sheets with a two-level ntass-balance paranteterization

Annals DJ Glaciology 2 1 1995
© In ternational G laciological Society
Therll1.oll1.echanical ll1.odelling of Northern Hell1.isphere ice
sheets with a two-level ntass-balance paranteterization
PHILlPPE H G YBR ECHTS
Aljred-I Vegener-lnslitlll fiir Po/ar- und Nleel"esjorschllllg . Postfac/i 120161, D-27515 Brelllerhaven . Gerl1Za /~)' .
and
GeograJisch inslilulIl, VriJe Universiteil Brussef, Pleinlaan 2. B-1050 Brt/ssel, BelgiulI1
STEPHE:\ T'SIOBBEL
Geogrc!fisc/Z instiluut , Vrije Uni versiteil BTllssel, Pleill!aall 2. B-1050 Brussel, Belglllll1
ABSTRACT. A three-dimensiona l time-dependent th ermomechanical ice-sheet
model was used together with a two-l evel (snow-accumulation/runoff) mass- bala nce
model to investigate the Quaternary ice sheets of th e Northern H emisphere. The
model fre ely generates the ice-sheet geometry in rcs ponse to spec ifi ed cha nges in
surface temperature a nd mass bala ncc, a nd incl udes bedrock adjustment, basa l sliding
and a full te mpera ture calcul a ti on within the ice. The mass-balance para meteri 7.at ion
m akes a d istincti on between snowfall a nd melting. Yearl y sno,\"fa ll ra tes d epend o n the
present precipitation distribution, and a re vari ed proportionall y to cha nges in surface
temperature a nd the moisture content of the air. The a bla ti on model is based on the
positi" e-degree-day method, a nd distinguishes betll'een ice a nd snoll' meltin g. T hi s
paper disc usses stead y-state cha racteristi cs, conditio ns fo r g rowth and retreat, a nd
response time-scales of ice sheets as a function of a prescribed lowering of summer
tempera ture. Most notably, the modell ed ex tents of the Eurasia n ice sheet for a
summer temperature lowering of6- 7 K a nd of the La urentide ice sheet for a cooling of
9- 10 K are in reasona ble agreement \Vi th mos t reconstructions based on geological
e"idence, except [or the prese nce of a la rge ice sheet stretching from Alas ka across the
Bering Strait to most of eas tern Siberia. In add ition. wct basal conditions turned out to
be always confined to the margin , whereas centra l areas in these reconstructi o ns
remained a lways cold-based. This is of rele, "a nce fo r processes il1\'o h-in g reduced basal
traction.
1. INTRODUCTION cannot be direc tly inferred from the geological record. but
has to be es ti ma ted from models.
During th e Quaternary, the waxing a nd waning of ice
sheets on the continents o[ the Northern H em isphere
constitute a major driving force for global change a nd a re
the main so urce of global sea-level flu ctua ti o ns. It is
genera ll y accepted that the m aximum sea -l evel depressio
n during th e last glacial cycle was a ro und 125 m ,
la rgely originating from ice-sheet build-up in North
Ameri ca a nd Eurasia. This corres ponds to a n additiona l
So fa r , m os t ice-shee t mod elling studies, threedimensio
na l a nd two-dim ensio na l (horizontal plane)
ha, "e considered only a part of the Northern H emisphere
ice-sheet sys tem (e.g. Budd a nd Smith. 1987; Letreguill y
and R itz, 1993 ) or ha\"C concentrated on th e ice sheets as
a lower-bound a ry condition [or cl im ate models (D e­
blonde a nd Pcltier, 199 1; :'larsia t. 1992; Verbitsky and
O glesby, 1992 ). None of these mod els included thermod
global ice volume of a ro und 50 x 101 5m 3 (Fairbanks,
1989; Tushing ham and Peltier, 199 1). Whereas the
m aximum ice-sheet ex tent along the southern margins
of th e L a urentide and Fennoscandia n ice sheets seems to
be reasonably well documemed (e.g. D em on a nd Hug hes,
198 1), the distribu tion of ice sheets along the Russ ian sid e
ynamics. ~ e , "e rthel ess , ice temperature exerts a strong
of the Arctic O cean is till largely unresolved . H ere,
geological reconstructions ra nge from limited ice ex pa n­
sion over Scandinavia and Svalbard in the west (Boulto n,
1979) to a n unbroken Eurasian ice sheet ex tending all the
way from Britain to Scandinavia across the Ba rents a nd
K a ra Seas to most of eastern Siberia (Grosswald , 1980).
The thickness of these ice sheets, on th e other ha nd,
control on the ice ,·iscosit,· a nd subsequently on the
heigh t/ lV id th ra ti o. i\.lo reover, tem pera te ice a nd mel ti ng
a t the base a re necessary preconditions [or basal sed iment
d efo rmation a nd enhanced basal slidi ng. whi ch are often
menti onecl as mechanisms tha t potentiall y ca n cl es tabili ze
large com inental ice sheets by making them much fl a tter
towards the end o[ a glacial cycle (Boul to n and J ones,
1979; O erl ema ns. 1982 ) .
Here, \Ve present res ults obta ined \\"ith a threedimensiona
l th ermo mecha ni cal ice-sheet mod el which
cOl'ers all of the Northern H emisphere \\'here wid espread
continenta l glacia tio n is known to have taken place. T his
11 J

f-fuybm;!zls and T'siobbel : M odelling of Northern HemisjJ/zere ice sheets
mod el is time-dependent, includes geod yna mi cs and
freely genera tes th e ice-shee t geometry in res ponse to
cha nges in environmenta l conditions. The mod el has been
ex tensively tes ted and valid a ted on th e present-d ay ice
sheets of Greenla nd a nd Antarcti ca (Huybrechts, 1990;
H uybrec h t and others, 199 1). The methods adopted to
es tima te th e mass-bala nce components a re simil ar to
those tha t proved their a pplicability on these ice sheets.
Though the prescription of clima ti c bounda ry conditions
is likely to be more complex a t mid-la titudes th a n in th e
pola r regions, this is seen as part of an inve rse modelling
exercise, in whi ch an a ttempt is made to inves ti gate th e
clima ti c conditions tha t produced these ice sheets in th e
first place. This pa per aims to doc ument so me basic
characteristi cs of th e Northern H emisphere ice sheets (ice
volume, ice-shee t geometry, res ponse time-scales and basal
tempera ture co nditions) as a fun c ti on of an imposed
tempera ture 100\·ering. Of special interes t a re th e various
thres holds required to grow and decay the individual ice
shee ts that com posed the Qua terna ry glacial sys tem .
Time-d ependent simula ti ons in voking glacial cyc les will ,
however, be presented elsewh ere (pa per in prepara ti on by
P. Huybrechts and S. T'siobbel).
2. MODEL SET-UP
The ice-shee t model closely resembles th e \'e rSlO n
desc ribed by Huybrechts ( 1993 ). It basica ll y solves
conse rva tion equations for mass a nd heat and has a full
coupling between th e fl ow a nd tempera ture fi elds. Only
grounded ice fl ow is taken into account, with a Glen-type
fl ow la w a nd a tempera ture-depend ent ra te factor give n
by a n Arrhenius rela ti onship. Longitudina l d evi a toric
stresses a re disregard ed and basal sliding (of VV ecrtma n
type) is res tricted to a reas a t tb e press ure-melting point.
In th e present formula ti on, the poss ibility of ice shelves
a nd grounding-line d yna mi cs was excluded a nd the
maximum poss ible extent of grounded ice was constrained
by specifyin g a coastline fo ll owing th e - 500 m
isoba th. This a pprox im a tely coincid es with th e ma rgin of
the continenta l pla tform in th e Arcti c basin, over whi ch
ice shee ts can freely expa nd provid ed the surface mass
bala nce is sufTi cien tI y p os i ti ve. Beyond th is pre-se t
boundary, a ll ice is los t as calf ice.
The th erm od yna mi c calcula ti ons employ standard
procedures. Heat transfer is consid ered to res ult from
verti ca l diffusion, th ree-di mensiona l ad vecti o n and
deform a ti ona l hea ti ng a t la yeI' interfaces. In the timedep
endent mode, heat can also fl ow in to an underl ying
roc k sla b 0 1' 2 km thickn ess. The lower-bo unda r y
condition on tempera ture corres ponds to a geothermal
heat flu x of 42mW m 2 . Bedrock adjustments are
mod ell ed as a d a mped return with a stead y-sta te
del1ec ti on given by local isos ta ti c equi li brium. The e­
foldin g time scale is se t a t 3000 years, with a mantle
densi ty which is 3.6 times th a t of ice. All calcul a ti ons ta ke
place on the same grid. It comprises 193 x 193 grid cells
tha t a re laid out over a pola r stereogra phic ma p
projection with sta ndard pa rallel a t 60° N . With this
standard pa ra ll el, distortions in distance range from a
factor of 0.92 a t 45° N to a factor of 1.07 a t the pole, th e
effec t of which has been ta ken into account to calcula te
the ice [luxes and the ice volume. The horizon tal mesh size
is 50 km , and there a re 11 layers in the vertical , conce
n tra ted towards the base. This resolu ti on is the
minimum required to in corpora te realisti c geogra phy
a nd to capture th e esse n ti al characteristi cs of th e vertical
velocity a nd tempera ture profiles.
The mass-bala nce model distinguishes between snow
accumula tion and abla ti on and is driven by a prescribed
" background" tempera ture change th a t is uniform in
space but 50% hi gher in J a nua ry than inJuly. The la tter
feature is a cha racteristi c common to mos t genera l­
circul a ti on model (GCM) simula tions (e.g. M ana be and
Broccoli , 1985) a nd is also supported by palaeoclima ti c
reconstructions based o n geologica l a nd bi ological
evidence (Frenzel and others, 1992). This feature is
usua ll y a ttributed to the a lbedo-tempera ture effect a nd a
sta ble ve rti cal stratificati on in th e lower stra tosp here,
whi ch prevents la rge-scale mi xing of the air, especia ll y
during winter. The basic inputs are data se ts for the mean
monthly sea-l evel temperature and th e mean monthly
precipita ti on ra te over the entire grid. These reference
c1im a tologies were ta ken from precipita ti on maps Uaeger,
1976) and from tempera ture d ata used to initia li ze th e
H a mburg GCM model (ECHAM-I in the T 2 1 mode) a t
the 1000 hPa level. Surface tempera tures were calcula ted
using a la pse ra te of 8 K km- I, a va lue so mewh a t higher
tha n the sta ndard la pse ra te for th e free a tmosphere. This
is in I i ne wi th measu remen ts on th e ice sheets of
Antarcti ca and Greenland, a nd can be ex plained by
radia tive cooli ng at th e surface, particularly during the
winter season. The corres ponding surface elevati on was
ta ken as th e maximum of either the mean elevation of a
grid ce ll during the calcula ti ons or th e hi ghes t peak
within this grid cell for th e pre ent topogra phy. This is
because the glaciation thres hold is to a la rge ex tent
determined by the mos t el e\'ated terrain , a piece of
info rmation tha t is otherwise lost when valu es a re
averaged on th e 50km grid.
The model consid ers only changes of' precipita ti on
intensity but keeps th e precipita ti on pa ttern uncha nged.
The tota l precipita ti on is se t proportiona l to the moistureholding
capacity of an air column, and has a sensitivity of
4% K- 1 • This seems to be a reasonable ass umption a t
pola r la titudes, supported by ana lyses of Anta rcti c a nd
Greenland ice cores (Vi ou and others, 1985; Cla usen and
others, 1988), but its validity during maximum glacia tion
a t mid-Ia ti tudes can be ques tioned . H ere, preci pi tation is
likely to be increasingly a fun ction 0[' such factors as
a tmospheric circul a tion, continen tali ty a nd orography. A
more sophisti cated a pproach, however, is deemed fa r
beyond the purpose of the present stud y. The fracti on of
prec ipita tion fa lling as snow is determined by the surface
temperature, a nd varies from one to zero for mean
mon thly tempera tures in the range of 263- 280 K. Such a
rela ti on is suggested from meteorological observa tions in
Ca nad a a nd Russia . Ice a nd snow abla tion, on the other
ha nd, a re d ealt with locall y. Following a procedure
previously adopted for the Greenl and ice sheet (R eeh ,
1989; Huybrechts and others, 1991 ), the melting ra te is
set proportional to the yearly sum of positive degree d ays
(PDD). Degree-d ay fa ctors were 3 mm a 1 jPDD for snow,
and 8 mm a 1 jPDD for ice. The mass-ba lance pa rameterization
furth ermore incorpora tes th e process of super-
112

Huybrechts and T'siobbel : ,\/odeUing oJ .,"ortliem Hemisphere ice sheets
imposed ice form a ti on, but neglects a p o. sible contribution
from rainfall , which is assumed to run off entirely. In
the model, summer tempera ture was taken as th e relel'ant
fo rcing p a ra m eter. This m ea ns th a t the "effec tive"
abla ti o n tempera ture ro ug hl y equals the applied tempera
ture drop, but that th e effective (i. e. mean a nnua l)
tempera ture for the calcula ti on of the prec ipita ti o n
intensity is 2S% hig her. For the latter calcula tions, a n
additio na l tempera ture cha nge res ulting from elel'a ti on
cha nges was not ta ken into account.
3. RESULTS
3. 1. Ice-sheet geornetries
First of all, th e mod el was run under present clima ti c
conditions with a zero temperature perturbation sta rting
from no ice cover a t a ll. The res ult, a ft er a tota l
integra tion time of 10 5 years, is shown as th e upper left
pa nel in Figure I a. As d emonstra ted in this fi g ure. the
simula tion is quite reali sti c. The Greenl a nd ice sheet is
well reproduced , a nd the sma ll er ice masses turn up in
almost the sam e places as they a re observed today. Thi . is
the case for the Arcti c isla nds (northern Novaya Zemlya,
Svalba rd, Fra nz J osefLa nd a nd Sel'ernaya Zeml ya); but
a lso the location of ice in Scandinavia Uos ted a lsbreen a nd
Svartise n), th e Alps, southeas tern I cela nd (V a tn ajokull ),
Al aska a nd Kamcha tk a is in good agreement with the
present situa tion. Apparently, the mass-ba la nce model is
a bl e to id entify th e correct a reas with a pos itil'e mass
ba la nce. The onl y real d evia ti on from th e present-day
situa tion is fo und over th e Ca nadi a n Arc ti c. Here, th c
model produces a unified ice cap over Ell es mere Isla nd,
Axel H eiberg Isla nd a nd D evon Isla nd of O\U 2000 m
altitude, proba bly because of a n in ad equa te representati
on of the coastline a nd sma ll er-scale fj ords, a ll owing
sm a ll glaciers a nd ice caps to merge into a la rger ice cap.
The present sta te was then taken as a n initia l
cond i ti on for th e e1i ma te sensi ti I·i ty ex peri men ts, a nd
mod el calcul a ti ons ran until a full stead y sta te was
reached. R es ulting geometries for summer tempera ture
lowerings in the range 0 (' - 2 to - 10 K are shown in Fig ure
I a . I t a ppears tha t maj or ice sheets spread from g lacia ti on
centres tha t a re a ll present in proto-form tod ay. In I\o rth
Ameri ca, two sepa ra te ice shee ts build up O\'er th e coasta l
R ocki es and the Canadia n Arcti c Isla nds. A cooling o f
more tha n S Kis required for the latter ice sheet to cross
Hudson Bay a nd cove r th e Ungava Peninsul a a nd
La brad or plateaus, which themselves d o no t a ct as
independent in ception a reas. During this evolution, the
summit of the La urentide ice sheet mig ra tes wes t tOI'\'ards
the Atlantic a nd reaches a maximum elcl'a tion of around
4000 m. A very substa ntial summer cooling of 10 K (in the
mod el this corres ponds to - 12.S K in the a nnua l mean
a nd - IS K in winter) is required for th e Laurentide ice
sheet to merge with the Cordillera n ice sheet, but the
respecti ve ice domes are well conse rved. The mod el has
difficulty growing the La urentide ice sheet far enough to
the south in the ~lidw es t e rn U.S.A. This may \\'e11
indicate tha t the mod el underes tima tes precipita tion ra tes
there and that a reorgani zation of the a tmos pheri c
circul a ti on produced much wetter conditio ns during
m aximum g lacia ti on in continenta l North Ameri ca.
In Eurasia, th e mod el produces the Ba rents a nd K a ra
ice shee ts for a mod era le cooling of a bout 4 K . a t the sa me
time as the Fennoscand ia n ice sheet is still la rgely
confined to the Norwegia n mo unta ins. This supports the
\·ie\\· th a t the Siberi a n ice sheets ori gin a ted in the Arcti c
basin and spread " from th e sea" into th e adjacent
continent (Gross\\'a ld . 1980). tho ug h such a n in fe rence
should be resen 'ed because th e model d oes no t expli citl y
d eal with marine ice-sheet d yna mics . For a summer
tempera ture lowering of 6 7 K , the simula ted Eurasia n
ice shee t is in broad agreemen t wi th mos t geologic a l
reconstructions fo r the Last Glacia l ~l ax imum, th oug h
th ere a re so me regio na l d el·ia ti ons . .\fa ximum elel'a ti ons
a re abo ut 3500 m here.
Proba bk th e larges t d el'ia ti on (i'om \I'ha t is kno\l'n of
th e Qua terna ry glacia l cycles is th e continuous ice sheet
cO \'ering Al aska. th e Bering Stra il a nd northeastern
Siberi a, \I'hi ch ultima tely (for a cooling below 8 K )
merges with th e Eurasia n ice sheet a nd an ice cap north of
the Sea ofOkh o tsk to fo rm a huge circuma rcti c ice mass.
There is no el'id ence to support glacia li on in northern
Al aska a nd th e Bering Stra it, thoug h se\'era l reconstructi
ons imply a t least some ice in coasta l eastern Si beri a a nd
the hi gher pl a teaus further so uth (D enton a nd Hug hes,
198 1: Tushing ha m a nd Pelti er, 199 1). A pl a usib le
expla na ti on for th e disc repa ncy would be cha nges in
precipita ti on pa tterns, not accounted for in o ur massba
la nce pa ra m eteri zati on. Fo r insta nce, the d Cl'e1opmen l
o f a n ice sheet O\'e r so uthern Al aska a nd perma nent sea
ice in the Arcti c O cean may well hm'e d epri\'Cd th e
northern coasta l a reas o f suffi cient moisture.
3.2. Bas al telIlperature conditions
Fig ure I b shows th e stead y-sta te thermal conditio ns a t the
base associa ted with th ese climate sensiti \'it y experiments.
The distribution of a reas a t press ure-melting poinL is
importa nt beca use th e production oC basal water is a
necessary prereq ui site for basal sliding a nd th e possibility
of enha nced ice now due to the d eforma ti on of underl ying
sediments. lnteres ting ly, wet-based a reas in th ese reconstructi
ons a re confin ed to th e ou ter regions, \I'hereas
centra l a reas remain a lways cold-based. Despite lower
accumulation ra tes in cold er clima tes , implying less
adl'ecti on of cold ice to\l'ards the base, a nd centra l ice
thicknesses a bove 34 km , contributing to a basal
wa rming because of th e " insul a ting effect", the simulated
No rthern Hemisphere ice sheels fa il to become temperate
OI'er the large a reas need ed fo r the possibility of some kind
of sliding insta bility. T ypicall y. m ea n a nnual surface
tempera lUres over th e hi gher pa rts of th e ice sheets
simula ted for a cooling of 10 K a re of th e order of 220-
230 K , with correspo nding basal tempera lures d OlI'l1 to
15- 20K below the press ure-melting po int. Consequently,
these simula ti o ns d o no t support ice-dyna mi c th eories
th a t illl'o ke th ermal switches a t th e base.
3.3. Ice volulIle
The corresponding ice I'o lumes a rc summa rized III the
solutio n diagra m sho wn in Fig ure 2 . Two se ts o f m od e l
11 3

HlIybrechts and T'siobbe!: llIodel/il/g qf. \ 'orthem Hemis/Jhere ice sheets
a
..
b
Fig. l.a. Lll odelled stearo'-state ice-sheet geol71etriesjor slimmer tem/Jerature /Jertllrbations below present levels as indicated.
Contours areIor slIIJace eLevaliol1 al/d are spaced 500111 a/Jart. These eX/Jeriments started wiliz a simulalio71 01 the /Hesent
ice-sheet distributiol/ (shown ill the upper left /Jallel) as illitial cOl/figuration. b. Basal tem/Jerature cOllditions con esjJonding
to the simulations shown ill Figure 1. Dark shadillg indicates where the base is at the pressure-melting /Joint, and basal
sliding call O[[lIr; intermediate shading is JOT frozen basal cOlldilions; light shaded areas are ice-jree.
114

Hlqbrechts and T'siobbel : M odelling oJ }/orthem HemisjJ /iere ice sheets
runs a re displ ayed, one in whi ch the present ice-sheet
distribution was used as a n initia l condition (" interglacia
l condirio ns") a nd one in which rhe ice-sheer
confi g ura ti on for 10 K se ryed to sta rt the calcul a ti ons
up ("glacial conditions" ). There a re two so lutions,
d epending on whether the ice sheets were a lread y
present or no t, a behavio ul' well d escribed for ice sheets
where the m ass-ba lance field is a fun cti on of surface
e1 e\'ati o ll (O erl em a ns a nd V a n d e r V een , 1984) .
T y pi call y, th e "width" of th e hys teresis is found to be
a bo ut 2 K. An a dditio na l ice \'olume o f a bo ut
4 .5 x 10 16 m 3 , which is a reasona ble es timate [o r rh e
L as t G lacia l ~1 ax imum contribution of th e N orthern
H emisphere ice sheets, is seen to be p roduced [or a
summer tempera ture lowering o f" 6- 7 K. This value
12
10
et)
E
(l)
E.
2
0
-12 -10 -8 -6 -4 -2 0 2
Temperature perturbation relative to present (K)
12
10
M
E
CD 8
a ,....
Q)
6
E
::>
~ 4
(l)
E.
2
0
0 25
_---,-10K
~ __ --; -9K
__ ------1 -8 K
__ -----------, -7K
__ -----1 -6 K
__-----~-5K
_------~ -4 K
50 75 100 125 150
Time (kvr)
Fig. 3. T ime-scales Jor ice-sheet build-up after the model
was submitted 10 a sudden clwwtic cooling of the
magnitude shown at the right . T he jJresent interglacial
state served as an initial condition.
Another kind of (tenta ti ve) inference can be made
when rela ting the ice-vo lume CLln'es of Figure 2 to the
reconstructi ons shown in Figure 1 b. For insta nce, th e iceshee
t reconstruction (o r a temperature lowering of 6 K
contains roughl y rhe ri ght a mounr o[addiriona l LG~1 ice.
but shows a La urentide ice hee t that spreads fa r less [0
th e so uthwes t th an indicated by the geological record. As
th e ex tent of the Eurasian ice sheet corres ponds better
with mos t reconstructi ons, this mi ght indicate th a t ice
shee ts during rh e Last Gl ac ial .\Iax imum were significantly
thinner th a n rh e mod el simula ri ons suggest.
Fig. 2. Solutioll diagram giving stead),-state ice volume as
a jill1ctioll oJ the temjJe1"{/tme perll/rbatioll . T he J II II
jqllares are Jar model rUlls ill wlzich the jJresent
'" intelg/aria/" ' state was taken as an initial conditioll:
tlte open squares started Jrom the "glacial" ice sheet
simulated Jor a a temperature change of - 10 K. As aJirst
estimate, 10 milliollkm J (i.e.lO/GII/) of ice conesjJonds to
a worldwide sea-/e/'el lowering cif abouL 25 m.
4. CONCLUSION
This pa per d isc ussed Northern H emisphere ice-sheet
simula ti ons obtained with a three-dimensi onal thermomecha
ni cal ice-sheet model cou pl ed wi th a parameteri zed
mass-ba la nce model. The mos t important find ings th a t
camc out of th ese experiments can be summari zed as
[0 11 0\-\,,5 :
refe rs to a stead y state, however. As d monstra ted in
Fig ure 3, th ere a re lon g time-scales required to build
ice sheers up . T ypical e-folding time-scales a ppear to be
of the order of 40000 60000 yeal's, m a king it quite
unlikely tha t the N o rthern H emisphere ice shee ts
during the LGM were in [ull equilibl'ium w ith the
clima te a r th a t tim e. Consequentl y, the inferred cooling
sho uld be considered as a lower bound. M elting of ice
sheets, on the other ha nd , is a much faster process
because oC the hi gher magnitude of a bla ti o n I'ates .
According to the curves displayed in Fi g ure 4, it may
ra ke as little as 5000 6000 years [0 entirely rem ove the
L a ure ntide a nd Euras ia n ice sh eets fro m the ir
continenta l base when the clima te switches from fu ll
g lacia l to fu ll interglacia l conditions. In tha t case, only
a sm a ll ice cap rema ins centred over no rthern No\"aya
Zeml ya and th e adjoining K a ra Sea th a t would require
a n add i ti ona l m echa nism oC perha ps manne o n g Ill [or
its d ecay.
M
E
ID
...
0
(l)
E
::l
0
>
(l)
..S:1
12
10
8
6
,
-
- ~
-
~ -
~
4
~
2 -
0 I
o 25
I
I
-9 K
-8K
-7 K
.oK
-5K
-4K
-3K
-2 K
-1 K
OK
\
50 75 100
Time (kyr)
Fig. -I. Evolution curves Jar c 'orLhem Hemisphere ice
volume Jar various temperaLlae rises above - 10 K. T hese
calClllations started with Ihe glacial ice-sheet configuration
as an initial condition.
11 5

Huybrechts and T'siobbeL: A10deLling oJ Norlhem Hemisphere ice sheets
(i)
T he degree-day method es timating runoff based on
m easurements in Greenl a nd seems to have a
continent-wide validity, at least for present-day
climatic conditions. This follows from a basicall y
correct identifi cation oC abla ti on areas for th e prese n t
state.
(ii ) The Eurasian ice sheet reaches approximately its
full extent for a summer temperature lowering of6-
7 K.
(iii ) A North American ice sheet in rough agreement with
LGM reconstructions is only produced for coolings of
below 9- 10 K.
(iv) The Barents- K ara ice-sheet complex ori ginated on
isla nds in the Arctic O cean and spread from there to
the adjacen t con ti nen t.
(v) Basal temperatures in th e central parts of th e
simulated ice sheets remain always well below the
melting point, and wet basal conditions a re confined
to the margins.
(vi) Several ten thousand s of years a re required to grow
the large Northern H emisphere ice sheets to their full
sIze.
(vii ) D eca y of full-grown ice sheets by surface melting can
be accomplished in a bout 5000 years under an
interglacial climate.
Nevertheless, this study has also highlighted so me of
the shortcomings of the present model. The most
importa nt ones are probably related to the influence of
the ice sheets on the a tmospheri c circulation, in particular
with res pect to changes in precipitation pa tterns, a nd to
the way marine ice-sheet dynamics are treated in th e
model. A furth er logical step is then also to couple th e icesheet
model with an ice-shelf model a nd to incorporate an
a tmospheric-flow model that d eals with changes in the
wind fi eld as the ice sheets grow into the troposphere.
These developments a re presently under way.
ACKNOWLEDGEMENTS
This paper is a contribution to the Belgian Impulse
Programme on Global Change, initiated by the Science
Poli cy Office (Services of the Prime Ministel-). During this
research, P. Huybrechts was on leave as a postdoctoral
researcher with the Belgian National Fund for Scientific
R esearch (NFWO). We thank W. Budd, A. Letreguilly
a nd C. Ritl: for their constructive reviews of the
manusc ript.
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