Description of snow transport and accumulation in a mathematical model of surface mass balance of a mountain glacier. Part I. Theory and basic algorithms

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

1Sochi Research Center of RAS, Sochi, Theatralnaya, 8a

2Branch of Institute of Natural and Technical Systems, Sochi, Kurortny avenue, 99/18


3Y.A. Izrael Institute of Global Climate and Ecology, Moscow, Glebovskaya, 20b


DOI: 10.33075/2220-5861-2019-3-70-78

UDC 551.321.86


   Realistic description of a mountain glacier dynamics and reliable prediction of its evolution using methods of mathematical modeling faces the problem of formalization of snow accumulation including spatial peculiarities of hard precipitation and redistribution of already precipitated snow (snowstorm transport, avalanche feeding etc.).  Processes of spatial post-depositional redistribution of snow are sufficiently well-studied, relevant theories as well as computational algorithms on their basis are elaborated. However, modern methods are mostly applicable to short term predictions. Relevant mathematical models are hardly useful for long-term prognostic calculations because they are excessively demanding to input meteorological information. And vice versa, processes of accumulation are often too much oversimplified and do not take into account either peculiarities of the relief or prevailing patterns of micro- and meso-circulation of the atmosphere while calculating both snow transportation and snow accumulation.

   In the current study, we consider some aspects of the simplified approach for calculation of spatial redistribution of snow. The purpose of the research is to overcome dependency of sophisticated models on input data. Within the frames of the simplified approach, a schematic simulation of the mechanisms of deflation, transportation and accumulation is implemented for a limited domain. In the paper, a computational algorithm for transportation and accumulation of snow is discussed. The algorithm is based on the solution of the advection-diffusion equation with semi-empirical description of the transportation rate. In numerical experiments with schematically prescribed terrain, some key consistent patterns of snow redistribution are studied. In particular, maximum growth of snow cover thickness on leeward slopes behind hill summit in the area of flow convergence is experimentally confirmed.

Keywords: mountain glacier, accumulation, snow cover, snow storm transportation, mathematical model.

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  1. Machtguth H., Eisen O., Paul F., Hoelze M. Strong spatial variability of snow accumulation observed with helicopter-borne GPR on two adjacent Alpine glaciers // Geophysical Research Letters. 2006. V. 33. L13503. doi:10.1029/2006GL026576.
  2. Panov V. D., Lurie P. M., 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 territories. 2010. Vol. 2. № 3. P. 69-73.
  3. Toropov P. A., Mikhailenko V. N., Kutuzov S. S. and others. Temperature and radiation regime of glaciers on the slopes of Elbrus during the ablation period for the last 65 years / / Ice and Snow. 2016. Vol. 56. № 1. P. 5-19. doi:10.15356/2076-6734-2016-1-5-19.
  4. Morozova P. A., Rybak O. O. Regionalization of global climate modeling data for calculating the mass balance of mountain glaciers / / Ice and Snow. 2017. Vol. 57. № 4. P. 437-452. doi: 10.15356/2076-6734-2017-4-437-452.
  5. Rybak O. O., Rybak E. A. Application of data from network meteorological stations for calculating the mass balance of glaciers (on the example of the dzhankuat glacier, Central Caucasus) // Monitoring systems of environment. 2017. No. 9 (29). P. 100-108.
  6. Mikhalenko V., Sokratov S., Kutuzov S. et al. Investigation of a deep ice core from the Elbrus western plateau, the Caucasus, Russia // The Cryosphere. 2015. V. 9. P. 2253–2270. doi:10.5194/tc-9-2253-2015.
  7. Lehning M., Löwe H., Ryser M., Raderschall N. Inhomogeneous precipitation distribution and snow transport in steep terrain // Water Resources Research. 2008. V. 44. W07404. doi:10.1029/2007WR006545.
  8. Shmakin A. B., Turkov D. V., Mikhailov A. Yu. Model of snow cover taking into account the layered structure and its seasonal evolution / / Cryosphere of the Earth. 2009. Vol. XIII. # 4. Pp. 69-79.
  9. Xiao J., Bintanja R., Déry S.J. et al. An intercomparison among four models of blowing snow // Boundary-Layer Meteorology. 2000. V. 97. P. 109–135.
  10. Liston G.E., Haehnel R.B., Sturm M., Heimstra A., Berezovskaya S., Tabler R.D. Simulating complex snow distributions in windy environments using SnowTran-3D // Journal of Glaciology. 2007. V. 53 (181). P. 241–256.
  11. Ohara N. A Practical formulation of snow surface diffusion by wind for watershed-scale applications // Water Resources Research. 2014. V. 50. P. 5074–5089. doi:10.1002/2013WR014744.
  12. Dyunin A.K. Mechanics of snowstorms (Questions of the theory of design of snow-regulating means). Novosibirsk: publishing house of the Siberian branch of the USSR Academy of Sciences, 1963. P. 380.
  13. Dyunin A.K., Kotlyakov V.M. Redistribution of snowind the mountains under the effect of heavy snow-storms // Cold Regions Science and Technology. 1980. V. 3. P. 287–294.
  14. Ryan B.C. A Mathematical Model for Diagnosis and Prediction of Surface Winds in Mountainous Terrain. Journal of Applied Meteorology. 1977. V. 16. P. 571–584.

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