Thermal conductivity of a two-layer snow cover

The subject of the research is the functional relationship between the thermal conductivity coefficient of snow and its density in a layered structure of the snow cover with various types of snow. The purpose of the research: to determine the range of possible averaging of the thermal conductivity values of a two-layer snow cover, including granular snow and hoarfrost. To achieve this goal, a comparative assessment of the accuracy of formulas for determining the thermal conductivity coefficient of granular snow and hoarfrost was made, which, at the same density, differ in thermal physical characteristics due to varying structures. Well-known linear formulas by Pavlov, Sulakvelidze, and Chernov for hoarfrost and granular snow were used for comparison. The influence of temperature on snow properties was not considered. The two-layer snow cover was regarded as a medium with arbitrarily varying layers in height, the thermal conductivity of each of which is defined by different formulas. To obtain the average thermal conductivity coefficient, the concept of a weighted average parameter was used. In this case, it is the sum of the products of the thermal conductivity coefficient of each layer by its thickness, divided by the thickness of the entire snow cover. The overall formula includes an arbitrary ratio of the layers in the snow cover. As a result of the analysis of variant calculations, the following patterns emerging from the averaging of the thermal conductivity coefficient of the two-layer snow cover were established. When ignoring the presence of layers in the snow cover and calculating its thermal conductivity only according to the formula characteristic of granular snow, the maximum absolute error (depending on the ratio of layer thicknesses) does not exceed 50%. When calculating using the formula characteristic of hoarfrost, the maximum absolute error is approximately twice as large and amounts to almost 100%. The scientific novelty of the research lies in establishing a general quantitative pattern of change in the error of calculating the thermal conductivity coefficient of layered snow cover when using formulas derived for granular snow or only according to formulas characteristic of hoarfrost. The results of variant calculations of the errors that arise when not accounting for the layered structure of the snow cover and when considering layering using the weighted average thermal conductivity coefficient are presented in the form of 2D and 3D graphs, allowing for a visual confirmation of the validity of the conducted research and the conclusions drawn.