Andrey N. Salamatin

Bubbly-ice densification in ice sheets : II. Applications

A mathematical model for simulating the densification of bubbly glacier ice is used to interpret the following experimental data from the Vostok (central Antarctica) ice core: two ice-porosity profiles obtained by independent methods and a bubble-pressure profile obtained by direct measurements of air pressure within individual bubbles. The rheological properties of pure polycrystalline ice are deduced from the solution of the inverse problem. The model and the inferred ice-flow law are then validated, using porosity profiles from seven other ice cores drilled in Antarctica and Greenland, in the temperature range from -55° to -20°C. The following expression is adopted for the constitutive law: 2e˙ = (τ/μ 1 + τ α /μ 2 ) exp[Q(1/T s - 1/T)/R s ] where e˙ and τ are the effective strain rate and stress, respectively, α is the creep exponent taken as 3.5, R s is the gas constant and T(T s ) is the temperature (standard temperature). The numerical values obtained for the linear and non-linear viscosities are: μ 1 = 2.9 ± 1.3 MPayear and μ 2 = 0.051 ± 0.019 MPa α year, and the apparent activation energy Q is confirmed to be 60 kJ mole -1 . The corresponding flow law is in good agreement with results of both mechanical tests and independent estimations based on the analysis of different natural phenomena associated with glacier-ice deformation. When the model is constrained by the porosity and bubble-pressure profiles from Vostok, the mean air content in Holocene ice is inferred to be about 0.088 cm 3 g -1 . The corresponding mean air pressure in bubbles at the end of pore closure is about 0.083 MPa, whereas the atmospheric pressure at this depth level would be 0.063 MPa. The influence of the climatic change on the ice-porosity profile is discussed. It resulted in an increased air content in ice at Vostok during the Last Glacial Maximum: 0.096 cm 3 g -1 .

Characteristics of a crater glacier at Ushkovsky volcano, Kamchatka, Russia, as revealed by the physical properties of ice cores and borehole thermometry

A glacier at the summit of Ushkovsky volcano, Kamchatka peninsula, Russia, was studied in order to obtain information about the physical characteristics of a glacier that fills a volcanic crater. The glacier has a gentle surface and a concave basal profile with a maximum measured depth of 240 m at site K2. The annual accumulation rate was 0.54 m a -1 w.e., and the 10 m depth temperature was -15.8°C. A 211.70 m long ice core drilled at K2 indicates that (1) the site is categorized as a percolation zone, (2) the stress field in the glacier changes at 180 m depth from vertical and longitudinal compression with transversal extension, which is divergent flow, to a shear-dominated stress field, and (3) the frequent occurrence of ash layers can be a good tool for dating the ice core. The borehole temperature profiles were considered to be non-stationary, but the linear profile made it possible to estimate the basal temperature and the geothermal heat flux at K2. Assuming constant surface and the basal boundary conditions, we constructed two depth-age relationships at K2. These predicted that the bottom ages of the ice core were about 511 or 603 years.

Modelling dynamics of glaciers in volcanic craters

General equations of ice dynamics are re-examined, using scale analysis, in order to derive a simplified thermomechanically coupled model for ice flow and heat transfer in ice caps filling volcanic craters. Relatively large aspect ratios between crater depths and diameters, low surface temperatures and intense volcanic heating are the principal characteristics of such craters. The conventional boundary-layer (shallow-ice) approximation is revised to account for these conditions and, in addition, the variable density of the snow, firn and bubbly ice. Large crater depths and intense bottom melting result in low longitudinal balance velocities, controlled by both shear and longitudinal stresses, and hence small surface slopes. In such situations ice can be assumed to be linearly viscous. A flowline model of the glacier dynamics is developed using this assumption. Explicit predictive formulas for ice-particle trajectories and age-depth relations, thus obtained, suggest that the age of ice at the bottom of glaciers in volcanic craters on Kamchatka Peninsula, Russia, may reach hundreds or thousands of years. Ice cores from these glaciers represent unique climatic and volcanic archives.

Depth–age and temperature prediction at Dome Fuji station, East Antarctica

Abstract The geophysical metronome (Milankovitch components of the past surface temperature variations) and the isotope–temperature transfer function deduced from the borehole temperature profile at Vostok station, Antarctica, are applied to date the 2500 mdeep ice core from Dome Fuji station, Antarctica, and to reconstruct paleoclimatic conditions at the drilling site on the basis of the local δ18O isotope record. Special attention is paid to consistency of this depth–age relation with the mass-balance reconstruction and predictions of ice-flow modeling. the present-day ice mass-balance rate at Dome Fuji is estimated as 3.2 cm a–1. the ice age at the borehole bottom (590m above the bedrock) is around 335 ± 4.5 kyr and may reach 2000 kyr at about 3000 mdepth.The difference in the ice-sheet surface temperatures between Holocene optimum and Last Glacial Maximum is found to be 17.8˚C at the temporal isotope/temperature slope, about 30% lower than the modern geographical estimates. A good agreement between modeled and measured (preliminary data) borehole temperatures is obtained at the geothermal flux 0.059 Wm–2 and ice-fusion temperature (–2˚C) at the ice–rock interface with minimum (zero) melt rates.

Bubbly-ice densification in ice sheets: I. Theory

Dry snow on the surface of polar ice ice sheets is first densified and metamorphosed to produce firn. Bubbly ice is the next stage of the transformation process which takes place below the depth of pore closure. This stage extends to the transition zone where, due to high pressures and low temperatures, air trapped in bubbles and ice begins to form the mixed air clathrate hydrates, while the gas phase progressively disappears. Here we develop a model of bubbly-ice rheology and ice-sheet dynamics taking into account glacier-ice compressibility. The interaction between hydrostatic compression of air bubbles, deviatoric (uniaxial) compressive deformation of the ice matrix and global deformations of the glacier body is considered. The ice-matrix pressure and the absolute-load pressure are distinguished. Similarity theory and scale analysis are used to examine the resultant mathematical model of bubbly-ice densification. The initial rate of bubble compression in ice sheets appears to be relatively high, so that the pressure (density) relaxation process takes place only 150-200 m in depth (below pore close-off) to reach its asymptotic phase, wherein the minimal drop between bubble and ice pressures is governed by the rate of loading (ice accumulation). This makes it possible to consider densification under stationary (present-day) conditions of ice formation as a special case of primary interest. The computational tests performed with the model indicate that both ice-porosity and bubble-pressure profiles in ice sheets are sensitive to variations of the rheological parameters of pure ice. However, only the bubble-pressure profile distinguishes between the rheological properties at low and high stresses. The porosity profile at the asymptotic phase is mostly determined by the air content in the ice. In the companion paper (Lipenkov and others, 1997), we apply the model to experimental data from polar ice cores and deduce, through an inverse procedure, the rheological properties of pure ice as well as the mean air content in Holocene and glacial ice sediments at Vostok Station (Antarctica).

Spatial distribution of air molecules within individual clathrate hydrates in polar ice sheets

Abstract We measured the N2/O2 ratios in clathrate hydrate crystals from Vostok Antarctic ice cores using Raman spectroscopy in order to investigate the spatial distribution of air molecules within a crystal. The results showed that the pattern of the spatial distribution of air molecules in clathrate hydrate depends on the crystal. Some clathrate hydrates have inhomogeneous distributions of the N2/O2 ratio within the crystals, while others are practically homogeneous. The spatial distribution of air molecules within an individual clathrate hydrate changes with time due to three processes: (1) the initial selective enclathration caused by the difference between the dissociation pressures of pure N2- and O2–clathrate hydrates, (2) the diffusive mass transfer of air molecules from surrounding air bubbles through the ice matrix, and (3) diffusion of air molecules in the clathrate hydrate crystal. The dissociation pressures and the diffusion rates of air molecules in ice and clathrate hydrate strongly depend on temperature. Therefore, it is concluded that the pattern of the spatial distribution of air molecules in clathrate hydrate is mainly determined by the depth at which they formed and the temperature in the ice sheet.