Effective coefficient of diffusion and permeability of firn at Dome C and Lock In, Antarctica, and of various snow types – estimates over the 100–850 kg m−3 density range

• Published in: The Cryosphere
• Main Authors: Calonne, Neige, Burr, Alexis, Philip, Armelle, Flin, Frédéric, Geindreau, Christian
• Format: Text
• Language: English
• Published: 2022
• Subjects: Greenland; Antarc*; Antarctica
• Online Access: https://doi.org/10.5194/tc-16-967-2022; https://tc.copernicus.org/articles/16/967/2022/

Modeling air transport through the entire firn column of polar ice sheets is needed to interpret climate archives. To this end, different regressions have been proposed in the past to estimate the effective coefficient of diffusion and permeability of firn. These regressions are often valid for specific depth or porosity ranges only. Also, they constitute a source of uncertainty as evaluations have been limited by the lack of reliable data of firn transport properties. To contribute with a new dataset, this study presents the effective coefficient of diffusion and the permeability at Dome C and Lock In, Antarctica, from the near-surface to the close-off (23 to 133 m depth). Also, microstructure is characterized based on density, specific surface area, closed porosity ratio, connectivity index, and structural anisotropy through the correlation lengths. All properties were estimated based on pore-scale computations from 3D tomographic images of firn samples. The normalized diffusion coefficient ranges from 1.9 × 10 −1 to 8.3 × 10 −5 , and permeability ranges from 1.2 × 10 −9 to 1.1 × 10 −12 m 2 , for densities between 565 and 888 kg m −3 . No or little anisotropy is reported. Next, we investigate the relationship of the transport properties with density over the firn density range (550–850 kg m −3 ), as well as over the entire density range encountered in the ice sheets (100–850 kg m −3 ), by extending the datasets with transport properties of alpine and artificial snow from previous studies. Classical analytical models and regressions from literature are evaluated against the estimates from pore-scale simulations. For firn, good agreements are found for permeability and the diffusion coefficient with two existing regressions of the literature based on open porosity despite the rather different site conditions (Greenland). Over the entire 100–850 kg m −3 density range, permeability is accurately reproduced by the Carman–Kozeny and self-consistent (spherical bi-composite) models when expressed in terms of a rescaled porosity, <math xmlns="http://www.w3.org/1998/Math/MathML" id="M15" display="inline" overflow="scroll" dspmath="mathml"><mrow><msub><mi mathvariant="italic">ϕ</mi><mi mathvariant="normal">res</mi></msub><mo>=</mo><mo>(</mo><mi mathvariant="italic">ϕ</mi><mo>-</mo><msub><mi mathvariant="italic">ϕ</mi><mi mathvariant="normal">off</mi></msub><mo>)</mo><mo>/</mo><mo>(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mi mathvariant="italic">ϕ</mi><mi mathvariant="normal">off</mi></msub><mo>)</mo></mrow></math> <svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="128pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="2179c8ebbdf91346e5cabed3daca5e0b"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tc-16-967-2022-ie00001.svg" width="128pt" height="14pt" src="tc-16-967-2022-ie00001.png"/></svg:svg> , to account for pore closure, where ϕ off is the close-off porosity. For the normalized diffusion coefficient, none of the evaluated formulas were satisfactory, so we propose a new regression based on the rescaled porosity that reads <math xmlns="http://www.w3.org/1998/Math/MathML" id="M17" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>D</mi><mo>/</mo><msup><mi>D</mi><mi mathvariant="normal">air</mi></msup><mo>=</mo><mo>(</mo><msub><mi mathvariant="italic">ϕ</mi><mi mathvariant="normal">res</mi></msub><msup><mo>)</mo><mn mathvariant="normal">1.61</mn></msup></mrow></math> <svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="90pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="6be918eb4a3df42d714fb732af27cc09"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tc-16-967-2022-ie00002.svg" width="90pt" height="16pt" src="tc-16-967-2022-ie00002.png"/></svg:svg> .