Description of snow transport and accumulation in  mathematical model of surface mass balance of  mountain glacier. Part II. Parameterization of avalanche feeding

О.О. Rybak1,2, Е.А. Rybak1,2, I.A. Korneva2,3

 1Sochi Research Center of RAS, Sochi

2Branch of Institute of Natural and Technical Systems, Sochi


3Yu.A. Israel Institute of Global Climate and Ecology, Moscow


DOI: 10.33075/2220-5861-2019-4-72-80

UDC 551.321.86


     Snow avalanches are able to contribute essentially to the income part of the surface mass balance of a mountain glacier. Morphology of a glacier and surrounding mountain slopes is the key factor determining the degree of significance of avalanche feeding of a glacier. This is true first of all for the glaciers located in depressions (corrie glaciers, valley glaciers etc.). Moreover, it is avalanche feeding that supports the stability of corrie glaciers, for instance. According to various estimates, contribution of avalanche feeding to the total mass income of the North Caucasus glaciers varies from 3% to 76%.

     At present, two approaches are generally used for prediction of snow avalanches – statistical and physico-mathematical. Both approaches focus mainly on operational forecasts of avalanche emerging. The purpose of the current research was somewhat different – we focused on adaptation of existing techniques of schematizations of avalanche feeding for simulation of the income part of the surface mass balance of a mountain glacier. We employed a cellular automaton model for imitation of the vertical redistribution of snow mass. Such models have been used for quite some time for evaluation of avalanche danger. The simplified algorithm, which was implemented in the numerical experiments, did not account for some important features like physical properties of snow, their change in time as well as snow structure, The only property which changes in the process of the vertical redistribution is snow depth. Indeed, regularities established in the numerical experiments can be attributed to the idealized case. Nevertheless, we demonstrated that it was possible to reproduce basic characteristics of snow post-depositional redistribution in the mountainous terrain using rather simple method. This method is planned to be implemented in a more general surface mass balance model.

 Key words: mountain glacier, accumulation, snow cover, avalanche, avalanche feeding, mathematical model, surface mass balance, cellular automaton.

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  1. Popovnin V.V., Sergievskaya Y.Е. Feedback on the share of avalanche power with glacier accumulation // Ice and Snow. 2018. V. 58. № 4. P. 437–447. doi: 10.15356/2076-6734-2018-4-437-447
  2. Response of Central Caucasus glaciers in 2001-2010 to changes in temperature and precipitation / G.А. Nosenko, Т.Е. Chromova, О.V. Rototaeva et al // Ice and Snow. 2013. V. № 1. P. 26–33.
  3. Panov V.D., Lurie P.М., Ilichev Yu.G. State of modern glaciation of the Northern slope of the Greater Caucasus at the beginning of the XXI century // Sustainable development of mountain areas. 2010. V. 2. № 3. P. 69–73.
  4. Popovnin V.V., Pylaeva Т.V. Avalanche food glacier Djankuat //Ice and Snow. 2015. V. 55. № P. 21–32. doi:10 .15356/2076-6734-2015-2-21-32
  5. Nosenko G.А., Rototaeva О.V., Nikitin S.А. Features of changes in the Kolka glacier from 2002 to 2016 // Ice and Snow. 2017. V. 57. № P. 468–482. doi: 10.15356/2076-6734-2017-4-468-482
  6. To the Holocene history of the glacier Ulucam / О.N. Solomina, I.S. Bushueva, Т.М. КKuderina et al // Ice and Snow. 2012. V. № 1. P. 85–94.
  7. Schweizer J., Jamieson J.B., Schneebeli M. Snow avalanche formation // Reviews of Geophysics. 2003. Vol. 41(4). 1016. doi:10.1029/ 2002RG000123
  8. Avolio M.V., Errera A., Lupiano V. et al. VALANCA: A Cellular Automata Model for Simulating Snow, Avalanches // Journal of Cellular Automata. 2012. Vol. 12. P. 309–332
  9. Kronholm K., Birkenland K.W. Integrating spatial patterns into a snow avalanche cellular automata model // Geophysical Research Letters. 2005. Vol. 32. L19504. doi:10.1029/2005GL024373
  10. Bernhardt M., Schulz K. SnowSlide: A simple routine for calculating gravitational snow transport // Geophysical Research Letters. 2010. Vol. 37. L11502. doi:10.1029/2010GL043086
  11. Fonseca P., Colls M., Casanovas J. A novel model to predict a slab avalanche configuration using m:n-CAk cellular automata // Computers, Environment and Urban Systems. 2011. Vol. 35. P. 12– doi:10.1016/j.compenvurbsys.2010.07.002.
  12. Soloviev А.S., Kalach А.V. Some aspects of the prediction of avalanches // Technology of technosphere safety. Online magazine. 2011. Issue 1 (35). P. 1-5 [Electronic resource]. URL: (date of issue: 23.06.2019).
  13. Schweizer J., Jamieson J.B. Snow cover properties for skier triggering of avalanches // Cold Regions Science and Technology. 2001. Vol. 33. P. 207–221.
  14. D’Ambrosio D., Di Gregorio S., Iovine G. et al. Simulating the Curti-Sarno debris flow through cellular automata: the model SCIDICA (release S2) // Physics and Chemistry of the Earth. 2002. Vol. 27. P. 1577–1585
  15. Ohara N. A practical formulation of snow surface diffusion by wind for watershed-scale applications // Water Resources Research. 2014. Vol. 50. P. 5074– doi:10.1002/2013WR014744.
  16. Liston G.E., Haehnel R.B., Sturm M. et al. Simulating complex snow distributions in windy environments using SnowTran-3D // Journal of Glaciology. 2007. Vol. 53(181). P. 241–256
  17. Rybak О.О., Rybak Е.А., Korneva I.А. Description of snow transport and accumulation in a mathematical model of surface mass balance of a mountain glacier. Part I. Theory and basic algorithms // Monitoring systems of environment. Issue 3 (37). P. 70–78.  DOI: 10.33075/2220-5861-2019-3-70-78
  18. Bernhardt M., Schulz K. SnowSlide: A simple routine for calculating gravitational snow transport // Geophysical Research Letters. 2010. Vol. 37. L11502. doi:10.1029/2010GL043086
  19. Liston G.E., Sturm M. A snow-transport model for complex terrain // Journal of Glaciology. 1998. Vol. 44, No. 148. P. 499–516

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