trend in ocen het content in the upper 7 m gives totl chnge of J from 1961 to 23 (equivlent to n ir se het flux of W m 22 over the ocen surfce re considered, m 2 ; ll error estimtes quoted re one stndrd devition), with out 91% stored in the upper 3 m. For thermosteric Ocen het content ( 1 22 J) Agung Agung Chichon Chichon Pintuo Pintuo Figure 1 Estimtes of ocen het content nd se surfce temperture., Comprison of our upper-ocen het content (lck; grey shding indictes n estimte of one stndrd devition error) with previous estimtes (red 1 nd lue 12 ) for the upper 7 m. The stright lines re liner fits to the estimtes. The glol men strtospheric opticl depth 31 (eige, ritrry scle) t the ottom indictes the timing of mjor volcnic eruptions. The rown curve is three-yer running verge of these vlues, included for comprison with the smoothed oservtions., Comprison of our 7-m (thick lck line, s in ) nd 1-m (thick red line; thin red lines indicte estimtes of one stndrd devition error) results with se surfce temperture 3 (lue; right-hnd scle). All time series were smoothed with three-yer running verge nd re reltive to Se surfce temperture ( C) 1 Centre for Austrlin Wether nd Climte Reserch, CSIRO Mrine nd Atmospheric Reserch, GPO Box 1538, Hort, Tsmni 71, Austrli. 2 Antrctic Climte nd Ecosystems Coopertive Reserch Centre, Hort, Privte Bg 8, Tsmni 71, Austrli. 3 Progrm for Climte Model Dignosis nd Intercomprison, Lwrence Livermore Ntionl Lortory, Mil Code L-13, 7 Est Avenue, Livermore, Cliforni 9455, USA Mcmilln Pulishers Limited. All rights reserved

2 NATURE Vol June 28 se level, the rise is out 22 mm ( trend of mm yr 21, with out 97% in the upper 3 m). These ocen wrming nd therml expnsion rtes re more thn 5% lrger thn previous estimtes for the upper 3 m (refs 1, 13) nd re out 5% lrger for the upper 7 m (refs 1, 12, 13). Since 1976, the equivlent rtes hve een.4 W m 22 nd.59 mm yr 21, nd for the period of the modern stellite ltimeter record from 1993 to 23 they hve een.35 W m 22 nd.79 mm yr 21, less thn previous estimtes 15, which were ised high y errors in the fll rte of XBTs 8 1. Exclusion of the XBT dt from the reconstructions produces equivlent trends ut with lrger uncertinties ecuse of the reduced sptil coverge. Our time series of het content nd thermosteric se level (Figs 1, 2) now show little indiction of the lrge spurious rise in the erly 197s nd the susequent decrese in the erly 198s (out J nd out 1 mm), which dominte previous estimtes 1,12,13 nd were lrgely the result of instrumentl ises 8. This result is confirmed if we remove the XBT dt from the reconstructions. However, there re smller vritions in het content (less thn J) nd thermosteric se level (less thn 5 mm), roughly consistent in oth mplitude nd timing with the impct of volcnic eruptions in 1963, 1982 nd 1991 (refs 16 18). We compre our estimtes for the upper 3 m (not shown) nd 7 m (Fig. 2) with equivlent vlues from simultions of the twentieth century in the World Climte Reserch Progrmme s Coupled Model Intercomprison Project Phse 3 (WCRP CMIP-3) conducted in support of the Intergovernmentl Pnel on Climte Chnge Fourth Assessment Report (IPCC AR4). The CMIP-3 simultions exmined here re summrized in Supplementry Informtion. For models tht do not include volcnic (strtospheric) erosols, the chnges in simulted ocen het content nd thermosteric se level hve smller decdl vriility thn the oservtions nd lrger long-term trends (Fig. 2, ). For simultions with volcnic forcing (ut excluding two models, one tht simultes the volcnic forcing y djusting the solr constnt (ple green dimond), nd one tht responds more strongly to the Agung eruption (ornge circle) thn the other models 17 ), the oserved nd modelled het content nd therml expnsion time series re similr, with comprle flls in het content nd se level fter volcnic eruptions (Fig. 2c, d). After removl of liner trend for , the verge of the model vrinces is mrginlly lrger thn the vrince of the (smoothed) oserved time series (which lso contins oservtionl uncertinty). The simulted nd the oserved time series re correlted t zero lg (verge correltion coefficient of.6). The mgnitude of these simulted responses vries ecuse of differences in model physics nd estimted volcnic forcings In ddition, there re significnt differences etween ensemle memers of the sme model. From 1961 to 1999, the simultions with volcnic forcing hve multi-decdl trends in het storge nd thermosteric se-level rise sustntilly smller thn those without volcnic forcing. The model trends with volcnic forcing re closer to the oservtions ut re on verge out 28% smller in the upper 3 m nd out 1% smller in the upper 7 m; tht is, 73% of the het storge in the models is in the upper 3 m, in contrst with 93% in the oservtions. We comine our estimtes of thermosteric se level with estimtes of therml expnsion in the deep ocen nd of the incresed mss of the ocen in n ttempt to lnce the se-level udget (Fig. 3). Although oservtions nd models confirm tht recent wrming is gretest in the upper ocen, there re widespred oservtions of wrming deeper thn 7 m (refs 19 21). The only glol oservtionl estimte of therml expnsion in the deep ocen 13 indictes tht integrting to 3, m gives 2% increse on the vlue for the upper 7 m (or.7 mm yr 21 ). This vlue is proly underestimted ecuse of the use of stndrd optiml interpoltion techniques nd the sprse deep oservtionl dtse, prticulrly in the Southern Hemisphere 14. In the ocen renlysis from the Germn Consortium for Estimting the Circultion nd Climte of the Ocen model, the ocen therml expnsion ws out.6 mm yr 21 in the upper 7 m, with n dditionl 5% (out.3 mm yr 21 ) from the ocen elow 7 m (ref. 22). For estimting 4 3 OHC ( 1 22 J) 2 1 CCCm CGCM3.1 CNRM CM3 CSIRO Mk3. GISS AOM FGOALS g1. UKMO HdCM3 c 2 1 CCSM3 GFDL CM2. GISS EH GISS ER MIROC3.2 (high resolution) MIROC3.2 (medium resolution) MRI CGCM Agung Chichon Pintuo 1 4 d 3 7 m 2 7 m ThSL (mm) Figure 2 Comprison of oserved nd simulted ocen het content (OHC) nd thermosteric se level (ThSL) estimtes for the upper 7 m.,, Models without volcnic forcing. c, d, Models with volcnic forcing. The oservtions re smoothed s in Fig. 1 nd the model results re yerly verges. All models include greenhouse gs nd tropospheric erosol forcings. See Supplementry Informtion for more detils of the models nd 1 28 Mcmilln Pulishers Limited. All rights reserved Agung Chichon Pintuo the climtic forcings. The strtospheric erosol lodings 31 of the mjor volcnic eruptions re shown t the ottom of c nd d. The rown curve is three-yer running verge of these vlues, included for comprison with the smoothed oservtions. The grey shding indictes estimtes of one stndrd devition error for the oserved time series, nd ll time series re reltive to

3 NATURE Vol June 28 the se-level udget we use deep-ocen therml expnsion of mm yr 21 (Fig. 3) ut recognize tht this vlue is uncertin. This therml expnsion rte implies dditionl het storge of out J (.2 W m 22 ) in the deep ocen. For , glciers nd ice cps contriute mm yr 21 to glol se-level rise (Fig. 3), incresing to mm yr 21 for (ref. 23). For , the estimted contriutions for the Greenlnd nd Antrctic ice sheets re nd mm yr 21, respectively 2. There is little informtion to constrin ice sheet contriutions for previous decdes, ut it is thought tht the Greenlnd contriution hs incresed significntly in recent yers 24. We use contriution tht increses linerly from zero in 1961 to the 199s vlue. The Antrctic ice sheet is thought to e still responding to chnges since the lst glcil mximum 19. These long timescles suggest tht there my hve een little chnge in the Antrctic contriution since Hydrologicl models indicte decdl chnges in terrestril wter storge ut little long-term trend 25 (Fig. 3). Terrestril storge ssocited with multi-decdl humn interference in the wter system is poorly determined. The two lrgest terms, the uilding of dms (out.55 mm yr 21 over the pst hlf century 26 ) nd the mining of groundwter 19, re likely to e of similr size ut of opposite sign. For this reson we hve not included these terms in Fig. 3. We updte in situ estimtes of glolly verged se level y pplying estlished techniques 6,7, ut using empiricl orthogonl functions determined from longer set of ltimeter dt ( ), using lrger numer of tide guges thn in previous studies nd Se level (mm) Figure 3 Totl oserved se-level rise nd its components., The components re therml expnsion in the upper 7 m (red), therml expnsion in the deep ocen (ornge), the ice sheets of Antrctic nd Greenlnd (cyn), glciers nd ice cps (drk lue) nd terrestril storge (green)., The estimted se levels re indicted y the lck line (this study), the yellow dotted line 28 nd the red dotted line (from stellite ltimeter oservtions). The sum of the contriutions is shown y the lue line. Estimtes of one stndrd devition error for the se level re indicted y the grey shding. For the sum of components, we include our rigorous estimtes of one stndrd devition error for upper-ocen therml expnsion; these re shown y the thin lue lines. All time series were smoothed with three-yer running verge nd re reltive to correcting the tide-guge dt for the impct of tmospheric pressure 27, s well s glcil isosttic djustment. The glolly verged se-level trend from this new estimte nd one using n independent technique 28 re lmost identicl from 1961 to 23, with trend of mm yr 21 (Fig. 3). The sum of contriutions to se-level rise is mm yr 21, not significntly different from the estimted vlue. The lmost exct greement in 23 is fortuitous nd the different decdl vriility is n indiction of the uncertinty in the estimtes nd the (unknown) vriility in the cryospheric nd deep-ocen contriutions. From 1993 to 23, the sum of contriutions is 2.4 mm yr 21, gin lmost equl to the estimted trend from tide guges of 2.3 mm yr 21 nd still in the upper qurtile of the IPCC projections from 199 (ref. 29). Note tht the se level estimted from stellite ltimeter oservtions follows the in situ estimte closely up to 1999 nd then egins to diverge, implying higher rte of rise. It is uncler why the in situ nd stellite estimtes diverge, nd creful comprison is urgently needed. The improved closure of the se-level udget over multi-decdl periods (Fig. 3) nd the etter greement in the mgnitude of oserved nd simulted decdl vriility (Fig. 2c, d) increse confidence in the present results nd represent progress since the lst two IPCC reports 2,19. The results indicte n ongoing need for creful qulity control of oservtionl dt nd lso for detiled glol nd regionl comprisons of oservtionl estimtes with climte models to understnd the implictions for the detection, ttriution nd projection of climte chnge nd se-level rise. METHODS SUMMARY We reconstructed ner-glol monthly thermosteric se level nomlies for nd for different depth levels (1, 2, 3, 4, 5 nd 7 m), using reduced-spce optiml interpoltion technique 5. This technique is designed to recover the lrge-scle roust ptterns tht cn e derived from sprse dt nd hs previously een used to estimte glol se surfce temperture 3, tmospheric pressure 27 nd se level 6,7. The glolly verged time series were computed with equl-re weighting. We converted the thermosteric selevel fields into chnges in ocen het content using sptilly vrile regression. Becuse of the sprse sptil coverge, prticulrly in the erlier prt of the period, the monthly reconstructed fields contined sustntil noise tht were reduced y forming three-yer running mens. Full Methods nd ny ssocited references re ville in the online version of the pper t Received 27 Decemer 27; ccepted 3 My Levitus, S., Antonov, J. & Boyer, T. T. Wrming of the world ocen, Geophys. Res. Lett. 32, L264, doi:1.129/24gl21592 (25). 2. Bindoff, N. L. et l. in Climte Chnge 27: The Physicl Science Bsis. Contriution of Working Group 1 to the Fourth Assessment Report of the Intergovernmentl Pnel on Climte Chnge (eds Solomon, S. et l.) (Intergovernmentl Pnel on Climte Chnge, Cmridge, 27). 3. Gregory, J. M., Bnks, H. T., Stott, P. A., Lowe, J. A. & Plmer, M. D. Simulted nd oserved decdl vriility in ocen het content. Geophys. Res. Lett. 31, L15312, doi:1.129/24gl258 (24). 4. AchutRo, K. M. et l. Simulted nd oserved vriility in ocen temperture nd het content. Proc. Ntl Acd. Sci. USA 24, (27). 5. Kpln, A., Kushnir, Y. & Cne, M. A. Reduced spce optiml interpoltion of historicl mrine se level pressure. J. Clim. 13, (2). 6. Church, J. A., White, N. J., Colemn, R., Lmeck, K. & Mitrovic, J. X. Estimtes of the regionl distriution of se-level rise over the 195 to 2 period. J. Clim. 17, (24). 7. Church, J. A. & White, N. J. A 2th century ccelertion in glol se-level rise. Geophys. Res. Lett. 33, L162, doi:1.129/25gl24826 (26). 8. Wijffels, S. E. et l. Chnging expendle BthyThermogrph fll-rtes nd their impct on estimtes of thermosteric se level rise. J. Clim. doi:1.1175/ 28JCLI229.1 (in the press). 9. Gouretski, V. & Koltermnn, K. P. How much is the ocen relly wrming? Geophys. Res. Lett. 34, L161, doi:1.129/26gl27834 (27). 1. Willis, J., Lymn, J. M., Johnson, G. C. & Gilson, J. Correctionto Recent coolingofthe upper ocen. Geophys. Res. Lett. 34, L1661, doi:1.129/27gl3323 (27). 11. Ingley, B. & Huddleston, M. Qulity control of ocen temperture nd slinity profiles historicl nd rel time dt. J. Mr. Syst. 65, (27). 12. Ishii, M., Kimoto, M., Skmoto, K. & Iwski, S.-I. Steric se level chnges estimted from historicl ocen susurfce temperture nd slinity nlyses. J. Ocenogr. 62, (26) Mcmilln Pulishers Limited. All rights reserved

4 NATURE Vol June Antonov, J. I., Levitus, S. & Boyer, T. P. Thermosteric se level rise, Geophys. Res. Lett. 32, L1262, doi:1.129/25gl23112 (25). 14. Gille, S. T. Decdl-scle temperture trends in the Southern Hemisphere ocen. J. Clim /28JCLI (in the press). 15. Willis, J., Roemmich, D. & Cornuelle, B. Internnul vriility in upper-ocen het content, temperture nd thermosteric expnsion on glol scles. J. Geophys. Res. 19, C1237, doi: jc226 (24). 16. Church, J. A., White, N. J. & Arlster, J. M. Significnt decdl-scle impct of volcnic eruptions on se level nd ocen het content. Nture 438, (25). 17. Gleckler, P. J. et l. Krkto lives: The effect of volcnic eruptions on ocen het content nd therml expnsion. Geophys. Res. Lett. 33, L1772, doi:1.129/ 26GL26771 (26). 18. Delworth, T. L., Rmswmy, V. & Stenchikov, G. L. The impct of erosols on simulted ocen temperture, het content, nd se level in the 2th century. Geophys. Res. Lett. 32, L2479, doi:1.129/25gl24457 (25). 19. Church, J. A. et l. in Climte Chnge 21: The Scientific Bsis. Contriution of Working Group 1 to the Third Assessment Report of the Intergovernmentl Pnel on Climte Chnge (eds Houghton, J. T. et l.) (Cmridge Univ. Press, Cmridge, 21). 2. Johnson, G. C. & Doney, S. C. Recent western South Atlntic ottom wter wrming. Geophys. Res. Lett. 33, L14614, doi:1.129/26gl26769 (26). 21. Johnson, G. C., Mecking, S., Sloyn, B. M. & Wijffels, S. E. Recent ottom wter wrming in the Pcific Ocen. J. Clim. 13, (27). 22. Köhl, A., Stmmer, D. D. & Cournelle, B. Internnul to decdl chnges in the ECCO Glol Synthesis. J. Phys. Ocenogr. 37, (27). 23. Dyurgerov, M. B. & Meier, M. F. Glciers nd the Chnging Erth System: A 24 Snpshot (Occsionl Pper 58, Institute of Arctic nd Alpine Reserch, Univ. of Colordo, 25). 24. Lemke, P. et l. in Climte Chnge 27: The Physicl Science Bsis. Contriution of Working Group 1 to the Fourth Assessment Report of the Intergovernmentl Pnel on Climte Chnge (eds Solomon, S. et l.) (Intergovernmentl Pnel on Climte Chnge, Cmridge, 27). 25. Ngo-Duc, T., Lvl, K., Polcher, J., Lomrd, A. & Czenve, A. Effects of lnd wter storge on glol men se level over the pst hlf century. Geophys. Res. Lett. 32, (25). 26. Cho, B. F., Wu, Y. H. & Li, Y. S. Impct of rtificil reservoir wter impoundment on glol se level. Science 32, (28). 27. Alln, R. & Ansell, T. J. A new glolly complete monthly historicl men se level pressure dtset (HdSLP2): J. Clim. 19, (26). 28. Jevrejev, S., Grinsted, A., Moore, J. C. & Holgte, S. J. Nonliner trends nd multiyer cycles in se level records. J. Geophys. Res. 111, C912, doi:1.129/ 25JC3229 (26). 29. Rhmstorf, S. et l. Recent climte oservtions compred to projections. Science 316, 79, doi:1.1126/science (26). 3. Ryner, N. et l. Glol nlyses of se surfce temperture, se ice, nd night mrine ir temperture since the lte nineteenth century. J. Geophys. Res. 18, 447, doi:1.129/22jd267 (23). 31. Ammnn, C. M., Meehl, G. A. & Wshington, W. M. A monthly nd ltitudinlly vrying volcnic forcing dtset in simultions of the 2th century climte. Geophys. Res. Lett. 3, 16257, doi:1.129/23gl16875 (23). Supplementry Informtion is linked to the online version of the pper t Acknowledgements This pper is contriution to the Commonwelth Scientific Industril Reserch Orgniztion (CSIRO) Climte Chnge Reserch Progrm nd Welth from Ocens Flgship nd ws supported y the Austrlin Government s Coopertive Reserch Centres Progrmme through the Antrctic Climte nd Ecosystems Coopertive Reserch Centre. C.M.D., J.A.C., N.J.W. nd S.E.W. were prtly funded y the Austrlin Climte Chnge Science Progrm. We cknowledge the modelling groups, the Progrm for Climte Model Dignosis nd Intercomprison (PCMDI) nd the WCRP s Working Group on Coupled Modelling (WGCM) for their roles in mking ville the WCRP CMIP-3 multi-model dt set. Support for P.J.G. nd this dt set t the Lwrence Livermore Ntionl Lortory ws provided y the Office of Science, US Deprtment of Energy. The Centre for Austrlin Wether nd Climte Reserch is prtnership etween CSIRO nd the Austrlin Bureu of Meteorology. Author Contriutions C.M.D. completed the nlysis to determine the chnges in ocen het content nd thermosteric se-level rise nd shred responsiility for writing the mnuscript. J.A.C. conceived the study, directed the nlysis nd shred responsiility for writing the mnuscript. N.J.W. completed the nlysis of the se-level dt nd provided the softwre for the se-level nd thermosteric se-level reconstructions. P.J.G. nlysed the model results. S.E.W. provided the corrections for the XBT dt nd the climtology, nd mde vlule comments. P.M.B. provided the pressure corrections to the Argo dt. J.R.D. qulity-controlled the Argo dt. All uthors contriuted to the finl version of the mnuscript. Author Informtion Reprints nd permissions informtion is ville t Correspondence nd requests for mterils should e ddressed to C.M.D. (cti.domingues@csiro.u). 28 Mcmilln Pulishers Limited. All rights reserved 193

5 doi:1.138/nture78 METHODS Ocen temperture dt. To estimte ocen het content for the upper 3 m nd 7 m nd the ssocited thermosteric se level from 195 to 23, we used out 2.3 nd 1.8 million profiles (shllow nd deep, respectively) from the ville 6 million ocen temperture profiles in the ENACT/ENSEMBLES version 3 (herefter EN3) dt set 11. We discrded profiles (out 1.7 million) tht hd d qulity flgs, hd corse verticl resolution, were shllower thn 1 m depth or were from higher ltitudes thn 65u N nd 65u S. We crefully selected only the temperture profiles tht were clerly identified nd mesured y XBTs (out 1.2 million nd 1. million), for which we could pply correction for the systemtic errors 8, ottles (out 1.1 million) nd CTDs (out 7,). We did not include temperture profiles from the remining instrument types (1.8 million profiles, of which out 1.2 million re from Mechnicl Bthy- Thermogrphs (MBTs)) ecuse of lck of understnding of their potentil systemtic ises 8. To complement the XBTs, ottles nd CTDs from the EN3 dt set, we used the most recent version of our own qulity-controlled Argo profiling flots (out 6,), including corrections for pressure-sensor drift. Temperture climtology. We produced climtology from the oservtions y using technique developed previously 32, which includes sptilly dependent terms nd nnul, semi-nnul nd liner trend terms t ech grid point. We elieve this is superior to most other ville climtologies in which ll yers re simply verged together, yielding young medin oservtion dtes in the Southern Hemisphere nd old medin dtes in the dt-rich res of the Northern Hemisphere. Attempts to resolve more thn liner trend in time were lso considered, ut estimtes were poorly constrined y the dt. Thermosteric se level nd ocen het content. We converted temperture profiles into thermosteric se level nd ocen het content reltive to numer of fixed-depth reference levels, ssuming climtologicl slinities from the World Ocen Atls 33. We clculted nomlies reltive to their monthly men fields nd inned them to 1 month 3 1u 3 1u grid for the ice-free ocen equtorwrd of 65u N nd 65u S. Our deepest clcultion ws performed with respect to 7 m, for comprison with erlier results 1,12,13 nd ecuse mny XBTs mesure to this depth 8. To tke dvntge of the greter numer of oservtions in the upper ocen, the 7-m estimtes re sum of two depth integrtions, 3 m nd 3 7 m. Reconstruction detils. In our reconstruction we used the sprse ut reltively long record of thermosteric se-level nomlies to determine monthly mplitudes of the leding 3 empiricl orthogonl functions (EOFs). The EOFs were used to model vriility of the time-vrying se level nd were clculted from 14 yers ( ) of stellite ltimeter dt. An dditionl constnt (essentilly sptilly uniform field) ws included in the reconstruction to represent chnges in the glol men 6,7. Before computing the EOFs, we pplied n inverted rometer correction nd removed nnul nd semi-nnul signls s well s glolly verged se-level trend from the ltimeter dt. Error estimtes. The reduced-spce optiml interpoltion formlism 5 provides estimtes of errors on the sis of the dt distriution nd uncertinties in the hydrogrphic oservtions (instrumentl nd geophysicl errors) s well s ocen eddy vriility determined from stellite ltimeter dt. The ltter two were comined in qudrture. The forml error estimtes quoted in the text re for one stndrd devition. Systemtic error corrections. We hve significntly reduced the systemtic ises present in previous nlyses y eliminting dt sets with unknown errors (for exmple MBTs), correcting the XBT fll-rte errors nd y using the reduced-spce optiml interpoltion technique. Further refinements in identifying nd correcting XBT errors my e possile in the future 8 ut it is likely tht more thn 7% of the erlier XBT ises hve een corrected in this nlysis. Further corrections re complex issue tht is currently eing ddressed y n interntionl working group. Ocen het content regression. We converted the reconstructed ner-glol monthly mps of thermosteric se level into ocen het content mps y using coefficients otined from sptilly vrile liner regression etween estimtes of ocen het content nd thermosteric se level. The regressions re clculted from the temperture profiles in 1u 3 1u grid oxes (following the World Meteorologicl Orgniztion squres). The resultnt correltion coefficients re t lest Alory, G., Wijffels, S. & Meyers, G. M. Oserved temperture trends in the Indin Ocen over nd ssocited mechnisms. Geophys. Res. Lett. 34, L /26GL2844 (27). 33. Conkright, M. E. et l. World Ocen Atls 21: Ojective Anlyses, Dt Sttistics, nd Figures, CD-ROM Documenttion (Ntionl Ocenogrphic Dt Center, Silver Spring, MD, 22). 28 Mcmilln Pulishers Limited. All rights reserved