Parametric criterion (simplex) of the thermal conductivity coefficient of snow.

The subject of the research was the functional dependence of the thermal conductivity coefficient of snow on density at various temperatures. The goal of the research was to establish a connection between the dimensionless value of the thermal conductivity coefficient (the thermal conductivity simplex) and the dimensionless value of density (the density simplex) of snow. To obtain dimensionless parametric criteria (simplexes), the thermal conductivity coefficient and the density of ice were used as scale units, which are generally a function of temperature. The dependence of the thermal conductivity coefficient and the density of ice on temperature was examined in detail, represented as linear functional relationships. Special attention was given to the assessment of errors that arise from linearizing functional dependencies and averaging the original data. The classic formula of G.P. Abels was used as the basic functional dependence of the thermal conductivity coefficient of snow on density. The method of natural scales was used to obtain parametric criteria (simplexes) of the thermal conductivity coefficient and the density of snow, allowing the conversion of dimensional physical quantities to dimensionless parameters. The average values of the thermal conductivity coefficient and the density of ice within a specified temperature range were used as scale units. Using the method of natural scales, parametric criteria (simplexes) of the thermal conductivity coefficient and density of snow were obtained. Based on the classic formula of G.P. Abels, a functional relationship was established between the found parametric criteria, which can be formulated as follows: "The simplex of the thermal conductivity of snow is equal to the square of the simplex of its density." This regularity has been obtained for the first time and defines the scientific novelty of the theoretical research conducted. Using the dependence of the thermal conductivity coefficient and the density of ice on temperature, it is easy to determine the influence of temperature on the change of the thermal conductivity coefficient of snow concerning density with known values of the simplexes. An assessment was made of the errors that arise when averaged scale units are used in calculations. It was shown that averaging the original quantities does not lead to errors larger than the acceptable values adopted in engineering practice. For example, the error in determining the proportionality coefficient between the simplexes of thermal conductivity and density varies from ±9.0% in the temperature range from 0 to -40°C. In the most realistic range of temperature change for snow (from -5 to -20°C), the average error does not exceed 3.0%.