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During the austral summers of 1976–77 and 1978–79, several ice cores were taken from the McMurdo Ice Shelf brine zone to investigate its thermal, physical, and chemical properties. This brine zone consists of a series of superimposed brine layers (waves) that originate at the seaward edge of the ice shelf and migrate at various rates, depending on their age and position in the ice shelf. The brine in these layers becomes increasingly concentrated as the waves migrate inland through the permeable ice-shelf firn. Chemical analyses of brine samples from the youngest (uppermost) brine wave show that, except for the advancing front, it contains sea salts in normal sea-water proportions. Further inland, deeper and older brine layers, though highly saline (S > 200°/00), are severely depleted in SO42-, with the SO42-/Na+ ratio being an order of magnitude less than that of normal sea-water. Consideration of the solubility of alternative salts, together with analyses of Na+, K+, Ca2+, Mg2+, SO42-, and Cl- concentrations, shows that the sulfate depletion is probably due to selective precipitation of mirabilite, Na2SO4·10H2O. The location of the inland boundary of brine penetration is closely related to the depth at which the brine encounters the firn/ice transition. However, a small but measureable migration of brine is still occurring in otherwise impermeable ice; this is attributed to eutectic dissolution of the ice by concentrated brine as it moves into deeper and warmer parts of the McMurdo Ice Shelf.
The time-scale for the onset of the explosive growth of a finite-amplitude shear-heating instability in the down-slope creep of a thick ice sheet is determined by integrating the equation for the temporal evolution of the temperature-depth profile subsequent to a sudden change in ice thickness. All instabilities eventually grow explosively after a prolonged period of simmering or relatively slow monotonic growth. Though times for explosive growth depend on initial and final ice thicknesses, surface temperature, accumulation rate, basal heat flux, and ice rheological parameters, the explosion times are extremely sensitive to the activation energy and the pre-exponential constant of the ice-creep law. Sudden increases in ice-sheet thickness of 1–2 km due to a rapid climatic deterioration can lead to explosive instability and melting of the basal shear layer in only thousands of years if ice-creep activation energies are lower than about 60 kJ mol-1.
Data from experimental tests of snow-block impact against vertical barriers are used to establish values of parameters in order to computer-model the impact mechanics. The results show that total impulse, impact force, and duration of impact can be modeled by accurate specification of the kinematic viscosity in the fluid representation. In modeling the highly transient impact, kinematic viscosity of the material is determined to vary linearly with the impact velocity. This non-physical condition is attributed to lack of accountability of compressibility effects in the computer model, and reduces modeling to an empirical approach. A biviscous modeling of the impact process is in near correspondence to linear viscous modeling, due to dominant importance of block momentum on impact rather than fluidity of material in the impact region.
Wave ogives arise in a solution of the continuity equation by the method of characteristics. Steady ice flow is assumed. Ice velocity, channel width, and mass-balance functions combine to form a wave-excitation potential that yields the forcing function for wave ogives. This linear-systems formulation extends the ogive theory of Nye. Convolution of the temporal cumulative mass balance and spatial forcing functions gives the total wave pattern below an ice fall. Many ice falls do not generate ogives because the wave amplitude is modulated by a factor related to ice-fall length. The wave ogives at Austerdalsbreen, Norway, are due almost entirely to ice acceleration at the top of the ice-fall, i.e. the same zone that King and Lewis showed was responsible for forming Forbes bands.
The “vertically” integrated, exact longitudinal stress-equilibrium equation of Budd (1970) is developed further in such a way as to yield an equation that gives explicitly and exactly the contributions to the basal shear stress made by surface and bed slope, surface curvature, longitudinal stress deviators, and longitudinal stress gradients in a glacier flowing in plane strain over a bed of longitudinally varying slope. With this exact equation, questions raised by various approximate forms of the longitudinal equilibrium equation can be answered decisively, and the magnitude of errors in the approximations can be estimated. To first order, in the angle δ that describes fluctuations in the surface slope α from its mean value, the exact equilibrium equation reduces to
where G and T are the well-known stress-deviator-gradient and “variational stress” terms, K is a “longitudinal curvature” term, and B is a “basal drag” term that contributes a resistance to sliding across basal hills and valleys. Except for T, these terms are expressed in simple form and evaluated for practical situations. The bed slope θ (relative to the mean slope) is not assumed to be small, which allows the effects of bedrock topography to be determined, particularly through their appearance in the B term.
The “T term” in the longitudinal stress-equilibrium equation for glacier mechanics, a double y-integral of ∂2τxy/∂x2 where x is a longitudinal coordinate and y is roughly normal to the ice surface, can be evaluated within the framework of longitudinal flow-coupling theory by linking the local shear stress τxy at any depth to the local shear stress τB at the base, which is determined by the theory. This approach leads to a modified longitudinal flow-coupling equation, in which the modifications deriving from the T term are as follows: 1. The longitudinal coupling length is increased by about 5%. 2. The asymmetry parameter σ is altered by a variable but small amount depending on longitudinal gradients in ice thickness h and surface slope α. 3. There is a significant direct modification of the influence of local h and α on flow, which represents a distinct “driving force” in glacier mechanics, whose origin is in pressure gradients linked to stress gradients of the type ∂τxy/∂x. For longitudinal variations in h, the “T force” varies as d2h/dx2 and results in an in-phase enhancement of the flow response to the variations in h, describable (for sinusoidal variations) by a wavelength-dependent enhancement factor. For longitudinal variations in α, the “force” varies as dα/dx and gives a phase-shifted flow response. Although the “T force” is not negligible, its actual effect on τB and on ice flow proves to be small, because it is attenuated by longitudinal stress coupling. The greatest effect is at shortest wavelengths (λ 2.5h), where the flow response to variations in h does not tend to zero as it would otherwise do because of longitudinal coupling, but instead, because of the effect of the “T force”, tends to a response about 4% of what would occur in the absence of longitudinal coupling. If an effect of this small size can be considered negligible, then the influence of the T term can be disregarded. It is then unnecessary to distinguish in glacier mechanics between two length scales for longitudinal averaging of τb, one over which the T term is negligible and one over which it is not.
Longitudinal flow-coupling theory also provides a basis for evaluating the additional datum-state effects of the T term on the flow perturbations Δu that result from perturbations Δh and Δα from a datum state with longitudinal stress gradients. Although there are many small effects at the ~1% level, none of them seems to stand out significantly, and at the 10% level all can be neglected.
The foregoing conclusions apply for long wavelengths λh. For short wavelengths (λ h), effects of the T term become important in longitudinal coupling, as will be shown in a later paper in this series.
“Avalanche-type” medial moraines are described on four Torngat Mountains glaciers with single, rather than compound, firn basins. They form from debris avalanching down couloirs and are exposed by ice melt to form extensive debris covers on glacier snouts in the Torngat Mountains. The debris may play an important part in helping the glacier survive periods with warm summers and/or dry winters since, in the Torngat Mountains, average ice melt on debris-covered sites is approximately one-third that on exposed ice.
Mount Redoubt, a volcano located west of Cook Inlet in Alaska, erupted from 1966 to 1968. This eruptive cycle removed about 6 × 107 m3 of glacier ice from the upper part of Drift Glacier and decoupled it from the lower part during a sequence of jökulhlaups which originated in the Summit Crater and flooded Drift River. The same events blanketed the lower part of the glacier with sand and ash, reducing ice ablation. Normal snowfall, augmented by intense avalanching, regenerated the upper part of the glacier by 1976, 8 years after the eruptions. When the regenerated glacier connected with the rest of Drift Glacier, it triggered a kinematic wave of thickening ice accompanied by accelerating surface velocities in the lower part of the glacier. Surface velocities increased by an order of magnitude and were accompanied by thickening of 70 m or more. At the same time, parts of the upper glacier thinned 70 m. The glacier appears to be returning to its pre-eruption equilibrium condition.
Two isotropic points measured by Meier and others (1985) on Columbia Glacier, Alaska, are examined. The pattern classification of the upper one is on the borderline between monstar and lemon, and this is traced to the fact that the variation of strain-rate in the longitudinal direction is approximately equal to that in the transverse direction, contrary to the assumption made in Nye (1983). The conditions for the lower isotropic point to have the star pattern, as observed, are believed to be typical for a glacier that ends in an ice cliff, like this one, which calves icebergs. Where, as in this case, there is only a small transverse velocity, the isotropic points on a glacier must nearly coincide with stationary points for the speed, and these are almost always either maxima or saddles, alternating. The maxima correspond to lemon or monstar patterns, and the saddles to star patterns.
Two situations are studied in relation to the flow law of polar ice. In each case, models are used with a flow-law exponent of one, and with the more traditional exponent of three. The horizontal velocity profile at Devon Island, Arctic Canada, is better fitted by n = 1; for the vertical velocity profile, n = 3 gives a better fit, but both model profiles fall well within experimental error. For the Camp Century age–depth profile, only n = 1 gives an acceptable fit when temperature is allowed for. The large discrepancy between isothermal and non-isothermal models for n = 3 shows the importance of allowing for temperature in studies of ice-sheet properties.
A theoretical examination of salinity and porosity changes introduced in sea-ice samples by brine expulsion and gas entrapment caused by thermal cycling during shipping and storage shows that in extreme cases such effects can be significant, resulting in 15% reductions in porosity (n) More representative scenarios give porosity changes of less than 2% which, assuming that ice-property variations scale with n1/2, result in property variations of less than 1%.
VLF surface-impedance measurements have been used in the past for sub-surface mapping. The application of this technique to glacial ice probing is discussed theoretically and results of measurements on Brewster Glacier, New Zealand, are presented. Results were fitted to a three-layer model and a section profile is given. Dramatic changes in the phase of the surface impedance were observed in the vicinity of crevasses. Results indicate that the technique has potential as a tool for quick, reliable, and non-invasive ice-thickness measurements.
The surface condition of the North Water was investigated during two winters (i.e. the three polynyas: Smith Sound polynya, Lady Ann Strait polynya, and Barrow Strait polynya). Since no detailed information was available on ice conditions and the extent of open water during winter, radiometric temperature measurements of the sea surface had to be taken along a flight line of 2650 km from an altitude of 300 m. From November to March 1978-79 and 1980-81, 14 remote-sensing flights were carried out. On the basis of the radiometric measurements, the following ice types were identified: ice-free, dark nilas, light nilas, grey ice, grey-white ice, and white ice. A comparison between the thermal and the visual ice classification (the latter being based on grey tones of the aerial images) showed a deviation of 3%. The analysis showed that in November, December, and January more than 50% of the Smith Sound polynya was covered by young ice, nilas, and ice-free, whereas in February and March white ice was dominant. Moreover, it was found that the two polynyas in Smith Sound and Lady Ann Strait were much smaller than previously believed. In Barrow Strait, a semi-permanent polynya was observed in the winter of 1980-81. The occurrence of polynyas in Barrow Strait seems to be connected with the location of the fast-ice edge. On the basis of the calculated ice-type distribution and heat-flux rates for different ice types, an energy loss of 178 W m-2 was found on the surface of the Smith Sound polynya due to open water and thin ice for the winter months November to March. Compared with other ice-covered sea surfaces in the Arctic, the heat release by the sea-water in the Smith Sound polynya is about 100 W m-2 larger.
The average three-dimensional coordination number, n3, is an important measure of firn structure. The value of n3 can be estimated from n2, the average measured two-dimensional coordination number, and from a function, Γ, that depends only on the ratio of average bond radius to grain radius in the sample. This method is easy to apply and does not require the use of unknown shape factors or tunable parameters.
Series of experiments were conducted with the aim of determining the influences of the following factors on freeze-bonding between contacting ice blocks in floating ice rubble: pressure normal to the contact plane, period and area of contact, and salinity of the water in which freeze-bonding occurred. Freeze-bonding between ice blocks in air was also investigated. The experiments were conducted with water and air temperatures of about 0°C and normal pressures, between ice blocks, up to 4 kPa. This range of normal pressures may occur hydrostatically between ice blocks in layers of floating ice rubble up to about 10 m thick, or in 2-3 m thick layers which are in a passive Rankine state of pressure. The experiments show that stronger freeze-bonds develop between ice blocks in distilled water, tap water, and water from the Iowa River than develop between ice blocks contacting in air at 0°C. However, stronger freeze-bonds developed in air at 0°C than developed between ice blocks in 0°C saline (NaCl) solutions with salinities in excess of 12.5% by weight. The strength of freeze-bonding increased linearly with contact period for ice blocks in distilled, tap, and river waters, but did not increase with contact period for ice blocks contacting in saline solutions or in air. The results of the experiments are useful contributions to explanations of the shear-strength behavior of a layer of floating ice rubble. For example, thicker layers of ice rubble may show greater cohesive behavior, because normal pressures and thus freeze-bond strengths increase with layer thickness.
Existence of a very thin layer of adsorbed water adjacent to particles embedded in ice allows relative motion between ice and particles even at sub-freezing temperatures if there are either applied stresses or macroscopic temperature gradients. Theoretical analysis of such motion involving a single sphere demonstrates that such motion is dominantly due either to “viscous” deformation in the ice or to mass transport in the liquid layer at temperatures below the nominal pressure melting-point, depending on the ratio of the sphere’s radius to a temperature-dependent “transition radius”. This result should also hold for motion of a cylinder (for which the creeping flow problem has no known analytical solution). Reviewing data on wire regelation at sub-freezing temperatures in the context of this analysis suggests that all “anomalous” data correspond to cases in which wire radii were greater than the transition radius, leading to dominance of ice-deformation effects. Ice motion past very small particles, on the other hand, is essentially accommodated entirely by mass transfer through the liquid layer. This result lends support to the “rigid-ice” model of frost heaving as proposed by R.D. Miller and co-workers, and permits approximate analysis of ice movement through a porous soil. In all cases involving relative motion between ice and particles at sub-freezing temperatures, the existence of macroscopic temperature gradients plays an important role.
Many observations regarding grain growth in ice sheets are glaciologically interesting but imperfectly understood. Here we develop the theory of grain growth in ice that is not deforming rapidly, and in the succeeding paper we use this theory to explain observations from glacial ice. In the absence of significant strain energy, the driving force for grain growth arises from grain-boundary curvature. Grain growth is slowed by the interaction of grain boundaries with extrinsic materials (microparticles, bubbles, and dissolved impurities). If the driving force for growth is not large enough to cause boundaries to separate from an extrinsic material, then the grain-boundary velocity is determined by the velocity characteristic of the extrinsic material (low-velocity regime). If the driving force is large enough to cause separation, then boundaries migrate more rapidly than the extrinsic material (high-velocity regime) but the net driving force is reduced through transient pinning by the extrinsic material. Polar ice is typically in the low-velocity regime relative to dissolved impurities and the high-velocity regime relative to microparticles and bubbles. Cross-sectional area of grains is predicted to increase linearly with time under most but not all circumstances.
Grain growth observed in polar ice that is not deforming rapidly can be accounted for if concentrations and distributions of extrinsic materials (microparticles, bubbles, and dissolved impurities) are characterized fully. Dissolved impurities segregate to grain boundaries and slow grain growth in all cold glacial ice. The high concentration of soluble impurities in Wisconsinan ice from the Dome C (Antarctica) ice core (and perhaps other ice cores) probably causes the small grain-sizes observed in that ice. Microparticles have little effect on grain growth in ordinary ice. In ice layers that appear dirty owing to concentrations of volcanic tephra (such as in the Byrd Station (Antarctica) ice core) or of morainal material, micro particles reduce grain-growth rates significantly. The relatively high vapor pressure of ice allows rapid growth and high mobility of intergranular necks, so grain growth in firn is limited by boundary migration rather than by neck growth. Bubbles formed by pore close-off at the firn-ice transition are less mobile than grain boundaries, causing bubble-boundary separation whenever geometric constraints are satisfied; however, such separation reduces grain-growth rates by only about 10%. The observed linear increase of grain area with time is thus predicted by theory, but the growth rate depends on soluble-impurity concentrations as well as on temperature.
A statistical model characterizing the granular structure of snow is developed using quantitative stereology. The model is based on specific parameters (e.g. bond radius, grain-size, etc.) which take the form of internal-state variables in a constitutive theory for high-rate deformation of snow. In addition to parameters developed by other authors in previous investigations, a new parameter characterizing the mean bond length is developed. More significantly, general relations are derived for the mean number of bonds per grain and mean number of grains per unit volume without making any assumptions regarding the shape or size of the ice grains, or their respective distributions.
A theoretical model is developed to describe the steady-state behavior of interconnected, water-filled cavities at the glacier bed. Physically plausible cavities should contain constrictions along the flow path, with flow in the wider sections being relatively sluggish. Mean flow rates in cavities may be at least one order of magnitude less than in channels incised into the basal ice (R channels). Melting due to viscous dissipation - the process that allows R channels to exist - probably plays a minor or negligible role, as compared to glacier sliding, in determining the size of cavities. Furthermore, a system of subglacial cavities should not show a tendency for localization of flow in a few main conduits, as does an R-channel system. If water pressure rises to within several bars of overburden pressure, the rate of cavity closure by creep falls below the rate of cavity opening by sliding and melting, with cavities then becoming unstable. Subsequent evolution of the drainage system should depend upon the total melt-water flux. Circumstances may arise in which cavities and channels act as conduits for melt water; such a configuration would probably show unusual transient behavior.