# Probabilistic Analysis as a Method for Ground Freezing Depth Estimation
## 2 Material and Methodology  
### Measurements of Soil Temperature  
The Earth's surface is heated by the absorption of solar radiation. The variety of the substrate results in different heating mechanism. Snow and ice covering the ground reflects most of the radiation [11]. Water, due to its partial transparency, absorbs radiation throughout the layer to which it reaches, and the ground absorbs radiation in a thin surface layer [12]. Changes in ground temperature depend on its vegetation coverage, chemical composition, and to a large extent on water and air content. The source of heat in the ground can also be heat exchange with the atmosphere; thawing and freezing processes of water contained in the ground; precipitation heat and biological, chemical, and physical processes in the soil [13]. Soil, which is not covered with vegetation, is most strongly heated during the day in clear weather; at night in the same conditions, it intensely radiates heat. The size of the heat flux absorbed or given away by the soil depends on the temperature difference and the thermal capacity of the soil [14,15]. The thermal capacity of the soil is influenced by its mineral composition, water and air content. There is a very large impact of the snow cover on the depth of the zero isotherm position. The maximum positions of zero isotherms in the ground without snow cover are even more than twice as deep as in snow-covered soils [16,17]. Soil freezing (frost) depth can be determined using a number of direct approaches, for example, by direct measurement by thermometers installed in the ground. Another approach is to use the concept of 'degree days'--freezing degree days (FDDs) and thawing degree days (TDDs)--as a surrogate for frost depth. The advantage of the 'degree day' approach is that meteorological data is easier to obtain and less intrusive than the other described approaches. A limitation of the degree-day approach is the representativeness of temperature data taken off-site [18]. In Poland, the soil temperature is measured every day at the meteorological stations of the Institute for Meteorology and Water Management--State Research Institute (IMGW-PIB). The measurements were taken in the last 40 years using mercury-in-glass thermometers, at 6:00 and 18:00 UTC at the depths of 5 cm, 10 cm, 20 cm, and 50 cm and at the depth of 1.0 m but only at 12:00 UTC [19]. Measurements at this last depth have been made only since 1982. Currently, the measurements are automated, performed every minute with an accuracy of 0.1 \({}^{\circ}\)C. Measurements of the minimum temperature above the surface of the exposed soil and the ground temperature are made on the testing site. This measuring field is a part of the ground with area of 2 \(\times\) 4 m; the longer sides of the plot are directed in the direction E-W. Experimental plot are free of the grass. The measurement technique for the soil temperature and the method of calculation of the zero configrade depth were described in the instruction for meteorological measurements [20; 21]. Freezing the ground is a physical process consisting of the freezing of water present in the ground and its molecules into a hard permafrost. The water contained in the soil is a solution of different salts of varying concentrations, the higher their concentration, the lower the ground freezing temperature. This temperature may drop to \(-2\)\({}^{\circ}\)C and below. Freezing of the ground depends on the air temperature, the duration of the negative temperatures, the thickness and type of snow cover, the terrain profile, and the structure and humidity of the ground. The low air temperature that persists for a long time lowers the temperature of deeper and deeper layers of the ground, while strong but short-term temperature drops have less impact on the freezing depth of the ground. An important role is played by the snow cover: a thicker, less dense and even layer of snow inhibits the process of freezing the ground. Different types of soils are characterized by different ease of freezing.