AnnalscifGlaciology 25 1997 r Internati ona l Gl ac iologica l Society

How well can we paraIll.eterize past accuIll.ulation rates in polar ice sheets?

ERIC J. STEIG

Institute cif Arctic and AI/Jine Research, UniversifY rljColorado, Boulde1; CO 80309 -0450, C S.A .

ABSTRACT. A n important component o f model s of the cryosphere is the ca lcul ati on of acc umula ti on rates O\'cr po la r ice shcets. As a first-order approx imation, many model s rely on the assumption that temperature is the main controlling factor for prec ipita tion. H owever, compil ati on of m'a il able ice-core da ta, includi ng a new co re from 1aylor D ome, East Anta rctica, suggests that precipita ti on is significamly decoupl ed from tcmperature for a la rge proporti on of bot h the Greenl and a nd Anta rctic ice shee ts. \ Vhile the estima ted glacia l-to-interglac ia l cha nge in temperature does not d iffer g reatly among ice co res from each ice sheet, the estim ated change ill acc umul ati on ra te \'a ri es by more tha n a fac tor of 2. A simpl e vapor-prcssure pa rame terizati on gives reasonable estimates of acc um ula ti on in the ice-shee t interior, but this is not necessaril y the case close to the ice-sheet ma rgin, where synoptic weathcr systems a re important.

INTRODUCTION

In recent years, much effort has been devoted to the de\'el­opment of models that can acc ura tcly simulate modern acc umul ation patterns over pola l' ice sheets (e.g. Fonuin a nd O erlemans, 1990; Bromwich a nd others, 1993; FaSLOok a nd Prentice, 1994). There has a lso been an effort to estim ate

the magnitude of acc umulation-rate changes under future g reenhouse-warming scena rios (e.g. Huybrechts a nd O erl e­mans, 1990; Verbirsky and Sa ltzman, 1995; Verbitsky a nd O glesby, 1995). Somewhat less emphasis has been pl aced on the ca lcul ati on of acc umul ati on under pas t climate condi­tions. Such research is importa nt because acc umul ation is onc of the determining factors in ice-sheet response to clim ate. Although numerical model s of former ice-shee t configurati ons ha\'e been de\'C loped, comparison of these res ults with g lacia l-geo logic da ta (e.g. Stui\ 'Cr and others, 1981; Del1ton and others, 1989; Bromwich and others, 1991; Huybrechts, 1993) does not prO\' ide sufficient va lidation a lone (Oreskes and others, 1994).

Accumul ation rate is one of the fund amenta l pa rameters ava il abl e from analysis of ice co res in pola r regions. As the a real coverage and qua li ty of ice-co re reco rds increases, it becomes increasingly worthwhi le to consider the extcnt of agreement between model estimates a nd empirical meas­urements. In thi s paper, common approac hes to the pa ra­meteri zation of acc umulation rates on pola r ice sheets a rc re\' iewed, a nd these approaches a re di scussed in the li ght of ice-co rc data from both hem ispheres. Such compari sons provide an important tes t of t he fidel it y of numeri cal models.

PARAMETERIZATION OF ACCUMULATION IN NUMERICAL MODELS

The most straightforwa rd approach to modeling acc umul a­ti on ove r pola r ice sheets is to ass ume tha t precipita ti on is prim a ril y thermodynamicall y controll ed. That is, the

418

amo unt o f water prec ipi ta ted is p roporti onal to the moist­ure-ca rrying capacity of the a ir mass, according to the rela­ti onship between temperature (T ) and the saturation va por p ressure (P ) O\'er ice, which follows a n Arrhenius rela tion­shi p:

P = Cl:, (-.i/T ) + c (1)

where Cl:, (3 and care empi rica l constants. Note that [or polar

ice shee ts, other than \'e ry nea r the margin, it may be ass umed tha t ablation is minim al and that acc umulation ~ p rec i pi ta tion.

O\'C r large pa rts of A nta rctica there is a strong con"e la­ti on between acc umulation rate, P and T abo\'e the surface inve rsion layer (Robin, 1977). The correlati on can be im­

pro\ 'ed further by accounting empiricall y for orographic effccts. For example, l<as took a nd Prcntice (1994) use the obse l'\ 'Cd p rescnt-day Anta rcti c acc umulation p allern to determine a fun ction rela ting acc umulat ion rate (6) to lhe ave rage surface slop e (5 ) a nd the saturation \'apor pressure:

(2)

where, A, B a nd Care cm pi rical eonstam s. FOI"tuin and O erl emans (1990) and Huybrechts (1993, (994) take a more direct app roach, express ing 6 simply as a n empirica l fun c­ti on of mean a nnua l temperature:

b = 0.78 + 2.525 x 1O- 2T + 2.225 x 1O-~T2 . (3)

In modeling modern acc umu lation rates over the G reenl and ice shee t, Bromwich a nd o thers (1993) take a considerabl y more sophisticated a pproac h, using empi ri ca l measures of a tmospheric dynamics:

b = APVv + BPVG \l H (4)

where H is the terrain height, a nd VG a nd 11" a re parameter­izations for the geos trophic- a nd ve rtica l-wind velocity, rcs­pec ti\·e1y. In Equation (4), as in Equations (2) and (3), P may be considered an empirical fun ction of T.

C learly, if we wish to appl y models such as those gi\'en

abO\T to pas t clim a te conditi ons, we will be limited by th c ass umpti on that thc em piricall y deri\"cd coeffi cients (a nd in th e case of Eq ua tion ("~), the a tmosp he ric dy na mics ) rem ain

co nstant. Because of this inherent limita ti on oC cmpiri ca l

m odel s, wc may cons ider turning to m ore sophisticated

a tm os pheric ge nera l circul a ti on m odels (G C i\,[s), which ex­plicitl y so k e fo r sy noptic-scale \ 'a ri a bles such as storm ('rcq ucncy, C urrcnt-ge nera tio n GCl\ls, howe\Tr, a re no to r­io usly poo r a t simula ting prec ipita ti on in po la r regions,

tending to prod uce higher-th a n- obsc r\'ed acc umul a ti on

ra tes O\"(' r bo th Greenland a nd A nt a rctica (G ates a nd

o thers, 1990; Tzeng a nd others, 1993; Bro mwich a nd others, 199+), T he d isc rete nature 0 (' prec ipita ti o n e\'ent s is in con­tras t to such c li mate \"ari ables as prcssure a nd tempera ture, fo r which long-term a nnua l a\'erage \'alues p rO\' ide resolu­

tion suffi cient fo r ma ny applicati ons, T hi s p roblem has no t

bee n reso h 'ed , bu t must, in pa rt, be a co nsequence of the in­

a bility o f these m ode ls to simula te adequa tely cyc loni c sys­

tems (Bromw ich a nd othe rs, 1991; Conn oll ey a nd Cattle, 1994) a nd to inco rporate full y the seasona l cycle Uo ussaume andJo uzel, 1993; C ha rl es a nd o th ers, 199"1,).

In sum m a r y, wc are curren tl y li m ited LO "low-order" em­

pirica l models, whic h can be tuned to fit obser\'ed acc umu­

la ti on patterns to an arbitra ry deg ree of acc uracy, bu t a rc li m ited in their abilit y to simula te tempora l cha nges; o r to "hi gh- o rder" GCl\ls th at a rc currentl y unsat isfactor y fo r model ing po lar p rec ipita tion, A p oss ibl e way aro und this

d ilemma is to assume tha t the changes in the c lima te va ri­

a bles p red icted by a G CM a rc m ore prec isc th a n thc a bso­

lut e \'a lues predicted (e.g, Ku tzbach a nd Gue ll e l~ 1986; COH.\Ir\P m em bers, 1988; Verbitsky a nd Sa ltz m a n, 1995), H oweHT, such a n a pproach still requires em pirical obser­\'a ti ons for sca ling the model- output da ta, f o r th e immedi­

a te future a t least, wc will be reli a nt on empirica l m odels,

a nd it is th erefo re imp ortant to co nsider th e ex tent o f agree­

ment be twee n th e pred ictions of such models a ndthc p a leo­clim a tc reco rd from ice cores.

DATA

In rCTiewing em pirical m eas ure ments o f acc umul a ti on ra te, the tra nsiti on from th e L as t Glac ia l l\Iax imum (LG l\I ) (abo ut 20 ka BP) to the H olocene is conside red , since it rep­rese nts th e la rgest cl im ate cha nge fo r which th ere is a rea­

so na blc iee-co re da tase t a\'ail ablc.

For the \ 'osto k ice core (Fig. I), Eas t Anta rc tica, Lorius a nd o th ers (1985) est ima ted acc umul a ti on rates O\'e r the las t 150000 years by ass uming, as in the models di sc ussed a bO\'C, th a t acc umul a ti on is thermod ynamica ll y controll ed. The

temperature hi sto ry is ta ken from isoto pic measurem ents

(OIHO or oD ) acco rd ing to:

T=ab'+b (5)

where T is th e temp era ture a bo\ 'C th e surface im'e rsion laye r, a nd a a nd b a rc co nsta nts. Ta king into acco unt

cha nges in thc isoLOpic co nt ent o f sea water in the ca lcula­ti on of T, a nd using a = 9%0 QC I fo r c5D (Jo uze! and othe rs,

1996), thi s para meterizatio n g i\'es a L G M lowering of acc umul a ti o n a t Vostok LO aho ut 50% o f th e present-day \'a lue. Tt should be no ted th a t bo reho le tem pera ture meas­urements a t Vostok (Sa lam a tin a nd oth e rs, 199+) suggest

tha t the assumption of a co nsta nt c5 - T rel a ti onship i prob­

a bly rcasona ble for th e E as t A nta rcti c interi o r. That the

S/eig: Past aCCIll71llla/ion rates ill polar ice sheets

-55

1.4

1.2 -60 o o -

<I> ~ .... 1.0 c .Q lQ :::J 0.8 E -65 :::J U U ca <I> 0.6

.~

lQ <I> ....

0.4

0 .2-+.........,r-T"'I"......., ........................... .,..,.,.........-I

o 5 1 0 15 20

Age (EGT ka S.P.)

FI~[{. I. [ f)/)er line: SII/face tell7/matllre at [ostok, , intarctiea, Ol'er t/ie last 25 ka all t/ie "PI tended gl({ciological time-scale" (E(;T ) (Joll;:e/ and others. 1993). Lower Jolid line: the re­/a/ille a[[lIl11l1la/ion rate (Ilormali.::,ed to a lIIodern l'a/Ile of 1) ca/ClI/atedfrol71 the vajJ01'-jJ1'Cssure rela/ionshil) ( Lorius and a/hers, 1.985). Dolled line: t/ie re/a/iz'e accl/lIlll/a/ion rate ca/­CIIla ter/froll/ {I) Be concentrations ( Raisbeck and others. 1.987).

ori g ina l \ 'os tok time-sca le (Lorius a nd o th ers, 1985) com­

pa res fa\'o ra bl y with rece nt a nd m ore acc ura te determina­

ti ons o f the Vosto k age-depth rela ti onship (jo uzel a nd

o th ers, 1993; Sowers and o th ers, 1993; Sowers a nd Bender, 1995) sup po rt s th e \'a lidit ), o f thi s para me teri zat ion, a tlcast in centra l East A nta rctica. Tt is further supported by lOBe meas urem ents in the \ 'ostok core, which sho\\' a 50'10- 60% decrease in co ncentra ti on fo ll owing th e LG?d (R a isbec k

a nd others, 1987; J ouzel a nd others, 1989). A strong im'Crse correl a ti on be tween snow acc umul a ti on a nd lO Be conce n­trati on is expec ted because lOBe depos iti on a t low-acc umu­la ti on-ra te sites such as Vosto k is predomina ntl y by dr y

fa ll out (R a isbec k a nd Yio u, 1985; Yi ou a nd o th ers, 1985; L or­

ius a nd Olhers, 1989; Steig a nd o th ers, in press ); a lso the

pola r a tmospheric co ncentra ti on of lOBe is unlikely to ha\'C

cha nged by m ore th a n a few perce nt o\,er th e las t 20 ka (Steig a nd o th ers, 1996).

The best es tima tes of acc umul a ti on ra tes in Greenland a rc derived from combined ice-fl ow m odel /laye r-thickness

m easurements on the U S, a nd Eu ropean ice co res a t Sum­

mit (G TSP2 a nd GRIP; res pectivel y). Da hl:Jense n a nd o the rs (1993) caleula ted tha t acc umula ti on ra tes a t th e GRIP site were a bout 30% of prese nt-day \'a lues a t the L C t-. I; C utler a nd o th ers (1995) a nd C uffe)' a nd C lose (in

press ) g i\'e \ 'C ry simila r estima tes o f th e LG~I acc umul a ti on

rate a t G IS P2 (30 km a \\'ay ).

419

S!el~!t: Pas! acculllulation rates ill jJo/rn iCf siteets

For many other Greenland ice cores, particularly those closer to the coast, the estimated LG~r-Holocene change in accumulation rate is larger than at Summit. Dcpending on the time-scale adopted and the [low-model assumptions employed, the LG~l accumulation rale al Camp Century, northwest Greenland, was as loll' as 20% of the Holocene \'a lue (Reeh, 1990). Sim ilar estimates ha\'e been obtained for the southwestern Greenland site, Dye3 (Reeh and others, 1985; Reeh, 1990), whi le a LGM lowering of accumu­lation to as little as 10 % of present \'alues was calcu lated for the De\'on Ice Cap, eastern Arctic Canada (Paterson and Wadd i ngton, 198-!).

In Antarctica, as in Green land, warmer, less continental sites appear to ha\"e experienced a somewhat larger change in accumu lation rates dur ing the LGM Holocene trans­ition. \ "hi le accumulation-rate histories at Dome Cirque and Dome B (intcrior East Antarctica ) arc apparently simi lar to those at Vostok Uouzel and olhcrs, 1989; 1995), esti­mates from IIlBe measurements (Beer and others, 1987) and

from recent refinements to the age-depth relationship (Hammer and others, 1994) suggest that accumulation rates at BYI'd Station, \ Vest Antarctica, during the LG~r were at most W% ofHolocene \·alues. At h1.),lor Dome (Fig. 2), j LIst inland of the ~nansantarctic ~ Iountains in East Antarc tica (Grootes and Steig, 1992; Waddington and others, 1993; Grootes and others, 1994), there is an even greater LG~[ Holocene contrast: both preliminary [low-model calcu la­tions and IIlBe measurcments (Steig, 1996) indicate that the acculllulation rate during the LGM was at lllost 20 25'% or thc Holocene \·alue.

420

1.4

1.2 Q) -~ ... c 1.0 0

~ :J 0.8 E :J () () ~ 0.6 Q)

.~ iU 0.4 Qi ...

0.2

o 5 10 15 20 Age (EGT ka B.P.)

-40

-44

-48

-52

0 0 -I-t/l

Fig. 2. Up/Jer line: Sll/face lell1jJemtllre at Ta..)llor Dome, Ant­arclica, calCillatedfrom (PO measuremenls at Ta..ylor Dome.

assuming Ihal15180 = 8 bD+ 10 alld DI5D/aT = 9%o/C (aJterJou<.el and o/liers, /996). Lower line: relatil'e amllllll­lation mteJrolll j() Be lIleaSll1'ements (Steig, /996).

COMPARISON OF MODEL RESULTS AND ICE-CORE DATA

Analysis oC borehole temperature meas urements in thc Summit eores (Cufley and others, 199-!, 1995; Johnsen and others, 199.')) reveal that the slope of the bIHO-T relationship (the \ 'a lue of a in Equation (5)) in central Greenland is much lower (r-.-O.2 ) for the LGM Holocene transition than the modern \'alue of about 0.6. Thus, we cannot use the sa me parameterization for the Summit cores as gi\'en abO\'C for \ 'ostok. However, assuming that the thermodynamic rel a­tionship applies at Summit, the surCace-temperalLire history deri"ed from borehole ana lyses yields an accumulation profile that is highly compatible with the inferred history from ice-[low modeling (Cuiley and C low, in press ). These results arc shown in Figure 3. The assumption has been made that accumulation is most high ly corre lated with the temperat ure abO\'C the surface im'Crsion layer 1i (K), wh ich can be estimated from the surface temperature 1'., ( l'ortuin and Oerlemans, 1990):

1i = 0.67(1'.,) + 88.9 . (6)

G iven the strong apparent correlation betll'een accumu­lation and temperalure at both Summit and at \'ostok, it is tempting to conclude that accumulation rates over polar ice sheets can geneml£), be parameterizecl in terms of a simple thermodynamic relat ionship (Equation (1)). However, results ['rom the Tay lor Dome core bring this into question. As ill ustrated in Figure 2, accumulation at laylor Dome

-30

0 -35 ~

t/l f-

1.2 -40

Q) 1.0 -45 iU ... c .2 iU 0.8 :; E :J 0 0 0.6 ca Q)

.~ iU ~ 0.4

0.2 -t---'--""T""--,---i

o 5 10 15 20

Age (GISP2 ka S.P.)

Fi~!t. 3. U/I/JeT line: sllrface temjierature at Summit, Greenlalld, calculatedji'Oln borehole tem/Jeratllres and {j1ll0 values (Oif­Rv and others, 1995). Lower solid line: rei alille acCl! mul a I ion rale (({[clllaledfrom Ihe l'apor-presslire relationship ( Larilis alld others, 1985). Dolled line:jloll·-model calculations o/ac­(Il/nlllation (O!fky and Clolt'. ill jJress).

does not parallclthe temperature history inferred from 15 1110 analyses. Although Taylor D ome appears to have experi­

enced a somewhat different temperature history than did Vostok, it is likely that the 15 - T relationship is simil a r at both sites, gi\·en the similarity in the magnitude and tim.ing of the LGl\l H oloeene shift in stable-i sotope values (Grootes and others, 1994) and the probable simil arity in

moisture prO\·enance (Petit and others, 1991; Mayewski and

others, 1996). The noticeable differences between the infer­red temperature and acc umul ation histori es at Taylor Dome strongly imply tha t non-thermal effects, such as the degree of storminess, must play a role in dctermining accumulation at Taylor Dome. Although the differences a re not as dra m­

at ic, a simil ar argument appl ies to the Byrd resuit s, a nd probably to the Camp Century, D ye3 and De\·on Island cores: in genera l, the magnitude of temperature change during I he LG l\f- Holoccne tra nsiti on is compa ra ble among cores on each icc sheet, but the estimated accumula­tion-rate change varies by at least a i"actor of 2.

A more favorable comparison bet weell data and model

results can be obtained if empirical fits to the modern di stri­bution of acc umul ation arc used , rather tha n the simple parameterization gi\Tn in Equation (I). Common to each of the models di scussed abo\"C (Equations (2) and (3)) is that the sensitivit y oi"accumulation rate to temperature change

decreascs with dista nce from the icc-shcet margin, bearing in mind that the mean a nnu altcmperature (T ) in a llthrce models is a function of latitude and alt itude. (That is. th e derivat i\·es ab/aT of each express ion for b increase \\"i th T O\·er a n appropr iate range of tcmperatures.) For example, if wc postulate a decrease in T oi" 10 C and assumc that a ll

other parameters remai n constant, wc calculate from the H uybrechts (1993) model (Equation (3)) that a site witb a current T of-30 ' C (e.g. Byrd Station ) would expericnce a drop in accumulation to about 50'Yo of prescnt-day \·"dues. A site with current T of 55 'C (e.g. VosLO k) would ex peri­ence a much sm aller (about 10 % ) dec rcase in acc umul a­tion . The yalues gi\·en by Fastook a nd Prentiec (1994) for the coefficients in Equation (1) yield similar results, as does Bromwich and others' (1993) model for Grecnland. :\Totc, howe\·er, that wh il e the sig n of the calculated differcllce ill response is correct, these parameterizations g rea tly o\Tr­estimate tht' difference among ict'-core sitcs, suggesting th at

the assumption of constant coeffic ients is invalid.

CONCLUSIONS

In genera l, it appears that the accumu lation hi story of the interior oflarge icc sheets is quitc reasonably approximated

by a simple thermodynamic rel a tionship:

(7)

Although this conelusion is in agreement with the early

work of Robin (1977) and Lorius and others (1985) in Ant­

arctica, it is in ma rked contrast to that of K apsner and

others ( 199"~) , who suggested that a tmospheric circulation, rather tha n temperature, driyes acc umul a tion-ra te \·aria­tions at Summit, Greenl and.

Away from the icc·-sheet interior, ho\\'e\"er, l1eithcT the simple relationship gi\"Cn abo\T, nor empiri ca l parame teri­

zations oi" the distribution of accumulation under modern cond iti ons, can be used to determine reli abl y past aCC UIllLl-

Sleig: Pasl acculllulatioll ra/eo ill Iwla,. ice sizeelo

lation ra tes. Result s from ice cores such as Taylor Dome and Byrd in Antarctica, a nd Camp Century and D ye3 in Green­

land, sugges t that changes in a tmospheric circulation, a nd poss ibl y other factors, must play a m<uor role in determining regional accumulati on pa tterns.

Fina lly, it is import a nt 10 note that empirical model s such as those of Hu ybrcchts (1993) and HISLOOk and Premice

(1994), in which T is the only free yariable, tend to O\"Cr­

estimate the diflcrence in sensiti\·ity of interior and coasta l areas with rega rd to accumulatio n rate during co lder-than­present climates. I naccuracies of thi s nature suggest that l1ulllerica llll ocl cl s ofice-shect config uration thal use simple thermod ynamic relationships in their pa rameterization of acc umulation rate lllust be treated \I·ith cautioll.

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