GEOPHYSICAL
RESEARCH
LETTERS,VOL.25,NO. 2, PAGES163-166,JANUARY15,1998
Using the sunspotcycleto date ice cores
Eric J. Steig
Instituteof ArcticandAlpineResearch,
Universityof Colorado,
Boulder,Colorado
DavidL. Morse
• andEdwinD. Waddington
Geophysics
Program,
University
of Washington,
Seattle,Washington
Pratigya
J.Polissar
2
Schoolof NaturalSciences,
Hmnpshire
College,Amherst,Massachusetts
Abstract. For manyice cores,the snowaccumulation
rate is too
Ice coresare drilledto meettwo possible
goals:recovering
low to preserveannualstratigraphy,
precludingdirect measure- high-resolution
records
andrecovering
oldice. H)gh-resolution
mentof annuallayer thickness.For selectedHolocenesectionsof records
requiresiteswheretheaccumulation
rate,b, is relatively
the Taylor Dome core, East Antarctica,we insteaduse high-
high(> 0.2 m ice a-l). Undertheseconditions,
annualstrati-
resolution
•øBemeasurements
to establish
a nominal
l l-year graphiclayersare generallypreservedin the ice, andtheirthickthickness,
takingadvantage
of thesolarcyclein cosmogenic
iso- nesscan be measureddirectlyusingseasonal
indicatorssuchas
tope production. We comparemeasuredthicknesseswith the
layer thicknessprofile predictedby a finite elementice flow
•5•80
cycles
[Hammer
etal., 1986]orvisible
differences
between
summer
andwintersnowfall[Alleyet al., 1993]. Theage-depth
model. The resultsare in goodagreement,
supporting
the as- relationship
for the corecanthenbe obtained
by directlayer
sumptionthat the lengthof the solarcycle has remainedessen- counting.Also,differences
between
observed
andpredicted
layer
tially constantthroughoutthe Holocene.For ice coreswherean- thickness
can be usedto determine
accumulation
ratehistory
nuallayers
arenotpreserved,
the•øBe1l-yearlayermethod
can [Cutleret al., 1995],essential
for estimating
fluxesof chemical
be usedasan independent
checkon flow-modelestimates
of layer tracersfromtheirobserved
concentrations
[Alleyet al., 1995;
thicknessand to estimatepastaccumulationrates. It shouldbe Waddington,1996]
possibleto accuratelydateice coresby counting1l-year layers
Often,the goalof obtaininghigh-resolution
recordsconflicts
detected
withcontinuous
high-resolution
•øBe
measurements. withthegoalof recovering
old ice. An example
is theTaylor
Dome ice core, retrieved in 1994 from a local ice-accumulation
area near McMurdo Sound, Antarctica(77ø59'S, 158ø59'E).
Thiscoreis of potentially
greatimportance
because
of itsproximityto the RossSeaembayment,
wheredramatic
changes
in
Introduction
Followingburialandfirnificationat the surfaceof a glacieror oceanandice-sheet
conditions
havetakenplacethrough
glacialice sheet,annuallyaccumulated
layersof snowundergothinning interglacial
cycles[Dentonet al., 1989;Steiget al., 1997]. At
due to glacierflow. Eachglacieror ice sheethasa characteristic TaylorDome(T ~ 104 years)
iceflowmodels
canreconstruct
time scale,T, for ice deformationgivenby
Holocene
ice flow patterns
withreasonable
precision.However,
theaccumulation
rate(b = 0.07micea'l) istoolowtopreserve
H
T = -•b
(1)
annualstratigraphy
beyondthe upper20 metersof firn [Grootes
and Steig, 1992].
whereH istheicethickness
and• istheice-equivalent
accu-
In thispaper,we present
a newmethod
for measuring
layer
mulationrate. Typical valuesof T rangefrom a I•w hundred thicknesses
in low-accumulation
ice cores.UsingTaylorDome
usinghighyears
fortemperate
valleyglaciers
to~105years
forthelargepo- as a testcase,we determinean 1l-year stratigraphy
measurements
of cosmogenic
•øBe.We demonstrate
lar ice sheets.The thinningprocess
canbe described
by a func- resolution
tion that givesthe ratio betweenthe thickness
at depthandthe the applicability
of the methodby comparing
measured
layer
initial (ice equivalent)thicknessat the surface. The thinning thicknesseswith resultsfrom a finite elementice flow model,
functionis usuallyestimatedwith a geophysical
ice flow model
whichcalculates
the totalverticalstrainexperienced
by ice particlesastheytraveldownwardfromthesurface[Waddington
et al., The 11-year cycle
1993]. For ageslessthan T, layerthicknesses
cangenerallybe
Theessence
of ourapproach
is therecognition
thatthepro-
predictedwith confidence.
duction
of•øBe
bycosmic-ray
interactions
withatmospheric
N,O
andotherelements
is periodic[Lal and Peters,1967],andthat
canbedetected
in •øBedeposited
at theearth's
•NowatInstitute
forGeophysics,
University
ofTexas,
Austin,
Texas. thisperiodicity
2Nowat Department
of Geosciences,
University
of Massachusetts,
surface. Of particularinterestis the well-knownSchwabesunAmherst, Massachusetts.
spotcycle,havinga periodaveraging
11 years.Averaged
over
theentireearth,
theamplitude
of tøBeproduction
overthecourse
Copyright
1998by theAmericanGeophysical
Union.
of a typical11-yearcycleis about10%. At polarlatitudes,
this
amplitude
increases
to > 20 % andis therefore
relatively
easyto
detectin polarice cores.Otherchanges
in production
rateare
Papernumber97GL03566.
0094-8534/98/97GL-03566505.00
163
164
STEIG
ETAI.,.'USING
THESUNSPOT
CYCLE
TODATE
ICECORES
etal.,1996].Additional
•øBe
analyses
wereconducted
at
eithermuchsmaller
in amplitude
(the90 yearGleissberg
solar [Steig
cycle
[Beer
etal.,1994]),
arenon-periodic
(short-lived
periods
of 49.12-51.25m, 130.00-131.00m, 220.12-221.12m and298.60-
anomalously
highproduction
[Raisbeck
et al., 1987]),or occur 299.80metersin theTaylorDomeice core. We referto these
asB through
E in orderof increasing
depth.Samples
overmuchlongertimescales
(changes
in geomagnetic
field sections
and analyzedby accelerator
massspectrometry
strength
[Raisbeck
andYiou,1988]).Historical
records
of sun- wereprocessed
(AMS)
according
to
the
methods
described
by
Steig[1996],folspot
andaurora
observations
show
thatthe11-year
cycle
hasperRaisbeck
etal. [1978]andSouthon
etal. [1990].Precisistedfor at leastthe lastseveralhundred
years[Eddy,1988]. lowing
is betterthan+_5%. Section
B wassampled
The11-year
cycle
hasbeen
detected
intøBe
measurements
inice sionof theanalyses
of 10 m'•; sections
C, D andE weresampled
at 20
coresfrom bothGreenland[Beeret al., 1990] and Antarctica at a resolution
transitionin theTaylorDomeice
[Steig
etal.,1996].Attolini
etal.[1988]
have
shown
thatthe11- m'•. The Pleistocene-Holocene
core
occurs
at
a
depth
of--375
m,
asreadilyobserved
in icefabric
yearcycle
in tøBe
deposition
persisted
through
theMaunder
sun[Fit,rpatrick,
1994] and geochemical
profiles[Steig,1996;
spotminimum,
when
thevisible
sunspot
cycle
haddisappeared.
etal, 1996].Thus,thesections
analyzed
areallfrom
Ourworking
hypothesis
isthatthehistorical
behavior
ofthe11- Mayewski
the
Holocene
period.
yearsunspot
cycle
haspersisted
through
thecharacteristic
timesFigure1 shows
thatthere
isa cleardecrease
inthewavelength
caleoftheTaylor
Dome
core,
about
104
years.
of•øBe
variations
withdepth.
Neither
high-resolution
15•80
[Steig
etal., 1996]norelectrical
conductivity
measurements
[K. Taylor,
DeterminatiOn
oflayerthickness
with•øBe
personal
communication,
1995]ontheTaylorDomecoreshow
ofperiodicity
atornear
thatobserved
inl()Be.
WeconSection
A inFigure
1shows
theresults
ofløBe
analyses
froma evidence
shallow
firncoreat TaylorDome.Theperiodicity
in section
A
cludethatthe obvious,strongcyclesin sections
B throughE,
having
amplitudes
comparable
to thosein section
A, cannot
be
hasbeenindependently
dated
using
seasonal
8•80stratigraphy
bymeteorological
factors,
butlikelyreflectSchwabeandidentification
of AD 1954and1964bomb-radioactivity
hori- explained
variations.
Theobserved
amplitudes
areas
zons,andisdemonstrably
associated
withthe11-year
solarcycle cycleproduction-rate
large
as,orlarger
than,
predicted
forproduction
of•øBe
inthe
polaratmosphere.
Thesignificance
of thisresultwithrespect
to
atmospheric
mixing
processes
isdiscussed
bySteigetal. [ 1996].
A
Wedetermine
theaverage
wavelengths,
zXF,,
of•(•Be
variations
in sections
B through
E by measuring
peak-to-peak
andtroughto-trough
distances.
In theeventthata peakortrough
isdefined
2.0
bymorethanonedatapoint,theaverage
depth
isadopted.
We
usemeasured
densities,
p [Fitzpatrick,
1994],to calculate
the
ice-equivalent
11-year
layerthickness,
2•, asa function
of ice
equivalent
depth,z*. Results
areshown
inTable1 andplotted
in Figure2. Errorbarstakeintoaccount
bothanalytical
uncertaintyandthevariable
length
ofthenominal
11-year
cycle.From
thehistorical
sunspot
data[Stephenson,
1990],wetakethiscycle
length
as 11+_2/•/n years(1 standard
deviation)
forn consecutivecycles.Weemphasize
thatweareassulning,
asa working
hypothesis,
thatthehistorical
behavior
of thesunspot
cycleis
representative
of thepre-historical
period.Thepossibility
of
6.0
10.0
49.5
larger
variations
incycle
length
could
betested
with•øBe
measurements
in annual-layer-counted
cores
fromcentral
Greenland.
I
50.5
I
Determinationof layer thicknesswith an ice flow
model
130.0
We usethe two-dimensional
finite elementflow modeldevel-
130.5
opedby Raymond
[1983]to modelthe flow of ice passing
through
theTaylorDomecoresite[Waddiugton
et al., 1993].
D
220.5
Themodelusesa Glen-type
flowlaw[e.g.Paterson,
1994]:
• = Ar n
(2)
221.0
where •
'
299.0
i
E
i
i
i
i
i
299.5
,
shearstress
andthestress
exponent,
n, is equalto 3. Themodel
,
l
i
i
i
i
10
20
is the effective strain rate, A is the temperature-
dependent
theological
softness
parameter,
z is the effective
30
øBe(103atoms/g)
geometry
isprovided
bydetailed
surface
andbedrock
topography
fromground-based
surveys
andice-penetrating
radar[Morse
and
Waddington,
1992;Morse,1997].Themodelallows
thesurface
to evolveto steady-state
withthemodernaccumulation
ratepattern,takenfroma networkof accumulation
stakes,shallowcores
andsnowpits[Grootes
andSteig,1992;Waddington
andMorse,
Figure1. •øBeconcentrations
tbr selected
depthintervals
at
surface
Taylor
Dome.Thepanel
labels
"A","B"etc.correspond
tothe 1994;Morse,1997]. A is adjusteduntilthe steady-state
section namesreferred to in the text.
topography
matches
themodern
profile.Wecalculate
thetensor
STEIG ET AL.' USING THE SUNSPOT CYCLE TO DATE ICE CORES
165
Table 1. MeasuredI l-yearlayerthickness
at TaylorDome. Uncertainties
(+ I standard
deviation)takeinto
accountmeasurement
precisionandthevariablelengthof the 1l-yearcycle.
SectionTrue
MidpointIceEquivalent I l-year
Layer
Name Depth,•: (m) Depth,•:* (m) Thickness,
• (m)
Density,
a
/9 (kgm-•)
IceEquiv.
I 1-year
Thickness,
';[11
(m)
A
6.00
2.7
2.04 + 0.20
354.3C + 5
0.79 + 0.10
B
49.50
32.4
0.93 + 0.05
712.75 + 5
0.72 + 0.10
C
130.50
108.0
0.55 + 0.02
908.78 + 5
0.54 + 0.07
D
220.50
197.4
0.39 + 0.02
914.45 + 5
0.39 _+0.05
E
299.55
276.0
0.24 + 0.04
916.95 + 5
0.24 + 0.04
finite strainexperiencedby ice particlesalong trajectoriesthat
intersectthe ice core location,and use the layer normal strainto
determinethe layer thinningfunction.
We use the layer thinningfunctionand an assumedconstant
Among the five shortertime intervals where we have measured
løBeat higherresolution
to determine
thenominal
11-year
layer
thickness,the averageconcentrationvariesby lessthan 5 %. We
plot the derivedlayer thicknessprofile, A l•, asa functionof z *
accumulation
rateof b = 0.07 m ice a'l (themeasured
modern in Figure 2. For comparison,we also showcalculated10 and 12in Figure2, againusing/•= 0.07m icea-•.
value at the core site) to calculatethe l l-year layer thickness yearlayerprofiles
profile. We emphasizethat the differencebetweenthe true and Clearly, it is the 11-yearlayer thicknessprofile that corresponds
closely
tothemeasured
løBewavelengths.
assumedaccumulationratemnot the shapeof the model-derived most
thinningfunction--is the chief uncertaintyin this calculation.
The assumptionthat b is constantis reasonable.For time interDiscussion
vals muchlongerthan 11 years,averageb is the dominantcon-
trolling
factor
onaverage
•øBe
concentration
[Raisbeck
andYiou, Theagreement
of themeasured
løBewavelengths
andthepre1985].For-200 yearaverages,
Holocene
løBeconcentrations
in dicted l 1-year layer thicknessis excellent. As Figure 2 illusthe Taylor Dome core vary by less than 10 % [Steig, 1997].
i*i ' ' I ' ' ' I ' ' ' I ' -'
0.8 '"
0.7
0.6
0.5
0.4
trates,the profile from the glacierflow modelfits the data, in all
cases,to within less than 0.5 standarddeviations. This comparisonsprovide a compatibilitytest of both the assumptionsof the
flow model and the uniformityof the Schwabeperiodthroughthe
Holocene.
Weconclude
thefollowing:(1) Thecyclicity
of •Be
concentrationsmeasuredin the Taylor Dome core is due to
Schwabe-cycle(11-year) productionrate variations. (2) The assumptionof constantaccumulationfor the time intervalsconsidered, the shapeof the model-derivedthinning function, and the
assumedstability of the Schwabeperiod are either mutually correct or are deviouslyin error suchthat their et"l•ctscancelto give
the impressionof the former.
Valuable absolutechronologiesand accumulationhistoriesderived from annuallayer countingand layer thicknessobservations
have beenobtainedfor ice coresfrom high accumulationareasin
central Greenland. While existing and planned Antarctic ice
corescan provide a wealth of paleoclimateinformationover time
scales
of T - l04to 105years,
annual
stratigraphy
is generally
0.3
not preservedat sites with thesedesirablelong times scales. In
principle,a depth-agescalebasedon counted11-yearsolarcycles
could be producedfor such sites by continuoushigh-resolution
0.2
•øBe
sampling.
Thismaycurrently
beimpractical
duetothehigh
costof løBeanalyses.In the meantime,
high-resolution
løBe
0.1
0
100
200
300
samplingat judiciously spaceddepth intervalstightly constrains
the depth-agecurve by measuringits slopeand, when used with
thinning functions from ice flow models, provides a means to
determinepastaccumulationrates.
Continuous
l{•Besampling
maybetheonlytechnique
capable
of providing a layer-countedchronologyfor important climate
eventssuchas the "AntarcticCold Reversal"[Jouzelet al., 1995]
Figure 2. Comparisonof 11-yearlayer thicknesses
(,4.11)from in low-accumulationcoresfrom East Antarctica. As an example,
high-resolution Be data (+) and calculatedlayer thicknesspro- at a depthof 380 metersin the Taylor Dome ice core, the age is
file ( All ) froma finiteelementiceflow model(•)
assuming
about 15,000 years[Steig, 1996]. At this depth,the annuallayer
a constantHolocene accumulationrate of 0.07 m ice equiv. per
thicknessis about0.2 cm and the løBeconcentration
is about105
ice equivalentdepth(m)
year. Errorbarsshowuncertainty
(0.5 standard
deviations)
of the
measuredthicknesses,taking into accountthe variablelengthof
the nonfinal11-yearcycle. Upper and lower dashedlines show
calculated12 and 1O-yearlayerthicknessprofiles,respectively.
atomsper gram of ice. Given that « the crosssectionalarea of
the 15 cm diameter core is available, sampling at single-year
resolution
yields15g of ice,or about1.5x 106atoms
of løBe,
166
STEIG ET AL.: USING TIlE SUNSPOT CYCLE TO DATE ICE CORES
measurableat currentAMS detectionlimits. Sinceit may be rea-
sonableto define11-yearcycleson the basisof biannualresolution (i.e. 5.5 samplesper cycle),it shouldbe possibleto extend
the limit of our methodto about30,000 yearsat Taylor Dome.
At othersitesin East Antarctica,accumulation
ratesare often
lower,butWBeconcentrations
arecorrespondingly
higher.This,
J. Thomas,K. Kreutz, P.M. Grootes,D. Morse, E. Steig,E. D. Waddington,E. S. Saltzman,P.-Y. Whung, and K. C. Taylor, Climate
changeduringthe lastdeglaciationin Antarctica,Science,272, 16361638, 1996.
Morse,D. L. Glacier Geophysics
at Taylor Dome.Antarctica,Ph.D. thesis,Universityof Washington,1997.
Morse, D. L. and E. D. Waddington,Glacier geophysicalstudiesfor an
ice-coresiteat Taylor Dome:Year two,Ant. J. U.S., 27, 59-61, 1992.
Paterson,W, S. B., Th.ePhysicsof Glaciers,ElsevierScience,Oxford,
and the fact that thinningis less extremewhere the total ice
thickness
is greater,meansthat the practicallimit of our method
1994.
at sitessuchasVostokmaybe asgreatas-,-50,000years.
Raisbeck,G. M., F. Yiou, M. FruneauandJ. M. Loiseaux,Beryllium-10
massspectrometry
with a cyclotron,Science,202, 215-217, 1978.
Acknowledgments.We are gratefulto R. Finkel and othersat the
Center for AcceleratorMass Spectrometry
at LawrenceLivermoreNa-
Raisbeck, G. M., F. Yiou, D. Bourles, C. Lorius, J. Jouzel, and N. I.
tionalLaboratory
for robeanalyses.
Themanuscript
benefited
fromin-
Antarctic ice during the last glacial period, Nature, 326, 273-277,
sightfulreviewsby R. Alleyandananonymous
reviewer.Thisstudywas
1987.
and9421644andby a U.S. DOE GlobalChangeFellowship
to EJS.
solaractivity and geomagnetic
field intensityduringthe last 10,000
years,in Stephenson,
F. R. andA. W. Wolfendale(Eds.),SecularSolar and GeomagneticVariations in the Last 10,000 Years,Kluwer
Barkov,Evidence
for twointervals
of enhanced
robedeposition
in
G. M. andF. Yiou,WBeasa proxyindicator
of variations
in
supported
bytheU.S.Antarctic
Program
under
grants
NsF-oPP
9316162 Raisbeck,
References
Alley,
R.B.,D.A.Meese,
C.A.Shinnan,
A.J.Gow,
K.C.Taylor,
P.M.
Academic Publishers, Boston, 287-296, 1988.
Raisbeck,
G. M. andF. Yiou,•øBein polariceandatmospheres,
Annal.
Glaciol., 7, 138-140, 1985.
Grootes,J. W. C. White, M. Ram, E. D. Waddington,P. Mayewski Raymond,C. F., Deformationin the vicinity of ice divides,J. Glaciol.,
29, 358-373, 1983.
andG. A. Zielinski,Abruptincreasein Greenlandsnowaccumulation
Southon, J. R., M. W. Caffee, J.C.Davis, T. L. Moore, I.D. Proctor, B.
at theendof theYoungerDryasevent,Nature,362,527-529, 1993.
Schumacherand J. S. Vogel, The new LLNL AMS spectrometer,
Alley, R.B., R.C. Finkel,K. Nishiizu•ni,S. Anandakrishnan,
C.A. ShuNucl. Instr. Meth. Phys.Res.,B52, 301-305, 1990.
man, G.R. Mershon, G.A. Zielinski and P.A. Mayewski, Changesin
continentaland sea-saltatmosphericloadingsin central Greenland Steig,E. J., Beryllium-10in the Taylor Dome Ice Core: Applicationsto
Antarctic Glaciologyand Paleoclinmtology,Ph.D. thesis,University
duringthe mostrecentdeglaciation:
model-based
estimates,
J. Glaciol., 41,503-514, 1995.
of Washington,1996.
Steig,E. J., How well can we parameterize
pastaccumulation
ratesin
Attolini, M. R., S. Cecchini,G. C. Castagnoli,M. Galli and T. Namni,
polarice sheets?
J. Glaciol.,in press,1997.
On the existenceof the 1l-year cycle in solar activity beforethe
Steig,E. J., P. J. Polissar,M. Stuiver,P.M. Grootesand R. C. Finkel,
Maunderminimum,J. Geophys.Res.,93, 12729-12734,1988.
Beer, J., A. Blinov, G. Bonani, R. C. Finkel, H. J. Holmann, B. Leh•nann,
Largeamplitude
solarmodulation
cycles
of •}Bein Antarctica:
impli-
cationsfor atmospheric
mixingprocesses
andinterpretation
of the ice
corerecord,Geophys.Res.Lett., 23, 523-526, 1996.
SuterandW. W61fli,Useof WBein polaricetotracetheI l-yearcySteig,E.J., C. P. Hart, J. W. C. White, W. L. Cunningham,M.D. Davis
cle of solaractivity,Nature, 347, 164-166, 1990.
and E. S. Saltzman,Changesin climate,oceanand ice sheetcondiBeer,J., F. Joos,C. Lukasczyk,W. Mende,J. Rodriguez,U. Siegenthaler,
tionsin the RossEmbaymentat 6 ka, Annal. Glaciol., in press,1997.
andR. Stellmacher,
robeasan indicator
of solarvariability
andcliF. R. Historicalevidenceconcerning
the Sun;interpretation
mate, in Nesme-Ribes,E. (Ed.), The Solar Engineand Its Influence Stephenson,
of sunspotrecordsduringthe telescopicand pretelescopic
eras,Phil.
on TerrestrialAtmosphere
and Climate,Springer-Verlag,
Berlin,221Trans.RoyalSoc.Lond.,33A, 499-512, I990.
233, 1994.
Waddington,E. D., Where are we going? The ice core-paleoclimate
inCutler, N. N., C. F. Raymond,E. D. Waddington,D. A. MeeseandR. B.
verseproblem,in Wolff, E. W. and R. C. Bales(Eds.), Processes
of
Alley, The effect of ice-sheetthicknesschangeon the accumulation
chetnical exchange between the atmosphereand polar snow,
historyinferredfromtheGISP2layerthicknesses,
Annai.Ghtciol.,21,
26-32, 1995.
Springer-Verlag,
Berlin,629-640, 1996.
Denton, G. H., J. G. Bockheim, S.C. Wilson and M. Stuiver, Late WisWaddington,E. D. andD. L. Morse,Spatialvariationsof localclimateat
Taylor Dome: implicationsfor paleocli•nate
frownice cores,Annal.
consinand Early HoloceneGlacial History,InnerRossEmbayment,
H. Oeschger,
A. Sigg,J. Schwander,
T. Staffelbach,
B. Stauffer,M.
Antarctica, Quat. Res., 31, 151-182, 1989.
Eddy,J. A., Variabilityof the presentandancientsun:a testof solaruniformitarianism,
in Stephenson,
F. R. and A. W. Wolfendale(Eds.),
SecularSolar and GeomagneticVariationsin the Last 10,000 Years,
Kluwer Academic Publishers,Boston, 1-23, 1988.
Glaciol.. 20, 219-225, 1994.
Waddington,E. D., D. L. Morse,P.M. GrootesandE. J. Steig,The connection between ice dynamicsand paleoclimatefrom ice cores:a
studyof Taylor Dome, Antarctica,in Peltier,W. R. (Ed.), Ice in the
ClimateSystem,Springer-Verlag,
Berlin,499-516, 1993.
Fitzpatrick,J. J., Preliminaryreporton the physicaland stratigraphic
E. J. Steig, Instituteof Ad'cticand Alpine Research,Universityof
properties
of theTaylorDomeicecore,Ant.J. U.S.,29, 84-86, 1994.
Colorado,Boulder,CO 80309. (e-mail: [email protected])
Grootes,P.M. and E. J. Steig,Taylor Dome ice corestudy,Ant. J. U.S.,
27, 57-58, 1992.
Hammer, C. U., H. B. Clausenand H. Tauber, Ice-coredating of the
Pleistocene/Holocene
boundary
applied
to a calibration
of the•4C
timescale,Radiocarbon, 28, 284-291, 1986.
Jouzel, J., R. Vaikmae, J. R. Petit, M. Martin, Y. Duclos, M. Stievenard,
C. Lorius, M. Toots, M. A. M61iCres,L. H. Burckle, N. I. Barkov, and
V. M. Kotlyakov,The two-stepshapeandtimingof thelastdeglaciation in Antarctica, Clint. Dvn., 11, 151-161, 1995.
Lal, D. and B. Peters,Cosmicray producedradioactivityon the earth,
Handbuchder Physik,46, 551-612, 1967.
Mayewski,P. A., M. S. Twickler,S. I. Whitlow,L. D. Meeker,Q. Yang,
D. L. Morse, Institute for Geophysics,University of Texas, 4412
SpicewoodSpringsRd., Bldg. 600, Austin, TX
78759. (e-mail:
[email protected])
E. D. Waddington,GeophysicsProgram 351650, University of
Washington,Seattle,WA 98185 (e-mail:[email protected])
P. J. Polissar,Departmentof Geosciences,
Universityof Massachusetts,233 Morrill ScienceCenter, Amherst,MA 01003. (e-mail: [email protected])
(ReceivedJuly 18, 1997;revisedNovember18, 1997;
acceptedNovember21, 1997)