the antarctic ice sheet and its probable bi-modal response...

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MASS BUDGETS : ICE AGES 347 ROBIN, G. DE Q. and ADIE, R. J. 1964. The ice cover. Antarctic Research. ROBINSON, E. S. 1966. On the relationship of ice surface topography to bed topography on the South Polar Plateau. J. Glaciology, Vol. 6, No. 43, 43-54. SHUMSKY, P. A. 1963. The fields of pressure and density in glaciers. Clac. Issled., No. 9. VORONOV, P. S. 1964. On the dimensions of the Antarctic continent and the character of its denudation (in Russian). Problems of Arctic and Antarctic 17. WERTH, E. 1908. Aufbau und Gestaltung von Kerguelen. Deutsche Südpolar- expedition 1901-1903 Bd. II, H.2. WRIGHT, C. S. and PRIESTLEY, R. E. 1922. Claciology. British Antarctic Expedition, 1910-1913. The Antarctic ice sheet and its probable bi-modal response to climate BY MARIO B. GIOVINETTO Department of Geography, University of California-Berkeley, Ca., U.S.A. Contribution No. 225, Geophysical and Polar Research Center, Depart- ment of Geology, University of Wisconsin, Madison, Wise, U.S.A. ABSTRACT The net mass budget estimates reported elsewhere for the Amery Ice Shelf drainage system and the eastern and western parts of the Ross Ice Shelf system are combined with (i) an alternate estimate for the Amery Ice Shelf system, and (ii) alternate estimates for the eastern part of the Filchner Ice Shelf system. These systems make up the interior province of Antarctica and their combined net budget is estimated to be positive and in the order of (3 ± 1) 10 17 g yr" 1 . The Ross Ice Shelf system as a whole is the only system of the interior province for which the estimate of a positive net budget is significant ((18 ± 5 ) 10 16 g yr- 1 ); direct and indirect evidence confirms that the western part of the system is a region within the interior province where the net budget is positive. The interior province accounts for approximately one half of both the area and the mass of the ice sheet, and one third of the total mass input; engulfed ice shelves are the agents of drainage, and the net mass gain is equivalent to approximately one half the annual input in the province. The remaining drainage systems are split into three groups and make up the peripheral province. This province accounts for the remaining one half of both the area and the mass of the ice sheet, and two thirds of the total mass input; the agents of drainage are marginal ice shelves, glacier tongues and grounded ice termini. A comparison of the net budget for the interior province with data on sea level change during the last 100 years, indicates that the net budget in the peripheral province should be negative. Empirical and heuristic two-province models of the ice sheet suggest that

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Page 1: The Antarctic ice sheet and its probable bi-modal response ...hydrologie.org/redbooks/a086/086038.pdf · character of its denudation (in Russian). Problems of Arctic and Antarctic

MASS BUDGETS : ICE AGES 347

ROBIN, G. DE Q. and ADIE, R. J. 1964. The ice cover. Antarctic Research.ROBINSON, E. S. 1966. On the relationship of ice surface topography to bed

topography on the South Polar Plateau. J. Glaciology, Vol. 6, No. 43, 43-54.SHUMSKY, P. A. 1963. The fields of pressure and density in glaciers. Clac.

Issled., No. 9.VORONOV, P. S. 1964. On the dimensions of the Antarctic continent and the

character of its denudation (in Russian). Problems of Arctic and Antarctic 17.WERTH, E. 1908. Aufbau und Gestaltung von Kerguelen. Deutsche Südpolar-

expedition 1901-1903 Bd. II, H.2.WRIGHT, C. S. and PRIESTLEY, R. E. 1922. Claciology. British Antarctic

Expedition, 1910-1913.

The Antarctic ice sheet and its probable bi-modal response to

climate

BY

MARIO B. GIOVINETTODepartment of Geography, University of California-Berkeley, Ca., U.S.A.

Contribution No. 225, Geophysical and Polar Research Center, Depart-ment of Geology, University of Wisconsin, Madison, Wise, U.S.A.

ABSTRACT

The net mass budget estimates reported elsewhere for the Amery IceShelf drainage system and the eastern and western parts of the Ross IceShelf system are combined with (i) an alternate estimate for the AmeryIce Shelf system, and (ii) alternate estimates for the eastern part of theFilchner Ice Shelf system. These systems make up the interior provinceof Antarctica and their combined net budget is estimated to be positiveand in the order of (3 ± 1) 1017 g yr"1. The Ross Ice Shelf system as awhole is the only system of the interior province for which the estimate ofa positive net budget is significant ((18 ± 5 ) 1016 g yr-1); direct andindirect evidence confirms that the western part of the system is a regionwithin the interior province where the net budget is positive. The interiorprovince accounts for approximately one half of both the area and themass of the ice sheet, and one third of the total mass input; engulfed iceshelves are the agents of drainage, and the net mass gain is equivalent toapproximately one half the annual input in the province. The remainingdrainage systems are split into three groups and make up the peripheralprovince. This province accounts for the remaining one half of boththe area and the mass of the ice sheet, and two thirds of the total massinput; the agents of drainage are marginal ice shelves, glacier tonguesand grounded ice termini. A comparison of the net budget for theinterior province with data on sea level change during the last 100 years,indicates that the net budget in the peripheral province should be negative.Empirical and heuristic two-province models of the ice sheet suggest that

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348 ISAGE

its response is bi-modal to the present and as yet undetermined climaticregime.

Introduction

Recent mass budget studies for the Ross and Amery ice shelves drainagesystems (Fig. 1) suggest net positive budgets greater than the errorestimates by factors >\ and g 3 (Budd et al., 1967; Giovinetto et al.1966; Giovinetto and Zumberge, in press). These systems, and theeastern part of the Filchner Ice Shelf system, make up the interiorprovince of Antarctica. The interior province accounts for approximatelyone half the area («^7 x 106 km2) and more than one half of the icemass (^1 X 1022 g) of the ice sheet (Giovinetto, 1964).

In the following sections the budget estimates for each of the systems inthe interior province are discussed in terms of a probable bi-modal

9 0 ° W - I ti=?—I—-H-90-E

600 KM

FIG. 1. The drainage divides in Antarctica are depicted by lines of dashes and dots(after Giovinetto, 1964). The areas of the eastern and western parts of the RossIce Shelf drainage system (EF) are shaded with slanted and vertical lines, respectively.The areas of the Amery Ice Shelf (BC) and eastern Filchner Ice Shelf (J'K) drainagesystems are also shaded. Ice discharge from the southern ice stream basin (SISB)may drain south and west of Berkner Island (Fig. 2).

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MASS BUDGETS : ICE AGES 349

response of the ice sheet to the present and as yet undetermined climaticregime. The models proposed are dependent on assumptions related tothe mass budget of the peripheral province of Antarctica and eustaticsea-level changes.

The regimen of the interior province

The Amery Ice ShelJ drainage system. Budd and others (1967) haveestimated ice discharge across the northern boundary of the Amery IceShelf at (27 ± 9) 1015 g yr-1 (Table 1). They estimate net accumulation

TABLE 1THE REGIMEN OF THE INTERIOR PROVINCE

Drainage system

Amery I.S.A.I.S. (alt.)

R.I.S. (cast.)R.I.S. (west.)R.I.S. (whole)

F.I.S. (east.)F.I.S. (east.; alt.)a

All systemsAll systems (alt.)

Area

105 km2

16± 516±5

12 ± 218 ± 330 ±4

25 ±519 ± 5

71 ± 865 ± 8

Input

10'Sgyr1

85 ±43131 ±36

301 -•- 4696 ±25

349 ±51

215 + 58155 J_ 58

695 -r 85589 ± 88

Output1Q15 g y r - l

27 ± 927 ± 9

168 ± 1848 ± 15

168 ± 18

108 ±40108 ± 40

303 ± 45303 ± 45

Net budget

101« g y r - i6±4t

10 ±4*

13±55±3

18±5*f

1 1 4 - 7 *(5 ± 7)t

10"gyr-'(4± 1)*(3 ± m

1 Excluding the southern ice stream basin ("S.I.S.B.", Fig. 1).

at the surface for the area of the Amery Ice Shelf drainage system at(85 i 43) 10]5 g yr"1, and suggest that subglacial net mass flux on the iceshelf is relatively small; from these data the net budget is here estimatedat (6 ± 4) 1010 g yr-1.

Budd and his colleagues estimated net accumulation at the surface forthe whole area of the system assuming that the bulk of the net ablationat the surface in the Lambert Glacier (Fig. 1, between and south of B'B")—and on the grounded ice sheet slopes to the east, south, and west of theglacier—is lost as evaporation, deflation, and surface melt run-off whichreach the sea somewhere in the southern part of the Amery Ice Shelf.However, evaporation is relatively small and it is improbable that surfacemelt run-off could reach the sea somewhere near the grounded ice bound-ary, where ice thickness is greater than 450 m (Budd, 1966). Moreover,the whole width of the Lambert Glacier is heavily crevassed, and a largeproportion of the drifting snow and melt run-off would be trapped

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350 ISAGE

(cnglacial accumulation*); drifting snow and melt run-off also wouldaccumulate on the flat surface of the ice shelf.

Assuming that net abation at the surface of the Lambert Glacier isaccounted for by englacial accumulation and by an increase of the rateof net accumulation at the surface of the ice shelf near the grounded iceboundary, the preceding estimate of mass input based on the data ofBudd et al. (1967) could be replaced by an earlier estimate which isapproximately 65 per cent greater ((131 ± 36) 1015 g yr"1; Giovinetto,1964).

The resulting alternate estimate of the net budget ((10 ± 4) 101G g yr - 1 ;Table 1) is greater than the error estimate by a factor of 2-5, indicating aprobable positive budget.

The Ross Ice Shelf drainage system. In Table 1 the area and mass inputand output terms for the eastern and western parts of the Ross Ice Shelfsystem are compared with the same data for the whole system. Thesummation of input terms amounts to (349 ± 51) 1015 g yr"1. Theitemized terms follow: (i) Net accumulation at the surface in the easternpart, which includes the ice shelf, and the minimum estimate of netsubglacial freezing are (208 ± 44) 1O1S g yr"1 and 45 x 1015 g yr-1,respectively (Giovinetto and Zumberge, in press), (ii) Net accumulationat the surface in the western part is (96 ± 25) 1015 g yr - 1 (Giovinettoet al., 1966).

The rate of mass output across a drainage section not coincident withthe ice terminus, and extending between Cape Spencer-Smith in 78°S,167°3O'E and Edward VII Peninsula in 77°45'S, 158°W, is (168 ± 18)1015 g yr~a (Giovinetto and Zumberge, in press). Therefore, the netbudget for the whole Ross Ice Shelf system is estimated here at (18 ± 5)1016 g yr -1. The composite error ( ± 28 per cent) in this estimate confirmsthe positive estimates indicated for each of the two parts of the system;in the estimates for the eastern and western parts the standard errors are± 38 per cent and ± 60 per cent, respectively.

The eastern part of the Filchner Ice Shelf drainage system. The estimatesof area and net accumulation at the surface of the eastern part of theFilchner Ice Shelf system are (25 ± 5) 105 km2 and (200 ± 58) 1015 g yr-1,respectively (Giovinetto, 1964). Using the same model adopted for theRoss Ice Shelf to estimate subglacial net mass flux (Giovinetto andZumberge, in press), the minimum net freezing in the eastern part of theice shelf is estimated to be approximately 15 X 1015 g yr-1. The sum-mation of net accumulation at the surface and net subglacial freezing is(215 ± 5 8 ) 1015 g yr-1 (Table 1).

* As implied by Budd et al. (1967): "The crevasses may accumulate snow andmelt water, but this does not imply a gain, but rather a redistribution of mass."Accounting for this redistribution, their estimate of net accumulation can be increasedby 1016 g yr~l to 95 x 1015 g yr"1, i.e. the minimum estimate made by Giovinetto(1964). To be sure, this alternate estimate is not valid if a large proportion of thegross ablation in the area is due to evaporation.

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MASS BUDGETS : ICE AGES 351

Ice discharge east of Berkner Island (Fig. 2), has been estimated byBehrendt (1962) and Lisignoli (1964). Their estimates are here revisedcombining the results of both studies: the mean ice velocity is approxi-mately 1500 m yr-1, and the mean ice thickness for the 240 km segmentis approximately 300 m. From these data, ice discharge is estimatedat (108 ± 40) 1015 g yr '1 (Table 1). This estimate is in agreement withthose made by Behrendt and Lisignoli, although it is based on the meanice thickness estimated by Behrendt (300 m), which is greater than thatused by Lisignoli (250 m).

The composite error ( ± 3 7 per cent) is the summation of: (i) An errorof approximately ± 20 per cent in the estimate of mean ice thickness,which Behrendt (1962 and personal communication) estimated from dataon ice surface elevation, (ii) An error of approximately ± 30 per centin the estimate of mean ice velocity, which Lisignoli (1964) estimated fromchanges in the grid-position of stations for periods from three to sixyears (the error in the standard astronomical determination of latitudein Antarctica is at least ± 1000 m; Chapman, personal communication).To be sure the relative error is very small in the estimate of velocities forthe eastern segment of the drainage section, between General BelgranoBase (Fig. 2) and the Moltke Nunataks (approximately 78°10'S, 35°1O'W),but it is greater than ± 30 per cent in the western segment of the section,between General Belgrano Base and Berkner Island, (iii) An assumederror of approximately ± 10 per cent in the estimate of the smoothedlength of the barrier.

The net budget estimate ((11 ± 7) 1016 g yr -1) is greater than the errorestimate by a factor of 1-6, and the result is inconclusive. This estimateis invalidated even further if there is ice shelf discharge toward the westalong the southern edge of Berkner Island, a possibility not taken intoaccount in the error estimate.

Ice surface data collected along the route of aircraft flights and onlanding sites during the 1963-64 and 1964-65 field seasons (Behrendt,1965) suggest that a large ice stream may flow south and west of the Pensa-cola Mountains (Fig. 2, centered approximately at 83°3O'S, 52°00'W). Ifthe ice contributed by this stream into the ice shelf ultimately dischargesparallel and along the southern and western flanks of Berkner Islandinstead of the eastern flank, then the budget estimate would be smallerin relation to the error magnitude. An ice stream draining south andwest of the Pensacola Mountains could account for a mass output of atleast 5 X 1016 g yr~a, i.e. for the whole net accumulation at the surfacein the southern area of the system (Fig. 1). Ice shelf thickness datasouth of Berkner Island (Behrendt, 1962) and the recent discovery of alarge zone of shear in the ice shelf (near the barrier and approximately100 km west of Berkner Island as shown in the American GeographicalSociety's chart of Antarctica, 1:5,000,000, 1965) suggest that the icestream may indeed exist, and that it may discharge westward and southof Berkner Island. If this is shown to be true by future field work, the

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352 ISAGE

0 100 200 300 400 500 KILOMETERS

! ! I ! I I

Co^'ot' initivol 200 mtitncicept on Ice Shelf wt-.«re

tOO meters is shown

FIG. 2. Surface relief in the Filchner Ice Shelf area of Antarctica (after Behrendt,1965), where a trough approximately from 87°S, 90" W, to 83°S, 60°W suggests thata large ice stream flows west of the Pensacola Mountains (approximately at 83°3O'S,52°0O'W) and south and west of Bcrkner Island.

area and the rate of mass input in a redefined "eastern part" of the FilchnerIce Shelf system would have to be reduced by excluding the southern icestream basin (Fig. 1, "S.I.S.B."). An estimate of the net budget for a

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MASS BUDGETS : ICE AGES 353

drainage system such as that would be within the error magnitude because:(i) The rate of mass output would remain the same; (ii) The rate of massinput would be reduced approximately by 5 x 1016 g yr~x in terms ofnet accumulation at the surface, and by 1 X 1016 g yr~l in terms of netsubglacial freezing. Assuming, for purposes of discussion only, that theerror estimates remain the same, the net budget for the eastern part of theFilchner Ice Shelf system excluding the southern ice stream basin issmaller than the error estimate.

The net mass budget of the interior province. From the precedingsections, it is evident that except for the whole Ross Ice Shelf system, onecannot draw any conclusions on the regimen of each of the other twosystems. However, if all systems in the interior province are combinedto form a single drainage system, it is possible substantially to reduce theerror in the estimates of area and net accumulation at the surface. Theuncertainties on the placement of the drainage divides and the determina-tion of net accumulation at particular locations are largest in the regionwhere the three systems join (Giovinetto, 1964). For example, segmentsof drainage divides in the interior of East Antarctica were assignedmaximum placement errors of ± 300 km, and the mean net accumulationin the area within the 5 g cm"2 yr - 1 isopleth was estimated at 3-0 ± 1-5g cm"2 yr - 1 (Giovinetto, 1964). Recent data on ice surface topography(Zotikov et al., 1965; Beitzel, personal communication) and net accumula-tion (Picciotto et al., 1968) indicate that the magnitude of the errorsassigned to factors used to estimate mass input were excessive, as intended,by at least a factor of 2. Nevertheless, without reducing the errorestimates, but joining the three systems, and as a first approximation, thearea and the rate of mass input for the three systems as a whole areestimated to be (71 ± 8) 105 km2 and (695 ± 85) IO15 g yi-1, respectively(Table 1). This estimate of mass input incorporates the alternate netbudget estimated for the Amery Ice Shelf system and includes the southernice stream basin lying south-east of the Filchner Ice Shelf.

The summation of the rates of mass output is (303 ~ 45) 1015 g yr"1,and the net budget of the interior province is (4 -± 1) 1017 g yr"1, indicatingthat the net budget is positive. This result is not changed by the con-sideration of the budget estimates of the Amery Ice Shelf system by Buddet al. (1967), and of the budget estimate of the eastern part of the FilchnerIce Shelf system excluding the southern ice stream basin (total area forall systems: (65 Az 8) 105 km2), because the net budget would still begreater than the error estimate by a factor 2;3, i.e. (3 ^ 1) IO17 g yr~'.

The regimen of the interior province and eustatic sea level changes of thelast hundred years

Considering the magnitude of the error in the net budget estimate of theinterior province, and the fact that subglacial net freezing in the ice shelvescontributes at least 6 X 10lf> g yr - 1 to the net mass increase, the net

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354 ISAGE

budget of the inland ice is equivalent to a lowering of sea level of approxi-mately 1 mm. yr"1 (ocean area: 36 x 107 km2). From the mid 1800'sto the 1950's, sea level has been rising at a mean rate of approximately1 mm yr"1 (Fairbridge, 1961), although there are indications that the rateincreased during the 193O's (Gutenberg, 1954), and decreased during the1950's (Kaye, 1964). The summation of the observed eustatic rise andthe estimated net mass increase of the Antarctic interior province amountsto a potential rise in sea level of approximately 2 mm yr-1. The regimenof the grounded Antarctic ice notwithstanding, the phenomena relatedto the world's hydrological cycle which would contribute to a rising of sealevel are: (i) An increase of the amount of free water on Earth, includinggroundwater, due to an addition of juvenile water, (ii) A decrease ofabsolute humidity in the atmosphere, (iii) A decrease of landlocked freewater postceding the Industrial Revolution due to man's modification ofnatural drainage and overdraft of groundwater for irrigation in arid andsemi-arid lands, (iv) An increase in the mean temperature of the world'socean, (v) A negative net budget of the Greenland ice sheet.

The water mass related to the first three phenomena is considered to berelatively very small, and the effect of the probable increase in the meantemperature of the ocean is also relatively small. Assuming that theincrease of approximately 6°C determined for the surface-water tempera-ture at tropical and subtropical latitudes since 11,000 BP (Emiliani, 1955and 1957) represents approximately one half of the mean temperaturechange of surface-waters at all latitudes, and reducing this figure againby one half to account for the whole water mass (mean depth: ~38OO m)the sea level rise due to thermal expansion would be approximately 1 m,or a mean of 0-1 mm yr - 1; this is only a fraction of the rise of 1 mm yr - 1

observed, and of the equivalent rise of 2 mm yr - 1 which seems likely forthe last 100 years if we assume that the ice sheet's regimen does not changefrom decade to decade.

On the basis of relative volume alone, the net budget of the Greenlandice can be assumed to be at a maximum in the order of 1017 g yr -1, thusaccounting for approximately 15 per cent of the 2 mm yr"1 potential rise.It follows that the major single source of water to maintain at least 80per cent of the potential rate of increase is a negative budget in some orall of the Antarctic drainage systems which together make up the peripheralprovince of the ice sheet.

An empirical modelA net negative budget equivalent to 2 mm yr-1 of the world's ocean

represents a loss of approximately 7 x 1017 g yr -1. The model ofAntarctica here postulated (Table 2) is characterized by: (i) An interiorprovince which accounts for one half the area (and ^50 per cent of themass) of the ice sheet and one third of the total mass input, where theoutlets are relatively narrow and consist of engulfed ice shelves, and thenet gain is equivalent to one half of the annual mass input in the province.

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MASS BUDGETS : ICE AGES 355

TABLE 2ICE SHEET MODELS

Model typeand province

Empirical:InteriorPeripheralAntarctica

Heuristic:Int. (emp.; alt.)Per. (heur.)Antarctica

Area

105 km2

7169

140

6575

140

Mass

10" g

>\,vli

2

IIA

2

Input

10l'gyr"1

71522

61622

Output

10"gyr-1

32225

31922

Netbudget

10» g yr-1

4—7—3

3—3

0

(ii) A peripheral province which accounts for the remaining one half thearea (and ^50 per cent of the mass) of the ice sheet, and two thirds of thetotal mass input, where the broad outlets consist of marginal ice shelves,glacier tongues, and grounded ice termini, and the net loss is equivalentto one half of the annual mass input in the province. This model cannotbe substantiated at present. It requires a negative net budget for thewhole ice sheet in the order of 3 x 1017 g yr-1 at least until the late 1950's,when the eustatic rise of 1 mm yr - 1 may have started to show a decline(Kaye, 1964). This requirement would render the model untenableconsidering that the net budget's error estimate for the whole ice sheet is± 1 X 1018 g yr-1 (Giovinetto, 1964). Nevertheless, the scant andindirect evidence there is agrees with the two-province model.

In the peripheral province, near Mount Gaussberg (approximately66°45'S, 89°10'E) the thickness of the ice sheet has decreased by anaverage of 8-1 m from 1902 to 1957; the minimum decrease is 5-8 m amongthe 15 points surveyed, and the maximum is 21-7 m (Feodosyev, inDolgushin et ai, 1962). In addition, there is evidence of a recent thick-ness decrease in snow fields near the ice terminus at approximately40°E and 110cE in the peripheral province (Hollin, personal communica-tion).

In the interior province the first direct evidence of an increase in thethickness of the ice sheet was reported by Koerner (1964) at approximately82°30'S, 106°00'W. There, corrasion features caused by drifting snow ona granitic nunatak are being buried by the ice. Koerner indicates,however, that the area for which this ice thickness increase may berepresentative is unknown. Recent electromagnetic soundings across theice shelf-grounded ice boundary in the eastern part of the Ross Ice Shelfdrainage system show that the grounded ice is, or recently has beenadvancing (Robin et al., 1968). In addition, there is evidence of a signifi-cant increase in the rate of net accumulation at the surface at the SouthPole from ca. 1760 to 1957, but the area of the region for which there is a

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356 ISAGE

positive secular change of accumulation is unknown (Giovinetto andSchwerdtfeger, 1966). Part of the long-interval increase in the rate ofaccumulation could be explained by the position of the stratigraphiecolumn relative to the snow surface's migrating ridge and trough topo-graphy, as implied by the findings of Gow and Rowland (1965). However,the cumulative sequence of short-interval increases in the rate of accumula-tion cannot be explained by the migration of topographic features alone.

Unless relatively complex assumptions are brought into the discussionof sea level changes*, the relatively simple assumption that Antarcticacan be ascribed the major role on present eustatic sea level changes, and apositive budget for the interior province, are the only effective constraintson the empirical model presented in Table 2. The facts that more thannine tenths of the ablation occurs at the periphery, and that the distributionof atmospheric and oceanic phenomena is approximately concentricalrelative to either the pole of rotation or to the pole of maximum inaccesi-bility (approximately at 87°S, 65°E) suggest that, at present, the responseof the ice sheet is bi-modal to the as yet undetermined climatic regime.This is not to say that the net budget is positive in all systems of the interiorprovince; this is to say that the net budget is positive in at least one of thesystems (or parts of it). The findings of Koerner (1964) and Robin et al.(1968), together with the estimates of Giovinetto and Zumberge (in press),indicate that the eastern part of the Ross Ice Shelf system may includebasin(s) which contribute a large share of the net mass gain in the two-partsystem.

An alternate (heuristic) model

The viability of the hypothesis that at present the response of the icesheet is bi-modal to the climatic regime is not affected by a considerationof a possible decrease in the rate of sea level change since the 1950's.Assuming that the rate of sea level change is close to zero or that a sea-levelrise, if any, is due for example, to an increase in the mean temperatureof the ocean, an alternate model of the peripheral province can be statedby ascribing to it a negative budget between 3 x 1017 g yr - 1 and 4 x 1017

g yr - 1 (Table 2). This reduces the rate of mass output from 22 x 1017

g y 1 to approximately 19 X 1017 g yr-1. It may be of significance thatthis total output figure for the peripheral province amounts to a meanoutputf of approximately 9 X 1013 g km"1 yr"1. A comparable rate ofoutput has been estimated (8 X 1013 g km-1 yr"1) by cross examining

* Such as: (i) The relationship between continental isostasy and the depth ofocean basins; (ii) The variability of the rate of heat exchange at the air-sea interfaceand of geothermal heat flux; (iii) The effects of crustal differentiation on the shapeof the geoid or of erosion and deposition on the mean porosity of the upper crust,etc. The probable secular variability of these phenomena cannot be easily fittedwith the short-interval variability apparent in sea level records, except for a possiblevariability of the rate of heat exchange at the air-ocean interface.

f The length of the ice terminus, excluding segments BC, EF, IJ and J'K, isapproximately 20,500 km.

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MASS BUDGETS : ICE AGES 357

twelve independent mass budget estimates for the whole ice sheet(Giovinetto, in press). This mean output rate was obtained by assigningspecific ablation rates to particular glacier forms; the estimate, however,includes the drainage sections of the interior province, i.e. a total lengthof approximately 22,500 km.

The alternate and heuristic model of the ice sheet shown in Table 2still requires a bi-modal response to climate. Modifying the regimen ofthe interior province by adopting the smaller of the two budget estimates(Table 1), and to maintain balance (Table 2), the peripheral province isrequired to account for an input of 16 X 1017 g yr-1, and an output of19 X 1017 g yr-1. The net budget for the peripheral province is— 3 X 1017 g yr -1, and for Antarctica is zero. As stated, the modelclosely fits the conclusion reached by Dolgushin et al. (1962) followingthe classical procedure of estimating the net budget for Antarctica as awhole: "The available evidence indicates that the ice sheet is in a stateof equilibrium, but it is possible that the mass is somewhat increasing inthe inland regions." To fit the alternate model, the only requiredmodification of their statement is the assertion of a positive budget in theinland regions.

AcknowledgementsIt is a pleasure to acknowledge the critical comments offered by C. R.

Bentley and W. Schwerdtfeger. The research was supported by NationalScience Foundation Grant GA-245 to the University of Wisconsin.

REFERENCES

BEHRENDT, J. C. 1962. Geophysical and glaciological studies in the FilchnerIce Shelf of Antarctica. J. Geophys. Res., Vol. 67, No. 1, p. 221-34.

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Climatic causes of alpine glacier fluctuation, southern Victoria

Land

BY

WAKEFIELD DORT, JUN.Department of Geology, The University of Kansas, Lawrence,

Kansas, U.S.A.

Introduction

Although southern Victoria Land is well known for the present develop-ment of "oases" or dry (i.e. ice-free) valley areas, there is ample evidencethat this region has been much more extensively glacierized in the past.Till and erratics are widespread; recessional moraines are numerous.The retreat has affected all types of glaciers—outlet glaciers from theinterior ice cap, piedmont glaciers along the coast, and local alpineglaciers emanating from cirques and high basins. Field evidence suggeststhat fluctuations of the alpine glaciers have been caused by local climaticvariations in the mountainous area which, in turn, reflect regional changes.