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Modelling of water flow through Snowpacks

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Part of the book series: NATO ASI Series ((ASIC,volume 211))

Abstract

In this chapter physics-based models for the movement of water through snow are described. The conservation and constitutive equations for a mixture of ice, water, water vapour and air are derived and the various simplified forms of these equations used in current models are explained. The relation between microscopic physics-based and macroscopic empirical constitutive equations is discussed. Finally boundary conditions for the models are defined in terms of energy and mass fluxes and methods of calculating these fluxes from meteorological and hydrological data described.

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References

  • Akan (1984) ‘Simulation of runoff from snow covered hillslopes.’ Water Resources Research Vol.20 No.6 p.707–713.

    Article  Google Scholar 

  • Anderson, E.A. (1976). ‘A point energy and mass balance model of a snow cover.’ NOAA Technical Report, National Weather Service 19, U.S. Department of Commerce.

    Google Scholar 

  • Bender, J.A. (1957). ‘Air permeability of snow’. Research Report 37. Snow, Ice and Permafrost Research Establishment. (U.S. Army Corps of Engineers) Wilmette, Illinois.

    Google Scholar 

  • Bergen, J.D. (1968). ‘Some measurements of air permeability in a mountain snowcover’. IAHS Bulletin Vol.13 No,3 p.5–13.

    Google Scholar 

  • Brutsaert, W. (1975). ‘On a derivable formula for long-wave radiation from clear skies’. Water Resources Research Vol.11 No.5 p.742–744.

    Article  Google Scholar 

  • Businger, J.A. (1965). ‘Eddy diffusion and settling speed in blown snow’. Journal of Geophysical Research Vol.70 p.3307–3313.

    Article  Google Scholar 

  • Businger, J.A., Wyngaard, J.C., Izumi, Y. and Bradley, E.F.(1971). ‘Flux-profile relationships in the atmospheric surface layer’. Journal of Atmospheric Science Vol.28 p.181–189.

    Article  Google Scholar 

  • Chamberlain, A.C. (1983) ‘Roughness length of sea, sand and snow.’ Boundary Layer Meteorology Vol.25 No.4 p.405–410.

    Article  Google Scholar 

  • Colbeck, S.C. (1972). ‘A theory of water percolation in snow’. Journal of Glaciology Vol.11 No.63 p.369–385.

    Google Scholar 

  • Colbeck, S.C. (1974) ‘On predicting water runoff from a snow cover. ‘ In: Advanced concepts in the study of snow and ice resources. (US National Academy of Sciences) Monterey, 1973, p.55–66.

    Google Scholar 

  • Colbeck, S.C. (1975) ‘Grain and bond growth in wet snow’. Proc. Grindelwald Symp. IAHS Publ 114.

    Google Scholar 

  • Colbeck, S.C. (1976) ‘Effects of radiation penetration snowmelt runoff hydrographs.’ US Army Cold Regions REsearch and Engineering Laboratory Report 76–11.

    Google Scholar 

  • Colbeck, S.C. (1978). ‘The difficulties of measuring the water saturation and porosity of snow’.Journal of Glaciology Vol.20 No.82 p.189–201.

    Google Scholar 

  • Colbeck, S.C. (1979). ‘Grain clusters in wet snow.’ Journal of Colloid and Interface Science. Vol.72 No.3 p.371–384.

    Article  Google Scholar 

  • Colbeck, S.C. and Anderson, E.A. (1982) ‘The permeability of a melting snow cover.’ Hater Resources Research Vol.18 No.4 p.904–908.

    Article  Google Scholar 

  • Cooperative Snow Investigations (1946). ‘Heat transmission constants of snow’. Technical Report 3 (Draft). (North Pacific Division, U.S. Army Corps of Engineers.

    Google Scholar 

  • Dalrymple, P.C., Lettau, H.H. and Wollaston, S.H. (1963) ‘South pole micrometeorology program’. Technical Report ES-7, Contribution No.20. Institute of Polar Studies, Ohio State University.

    Google Scholar 

  • de la Casiniere, A.C. (1974) ‘Heat exchange over a melting snow surface’. Journal of Glaciology Vol.13 No.69 p.55–72.

    Google Scholar 

  • Denoth, A., Seidenbusch, W., Blumthaler, M. and Kirchenlechner, P. (1979). ‘Some experimental data on water percolation through homogeneous snow’. In: Modelling of snow cover runoff. Ed: S.C. Colbeck and M. Ray (US Army Cold Regions Research and Engineering Laboratory) Hanover, NH Sept. 1978 p.253–256.

    Google Scholar 

  • Devaux, J. (1933). ‘L’economie radio-thermique des champs de neige et des glaciers’. Annales de Physique Vol.20 Pt.10 p.5–67.

    Google Scholar 

  • Dozier, J. (1978) ‘A solar radiation model for a snow surface in mountainous terrain’. In: Modeling of snow cover runoff. Ed: S.C. Colbeck and M. Ray (US Army Cold Regions Research and Engineering Laboratory) Hanover, N.H. September 1978 p.144–153.

    Google Scholar 

  • Dunne, T., Price, A.G. and Colbeck, S.C. (1976). - ‘The generation of runoff from sub-arctic snowpacks’. Water Resources Research Vol.12 No.4 p.677–685.

    Article  Google Scholar 

  • Dyer, A.J. and Hicks, B.B. (1970). ‘Flux gradient relationships in the constant flux layer’. Quarterly Journal of the Royal Meteorological Society Vol.96 p.715–721.

    Article  Google Scholar 

  • Gamier, B.J. and Ohmura, A. (1968). ‘A method of calculating the direct shortwave radiation income of a slope’. Journal of Applied Meteorology Vol.7 p.796–800.

    Article  Google Scholar 

  • Gerdel, R.W. (1954). ‘The transmission of water through snow’. Transactions of the American Geophysical Union. Vol.35 No.3 p.475–485.

    Google Scholar 

  • Granger, R.J. (1977). ‘Energy exchange during melt on a prairie snowcover’. M.Sc. Thesis, Department of Mechanical Engineering, University of Sakatchewan.

    Google Scholar 

  • Granger, R.J. and Male, D.H. (1978) ‘Melting of a prairie snowpack’. Journal of Applied Meteorology Vol.17 No.12 p.1833–1842.

    Article  Google Scholar 

  • Harding, R.J. (1986) ‘Exchanges of energy and mass associated with a melting snowpack’ In: Modelling Snowme It-Induced Processes. IAHS Publ.155. p.3–15.

    Google Scholar 

  • Jaafar, H. and Picot, J.J.C. (1970). ‘Thermal conductivity of snow by a transient state probe method.’ Uater Resources Research Vol.6 No.1 p.333–335.

    Article  Google Scholar 

  • Jansson, M. (1901) ‘Ueber die Warmeleitungsfahigkeit des Schnees.’ Ofversigt Af. Kgl. Vetenskahakademiens Forhandliger Vol.58 p.207–222.

    Google Scholar 

  • Kelly, R.J., Morland, L.W. and Morris, E.M. (1986) ‘A three phase mixture for melting snow.’ Ins Modelling Snowmelt-induced processes. IAHS Publication No.155 p.17–26.

    Google Scholar 

  • Ketchem, W.M. and Hobbs, P.V. (1969) A experimental determination/Of the surface energies of ice.’ Philosophical Magazine. Vol.19 p.1161–1173.

    Article  Google Scholar 

  • Kuroiwa, D. (1968) ‘Liquid permeability of snow.’ Lou Temperature Science Ser.A. No.26 p.29–52.

    Google Scholar 

  • Kuz’min, P.P. (1961). ‘Melting of snow cover.’ Translation TT71–50095 Israel Program for Scientific Translations, 1972.

    Google Scholar 

  • List, R.J. (1966) Smithsonian Meteorological Tables. 6th revised edition. Smithsonian Institute, Washington D.C.

    Google Scholar 

  • Male, D.H., Norum, D.I. and Besant, R.W. (1973) ‘A dimensional analysis of heat and mass transfer in a snowpack. In: The role of snow and ice in hydrology. Proc. Banff Symp. September 1972 Vol.1 (UNESCO-WMO-IAHS) 1973 p.258–290.

    Google Scholar 

  • Mellor, M. (1977). ‘Engineering properties of snow.’ Journal of Glaciology Vol.19 No.81 p.15–65.

    Google Scholar 

  • Morris E.M. and Godfrey, J. (1979). ‘The European Hydrological System snow routine’. In: Modeling of snow cover runoff. Ed: S.C. Colpeck and M. Ray (U.S. Army Cold Regions Research and Engineering Laboratory) Hanover, N.H. September 1978 p.269–278.

    Google Scholar 

  • Morris, E.M. (1983) ‘Modelling the flow of mass and energy within a snowpack for hydrological forecasting’. Annals of Glaciology Vol.4 p.198–203.

    Google Scholar 

  • Moskalev, Yu.D. (1966). Avalanche Mechanics. (Hydrometeorological Publishing House, Leningrad).

    Google Scholar 

  • Munn, P.E. (1966) Descriptive Micrometeorology. New York Academic Press.

    Google Scholar 

  • Navarre, J.P. (1977) ‘Modele unidimensionnel d’evolution de la neige deposee’. Meteorologie Applie p.109–120.

    Google Scholar 

  • Obled, C. and Rosse, B. (1977) ‘Mathematical Models of a melting snowpack at an index plot’. Journal of Hydrology Vol.32 No.1/2 p.139–163.

    Article  Google Scholar 

  • O’Brien, H.W. and Munis, R.H. (1975). ‘Red and near infrared spectral reflectance of snow’. In: Operational Applications of Satellite Snowcover Observations (ed. A. Rango) NASA SP-391 p.345–360.

    Google Scholar 

  • Ohumura, A. (1982). ‘Climate and energy balance on the Arctic tundra’. Journal of Climatology Vol.2 p.65–84.

    Article  Google Scholar 

  • Panofsky, H.A., Blakador, A.K. and McVehil, G.E. (1960). ‘The diabatic wind profile’. Quarterly Journal of the Royal Meteorological Society Vol.86 p.390–398.

    Article  Google Scholar 

  • Petzold, D.E. (1977) ‘An estimation technique for snow surface albedo’. McGill University CIimatological Bulletin Vol.21 p.1–11.

    Google Scholar 

  • Price, A.G. and Dunne, T. (1976). Energy balance computations of snowmelt in a subarctic area. Water Resources Research Vol.12 No.4 p.686–694.

    Article  Google Scholar 

  • Schmidt, R.A. (1982). ‘Vertical profiles of wind speed, snow concentration and humidity in blowing snow’. Boundary Layer Meteorology Vol.23 p.233–246.

    Article  Google Scholar 

  • Shimizu, H. (1970). ‘Air permeability of deposited snow’. Lou Temperature Science, Series A 22 p.1–32.

    Google Scholar 

  • Sommerfeld, R. and Businger, J.A. (1965). ‘The density profile of blown snow’. Journal of Geophysical Research Vol.70 p.3303–3306.

    Article  Google Scholar 

  • Steinemann (1958). ‘Experimentelle Untersuchungen zur Plastizitat von Eis.’ Beitrage zur Geologie der Schweiz. Hydrologie Nr.10.

    Google Scholar 

  • Sulakvelidze, G.K. (1959) ‘Thermoconductivity equation for porous media containing saturated vapour, water and ice.’ Bulletin of the Academy of Sciences of the USSR, Geophysics Series p.186-188

    Google Scholar 

  • Thorpe, M.R., Banks, E.G. and Smith, J.B. (1973). ‘Eddy correlation measurements of evaporation and sensible heat over arctic sea ice’. Journal of Geophysical Research Vol.78 Pt.18 p.3573–3584.

    Article  Google Scholar 

  • Wankiewicz, A. (1976). ‘Water percolation within a deep snowpack-field investigations at a site on Mt Seymour, British Columbia’. PhD Thesis, University of British Columbia.

    Google Scholar 

  • Wankiewicz, A. (1978). ‘Water pressure in ripe snowpacks’. Hater Resources Research Vol.14 No.4 p.593–600.

    Article  Google Scholar 

  • Warren, S.G. (1982) Optical properties of snow. Reviews of Geophysics and Space Physics Vol.20 No.1 p.67–89.

    Article  Google Scholar 

  • Webb, E.K. (1970). ‘Profile relationships: The log-linear range and extension to strong stability’. Quarteriy Journai of the Royai Meteorological Society Vol.96 p.67–90.

    Article  Google Scholar 

  • Weller, G.E. and Schwertfeger, P. (1971). ‘New data on the thermal conductivity of natural snow’. Journal of Glaciology Vol.10 No.59 p.309–311.

    Google Scholar 

  • Yen, Y.C. (1962) ‘Effective thermal conductivity of ventilated snow’. Journal of Geophysical Research Vol.67 p.1091–1098.

    Article  Google Scholar 

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© 1987 D. Reidel Publishing Company

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Morris, E.M. (1987). Modelling of water flow through Snowpacks. In: Jones, H.G., Orville-Thomas, W.J. (eds) Seasonal Snowcovers: Physics, Chemistry, Hydrology. NATO ASI Series, vol 211. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3947-9_11

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  • DOI: https://doi.org/10.1007/978-94-009-3947-9_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8251-8

  • Online ISBN: 978-94-009-3947-9

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