Glacier composition mechanics and dynamics

Department of the Environment and Heritage, Australian Antarctic Division, Channel Highway, Kingston, Tasmania, 7150, Australia

56.1 Introduction

The interrelations between the Earth's glaciers and global change (primarily climate change) are largely due to changes in the size and shape of the glaciers. The largest of these glaciers, by far, are the polar ice sheets of Antarctica and Greenland. Be that as it may, the temperate glaciers are important on time-scales <100 yr because, with the climatic warming rates currently evident across the planet, many of these glaciers are dramatically reducing in size and their contents are adding to sea-level rise. Of course the mass of water released by these glaciers is tiny compared with that trapped in the polar ice sheets. However, because the average temperature of the polar ice sheets is about -30°C, there is no realistic possibility, even with a large increase in atmospheric greenhouse gas concentrations, that they will completely melt within the next millennium (DeConto & Pollard, 2003) (at least without major changes in the orbital and solar parameters controlling Earth's climate). In fact a warmer climate is, on average, a wetter climate, and at temperatures typical of the polar regions, the extra precipitation falls as snow. Thus it is likely, for the Antarctic ice sheet at least, that it will increase in mass with global atmospheric and oceanic warming. Here lies one of our most challenging problems (The ISMASS Committee, 2004). We do not yet know for certain, even whether the polar ice sheets are actually increasing in mass (i.e. have a positive mass balance) or decreasing (i.e. a negative mass balance), but we have seen changes over the past decade that have been much more dramatic than previously anticipated; e.g. rapid glacier retreat and thinning (Rignot, 1998, 2001; Rignot & Thomas, 2002; Shepherd et al., 2002; Zwally et al., 2002a), ice-shelf collapse (Skvarca, 1993,1994; Rott et al., 1996) and unexpected changes in ice-stream velocities (Stephenson & Bindschadler, 1988; Joughin et al., 2002; Rignot et al., 2002). Satellite- and ground-based remote sensing and over-snow or aerial survey measurements are now beginning to shed more light on the mass balance state of the polar ice sheets, and results indicate some areas of rapid mass loss, whereas other areas indicate mass gain. Rignot & Thomas (2002) estimated a net mass gain for the East Antarctic ice sheet of 22km3yr-1, yet a net mass loss of 48km3yr-1 for the West Antarctic ice sheet.

Other research that is important for estimating changes in ice mass includes computer modelling. We can never cover the entire Antarctic or Greenland ice sheets, or every glacier with ground-based measurements, but with ice-sheet computer models we can calculate physical characteristics over entire ice sheets. Computer models also can be coupled with ocean models and atmospheric models, leading to a much improved understanding of the feedbacks and relationships between the ice, ocean and atmosphere. Once they are proven (by testing against known observations), ice-sheet computer models can be used to tell us more about the ice sheets and glaciers in the past—useful for understanding past changes—and to forecast what the ice sheets will look like in the future (along with the effects on ocean and atmosphere). To develop accurate and reliable computer models, however, and to properly interpret results from both the computer modelling and remote sensing results, it is essential that we understand the processes involved, i.e. the physics of how ice flows. In turn, as you will read in the following chapters, the physics depends on the composition of the glaciers.

Of course, all glaciers and ice sheets are composed of ice. But it is not that simple. Above the ice is a layer of recently precipitated snow (typically with a surface density, p « 0.3gcm-3). The snow increases in density as a result of compaction under its own weight (and is usually termed 'firn' at densities greater than « 0.3gcm-3), to eventually form ice. In some cases this process is not complete until a depth of >100m. During compaction, atmospheric air is trapped in the firn and once the firn has reached a density of ca. 0.83 g cm-3 the air pockets have been isolated from the atmosphere. We call this process 'close-off' and it is a very important concept for understanding ice-core measurements of past gas composition of the atmosphere (see chapters of this book on ice-core and climate studies). Once close-off has occurred, the air pockets are bubbles. Glacier ice is riddled with bubbles under high hydrostatic pressure and they constitute impurities within the ice. The ice flow parameters are affected in proportion to the decrease in density due to the bubbles, because the air has no resistance to deformation and, at densities higher than the close-off density, these bubbles seem to be (and no laboratory experiment has contradicted this) of little consequence in terms of the physics of the ice flow. Although deformation rates for snow are higher than for ice, once the close-off density has been attained, laboratory measurements indicate flow rates similar to those for solid ice (Mellor & Smith, 1966; Jacka, 1994). Below the close-off depth in the ice sheets and glaciers, the ice density continues to increase until it reaches a final density of ca. 0.91 gcm-3.

For the polar ice sheets, the ice in the upper layers is very clean, although that has not always been the case and deeper layers of the ice sheets (especially the ice sheets of the Northern Hemisphere; e.g. Agassiz and Greenland) show layers of dust from past times. For temperate glaciers, the ice is not so clean. It often contains rocks, from boulder size to pebbles, and dust emanating from surrounding hills and mountains. All glaciers, polar and temperate, also contain atmospheric borne impurities, including fine insoluble impurities (dust, fine enough to be transported in the high atmosphere) and soluble impurities dissolved in the snow that makes up the glacier. Volcanic eruptions, for example, are one source of the soluble and insoluble impurities. Another is dust transported from the non-ice-covered deserts of surrounding land masses. Again at times past, e.g. during the last glacial period when there were greater areas of desert on the planet, there was (on average) a higher concentration of these atmospheric borne impurities blown by the wind over the Greenland and (to a lesser degree) Antarctic ice sheets, and so these impurities are in higher concentrations in deeper layers of the glaciers and ice sheets. Some notable peaks, however, do appear in the not-so-deep layers (e.g. from recent volcanic eruptions). The effect, on the flow of the ice, of these soluble and insoluble impurities needs to be known.

In the basal layers, the ice picks up dirt and rocks as it moves over the bedrock. Complicated flow therefore results in the basal layers that consist of a mix of ice with different impurity types and levels. In addition, the flow is complicated by folding, faults and shear of the ice. The flow of ice is strongly dependent upon temperature. Temperate glaciers are warm (at the melting point) throughout. The temperature just 10 to 20 m below the ice surface in the polar ice sheets is close to the mean annual air temperature. Geothermal heat from the Earth's interior heats the base of the ice, resulting in a temperature profile that is not far from isothermal in the top layer, and increasing approximately linearly in deeper layers, to the basal temperature. The depth of the isothermal layer depends on the snow accumulation rate, and in central Antarctica (e.g Vostok, Dome Fuji, Dome C) where the accumulation rate is extremely low, the isothermal layer is almost non-existent. The basal temperature in many parts of the polar ice sheets is at the pressure melting point, which results from the high hydrostatic pressure, at about -1 to —2°C. So, this dirty basal ice is also relatively warm. There is some uncertainty about the effect on ice flow of the impurities; there is very little question concerning the temperature effects. Certainly, the flow of the basal ice in polar ice sheets has a strong effect on the flow of the ice sheets as a whole.

As mentioned above, the basal ice is warm. Thus it also contains another impurity—water! Water exists on grain boundaries and dislocations within the ice (Wettlaufer, 1999), possibly at temperatures as low as —25°C. Certainly at —10°C, water is present, and it has a profound effect on ice flow at temperatures greater than —5°C (Duval, 1977; Morgan, 1991). This effect can also include sliding of the ice over the bedrock, lubricated by a thin film of water.

For much of the area of the polar ice sheets, the basal ice is frozen to the solid bed; in other areas sliding occurs. There are also some situations in which the bed itself deforms. The best (or at least best known) examples of this are in areas where the West Antarctic ice sheet drains into the Ross Ice Shelf. Even though this ice is not 'channelled' by glacial valleys in the rock below, ice movement rates are sometimes extremely high (up to 20kmyr—'), and incredibly these high velocity 'pulses' can last for periods of just hours, to years (Tulaczyk, this volume, Chapter 70). These areas are known as 'ice streams' and the rapid accelerations and subsequent retardations are attributed to sliding of the ice and deformation of the under-riding till. Although, as Tulaczyk points out in Chapter 70, some ice streams have been observed even in regions with a hard bed.

Let us now examine in more detail six of the chapters in Part 4. Three of the chapters are concerned, in one way or another, with the flow of glacier and ice-sheet ice generally, and they each (with necessarily, some overlap) are concerned with processes of how ice flows: Duval and Montagnat (Chapter 59) with the crystalline microprocesses leading to an ice flow law; Cuffey (Chapter 57) with a detailed mathematical approach, incorporating the flow law along with equations for the dynamics of glacier flow; and Tulaczyk (Chapter 70) with a more descriptive explanation of fast ice flow in which basal processes are of uppermost consideration. Basal ice observations are then examined in greater detail—not surprising given their importance as outlined earlier—in three other chapters of Part 4. Again in this second group of three chapters, there is much overlap. Hubbard (Chapter 67) provides a background and an approach for development of a model of temperate glacier flow. Fitzsimons (Chapter 65) examines laboratory and field observations in cold-based glaciers of the McMurdo Dry Valleys (Antarctica). He concludes we need to recognize a 'continuum of material properties and deformation properties which is variable in time and space'. Finally, Lawson (Chapter 63) looks at environmental controls on glacier dynamic behaviour.

56.2 Clean ice

In Chapter 59 Duval and Montagnat investigate the physical mechanisms involved in the flow of clean ice, and they also include discussion of the effects of impurities, including water, on the flow. We now have a good understanding, I think Duval and Montagnat will agree, of the rheological properties for clean ice at temperatures above about —15°C and driving stresses higher than 0.2 MPa. For this ice Glen's (modified) ice-flow law (Glen, 1955)

4 = EAtn which in one form or another is quoted in every one of the following six chapters, suffices well with power exponent n = 3. This expression relates strain rate (here the root mean square of the tensor deviators or 'octahedral' value), e0, to the octahedral (devi-ator or driving) stress, t0, where n is a constant, A is related to temperature through the Arrhenius relation, and E is an enhancement factor due to anisotropic fabric development.

The effect of water entrapped in the ice lattice at the warmer temperatures is already accounted for in the value of A above as



102 T

Figure 56.1 Activation energy as a function of the inverse of temperature, based on the results of ice-deformation tests at temperatures near the melting point by Morgan (1991).

this flow law is an empirical law, i.e. based on observations from the laboratory and from the field. The relation A is a function of temperature and of the creep activation energy. Figure 56.1 shows activation energy as a function of the inverse of temperature, based on the results of ice deformation tests at temperatures near the melting point by Morgan (1991). For most materials the activation energy is constant, and we see from Fig. 56.1 that for ice colder than ca. -10°C (1/T = 0.0038 K-1) this is the case. At higher temperatures, however, the activation energy increases rapidly as a function of temperature as a consequence of the presence of water in the ice lattice.

Even for anisotropic ice (see Duval and Montagnat's section on 'Fabric development') at relatively high temperatures and stresses, the flow enhancement, E, due to fabric development (ca. 3 in compression; ca. 12 in simple shear) is generally agreed upon. The flow configuration in glaciers and ice sheets is vertical compression near the surface (due to the weight of the accumulation above), and 'bed parallel' simple shear in the deeper layers. Through most of the ice mass then, the predominant stress configuration is a combination (in different ratios) of compression and shear. Thus we need to know the enhancement factor for any combination. Li et al. (1996) have carried out laboratory tests aimed at this. The octahedral stress, T0, and strain rate, e0, relations for this stress combination are given by

where s is the confined normal stress and e is the compressive strain rate, and where t is the 'bed parallel' shear stress and j the strain rate due to shear. Figure 56.2 shows results from the tests of Li et al. (1996), which were all carried out at the same octahedral values. It is seen first that the minimum isotropic strain rates

Figure 56.1 Activation energy as a function of the inverse of temperature, based on the results of ice-deformation tests at temperatures near the melting point by Morgan (1991).







a aai^ao

a a* a


x A+D.

+□ aa

a o

• x xx



o . o a 4- □ a



* •x

a 0.16 0.34

0.48 0.46

a 0.49 • 0.73 0.90 0.98

0.42 0.32 0.19 0.00


0.1 1 10 Octahedral Shear Strain, %

Figure 56.2 Creep curves (log-log plots of octahedral strain rate as a function of octahedral strain) for ice-deformation tests in various combinations (indicated) of compression and shear. The combined octahedral stress for all tests was 0.4 MPa. The test temperature was —2.0°C. (After Li et al., 1996.) Reproduced by permission of the International Glaciological Society.

are the same for compression and shear—the use of root mean square values of the deviator tensors ensures this (Nye, 1953)— and second that the tertiary, steady-state strain rates vary between a factor of 3 and up to 12 times the minimum isotropic strain rates, depending on the ratio of compression to shear. Warner et al. (1999) have developed a formulation which fits these data well and which allows a simple modified form of the Glen flow relations to be used. They note for the individual component strain rates that the addition of a compressive stress increases the shear strain rate by less than the Glen flow law would indicate, whereas the addition of a shear stress increases the compression strain rate by more than the Glen flow law provides for. This means that for tertiary (anisotropic) flow, shear stress has more effect on the (normal) compression rate than the compression has on the shear rate. For a shear stress, t, and compression deviator, S

Eij = AT0Sij where the octahedral shear stress, t0, has been replaced by an 'anisotropic mean' stress given by

in which a and b are related to the tertiary strain rate enhancements in shear alone, ES (~ 12), and compression alone,

For the temperate glaciers and the warm basal ice of the polar ice sheets, Glen's ice-flow law (as modified above) might suffice, except for the complications imposed by the soluble and insoluble impurities.

For the colder ice (temperatures as low as -60°C in Antarctica) and low driving stresses (<0.2 MPa) relevant to the flow by internal deformation of the bulk of the polar ice masses, there is still some question as to an appropriate n value to use in computations of flow rates. Duval and Montagnac (Chapter 59) argue, with strong emphasis on analysis of crystalline deformation mechanisms, for n < 2. Unfortunately, however, there is no direct laboratory confirmation—there cannot be because of the large times (tens to hundreds of years) required to attain minimum isotropic or tertiary steady state (anisotropic) flow rates at these low values.

For the enhancement factor, E, due to the steady-state aniso-tropic fabric development in clean cold ice with low driving stress, there is now laboratory evidence (at least in uniaxial compression) that as temperature and stress decrease, so does E, from 3 to 1, i.e. no enhancement (Jacka & Li, 2000). This seems to be a result of a reducing capacity, as temperature and stress decrease, for anisotropic fabrics to develop. Figure 56.3a shows a series of creep curves (plots of strain rate as a function of strain) and crystal orientation fabrics from Jacka and Li's laboratory experiments at —19°C in which compressive stress ranges from 0.8 to 0.1 MPa, and Figure 56.3b shows a series at 0.2 MPa in which temperature ranges from —5 to —21°C. These tests suggest E itself may be better described by a function of temperature and deviatoric stress.

56.3 Glacier dynamics, fast flow and ice streaming

Cuffey (Chapter 57) expands the crystal scale to the glacier or icesheet scale. He introduces the fundamental glacier mass balance equation that temporal change in ice thickness is governed by the difference between the accumulated mass of snow and the horizontal discharge of the mass (the flux). Cuffey then considers the simplest case in which the bed is mechanically strong, and the ice flow is not affected by impurities. For this case he derives a flatbed expression for the ice thickness. After a discussion of the consequences of this solution, he examines the added complication of a weak-bed, i.e. applicable to ice streams.

Tulaczyk (Chapter 70) provides us with comprehensive descriptive definitions of fast glacier flow. Of particular concern to him is the ice-stream flow formed in those sections of the West Antarctic Siple Coast ice sheet flowing into the Ross Ice Shelf. The 'definition' after Bindschadler et al. (2001a) that slow ice flow is that due to internal deformation alone, whereas fast ice flow is due to rapid basal motion, is useful. It might, for example, be utilized to explain some glacier surges. That is, some glaciers are in slow ice-flow mode most of the time, but as upstream accumulation adds to the thickness basal melt increases, and fast ice flow is activated. Once the additional mass is discharged to the front of the glacier (by a wave-like passage of thicker ice down the glacier) and the glacier is thinned (although longer), basal melting is reduced and slow ice flow is reinstated until, as the front retreats, the up-stream accumulation again builds up.

The West Antarctic ice streams are not surging (in the sense described above). They are (at least some of the time) in fast flow mode but exhibit extraordinarily rapid accelerations and retardations. The mechanisms behind this 'stick-slip' motion are not completely understood, but in some cases seem related to tidally triggered spurts. Tulaczyk (Chapter 70) provides us with a comprehensive account of the theories and arguments that have been proposed. Whatever the mechanisms are, there is no doubt that to properly model ice-stream flow, knowledge of till rheology is also required (Alley et al., 1987a). Tulaczyk presents the case for a power flow law for till, with exponent ca. 1 to 2, and for a Coulomb-plastic flow law, as favoured by laboratory tests of till deformation. As he states, fast ice streaming is enabled by the presence of subglacial water at pressures close to the overburden pressure, and understanding subglacial water generation, storage and transport is key to understanding ice-stream flow and consequently to grasping a full knowledge of ice-sheet mass balance changes. Observations of subglacial processes, however, are particularly difficult (see Alley, this volume, Chapter 72).

56.4 Dirty ice

Lawson (Chapter 63), Fitzsimon (Chapter 65) and Hubbard (Chapter 67) deal with basal ice—ice near the bedrock that is warm, has a high concentration of impurities including a range of dissolved species, insoluble fine dust particles, rocks and boulders, and is folding, faulting, at times shearing and at other times sliding on the bed, which itself may be deforming. To study the flow of dirty ice, we need to consider the effects of (i) insoluble atmosphere-borne dust, (ii) soluble impurities and (iii) basal

= 0.8 MPa

= 0.4 MPa

=. 0.3 MPa

! 0.2 MPa

= 0.1 MPa

0.1 1 10 100 0.1 1 10 100 0.1 1 10 100 0.1 1 10 100 0.1 1 10 100

Octahedral shear strain (%)



! -5°C

! .-10° C

! -15° C

! -19° C

! -21°C



10 100 0.1 1 10 100 0.1 Octahedral shear strain (%)

10 100 0.1 1 10 100 0.1 Octahedral shear strain (%)

87 axes

Figure 56.3 (a) A series of creep curves (normalized to a minimum strain rate of 1, and with a dashed line indicating a flow enhancement of 3) and crystal orientation fabrics (after Jacka & Li, 2000) from laboratory experiments at —19°C in which compressive stress ranges from 0.8 to 0.1 MPa. (b) A series of creep curves (normalized to a minimum strain rate of 1, and with a dashed line indicating a flow enhancement of 3) and crystal orientation fabrics (after Jacka & Li, 2000) from laboratory experiments at 0.2 MPa compressive stress in which temperature ranges from —5.0 to —21°C. Reproduced by permission of Hokkaido University Press.

87 axes

Figure 56.3 (a) A series of creep curves (normalized to a minimum strain rate of 1, and with a dashed line indicating a flow enhancement of 3) and crystal orientation fabrics (after Jacka & Li, 2000) from laboratory experiments at —19°C in which compressive stress ranges from 0.8 to 0.1 MPa. (b) A series of creep curves (normalized to a minimum strain rate of 1, and with a dashed line indicating a flow enhancement of 3) and crystal orientation fabrics (after Jacka & Li, 2000) from laboratory experiments at 0.2 MPa compressive stress in which temperature ranges from —5.0 to —21°C. Reproduced by permission of Hokkaido University Press.

debris. Note that dust delivered to the glaciers and polar ice sheets by atmospheric transport, i.e. in the wind, is necessarily very fine (microparticles) and will be incorporated in the ice within the crystal lattice and at grain boundaries. Similarly, soluble impurities, dissolved in the snow that is deposited to form the ice, are included within the ice lattice and at grain boundaries. Basal debris, however, also includes material that is of the same order of magnitude or much larger than the crystals themselves.

As the presence in the ice of the dust and soluble impurities has an influence on crystal structure (size and orientation fabric development) we need to first consider these interactions and consequences for the ice flow. We know that mean crystal area, in clean ice under little or no stress, increases linearly with time at a rate dependent on temperature through the Arrhenius relation

(Stephenson, 1967; Gow, 1969)—often referred to as 'normal crystal growth'. In deforming ice the deformation itself controls the crystal size, which in steady state is a function primarily of the stress (Gow & Williamson, 1976; Jacka & Li, 1994). From ice from the lowest levels of the Greenland, Agassiz and Antarctic ice sheets (e.g. Dahl-Jensen & Gundestrup, 1987; Fisher & Koerner, 1986) and from laboratory tests (Li et al., 1998) we have seen that crystal growth rates seem to be unaffected by dust content, provided that the content does not exceed ca. 104g—'. Figure 56.4 (after Li et al., 1998) shows crystal size plotted as a function of microparticle concentration. Data are from ice core DSS, on Law Dome, East Antarctica, from clean ice within the Holocene depth interval, from Last Glacial Maximum (LGM) samples and from samples from the beginning of the last glacial period. One datum is from a Dye 3 (Greenland) LGM sample containing high microparticle

to 102

ra c CB

Dfln 0

—i—i—111111—i—i—111111—i—i—111ii i—i—i—11111

Number of particles (g 1)

Figure 56.4 Crystal mean area plotted as a function of microparticle concentration. Data represented by squares are from ice core DSS, on Law Dome, East Antarctica, and samples are from within the Holocene depth interval. Solid triangles represent DSS Last Glacial Maximum (LGM) samples. Circles represent samples from the beginning of the last glacial period. The cross is a datum from a Dye 3 (Greenland) LGM sample. (After Li et al., 1998.) Reproduced by permission of the International Glaciological Society.

content. If dust content does exceed ca. 104g-1, it seems that crystal growth is inhibited as a function (power law exponent ca. -1.5) of microparticle content. This is seen also in the lowest levels of some of the ice cores where crystals are extremely small and dust content very high.

Thin layers, 'spikes', of very small crystals have been located in some ice cores at levels well above the base. These have been associated with higher concentrations of soluble and insoluble impurities, high shear rates and strongly anisotropic crystal orientation fabrics. There is still considerable debate concerning which of these factors are cause, which are effect and which are unrelated. Because of simultaneous spikes in the oxygen isotope ratio, it is clear that some, although not all, of these spikes are related to climatic cool periods—colder, dryer conditions lead to greater amounts of atmospheric borne soluble and insoluble species. It has been argued (e.g. Paterson, 1991) that the higher impurity concentrations lead to smaller crystals and that these smaller crystals will facilitate higher deformation rates and thus development of anisotropic crystal fabrics. On the other hand, as indicated above, insoluble impurities in these layers are not expected to lead to smaller crystals because concentrations are below the threshold of 104g-1. In addition, Duval & LeGac (1980) and Jacka (1984) found that for the crystal sizes usually found in glaciers and polar ice sheets (ca. 1-10mm), and within the temperature and stress regime in which n = 3, crystal size does not significantly affect ice-flow rates. For much smaller crystals, however, Goldsby & Kohlstedt (1997) do find a crystal size effect on flow rate, and for the fine-grained, dirty ice from Merserve Glacier (Antarctica) and Dye 3 (Greenland), Cuffey et al. (2000a,b) argue that there is a grain-size effect on the ice flow.

Another explanation for the shear spikes, as yet not satisfactorily tested in the field or laboratory, may be that some soluble impurities, e.g. F- (Jones & Glen, 1969) or NH+, which are found along with high insoluble impurity levels because they are generated by the same events, e.g. volcanic eruptions and forest fires (Alley & Woods, 1996), may facilitate accelerated development of anisotropic crystal orientation fabrics in shear. This will lead to even higher shear rates and, as a result, smaller crystals.

Let us now consider the direct effect of the impurities on the ice flow. For the soluble and insoluble atmosphere-borne impurities, concentration levels in Earth's glaciers and polar ice sheets are very low. It seems reasonable to expect that any effect they may have on the ice-flow rates will be by indirect processes such as described above, i.e. by their effect on the ability of the ice to develop crystal anisotropies that accelerate or retard the flow. For the larger impurities, e.g. basal debris and debris originating on valley walls of mountain glaciers, primarily because of the importance of understanding the flow of the basal layers of polar ice sheets, many laboratory studies (Shoji & Langway, 1984; Fitzsimons et al., 1999) and field studies (Holdsworth & Bull, 1970; Anderton, 1973; Fisher & Koerner, 1986; Echelmeyer & Wang, 1987; Tison et al., 1993,1994; Gow & Meese, 1996; Lawson, 1996) have been carried out. Despite this, we still do not have a full understanding, even of whether the presence of solid debris accelerates or retards ice-flow rates. Several of the authors cited above have found enhanced flow for debris-laden ice, especially at higher temperatures (Lawson, 1996). However, Butkovich & Landauer (1959), Nickling & Bennett (1984) and, at temperatures below —5°C, Lawson (1996) found retarded flow for higher debris content. Hooke et al. (1972) and Jacka et al. (2003) provided evidence for no significant dependence of flow rate on debris content. The picture of whether debris content accelerates or retards ice-flow rate is confusing and further laboratory and field studies are required. Overall it seems likely that there is a flow rate enhancement at high temperatures, at high stresses, and possibly only for high debris content. Little attention has been paid in the studies so far to the development of crystal anisotropies in debris-laden ice. Only Jacka et al. (2003) have examined tertiary flow of debris-laden ice, and their results were similar to those for minimum isotropic ice.

56.5 Conclusions

I have attempted to provide a summary of the 'state of the art' at the time of writing, of our development of an ice-flow law suitable for use in glacier and ice-sheet models. For clean ice, Glen's ice-flow law with n = 3, and with modifications for flow enhancement due to the development of crystal anisotropy (varying from ca. 3 to ca. 12, depending on the ratio of compression to shear), suffices well for temperate glaciers and warmer conditions in polar ice sheets. For the colder bulk of the polar ice masses there is still some debate concerning the most appropriate value for n, which possibly may be <2. There is some evidence also that the development of crystal orientation fabrics may be retarded at the lower temperatures and stresses, so that the flow enhancement is reduced as a function of these parameters.

For ice containing soluble impurities, I have argued that some species may accelerate crystal fabric development, causing the spikes in shear and associated very small crystal sizes that have been located in some polar ice sheets. I have argued that insoluble microparticles do not affect ice-flow rates, but are co-located in these high-shear spikes only because they are deposited on the ice sheets along with the soluble species. At the base of the ice sheets, where the concentration of micro- and of larger particles can be very high, crystal growth is retarded by these high concentrations. Our knowledge of the flow of the basal ice due to these larger particles remains the area of greatest doubt. The results from field and laboratory studies are still unclear, and only a very small amount of research has been carried out to understand the steady-state flow of this dirty ice.

Understanding the processes involved in ice-stream flow is of particular importance for modelling ice sheets, and for estimating the mass balance, particularly of the Antarctic ice sheet. Improvements are required in our understanding of till rheology and of subglacial water generation, storage and transport.

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