DOI: 10.1126/science.1084123 , 479 (2003); 301Science

et al.B. D. Santer,to Recent Tropopause Height ChangesContributions of Anthropogenic and Natural Forcing

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Contributions of Anthropogenicand Natural Forcing to RecentTropopause Height Changes

B. D. Santer,1* M. F. Wehner,2 T. M. L. Wigley,3 R. Sausen,4

G. A. Meehl,3 K. E. Taylor,1 C. Ammann,3 J. Arblaster,3

W. M. Washington,3 J. S. Boyle,1 W. Bruggemann5

Observations indicate that the height of the tropopause—the boundary betweenthe stratosphere and troposphere—has increased by several hundred meters since1979. Comparable increases are evident in climate model experiments. The lattershow that human-induced changes in ozone and well-mixed greenhouse gasesaccount for�80%of the simulated rise in tropopause height over 1979–1999. Theirprimary contributions are through cooling of the stratosphere (caused byozone) andwarming of the troposphere (caused by well-mixed greenhouse gases). A model-predicted fingerprint of tropopause height changes is statistically detectable in twodifferent observational (“reanalysis”) data sets. This positive detection result allowsus to attribute overall tropopauseheight changes to a combinationof anthropogenicand natural external forcings, with the anthropogenic component predominating.

The tropopause represents the boundary be-tween the troposphere and stratosphere and ismarked by large changes in the thermal, dy-namical, and chemical structure of the atmos-phere (1–3). Increases in tropopause heightover the past several decades have been iden-tified in radiosonde data (2, 4 ), in optimalcombinations of numerical weather forecastsand observations (“reanalyses”) (3, 5), and inclimate models forced by combined naturaland anthropogenic effects (6 ). Model exper-iments suggest that such increases cannot beexplained by natural climate variability alone(6, 7 ).

To date, no study has quantified the contri-butions of different anthropogenic and naturalforcings to 20th-century tropopause heightchanges. We estimate these contributions hereand demonstrate the usefulness of the thermallydefined tropopause as an integrated indicator ofhuman-induced climate change. We also iden-tify a model-predicted “fingerprint” of tropo-pause height changes in reanalysis data.Detection of this fingerprint enables us toattribute tropopause height changes to thecombined effects of anthropogenic and nat-ural forcing.

The anthropogenic forcings we considerare changes in well-mixed greenhouse gases(G), the direct scattering effects of sulfateaerosols (A), and tropospheric and strato-spheric ozone (O). The natural forcings con-sidered are changes in solar irradiance (S)and volcanic aerosols (V). All of these fac-tors are likely to have modified the thermalstructure and static stability of the atmos-phere (6–11), thus affecting tropopauseheight. To isolate the thermal responses thatdrive tropopause height changes, we analyzethe effects of G, A, O, S, and V on temper-atures averaged over broad layers of thestratosphere and troposphere.Model and reanalysis data. We used

the Department of Energy Parallel ClimateModel (PCM) developed by the NationalCenter for Atmospheric Research (NCAR)and Los Alamos National Laboratory (12). Awide range of experiments has been per-formed with PCM, of which seven were an-alyzed here for tropopause height changes. Inthe first five experiments, only a single forc-ing is changed at a time; for example, Gvaries according to historical estimates ofgreenhouse gas concentration changes,whereas A, O, S, and V are all held constantat preindustrial levels (13–18). In the sixthexperiment (ALL), all five forcings are variedsimultaneously. Both natural forcings arechanged in the seventh experiment (SV). G,A, O, and S commence in 1872, whereas V,SV, and ALL start in 1890. The experimentsend in 1999. To obtain better estimates of theunderlying responses to the imposed forc-ings, four realizations of each experimentwere performed. Each realization of a given

experiment has identical forcing but com-mences from different initial conditions of anunforced control run.

The detection part of our study requiresestimates of observed tropopause height chang-es, which were obtained from two reanalyses(19, 20). The first is from the National Centerfor Environmental Prediction and the NationalCenter for Atmospheric Research (NCEP); thesecond is from the European Centre for Medi-um-Range Weather Forecasts (ERA). Reanaly-ses use an atmospheric numerical weather fore-cast model with no changes over time in eitherthe model itself or in the observational dataassimilation system. NCEP data were availablefrom 1948 to 2001, but data before January1979 were excluded because of well-document-ed inhomogeneities (21, 22). ERA spans theshorter period from 1979 to 1993.

We estimate tropopause height using astandard thermal definition of pLRT, the pres-sure of the lapse-rate tropopause (23). Thisdefinition has the advantage that it can beapplied globally and is easily calculated fromvertical profiles of atmospheric temperatureunder most meteorological conditions (24,25). The algorithm that we used to computepLRT primarily monitors large-scale changesin the thermal structure of the atmosphere.

Multidecadal changes in pLRT are gener-ally smaller than the vertical resolution of theatmospheric models used in PCM and the tworeanalyses (Fig. 1A). This raises concernsregarding the sensitivity of our estimatedpLRT trends to the vertical resolution of theinput temperature data in the vicinity of thetropopause. Three independent pieces of ev-idence support the reliability of our pLRT

changes. First, calculations of NCEP pLRT

trends performed at high and low verticalresolution are in close agreement (26 ). Sec-ond, climate models with different verticalresolutions yield similar pLRT trends in re-sponse to external forcing (6 ). Finally, pLRT

trends computed from ERA and NCEP are ingood agreement with pLRT changes obtainedfrom high-resolution radiosonde temperaturesoundings (4, 6 ). All three lines of evidenceenhance confidence in the robustness of ourprocedure for estimating pLRT changes.

At each grid point in the model and reanal-ysis data, we compute pLRT from the monthlymean temperature profile at discrete pressurelevels (25). For PCM, we also calculate strato-spheric and tropospheric temperatures equiva-lent to those monitored by channels 4 and 2 (T4and T2) of the satellite-based MicrowaveSounding Unit (MSU) (22, 27–29). The simu-lated MSU data are useful in relating changes inpLRT to broad changes in atmospheric thermalstructure. Direct comparisons with observedMSU T4 and T2 data are given elsewhere (30).

1Program for Climate Model Diagnosis and Intercom-parison, Lawrence Livermore National Laboratory, Liv-ermore, CA 94550, USA. 2Lawrence Berkeley NationalLaboratory, Berkeley, CA 94720, USA. 3National Cen-ter for Atmospheric Research, Boulder, CO 80303,USA. 4Deutsches Zentrum fur Luft- und Raumfahrt,Institut fur Physik der Atmosphare, Oberpfaffenhofen,D-82234 Wessling, Germany. 5University of Birming-ham, Edgbaston, Birmingham B15 2TT, UK.

*To whom correspondence should be addressed. E-mail:santer1@llnl.gov

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Global-scale changes. For any specifiedforcing, the ensemble members define an en-velope of possible climate trajectories (Fig.1A). The time at which the ALL and SVenvelopes separate completely (and remainseparated) is a simple qualitative measure ofthe detectability of an anthropogenic signal inPCM data. For tropopause height, this sepa-ration occurs in the mid-1980s. Divergenceof the ALL and SV solutions occurs earlierfor T4 data [before the eruption of Mt.Agung in 1963 (Fig. 1C)] and later for T2[in the early 1990s (Fig. 1E)].

The short-term (3- to 4-year) pLRT signa-tures of major volcanic eruptions are clearlyevident in reanalyses and the SV and ALLexperiments (Fig. 1A). Large explosive volca-nic eruptions warm the lower stratosphere andcool the troposphere (Fig. 1, C and E). Botheffects decrease tropopause height and increasepLRT (6 ). In PCM, pLRT changes after theeruptions of Santa Maria, Agung, El Chi-chon, and Pinatubo are large, relative toboth the “between realization” variabilityof pLRT and the pLRT variability duringvolcanically quiescent periods.

The total linear pLRT decrease in ALL is 2.9hPa over 1979–1999, corresponding to a tropo-pause height increase of roughly 120 m (Fig.1A). Tropopause height in NCEP rises by �190m. The smaller increase in PCM is primarily dueto two factors. The first is the unrealistically largestratospheric cooling in NCEP (31). Becausestratospheric cooling tends to increase tropopauseheight (4, 6), excessive cooling amplifiesNCEP’s height increase. The second factor isPCM’s overestimate of volcanically inducedstratospheric warming (30). Excessive strato-spheric warming yields a volcanically inducedtropopause height decrease that is too large, thusreducing the overall height increase in ALL.

The largest contributions to PCM’s overalltropopause height increases are from changes in

Fig. 1. Time series of global mean, monthly mean anom-alies in tropopause pressure (pLRT)(A and B), stratospherictemperature (T4) (C and D), and mid- to upper tropo-spheric temperature (T2) (E and F). Model results are fromseven different PCM ensemble experiments (12, 14, 16,17). Five experiments use a single forcing only (G, A, O, S,or V ). Two integrations involve combined forcing changes,either in natural forcings (SV ), or in all forcings (ALL).There are four realizations of each experiment. In (B), (D),and (F), only low-pass filtered ensemble means are shown.In (A), (C), and (E), both the low-pass filtered ensemblemean and the (unfiltered) range between the highest andlowest values of the realizations are given. All modelanomalies are defined relative to climatological monthlymeans computed over 1890–1909. Reanalysis-based pLRTestimates from NCEP (19) and ERA (20) were filtered inthe same way as model data (A). NCEP pLRT data areavailable from 1948–2001, but pre-1960 data were ig-nored because of deficiencies in the coverage and qualityof assimilated radiosonde data (22). The ERA record spans1979–1993. NCEP (ERA) was forced to have the samemean as ALL over 1960–1999 (1979–1993). The SUMresults [(B), (D), and (F)] are the sum of the filteredensemble-mean responses from G, A, O, S, and V.

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well-mixed greenhouse gases and ozone (Fig.1B). To quantify these contributions, we exam-ine the total linear pLRT trends in the ensemblemeans of the G, A, O, S, and V experiments(32). Linear trends are computed over four dif-ferent time horizons: the 20th century, 1900–1949, 1950–1999, and the satellite era (1979–1999) (Fig. 2A). Contributions of individualforcings are expressed as a percentage of thetotal linear change in ALL (33). Because someforcings increase tropopause height and otherslower it, the contributions of individual forcingscan in some cases exceed 100%. This simplymeans that in the absence of other influences,the trend due to a specific forcing can be largerthan that obtained when all five forcings act inconcert.

During the 20th century, G and O account for77 and 88% (respectively) of the total increase intropopause height in ALL. Their combined per-centage contribution of 165% is partly offset bythe smaller decreases in height caused by A andV (�32 and �39%). Solar irradiance changesmake a small positive contribution to the heightincrease in ALL. The relative contribution ofeach forcing varies with time. Whereas G and Omake roughly equivalent contributions to tropo-pause height change over 1900–1949, ozonebecomes more important in the second half ofthe century and during the satellite era (Fig. 2A).Similarly, S and V together explain 74% of thetotal tropopause height change over 1900–1949,but their net contribution to ALL is only �40%over 1950–1999. The large influence of V over1900–1949 arises from the Santa Maria eruptionin 1902 (Fig. 1A).

Decadal-scale increases in the height of thetropopause are driven by temperature changesabove and below the tropopause. Temperaturesin this region are influenced primarily by ozone-and greenhouse gas–induced cooling of thestratosphere and greenhouse gas–induced warm-ing of the troposphere. Both of these effects tendto raise tropopause height (4, 6). To first order,the global mean changes in pLRT over a stipulat-ed time period are linearly related to �T4 ��T2. A key question, therefore, is whether thesimulated height increase in ALL could haveoccurred solely through stratospheric coolingand without significant anthropogenically in-duced warming of the troposphere. We addressthis question by estimating the contributions ofindividual forcings to T4 and T2 changes.

Previous model-based work suggests thatozone forcing is the major driver of recent strato-spheric cooling (10, 34). A similar result holdsin PCM: Ozone changes account for 123% of thetotal linear change in T4 over 1950–1999 andfor 82% of the T4 decrease during the satelliteera (Figs. 1D and 2B). The corresponding con-tributions of greenhouse gas forcing to T4changes are only 9 and 3%, respectively (6). Incontrast, well-mixed greenhouse gases are themajor contributor to PCM’s tropospheric warm-ing and explain 174% of the total change in T2

over 1950–1999 (Figs. 1F and 2C). The ozonecomponent of T2 changes is small over thisperiod (�6%) (35). In PCM, therefore, the maineffect of well-mixed greenhouse gases on tropo-pause height is through warming the troposphererather than cooling the stratosphere.

Several additional features are noteworthy.Anthropogenic sulfate aerosols decrease tropo-pause height, primarily by cooling the tropo-sphere (Figs. 1F and 2C). In the model, sulfateaerosols cause only a small decrease in T4(Figs. 1D and 2B). Solar irradiance changesover the 20th century warm both the tropo-sphere and the stratosphere, with offsettingeffects on tropopause height. The sign ofthe solar effect on pLRT must therefore dependon the relative magnitudes of solar-inducedstratospheric and tropospheric warming. Thesmall rise in tropopause height in S (Fig. 1B)suggests that for solar forcing, troposphericwarming is more important.

A key assumption in many detection stud-ies is that the sum of the individual climateresponses to several different forcing mech-anisms is equal to the response obtainedwhen these forcings are varied simultaneous-ly (8, 9, 36 ). This implies that there are nostrong interactions between individual forc-ings. We tested this assumption for pLRT, T4,and T2 by comparing ALL results with thesum of the individual responses to G, A, O, S,and V (SUM). ALL and SUM show verysimilar global mean changes (Fig. 1, B, D,and F). For the three variables consideredhere, the estimated linear changes in SUM arewithin 10% (37 ) of the corresponding ALLvalues (Fig. 2). For these global-scale

changes, additivity is a reasonable assumption.Fingerprint analysis. We next used a

standard detection method (38, 39) to determinewhether a model-predicted spatial pattern ofexternally forced pLRT changes can be identi-fied in reanalysis data. Our detection methodassumes that the searched-for signal (the finger-print,

3

f ) is well represented by the first empir-ical orthogonal function (EOF) of the ALLensemble mean (30). We search for an increas-ing expression of

3

f in the NCEP and ERApLRT data and estimate the detection time—thetime at which

3

f becomes consistently identifi-able at a stipulated 5% significance level. Theclimate noise estimates required for assessingstatistical significance are obtained from 300-year control runs performed with PCM and theECHAM model of the Max-Planck Institute forMeteorology in Hamburg (40).

Detection times are computed both with andwithout the global mean component of tropo-pause height change (30). If the spatial mean isincluded, detection results can be dominated bylarge global-scale changes. Removing the spa-tial mean focuses attention on smaller-scalemodel-data pattern similarities and provides amore stringent test of model performance.

We first describe the patterns of tropopauseheight change in PCM and reanalyses. Maps oflinear pLRT trends over 1979–1999 are similarin NCEP and PCM (Fig. 3, A and C). Bothshow spatially coherent increases in tropopauseheight (negative trends in pLRT), with the small-est changes in the tropics and the largest in-creases toward the poles, particularly in theSouthern Hemisphere (6). Tropopause heightchanges in ERA (Fig. 3B) are less coherent than

Fig. 2. Total linear changes (32) in global mean, monthly mean tropopause height (A), stratospherictemperature (B), and tropospheric temperature (C) in PCM experiments with individual forcings (G,A, O, S, and V ) and combined natural and anthropogenic forcings (ALL). Linear changes arecomputed over four different time intervals using the (unfiltered) ensemble-mean data from Fig.1. For each time period, anomalies were defined relative to climatological monthly meanscomputed over 1900–1999. SUM denotes the sum of the linear changes in G, A, O, S, and V.

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in NCEP or PCM, with slight decreases inheight in the tropics. This largely reflects theshorter record length of ERA, which ends at atime when Pinatubo decreased tropopauseheight (Fig. 1, A and B). The ALL “meanincluded” pLRT fingerprint is similar to thePCM and NCEP linear trend patterns, withuniform sign, largest loadings at high latitudesin the Southern Hemisphere, and strong zonalstructure (Fig. 3D). Removal of the spatialmeans emphasizes the strong equator-to-polegradients and hemispheric asymmetry of thefingerprint (Fig. 3E).

When our detection method is appliedwith spatial means included, the ALL tropo-pause height fingerprint is consistently iden-tifiable in both reanalyses (fig. S1). AlthoughERA tropopause height increases are less co-herent than in NCEP and are visually lesssimilar to the ALL fingerprint,

3

f is still readi-ly detectable. In all four cases considered (41),fingerprint detection occurs in 1988, only 10years after the start of our analysis period(1979). With our strategy, 1988 is the earliesttime at which detection can be achieved.

The removal of spatial means still yields anidentifiable fingerprint, but only in NCEP. Thispositive result arises from model-data similari-ties in the equator-to-pole gradient and thehemispheric asymmetry of tropopause heightchanges (Fig. 3, A and E). Detection of

3

f inNCEP data occurs in 1995 (fig. S1), 7 yearslater than in the “mean included” case andafter the end of the ERA record. This sug-gests that the ERA record is simply tooshort to achieve positive detection of sub-global features of the predicted tropopauseheight changes.Conclusions. Our results are relevant to

the issue of whether the “real-world” tropo-sphere has warmed during the satellite era.PCM provides both direct and indirect evi-dence in support of a warming troposphere.The direct evidence is that in the ALL exper-iment, the troposphere warms by 0.07°C/decade over 1979–1999 (30). This warmingis predominantly due to increases in well-mixed greenhouse gases (Fig. 2C). We havepreviously shown (30) that the T2 fingerprintestimated from ALL is identifiable in a sat-

ellite data set with a warming troposphere(27 ) but not in a satellite data set with littleoverall tropospheric temperature change (28).

The second (and more indirect) line of evi-dence relies on the relation between changes intropopause height and changes in tropospherictemperature. Our detection results show consis-tency between the patterns of tropopause heightincrease in ALL and reanalyses. The PCM in-dividual forcing experiments help to identifythe main drivers of this change. Over 1979–1999, roughly 30% of the increase in tropo-pause height in ALL is explained by green-house gas–induced warming of the troposphere(Fig. 2A). Anthropogenically driven tropo-spheric warming is therefore an importantfactor in explaining modeled changes intropopause height. Without this troposphericwarming effect in the model, simulated heightchanges would be markedly reduced, and thecorrespondence that we find between modeledand observed �pLRT would be substantiallydegraded. The inference is that human-inducedtropospheric warming may also be an importantdriver of observed increases in tropopauseheight. Both the direct and indirect lines ofevidence support the contention that the tropo-sphere has warmed during the satellite era.

We have shown that both stratospheric cool-ing and tropospheric warming lead to increasesin tropopause height. However, the relative im-portance of these two factors is uncertain. In theNCEP reanalysis, which has documented errorsin stratospheric temperature (31), tropopauseheight increases even though the tropospherecools. In ERA (22) and PCM, the tropospherewarms, and both stratospheric cooling and tro-pospheric warming contribute to tropopauseheight increases. Clarification of the relativeroles of T2 and T4 changes in recent tropopauseheight increases is clearly required. This may befacilitated by second-generation reanalyses(such as the recently completed ERA-40 reanal-ysis), by further study of radiosonde-based tem-perature soundings, and by high-resolutionmeasurements of the tropopause from GlobalPositioning System (GPS) data (42).

References and Notes1. K. P. Hoinka, Mon. Weath. Rev. 126, 3303 (1998).2. D. J. Seidel, R. J. Ross, J. K. Angell, G. C. Reid, J.Geophys. Res. 106, 7857 (2001).

3. E. J. Highwood, B. J. Hoskins, Q. J. R. Meteorol. Soc.124, 1579 (1998).

4. E. J. Highwood, B. J. Hoskins, P. Berrisford, Q. J. R.Meteorol. Soc. 126, 1515 (2000).

5. W. J. Randel, F. Wu, D. J. Gaffen, J. Geophys. Res. 105,15509 (2000).

6. B. D. Santer et al., J. Geophys. Res. 108, 4002 (2003)(DOI 10.1029/2002JD002258).

7. R. Sausen, B. D. Santer, Meteorol. Zeit. 12, 131 (2003).8. B. D. Santer et al., Nature 382, 39 (1996).9. S. F. B. Tett, J. F. B. Mitchell, D. E. Parker, M. R. Allen,Science 274, 1170 (1996).

10. V. Ramaswamy et al., Rev. Geophys. 39, 71 (2001).11. J. E. Hansen et al., J. Geophys. Res. 107, 4347 (2002)

(DOI 10.1029/2001JD001143).12. W. M. Washington et al., Clim. Dyn. 16, 755 (2000).13. J. T. Kiehl, T. L. Schneider, R. W. Portmann, S. So-

lomon, J. Geophys. Res. 104, 31239 (1999).

Fig. 3. Least-squares linear trends and finger-prints of tropopause height change. Trends inglobal mean, monthly mean pLRT data (in hPaper decade) were computed over 1979–1999for NCEP (A) and the PCM ALL experiment(C) and over 1979–1993 for ERA (B). ThepLRT climate change fingerprints were com-puted from the ensemble-mean ALL results(D and E). Results are shown for analyseswith the spatial mean included (D) and withthe mean removed (E).

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14. A. Dai, T. M. L. Wigley, B. A. Boville, J. T. Kiehl, L. E.Buja, J. Clim. 14, 485 (2001).

15. D. V. Hoyt, K. H. Schatten, J. Geophys. Res. 98, 18895(1993).

16. G. A. Meehl, W. M. Washington, T. M. L. Wigley, J. M.Arblaster, A. Dai, J. Clim. 16, 426 (2003).

17. C. Ammann, G. A. Meehl, W. M. Washington, C. S.Zender, Geophys. Res. Lett. 30, 1657 (2003) (DOI10.1029/2003GL016875).

18. The G, A, and O forcings in the PCM experiments areidentical to those used in integrations performedwith the NCAR Climate System Model (13, 14). Totalsolar irradiance changes were prescribed according toHoyt and Schatten (15) and updated as in (16), withno wavelength dependence of the forcing. Volcanicforcing was based on estimates of total sulfate load-ing and a simplified model of aerosol distribution anddecay (17).

19. E. Kalnay et al., Bull. Am. Meteorol. Soc. 77, 437(1996).

20. J. K. Gibson et al., ECMWF Re-Analysis Project ReportsSeries 1 (European Centre for Medium-Range Weath-er Forecasts, Reading, UK, 1997), 66 pp.

21. S. Pawson, M. Fiorino, Clim. Dyn. 15, 241 (1999).22. B. D. Santer et al., J. Geophys. Res. 104, 6305 (1999).23. World Meteorological Organization (WMO), Mete-

orology—A Three-Dimensional Science: Second Ses-sion of the Commission for Aerology [WMO BulletinIV(4), WMO, Geneva, 1957], pp. 134–138.

24. T. Reichler, M. Dameris, R. Sausen, D. Nodorp, AGlobal Climatology of the Tropopause Height Basedon ECMWF Analyses (Institut fur Physik der Atmos-phare, Report 57, Deutsche Forschungsanstalt furLuft und Raumfahrt, Wessling, Germany, 1996).

25. We estimate pLRT from reanalysis and model data byinterpolation of the lapse rate in a p� coordinate sys-tem, where p denotes pressure, � � R/cp, and R and cpare the gas constant for dry air and the specific heatcapacity of dry air at constant pressure (24). The algo-rithm identifies the threshold model level at which thelapse rate falls below 2°C/km and then remains lessthan this critical value for a specified vertical distance(23). The exact pressure at which the lapse rate attainsthe critical value is determined by linear interpolation oflapse rates in the layers immediately above and belowthe threshold level. This definition of tropopause heightis robust under most conditions. Exceptions includesituations where the atmosphere is relatively isother-mal or where multiple stable layers are present (24). Toavoid unrealistically high or low pLRT values, searchlimits are restricted to pressure levels between roughly550 and 75 hPa. Decadal-scale trends in pLRT are rela-tively insensitive to the temporal resolution of the inputtemperature data (3, 6).

26. The NCEP pLRT calculation performed here usedmonthly mean temperature data at 17 model pres-sure levels. A similar calculation used the 6-hourlytemperature data available at 28 model sigma levels,with higher resolution in the vicinity of the tropicaltropopause (6).

27. C. A. Mears, M. C. Schabel, F. W. Wentz, J. Clim., inpress.

28. J. R. Christy, R. W. Spencer, W. D. Braswell, J. Atmos.Ocean. Tech. 17, 1153 (2000).

29. The radiative emissions contributing to the T4 and T2measurements peak at roughly 74 and 595 hPa,respectively. In the tropics, emissions from the tro-posphere make a substantial contribution to estimat-ed T4 temperatures.

30. B. D. Santer et al., Science 300, 1280 (2003).31. The total linear change in T4 in NCEP is �1.65°C over

1979–1999 (32). This is considerably larger than thesimulated T4 change of �0.73°C in ALL or the estimat-ed observed MSU T4 changes of �0.93°C (27) and�1.07°C (28). NCEP’s excessive stratospheric cooling isdue to biases in both the satellite-derived temperatureretrievals and the assimilated radiosonde data (6, 21).Because T2 receives a small (roughly 10% globally)contribution from the stratosphere, any error in NCEP’sT4 trends will propagate into �T2. This partly explainswhy NCEP’s troposphere cools markedly over 1979–1999, with a total linear change in T2 of �0.22°C.

32. The total linear change is defined as b � n, where b isthe slope parameter of the linear trend (in hPa per

month or °C per month) fitted by the standard least-squares method over a specified period of n months.

33. For forcing component x, this is calculated as (x/y) �100, where x is the total linear change in pLRT over astipulated time interval (due to x) and y is the linearchange in pLRT (over the same interval) due to ALL.This definition is not applicable if the linear change inALL is close to zero, a situation that never arises here.

34. V. Ramaswamy, M. D. Schwarzkopf, W. Randel, Na-ture 382, 616 (1996).

35. Because the O experiment does not separate tropo-spheric and stratospheric ozone changes, we cannotquantify their individual contributions to overallchanges in pLRT. Historical increases in troposphericozone are expected to warm T2, thereby increasingtropopause height. Such warming is not evident inthe O integration (Fig. 2C) because of the coolingeffect of stratospheric ozone depletion on the uppertroposphere. Figure 2 indicates that in PCM, ozone-induced increases in tropopause height arise primar-ily through stratospheric ozone depletion and theresultant cooling of T4, not through troposphericozone changes.

36. P. A. Stott et al., Science 290, 2133 (2000).37. Linear changes in tropopause height over 1979–1999

are the sole exception: SUM results are 19% smallerthan in ALL. This difference is largely attributable tonoise differences. SUM is a linear combination of fiveclimate responses plus five different (ensemble-aver-aged) noise estimates, and must therefore be noisierthan ALL. ALL versus SUM noise differences are likely tohave the greatest impact on trends calculated overrelatively short periods.

38. K. Hasselmann, in Meteorology of Tropical Oceans,D. B. Shaw, Ed. (Royal Meteorological Society ofLondon, London, UK, 1979), pp. 251–259.

39. B. D. Santer et al., J. Geophys. Res. 100, 10693(1995).

40. E. Roeckner, L. Bengtsson, J. Feichter, J. Lelieveld, H.Rodhe, J. Clim. 12, 3004 (1999).

41. Two reanalyses (NCEP and ERA) combined with twonoise data sets for calculation of natural variabilitystatistics (PCM and ECHAM) yields four nonopti-mized detection time estimates.

42. W. J. Randel, F. Wu, W. R. Rios, J. Geophys. Res. 108,4024 (2003) (DOI 10.1029/2002JD002595).

43. Work at Lawrence Livermore National Laboratorywas performed under the auspices of the U.S. Depart-ment of Energy (DOE), Environmental Sciences Divi-sion, contract W-7405-ENG-48. T.M.L.W. was sup-ported by the National Oceanic and AtmosphericAdministration Office of Global Programs (ClimateChange Data and Detection) grant no. NA87GP0105and by DOE grant no. DE-FG02-98ER62601. A por-tion of this study was supported by the DOE Office ofBiological and Environmental Research, as part of itsClimate Change Prediction Program. The MSUweighting functions were provided by J. Christy(Univ. of Alabama in Huntsville). E. Roeckner (Max-Planck Institut fur Meteorologie, Hamburg, Germany)supplied ECHAM control run data. Review commentsfrom B. Hoskins and S. Pawson substantially im-proved the manuscript. We also thank R. Anthes, W.Randel, and J. Bates for bringing GPS-based monitor-ing of tropopause height to our attention.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/301/5632/479/DC1SOM TextFig. S1

4 March 2003; accepted 30 May 2003

Dense Packing and Symmetry inSmall Clusters of MicrospheresVinothan N. Manoharan,1 Mark T. Elsesser,1 David J. Pine1,2*

Whensmall numbersof colloidalmicrospheres are attached to the surfacesof liquidemulsion droplets, removing fluid from the droplets leads to packings of spheresthat minimize the second moment of the mass distribution. The structures of thepackings range from sphere doublets, triangles, and tetrahedra to exotic polyhedranot found in infinite lattice packings, molecules, or minimum–potential energyclusters. The emulsion system presents a route to produce new colloidal structuresand a means to study how different physical constraints affect symmetry in smallparcels of matter.

What defines an optimal packing of a set of nidentical spheres? Although centuries old,this question remains both pertinent and per-vasive in mathematics and science (1). Forpackings of an infinite number of spheres, theobvious measure of optimality is the bulkdensity. As Kepler conjectured and Halesproved (2, 3), the optimal infinite packing isthe face-centered cubic (fcc) arrangement,which maximizes the density or, equivalent-ly, minimizes the volume per sphere. But fora finite group of spheres there is no compel-ling definition of density, and optimality in

finite sphere packings can be defined by theminimization of any physically reasonablevariable, such as potential energy or surfacearea, for example. Different minimization cri-teria can lead to dramatically different se-quences of packings (4 ), with symmetriesthat are rarely consistent with that of aninfinite (bulk) packing.

In nature, differences in symmetry be-tween finite and bulk packings manifestthemselves in a variety of phenomena. Theinteractions between atoms or particles inmany systems, including metals, noble gases,and colloids, are nearly spherically isotropic,and the equilibrium structures at high densityare fcc, a consequence of Kepler’s conjec-ture. But finite packings of such particles, asfound in isolated clusters, complexes, or localarrangements of bulk phases, frequently

1Department of Chemical Engineering, 2Departmentof Materials, University of California, Santa Barbara,CA 93106, USA.

*To whom correspondence should be addressed. E-mail: pine@mrl.ucsb.edu

R E S E A R C H A R T I C L E S

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