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

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

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

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

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

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 m deep 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 (590 m above the bedrock) is around 335 ± 4.5 kyr and may reach 2000 kyr at about 3000 m depth. 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 W m-2 and ice-fusion temperature (-2°C) at the ice-rock interface with minimum (zero) melt rates

State dependence of climatic instability over the past 720,000 years from Antarctic ice cores and climate modeling

Climatic variabilities on millennial and longer time scales with a bipolar seesaw pattern have been documented in paleoclimatic records, but their frequencies, relationships with mean climatic state, and mechanisms remain unclear. Understanding the processes and sensitivities that underlie these changes will underpin better understanding of the climate system and projections of its future change. We investigate the long-term characteristics of climatic variability using a new ice-core record from Dome Fuji, East Antarctica, combined with an existing long record from the Dome C ice core. Antarctic warming events over the past 720,000 years are most frequent when the Antarctic temperature is slightly below average on orbital time scales, equivalent to an intermediate climate during glacial periods, whereas interglacial and fully glaciated climates are unfavourable for a millennial-scale bipolar seesaw. Numerical experiments using a fully coupled atmosphere-ocean general circulation model with freshwater hosing in the northern North Atlantic showed that climate becomes most unstable in intermediate glacial conditions associated with large changes in sea ice and the Atlantic Meridional Overturning Circulation. Model sensitivity experiments suggest that the prerequisite for the most frequent climate instability with bipolar seesaw pattern during the late Pleistocene era is associated with reduced atmospheric CO2 concentration via global cooling and sea ice formation in the North Atlantic, in addition to extended Northern Hemisphere ice sheets

Dislocation mechanism for transformation between cubic ice I-c and hexagonal ice I-h

Cubic ice I-c is metastable, yet can form by the freezing of supercooled water, vapour deposition at low temperatures and by depressurizing high-pressure forms of ice. Its structure differs from that of common hexagonal ice I-h in the order its molecular layers are stacked. This stacking order, however, typically has considerable disorder; that is, not purely cubic, but alternating in hexagonal and cubic layers. In time, stacking-disordered ice gradually decreases in cubicity (fraction having cubic structure), transforming to hexagonal ice. But, how does this disorder originate and how does it transform to hexagonal ice? Here we use numerical data on dislocations in hexagonal ice I-h to show that (1) stacking-disordered ice (or I-c) can be viewed as fine-grained polycrystalline ice with a high density of extended dislocations, each a widely extended stacking fault bounded by partial dislocations, and (2) the transformation from ice I-c to I-h is caused by the reaction and motion of these partial dislocations. Moreover, the stacking disorder may be in either a higher stored energy state consisting of a sub-boundary network arrangement of partial dislocations bounding stacking faults, or a lower stored energy state consisting of a grain structure with a high density of stacking faults, but without bounding partial dislocations. Each state transforms to I-h differently, with a duration to fully transform that strongly depends on temperature and crystal grain size. The results are consistent with the observed transformation rates, transformation temperatures and wide range in heat of transformation