PALEOCEANOGRAPHY,
VOL. 13,NO. 1, PAGES1-9,FEBRUARY1998
Origin of the middle Pleistocene transition
by ice sheet erosion of regolith
Peter U. Clark
Departmentof Geosciences,
OregonStateUniversity,Corvallis
David
Pollard
EarthSystemScienceCenter,Pennsylvania
StateUniversity,UniversityPark
Abstract. The transition
in the middlePleistocene
(-0.9 Ma) seenin •180 deep-sea-core
records
fromrelativelylowamplitude,high-frequency
(41 kyr) to high-amplitude,
low-frequency
(100 kyr) ice volumevariationsunderessentially
the
sameorbitalforcingcanbe attributedto a changefrom an all soft-bedded
to a mixed hard-softbedded
Laurentideice sheet
throughglacialerosionof a thickregolithandresultingexposureof unweathered
crystallinebedrock. A one-dimensional
ice sheetand bedrockmodelwhich includestransportof sedimentandice by subglacialsedimentdeformationdemonstratesthata widespread
deformingsediment
layermaintainsthin ice sheetsbeforethe transitionwhich respondlinearly
to the dominant(23 and41 kyr) orbitalforcing. Progressive
removalof the sedimentlayer eventuallycausesa transition
to thickerice sheetswhosedominanttimescaleof change(100 kyr) reflectsnonlineardeglaciation
processes.In model
simulationsover the last 3 Ma initialized with no ice and a uniform 50 rn sedimentlayer the time seriesof ice volume
andextentagreein severalimportantaspectswith theobserved
records.
1. Introduction
To achieve the latter, it has been necessaryto include addi-
Oxygenisotopes(5•80) measured
in benthicforaminifera tional physical processes(e.g., calving [Pollard, 1983], meltfrom deep-seasediments reveal that former northern hemisphereice sheetscyclicly waxed and wanedat the same periodicities (100, 41, and 23 kyr) as the orbital parametersthat
control the amount and distribution
of solar radiation
received
by the Earth, suggestinga causalrelationship between orbital
changesin insolationand ice volume (Milankovitch hypothesis) [Hays et al., 1976; Irnbrie et al., 1984]. However, there
are two significant problems in explaining global ice volume
variations since the onset of northern hemispherecontinental
glaciation at-2.8 Ma solely by orbital variations in insolation: (1) a transition, in the middle Pleistocene (-0.9 Ma),
from low-amplitude, higher-frequency (41 kyr) to highamplitude,lower-frequency(100 kyr) ice volume variationsunder essentiallythe same orbital forcing and (2) the dominance
of the 100 kyr ice volume signal since the middle Pleistocene
when insolation forcing at that period (eccentricity)has essentially no power (Figure 1) [Shackleton and Opdyke, 1976;
Pisias and Moore, 1981; Start and Prell, 1984; Ruddiman et al.,
1989; Imbrie et al., 1993; Mix et al., 1995].
Many hypotheses(summarizedby Imbrie et al. [1993]) have
been developedto explain these two aspectsof the evolution
and responseof the earth's climate system to the known orbital forcing. Generally speaking, a large number of models
have successfullyreproducedthe -23 and 41 kyr cycles in direct responseto the orbital Milankovitch forcing, but only a
few have reproducedthe observeddominant 100 kyr cycles
with rapid and completedeglaciationsover the last -0.9 Myr.
water dischargefeedback[Pollard, 1983; DeBlonde and Peltier,
1991], or snow aging [Gallee et al., 1992]) or to prescribe additional time-dependentforcing (atmospheric dust loading
[Peltier and Marshall, 1995] or atmosphericCO2 variations
[DeBlondeet al., 1996]). Furthermore,relatively few attempts
have been made to model the middle Pleistocene
transition
ob-
servedin marine5•80 records,
i.e., with relativelylittle 100
kyr powerbefore -0.9 Ma, and dominant 100 kyr cycles after
that time. In general,theseice sheet-climatemodelsproducea
transition as a nonlinear responseto a prescribedlong-term
cooling trend [Oerlemans, 1984; Saltzman and Maasch, 1991;
Abe-Ouchi, 1996] or to a suddenlyimposed switch in model
physics [DeBlonde and Peltier, 1991; Mudelsee and Schulz,
1997]. However, evidencefor a generalcooling trend or decreasein CO2over the last 2 Ma is uncertain[Raymo et al.,
1997]. Nevertheless,a gradualglobal cooling continuing
throughthe last million years wouldbe a viable candidatefor
the cause of the middle
Pleistocene
transition.
Previousworkershave also suggestedthat a changefrom a
land-basedto a marine-basedice sheetthroughlong-term glacial erosionwas responsiblefor the middle Pleistocenetransition [Pisiasand Moore, 1981; Berger and Jansen,1994]. Deep
erosionbeneaththe large Laurentideice sheet,causingit to become a marine-basedice sheet [Pisias and Moore, 1981], however, doesnot appearto be a viable hypothesis[Sugden, 1976;
Bell and Laine, 1985; Dyke et al., 1989]. A transitionto a marine-basedcondition may have occurredbeneath the Barents
Seaice sheet[Bergerand Jansen,1994],but the timing of such
Copyright1998by theAmericanGeophysical
Union.
a transition is not well constrained [Hjelstuen et al., 1996;
Solheim et al., 1996], and the small size of the Barents Sea ice
Papernumber97PA02660.
sheetcouldnotaccount
for thespectral
changeseenin the /5•O
0883-8305/98/97PA-02660512.00
record(Figure 1).
2
CLARK AND PO•:
ORIGIN OF THE MIDDLE PLEISTOCENE TRANSITION
Geologicrecordssuggestthat the Laurentideice sheetwas at
timesas or moreextensivein the late Plioceneandearly Pleistocenethanit wasin the late Pleistocene. Severaltills depos-
415
ited by the Laurentideice sheetin Iowa and Nebraska,or south
of theicemarginduringthelastglacialmaximum
(-21 ka), are
overlain by the HuckleberryRidge Ash [Boellstorff, 1973,
1978], which was derivedfrom the eruptionof the Yellowstone
395
caldera at 1.97 Ma [Sarna-Wojcicki and Davis, 1991].
375
larly,a õ•80record
fromtheGulfof Mexicosuggests
thatthe
5
3
(Ma)
i
,
ß
| , ][
ß
2
2
southernmargin of the Laurentideice sheetrepeatedlyentered
the Mississippi River drainageafter -2.3 Ma and discharged
light õ•80 meltwaters
to the Gulfof Mexico [Joyceet al.,
blSite849
5
o
Simi-
1
0
(Ma)
Figure1. (a) Summerhalf-yearinsolation
(in W m'2)at 55øNforthelast
3 Myr computedusingorbitalelementsfrom Berger and Loutre[ 1991].
(b) Oxygen isotoperecordsfor Ocean Drilling ProgramSites677 and
849 over the last 3 Myr (data and age modelsare from Mix et al.
[1995]).
1993].
Because
theglobalõ•80recordsuggests
that latePlioceneearly Pleistocene ice sheetswere volumetrically betweenone
half to two thirdsas largeas late Pleistoceneice sheets(Figure
1), the existenceof a Laurenfideice sheet duringthe late Plioceneand early Pleistocenethat was as extensive as duringthe
late Pleistocene must reflect a change from a thinner to a
thicker ice sheet. Ice sheetthicknessis controlledprimarily
by mechanismsat the base of the ice sheet which control ice
movement. Ice sheetswhich move entirely by internal deformation of ice will generally be thicker than ice sheetswhich
move by some combination of internal ice deformation, basal
sliding, and subglacial sediment deformation (soft beds)
[Paterson, 1994]. A change from a thinner to a thicker ice
sheetduringthe middlePleistocene
thusimplicatesa changein
the basal boundaryconditionwhich governsice thickness.
Severalcharacteristiclandformand sedimentassemblages
We describegeologic data and modeling results which suggest that a change in the basal boundary condition of the
Laurentideice sheetwas responsiblefor the middle Pleistocene
transition. In particular, our hypothesisinvokes only internal
ice sheetmechanismswith no prescribedexternaltrendsexcept
for Milankovitch orbital forcing. Our proposedmechanism
accountsfor the otherwise perplexing evidencethat the late
Pliocene-earlyPleistoceneLaurentideice sheet was as extensive as but volumetrically significantly smaller (Figure 1) than
the later, similarly extensivebut volumetrically larger Laurentide ice sheet. Furthermore,modelingresultsidentify how this
changein ice sheetsize, in turn, resultedin a differentresponse
of the ice sheetto the same orbital forcing, giving rise to the
middle Pleistocenespectralchange.
2. Geologic Records for Change
in Basal Boundary Condition
suggestthat soft bedsunderlaida a significant fraction (of the
orderof 50%) of formernorthernhemisphereice sheetsduring
the last glacial maximum [Alley, 1991; Hicock and Dreimanis,
1992; Clark and Walder, 1994; Clark, 1997]. In the areascov-
ered by the Laurentideice sheet, easily deformablefinely
grainedtill nearly completelymantlesareasof sedimentary
bedrock, so exposedbedrockis largely absent. In contrast,
hard-bedded
areas, which are characterizedby discontinuous,
coarselygrainedtill with a large fraction of exposedbedrock,
are typical of crystalline bedrockareasunderlyingthe Laurentide ice sheet such as the Canadian shield [Marshall et al.,
1996]. A numerical reconstruction of the Laurentide ice sheet
with this prescribeddistributionof hard and soft beds[Clark et
al., 1996] agrees with the ICE-4G reconstruction [Peltier,
1994]bothin surfacetopography
andice volume. This agreement suggeststhat the distribution of soft beds provides a
glaciological explanation for the shape and volume of the
Laurentideice sheet during the last glacial maximumthat is
The Laurentideand Fennoscandian
ice sheetsboth developed most consistent with observations of relative sea level and
at 2.6-2.8 Ma [Raymo, 1994; Clemens et al., 1996], but the
other geodynamicconsiderations[Clark et al., 1996].
Fennoscandian ice sheet has remained much smaller than the
We arguethat prior to the middle Pleistocene transition the
Laurentide. (We note that our proposed mechanismfor the Laurentide ice sheet was thinner because it was underlain evemiddlePleistocenetransition may equally well apply to the rywhere by a soft, easily deformablesubstrateand that the
Fennoscandianice sheet). The East Antarctic Ice Sheet has retransitionto a thick ice sheet'duringthe middlePleistoceneremained stable since the middle Miocene [Marchant et al.,
sultedfrom a changeto an ice sheetwith an increasing
distribu-
1996], with orbital-scale changesin the ice sheet being
"paced"by global sea level changesdriven from the northern
hemisphere[Denton et al., 1986]. We thus assumethat the
tion of hardbeds. Geologicdataand modelingresultsdiscussed
below suggestthat the changefrom all soil-beddedto a mixed-
beddedice sheetoccurredas thick, clayey soils (regoliths),
Laurentide
icesheethasdominated
the globalõ•O signaldur- which had developedby chemicalweatheringof crystalline
ing the last -2.8 Myr.
bedrock,were progressively
erodedby successive
glaciations,
CLARK AND PO•:
ORIGIN OF THE MIDDLE PLEISTOCENETRANSITION
3
Table 1. Heavy Mineral Percentagesin Tills from Nebraska
Till Unit
Hornblende
Biotite
Apatite
"A" tills
30.7
4.3
0.8
"B" tills
"C" tills
21.1
8.6
3.3
1.6
0.7
0.1
Limonite
6.'4
14.3
31.4
Hematite
' 2.5
3.5
6.8
Opaques
21.8
35.9
61.3
Data from tills exposedat City Wide Rock Quarry section,Nebraska[Boellstorff,1973, 1978; Gravenor, 1975].
The "C" tills are overlainby volcanicashfrom the Yellowstonecalderadatedat 1.97 Ma, the "B" tills overlaya Yellowstoneashdatedat 1.27 Ma, anda Yellowstoneash datedat 0.62 Ma is interbeddedwith the "A" tills [Boellstorf-f,
1973, 1978; Sarna-Wojcickiand Davis, 1991].
eventually exposing crystalline bedrockto the ice sheet as a
hard bed.
The developmentof sucha regolith is expectedgiven the
long time (of the orderof 107-108years)that the crystalline
bedrockwas exposedto weatheringprior to the inception of
northernhemisphereglaciation. Direct evidencefor this regolith comes from glaciated central and westernMinnesota,
where a deep saprolite developedin Precambriancrystalline
bedrockis preserved[Goldich, 1938; Parham, 1970; Setterholm and Morey, 1995]. Stratigraphicrelations suggestthat
the saprolite formed during the Mesozoic and possibly the
early Tertiary, when global climate was significantly warmer
thanpresent[Crowleyand North, 1991]. The weatheringprofile averages30 m in thickness,but locally is as thick as 60 m
[Parham, 1970; Setterholm and Morey, 1995].
Similar,
thoughless extensive, pre-Quaternarysaprolites preservedon
glaciated crystalline bedrock also occur in eastern Canada
[Wang et al., 1981, 1982; McKeagueet al., 1983], and welldevelopedsaprolites are common in the Appalachian Mountains southof the glacial border [Mills and Delcourt, 1991].
Chemical weatheringinvolvesthe removal of the more reactive mineral species,resultingin a composition that reflects
the more resistantmineralsas well as the productsof chemical
weathering of the more reactive species. During chemical
weathering, amphiboles alter first, followed by biotite, then
the feldspars,and lastly quartz [Goldich, 1938; Setterholmand
Morey, 1995]. Plagioclasefeldsparsare more reactive than Kfeldspar, and quartz persists in all but the most intensely
weatheredsaprolite. Dissolutionof hornblendeand biotite releases ferrous iron, which migrates upwardto a level where
oxidizing conditions fix it as either goethite or hematite.
Chemicalweatheringalso involvesthe dissolutionof feldspars
and the concurrent removal of Ca, Na, and K.
Al is concen-
tratedin the remaining residueand is thus available to form
kaolinite.
These relations suggestthat erosion and transport of a regolith will yield mineralogies that differ from those of the
sourcerocksbut resemblethosefound in the weatheringprofile
mantling the source rocks. Sedimentsderivedfrom fresh bedrock by glacial and fluvial abrasion which have undergone
minimal chemical weathering have essentially the same bulk
mineralogy as the bedrock source[Nesbitt and Young, 1996].
In contrast,the mineralogy of sedimentsderivedfrom a heavily weatheredcrystalline bedrock reflect the composition of
the regolith, not the bedrock [Nesbittet al., 1996].
Existing geologic data are consistent in identifying a
change in sediment sourcefrom a regolith to fresh bedrock
around the time of the middle Pleistocene
transition.
The old-
est (unweathered)tills in the glaciated midcontinent (>2 Ma)
are relatively enrichedin stable mineralsand weatheredproducts (iron oxides) and depleted in unstable minerals
(hornblende, biotite, and apatite) comparedto younger tills
(Table 1) [Boellstorff, 1978]. The oldest tills also contain allochthonous fragments of bauxite (a product of prolonged
chemical weathering under tropical to subtropical climates)
[Gravenor, 1975]. Finally, the older tills are enriched in sedimentary rock clasts (-90%) whereasthe youngertills are enriched in crystalline lithologies [Boellstorff, 1978], which
may reflect the changein sourcefrom erosionof highly weathered to fresh crystallinebedrock.
Additional mineralogical evidence for a change in basal
boundaryconditionsduring the middle Pleistocenecomesfrom
sedimentsdrilled by OceanDrilling Program(ODP) site 645 in
Baffin Bay (-7 IøN), which recorda directinfluencefrom the ad-
jacentLaurentideand Greenlandice sheetsbeginningwith the
first ice rafting of pebbles in the Pliocene [Thiebault et al.,
1989]. In particular, there is a significant changein mineralogy at -0.95 Ma; sedimentsolder than 0.95 Ma are characterized by clay minerals originating from weatheredcontinental
deposits (irregular mixed layer clays and "smectite"), whereas
sedimentsyoungerthan 0.95Ma show an increasein clay minerals derived from crystalline bedrock (chlorite and illire)
[Thiebault et al., 1989; Andrews, 1993]. Coincident with this
transition is a significant increase in feldspar [Andrews,
1993], which is consistent with a sourcechange from a regolith, in which feldsparshave weathered,to crystalline bedrock.
3. Modeling the Transition
We testedour hypothesisusing a one-dimensionalice sheet
and bedrock model, in which ice thickness and bedrock eleva-
tion are predictedas functionsof latitudeand time, representing a roughly north-southprofile along a typical flow line
throughthe Laurentideice sheet. Such models have been used
extensively to model long-term ice sheet cycles [Oerlemans,
1980; Pollard, 1983; Birchfield and Grumbine, 1985; DeBlondeand Peltier, 1991]. Ice flow is described
by a vertically
integratedcontinuityequationfor ice thickness,assumingthe
ice sheetdeformsmainly by shearat or near its base underits
own weight:
• =-• Ah•
c•h
i c•
[ c•(
hi+•hs+hh)l•cg(h
i+hs+h/•)]
o3c
[us
(0)hi]+B-C
(•)
4
CLARK AND POLLARD: ORIGIN OF THE MIDDLE PLEISTOCENE TRANSITION
Table 2. Symbols Used in the Model
Symbol
Meaning
Value
Units
x
t
north-southdistance
time
independentvariable
independentvariable
m
yr
hi (x,t)
h• (x,t)
hb(x,t)
ice sheetthickness
sediment
layerthickness
bedrockelevationabovesealevel
sea
level
prescribedversusx (seetext)
m
m
m
h•q
equilibriumbedrockelevationabove
prognostic
variable
prognostic
variable
prognostic
variable
B
C
A
massbalanceon ice surface
removalof iceby calving
icerheologycoefficient
prescribed
pattern(seetext)
20 if "floating"
(seetext)
5.77x 104
m yr4
m yr4
m-3yr'•
ot
ice rheologyexponent
5
]J
icerheology
exponent
2
x
timescaleof bedrockrelaxation
5000
yr
Pi
p•
pb
icedensity
sediment
density
(saturated
bulk)
bedrock
density
910
2390
3370
kgm'3
kgm'3
kg m-3
u
sediment
horizontal
velocity
diagnostic
versus
z (seetext)
m yr4
z
vertical coordinatein sedimentlayer
D•o
a
independentvariable
shearstressat ice-sedimentinterface
Pa
degrees
d(sediment
shearstrength)/dz
prescribed
(seetext)
sedimentangleof internalfriction
22
n
sediment
rheology
exponent
sediment
reference
viscosity
wherex is north-south distance, h,(x,t) is the ice thickness,
h,(x,t) is the sedimentthickness,h•,(x,t) is the bedrockeleva-
tionabovesealevel,A = 5.77 x 104m-3yr-•, at= 5, and• = 2
(Table 2). The first term on the right-hand side representsinternal ice shearand/or basal sliding at the ice-bed interface, as
in the earlier models. The secondterm, involving u.dO
), is due
to horizontal shear within the sedimentlayer below the ice, as
B is the net annual mass balance on the ice
surface,representingthe climatic distributionof precipitation
and ice melt, and is prescribedas a function of latitude and ele-
vationthatis shiftedverticallyin proportion
(35 m W4 m'2)to
long-term orbital variations in the summerhalf-year insolation at 55øN [Oerlernans, 1980; Berger and Loutre, 1991] (see
Figure 1).
The last term C represents calving by proglacial lakes
and/or marine incursions[Pollard, 1983]. A large body of water is assumedto form adjacentto the ice sheet whenever the
bedrock falls below sea level at the margin. The term C is set
to 20 m yr'l at anyice sheetgridpoint if its baseis belowsea
level (hs+ h• < 0) and if it or one of its neighboring points has
floatingice [p,h,<-pw(h•.+ h•,)]. The secondcondition protects
the thick interior ice and limits calving, generally, to the outermost 50-150 km of the ice sheet. In practice, the southern
tip is attackedin this way only during deglaciationsand is responsiblefor the model'srealistic simulationof the dominant
100 kyr cyclesduringthe last --1 Myr [Pollard, 1983].
The depressionor reboundof the underlyingbedrockis simply a local relaxationto isostaticequilibrium,laggedby 5000
years[Peltier and Marshall, 1995]:
S'l
diagnostic(seetext)
•
described below.
m
sediment
reference
deformation
rate 7.9x 10'7
b
#o
m
Pam'l
3 x 109(Figure
2a),10• (Figure
2b),3 x 108 Pas
(Figure2c),6 x l09(Figure2d)
1.25(except
3 in Figure
2d)
70øN, ramping linearly down to-500 m at 74"N to represent
the Arctic Ocean (which limits the northern extent of the ice
sheetvia calving).Also,'r = 5000 years,p•,= 3370 kg m'3is
thebedrockdensity,
Pi= 910kg m-3is theicedensity,
andp,.=
2390kg m'3is thesediment
(saturated
bulk)density.
Equations(1) and (2) are standardexceptfor calving and the
extra ice motion due to deforming sediment(secondterm on the
right-hand side of (1)). The latter is modeledby a sediment
layer of thicknessh,.(x,t) resting on bedrock. Deformation
within the sedimentlayer follows Jenson et al. [1995, 1996],
in which the sedimentshearsaccordingto a slightly nonlinear
flow law in responseto horizontal shearstressappliedby the
ice sheetat the top of the sediment. The sedimentis assumed
to be saturatedwith liquid water, which transmitsthe weight of
the ice through the upper sedimentto the uncleforminglayers
below, so that the effective confining pressurein the shear
zone is small and dueonly to the buoyant weight of the sediment itself. By solving their equation (2) the resulting horizontal velocity profile within the sediment is
Us(Z
) =
2D0 a
a
(n+l) b 2Do/•o
1 b
a
wherez is the vertical coordinate increasing downwardfrom
zeroattheice-sediment
interface,
a = p,gh,
I c)(hi
+hs+ h•)/ • I
is the shear stressat the ice-sedimentinterface, and b = (p,. -
pw)gtan(•)is the rate of increaseof shearstrengthwith depth.
The u,(z) is taken to be zero at and below the bottom of the
(2)
shearzone at z = a/b or at the bottom of the sedimentlayer itself at z = h, if hs< a/b. The shear-zonethicknessa/b depends
on the ice sheetslopeand thicknessbut is typically 1-10 m in
eq
whereh•, is the ice-freeequilibrium
bedrockelevationabove our model. We useJensonet al. 's [ 1995, 1996] nominfilvalues
sea level, taken to be 500 m above sea level southward of
for the sedimentrheology, • = 22" for the angle of internal
c)h
b 1 hb - hb-
CLARK AND POLLARD: ORIGIN OF THE MIDDLE PLEISTOCENE TRANSITION
5
friction,Do= 7.9 x 10'7s
'l for thereference
deformation
rate,Ix,,
During the first -1 Myr of this run the sedimentlayer is ad= 3 x 109Pas for the reference
viscosity,n = 1.25 for the ex- vectedrapidlytowardthe northernand southernmarginsof the
kg m'3is theliquidwaterdensityandg - 9.80616 m s'2 is the
ice sheet(Plate 1). By -2 Ma mostsedimenthas been removed
polewardof -62 øN but remainsthick underthe southernflanks
gravitational acceleration. Equation (3) assumesthat the ice
sheetbaseis at the melting point, allowing the till to be saturated. This assumptioncan be relaxedby includingice thermodynamicsin the model, but as describedbelow, we find that
this makes very little difference to the results, at least with a
relatively simple treatmentof ice temperatures.
aroundthis time. Thus the southernslopes and total ice volumesare still inhibited by the sediment. It is not until -1.5
Ma, when the marginal sedimenthas been graduallycleared
severaldegreeslatitudefurthersouth(Figure 3 and Plate 1), that
the centralzone of crystallinebedrockis sufficientlywide to
ponent,and sedimentcohesionis neglected. Also, Pw= 1000
All
the runs below
were initialized
with
a uniform
50
m
thick layer of sediment at 3 Ma (h, = 50 m everywhere) as
might be expected from the geologic evidence of preserved
saprolitesmentionedabove. Thereafterthe sedimentthickness
variesaccordingto
•hx
• [lmin(h•,a/h)
]
& = &
0
u.,,(z)&
(4)
The conditionhs< 100 m is imposedfor areasthat are ice free
(hi = 0) and representsrapid erosion of excesssedimentin an
ice-free
environment.
Without
some removal
of sediment
dur-
ing ice-free periodsthe sedimentin our model accumulatesunrealisticallyto valuesof-500 m aroundand underthe southern
margins by the late Pleistocene, which, in reality, must have
been avoidedby relatively rapid erosion,probablyby river and
eolian transport. The imposedcondition includesthis process
as simply as possible with a minimum of free parameters;the
value of 100 m is basedroughly on the maximum thicknesses
of observed Pleistocene tills [Mickelson et al., 1983' Klassen,
1989]. The resultsshown below are quite insensitive to this
value, at least in the range 50-100 m, and also change little
when this condition is replaced by horizontal diffusion of
of the ice sheet, whose maximum stands extend to -54"N
supportice volumes close to maximum Pleistocenevalues. Af-
ter 1.5 Ma the central bedrockdepressionsare deepenough
(Figure3)to allow significant calving, andthe first complete
deglaciation
occursat 1.45 Ma, with dominant100 kyr cycles
from thenon as given by Pollard[1983]. Althoughthe longterm erosion of model sedimentand deepeningof maximum
bedrockdepressions
are gradual,the transitionto 100 kyr cyclesis suddenbecause
the onset of the model'scalving events
is highly nonlinearand dependsmainly on whetherthe southern tip dropsbelow sealevel as the ice sheetrecedes. The transition in Figure 2a from relatively thin ice sheetsand-20-40
kyr cycles before 1.5 Ma to thicker ice sheets and dominant
-100 kyr cycles after that time (e.g., Figure 3) is in basic
agreement with the observed middle Pleistocene transition in
long-term•5•80records,wherebythe observed
transitionbeginsat -1.2 Ma andis completeby -0.9 Ma (Figure 1). (It is
still uncertainhow abrupt the transition was [Maasch, 1988;
Ruddimanet al., 1989; Park and Maasch, 1993].)
As discussed
by Jensonet al. [1995, 1996], the most appropriatevaluesfor the sedimentviscosity!to andthe exponent
n in (4) areuncertain. Severaldiversemodelingand experimentalstudieson deformabletills suggestthat It,,might range
from 108to 10• Pas andthatn mightlie between1.25 and-3
sedimentin ice-free areas (not shown).
The horizontal velocity u•.(0)at the ice-sedimentinterface
given by (3) causesadditional ice sheettransportvia the second term in (1), which generally dominates the internal
flow/basalsliding(first term in (1)) unlessthe sedimentis very
thin. Note that any basal sliding at the ice-sedimentinterface
is not included in the sediment model but is considered to con-
tributeto the first term in (1). The systemof equations(1)-(4)
are solved numerically on a 0.5" latitudinal grid with a time
step of 1 year.
•oooo
i•)...........................
4ooo
5000
E
2000
o
!
i
i
i
I
i
i
,
I
!
i
i
I
I
i
i
i
i
i
i
I
i
i
i
o
i
E
O
L
0
5000
2000
'•'
X
0
4. Model
Results
o
o
'
A 3 Myr modelrun with the nominalparametervaluesgiven
above (Table 2) shows ice sheet "volume" (cross-sectionalarea
of ice in the latitude versusheight plane) and extent (distance
from northernto southerntip) (Figure2a). The only external
forcingis the vertical shift of the massbalancepatternB in (1)
due to orbital insolation
variations.
From 3 Ma to -2 Ma the
'
'
'
'
'
i
i
,
,
,
,
,
i
0
i
(•)
0
0
•
I
.*.-
I
5000
2000
o•
o
o
o
o
o
'(d)
o
5000
2o00
ice transportis dominatedby sedimentdeformation,which restricts the basal shear stresses to small values and constrains
the ice sheet to remain relatively thin (-1.5 km) with gentle
slopesnear the margins(Figure 3). This resultsin wide southern ablation zones and preventsthe ice sheetfrom achieving
large volumes; however, the maximum linear extents (dashed
curve)are close to those of the late Pleistocenein agreement
with early observedice limits as mentionedabove.
0
$.0
2.5
2.0
1.5
1.0
0.5
0.0
0
(Uo)
Figure 2. Ice sheetcross-sectional
area (thick lines) and north-south
extent(thinlines)for simulations
over the last3 Myr: (a) with nominal
parameter
values
givenin thetext,including
sediment
viscosity
It,, = 3 x
109Pasandn= 1.25;
(b)withIt,,= 10• Pasandn= 1.25;
(c)withIt,,=
3 x 108Pasandn = 1.25'and(d)withIt,,= 6 x 109Pasandn = 3.
6
CLARK AND POLLARD: ORIGIN OF THE MIDDLE PLEISTOCENETRANSmON
2500
o
• 2,534,000¾rBP
• 78,000 ¾rBP
•
1500
>
75
70
65
60
55
70
65
60
55
latitude (o N)
latitude (o N)
Figure3. Crosssections
of icesheet,sediment
(solid),andbedrock(stippled)
at twodifferenttimesfromtherun in Figure2a.
Althoughthelinearnorth-south
extentsarethesameat thetwotimes,thereis stillsediment
undermuchof theice sheetduring
the earliertime so the ice sheetis relativelythin andthe bedrockdepression
is shallow. In contrast,duringthe later time, there
is no sedimentremainingunderthe ice sheetsotheice sheetis thickerandthebedrockdepression
is deeper.
5.0
2.5
2.0
1.5
1.0
0.0
0.5
(Ma)
ß01
.1
1
25
50
50
75
100
125
Plate 1. Changesin sedimentlayer thicknesses
(h.,) (in meters)from the nominalrun (Figure 2a). Blank areas indicate
negligiblesediment(h.,.< .01 m), and the "50-50"contourintervalshowsthe initial50 m thickness
value. The dashedlines
showthe latitudesof the ice sheet'snorthernand southerntips.
50
CLARK AND POLLARD: ORIGIN OF THE MIDDLE PLEISTOCENE TRANSITION
[Boultonand Hindmarsh,1987; Alley, 1989; Paterson,1994;
Velaet al., 1996],althoughmuchhighervaluesof n havebeen
suggested[Kamb, 1991]. We examined the effects of different
7
is uncertain.
Nevertheless,
several
of theseothermodels
rely
onthesamebasicbehavior
ashere:thatat roughly100kyr in-
tervalsthe ice sheetmustbecomevery largeandthick with a
sediment
viscosities,
withn fixedat 1.25. With muchlarger deepbedrock
depression,
andthussusceptible
to complete
and
viscosity(Figure2b), sedimentdeformationand the associated rapid deglaciationin the next warm-orbitinterval. A deforming sedimentlayerpreventstheseconditions
before~1 Ma and
vertsto the no-sediment
modelof Pollard [ 1983]with thick ice
allows them after it has been eroded,so the sedimentmodel
sheets,
calving,anddominant
~100 kyr cyclesthroughout
the proposedheremight be expectedto producethe samemiddle
run. With muchsmallerviscosity(Figure 2c), basal shear Pleistocenetransitionindependent
of the exactmechanismfor
stresses
at theice-sediment
interface
are verylow andseverely the 100 kyr cycles.
limit the ice sheetvolumes. Also, the sedimentshearzone a?b
ice transport
become
negligible,
andthemodelessentially
re-
is muchthinner,andthe verticallyintegrated
sedimenttransport in (4) is smaller[Jensonet al., 1995], so the initial 50 m
sediment
layertakeslongerto be clearedaway. Thusice volumesremainsmallovertheentirerun (Figure2c), andthe 100
kyr transitiondoesnot occuruntil -0.2 Ma. Althoughwe
mightclaimfromtheseresults(Figures2a-2c)that3 x 10• Pa s
is themostrealistic
valueof sediment
viscosity,thisis really
onlyan order-of-magnitude
constraint
sincethetimingof the
transitionalsodepends
on oursomewhat
arbitrarychoicesof
initial sediment
thickness
(50 m)andstartdate(3 Ma). By
varyingthoseparameters
wecouldprobablyadjustthetiming
of thetransition
in the currentmodelto agreemoreclosely
with the observed
transitionat-0.9 Ma (Figure1); however.
wefeelthatsortof fine tuningwill be moremeaningful
at a
laterstageaftersomeof the modeldevelopments
mentioned
below.At thatstage,objective
statistical
testswill probably
be needed
to compare
the modelandobserved
curves,
espe-
Anotherassumption
is thatthesediment
is alwayssaturated
withjustenough
liquidwatertotransmit
theverticalweightof
theice sheet.Thisrequires
theice sheetbaseto be at the melting point; otherwise,the till is frozen, andno sedimentdefor-
mation
canoccur.We havetested
thisassumption
by predictingicetemperatures
in themodel,usinga standard
equation
of
verticalheattransferinvolvingconduction
andverticaladvection, with lowerboundaryconditionfrombasalfrictionalheat-
ing andthe geothermal
heatflux, upperboundary
condition
fromspecified
annualmeansurface
ice temperatures,
andneglecting horizontal heat advection and thermal inertia
[Paterson,
1981]. Theannualsurface
ice temperature
is estimatedconsistently
withthemass-balance
parameterization
for
B in (1) [Oerlemans,
1980]by assuming
thatairtemperatures
at theequilibrium-line
altitudehaveanannualmeanof -10øC,a
seasonal
amplitude
of 25øC,andanatmospheric
lapserateof
-7øCkm'•. Thisequation
hasananalyticsolution[Paterson,
1981]thatgivesthesteady
statebasaltemperature
at eachgrid
cially sincethe exacttimingof the transitionis somewhatsubpointandtimestepin themodel.Whenever
thebasaltempera-
jectiveandhasbeenquotedasearlyas 1.2 Ma [Clemens
et al.,
19961.
Making the sedimentrheologymore nonlinearhas relativelylittleeffecton theresults(Figure2d). The valueof n we
tureis belowthepressure
meltingpoint,sedimentdeformation
from(3) andits associated
ice transportis resetto zero. The
resulting ice volume curves and sediment thickness distribu-
tionsfor the nominalmodelarevirtuallythe sameas our reused(= 3) is atthehighendof therangesuggested
by a number sults(Figure
2aandPlate1). Although
thebaseis usually
froof studies[BoultonandHindmarsh,1987; Alley, 1989; Paterzenin the centralregionswhenthe ice sheetis large,basal
son,1994; Velaet al., 1996]. If n wereincreased
by 1 or 2 ordersof magnitude
[Kamb,1991], onewouldexpectmoredra-
temperatures
nearerthe flanksareoften at the melting point
wheremostsedimenttransportoccurs,so sedimentthicknesses
maticeffectssincethe sedimentwouldbecomeessentially andicevolumes
evolveovertimein essentially
thesameway
asbefore.Theneglectof horizontalheatadvection
maybe
significantnearthe ice sheetflanks, andwe plan to include
1991]. However,suchlargevaluesof n arebeyondthe numerithatin futurework[Ritzet al., 1997]andto investigate
possical designof our model.
ble freeze-thaw
cyclesat the bed[MacAyeal,1992, 1993] and
plastic,andthe wholedeformingbedmechanism
couldbecome
unstableif feedbackfrom basalmeltingis considered
[Kamb,
5. Discussion
The modeldescribed
hereis obviouslyvery simplecomparedto realityandcontains
a numberof importantassumptions.We regard
it solelyasa firstquantitative
testof thehypothesisthat deformable
bedsare importantfor the middle
Pleistocene
transition. Oneassumption
is that the calving
mechanism
is important
for the 100 kyr cycles.Clearly,any
modeladdressing
the middlePleistocenetransition(with no
100kyr cyclesbeforeanddominantcyclesafterward)
mustbe
capableof simulatingthemat all. In our modela calving
mechanismis necessaryto augment the basic bedrockdepression/lapse-rate
feedbackto producethesecycles,but
other modelshave suggested
other mechanisms[Oerlemans,
1984; DeBlondeand Peltier, 1991; Saltzmanand Maasch,
1991; Galleeet al., 1992; Peltier and Marshall, 1995; DeBlondeet al., 1996; Abe-Ouchi,1996; MudelseeandSchulz,
1997],andtheirrelativeimportance
forthereal100kyr cycles
othervariationsin basalhydrology[Kamb, 1991; Fowlerand
Johnson, 1995].
However, the first-order inclusion of ice
temperaturesto date showsthat basal temperatures
near the
Laurentide
flankswereat themelting
pointoftenenough
to allow thesediment
transport
mechanism
proposed
hereto remain
viable. Otherpossiblefuturemodeldevelopments
area more
realisticnonlocalmodelfor the lithosphericand asthenosphericresponse[Birchfieldand Grumbine,1985; DeBlonde
and Peltier, 1991], the extensionto two horizontal dimensions
andthe useof two-dimensional(2-D) or 3-D climate models
[PeltierandMarshall,1995;DeBlondeet al., 1996], moreex,
plicit modelsof calvingwaterbodiesanddischarging
ice
shelves[Pollard,1983; van der Veen,1996],refinementof the
sediment
removalprocess
in (4b), andremoulding
of the sedimentunderthe ice causinglong-termchangesin sediment
rheology.
AsBirchfieldandGhil [1993] andothershavenoted,there
is relatively
little~23kyrspectral
powerin /5•Orecords
prior
8
CLARK AND POLLARD: ORIGIN OF THE MIDDLE PLEISTOCENE TRANSITION
to the middle Pleistocene transition as comparedto after the
transition. If the early ice sheetsdid extend as far south as in
the late Pleistocene, as suggestedby continental records,one
might expect substantial23 kyr power since variations of orbital precessionat those periodsdominatethe insolation signal more at low latitudes. There may be two reasonswhy this
signal is less before the transition. First, ice volume responds
to changesin accumulationand ablation over the whole ice
sheet, which, in turn, are affected by large-scale changes in
climate and circulationthat may differ for thin versusthick ice
sheets and do not just follow insolation variations at the
southern margin. In our simple model the climate forcing is
tied to insolationvariationsat an arbitrary latitude (55øN), and
global climate modelswill be neededto fully explore this possibility. Second, as suggestedby Birchfield and Ghil [1993],
there may simply be more downcoreloss of signal at shorter
periods(-23 kyr comparedto -41 kyr) becauseof postdepositional diffusive processessuch as bioturbation.
In conclusion, we have used a simple numerical model to
test the hypothesis that a change from soft-beddedto hard-
beddedconditionsdueto glacial erosionof an initially thick
and uniform regolith and progressiveexposureof unweathered
crystallinebedrockcausedthe middle Pleistocene transition in
õ•80records.Thisfirst quantitative
testshowsthatwithreasonablevaluesof sedimentrheology the northernhemisphere
ice sheetscouldhave erodedseveraltens of metersof regolith
within the right time frameof 1-2 Myr. Before the transition
the model's deforming sedimentmaintains relatively thin,
low-volumeice sheetsthat nevertheless,extendnearly as far
southas the later ice sheets,in agreementwith severallines of
evidencediscussed
above. The exposureof uncleforming
bedrock below the regolith allows ice sheetthicknessesand bedrock depressionsto becomelarge enoughto allow marineincursionsandcalving that areresponsibletbr completemodel
deglaciations and the introduction of the dominant nonlinear
-100 kyr responsein the middlePleistocene.
Acknowledgments.We thankJ. Jenson,A. Mix, C. Patterson,and N.
Pisiasfor helpfuldiscussions
and M. Delaney,C. Forsberg,and two
anonymous
reviewersfor comments
onthemanuscript.Thismanuscript
wassupported
by the NationalScienceFoundation
(ATM-9709684).
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