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

by

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

E-mail: o.o.rybak@gmail.com, elena.rybak@gmail.com

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

E-mail: comissa@mail.ru

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

UDC 551.321.86

 Abstract:

   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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