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Journal of Glaciology, ( ), .

:

.:

Jordan, R.E., Hardy, J.P., Perron, Jr. F.E. and Fisk, D.MRI

J., : Air permeability and capillary rise as mea-.

sures of the pore structure of snow: an experimen-Akitaya, E., : Studies on depth hoar. Contribu-

tal and theoretical study. Hydrological Processes.tions from the Institute of Low Temperature Sci-

, .ence, , pp.

:Albert, M.R. and Shultz E.F., : Snow and firn

.properties and air-snow transport processes at

: Liquid Permeability.Summit, Greenland. Atmospheric Environment,

., .

Luciano, C.L and Albert, M.R., : BidirectionalAlbert, M.R., Shultz E.F. and Perron Jr., F.E., :

permeability measurements of polar firn. AnnalsSnow and firn permeability at Siple Dome, Antarc-

of Glaciology, , .tica. Annals of Glaciology, , .

Maeno, N., Narita, H. and Araoka, K., : Measure-

ments of air permeability and elastic modulus of:

snow and firn drilled at Mizuho station, East Ant-.

arctica. Memoirs of National Institute of Polar Re-:

search. Special issue, , .

Murakami, S., Ozawa, H. and Yamada, T., : Perme-.

ability coe cient of water in snow and firn at theArakawa, H., Izumi, K. Kawashima, K. and Kawamura,

accumulation area of Yala Glacier, Nepal Hima-T., : Study on quantitative classification of sea-

laya. Bulletin of Glacier Research, , .sonal snow using specific surface area and intrinsic

Rick, U. and Albert, M., : Microstructure of westpermeability. Cold Regions Science and Technol-

antarctic firn and its e ect on air permeability.ogy, . doi: . /j.coldregions. . . .

CREEL TR- - , U.S. Army Cold Regions Re-Coléou, C., Lesa re, B., Brzoska, J.-B. and Flin, F., :

search and Engineering Laboratory, Hanover, N.Imaging by X-ray tomography: an interesting tool

H., pp.to study physical snow properties. Data of Glaci-

Shimizu, H., : Air permeability of depositedological Studies, , .

snow. Contributions from the Institute of LowConway, H. and Abrahamson, J., : Air permeabil-

Temperature Science, , pp.ity as a textual indicator of snow. Journal of Glaci-

:ology, ( ), .

.DeWiest, R. J., : Flow through porous media.

Sommerfeld, R.A. and Rocchio, J.E., : Permeabil-New York and London, Academic press, .

ity measurements on new equitemperature snow.Hardy, J.P. and Albert, D.G., : The permeability

Water Resources Research, ( ): .of temperate snow: Preliminary links to micro-

structure. Proceedings of the th Eastern Snow

:Conference and st Western Snow Conference,

.Quebec City, .

R.N. B.P., :Heggli, M., Frei, E. and Schneebeli, M., : Instru-

ments and methods snow replica method for three-

pp.dimensional X-ray microtomographic imaging.

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RAKAWA ZUMI AWASHIMA SHIIHayato A , Kaoru I , Katsuhisa K and Yoshiyuki I

: The intrinsic permeability (permeability) of various types of snow samples was com-

puted by multiplying the air permeability by the viscosity of the samples. The air permeability was

measured using a double-cylinder permeameter, and the viscosity was calculated using Sutherland’s

equation. Then, the mean grain size ( ) and mean pore size ( ) were measured using the run-length

method. These samples were collected at several sites in Hokkaido Prefecture and at one site in

Toyama Prefecture, Japan, over three winters. All the snow samples were dry and had densities ( )

ranging from to kg m ; permeabilities, from . to . m ; , from . to .

mm; and , from . to . mm. The prediction formula for permeability was derived using and

for all the snow samples as follows: . e . The permeability derived using the

prediction formula is more sensitive to than to . Additionally, the tortuosity of snow ratio of

the length of the curve of tube to the distance between the ends of it was estimated using the

capillary tube model. However, we were unable to obtain reasonable values of the tortuosity. In the

future, the objective is to measure the true tortuosity of snow.

) YAGAI-KAGAKU Co., Ltd.

, Naebo-cho, Higashi-Ku, Sapporo,

) Research Center for Natural Hazards and Disaster Recovery, Niigata University

, Ikarashi -no-cho, Nishi-ku, Niigata

) Institute of Low Temperature Science, Hokkaido University

Kita- , Nishi- , Kita-ku, Sapporo

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Abstract

Relationship between intrinsic permeability and microstructure

of seasonal snow cover

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