Analysis of formulas for determination of snow cover density

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

When snow is used as a building material and to control the thermal regime of soils in the permafrost zone, it is important to be able to predict the snow density depending on the thickness (depth) of the snow cover. The paper compares the basic formulas used to calculate snow density depending on the depth of the snow cover and estimates the differences between the results obtained in a given interval (range) of calculation accuracy. The most popular formulas of Abe, Defant, Kotlyakov and other domestic and foreign scientists are included in the comparison. A comparative analysis of the results of theoretical calculations showed that the discrepancy between the results can be significant. At the same time, taking into account the large variability of the initial data determining the existing functions of snow density on its depth, the calculation results for almost all of the formulas considered fall within the range of acceptable accuracy of ± 25%. An assessment is also made of the possibility and expediency of replacing the defining power functions in the considered formulas with linear ones. It is shown that the linearization error, for example, for the classical Abe formula, does not exceed 5%. It is established that Kotlyakov’s linear formulas show the greatest degree of disagreement with other analyzed formulas. For example, the degree of disagreement between one of Kotlyakov’s formulas and Abe’s linear formula varies from 35 to 45%. The results of variant calculations using the formulas are presented in the form of graphs, which allows for a visual verification of the main quantitative patterns obtained as a result of the conducted research.

Full Text

Restricted Access

About the authors

A. F. Galkin

Melnikov Permafrost Institute SB RAS

Author for correspondence.
Email: afgalkin@mail.ru

Doctor of Sciences (Engineering) 

Russian Federation, 36, Merzlotnaya Street, Yakutsk, 677010

V. Yu. Pankov

North-Eastern Federal University

Email: pankov1956@gmail.ru

Candidate of Sciences (Geology) 

Russian Federation, 58, Belinsky Street, Yakutsk, 677027

А. А. Adamov

North-Eastern Federal University

Email: adamov.90@list.ru

Engineer 

Russian Federation, 58, Belinsky Street, Yakutsk, 677027

References

  1. Voytkovsky K.F. Raschet sooruzhenii iz l’da i snega [Calculation of structures made of ice and snow]. Moscow: Publishing House of the USSR Academy of Sciences. 1954. 136 p.
  2. Shulgin A.M. Snezhnyi pokrov i ego ispol’zovanie v sel’skom khozyaistve [Snow cover and its use in agriculture]. Leningrad: Hydrometeoizdat. 1962. 84 p.
  3. Richter G.D. Snezhnyi pokrov, ego formirovanie i svoistva [Snow cover, its formation and properties]. Moscow: Publishing House of the USSR Academy of Sciences. 1945. 120 p.
  4. Pavlov A.V. Monitoring kryolitozony [Monitoring of the cryolithozone]. Novosibirsk: GEO. 2008. 230 p.
  5. Kruchinin I.N., Burmistrov D.V. Requirements for the transport and operational condition of winter logging roads. Modernizatsiya i nauchnye issledovaniya v transportnom komplekse. 2017. Vol. 1, pp. 209–212. (In Russian). EDN: ZULMIN
  6. Kruchinin I. N. Formation of snow rolling with specified properties on logging roads. Izvestiya of higher educational institutions. Forest magazine. 2012. No. 1 (325), pp. 38–41. (In Russian). EDN: OXBMCH
  7. Kuzmin P.P. Fizicheskie svoistva snezhnogo pokrova [Physical properties of snow cover]. Leningrad: Hydrometeoizdat. 1957. 179 p.
  8. Kirillin A.R., Zheleznyak M.N., Zhirkov A.F., Misailov I.E., Verkhoturov A.G., Sivtsev M.A. Features of snow accumulation and parameters of snow cover on the Elkon mountain range. Vestnik of the Transbaikal State University. 2020. Vol. 26. No. 7, pp. 62–76. (In Russian). https://doi.org/10.21209/2227-9245-2020-26-7-62-76
  9. Osokin N.I., Sosnovsky A.V., Chernov R.A. Influence of snow cover stratigraphy on its thermal resistance. Led i sneg. 2013. No. 3 (123), pp. 63–70. (In Russian). EDN: THBIWU
  10. Osokin N.I., Sosnovsky A.V. The influence of thermal resistance of snow cover on the stability of permafrost rocks. Kriosfera Zemli. 2016. Vol. 20. No. 3, pp. 105–112. (In Russian). EDN: WTHOLB
  11. Kotlyakov V.M., Sosnovsky A.V. Assessment of thermal resistance of snow cover by ground temperature. Led i sneg. 2021. Vol. 61. No. 2, pp. 195–205. (In Russian). EDN: XPBXXL. https://doi.org/10.31857/S2076673421020081
  12. Osokin N.I., Sosnovsky A.V., Chernov R.A. Thermal resistance of snow cover and its variability. Kriosfera Zemli. 2017. Vol. 21. No. 3, pp. 60–68. (In Russian).EDN: YPTHAJ
  13. Zhirkov A., Sivtsev M., Lytkin V., Séjourné A., Wen Z. An assessment of the possibility of restoration and protection of territories disturbed by thermokarst in Central Yakutia, Eastern Siberia. Land. 2023. Vol. 12 (1), 197. https://doi.org/10.3390/land12010197
  14. Patent RF 2813665. Sposob melioratsii zemel’ v kriolitozone [Method of land reclamation in the cryolithozone] / Galkin A.F., Zhirkov A.F., Zheleznyak M.N., Sivtsev M.A., Plotnikov N.A. Declared 22.04.2023. Published 14.02.2024. Bulletin No. 5. (In Russian).
  15. Vinnikov S.D., Viktorova N.V. Fizika vod sushi.[Physics of land waters]. St. Petersburg: RGGMU. 2009. 430 p. (In Russian).
  16. Oleinikov A.I., Skachkov M.N. Model of compacted bulk solids and some of its applications. Informatika i sistemy upravleniya. 2011. No. 4 (30), pp. 48–57. (In Russian). EDN: OJOJCL
  17. Borisov V.A., Akinin D.V., Payul A.D. Changes in snow density under compressive load. Resources and Technology. 2021. Vol. 18 (3), pp. 77–91. (In Russian). https://doi.org/10.15393/j2.art.2021.5843
  18. Tabler R.D., Furnish R.P. In-depth study of snow fences. Public Works. 1982. Vol. 113. No. 8, pp. 42–44.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Change in snow density at different snow cover depths calculated using the linearized Abe formula ρ=а+bH: 1 – а=180, b=325; 2 – а=185, b=325; 3 – а=180, b=350; 4, 5 – limits of the 5% accuracy range of the calculation results using the original Abe formula

Download (207KB)
Indexing metadata
3. Fig. 2. Error in determining snow density at different snow cover depths, calculated using the linearized formula (ρ=а+bH) compared to the original Abe formula: 1 – а=180, b=325; 2 – а=185, b=325; 3 – а=180, b=360; 4 – а=185, b=360

Download (201KB)
Indexing metadata
4. Fig. 3. Comparison of calculation results for determining snow density from depth using different formulas: 1 – formula (3); 2 – formula (4); 3 – formula (1); 4 – linearized version of formula (1)

Download (204KB)
Indexing metadata
5. Fig. 4. Change in snow density by snow cover thickness, calculated using linear formulas: 1 – formula (5); 2 – formula (6); 3 – linearized Abe formula

Download (155KB)
Indexing metadata
6. Fig. 5. Percentage degree of disagreement of the results of calculating snow density by snow cover thickness, calculated using the linear formulas of Kotlyakov and Abe: 1 – formulas (6) and (7); 2 – formulas (5) and (7); 3 – formulas (5) and (6)

Download (146KB)
Indexing metadata

Copyright (c) 2024 ООО РИФ "СТРОЙМАТЕРИАЛЫ"