Snowcover Simulation Model : A Review
Abstract
Numerical simulation of seasonal snowcover has attracted the interest of many scientists in the recent past. The present paper summarises chronologically developments in the understanding of snow properties and discusses various modelling approaches towards simulating the snowpack numerically. The authors describe the evolution of snowcover and the intricate relationship between the evolving snowpack and the atmosphere. The governing equations that describe the evolution of snowcover have been discussed. The merits and limitations of each equation pescribing a single process have been explained. Modelling strategies adopted by various workers have been analysed, and lastly the requirements of a perfect model have been brought out. In the absence of complete answers to many other processes, a strategy for the development of an operational snowcover model has been discussed.References
Bader, H. Theory of densification of dry snow on high polar glaciers, II. Cold Region Research
Engineering Laboratory (CRREL) Research RwR, 108, 1962. pp. 1-26.
Bader, H. Theory of densif~cationo f dry snow on high polar glaciers - 11. In Ice and snow;
properties, processes, and applications, edited by W .D. Kingery, Proceedings of a Conference held at the MIT, 12-16 February 1962. Cambridge, Mass, MIT Press, 1963.
Kojima, K. Densifidon of seasonal snow cover, physics of snow and ice. Proceedings of
International Conference on Low Temperature Sciences, Vol I, Part 11, Soppro, Japan, 1967.
Kojima, K. A field experiment on the rate of densification of natural snow layers under low
stresses. Proceedings of the Grindlewald Symposium, April 1974. Association of international‘ Snow Hydro10gy (AISH), 1974. Pub No. 114.
Keeler, M. Charles. Some physical properties of alpine snow. Cold Region Research Engineering Laboratory (CRREL) Research Report, 271, 1969.
Mellor, M. Avalanches. Cold Region Research Engineering Laboratory (CRREL) Monograph,
III-A38,1968.
Mellor, M. A review of basic snow mechanics. Proceedings of the Grindlewald Symposium,
April 1974, Association of International Snow Hydrology (AISH), 1974. Pub No. 114.
Yoshida, 2. et al. Physical Properties of snow. Contrib. Imt. Low Temp. Sci., 1955, 7, 19-74.
Anderson, E.A. A point energy and mass balance model of a snowcover. US Department of
Commerce, National Oceanic and Atmospheric Administration, 1955. Report No. TR-NWS -19.
Obled, C. Modele Mathematique de la fonte nivale., Universite Scientifique et Medicale de
Grenoble, 197 1. Thesis (Unpublished). Morris, E.M. & Godfiey, J. The European hydrological system snow routke. In PrGceedings of a Meeting on Modelling of Snow Cover
Run off, edited by SC Colbeck and M Ray, 26-28 September 1978. Hanover, New Hampshire. Cold Region Research Engineering Laboratory (CRREL), 1978. pp. 269-78.
Navarre, J.P. Modele unidimensionnel d'evolution de la neige deposee. Modele pece-neige. Meteorologie, 1975,4 (3), 103-20.
Brun, E.; Martin, E.; Simon, V.; Gendre, C. & Coleou, C. An energy and mass model of snowcover suitable for operational avalanche forecasting. Journal of Glaciology, 1989,
(121), 333-42.
Motoyama, Hideaki. Simulation of seasonal snowcover based on air temperature and
precipitation. J. Appl. Meteorol., 1990, 29, 1104-10.
Bader, H.P. & Weilenmann, P. Modelling temperature distribution, energy and mass flow in
a (phase changing) snowpack - I. Model and case studies. Cold Reg. Sci. Technol., 1992. 20, 157-81.
Morland, L.W.; Kelly, J.K. & Morris E. M. A mixture theory for a phase changing snowpack.
Cold Reg. Sci. Technol., 1990,17,271-85.
Ganju, A:; Agrawal, K.C. & Rao, D.L.S. Snowcover model. Proceedings of the SNOWSYMP-94. Snow and Avalanche Study Establishment, Manali, India, 1994.
Brun, E.; David, P.; Sudul, M. & Brunot, G. A numerical model to simulate snowcover
stratigraphy for operational avalanche forecasting. Journal of Glaciology, 1992, 38 (128), 13-22.
Yamazaki, T.; Kondo, J. et al. A one-dimensional model of the evolution of snowcover
characteristics. Annals of Glaciology, 1993, 18, 22-26.
Durand, et al.. A meteorological estimation of relevant parameters for snow models, Annals of Glaciology, 1993, 18,65-71.
Landauer, J.K. Creep of snow under continued stress. USA SIPRE Research Report No, 41,
Mellor, M. Properties of snow. Cold Region Research Engineering Laboratory (CRREL) Monograph, III-A, 1964.
Kojima, K. Densification of snow in Antarctica. Antarctic snow and ice studies, edited by
W.D. Mellor. American Geophy . Union, 1964.
Yoshida, Z. Pliysical properties of Snow. In Ice and Snow; properties, processes, and
applications, edited by W.D. Kingery. Proceedings of a Conference held at the MIT, 12-16 February 1962, Cambridge, Mass. MIT Press, 1963.
Agrawal, K.C. Analysis of snow behaviour under small and medium loads and dependence of response characteristics on microstructure. IIT Delhi, 1993. PhD Thesis (unpublished).
Lehning, M.; Bartelt, P. & Brown, B. Operational use of a snowpack model for the avalanche warning service in Switzerland:Model development and first e-riences. 25 years of Snow Avalanche Research, Voss 12-16 May 1998. NGI, 1998.203, pp. 169-74.
Rockwood, D.M. Stream flow* synthesis and reservoir regulation. US Army Corps Engineers
Divison, North Pacific, Portland, Oreg. 1964. Tech. Bull. No. 22.96 p.
Singh, A.K. A mathematical model for the study of temperature profile within a snowcover.
Proceedings of the SNOWSYMP-94, Snow and Avalanche Study Establishment, Manali, (HP), 1994. pp. 146-56.
Quick, M.C. A comparison of measured and theoretical snowpack temperatures. Journal of
Hydrology, 1967,5, 1-20.
Arons, E. M.; Colbeck, S.C.; Randy, W. & McGilvary. Effective medium approximation for
snow thermal conductivity. Proceedings of the SNOWSYMP-94, Snow and Avalanche Study
Establishment, Manali, 1994.
Brunt , D. Physical and dynamical meteorology. Cambridge Univ. Press, Cambridge, Mass,1952.
Gray, D.M. & Male, D.H. Handbook of snow: Principles, processes, management and use.
Pergmann Press, 1981.
Snow hydrology: Summary report of the snow investigations. US Army Corps of Engineers,
North Pacific Div., Portland, Oreg., 1981.
Deardorff, J.W. Dependence of air-sea transfer coefficient on bulk stability. J Geophys. Res., 1968.3(8), 2549-557.
Colbeck, S.C. Air movement in snow due to wind pumping. Journal of Glaciology, 1989, 35(120), 209-13.
Giddings, J.C. & LaChapelle, E. The formation rate of depth hoar, J. Geophys. Res., 1962, 67, 2377-383.
Colbeck, S.C. Thermodynamics of snow metamorphism due to variations in curvature.
Journal of Glaciology, 1980, 26(94), 29 1-301.
Colbeck, S.C. Theory of metamorphism of dry snow. J Geophy. Res., 1983. 88,5475-82.
Colbeck, S.C. The vapor diffision coegcient for snow. Water Resour. Res., 1993,29(7), 109-15.
Akitaya, E. Studies on depth hoar. Contrib. Inst. Low Temp. Sci., 1974. A 26.
Marbouty, D. An experimental study of temperature-gradient metamorphism in snow. Journal of Glaciology, 1980,26(94), 303-12.
Pahaut, E. & Marbouty.,D. Les Cristaux de neige, 2, Evolution. Neige valanches,1981,25,3-42.
Christon, M.; Bruns, P.; Thompson, E. & Sommerfield, R. Water vapour transport in snow.
A 2-D simulation of temperature-gradient metamorphism. In Seasonal snowcovers: Physics, chemistry, hydrology. dordrecht, etc., edited by H.G. Jones and W.J. Orville-Thomas. D. Reidel Publishing Co., 37-62.(NATO ASI Series C, 211), 1987.
Satyawali, P.K. Grain growth under temperature gradient: A simple approach. Proceedings of the SNOWSYMP-94, Snow and Avalanche Study Establishment, Manali, India., 1994. pp. 52-62
Fohn, P.; Camponovo, C. & Krusi, G. Depth-hoarcrystal growth in the surface layer under high temperature gradients. Annals of Glaciology, 1998,18,39-45.
Fierz, Charles. Field observations and modelling of weak layer evolution. Annals of Glaciology, 1998, 26,7-13.
Bader, H.; Haefeli, R.; Bucher, J. et al. Der schnee und seine metamorphose, reitrage zur geologie der schweiz, Geotechnische Serie, Hydrologie, Lieferung 3, Bern[English Translation: Snow and its metamorphism], Translation 14, Snow, Ice and Permafrost Research Establishment, 1939. 313 p.
Colbeck, S.C.; Akitaya, E.; Armstrong, R.; Gubler, H. et al. International classification for
seasonal snow on the ground. International Commission for Snow and Ice (IAHS). World
Data Center A for Glaciology, CIRES, Box 449, Univ. of Colorado, Boulder, Colorado 80309,
USA, 1990.
McClung, D. & Shaerer, P. The avalanche handbook. The Mountaineers, Seattle, Washington, 1993.271 p.
Fokuzaiva, T. & Akitaya, E. Depth-hoar crystal growth in the surface layer under high
temperature gradient Annals of Glaciology, 1993, 18,39-45.
Gubler, H. Model for dry snow metamorphism by interparticle vapour flux. J Geophys. Res., 1985, 90 (Dj), 8081-92.
Brown, R.L.; Edward, E.E. & Barber, Michael. Nonequilibrium thermodynamics applied to
inetamorphism of snow. Proceedings of the SNOW SYMP-94. Snow and Avalanche Study
Establishment, ManaIi, India., 1994. pp. 39-51.
Edens, M.Q. & Brown, RL. An experimental evaluation of changes in microstructure of
fine-grained snow due to equitemperature metamorphism. Cold Reg. Sci. Technol., 1998 (submitted).
Horton, R.E. The melting of snow. Mon. Weather Rev., 1915, 43,599-05.
Gerdel, R.W. The dynamics of liquid water in deep snow packs. Trans. Am. Geophy. Un., 1945, 26 (I), 83-90.
Himmel, J.M. Lysimeter studies of rain on snow phenomena, Res, note, coop, snow invest., Corps of Engineers, San Francisco, Calif., 195 1. 11 p.
Colbeck, S.C. A theory for water percolation in snow. Journal of Glaciology, 1972, 11(63),
-85.
Colbeck , S.C. & Davidson, G. Water percolation through homogeneous snow. Proceedings of the Banff Symposium on the role of ice and snow in hydrology, UNESCO-WMO-IASH, Geneva- Budapest-Paris, 1973. pp. 242-57.
Colbeck, S.C. The physical aspects of water flow through snow. Cold Region Research
Engineering Laboratory (CRREL) Report, 1978.
Wankiewicz, A. A review of water in snow. Cold Region Research Engineering Laboratory
(CRREL) Report, 1978.
Hill, D.E. & Parlange, J.Y. Wetting front instability in layered soils. Soil&i Soc. Am. Proc., 1972.36,697-02.
Parlange, J.Y. Water movement in soils. Geophysics Surveys, 1974,1,357-87.
Raats, P.A.C. Unstable wetting fronts in uniform and nonunifom soils. Soil Sci. Sac. Am. Proc., 1973,37,681-85.
Marshall, T.J. A relation between permeability and size distribution of pores, J Soil Sci., 195 8, 9 (1) 1-8.
Mellington & Quick Permeability of porous media. Nature, 1959,183,387-88.
Marsh, P. Water flux in melting snowcovers. NHRI mnh-ibution No. 89 - 055. In Advances in
Porous Media, Vol.1, edited by M.Y. Corapcioglu, 1990. Elsevier, Amsterdam, 1991.
Colbeck, S.C. The capillary effects on water percolation in homogeneous snow. Journal of
Glaciology, 1974,13(67), 85-97.
Colbeck, S.C. An analysis of water flow in dry snow. Water Resour. Res., 1976,12(3).
Shim-, H. Air &eability of deposited snow. Contrib- Imt. Low Temp. Sci., 1970, A22, 1-32.
LaChappelle, E.R. Properties of snow, prepared for College of Forest Resources, University of Washington, Seattle, 1969. 21 p.
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