# Near Real-Time Freeze Detection over Agricultural Plots Using Sentinel-1 Data
## 3 Materials and Methods
### Plot Surfaces Frozen/Unfrozen Detection Algorithm  
To flag a plot (\(p\)) as frozen at any given time, the difference between the S1 backscatter over that plot at current date '\(d_{i}\)' and a reference backscatter obtained from previous acquisitions needs to be compared against a threshold. In some studies, the acquired backscatter value at a certain date is compared directly to a threshold [16]. Over vegetated areas, C-band SAR backscatter \(\sigma^{\circ}\) is the contribution of both the soil and vegetation components [55]. The contribution of each one of these two components to the total SAR backscatter differs from one crop type to another. Thus, in the case of freezing, the SAR backscatter of different plots, even for the same land cover, will not decrease with the same magnitude as the characteristics of the soil and vegetation are not exactly the same.  
First, a maximum \(o^{0}\) is calculated over each plot \(p\) from S1 acquisitions acquired n days before, and up to the current date \(d_{i}\) (\(max\_o^{0}(d_{n},p)\)). The \(max\_o^{0}(d_{n},p)\) should not correspond to a freezing event previously detected. The number of days (n) on which the maximum calculation \(max\_o^{0}(d_{n},p)\) is carried out should not be too long to minimize the effect of vegetation growth. Therefore, for each plot \(p\) at date \(d_{i}\), \(max\_o^{0}(d_{n},p)\) is calculated based on the maximum of the \(o^{0}\)-values corresponding to S1 images acquired not more than 15 days before \(d_{i}\) (at least three images). At date \(d_{i+1}\), a new \(max\_o^{0}(d_{n},p)\) is calculated in plot \(p\) if, and only if, the time difference between \(d_{n}\) and \(d_{i+1}\) is greater than 15 days. If not, we use the last calculated \(max\_o^{0}(d_{n},p)\). Since \(max\_o^{0}(d_{n},p)\) is calculated using the maximum value of backscatters from n previous dates, sometimes, especially after heavy rainfall, or an irrigation event, the backscatter value at date \(d_{n}\) increases abruptly. Hence, to reduce the effects of such influences, when detecting the surface state of a plot \(p\) at \(d_{i}\), instead of calculating the difference between the backscatter value at date \(d_{i}\) and only the last calculated \(max\_o^{0}(d_{n},p)\), we will instead calculate the difference between \(o^{0}\) at date \(d_{i}\), and the mean of the last three calculated \(max\_o^{0}(d_{n},p)\). Therefore, after selecting \(max\_o^{0}(d_{n},p)\) for plot \(p\) at date '\(d_{i}\)', we first calculate the mean of the last three calculated \(max\_o^{0}(d_{n},p)\). This mean is the reference \(\sigma^{\circ}\) (\(ref\_o^{0}(p)\)) that will be used when calculating the difference between \(ref\_o^{0}(p)\) and \(o^{0}(d_{i},p)\) (\(\Delta o^{0}(d_{i},p)\)). Finally, \(\Delta o^{0}(d_{i},p)\) will be compared to a threshold range which depends on the land cover type (LC) of plot \(p\) and the S1 polarization (\([A_{lc},p_{lc}]\)). If \(\Delta o^{0}(d_{i},p)<A_{lc}\), plot \(p\) is considered as unfrozen at date '\(d_{i}\)'. If \(\Delta o^{0}(d_{i},p)\in[A_{lc},p_{lc}[\), plot \(p\) is considered as having a mild-to-moderate freeze occurrence. Finally, if \(\Delta o^{0}(d_{i},p)\geq B_{lc}\), plot \(p\) is considered as having a high freeze occurrence.