# Detection of Frozen Soil Using Sentinel-1 SAR Data
## 5 Discussion  
Mapping of frozen soils has some limitations. The presence of snow can lead to poor mapping. If the soil at the acquisition date of the image considered under an unfrozen soil condition is covered with wet snow (temperatures above 0 \({}^{\circ}\)C), the radar signal will be at least 3 dB lower [34] compared to the signal for snow-free surfaces or dry snow, which will cause confusion with the signal of a frozen soil and therefore will make it impossible to detect frozen soils. Thus, the difference between an image under a freezing condition and an image without frost but with wet snow will be quite small. The presence of dry snow on the reference image (unfrozen condition) does not lead to the misidentification of frozen soils because the backscatter is relatively high for dry snow or snow-free surfaces, whereas the backscatter can be 3 dB lower for wet snow. In this study, we assumed that the soil roughness does not change over time. If the roughness of some fields increases on the frost date, then in this case, the difference \(\Delta\sigma^{\circ}\) (\(\sigma^{\circ}\) with freezing and with high roughness, and \(\sigma^{\circ}\) without freezing with low roughness) will decrease and there may be poor detection of frozen soils. On the other hand, if the roughness decreases between the date of the image without freezing and the date of the image with freezing, the identification of frozen soils will be easier because the decrease of roughness on the date of the image with freezing will increase the signal difference \(\Delta\sigma^{\circ}\) (\(\sigma^{\circ}\) with freezing and with low roughness, and \(-\sigma^{\circ}\) without freezing with high roughness). To minimize the effect of a roughness change or the presence of snow on a date, the mapping frozen soils algorithm can use the average of all images acquired in an unfrozen condition before the acquisition date of the image to be analyzed under a freezing condition. If the soil volumetric moisture content mv increases between the date of the image acquired without freezing and the date of the image under freezing condition, the difference between the radar signal without freezing and the radar signal with freezing should be less than the difference that would have been obtained if there was no rain between the date of the two images. However, if the soil volumetric moisture content decreases between the image dates, the difference between the radar signal for unfrozen soils and the radar signal for frozen soils will be greater than the difference that would have been obtained if there was no drying of the soil between the two images. This soil drying configuration will lead to a negligible decrease in soil moisture content between the two dates because the soil freezing process is mainly observed in winter and the natural soil drying could be assumed low between two images acquired with a few days of lag. Knowing that the radar signal penetration depth in agricultural area is only a few centimeters at C-band [35], the C-band SAR images provide information on frozen soils only for the top soil surface layer. Thus, the few centimeters of C-band radar signal penetration depth do not allow obtaining information on deep frozen soils. This study also showed that, for temperatures slightly below 0 \({}^{\circ}\)C (around \(-\)4 \({}^{\circ}\)C), the freeze in forest stands is slightly visible, probably because these areas freeze at much lower temperatures. [PERSON] et al. [2] observed at 3 dB decrease in the ERS-1 radar signal (C-Band) when the soil and vegetation freeze (air temperature reaches \(-\)30 \({}^{\circ}\)C). It is worth mentioning that our study was carried out during the winter season with very low vegetation cover. In the case of more developed vegetation cover, possibly frozen areas mapping could be more difficult especially if the temperature is slightly below 0 \({}^{\circ}\)C (signal difference between unfrozen and frozen areas will be lower).