## 2 Materials and Methods
### Extraction of Features
The ground tracks of sea ice and water are depicted by magenta and blue, respectively. The DDMs of sea ice and water are presented with the area marked with cyan and green rectangle respectively. Figure 2a presents the continuous DDMs over the water-ice transition area marked with red rectangle. The corresponding delay waveforms (i.e., NCDW, NIDW and DDW) are shown in Figure 2b. As shown in Figure 2b, the shape of delay waveforms changes from water to ice surface. The largest change in delay waveforms is between DDM 487 and 488. Figure 2: DDMs and delay waveforms (NCDW, NIDW and DDW) of TDS-1 data collected on 15 January 2016. NCDW is the normalized central delay waveform. NIDW is the normalized integrated delay waveform, DDW is the differential delay waveform between NIDW and NCDW. (**a**) The magenta and blue plots represent the ground tracks of sea ice and water, respectively. The typical DDMs of ice marked with cyan rectangle and water marked with green rectangle are presented. The continuous DDMs from index 481 to 492 for water-ice transition area marked with red rectangle are shown. (**b**) The continuous delay waveforms of DDM 481 to 492. NCDW, NIDW and DDW are depicted by a blue dotted line, green line and magenta dashed line, respectively. A few feature parameters are derived from the delay waveforms to monitor sea ice. Figure 3 presents the NCDW, NIDW and DDW, which can be divided into a left edge (LE) and right edge (RE) according to the point with a delay value of zero. The spaceborne GNSS-R DDMs are generated through cross-correlating scattered signals with code replicas generated locally for different time delays and Doppler shifts [44]. The maximum power is tracked in the Doppler domain to identify the delay value of zero. The earth surface (e.g., sea surface height fluctuations, ice height above the ellipsoid) may affect the geometry and lead to incorrect estimation. This study mainly focuses on the relative change, and not on altimetry applications. Therefore, the impacts of those factors have not been taken into consideration. The LE is related to the area above the reflection surface, which results in its insensitivity to the characteristics of reflection surface. Only the RE-related observables are applied to monitor sea ice in this study. Six characteristic parameters termed as RE slope of CDW (RESC), RE slope of IDW (RESI), RE slope of DDW (RESD), RE waveform summation of CDW (REWC), RE waveform summation of IDW (REWI) and RE waveform summation of DDW (REWD) are extracted as features for monitoring sea ice. These features can be computed according to the equations summarized in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Features** & **Mathematical Description** \\ \hline RESC & \(\left(\sum_{i=1}^{n}\tau_{i}C_{i}^{R}-n\overline{\tau}\overline{C^{R}}\right) /\left(\sum_{i=1}^{n}\tau_{i}^{2}-n\overline{\tau}^{2}\right)\) \\ \hline RESI & \(\left(\sum_{i=1}^{n}\tau_{i}^{R}-n\overline{\tau}\overline{1^{R}}\right)/ \left(\sum_{i=1}^{n}\tau_{i}^{2}-n\overline{\tau}^{2}\right)\) \\ \hline RESD & \(\left(\sum_{i=1}^{n}\tau_{i}^{D}-n\overline{\tau}\overline{D^{R}}\right)/ \left(\sum_{i=1}^{n}\tau_{i}^{2}-n\overline{\tau}^{2}\right)\) \\ \hline REWC & \(\sum_{i=1}^{n}C_{i}^{R}\) \\ \hline REWI & \(\sum_{i=1}^{n}t_{i}^{R}\) \\ \hline REWD & \(\sum_{i=1}^{n}D_{i}^{R}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The mathematical description of six selected features (i.e., RESC, RESI, RESD, REWC, REWI, REWD). RESC is the right edge slope of CDW. RESI is the right edge slope of IDW. RESD is the right edge slope of DDW. REWC is the right edge waveform summation of CDW. REWI is the right edge waveform summation of DDW. Figure 3: Delay waveforms of sea water (cross line) and sea ice (dotted line). The NCDW, NIDW and DDW are plotted in blue, green and magenta, respectively. The waveforms are divided into the left edge (LE) and right edge (RE) by the red dashed line.