## 4 Results and Analysis  
### Time Series Displacement for Ice Motion  
In this study, we simply divided the ice period of Lake Khovsgol into three stages based on their change characteristics. The first stage, also known as primary lake ice formation, was from 7 December 2020 to 3 January 2021 (Figure 5). It represents primary lake ice formation and climate response. Figure 5(A1-B2) shows that the displacement in the EW and NS components was \(-\)3.8-0.6 m and \(-\)4.3-6.2 m, respectively. Displacement signals were only found in the southernmost and some surrounding areas of Lake Khovsgol, occupying \(\sim\)1/7 of the lake. This suggests that ice formation started from the southernmost part of Lake Khovsgol between 7 December 2020 and 17 December 2020. Between 17 and 27 December 2020, some new ice formed at the southern end of the lake, with displacement values of about \(-\)3.8 and 4.3 m in the EW and NS directions, respectively (Figure 5(C1,C2)). Then, between 27 December 2020 and 3 January 2021, the ice cover size rapidly extended to the north. Figure 5(D1,D2) shows that the ice covered the entire lake by 3 January 2021, and the ice displacement was up to 12 m in the northern area. Some areas (marked with blue lines in Figure 5(D1,D2)) lost signals because of the clouds on 3 January 2021. Our results show that the first stage started on 7 December 2020 and lasted about 26 days, after which its formation accelerated, and demonstrate that the ice formed from south to north. The second stage, also called the ice cover active period, was from 3 January 2021 to 18 April 2021, as shown in Figure 6. From 3-8 January 2021, the lake ice showed overall movement with a northward displacement value of 9.5 m and a westward displacement value of 7.8 m. From 8-13 January 2021, the EW displacements ranged from \(-\)3.1 to 2.9 m (Figure 6(B1)). In the NS direction (Figure 6(B2)), the displacement ranged from \(-\)4 to 6 m, and two clear displacement gradients were formed in the northern part of the lake (\(\sim\)51.5\({}^{\circ}\) N) and near the small island (\(\sim\)51.0\({}^{\circ}\) N), resulting in a blocky distribution of lake ice movement. By 18 January 2021 (Figure 6(C1,C2)), the lake ice displacement in the NS direction near the island increased to \(-\)8.1-2.2 m, and the movement area expanded to the north. However, in the EW component, the displacement of the lake ice tends to be stable, and the westward displacement of the lake center area reaches 8.1 m (the deepest area of the lake). From 18 January to 22 February 2021, the lake ice actively moved and the gradient of displacement change was obvious. Between 18 and 13 January, the lake ice moved up to 4.2 m westward and up to 6 m northward (Figure 6(D1,D2)). From February 22 to March 9, the trend of lake ice movement was weak, and the displacement value was around 2.4 m. \begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{2}{c}{**EW Displacement (meters)**} & \multicolumn{2}{c}{**NS Displacement (meters)**} \\ \cline{3-6}
**Reference-Image** & **Secondary-Image** & & **Mean** & **Standard** & **Mean** & **Standard** \\  & & & **Deviation** & **Deviation** & **Deviation** \\ \hline
12 December 2020 & 17 December 2020 & 0.3 & 1.4 & 1.3 & 1.3 \\
17 December 2020 & 27 February 2021 & \(-\)1.3 & 0.8 & \(-\)1.9 & 1.4 \\
8 January 2021 & 13 January 2021 & 2.3 & 1.0 & \(-\)1.5 & 1.1 \\
18 January 2021 & 23 January 2021 & \(-\)0.6 & 0.7 & \(-\)3.1 & 1.3 \\
7 February 2021 & 12 February 2021 & \(-\)1.0 & 1.2 & \(-\)1.6 & 1.3 \\
27 February 2021 & 4 March 2021 & \(-\)2.0 & 0.7 & 1.2 & 1.0 \\
18 April 2021 & 13 May 2021 & \(-\)0.3 & 2.3 & \(-\)2.2 & 2.3 \\
13 May 2021 & 18 May 2021 & 1.7 & 2.1 & 3.0 & 2.0 \\ \hline \end{tabular}
\end{table} 
Table 2: The mean and standard deviation of the displacements of the stable regions in the Sentinel-2A/B image pairs. Each value is calculated by averaging the five regions.