## 5 Discussion  
In this study, we found that sub-pixel offset measurements extracted from Sentinel-2 optical images performed well for monitoring lake ice. The Sentinel-2 optical images used in this study have a higher spatial resolution (10 m) and shorter revisit period (5 days) than other optical images (e.g., Landsat 8), which allowed us to improve the accuracy and time resolution of our POT measurements. Our results showed that the monitoring of spatial and temporal variations of ice sheet displacements can be accomplished with uninterrupted high-density data gain (112 Sentinel-2 optical images), continuous acquisition times (most were 5 days, and a few were 10 or 15 days), and high-resolution matching (10 m) when constructing horizontal displacement measurements of seasonal ice sheet movements from \(-\)12 to 12 m (with an uncertainty of 0.7-2.3 m). In previous studies, the displacement accuracies for the Pleiades (0.7 m), Worldview (0.5 m), SPOT6-7 (1.6 m), and Landsat (15 m) satellites were found to be 0.13, 0.3-0.56, 0.5, and 0.47-0.60 m, respectively [61; 65; 66; 67], suggesting that the COSI-Corr can reach an accuracy of 1/10 pixel [55; 56; 68; 69; 70]. We can also achieve an accuracy of 1/10 pixel in the second stage of lake ice. The InSAR technique was the first space-geodesy technique used in previous studies to detect ice displacement changes, such as in Prudhoe Bay and Barrow, Alaska [71; 72; 73]. However, InSAR has had limited applications in deriving lake ice displacement due to the need to penetrate microwaves into thick snow-covered ice, the highest achievable sensitivity for thin ice being a few tens of centimeters and probability of coherence loss [74]. For Lake Khovsgol, some studies have shown that InSAR measurements completely lack coherence and can only be used on land [74; 75; 76]. However, POT has shown strong potential to track ice changes, even during the growth seen in our study [77], so it also has strong potential for studies of the cryosphere (e.g., ice flow, river ice movement, and glacier ablation). Our results revealed dynamic lake ice movements on Lake Khovsgol from ice-on to ice-off lasting nearly 6 months from 7 December 2020 to 17 June 2021. In a previous study by [PERSON] et al. [47], in situ field survey records for several consecutive years showed that Lake Khovsgol started to freeze in November each year and started to melt in May or June of the following year. However, our results showed that in 2020, the lake freezing date was postponed to December, which proves that global warming is already having an impact on the icing trends of seasonal lake ice. We collected annual mean temperature data from NOAA for Lake Khovsgol from 1980 to 2020 (Figure 3). The data showed that the annual average temperature in the region had increased from \(-\)5 to \(-\)2.5 \({}^{\circ}\)C over the last 40 years, showing a generally linear increase. Appropriately, strong correlations between lake ice duration and global warming have long been demonstrated [11; 12; 13; 15; 16; 78; 79; 80]. [PERSON] et al. [16] showed that in lakes across the Northern Hemisphere from 1846 to 1995, the temperature increased by about 0.12 \({}^{\circ}\)C/decade, the freezing dates were delayed by 0.58 d/decade on average, and the thawing dates were advanced by 0.65 d/decade on average. In addition, [PERSON] et al. [9] collected lake ice observations from 18 lakes in Poland for the last 50 years (1961-2010), and they showed that lake ice had been appearing later and disappearing earlier and that the duration and thickness of ice cover had decreased. Thus, variations in lake ice are good indicators of climate change response. Additionally, lake ice has obvious regional characteristics, and its formation is closely related to local climatic factors [2]. Figure 2a shows that the local temperature started to sharply drop after 17 December 2020, when the ice of Lake Khovsgol happened to be rapidly growing.