Analysis of formulas for determination of snow cover density

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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.

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作者简介

A. Galkin

Melnikov Permafrost Institute SB RAS

编辑信件的主要联系方式.
Email: afgalkin@mail.ru

Doctor of Sciences (Engineering) 

俄罗斯联邦, 36, Merzlotnaya Street, Yakutsk, 677010

V. Pankov

North-Eastern Federal University

Email: pankov1956@gmail.ru

Candidate of Sciences (Geology) 

俄罗斯联邦, 58, Belinsky Street, Yakutsk, 677027

А. Adamov

North-Eastern Federal University

Email: adamov.90@list.ru

Engineer 

俄罗斯联邦, 58, Belinsky Street, Yakutsk, 677027

参考

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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

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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

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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)

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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

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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)

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