# Detection of Frozen Soil Using Sentinel-1 SAR Data
## 4 Results
### Frozen Soil Mapping  
Analysis of the results from the previous sections shows that, when the soil temperature is below 0 \({}^{\circ}\)C, there is a significant difference in the radar signal compared to the radar signal with temperatures above 0 \({}^{\circ}\)C. Therefore, a simple approach can be proposed for frozen soil mapping. The approach is based on the difference in \(\Delta\sigma^{\circ}\) for each field of the agricultural land cover between one image acquired under an unfrozen soil condition and one image acquired under a frozen condition. The date of the image under the non-freezing condition was acquired prior to that of the image acquired under the freezing condition. A difference greater than 2 dB corresponds to a frozen soil. In this approach, we assumed that soil surface roughness is constant between the dates used to calculate \(\Delta\sigma^{\circ}\).  
Figure 8: Histograms of the difference in \(\Delta\sigma^{\circ}\) for two dates calculated from Sentinel-1 images, one with an unfrozen soil condition (12 January 2017) and one with a frozen soil condition (18 January 2017): (**a**) 12 January 2017, VV polarization; (**b**) 12 January 2017, VH polarization; (**c**) 18 January 2017, VV polarization; and (**d**) 18 January 2017, VH polarization. \(\Delta\sigma^{\circ}\) at a given date t = \(\sigma^{\circ}\) (t\({}_{0}\)) \(-\)\(\sigma^{\circ}\) (t), where t\({}_{0}\) is a date corresponding to an unfrozen soil condition date earlier than t.  
Since the different images are not necessarily acquired at the same incidence angle (images in ascending/descending mode, with different strip map beams), it is necessary to reduce the incidence angle effect by normalizing the backscattering coefficients \(\sigma^{\circ}\) by a function that represents the angular dependence. Consequently, the backscattering coefficient \(\sigma^{0}_{\theta}\) acquired at an incidence angle \(\theta\) can be normalized to a fixed reference angle \(\theta_{\text{ref}}\) (for example 40\({}^{\circ}\)) using the following equation [32; 33]:  
\[\sigma^{0}_{\text{ref}}=\frac{\sigma^{0}_{\theta}\cos^{2}(\theta_{\text{ref}} )}{\cos^{2}(\theta)} \tag{16}\]  
Surface frozen soil maps were built for all available dates. Figure 9 shows the presence or absence of frozen soils for one date with a frozen soil condition and another date with an unfrozen soil condition. A mask was applied to exclude forest and urban areas, as well as mixed land cover (urban + agriculture or forest + agriculture). The maps do not show the presence of frozen soils on 12 January 2017, using VV or VH polarizations (Figure 9a,b), which is consistent with the temperature data. Figure 9c,d shows our basin in a frozen soil condition on 18 January 2017, with better identification of frozen fields with VH polarization (\(\Delta\sigma^{\circ}\) higher than 3 dB).  
Figure 9: Maps of the frozen/unfrozen soil conditions: one date (12 January 2017) in an unfrozen soil condition (**a**,**b**); and one date (18 January 2017) corresponding to a frozen soil condition (**c**,**d**). Only crop fields were considered: (**a**,**c**) using VV; and (**b**,**d**) using VH. The mask in white corresponds to forest stands, urban areas and some mixed land cover (urban + agriculture or forest + agriculture).  
For mapping frozen soils in an operational way, it is possible to classify the fields into three categories: (1) unfrozen soils for \(\Delta\sigma^{\circ}\) values lower than 2 dB; (2) soils touched by freezing for \(\Delta\sigma^{\circ}\) between 2 and 3; and (3) extremely frozen for fields with \(\Delta\sigma^{\circ}\) higher than 3.