Effect of density on electrical conductivity of chemically laden polar ice

Journal of Geophysical Research, Vol. 107, No. B2, p. 10.1029/2000JB000080, ESE 1-1 - ESE 1-14, 2002 

P.R.F. Barnes, E.W. Wolff, R. Mulvaney
British Antarctic Survey, Natural Environmental Research Council, Cambridge, England, UK.
R. Udisti
Department of Chemistry, University of Calabria, Arcavacata di Rende, Italy.
E. Castellano
Department of Public Health and Environmental Analytical Chemistry, University if Florence, Florence, Italy.
R. Röthlisberger
Climate and Environmental Physics, Physics Institute, University of Bern, Bern, Switzerland.
J.-P. Steffensen
Departement of Geophysics, The Niels Bohr Institute of Astronomy, Physics and Geophysics, University of Copenhagen.

ABSTRACT.
Electrical conductivity measurements made using the dielectric profiling technique (DEP) are compared to chemical data from the top 350 m of the Dome C ice core in Antarctica. The chemical data are used to calculate the concentration of the major acidic impurities in the core: sulphuric acid and hydrochloric acid. The conductivity coefficients in solid ice for sulphuric acid (β_H2SO4) and hydrochloric acid (β_HCl) are found to be 4.9 and 4.5 m^-1M^-1. These are consistent with previously found values for the acid conductivity coefficient at different sites and suggest that the same conductivity mechanisms are important in all polar ice. A method of rolling regression analysis is used to find the variation of the pure ice conductivity (σ _∞pure) and the conductivity and the conductivity coefficient of sulphuric acid, β_H2SO4, with depth. Then σ _∞pure and β_H2SO4 are assessed against changes in core density and hence volume fraction of ice, ν, due to the inclusion of air bubbles in the firn. Looyenga's model for dielectric mixtures applied to conduction in firn broadly predicts the variation observed in σ _∞pure but does not fit well for ice above 110 m. A previous application of the theory of percolation in random lattices is used to model the conductivity coefficient in firn. The coefficient β_H2SO4 is linked to n by the power law: β_H2SO4 (ν) ∝ β_H2SO4 (1)(ν - ν _c)^t; where ν_c is a threshold volume fraction below which no conduction can take place and is related to the geometry of the conducting lattice being modeled. The value of the exponent t is also dependent on the structure of the lattice and is here found to be t = 2.5, which is slightly lower than the previously obtained value of t = 2.7 for a structure where each grain has between 14 and 16 nearest neighbors. This model is consistent with the concept of conduction, via liquid H₂SO₄, taking place at two grain boundaries for firn. The model does not, however, preclude conduction taking place via acid situated at three grain boundaries or in an interconnected vein network at densities above 640 kg m^-3 .