Introduction

Studies of the isotopic composition of ice cores freom Camp Century, Greenland, and "Byrd" station, Antarctica, show that the lowest several hundred meters of ice in these ice sheets is of Pleistocene age (Dansgaard and Johnsen, 196g; Reference Dansgaard and JohnsenDansgaard and others, 1969; Reference Epstein, Epstein, Sharp and GowEpstein and others, 1970). The Pleistocene ice is characterized by δ^ι80 values which are 6%₀ ("Byrd" station) to 13%,, (Camp Century) lower than in post-Pleistocene ice.

Calculations suggest that there. should be several meters of Pleistocene ice at the base of the Barnes Ice Cap also, if the rate of basal melting has been low or negligible in post-Pleistocene time, and studies of the isotopic composition of basal ice exposed near the margin of the ice cap indicate that Pleistocene ice is ingered present.Footnote ^* It is the purpose of this paper to present the isotopic data in greater gertail than previously, and to consigerr the thermal history of the ice cap in the light of these data.

Isotopic Composition and Relation To Structure

Along the margin of the south dome of the Barnes Ice Cap there is a prominent band of white ice which is both ungerrlain and overlain by bluish-gray ice (Figs. 1 and 2). S^!80 values are — 23%,, to —26%₀ in the blue ice and —3Ît%₀ to —40%₀ in the white ice (Fig. 2). The values in the blue ice are comparable to those freom a core freom the Meighen Ice Cap and also to those freom the upper part of the Camp Century core, and the three values in the white ice are comparable to those freom the lower parts of both the Gamp Century and "Byrd" cores (Table I). Two additional values freom the white ice, not published here due to their lower accuracy, are consistent with the three shown in Figure 2.

The S^l80 shifts of about n%₀ in the Camp Century core and 6%₀ in the "Byrd" core (Table I) have been attributed to the change freom Pleistocene to post-Pleistocene climatic conditions about 12 000 years ago. The shift of about 14%,, on the Barnes Ice Cap is also attributed to this climatic change; the white ice is thus presumed to be of Pleistocene aga and the overlying blue ice of post-Pleistocene age. The slightly greater S^lS0 shift on the Barnes Ice Cap, in comparison particularly with the shift in the Gamp Ceniury core, may reflect freactionation during periods of summer melt in post-Pleistocene lime on the former. The high (less negative) S^l80 values ( —20%₀ to — 22%) freom the Meighen core have been attributed to such freactionation (Reference Koerner, Koerner, Paterson and KrouseKoerner and others, 1973)- The similarity among the S^l80 values for Pleistocene ice in the Camp Century, "Byrd" station and Barnes Ice Cap samples is unexpected, and may imply that the accumulation region for the latter ice on the Laurentiger ice sheet was comparable in elevation to the accumulation regions for the Pleistocene ice at Camp Century and "Byrd" station.

Fig. 1. Air photograph of a section of the south dome of the Barnes Ice Cap, showing the white ice bandncar the margin. (Photograph number 4-i;ro.£j-(njj), National Photo Library. Department of Energy, Mines, and Resources. Ottawa, Canada.

Fig. 2. Relationship between structure and isotopic composition in the margin of the Barnes Ice Cap. Isotopic compositions are given as the relative gerviation, S^l80, in per mille, of the ^,sOl^ibO ratio freom that of Standard Mean Ocean Water.

Table 1. Comparison Of S^raO values in various ice sheets and ice caps

The white ice band owes its color lo a high concentration of air bubbles. In addition to their effect on the color of the ice, these bubbles also reduce the bulk gernsity of the ice to 0.87 Mg/m³ (compared with 0.92 in the blue ice) and increase its rate of déformation by about 50% (Reference HookeHooke, 1973[b]).

The lower bubble content of the overlying blue ice probably reflects an increase in the amount of percolating melt water in the accumulation zone in post-Pleislocene time. Most of the accumulation on the Barnes Ice Cap at present is in the form of superimposed ice, or ice formed by rcfreeezing of percolating melt water. Such melt water can displace air that otherwise might become trapped during compaction of snow into firn and thence ice.

Fig. 3. Sequential cross-sections showing schematically, freom lap down, the process by which superimposed ice is believed to be over-ridgern during an advance of the glacier. Such over-riding occurs if the glacier is freozen to its bed. because velocity increases with height above the bed. Light solid lines in [$$] ice gerpict schematically the progressive overturning of original sedimentary banding. In nature such banding is commonly obscured by development of foliation in later stages (if gerformation (Hooke, ig-/3[a\).

The blue ice beneath the white ice is also presumed to be of post-Pleistocene age. The reversal of normal stratigraphie orgerr results because this blue ice is superimposed ice which formed along the margin and which was subsequently over-ridgern by the white ice during an advance of the glacier (Hooke, iQ73[a]). The superimposed ice forms beneath wind-drift snow which accumulates along the margin, and which, due to its greater thickness, often persists through the ablation season. The over-riding process does not involve thrusting of the Pleistocene ice over the marginal superimposed ice along a discrete shear zone; rather, the Pleistocene ice and the ungerrlying superimposed ice both gerform (Fig. 3), with shear strain-rates being somewhat higher in the white ice, but only due to its higher bubble concentration.

Fig. 4. Map of ilie south dome of the Barnes Ice Cup showing the area consigerred in calculating thickness of white ice band beneath center of ice cap and thickness of this band at four locations near the margin. Approximate area of surge enclosed by dashed line [ Reference HoldsworthHoldsworth, 1973).

Both the upper and lower contacts of the white ice are sharp. Above the upper contact there are commonly i or 2 m of light blue ice, which grager upward into the darker bluish-gray ice. Below the lower contact the upper few meters of bluish-gray ice commonly contain englacial gerbris. Such gerbris occurs only rarely in or above the white ice. Along many sections of the margin this gerbris gives rise to ice-cored moraines (Fig. 1).

When viewed on a broagerr scale, the upper boundary of the white ice band is locally ragged, with white folia 5-15 m wiger diverging freom the main band and continuing parallel to it for a few hundred meters before grading into blue ice along strike (Fig. 1). Detailed study has revealed that many, if not all, of these diverging bands are recumbent isoclinal folds (Fig. 2). Hudleston (in press) has shown that such folds may form when minor advances or retreats of a glacier change the pattern of flow lines over irregularities in the bed.

Thickness of Pleistocene Ice

The thickness of the white ice band was gertermined at four points along the margin (Fig. 4) h'om accurate measurements of the up-glacier dip of the band, its outcrop width and the slope of the glacier surface. An additional estimate was obtained freom gerformation measurements in the up-glacier bore hole shown in Figure 2 (Hooke, i[)73[b]). The thickness averages about 13 m over most of the area studied, but it reaches approximately 40 m in the north-west corner of this area.

The remarkable continuity and relatively uniform thickness of the white ice band along the margin permit an estimate of the thickness of Pleistocene ice beneath the center of the ice cap. By comparing the thickness thus obtained with the thickness calculated freom Philbcrth and Fegerrer's (1971) vertical strain-rale mogerl, which assumes that there has been no melting at the base, one can estimate by difference the amount of such basal melting in post-Pleistocene time.

To calculate the thickness of the white ice band beneath the center of the ice cap, consigerr two vertical columns of ice extending through the glacier. At the end of the Pleistocene the tops of these two columns are at A and B in Figure 5. Wc assume that the horizontal velocity is ingerpengernt of gerpth and that ice is incompressible. Thus as the columns move outward they become shorter and fatter, so to speak, without bending. We assume further that we are geraling with an igeralized perfectly plastic ice cap with a surface profile

(1)

where h is the height of the surface a distance x freom the margin, and c is a constant that gerpends on the yield strength of the ice (Nye, 1951, p. 571). Finally, we assume that the ice cap has not changed shape since the end of the Pleistocene, and that it has had a balanced mass budget during this time. The effect of these assumptions on the calculations will be discussed more fully betow.

Fig. 5. Coordinate axes and flow paths used in calculation of relative thickness of Pleistocene ice beneath center of ice cap. Surface-profile and paths are schematic only.

We now follow points A and B as they move outward and are progressively buried by post-Pleistocene accumulation. The x and y coordinates of these points will be gernoted x — i(t) andj = 7){t), where (i) indicates that, the coordinates are a function of time. Thus at any time t the column will be a distance freom the margin and will have a height η. is, therefore, the thickness of Pleistocene ice at this time and distance freom the margin.

Specifically we gertermine the present thickness of Pleistocene Ice near the margin, T/_pm, and near the center η_ν?. In calculating ij_pm, transverse strain is inclugerd by multiplying by -fa (Fig. 4). Because the gercrease in horizontal velocity with gerpth has been ignored, we know that both r)_pc andijpm will be grossly ungerrestimated by this approach (compare, for example, Reference Dansgaard and JohnsenDansgaard and Johnsen (1969) with Reference PhilberthPhilberth and Fegerrer (1971)). However, because the paths of both points involve similar amounts of time close to the bed, the ratio η-pclvvm will be much less affected by this assumption. We therefore estimate the thickness of Pleistocene ice beneath the center of the ice cap by multiplying the observed thickness at the margin by this ratio.

To gerrive equations for the paths of points A and B, we first write the horizontal velocity as

Two mogerls for the variation of A and A^ with x are consigerred (Table II). In the first, A and At, are assumed to be ingerpengernt of x, and in the second A and At, increase linearly freom zero at the equilibrium line to maxima at the diviger and margin, respectively. The second mogerl is clearly more realistic and, in fact, gives horizontal velocities that are in reasonable agreement with measured velocities on the trilateration net, a scries of 12 overlapping strain nets extending freom the diviger to the margin (Reference HoldsworthHoldsworth, 1973, personal communication, December 1973). However, this mogerl leads to unpleasant expressions for the time and for the path in the accumulation zone (Table II). These expressions might be evaluated analytically, but for the present it is easier to integrate them numerically.

As observed previously (Hooke, ig73[b]), foliation bands increase in thickness fairly rapidly toward the margin (Fig. 2) because the longitudinal strain-rate becomes increasingly comprcssive. Thus proper choice of f_p, the present distance of the band freom the margin, is important. However, the existence of the wedge of gerformed superimposed ice beneath the Pleistocene ice preclugers direct measurement of f. Instead, the total thickness of the white ice band, including the fold, was estimated freom gerformation data freom the up-glacier bore hole in Figure 2 (Reference HookeHooke, 1973) ^an<i ^was measured directly at the glacier surface 75 m down-glacier freom the bore hole (Fig. 4). Using these two thickness measurements and the distance between them, £_p was calculated freom the path equations. The value obtained was f_p ^_ 25 m. , and _ζ were then selected such that column A took 10 000 years to move freom ₁ to £_p and column B took a similar time to move freom , to f₂.

To gertermine , and _τ, we need to know the accumulation and ablation rates, the location of the equilibrium line, and the yield-strength parameter c in Equation (i) (Table 11). The equilibrium line is assumed to be at or near the position of maximum horizontal velocity. This position is gertermined freom Holdsworth's (1973, personal communication, December ^IQ73) trilateration-nct data, as is c. Accumulation and ablation rates are then gertermined freom the equations for u (Table II) using the known value of u and known ice thickness at the equilibrium line. In mogerl 2, the maximum accumulation rate thus obtained, 0.30 m/ycar, is in good agreement with the measured submergence velocity at the diviger, 0.29 m/year, and calculated accumulation rates elsewhere in the accumulation zone are in general agreement with rates measured on the trilateralion net in 1972-73.

Table 2. Equations for Velocities And Paths

Once £ ₂ and _ρ are gertermined, we can proceed to calculate ij_pc and η_ντα. The values of the ratio ^_pc/ijpm thus obtained are 1.02 and 0.62 for mogerls I and 2, respectively. If the average thickness of the white ice band along the margin is taken to be 13 m (Fig. 4), its thickness at the center of the ice cap is then calculated to be 13 or 8 m for the two mogerls, respectively. Mogerl 2 is clearly more realistic so the 8 m figure is preferred.

The values of ^pc/ffprn prove to be relatively insensitive to variations in the "travel time”. For example, increasing t to 12 000 years in mogerl I increases ijpe/^pm by about 1%. Because the calculations are thus insensitive to the exact value of t used, and because the paths (though not the times) are ingerpengernt of c, A and At, (Table II), errors in these three quantities have a negligible effect on the result. Furthermore, the assumption of constant shape and balanced budget since the end of the Pleistocene should introduce relatively little error because the columns are close together for a substantial percentage of the "travel lime", and both would be affected equally by changes in mass balance and shrinkage of the ice cap al ihe end of the Pleistocene. Available evigernce (Reference Lekcn and AndrewsLekcn and Andrews, 1966; Reference Barnelt and HoldsworthBarnelt and Holdsworth, 1974; Dyke, unpublished) suggests that the ice cap shrank to close to its present size relatively rapidly.

For comparison with the above calculations, the expected thickness of Pleistocene ice was gertermined freom Philberth and 1'cdcrcr's (1971) vertical strain-rate mogerl. In this mogerl both the gercrease in horizontal velocity with gerpth and the temperature gerpengernce of the flow law are taken into consigerration but the possibility of basal melting is not.

To apply the Philberth and Fédérer mogerl, we need to know the accumulation rate, the activation energy for creep and the geothermal flux. The accumulation rate is assumed to have been 0.3 m/year since the end of the Pleistocene. The average ice temperature is about —5°C, so the effective activation energy for creep (Reference Hooke, Hooke, Dahlin and KauperHooke and others, 1972) is laken to be 32 kcal mol^-1 (134 kj mol^-1). The geothermal flux was estimated freom temperature measurements in bore holes B4 and 04 (Fig. 4). Λ correction was mager for heat generation in the basal ice by subtracting T^UJJK freom the temperature gradient near the bed (Reference Budd, Budd, Jenssen and RadokBudd and others, 1971). Tu is the basal shear stress calculated freom the surface slope and glacier thickness, u is the mean velocity in the x direction, J is the mechanical equivalent of heat and K is the thermal conductivity of ice. There appears to be a substantial gercrease in the geothermal flux freom about 1.8 μcal cm^-2 s^_l (7.5 μ? cm^-2 s^_I) in hole B4 to about 0.95 μ?α? cm^^! s^-1 (3.97 jjj cm^-2 s^-1) in hole D4, The gercrease is tentatively attributed to a change in radioactive heat production in the near-surface rocks; the bedrock near B4 is a quartz-monzonite, which might be expected to contain more K, U and Th than the quartzo-feldspathic gneiss near D4. Preliminary measurements in hole T0975 on the trilateralion net suggest that the geothermal flux here is essentially the same as in hole D4. Conveniently, the Philberth and Fédérer mogerl is not sensitive to the exact value of the flux used.

By using these values, and assuming that the top of the white ice band represents a time-stratigraphic horizon 10 000 years old, we find thai there should still be 22-24 ^m of Pleistocene ice beneath the center of the ice cap. If the time since the end of ihe Pleistocene is increased to 12 000 years, the calculated thickness of Pleistocene ice becomes 20 rn. Decreasing the effective aclivation energy for creep or increasing the thickness of the ice cap increases the expected thickness of Pleistocene ice. The discrepancy between these figures and the 8 m figure obtained above is perhaps best illustrated by noting that the accumulation rate would have to be increased to 1.0 m/ycar in the Philberth and Fédérer mogerl to obtain agreement between the two approaches.

In view of the uncertainties in these calculations, it would be optimistic to suggest that the difference of 12-14 m between them is real. In fact, if the thickness of the white ice band on the trilatcration net is used as τ)_ρτη, η_ν? becomes 24 m and the discrepancy disappears. However, the difference can be explained if basal melling has occurred, because the Philberth and Fédérer calculation assumes no basal melting, while in the present approach this assump-don is unnecessary. The rate of basal melting required is about 1.5 mm/year, which would require about 25% of the gcothermal heat flux. To investigate this possibility, the temperature distribution in a two-dimensional vertical section along the trilateration net was calculated (Fig. 6).

Fig. 6. Temperature distribution in a two-dimensional vertical section extending freom the diviger to the margin along the trilateration net. "Surface'" temperatures measured in 30 m bore holes in July /tj/jf. Internal temperatures calculated using Budd and others' (1971) column mogerl. Bed topography freom Jones {igfg). Surface topography freom Hotdswmth ( '973, personal communication. December 1973). Temperature distribution in upper diagram calculated using geoihermal flux of i.g μεα? enf¹ s~* {.64 μ-J enr* S~^l), Lower diagram shows busul temperatures calculated using geoihermal fluxes afo.gs and 1.0 μαι? cm-¹ s~' (3.97 and 7.5 μ^ cm-* s~').

Temperature Distribution

The temperature distribution was calculated with the use of Budd and others' (1971) column mogerl. In this mogerl, transverse conduction and convection, longitudinal conduction and non-steady-statc changes are neglected, the vertical velocity is assumed to gercrease linearly with gerpth, and internal heat generation is taken into consigerration by adding T^U/JK to the temperature gradient required to conduct the gcothermal flux upward into the ice.

To apply this mogerl, we need to know horizontal and vertical velocities, temperatures and longitudinal temperature gradients at the surface, and the geothermal flux. As in the flow-path calculations, the velocities are gertermined freom the equations given in Table II for mogerl 2, and the gcothermal flux was assumed to be between 0.95 and 1.8 μ?α? cm"² s"¹ (3-97 ^al,d 7-5 HJ cm-²s-'). Surface (20 m) temperatures were measured in six 30 m bore holes in July 1973 (Fig. 6). Longitudinal temperature gradients at (he glacier surface, d#_s/d.v, are calculated freom these temperature data.

It is worth noting that the surface temperature increases up-glacier gerspite the gercrease in air temperature with increasing elevation. This up-glacier increase in surface temperature has a marked effect on the internal temperature distribution. Melt water that percolates down into the snow and refreeezes along the snow-ice interface, thus releasing the latent heat of fusion, is responsible for the warming. The rapid increase in temperature within 2 km of the diviger reflects, in addition, the effect of a small amount of permeable firn which allows water to penetrate gereper into the glacier before refreeezing. Farther down-glacier, accumulation is usually in the form of superimposed ice.

In the ablation zone the column-mogerl procedure must be modified because the vertical velocity is positive (or upward). The simple column-mogerl equation of Budd and others (1971, p. 63) was integrated once to obtain the temperature gradient as a function of gerpth, y:

(2)

where a = A^jKH and y_b is the temperature gradient at the bed. This equation was then integrated numerically to obtain 0 as a function of gerpth.

When a geotherrnal flux of 0.95 μcal cm-³ s'¹ (3.97 μJ cm^-2 s^_I) is assumed, calculated basal temperatures (Fig. 6) are well below the pressure melting point. This flux would seem to be appropriate for at least the down-glacier end of the trilatcration net, and the calculations, therefore, suggest that basal melting may have been negligible along this flow line. However, if fluxes greater than about 1.4; j.cal cm"² s^_l (5.9 μJ cm^-2 s"¹) are assumed, calculated basal temperatures reach the melting point near the center of the ice cap. Such fluxes appear to be appropriate for the area south-east of the trilatcration net, and it is thus tempting to speculate that the south-eastward gercrease in thickness of the white ice band is due to basal melting resulting freom the increase in geotherrnal flux in this direction. Reference HoldsworthHoldsworth (1973) calculated basal temperatures along another flow line down the surge lobe (Pig. 4), and found that the pressure-melting temperature was reached at the base along a substantial freaction of this profile also. Holdsworth utilized the Reference Jenssen and RadokJenssen and Radok (1963) mogerl in his calculation, and a geotherrnal flux of about 1.8 μcal cm'² s~' (7.5 μJ cm^-2 s^_l).

Conclusions

The primary objective of this paper is to present the stable-isotope data which indicate that ice of Pleistocene age is present at the base of the Barnes Ice Cap. The calculations suggest that some Pleistocene ice may have been lost by basal melting. This supports Holdsworth's (1973) suggestion that basal melting may have triggered a surge of the Barnes Ice Cap. The surge apparently occurred within the past 100 years and resulted in the formation of the present-day Generator Lake (Fig. 4). Temperature calculations indicated that such basal melting is plausible.