The Spatio-Temporal Patterns of Glacier Activities in the Eastern Pamir Plateau Investigated by Time Series Sub-Pixel Offsets From Sentinel-2 Optical Images

The eastern Pamir Plateau, with a mean altitude of 5000 m, forms a large-scale glacier region with a size of 2054 km2 that serves as an important environmental climate condition for central Asia. In this article, we estimated the spatio-temporal patterns of glacier activities in this region by using the time series sub-pixel offsets derived from 63 sentinel-2 optical images between December 31, 2020 and December 31, 2021. Our results indicated the mean glacier flow velocity in this region was 0.531 m/d ± 0.007 m/d in 2021, and the Kongur Tagh Glacier was much more active than the Kingata Glacier and Muztagh Ata Glacier. The time series observations revealed that the glacier motion involves a pre-melting period (January–April) with a velocity of 0.600 m/d ± 0.012 m/d, a melting period (May–August) with a velocity of 0.608 m/d ± 0.003 m/d, and a post-melting period (September–December) with a velocity of 0.659 m/d ± 0.006 m/d. In order to get insights into the characteristics of these glacier activities, we carried out a correlation analysis between the glacier flow velocity change and its potential caused reasons (i.e., topography, temperature, precipitation, glacier surges, debris-cover, and glacier thickness), and current results suggest that the glacier flow velocity is influenced by a combination of these factors.


I. INTRODUCTION
G LACIERS are a significant component of the cryosphere and have a direct impact on the sea-level rise, regional climate and global water cycle. Global glaciers are classified into two types: polar glaciers and mountain glaciers. Even though mountain glaciers outside of Antarctica and Greenland account for only 3% of the world's glacier area, their impact on sea-level rise exceeds that of the Antarctic and Greenland ice sheets [1]. Mountain glaciers can occasionally cause floods [2], [3], [4], [5]. As a result, monitoring mountain glaciers is critical for predicting their evolution in the face of global climate change [6], [7], [8]. In recent years, remote sensing observations have been widely used in glaciology, such as glacier area, flow velocity, elevation change and mass balance [9], [10], [11], [12]. Glacier flow velocity is a dynamic index factor that controls ice volume transmission. It is also an essential input parameter for early cryospheric disaster warnings such as glacier surges, ice avalanches, glacial lake outbursts, and climate change investigations [13], [14], [15]. Furthermore, large-scale glacier dynamic change also affects regional tectonic stress and affects tectonic activity [16]. The eastern Pamir Plateau is a massive mountain range located in western China. Current glacier research in the Pamir-Karakoram mountains includes various glacier features, such as length and area, debris cover [17], [18] and mass balance [10], [19], [20], [21]. Some of these previous studies debate that glaciers in the region have shown a positive mass balance in recent years [22], in contrast to a mass loss before the year 2000, which is termed the "Pamir-Karakoram (glacier) anomaly" [23]. Moreover, several surging glaciers were found in this region, for example, the Karayaylak Glacier surged in 2015, attesting the glacier is highly active. Therefore, studying the glacier surface velocity in the eastern Pamir Plateau is critical to understand these changes in glaciers.
In previous studies, Yan et al. [24] used ALOS PALSAR images to track the motion velocity of the Koksay Glacier; Peng et al. analyzed the surface velocity of the Karayaylak Glacier surge area using sentinel-1 images [25]; Lv et al. [26] found 13 throbbing glaciers in Kingata Mountain. Note that most of these previous studies focused on the motion of a single glacier, but a few on the overall characteristics of glacier movements in the eastern Pamir Plateau. Up to now, only one relatively complete set of kinematic velocity data for the eastern Pamir Plateau has been derived from Landsat images with a period of 1989 to 2020 [27], but their results with a low spatio-temporal resolution (i.e., a spatial resolution of 240 or 480 m, and a time resolution of 1 year). That is, a detailed glacier flow velocity change in the eastern Pamir is still poorly understood.
The pixel resolution of the large-scale sentinel-2 optical image is 10 m and the time resolution is five days, which greatly improves the detailed monitoring ability of the large-scale mountain glacier movement. We collected 63 available images from December 31, 2020 to December 31, 2021. Based on these images, the surface displacement was obtained by using the subpixel offset technique. Then, we analyzed the annual mean velocity and seasonal movement characteristics of the study area. Finally, we discussed the possible factors affecting glacier flow velocities, such as glacier size, slope, temperature, precipitation, glacier surge, debris cover and glacier thickness.

II. STUDY REGION
The Pamir Plateau is located in Central Asia (73°00 ∼76°30 E, 38°00 ∼41°00 N), covering Kyrgyzstan, Xinjiang Province of China, Afghanistan, and Tajikistan. The area within China is named the eastern Pamir Plateau (see Fig. 1). The topography of the region is complex, with several tall mountains like Kingata, Muztagh Ata, and Kongur Tagh. The mountains generally slope from northwest to southeast, with an average elevation of more than 4500 m and the highest peak, Kongur Tagh at 7719 m. The eastern Pamir Plateau is predominantly affected by westerly circulation and is characterized by a continental mountain climate [26], [28], [29], [30]. In history, this region receives little annual precipitation (75-100 mm), primarily from the mid-latitude regions of the Mediterranean Sea, the Black Sea, and the Caspian Sea [26], [28], [29], [31]. However, due to the influence of atmospheric circulation anomalies, precipitation has increased in recent years, the severity of drought is steadily diminishing [32]. In addition, some studies have found a large precipitation gradient in the region. At elevations below 3000 m, the average annual snow accumulation is reported to be almost ten times higher than the precipitation [33]. Low temperatures persist throughout the year for this region, with lows reaching −50°C and highs not exceeding 20°C, with January being the coldest. The Taxkorgan meteorological station (37°46 N, 75°14 E) recorded an annual mean temperature of 3.5°C and an annual mean precipitation of < 80 mm from 1960 to 2011 [34]. According to the Second Glacier Inventory of China [35], the eastern Pamir Plateau has 1179 glaciers covering a total area of 2054 km 2 . There are 434 glaciers in Kongur Tagh and Muztagh Ata, covering an area of 998 km 2 . These glaciers are mostly found in the Muji river, Gez river, and Kangxiwa river of the Tarim system. The region contains three large glaciers with an area larger than 50 km 2 , namely Karayaylak Glacier, Qimgan Glacier, and Koksay Glacier. The largest glacier is Karayaylak Glacier with an area of 115 km 2 .

A. Data Acquisition
Sentinel-2 optical images were used in this article to obtain the glacier flow velocity of the eastern Pamir. These images are free to access (https://scihub.copernicus.eu/dhus/#/home). The sentinel-2 satellite carries a multispectral imager at an altitude of 786 km. It has 13 spectral bands that range from visible and near-infrared to short-wave infrared. With a width of 290 km, the ground resolution is 10, 20, and 60 m, respectively. The revisit period is ten days for one satellite and 5 days for two satellites constellation (https://sentinels.copernicus.eu/ web/sentinel/user-guides/sentinel-2-msi). Sentinel-2 images, with their high temporal-spatial resolution, large-scale coverage, and open access data policy, have become an ideal data source for detecting time-series changes in land [36] in comparison to other optical remote sensing images [37], [38], [39]. Given the radiometric characteristics of different bands of sentinel-2 image for various surface targets, band 8 has been suggested to be more suitable for surface deformation monitoring with the pixel offset method than other bands [38], [40]. In this article, we also chose band 8 of sentinel-2 image as the experimental band for exploring glacier flow velocity.
The RGI 6.0 (Randolph Glacier Inventory) database (http: //www.glims.org/) was used to generate the glacier outlines. Additionally, we used ArcGIS10.6 to manually check and correct the glacier outline using sentinel-2 images (synthesized from bands 11, 8, and 4) as a reference. This article uses ASTER GDEM V3 (ASTER Globe digital elevation model, version 3) DEM data with a resolution of 30 m to obtain the elevation, slope, and other topographic information about the study area (http://reverb.echo.nasa.gov/reverb/).

B. Pixel Offset Estimation
In this article, the glacier movement was estimated by using the pixel offset tracking method with the co-registration of optically sensed images and correlation (COSI-Corr) package. The COSI-Corr package was developed for co-seismic ground displacement extraction with optical images [39] and integrated as a module in ENVI software platform (http://www.tectonics. caltech.edu), and it has been widely used to monitor the earth's surface changes [35], [40], [41], [42], [43] and glacier monitoring [15], [26], [33], [44], [45], [46], [47]. The output files of the COSI-Corr package include the horizontal ground displacement of the east-west (EW) and north-south (NS) components, as well as the relative signal-to-noise ratio (SNR) in each pair of images. Two correlators are available in COSI-Corr: frequency and statistical. The frequency correlator is Fourier-based and is more accurate than the statistical one. It should be used as a priority when correlating optical images. However, as this correlator is more sensitive to noise, it is recommended for high-quality optical images [39]. In this article, the initial and final window size was set as 32 × 32 pixels, with a moving step length of 8, and a robustness iteration of 2 [26], [41], [43]. Then, the EW and NS displacements were obtained with pixels SNR >0.9. Finally, the glacier displacement D and velocity V were estimated with the EW and NS displacements as follows: To improve the quality of the above displacements, some postprocessings were implemented in the COSI-Corr package. First, we removed any uncorrelated outliers brought on by clouds or snow using the replace/discard tool in COSI-Corr. Additionally, we performed the de-striping step and used a filter to remove the outlier caused by small cloud occlusion and water reflection. The filter in the COSI-Corr package implements a nonlocal means algorithm to reduce the additive Gaussian white noise while retaining local displacement features [41]. We chose a 7 × 7 pixels filter window, and the noise threshold was 1.6 times the standard deviation [42]. The data processing flow is shown in Fig. 2.

C. Accuracy Estimation
The displacement accuracy of pixel offset estimation is mainly determined by systematic errors, image quality and image coordination errors. However, due to the remote location of the study area, in situ observations are not available. Therefore, we consider the velocity uncertainty on ice-free terrain as an accuracy assessment metric. That is, it is assumed that there is no displacement changes on stable terrain in the nonglaciated area, i.e., the movement velocity value is 0 [43], [44]. This approach may lead to an overestimation of the measurement accuracy. Because the number of effective observations in ice-free areas is relatively large, which easily can result in a lower value of the standard error. However, this is a more reasonable and general accuracy analysis strategy under existing conditions [45], [46], [47]. Evaluation of glacier velocity errors using where e off is the motion velocity error in the ice-free stable terrain area, MED is the average motion velocity, SE is the motion velocity standard error, and the calculation formula of SE is where STDV is the standard deviation of the flow velocity in the ice-free stable terrain area, N eff represents the number of effective pixels to remove the autocorrelation effect in the icefree stable terrain area, and the formula is where N total represents the total number of pixels in the stable terrain area in the ice-free area, and PS is the pixel resolution. D is the spatial autocorrelation distance, which is generally 20 times the pixel resolution, to remove the influence of autocorrelation.
Using the above equations, we calculate the glacier flow velocity with an accuracy of up to ± 0.003 m/d.

IV. RESULTS
According to our pixel offset observations, the average annual flow velocity of glaciers in the eastern Pamir Plateau was 0.531 m/d ± 0.007 m/d (see Fig. 3). There was partial cloud cover due to the high elevation of some areas, resulting in signal loss. However, the general trend of glacier movement and the rate of glacier movement in the eastern Pamir Plateau are clear.  To understand the seasonal changes of glacier movement, the entire observation period was divided into three periods: the pre-melting period (January-April), the melting period (May-August), and the post-melting period (September-December) based on the work of [48] to analyze glacier flow velocity (see Fig. 4). The glacier flow velocity in the study area was 0.600 m/d ± 0.012 m/d during the pre-melting period [see The glacier movement of Kongur Tagh Glacier was relatively weak in the pre-melting period, while it became active during the other two periods [see Fig. 4(a), areas c, d, e, f], especially in areas e and f. However, glacier movement in region b was more active during the melting period than that in the pre-melting period. In the post-melting period, the active range of glacier movement in region b was smaller than that in the melting period. The Muztagh Ata Glacier was relatively quiet during the pre-melting period, and the glacier on the westward-facing glaciers began to move faster during the latter two periods (areas g and h). In general, the movements of Kongur Tagh Glacier and Muztagh Ata Glacier were similar throughout the year, with the pre-melting glaciers moving less movement than the latter two periods, particularly in the west-slope areas. As a result, when many scholars study the glaciers on the eastern Pamir Plateau [27], they also consider these two glaciers as a whole (Muztagh Ata -Kongur Tagh area) to study and discuss.
Additionally, we examined the central flow lines' velocity values throughout three different periods in numerous regions (a-f) of Fig. 4(a) (see Fig. 5). The central flow lines' locations are depicted in Fig. 6, and the numbers a-f in Fig. 5 correspond to a-f in Fig. 4. According to Fig. 5(a), the region a had the most active motion in the pre-melting period with a maximum velocity of 0.300 m/d, followed by the post-melting period with a maximum velocity of 0.250 m/d, and the smallest velocity in the melting period compared to the other two periods with a maximum velocity value of 0.225 m/d. According to Fig .5(b),     [49] obtained the annual average global glacier surface velocity derived from sentinel-1 SAR data, suggesting some of the highest glacier flow velocity values in Kongur Tagh were 0.897m/d (75°20 E, 38°33 N). As SAR data is out of correlation at high altitudes, the observations are non-signal in most of the eastern Pamir and should be overestimated to some extent. In comparison to these results, the pixel offset estimation based on sentinel-2 optical images in this article improves the accuracy of mountain glaciers monitoring, resulting from their higher spatial resolution (10 m) and a shorter revisit period (5 days).
The motion mechanism of glacier flow velocity is complex, involving many factors such as topographic slope, glacier size, meteorological factors, debris cover, glacier thickness and even glacier surge. In order to get insights into the characteristics of these glacier activities in eastern Pamir, we carried out a correlation analysis between the glacier flow velocity change and its potential reasons as follows.

A. Local Topography and Glacier Flow Velocity
Gravity has seemed to be an internal driving force for glacier flow, and it is controlled by topography, altitude, and topographic slope [50]. The slope is positively related to the glacier's shear stress, and the steeper the glacier, the fast it moves [51]. In this article, the elevation, slope and flow velocity of the central flow line were extracted [see Figs. [7][8][9]. From Fig 7(d)-(f), the movement is small and gentle in upstream of the glacier above about 5500 m above sea level, which is especially noticeable in Kongur Tagh [see Fig. 8(a)-(i)]. At high altitudes, the slope typically exceeds 40°. So it is not conducive to snow accumulation, and the thickness is generally thin, causing the glacier to move slowly. Fig. 8(a) shows that areas with slopes greater than 40°have more no-value areas. We suspect that the sub-pixel offset estimation technique fails or performs poorly in this slope range. It is also possible that the altitude is high in this slope range and the image may be affected by cloud cover. Figs. 7,8,and 9 show that the flow velocity increases and then decreases with the slope in 0°to 30°. This is consistent with the glacier equilibrium velocity principle [51], i.e., when the glacier accumulates to a certain level, it will move downward under the effect of gravity and the velocity of movement increases sharply. As the slope slows down, it tends to stabilize at the end. It is also a general phenomenon of mountain glacier movement [50], [52], [53]. Huang et al. [48] suggest the partial correlation coefficient between slope and glacier movement velocity was 0.665 (P<0.01) within the slope range of 0°to 30°. In addition, Figs. 7-9 show that the glaciers with an average slope in the range of 20°to 30°in the eastern Pamir Plateau have the highest movement velocity, reaching 0.48 m/d [see Fig. 8(d)].
The velocity of glacier movement on different slopes is proportional to the glacier's size. The glaciers on the southeast, southwest and west slopes are relatively large in scale, while the majority of the glaciers on the southern slope are small in scale. Within the same slope range, the larger the glacier is, the faster it moves. This phenomenon is consistent with the research findings from the Tianshan Mountains, the Nyenchenthanglha Mountains, and the Hengduan Mountains [54].

B. Temperature and Precipitation on Glacier Flow Velocity
Meteorological factors such as temperature, precipitation and sunshine influence the hydrological process beneath the ice, which in turn influences glacier movement. In this article, the changes in glacier flow velocity in the eastern Pamir Plateau were investigated using the average temperature and precipitation of the Taxkorgan meteorological station. According to Fig. 10(a), the change in the average flow velocity of glaciers in the eastern Pamir Plateau basically corresponds to the change in monthly average temperature in the study area, indicating a trend of high flow velocity in summer and low flow velocity in winter. As the melting period began, the temperature rose, and the flow velocity increased compared to the pre-melting period. Huang et al. [48] hold the view that the glacier velocity during the melting period was lower than that in the pre-melting and post-melting periods from 2013 to 2018. However, our results show that the flow velocity during the melting period and the post-melting period in 2021 is higher than that during the pre-melting period. We believe that as temperature rise, the glacier's melting period is extended, which explains why the flow velocity in the postmelting period is still higher than in the melting period (that is, the glacier is still active after entering September). Precipitation mainly affects the change of glacier velocity indirectly by increasing meltwater and changing the subglacial drainage system. If precipitation enters the bottom of the glacier, it may reduce the friction between the ice body and the ice bed, resulting in increased base slippage, thereby accelerating the flow velocity of the glacier [55]. Note that the precipitation mentioned above is liquid precipitation, and any precipitation corresponding to temperatures of 0°C will be considered snow, i.e., solid precipitation (SolP) [56].
Temperature and liquid precipitation act in concert during the summer, reducing glacial mass balance accumulation and increasing expenditures [57]. However, the glacier mass is most strongly influenced by SolP in cold and dry areas [56]. Bhattacharya et al. discovered a particularly strong correlation between SolP and glacier mass balance in such regions (r2 = 0.79 and p = 0.0007) [56]. However, the agreement with liquid precipitation data was weaker. This could be due to the relatively sparse network of weather stations located below the glacial topography. As a result, the in-situ measurements may not be completely representative of the glacier's precipitation. At the same time, weather stations at higher elevations may be more biased than those at lower elevations [58], [59]. Bhattacharya et al. [56] concluded that the increase in summer temperature in the Muztagh Ata region from the 1960s to the 1970s and since 2009 has been accompanied by an increase in the velocity of glacier mass loss. During 2001-2009, the region experienced a slight mass balance (+0.03 ± 0.10 m w.e.a −1 ). However, there was only a slight increase in summer temperature. Therefore, it could be influenced by the increase in SolP. After 2013, the mass loss (−0.12 ± 0.11 m w.e.a −1 ) is due to an increase in summer temperature and a decrease in SolP [56]. It has also been discovered that the apparent end of the mass increase anomaly in Karakorum corresponds to changes in summer precipitation and temperature [60], [61].

C. Surges on Glacier Flow Velocity
Glacier surges are typically defined as quasi-periodic advances or increases in flow velocity that are not caused by external triggers [62], [63]. Surge glaciers typically oscillate quasi-periodically between shorter active periods (days to years) and longer stationary periods [62], [64], [65], with surge periods having flow velocity that is at least ten times higher than stationary periods. There are two types of glacier surge mechanisms: hydrologically triggered mechanisms and thermally triggered mechanisms [63]. In the thermally controlled mechanism, an increase in air temperature causes an increase in ice temperature in the glacier bed [63], [66]. This thermally triggered mechanism operates only at the cold-warm interface of the subglacier, which is typically in the upper region of dendritic glacier tributaries [25]. In the hydrological control mechanism, excess meltwater formed by warming temperatures or other factors cannot drain out quickly due to changes or obstructions in the subglacial drainage system [67], [68]. After investigation the surging glaciers in the study area, such as Karayaylak Glacier (region b) and Jangmanjiar Glacier (region f) are mainly caused by a combination of thermal and hydrological trigger mechanisms [25], [26], [69], [70]. As a result, we consider that because the average monthly temperature in the study area from June to August exceeds 0°C and precipitation exceeds 60 mm, the input of surface meltwater increases the water pressure in the subglacial drainage system, causing the drainage system to fail and thus triggering glacier surges. Furthermore, surges are more common in glaciers with gentle slopes and longer lengths [69]. According to our findings, Karayaylak Glacier and Jangmanjiar Glacier are significantly longer and have slightly lower slopes than the other glaciers. Therefore, we speculate that the increase in flow velocity of these two glaciers after entering summer may also be influenced by surges.

D. Debris Cover on Glacier Flow Velocity
Recent research on high Mountain Asia glaciers has found that debris-covered glaciers have an impact on glacier flow velocity. For example, most scholars studying Himalayan glaciers have discovered that increased debris cover slows glacier movement [18], [71], [72], [73]. Similar findings were made for the Koxkar Glacier in Tian Shan [74] and the Western Nyainqentanglha Mountains [75]. On the one hand, a thick debris cover on the glacier causes less frontal retreat and a decrease in ice thickness and surface slope, which reduces ice flow velocity [76]. On the other hand, a certain thickness of debris cover forms an insulating layer on the glacier surface, slowing the glacier's response to climate warming and thus slowing glacier movement [77]. According to available data, debris covers 11.2% of the glaciers on the eastern Pamir Plateau, accounting for 60% of the total glacier area. 85% of glaciers larger than 10 km 2 have debris cover [48]. Besides, 58 debris-covered glaciers in Muztag Ata-Kongur Tagh [78], with an area of 644.3 ± 6.1 km 2 (total debris area of 120.61 ± 3.5 km 2 ) remained relatively stable (only reduced by 0.4 ± 0.1%) from 1976 to 2014. The remaining glaciers are either retreating or advancing. As a consequence, we speculate that this is a significant reason for the decrease in ice flow velocity or even the cessation of glacier movement at the glacier's terminus.
Furthermore, the glacier surface flow velocity is related to ice thickness [79], [80]. Some findings show regional surface velocity trends that correspond to changes in ice thickness. The fastest velocity slowdown is seen in rapidly thinning regions (Nyainqêntanglha), while regions nearing equilibrium or increasing mass experience a slight velocity acceleration (Karakoram, West Kunlun) [80]. However, while the Pamir-Karakoram region had a weak mass gain until 2013, it now has a mass loss [56], [60]. As a result, we hypothesize that the flow velocity of glaciers retreating in the study area may have been reduced compared to the previous period. However, this needs to be confirmed by long-term observations.

VI. CONCLUSION
We used sentinel-2 optical remote sensing images with the sub-pixel offset technique to measure flow velocity results for major glaciers in the eastern Pamir Plateau from December 31, 2020 to December 31, 2021, which reflect the detailed seasonal movement characteristics of these glaciers. Sentinel-2 with the near-infrared band (B8) performs well in the mountain glacier motion. The annual mean flow velocity of the main glaciers on the eastern Pamir Plateau in 2021 was 0.531m/d ± 0.007 m/d, and the most active glacier is the Kongur Tagh. The flow direction of the Kingata Glacier is along the southwest and northeast, the Kongur Tagh Glacier is along the southwest and southeast directions and the Muztagh Ata Glacier is along the west, southwest and southeast directions. What's more, the flow velocity of the pre-melting period in the study area was 0.600 m/d ± 0.012 m/d, the flow velocity of the melting period was 0.608 m/d ± 0.003 m/d, and the flow velocity of the post-melting period was 0.659 m/d ± 0.006 m/d. The reasons affecting the glacier flow velocity are multiple, such as temperature, precipitation, glacier surge, debris cover, and glacier thickness may be factors. Our results suggest that glacier velocity is influenced by a combination of these factors. Longer-term results are needed for further analysis if the dominant factor is to be determined.

ACKNOWLEDGMENT
The sentinel-2 optical data were provided by the ESA through their open data policy.
Ping He received the B.S. degree in science in sur-