Introduction

Present-day ice sheets drain the largest part of their ice through ice streams and fast-flowing outlet glaciers. This was presumably true for some of the paleo-ice sheets as well (e.g. Reference Brown, Hallet and BoothBrown and others, 1987; Reference MacAyealMacAyeal, 1993). Recent advances in remote-sensing techniques have revealed that ice streams are very widespread (e.g. Reference Fahnestock, Abdalati, Joughin, Brozena and GogineniFahnestock and others, 2001; RADARSAT-1 Antarctic Mapping Project mission), and that some of the fast flow associated with known ice streams inWest Antarctica affects a much larger part of the ice sheet and is much more far-reaching than previously thought (Reference JoughinJoughin and others, 1999).

It has been recognized that ice streams show a variety of behaviors. Reference BentleyBentley (1987) pointed out the strikingly different flow mechanism of the Ross ice streams compared to other known ice streams and outlet glaciers. It has become clear that a range of ice-stream types exist, ranging from the shallow and soft-based to the ones flowing through deep channels. In this paper, we discuss examples of the two end members. We will use Whillans Ice Stream as the archetypical soft-bedded, shallow ice stream, on the one hand, andJakobshavn Isbræ as the typical deep and steep isbræ.We will use acombination of data and modeling results to illustrate typical features, such as geometry and the flow, stress and temperature fields.

We also note there is a further type of ice stream, commonly termed an outlet glacier, which we define to be a glacier that drains an ice sheet through a bedrock channel in which the channel walls are exposed at the surface along much of the streaming part of the flow, as for instance Byrd, Leverett and Nimrod Glaciers (e.g. Reference McIntyreMcIntyre, 1985).

Field Data

Model

We used a finite-element (FE) model to calculate flow through these cross-sections. The model was constructed using a commercial package (Femlab¹) adapted to solve the incompressibility and momentum equations for a power-law ice rheology, with stress exponent n equal to 3. We solve for all three velocity components in a transverse cross-section, but we do not allow out-of-plane gradients (a so-called 2¹/2-dimensional model). The model has been tested against a number of analytical and previously calculated numerical solutions (Truffer, unpublished information), and was found to be very accurate and efficient.

The model inputs consist of the measured geometry and out-of-plane surface slope. The rate factor in the flow law was calculated at each point using interpolated temperatures within the cross-sections, with the Arrhenius temperature dependence given by Reference PatersonPaterson (1994).

In the case of WIS, we followed Reference Echelmeyer, Harrison, Larsen and MitchellEchelmeyer and others (1994) by introducing a laterally varying enhancement factor that is, in part, due to ice recrystallization under large strains. This enhancement factor was used to tune the model to match the observed surface velocities. The bed was kept frozen outside the ice stream (no basal slip there), and a constant basal shear stress of 3.5 kPa was prescribed under the ice stream, based on the observations of Reference Rooney, Blankenship, Alley and BentleyRooney and others (1987) and Reference KambKamb (1991), and the previous work of Reference Echelmeyer, Harrison, Larsen and MitchellEchelmeyer and others (1994).

The JHI model also used fabric-induced enhancement, but in a basal layer. We specified an enhancement factor of 3 based on measurements at Dye 3 by Reference Shoji and LangwayShoji and Langway (1988) and in situ borehole tilt measurements in the ice sheet next to our profile on JHI by Luthi and others (in press), who attribute the softening to increased dust and impurity ice content in the near-bed pre-Holocene ice (Paterson, 1981). The thickness of this enhanced basal layer was taken to be 150 m at the side of the ice stream and 900 m in the center, based on these observations. We also assumed that much of the basal ice was temperate, based on the temperature measurements, and the inferred and measured large vertical stretching of the basal ice described by Reference Iken, Echelmeyer, Harrison and FunkIken and others (1993) and Reference Luthi, Funk, Iken, Gogineni and TrufferLuthi and others (2002). The prescribed basal motion is based on measurements by Reference Luthi, Funk, Iken, Gogineni and TrufferLuthi and others (2002) at the margin, and is chosen to reproduce measured surface velocities. The thickness of temperate and enhanced basal layers, and the amount of basal motion are not well restricted by observations. The model presented here is only one of many possible ones that reproduce current observations. The subsequent discussion does not rely heavily on the exact model, however.

Reference Iken, Echelmeyer, Harrison and FunkIken and others (1993) have pointed out the three-dimensional nature of flow atJHI. The current model is not capable of addressing this adequately. This should be kept in mind in the following discussion. It will be less important for the more two-dimensional nature of flow atWIS.

Geometry

Figure 1 shows the cross-sections of the two ice streams with no vertical exaggeration. This figure serves to illustrate the tremendous differences in geometry. WIS is shallow (1000 m), with little variation in ice thickness at this scale. The aspect ratio of the ice stream (width (430 km) to depth (1km)) seems to imply that, except close to the margins, the ice would not be affected by the margins were it not for the slipperiness of the bed. For comparison, JHI flows in a narrow, 2700 m deep trough (Reference Clarke and EchelmeyerClarke and Echelmeyer, 1996). JHI is much steeper (a slope of 18×10⁻³ vs about 1.3×10⁻³ forWIS).WIS has a driving stress of about 11kPa, while that of JHI is about 208kPa, assuming a parabolic shape factor of 0.5.

Fig. 1. Cross-sections of Jakobshavn Isbræ (a) and Whillans Ice Stream (b). The figure is plotted without vertical exaggeration, in order to better illustrate the difference between the two types.

An important difference between the two ice streams is the downslope increase in ice thickness atJHI. This does not occur at WIS. In this paper, we limit the discussion to flow through one cross-section.

Ice Motion

Figure 2 shows contour plots of calculated out-of-plane velocities. The modeled surface velocities (solid curves) match measured values (symbols) closely, even in the marginal zones. The total flux through both ice streams at these locations is about 1×10¹⁰ m³ a⁻¹, despite their vastly different geometries (Fig. 1). In this section, we discuss the different basal motion and internal ice deformation that give rise to the modeled fit to the observations. It should be noted that while not strictly unique, the conclusions regarding these two contributions are robust if the details of the velocity profiles are modeled closely.

Fig. 2. (a) Velocity contours (in m a–1) for WSI. Note vertical exaggeration in this and other plots of WIS (cf. 1). This and subsequent plots of WIS only show one-half ice stream, with the ice-sheet side on the right. (b) Velocity contours (m a–1) forJHI. Units on the axis are in meters.

Ice deformation

Ice deformation inWIS is almost exclusively by lateral shear (Fig. 2). This figure also shows a somewhat more complicated flow regime (lateral as well as vertical strain rates) in the marginal area where the transition from a frozen to a soft bed occurs. As ice traverses the shear margin, it is exposed to a large amount of accumulated strain, and alignment of the ice crystals and fabric softening should therefore occur (e.g. Reference Jacka and BuddJacka and Budd, 1989). Fabric-induced flow enhancement is indeed necessary in any flow model to match observed surface velocities, but estimates range from factors of 2–3 (Reference Whillans and van der VeenWhillans and Van der Veen, 1997) to 410 (Reference Echelmeyer, Harrison, Larsen and MitchellEchelmeyer and others, 1994). The model we present here includes measured ice temperatures and measured topography, but not longitudinal gradients. Fabric-induced flow enhancement that is even larger than that predicted by the models of Reference Echelmeyer, Harrison, Larsen and MitchellEchelmeyer and others (1994) is required to match the observations. This is because the cold, stiff ice near the surface of the shear margin supports a larger amount of the driving stress than does the warmer (and softer) ice at depth.

The significant enhancement required by these flow models is robust with respect to any reasonable distribution of basal shear stress. But it must be noted that the range of estimates of the enhancement factor found by different studies is, to some extent, related to how well the details of the flow patterns are matched. If the observed near-margin shear strain rates and velocity profile are not fit as closely, then of course the required flow enhancement is less than the values we find here.

The slippery base of WIS makes its width W of primary importance to its center-line velocity, v. A simple analysis predicts v α W⁴ (Reference RaymondRaymond, 1996), and leads to a possible instability if the ice stream expands laterally, while maintaining its water-saturated, slippery base.

Figure 3 shows modeled velocities of JHI. The ice deformation field is more complex than in the case of WIS and involves significant vertical as well as lateral shear. Flow patterns are determined by the existence of the bedrock trough in that they resemble the flow of a valley glacier with rock walls. High deformation rates occur in the temperate basal layer (Reference Iken, Echelmeyer, Harrison and FunkIken and others, 1993; Reference Funk, Echelmeyer and IkenFunk and others, 1994; Reference Luthi, Funk, Iken, Gogineni and TrufferLuthi and others, 2002). The pre-Holocene basal ice layer (150–900m thick) has been observed to be softer than the overlying ice (Reference Shoji and LangwayShoji and Langway, 1988; Reference PatersonPaterson, 1991; Reference Luthi, Funk, Iken, Gogineni and TrufferLuthi and others, 2002).

Fig. 3. Shear stress magnitude contour plot (in 100 kPa) for of the (a) WIS and (b) JHI. Note the stress concentration in the cold upper part of the margin of WIS.

Stress Distribution

A large portion of the driving stress ofWIS is supported by its margins. In our model we find that they support about two-thirds of the total; other authors have suggested 50–100% (Reference Echelmeyer, Harrison, Larsen and MitchellEchelmeyer and others, 1994; Reference Whillans and van der VeenWhillans and Van der Veen, 1997; Reference Harrison, Echelmeyer and LarsenHarrison and others, 1998). The depth variation of stress is not uniform (Fig. 3). Large shear stress concentrations (up to 200 kPa) occur in the upper layers of the marginal zones, where the ice is cold (Reference Harrison, Echelmeyer and LarsenHarrison and others, 1998) and stiff. This explains, to some extent, why other studies using observations mainly from within the upper third to half of the ice-stream thickness (Reference Jackson and KambJackson and Kamb, 1997; Reference Harrison, Echelmeyer and LarsenHarrison and others, 1998) have found higher margin shear stresses, and thus infer a larger proportion of margin support.

The average basal shear stress of WIS is small, but nonzero. In this model we obtained a best fit to observed surface velocities with 3.5 kPa, close to the value of 5–6 kPa found by Reference Echelmeyer, Harrison, Larsen and MitchellEchelmeyer and others (1994). This value is higher than the measured shear strength of basal till samples (∼2 kPa; Reference Engelhardt, Humphrey, Kamb and FahnestockEngelhardt and others, 1990; Reference KambKamb, 1991), which suggests that some distribution of “sticky spots” serves to increase the average basal shear stress. It is interesting to note that there is no way to match both the observed center-line velocity and the marginal strain rates if we impose a basal shear stress of 2 kPa or less.

The shear stresses within the JHI cross-section exceed 300 kPa at the flanks, and are 4200 kPa in the temperate basal ice at the center of the channel (Figs 3 and 4). These stresses cause very large deformation rates, enabling the high flow velocities observed on the surface. The model produces a non-linear shear stress vs depth relation, contrary to the often-made assumption of linearity. This is in part due to the changes in ice temperature with depth and in part the geometry of the channel. Such a variation has also been predicted by models of temperate-valley glacier flow (Reference Truffer, Echelmeyer and HarrisonTruffer and others, 2001).

Fig. 4. Temperature contours (in °c) for (a) wis and (b) jhi. temperatures are relative to the local pressure-melting point and thus appear as 0˚c for the temperate layer.

Thermal Regime

The temperature field of WIS (Fig. 4) is influenced to some degree by the passage of ice through the shear margins into the ice stream. Two effects are important: first, strain heating due to large deformation rates and shear stresses and, second, chilling by cold air pooling in surface crevasses over winter. Reference Harrison, Echelmeyer and LarsenHarrison and others (1998) discussed both these effects, and used them to estimate shear stress in the upper third of the margin (200kPa; cf. Fig. 3), and the current margin migration rate.

Even though basal velocities are high, the low basal shear stresses lead to minimal strain heating at the base of the ice stream. Most of the gravitational energy of the moving ice is dissipated in the margins, where the ice is generally cold (except near the bed; Reference RaymondRaymond, 2001). Ice at the base of WIS is at the melting point, but no temperate layer is present. The geothermal heat flux is on the same order as the conductive heat flux into the ice. This means that small changes could lead to a switch between a melt and a freeze-on condition at the ice-stream base, providing a mechanism for ice-stream slow-down, or even shut-down (Reference Tulaczyk, Kamb and EngelhardtTulaczyk and others, 2000).

The coldest ice of JHI is found at a depth of about half the center-line maximum (1300 m; Fig. 4). This ice has been advected from upstream, where the ice is colder. The high stresses and deformation rates create enough strain heating to maintain a significant basal layer of temperate ice (Reference Funk, Echelmeyer and IkenFunk and others, 1994). In contrast to the situation at WIS, strain energy dissipation occurs mainly within the temperate ice, and it is therefore used to produce melt. The inferred basal melt rate beneathJHI is about 0.5 m a⁻¹.

Geometry of the Lateral Shear Zones

Distinct marginal shear zones are prominent features of most ice streams (e.g. Reference RaymondRaymond, 1996; Reference Raymond, Echelmeyer, Whillans, Doake, Alley and BindschadlerRaymond and others, 2001), delineating the faster-moving parts of both ice-stream types in satellite images and air photos. These zones are characterized by an abrupt transition from ice-sheet to ice-stream flow, with the associated large strain rates and intense crevassing. Visual observations, as well as measured and modeled velocity patterns, indicate that some of these characteristics are different for Siple Coast-type ice streams and isbræs.

The different patterns of strain rate across the two representative ice streams are clearly illustrated by a comparison of transverse strain rates on a normalized horizontal scale (Fig. 5). Four differences are of note. First, because the overall surface velocity is much larger onJHI than on WIS, the strain rates are also larger there, by a factor of more than two in this case. This is somewhat surprising in that one of the often-quoted “signatures” of the Ross ice streams has been the high lateral strain rates. We do note that this difference in strain-rate magnitude may vary down the length of different ice streams of each type. This is because the difference between the typical ice-stream velocity and that of the surrounding ice sheet increases in the downstream direction, and the width of the shear margins also changes, as discussed next.

Fig. 5. Transverse strain rates (a⁻¹) across the two ice streams. The horizontal axis is the distance across the ice stream normalized by the half-width at this location (18 km on WIS (solid line) and 4.5 km on JHI (dotted line)).

The second difference between the two types of margins is their relative width. The zone of high shear rates is much larger relative to the ice-stream width on JHI than on WIS. In our example, the shear margin on JHI represents nearly half of the overall isbræ width, while on WIS it is only about 20% of the total ice-stream width. This difference results from the underlying patterns of shear stress magnitude (Fig. 3). Ice deformation over much of the JHI section is strongly affected by the walls of the subglacial channel, while the ice in most of the WIS section does not directly “feel” the resistance offered by the ice outboard of the margin, and the zones of high strain rate are more localized.

The third difference is in the nature of the crevassing in the marginal zones, which is a direct consequence of the different stress and strain-rate fields. In the WIS margins, such as the“Dragon”and the“Snake”, the crevassing appears to be chaotic within a narrow zone, with large, arcuate crevasses on either side of the chaotic zone. On the other hand, the shear zones of JHI have abroad zone of less chaotic, but large crevasses. Below the grounding line, JHI surface crevassing becomes as chaotic as that typical of WIS, and the crevassing appears to be that typical of fast-moving tidewater glaciers.

A fourth difference is the relatively large influx of ice through the margins at JHI (not represented in the model). This leads to an advection of crevasses towards the ice-stream center. On the other hand, at WIS crevasses are continuously rotated in the flow field and recreated, leading to a much more chaotic crevasse zone.

It is likely that these differences in shear margin can be used to identify the type of ice stream using satellite imagery. And, because the marginal structure is linked to the bedrock topography, the characteristics of the margins may indicate presence or absence of a bedrock channel, and of the underlying flow mechanisms.

Basal Hydrology and Seasonal Velocity Fluctuations

Basal melting and surface melting are minimal on WIS. In contrast, surface melting is strong on the lower 80 km of JHI during summer (Reference Echelmeyer, Clarke and HarrisonEchelmeyer and others, 1991) and there is significant basal melting, as mentioned above. The high basal melt rates at JHI will affect the basal hydraulic system. A lack of seasonality in these melt rates might explain the lack of seasonality in isbræ speeds (Reference Echelmeyer and HarrisonEchelmeyer and Harrison, 1990). On the ice sheet adjacent to the isbr×, seasonality in velocity has been observed (Reference Luthi, Funk, Iken, Gogineni and TrufferLuthi and others, 2002). We hypothesize that the high basal melt rates of the isbræ maintain an efficient drainage system that leads to low basal water pressures, little basal motion and little seasonality in ice velocity there, even with the strong seasonal surface water influx. In this context, it is interesting to note that temperate LeConte Glacier, southeast Alaska, U.S.A., which flows at velocities and under basal shear stresses similar to those at JHI, also shows little seasonality in its velocities (Reference O’Neel, Echelmeyer and MotykaO’Neel and others, 2001). This is unusual for temperate glaciers (e.g. Reference WillisWillis, 1995), but could be explained by a well-maintained drainage system due to high basal melt rates.

Stability

It has been shown that the Siple Coast ice streams are not steady features (e.g. Reference Fahnestock, Scambos, Bindschadler and KvaranFahnestock and others, 2000). Ice Stream C shut down about 150 years ago (Reference RoseRose, 1979), and the margins of WIS have been shown to migrate (e.g. Reference Bindschadler and VornbergerBindschadler and Vornberger, 1998; Reference Echelmeyer and HarrisonEchelmeyer and Harrison, 1999). The simplified model of Reference Jacobson and RaymondJacobsen and Raymond (1998) has shown that ice-stream margins cannot be steady-state features because strain heating at the margins warms up the outboard ice and thus expands the thawed bed zone. A widening of the margins should lead to a speeding-up of the ice stream if basal friction is negligible. Yet Reference Echelmeyer and HarrisonEchelmeyer and Harrison (1999) observed slowing of WIS, at the same time that one margin was migrating outward. This indicates a simultaneous change in resistive drag at the base of the ice stream if the opposite margin is stationary or also migrating outward. Reference Tulaczyk, Kamb and EngelhardtTulaczyk and others (2000) proposed that freeze-on processes at the base of an ice stream could draw water from a basal till layer and increase the shear strength of the subglacial till. This could slow down or even shut down the ice stream if it is widening too quickly.

On the other hand, the dynamics of JHI do not offer any mechanisms that would make it unstable. It is well constrained by bedrock topography, with strain heating concentrated at the base rather than the margins. This reduces the potential for margin migration. Changes should therefore only be expected on longer time-scales, through either further erosion of the bedrock channel, exhaustion of the ice supply necessary to maintain fast motion, or changes in calving.

Classification of Ice Streams

The two extremes of fast-flowing ice streams presented here should be regarded as the end members in a continuum of ice-streaming behavior. In Table 1 we list several ice streams in Greenland and Antarctica. Using available information on width, slope, depth, speed and the nature of the shear margins, we have categorized them into probable ice-stream types. This characterization may be used to infer bedrock topography − deep channel or not − where such information is not yet available, and to give some insight into the relevant flow mechanisms.

Table 1. Arrow going down represents the transition from ice-stream type to isbræ type. The following abbreviations are used: WA, West Antarctica; EA, East Antarctica; G, Greenland; L, Laurentide/Cordilleran paleo-ice sheet

This survey shows that the Siple Coast-type ice streams are more limited in number than mixed or isbræ types. This implies that both isbræ-type and Siple Coast-type physics will be important for understanding such regions as the Pine Island–Thwaites drainage basin and possibly the large ice stream draining northeast Greenland. It also implies that ice-sheet stability questions require incorporation of these diverse ice-stream dynamics.

Conclusions

We have characterized ice-stream behavior by defining two end members of a spectrum: the Siple Coast “ice stream”and the Jakobshavn“isbræ”. The ice streams involve slippery beds, low driving stresses, and significant support by the margins, while isbræs involve significant internal ice deformation, have high driving stresses, and are strongly affected by basal as well as lateral drag. The surface expression of these two types is readily apparent: typically wide shear margins on isbræs and narrow ones on ice streams. These visual differences can possibly be used to infer underlying flow mechanisms and bedrock topography. The nature of paleo-ice streams can also be inferred using information on such factors as bedrock topography and the presence of till, as has been done previously by, for instance, Reference Brown, Hallet and BoothBrown and others (1987).

These results show that questions of ice-sheet stability will require an understanding of both types of ice streams, as they both appear to drain significant portions of both past and present ice sheets. They also show that the dynamics of the two types are quite different. This poses unique challenges to researchers modeling complex areas, where both types of flow occur in the same ice stream, such as Pine Island Glacier.