A mathematical model of snow-cover influence on soil freezing, taking into account the phase transition layer, water migration in soil, frost heave and ice-layer formation, has been developed. The modeled results are in good agreement with data observed in natural conditions. The influence of a possible delay between the time of negative temperature establishment in the air and the beginning of snow accumulation, and possible variations of the thermophysical properties of snow cover in the wide range previously reported were investigated by numerical experiments. It was found that the delay could change the frozen-soil depth up to 2–3 times, while different thermophysical characteristics of snow changed the resulting freezing depth 4–5 times.

The highly dynamic nature of snow requires frequent observations to study its various properties. Keeping this in mind, the present investigation presents results from the analysis of fully polarimetric synthetic aperture radar (POLSAR) parameters for the development of A snow depth (SD) inversion model for SD retrieval. Snow depth retrieved using ground penetrating radar (GPR) at 500 MHz over Austre Grønfjordbreen in the Svalbard region was used to understand the behaviour of certain polarimetric parameters. A significant correlation was found between field-measured SD and POLSAR parameters, namely coherence and normalized volume scattering power (R 2 = 0.84 and R 2 = 0.73, respectively.) Using the POLSAR scattering powers obtained from the six-component model-based decomposition (6SD), the heterogeneity and anisotropic behaviour in the firn areas are also explained. Further, based on the analyses shown in this work, A polarimetric parameter-based SD inversion algorithm have been proposed and validated. The univariate model with co-polarization coherence has the highest correlation (R 2 = 0.84, Root Mean Square Error (RMSE) = 0.18). We have even tested several multivariate models for the same, to conclude that A combination of coherence, normalized volume and double-bounce scattering have A high correlation with SD (R 2 = 0.84, RMSE = 0.18). Additionally, temporal and spatial variability in SD was also observed from three polarimetric SAR images acquired between 4 April 2015 and 15 May 2015 over the Western Nordenskiöld Land region. Increase in snow depth corresponding to snow precipitation events were also detected using the POLSAR data.Water 2020, 12, 21 2 of 23 depth and density. However, field-based single-point measurements of snow depth may not be A representative of the entire distribution of snowpack accumulation over A large area. Previous investigations [5-7] over Svalbard have indicated that deposition of snow on the glaciers in the region is highly diverse in space due to varying topoclimatological conditions. Snow deposition increases with elevation, but it is also observed that this altitudinal trend is highly variable due to the drifting wind and other local topoclimatological factors in Svalbard. Recent investigations [8][9][10][11][12] suggest that the altitudinal gradient of snow accumulation has decreased, and the average snow thickness on the Austre Grønfjordbreen has increased by 17 cm compared to average snow thickness in 1979. Spatial variability has also increased over the region. Hence, continuous monitoring of the spatial and temporal variability of snow cover depth is the need of the hour, which can be used to understand the state of the glacier and the changes and processes taking place in it.An alternative method to field-based manual measurements of snow depth is A ground penetrating radar (GPR) survey. This survey is an optimal technique to provide A spatial profile over large areas for understanding snow depth variability [8,9]. Apart from the spatial variability, snow accumulatio...

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