Simple relations for the close-off depth and age in dry-snow densification

A physical model for the snow/firn densification process (Salamatin and others, 2006) and Martinerie and others' (1992, 1994) correlation for the firn density at the pore closure are employed to perform a scale analysis and computational experiments in order to deduce simplified relations for the close-off depth and ice age in quasi-stationary ice formation conditions. The critical snow density at which ice-grain rearrangement stops is used to take into account variability of snow structures subjected to densification. The results obtained are validated on a representative set of ice-core data from 22 sites which covers wide ranges of present-day temperatures and ice accumulation rates. A simple analytical approximation for the density-depth profile is proposed

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)

Air-hydrate crystal growth in polar ice

Based on the theory of precipitation from supersaturated solutions proposed by Lifshitz and Slyozov (J. Phys. Chem. Solids 19 (1/2) (1961) 35), we develop a mathematical description of post-formation growth (ripening) of mixed air clathrate-hydrate crystalline inclusions in polar ice sheets. The growth is controlled by oxygen and nitrogen diffusion through the ice matrix. Hydrate populations in general go through three sequential stages: (1) a short transient characterized by the rapid composition relaxation and dissolution of the smallest hydrates, (2) a slow transformation of the resulting size distributions towards a steady-state pattern that is an attribute of (3) the asymptotic stage of ripening. A regularization procedure is used to numerically solve the initial value problem. Computer simulations of the hydrate size distributions are compared to the data from a 3300-m ice core from Vostok Station, East Antarctica. The asymptotic stage is likely unattainable in natural conditions. Data from the GRIP ice core (central Greenland) suggest that the activation energy of hydrate growth increases at the elevated temperature near the ice-sheet bottom. The theory predicts extinction of the climatically induced fluctuations in the hydrate number-concentration and mean-radius profiles in ice sheets with depth. © 2003 Elsevier B.V. All rights reserved

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: 2ė = (τ/μ1 + τα/μ2) exp[Q(1/Ts - 1/T)/Rs] where ė and τ are the effective strain rate and stress, respectively, α is the creep exponent taken as 3.5, Rs is the gas constant and T(Ts) is the temperature (standard temperature). The numerical values obtained for the "linear" and "non-linear" viscosities are: μ1 = 2.9 ± 1.3 MPa year and μ2 = 0.051 ± 0.019 MPaα 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 cm3g-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 cm3g-1

Variations of snow accumulation rate in Central Antarctica over the last 250 years

The present-day global climate changes, very likely caused by anthropogenic activity, may potentially present a serious threat to the whole human civilization in a near future. In order to develop a plan of measures aimed at elimination of these threats and adaptation to these undesirable changes, one should deeply understand the mechanism of past and present (and thus, future) climatic changes of our planet. In this study we compare the present-day data of instrumental observations of the air temperature and snow accumulation rate performed in Central Antarctica (the Vostok station) with the reconstructed paleogeographic data on a variability of these parameters in the past. First of all, the Vostok station is shown to be differing from other East Antarctic stations due to relatively higher rate of warming (1.6 °C per 100 years) since 1958. At the same time, according to paleogeographic data, from the late eighteenth century to early twenty-first one the total warming amounted to about 1 °C, which is consistent with data from other Antarctic regions. So, we can make a conclusion with high probability that the 30-year period of 1985–2015 was the warmest over the last 2.5 centuries. As for the snow accumulation rate, the paleogeographic data on this contain a certain part of noise that does not allow reliable concluding. However, we found a statistically significant relationship between the rate of snow accumulation and air temperature. This means that with further rise of temperature in Central Antarctica, the rate of solid precipitation accumulation will increase there, thus partially compensating increasing of the sea level

Post-nucleation conversion of an air bubble to clathrate air-hydrate crystal in ice

We present an attempt to model the process of conversion of an air bubble, trapped in ice, to clathrate air-hydrate crystal after its nucleation on the air-ice interface. Both counterparts of the transformation are considered: diffusion of interstitial water and air molecules through the growing hydrate layer that coats the bubble surface, and compressive deformation of the three-phase (air-hydrate-ice) system at a given temperature and load pressure. The mathematical model is constrained by laboratory experiments covering a wide range of thermodynamic conditions. Computational tests show that either diffusion or bubble compression can be the rate-limiting step in the post-nucleation growth of air-hydrate crystal. As a plastic material, air-hydrate appears to be, at least, one order harder than ice. The mass transfer coefficient for the diffusion of air and water molecules in air-hydrate is estimated to be 0.6-1.3 mm2/yr at 263 K with the activation energy not higher, than 30-50 kJ/mol. The mass flux of air, although small in comparison with that of water, plays an important role in the conversion. Special attention is paid to the case of air-hydrate growth in air bubbles in polar ice sheets. © 1998 Elsevier Science B.V. All rights reserved

Vostok (Antarctica) ice-core time-scale from datings of different origins

Three different approaches to ice-core age dating are employed to develop a depth-age relationship at Vostok, Antarctica: (1) correlating the ice-core isotope record to the geophysical metronome (Milankovich surface temperature cycles) inferred from the borehole temperature profile, (2) importing a known chronology from another (Devils Hole, Nevada, USA) paleoclimatic signal, and (3) direct ice-sheet flow modeling. Inverse Monte Carlo sampling is used to constrain the accumulation-rate reconstruction and ice-flow simulations in order to find the best-fit glaciological time-scale matched with the two other chronologies. The general uncertainty of the different age estimates varies from 2 to 6 kyr on average and reaches 6-15 kyr at maximum. Whatever the causes of this discrepancy might be, they are thought to be of different origins, and the age errors are assumed statistically independent. Thus, the average time-scale for the Vostok ice core down to 3350 m depth is deduced consistent with all three dating procedures within the standard deviation limits of ± 3.6kyr, and its accuracy is estimated as 2.2 kyr on average. The constrained ice-sheet flow model allows, at least theoretically, extrapolation of the ice age-depth curve further to the boundary with the accreted lake ice where (at 3530 m depth) the glacier-ice age may reach ∼2000 kyr

Российско-французский семинар 2015

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Simulated features of the air-hydrate formation process in the Antarctic ice sheet at Vostok

A recently developed theory of post-nucleation conversion of an air bubble to air-hydrate crystal in ice is applied to simulate two different types of air-hydrate formation in polar ice sheets. The work is focused on interpretation of the Vostok (Antarctica) ice-core data. The hydrostatic compression of bubbles is the rate-limiting step of the phase transformation which is additionally influenced by selective diffusion of the gas components from neighboring air bubbles. The latter process leads to the gas fractionation resulting in lower (higher) N2/O2 ratios in air hydrates (coexisting bubbles) with respect to atmospheric air. The typical time of the post-nucleation converstion decreases at Vostok from 1300-200 a at the beginning to 50-3 a at the end of the transition zone. The model of the diffusive transport of the air constituents from air bubbles to hydrate crystals is constrained by the data of Raman spectra measurements. The oxygen and nitrogen self-diffusion (permeation) coefficients in ice are determined at 220 K as 4.5 x 10-8 and 9.5 x 10-8 mm2 a-1, respectively, while the activation energy is estimated to be about 50 kJ mol-1. The gas-fractionation time-scale at Vostok, T(F) ~ 300 a, appears to be two orders of magnitude less than the typical time of the air-hydrate nucleation, T(Z) ~ 30-35 ka, and thus the condition for the extreme gas fractionation, T(F) << T(Z) is satisfied. Application of the theory to the GRIP and GISP2 ice cores shows that, on average, a significant gas fractionation cannot be expected for air hydrates in central Greenland. However, a noticeable (statistically valid) nitrogen enrichment might be observed in the last air bubbles at the end of the transition

Kinetics of air-hydrate nucleation in polar ice sheets

Nucleation of air clathrate hydrates in air bubbles and diffusive air-mass exchange between coexisting ensembles of bubbles and hydrate crystals are the major interrelated processes that determine the phase change in the air-ice system in polar ice. In continuation of Salamatin et al. where the post-nucleation conversion of single air bubbles to hydrates was considered, we present here a statistical description for transformation of air bubbles to air clathrate hydrates based on the general theory of evolution of these two ensembles, including the gas fractionation effects. The model is fit to data on ice cores from central Antarctica, and then compared to other ice-core data. The focus is on the rate of clathrate-hydrate nucleation, which is determined to be the product of the inverse relative bubble size raised to the power λ≈5.8 with the relative supersaturation to the power β≈2. The clathration-rate constant is k0≈3.2-4.5×10-6 yr-1 at 220 K. The N2- and O2-permeation coefficients in ice, at 220 K, are inferred to be DN(2) 0≈1.8-2.5×10-8 mm2 yr-1 and DO(2) 0≈5.4-7.5×10-8 mm2 yr-1, respectively. Comparison of observations to simulations of bubble-to-hydrate transformation in Greenland ice sheet gave estimates for activation energies of hydrate formation and air diffusion of QJ≈70 kJ mol-1 and Qd≈50 kJ mol-1, respectively