Velocities and strain-rates

Drainage Basin 5 extends approximately 30 km from the divide to the terminal ice cliffs (Fig. 1). To obtain measurements of ice-surface velocities and strain-rates, a network of 24 stakes was positioned within the basin (Fig. 2a). The stakes were arranged in two offset lines to form a series of triangles. Initial stake positioning was assisted by use of a satellite-navigation system, accurate to ±30 m. Each 5 m long aluminium pole was then frozen into a steam-drilled hole to a depth of 2–3 m. In the upper part of the basin, where ice-surface slopes were generally less than 1°, stakes were usually set 2–2.5 km apart. Towards the lower part of the network, distances between stakes were more normally 1–1.5 km. This ensured inter-visibility in what was an area of relatively rough ice-surface topography (Reference Dowdeswell and McIntyreDowdeswell and McIntyre, 1987). The network was orientated down the centre of the drainage basin, approximately parallel to the direction of maximum ice-surface slope. It was truncated, however, about 10 km from the tide-water margin of the basin due to increasingly heavy crevassing (Fig. 3).

After its emplacement, the trilateral network was surveyed in May 1986, and again during May 1987. The nearest bedrock outcrop to the network was 17 km distant, at Isispynten (Fig. 2), across severely crevassed ice. Point Y, located approximately at the ice divide, was therefore treated as fixed over the period of observation.

Fig. 3.

Vertical aerial photograph of surface crevassing in the lower part of Basin 5, including the terminal ice cliffs (Norsk Polarinstitutt Id. No. S77 1213; 21 August 1977). The scale bar is 1 km.

Angular and distance measurements were taken using a Wild T-2 theodolite and DI-3000 electronic distance-measuring instrument (EDM). At each station, horizontal and vertical angles to each of the four surrounding stations were measured. Individual angular readings were made to 1″ of arc. Distances were taken only along diagonals between the two stake lines, and were measured with a standard deviation of 7 mm over 2 km. Three sets of direct and reverse theodolite readings were made at each station, with a spread of less than 5″ of arc being permitted. Where greater spreads occurred, additional sets of readings were acquired. At three stations, results with errors of up to 15″ were retained. In two cases, poor weather prevented additional observations being made. In the third case, a 3 d break in the survey schedule caused by a blizzard meant that ice deformation between stations inflated errors. Errors were not distributed through the network, because the survey traverse did not begin and end at a single fixed point, from which cumulative errors could have been calculated. A correction for Earth curvature was applied to points in the network, but refraction corrections were minimal and, therefore, ignored.

Ice-surface and bed topography

Ice-surface and bedrock topography are derived from airborne radio echo-sounding (RES) conducted at a frequency of 60 MHz using SPRI Mk IV equipment. Details of the methods of data acquisition and reduction were reported by Reference Dowdeswell and DrewryDowdeswell and others (1986). Aircraft navigation was linked to ranges from transponder stations on the ice-cap surface, which were fixed to an accuracy of ±2 m using satellite geoceivers. The ice-surface topography, bed morphology, and ice thickness of Austfonna were also described in that paper. However, because the whole of Austfonna, together with the other ice caps on Nordaustlandet, was discussed, the level of detail given for individual drainage basins was limited. After data reduction, all airborne geophysical information for Nordaustlandet was stored in a direct-access data base. The data for Basin 5 are analysed at a more detailed scale as part of the present study, and the flight lines along which data were collected are shown in Figure 1c. Bed topography is now presented as a 50 m interval contour map (Fig. 2b).

Mass balance

Mass-balance data come from three sources. First, digital Landsat Multispectral Scanner (MSS) data for Austfonna were enhanced on an image analyser to indicate the position of the transient snow line as it retreated up the flow line during the melt season. Secondly, the 24 stakes for velocity and strain measurements were also used to measure changes in snow-surface height between May 1986 and May 1987. Thirdly, several snow pits were dug and a 10 m long core was taken on Austfonna. The core, collected on Isdomen about 25 km south-west of Basin 5 (labelled Is in Figure 1b), was analysed for tritium content, and the depth of the 1963 horizon was identified.

Subglacial melt water

Digital Landsat MSS data were also used to examine the waters immediately offshore of the terminal ice cliffs of eastern Austfonna for the possible presence of plumes of turbid subglacial melt water. This information is a potentially important indicator of the subglacial hydrological and basal thermal structure of the ice cap. Incoming solar radiation can penetrate shallow water only at certain frequencies, and MSS bands 4 (0.5–0.6 μm) and 5 (0.6-0.7 μm) are most appropriate for detecting the presence of suspended sediments in near-surface water (Reference RobinsonRobinson, 1983). Pixel brightness values in these bands were, therefore, enhanced on an image analyser to test for the presence of such plumes. It was possible to distinguish between melt-water plumes, sea-ice floes, and cloud cover through their differing spectral responses across the four Landsat MSS bands. The relative brightness of each plume also declined with distance from its ice-cap source, indicating that mixing and sediment deposition were occurring progressively.

Ice-surface velocities

Horizontal ice-surface velocities in Basin 5 increase progressively from 1 m a⁻¹ near the ice divide to maxima of 46.8 and 38.9 m a^–1 at stations 14 and 17 on the south-west and north-east stake lines, respectively (Figs 2a and 5; Table I). Beyond these stations, located at 18 and 20 km from the divide, surface velocities begin to decline. It is a characteristic of many ice masses that the mean position of the equilibrium line over a period coincides with that of maximum ice-surface velocity (Reference PatersonPaterson, 1981).

In the upper 12 km of Basin 5, the orientation of the network deviates progressively from the direction of ice flow (Fig. 5). This is because the ice divide does not parallel the coast and the ice-surface contours lower in the basin (Figs 1b and 2a). The divide is orientated at between 25– and 40– to the coast, this difference approximating the shift in orientation between horizontal velocity vectors in the upper and lower parts of the network. Horizontal velocity vectors close to the divide are very variable in orientation, but that for station Ζ has a value of 090– (Table I). This approximates the orientation of the ice divide, which descends from the main summit of Austfonna downward towards the north-east of the island (Fig. 1b). The 352° orientation of the horizontal velocity vector at station X also indicates that flow has reversed beyond the ice divide (Fig. 5; Table I).

The deviation of ice-flow direction from the orientation of the trilateral network means that, in the upper part of Basin 5, stations in the south-west line will be down-flow line from those in the north-east line. This is reflected in higher velocities for stations in the south-west line, relative to their neighbours to the northeast (Fig. 5; Table I). The orientation of horizontal velocity vectors below stations 8 and 9 approximates the general orientation of the trilateral network at about 140° (Table I). Some variability is introduced, however, by the increasingly rough ice-surface topography in the lower part of the network (Fig. 4), where local surface slopes deviate from the general pattern of flow orthogonal to the coast by up to 25°.

Vertical velocity vectors are orientated downward through most of the stake network, and possess values between 0.5 and 2.0 m a⁻¹. In the bottom third of the network they progressively approach zero, indicating the proximity of the equilibrium line.

Strain-rates

Principal strain-rates

and , summarizing velocity gradients, have been calculated for a series of triangles within the stake network on Basin 5 (Fig. 2a). Values for the two principal strain-rates, and the orientation of , are given in Table II and illustrated in Figure 6, is positive for all triangles and represents extensional ice flow in a down-basin direction, whereas is negative and therefore compressional.

In more detail, the principal strain-rate ε, varied between 0.118 × 10⁻² and 0.642 × 10⁻² a⁻¹. Minima in the value of

occurred close to the ice divide and at the lower end of the trilateral network, with the highest values falling between 11 and 17 km from the ice divide (Table II; Fig. 6). Strain-rate was variable down the network but clearly lowest in the two triangles nearest to the ice divide. Its maximum value reached −0.481 × 10⁻² a⁻¹. The co-incidence of low principal strain-rates with the ice divide supports the assumption that there is little flow in this region and that station Y was an appropriate point at which to pin the whole stake network.

Table 1

Horizontal and vertical ice-surface velocities. stakes are located in figure 2

Fig. 5.

Horizontal velocity vectors within the trilateration network on Basin 5. Vector length is proportional to horizontal ice-surface velocity.

Fig. 6.

Principal strain-rates within the trilateration network on Basin 5. Vectors represent the magnitude and orientation of

and

.

Table 2.

Experiments (δ values are shown in parts per thousand)

The orientations of principal strain-rate

for different triangles, although following a general down-basin trend, are more variable than those for horizontal velocities (Figs 5 and 6). The effects of rough ice-surface topography, and the combination of diagonals between stations straddling convex and concave areas resulting from this roughness, may contribute to this variability.

Snow lines and accumulation

The behaviour of the snow line on Austfonna during the melt season can be monitored from Landsat MSS imagery (Fig. 7). For the 1978 and 1979 seasons, for example, the snow line in Basin 5 had retreated approximately 20 km from the coast, to an elevation of about 500 m a.s.l. (Fig. 7b). In detail, the situation is more complex because, especially where surface topography is rough, snow accumulation is very variable on a kilometre scale. These local topographic effects are illustrated by the residual snow areas on the summer aerial photograph of the basin margin (Fig. 3).

The accumulation area extends lower than the snow line, however, through the development of a superimposed ice zone (Reference SchyttSchytt, 1964, 1969). The importance of superimposed ice development has also been reported from the 239 m summit of Storøyjøkulen, north-east of Nordaustlandet, where nourishment comes entirely from the refreezing of surface melt water (Reference JonssonJonssen, 1982). On Basin 5, ice was observed directly below winter snow cover in shallow pits as far up the network as station 12 (480 m elevation).

Horizontal ice-surface velocities reach a maximum at stations 14 and 17 on the two lines (Fig. 2a; Table I), and their vertical component progressively approaches zero in the bottom third of the network. Given the tendency for surface-velocity maxima to be associated with the equilibrium line, this evidence suggests that the ablation zone may begin at an elevation of between 330 and 400 m. A 9.8 m ice core collected in 1983 about 25 km to the south-west of Basin 5 at an elevation of 374 m (Isdomen, labelled Is in Figure 1b) supports this inference. The core was analysed for tritium content and the 1963 horizon was identified at a depth of 1 m. The presence of the layer shows that the accumulation of superimposed ice is still taking place at this relatively low elevation, and indicates an average net accumulation of 47 kg m⁻² a⁻¹. The equilibrium line cannot be far below this level, and this conclusion supports Schytt's (1964) suggestion that the equilibrium line in north-east Austfonna is at approximately 300 m. As a consequence, the accumulation zone comprises about 65–70% of the surface area of Basin 5.

The rate and spatial variability of accumulation within the basin is not well known. Measurements of the change in snow-surface height around stakes in the trilateral network between May 1986 and May 1987 did not yield useful information on net mass balance. In each of these years, considerable snow accumulation took place during spring blizzards, and the snow-surface height appeared to be dependent on such short-term factors rather than providing a useful record of the annual balance. Soviet analysis of a 204 m core taken at the summit of Austfonna, 30 km distant and 780 m in elevation, has shown an accumulation rate of between 400 and 500 kg m⁻² a⁻¹ over approximately the last 400 years (personal communication from V. Zagorodnov). Schytt (1964) recorded a similar value for net accumulation (530 kg m⁻² a⁻¹) on the summit of Vestfonna (622 m in elevation). Analysis of total β activity in a Soviet core from Vestfonna gave an accumulation rate of 810 kg m⁻² a⁻¹, averaged over a 19 year period (Reference Punning, Martma, Tyugu, Vaykmyae, Pourchet and PinglotPunning and others, 1985). Reference AhlmannAhlmann (1933) had earlier analysed snow stratigraphy in a number of pits on Austfonna and Vestfonna. He suggested a mean net balance of only 60–70 kg m⁻² a^°1 for the

Fig. 7.

The location of snow lines on Austfonna through the melt season. a. Landsat Multispectral Scanner (MSS) band 7 image, showing the position of the snow line on 13 August 1978 (Id. No. 3016112143). The part scene is 130 km wide. b. Locations of the snow line from four Landsat MSS images. Basin 5 is indicated.

accumulation zones, implying a very negative total net balance for the ice caps. However, the observations of both Schytt and Soviet workers on net accumulation show that these earlier values represent a considerable underestimate, probably accounted for by the complexity of the snow stratigraphy on Nordaustlandet.

Assuming an accumulation area of about 440 km² (65% of the basin), an averaged accumulation rate of between 0.3 and 0.4 m a⁻¹ of ice equivalent would yield a total net gain of 132–176 × 10⁶m³a⁻¹ of ice for that part of Basin 5 above the equilibrium line. A hypsometric curve for the accumulation area shows that approximately 45% of the accumulation basin lies above 600 m. The averaged accumulation rate is therefore weighted towards the values observed at higher elevations.

Balance velocity at the equilibrium line

Balance velocity represents the average velocity required to transport, through a given section, the areally integrated net mass balance above that cross-section. There is an assumption that the ice mass is in a steady state. Negative departures of balance velocity from observed average velocity indicate that net-volume change up-glacier is negative, whereas positive departures signal positive volume changes. Balance velocities (K^) are calculated from the following mass-continuity equation:

where W and H are the transverse width and mean ice thickness at a given section across the drainage basin, D_a is basin surface area, and A is the mean accumulation rate above the cross-section. No correction was made for the shape of the cross-section, since the geometry of the transverse profile is relatively simple.

The balance velocity is calculated for a transverse profile running through station 19 which, at an elevation of 330 m, approximates the position of the equilibrium line. The width of this cross-section through Basin 5, the mean ice thickness, and the basin area above it, are obtained from Figure 2. The average accumulation is less well defined at 0.4 ± 0.1 ma⁻¹, and balance velocities are therefore calculated for ±0.1 of the assumed mean value. The result is a balance velocity of 36.6 ± 9 m a⁻¹. Comparison with measured surface velocities at stations 17, 19, and 20 (39, 37, and 36 m a⁻¹; Table I) shows that the observed and calculated values are very comparable. This implies either that Basin 5 is approximately in steady state at the present, or that the spatially averaged values of net accumulation discussed above and used in calculation are considerably in error.

Ablation and iceberg calving

There are no data from the ablation area of Austfonna which can be used to estimate reliably the amount of mass loss through melting at relatively low elevations. In Basin 5, such measurements were particularly problematic due to heavy crevassing (Fig. 3). Only an order-of-magnitude value for the mass lost by iceberg calving can be presented.

Mass is lost at the tide-water terminus of Basin 5 through iceberg calving and by direct melting of the terminal ice cliffs. Both are difficult to quantify. Tabular icebergs of up to 600 m in length have been observed offshore of the east coast of Austfonna during airborne radio echo-sounding flights, and isolated icebergs can also be identified on aerial photographs and Landsat satellite imagery. However, remotely sensed data are not available with sufficient frequency to provide a useful time series of observations. Iceberg-calving rates cannot therefore be reconstructed directly.

However, order-of-magnitude calculations of the combined mass lost at the terminal ice cliffs from the processes of iceberg calving and direct melting may be made. Assume that Basin 5 is in steady state, with a velocity at its terminus of 40 m a⁻¹, and that it averages approximately 130 m in thickness (from RES data) along its 20 km interface with marine waters. For the ice-front position to be maintained, a mass of 100 × 10⁶ m³ a⁻¹ must be lost through the combined action of the two processes. Halving the velocity will clearly halve the rate of mass loss. The assumption that the ice front is stable is difficult to test because, although Landsat images are available for several different years, there is insufficient rock outcrop to fix accurately the ice front of Basin 5. However, the terminal ice cliffs of the basin immediately to the north-east of Basin 5 retreated by almost 500 m between 1976 and 1981 (Reference DowdeswellDowdeswell, 1986b). If the terminus of Basin 5 was also retreating during that period, the mass lost through calving may have been more than double that suggested above.