Navigation

Positional accuracy along each flight was limited by inertial navigation system drift. The 32 flight closures for the whole survey have a mean of 2.9 km and a standard deviation of 1.9 km, with a maximum closure of 7.4 km. Navigational errors of 1 or 2 km are also indicated by the positions recorded when passing over or near satellite-surveyed ground stations. Corrections to each flight were applied on the basis of an assumed linear drift with time.

Fig. 1. Map of the Siple Coast Project study region, showing 1987-88 and 1988-89 airborne radar coverage. Flights in 1987-88 (this paper) covered the nine blocks a-i. Flights in 1988-89 (Reference Retzlaff and BentleyRetzlaff and others, 1993) covered six blocks: A, B, C, E, 10 and 20. The heavy line denotes the grounding line. The origin of the rectangular grid coordinate system used on this and subsequent maps is at the South Pole; grid north is toward Greenwich and therefore toward the top of the map. Squares have sides of length equal to 1° of latitude. The boundaries of the glaciological features are taken from Reference Shabtaie and BentleyShabtaie and Bentley (1987).

Fig. 2. Map of the nine blocks in the 1987-88 survey, showing all the radar-sounding flight-lines. The transects along which the reflection-strength profiles of Figure 3 were drawn are indicated by the thinner hachured line segments; those along which the averages of Figure 6 were taken are indicated by the wider hachured segments.

Crossover corrections

The crossover errors for ice thickness (differences in measured values where two flight-lines cross) were used first to evaluate the effectiveness of the linear drift correction for navigation. Generally speaking, the standard deviation in ice-thickness crossover differences was substantially reduced by application of the drift correction in blocks where it was initially large (e.g. from 28 to 20 m (30%) for block a), whereas small standard deviations tended actually to be increased (e.g. from 6 to 8 m (33%) in block h). Overall, the standard deviation was decreased by 13%. Crossover errors remaining after the drift correction were then removed by linear distribution of the errors within each transect segment between two crossing points.

Interpolation

For mapping, the data had to be interpolated from their distribution every 60m along widely spaced transects to an evenly spaced grid. A minimum-curvature gridding program was used for this, although two other interpolation methods (kriging and inverse-distance) were considered. Minimum curvature is very fast and produced smooth contour lines that enhanced the trends of topographic features. (Kriging produced slightly belter maps but took much longer to compute.) The data were gridded at a density of one grid point every 1.11 km (0.01° of latitude). No smoothing was performed on the data after they were gridded. A standard public-domain contouring routine (Generic Mapping Tools) was applied to the gridded data to produce the ice-thickness map.

Basal-reflection strength

The basal-reflection strength, P _s, is the difference between the actual power in the basal echo, P _e, and a model for the received power, P _r, that uses the aircraft height above the ice, the ice thickness and the equipment calibrations to compensate for geometrical spreading, dielectric absorption and the receiver gain function. The model is given by

where P _tx is the transmitted power (500 W), P_rx is the gain before the calibration-insertion point of the system (includes transmit/receive-switch and feed-cable loss), P _tvg is the receiver gain after the calibration-insertion point, R _g is the geometrical spreading loss, given by

h _a is the aircraft height, h _i is the ice thickness, n is the index of refraction (1.75), λ is the wavelength in air (6 m at 50 MHz), G is the antenna gain (6 dB), R _t, is the loss due to dielectric absorption in the ice column, T _a is the transmission loss at the ice-air boundary (about 1 dB), S _v is the loss due to small-scale volume scattering in ice (about 6 dB), and S _b, is the scattering loss due to a rough ice-rock interface (about 0 dB). This model is adapted from the one used by Reference Shabtaie and BentleyShabtaie and others (1987), from whom we also obtained the numerical values cited. The P _tvg term was added because the radar system used in 1987 88 had a time-varying gain that provided more gain later in the record to compensate for the increasingly weak echoes.

The numerical value of the dielectric absorption, R _t, is not well known, both because the temperature in the ice column is not measured and because the temperature coefficient of absorption itself is not well determined, perhaps owing to a general failure in the literature to take varying impurity concentrations into account (Reference Corr, Moore and NichollsCorr and others, 1993). We therefore follow the procedure used by Reference Shabtaie and BentleyShabtaie and others (1987) and assume that the strongest reflections have a relative reflection strength of 0 dB. In our survey, the strongest echoes are found from the base of the ice shelf in front of Ice Stream C, a location where the reflection coefficient, from sea water, is maximal (theoretical reflectivity -0.6 dB). This leads to a value for R _t of 17.3 dB km^-1, a reasonable value (cf. Reference Shabtaie and BentleyShabtaie and others, 1987).

Measurements of raw received power, averaged over I km segments of flight line, are accurate to about 1 dB, the standard deviation of the values within a single segment. All the parameters in Equation (1) except R _t can be considered constant across our survey (the error in R _g that arises from uncertainties in h _a and h _i is less than 0.1 dB). Lateral variations in basal-reflection strengths (Fig. 3), as finally calculated, therefore reflect a combination of variations in the reflecting characteristics of the bed, which depend on its roughness and the impedance contrast between the ice and the bed, deviations of actual absorption in the ice from that assumed, and scattering of the downgoing and upgoing signals by large-scale disturbances within the ice (principally near-surface crevasses), to an accuracy of about ± 1 dB.

Ice-thickness map

The map of ice thickness that results from these high-density surveys (Fig. 4) is remarkably similar to the map previously produced from reconnaissance surveys (Reference Shabtaie and BentleyShabtaie and Bentley, 1988). Our analysis so far has revealed no significant differences between the two, so we will not discuss this map further here.

Reflection-strength map

As stated above, the reflection-strength map (Fig. 5) can be expected to depict variations in four quantities: basal reflectivity (a function of the impedance contrast), absorption in the ice, scattering from crevasses, and basal roughness (Reference Robin, Evans and BaileyRobin and others, 1969). We believe that the first three factors enter significantly into the variations seen in the map; the fourth is unlikely to contribute more than a few dB for a realistically rough surface and an outgoing pulse longer than ~0.2 (Reference Robin, Evans and BaileyRobin and others, 1969); the outgoing pulse length in our system is 0.3.

The reflection strengths P _s not only vary widely across the map, but also show strongly regional characteristics. We will examine the differences between four regions: Ice Stream B, Ice Stream C, ridge BC and the Ross Ice Shelf; to quantify those differences we have calculated the statistical characteristics of P _s along representative transects across each (Fig. 6 and Table 1; see Fig. 2 for locations of the transects). We will examine Crary Ice Rise separately, because the glaciological conditions there change so rapidly in short distances that the statistical approach is not very helpful.

The strongest reflections, not surprisingly, come from the Ross Ice Shelf. (We have only considered the portion of the Ross Ice Shelf in front of Ice Stream C, because of uncertainty as to just where the grounding line really is between the Ross Ice Shelf and Ice Stream B (Reference Shabtaie and BentleyShabtaie and Bentley, 1987; Reference BindschadlerBindschadler, 1993). The mean of P _s is -5 dB (Table 1); the peak in the distribution curve is at about -3 dB (Fig. 6). The distribution is strongly skewed, which we interpret to mean that there are several factors that can diminish P _s from the ideal obtained from a smooth reflector through ice without scattering losses — buried crevasses, a rough, mushy or unfavorably shaped interface, basal freeze-on of sea ice — but little that can enhance it. The absolute value of P_s is not significant; it simply represents a bias of about 2.5 dB (the difference between -3 dB and the theoretical reflection loss from a boundary between ice and sea water of-0.5 dB) in our calibrating assumption that the strongest reflection was at 0 dB.

On the grounded ice, the reflection-strength distribu-tions are approximately normal (Fig. 6). The mean difference in P _s between the Ross Ice Shelf and Ice Stream C is 8 dB, of which 3 dB can be attributed to the difference between the reflection coefficients from sea water and fresh water, respectively (Reference Shabtaie and BentleyShabtaie and others, 1987). The other 5 dB loss presumably is the effect of the subglacial sediment. (It is unlikely that there is any significant difference in the scattering losses from buried crevasses between Ice Stream C and the immediately downstream part of the Ross Ice Shelf, since the latter flows from the former.) Reference Shabtaie and BentleyShabtaie and others (1987) showed evidence for the pooling of water in some regions under Ice Stream C and its absence in other places; our results here accord with theirs, which may indeed explain the patchy character of P _s on Ice Stream C.

Fig. 4. Ice-thickness map from the 1987-88 survey. The contour interval is 50 m. The borders of the ice streams (from Reference Shabtaie and BentleyShabtaie and Bentley, 1987) are shaded.

It is noteworthy that the decrease in P _s between the Ross Ice Shelf and Ice Stream C is gradual, particularly across the grid south-central part of the grounding line (Fig. 5). This suggests that sea water may penetrate some distance inland from the grounding line, as suggested also by the recent observation of a tidal influence on subglacial earthquakes on Ice Stream C (Reference Anandakrishnan and AlleyAnandakrishnan and Alley, 1997). (Although Reference Anandakrishnan and AlleyAnandakrishnan and Alley (1997) discount propagation of the tidal influence in a subglacial water film because it would have to be several cm thick to produce the observed propagation speed, we note that Reference Shabtaie and BentleyShabtaie and others (1987) calculated just such a thickness for the water in the subglacial pools.) It is clear that the bed of Ice Stream C is not frozen, because if it were, P_H should decrease by some 20 dB (Reference JiracekJiracek, 1967). Apparently, the stagnation of Ice Stream C was not caused by its freezing to its bed. (This observation does not contradict either of the existing theories for the stagnation; both involve diversion of excess water, either into Ice Stream B (Reference Alley, Anandakrishnan, Bentley and LordAlley and others, 1994) or into channeled flow (Reference Retzlaff and BentleyRetzlaff and Bentley, 1993), but neither implies that the bed then froze.)

The average P _s on Ice Stream B is 7 dB less than on Ice Stream C. Since the beds of both are unfrozen, the difference must be attributable to some combination of crevasse scattering on Ice Stream B and differential absorption.

Absorption depends principally on temperature and impurities in the ice. It is unlikely that impurity levels vary much across the area mapped in this study. To begin with, the two ice streams draw their ice from the same interior region of the ice sheet. Furthermore, ridge BG is about the same distance as that interior region from the ocean north of Marie Byrd Land, the principal source of the moisture that precipitates in western West Antarctica (Reference Bromwich and Van LoonBromwich, 1984), so the ice there too probably has a similar concentration of ionic impurities, which come mainly from the ocean (Reference Corr, Moore and NichollsCorr and others, 1993). Direct evidence for similar impurity levels comes from Reference Langway, Herron and CraginLangway and others (1974) who found from measurements in a core from the Ross Ice Shelf that there was no consistent trend in cation concentrations with depth in the deeper part of the core, wherein depth is a proxy for distance inland from the grounding line. We will assume, therefore, that varying impurities do not cause significant differences in absorption between our sites.

As for temperature, there are, unfortunately, no actual measurements in the area of this survey; the closest are some 200 km upstream. Temperatures have been measured through the entire ice column at station UpB on Ice Stream B2, at station UpC on Ice Stream C, and at several sites on ridge B1/B2 (the “Unicorn”, Fig. 1) (Reference Engelhardt and KambEngelhardt and Kamb, 1994; personal communication from H. Engelhardt, 1997). At those upstream sites, the ice is colder at all depths (except near the surface) on the ridge than it is at the same relative depths on Ice Stream B; the temperatures at UpC are intermediate, but closer to those on the ridge. We have calculated the total absorption through the ice columns at the three locations, based on the assumption that the absorption constant varies in proportion to e^-E/RT , where T is the absolute temperature, R is the gas constant and E is the activation energy (taken to be 80 kJ mol^-1 from a fit to experimental data given by Reference Johari and CharetteJohari and Charette (1975)). We find that the total two-way absorption is the least on ridge B1/B2, 2 dB more at UpC and 8 dB more still at UpB. If these differences are transferred downstream unchanged (we believe it likely that the temperature difference is associated with I he widely different dynamic activity of the two ice streams and therefore would persist downstream), they imply that the smaller P _s values on Ice Stream B than on Ire Stream C could be caused entirely by the greater absorption in the warmer ice of Ice Stream B. The younger but still well-buried crevasses on Ice Stream B apparently do not cause significantly greater scatter than those on Ice Stream C.

Fig. 5. Map of basal-reflection strength, in dB relative to an assumed value of 0 dB on the Ross Ice Shelf in front of Ice Stream C. The color scale is shown in the figure. The borders of the ice streams as mapped by Reference Shabtaie and BentleyShabtaie and Bentley (1987) are shown by thin lines. In the lower left corner, part of a Landsat image of Siple Dome and the northern portion of Ice Stream C (kindly provided by R. A. Bindschadler, personal communication, 1997) has been superimposed.

Fig. 6. Normalized histograms of basal-reflection strengths from representative transects (Fig. 2) across ridge BC (RBC), Ice Stream B (ISB), Ice Stream C (ISC) and the Ross Ice Shelf (RIS). Normal distribution curves with the parameters given in Table 1 have been fitted to the first three histograms but not to that for RIS, which is clearly not normally distributed.

Basal-reflection strengths on ridge BC are 11 dB less, on average, than on Ire Stream C. Since ridge BC is free of crevasses (Reference RoseRose, 1979; Reference Shabtaie and BentleyShabtaie and Bentley, 1987; Reference Shabtaie and BentleyShabtaie and others, 1987; Reference Retzlaff and BentleyRetzlaff and Bentley, 1993), the two factors to consider in this case are the dielectric absorption and the reflectivity of the bed. But the results from upstream, if ridge B1/B2 is a valid analog to ridge BC, suggest that ridge BC should be slightly colder than Ice Stream C; it is most unlikely that it is the 4°C or so warmer that would be needed to produce an additional 11 dB absorption loss. Thus we attribute the weak reflections from the bed of ridge BC to a small basal reflection coefficient.

The loss upon reflection from a boundary between ice and frozen sediments varies widely, at least between 10 and 30 dB, depending on the type of sediment (Jiracek, 1967, table 5). That range is enough to explain the low reflectivities on the ridge if the bed there is frozen, even after allowing for the possibility of a lesser absorption on the ridge because of lower temperatures. If the bed were wet, on the other hand, it would be very difficult to explain a reflection coefficient of -20 dB or weaker. We consider it much more likely that the ice on ridge BC is frozen to its bed, as it is on ridge B1/B2 (personal communication from H. Engelhardt, 1997).

Bands with losses greater than 30 dB are closely associated with the previously mapped margin of Ice Stream B (Fig. 5), as would be expected as a result of extreme scattering in the highly disturbed ice of the marginal shear zones.

Surprisingly, such is not the case with Ice Stream C. On the grid-northern side of the ice stream, grid west of about 2.6° W (grid), the center of the mapped shear margin is associated with a strong gradient in reflection strength, from stronger under Ice Stream C to weaker under ridge BC, not with a minimum. We interpret this as being the boundary between the wet bed under Ice Stream C and the frozen bed under ridge BC. If that is correct, it suggests a cause-and-effect relationship, although it is not clear whether the ice-stream margin was there because it was the boundary of the frozen bed, or it was the position of the ice stream that determined where the bed was frozen. We also conclude from the absence of a minimum in reflection strength that even the crevasses in the marginal shear zone of this stagnant ice stream have healed to the point that they produce only weak scattering.

The grid southern margin of Ice Stream C is not marked by any reflection-strength signal, grid east of grid 3.8° W. In this area we believe the bed is unfrozen on both sides of the ancient shear margin. Around grid 4° W there is an intriguing suggestion that a reflection-strength minimum marks the boundary farther upstream and then splits into two forks, one associated for a short distance with the mapped shear margin of the ice stream and one with the “scar” on the flank of Siple Dome, clearly seen in the Landsat image (pasted into Fig. 5) that has been attributed to another former shear margin by Reference Stephenson and BindschadlerStephenson and Bindschadler (1990). Unfortunately, only short segments of the “scar” and the ice-stream margin upstream from the junction lie within the boundaries of the reflection-strength map.

Weak reflections are associated with the main body of Crary Ice Rise (around grid 7° S, 1°W), presumably because the bed is frozen (Reference Bindschadler, Roberts and IkenBindschadler and others, 1990). The grid northeastern boundary of the ice rise is sharply delineated by a contrast in reflection strength, with the stronger echoes coming from the base of the ice shelf to the grid northeast. The very weak reflections south of Crary Ice Rise are the result of the highly disturbed ice in the “wake” of the ice rise. The long “tail” of the ice rise that extends grid northwestward toward Ice Stream B is poorly defined by Figure 5, because there are only two, nearly parallel flight-lines in that area (Fig. 2); in any case, the actual boundaries of the ice rise are not themselves well known (Reference Shabtaie and BentleyShabtaie and Bentley, 1987; Reference BindschadlerBindschadler, 1993).

In several instances there are substantial deviations between the mapped positions of the ice-stream boundaries, where they approach and enter the Ross Ice Shelf, and the reflection-strength features that appear to be associated with them (Fig. 5). Careful examination of all the data (new and old) and comparison with satellite images probably would yield an explanation. We leave this for a future investigation.