# Detection of Frozen Soil Using Sentinel-1 SAR Data
## 4 Results
### Interpretation of Sentinel-1 Images  
Figure 7 illustrates the temporal behavior for a wheat field, forest stand, and urban area for the Sentinel-1 backscattering coefficient (\(\sigma^{\circ}\)) in the VV and VH polarizations. For our study site, the vegetation cover of winter crop plots (wheat for example) is relatively low between November and January (height of approximately 5-10 cm). For the wheat field shown in Figure 7a, a decrease in \(\sigma^{\circ}_{\rm VV}\) of approximately 3-4 dB is observed for the main dates of freezing (soil temperature between \(-0.6\) and \(-3.7\)\({}^{\circ}\)C): 1, 7 and 31 December 2016; 6 January 2017; and between 18 and 26 January 2017. In addition, a slight decrease in \(\sigma^{\circ}_{\rm VV}\) by approximately 1.5 dB is noted on 11 February 2017, when the soil was slightly frozen (soil temperature = \(-0.6\)\({}^{\circ}\)C). With VH polarization, the difference between \(\sigma^{\circ}\) of unfrozen soil and \(\sigma^{\circ}\) of frozen soil is 1-2 dB higher compared to results obtained in VV polarization, which indicates that the volume scattering strongly influences the cross-polarized signal. Figure 7b shows a slight decrease of the radar signal for the forest stand after a frost episode. This decrease is 3 dB in VH at most (on 18 January 2017) and 2 dB in VV. This decrease of the radar signal corresponds mainly to a decrease of the dielectric constant of ground. The time series of \(\sigma^{\circ}\) for an urban area logically shows a relatively stable signal independent of frozen soil conditions (Figure 7c).  
Figure 6: Difference in \(\Delta\sigma^{\circ}\) between the modeled backscattering coefficient of unfrozen soil with reference temperature Ts equal to 0 \({}^{\circ}\)C \({}^{\prime\prime}\sigma^{\circ}\) (Ts = 0\({}^{\circ}\))\({}^{\prime\prime}\) and the modeled backscattering coefficient of frozen soil with soil temperature between \(-20\)\({}^{\circ}\)C and \(10\)\({}^{\circ}\)C \({}^{\prime\prime}\sigma^{\circ}\) (Ts)\({}^{\prime\prime}\). Frozen soils correspond to Ts lower than 0 \({}^{\circ}\)C. Radar frequency f = 5.405 GHz, \(m_{v}=20\) vol%, \(Hrms=1\) cm, incidence angle \(\theta=40^{\circ}\), and polarization = VV.  
We calculated the difference in \(\Delta\sigma^{\circ}\) for all fields corresponding to agricultural land cover (1016 fields) at two dates from Sentinel-1 images (VV and VH), one with an unfrozen soil condition (12 January 2017) and one with a frozen soil condition (18 January 2017). The \(\Delta\sigma^{\circ}\) at a given date \(\mathrm{t}=\sigma^{\circ}\left(\mathrm{t}_{0}\right)-\sigma^{\circ}\left( \mathrm{t}\right)\), where \(\mathrm{t}_{0}\) is a date corresponding to the unfrozen soil condition date earlier than \(\mathrm{t}\). For a given field, \(\sigma^{\circ}\) corresponds to the average of \(\sigma^{\circ}\) of all pixels of the field. The histograms of the difference in \(\Delta\sigma^{\circ}\) show that the mean \(\Delta\sigma^{\circ}\) on 12 January 2017, is approximately \(-1.5\) dB in VV and \(-  
3.5 dB in VV and 5 dB in VH. Negative \(\Delta\sigma^{\circ}\) values correspond to unfrozen soil and positive \(\Delta\sigma^{\circ}\) values correspond to frozen soil. The \(\Delta\sigma^{\circ}\) values between \(-1\) and \(+1\) dB are difficult to interpret because the error corresponding to Sentinel-1 radiometric accuracy is approximately 0.70 dB (3\(\sigma\)) for the VV polarization and 1.0 dB (3\(\sigma\)) for the VH polarization [30; 31]. Fields with \(\Delta\sigma^{\circ}\) values larger than 2 dB have a high probability of being frozen. Higher \(\Delta\sigma^{\circ}\) values indicate a robust freezing degree. Figure 8a,b shows negative \(\Delta\sigma^{\circ}\) values (or \(\Delta\sigma^{\circ}\) \(<\) 1 dB) corresponding to unfrozen fields on 12 January 2017 (unfrozen condition). For 18 January 2017 (frozen condition), most fields are detected from Sentinel-1 data as frozen (Figure 8c,d) with better identification using VH polarization (most fields have \(\Delta\sigma^{\circ}\) \(>\) 2 dB).