**5. Discussion**

### *5.1. Comparison with Existing Studies*

### 5.1.1. Comparison of Inter-Annual Glacier Elevation Change Rate

We compared our results with those by other studies in each sub-region of the HMA (Figure 7). Overall, our results are consistent with most previous studies.

However, there are some discrepancies between our results and existing studies, which may be due to the use of different methods and data. As shown in Section 4.1, glacier elevation changes varied with elevations and slope aspects. As shown in Figure 4b, the glacier elevation changes on the east and west slopes of the Nyainqentanglha Mountains were different. At the same time, the distribution of ICESat-1&2 data points in different slope aspects will also affect the changes of glacier elevations. The ICESat-1&2 laser point data cannot be guaranteed to be evenly distributed in space. In general, a large area may have more data points. However, due to factors such as satellite orbit or cloud cover, the spatiotemporal distribution of available laser points is irregular. We selected

the computing unit (i.e., one 1◦ × 1◦ grid) around the Yalong glacier (96◦E~97◦E, 29◦N~30◦N) to investigate the distribution of ICESat-2 data and found that the data volume of ICESat-2 data in 2020 in the eastern slopes is about 1.6 times of that in the western slopes, while the area of glaciers in the eastern slopes is only 1.2 times of that in the western slope. In brief, the distribution of ICESat-1&2 data points will be different in various slope aspects due to the influence of topography, climate and satellite operation mode, which in turn affects the accuracy of the results of glacier elevation changes. Therefore, in this study, elevation and aspect are both factors that must be considered simultaneously when calculating the glacier elevation change.

**Figure 7.** Comparison of results on glacier elevation change rate in the HMA in 2003–2020 and 2003–2008 between this study with existing studies. Wang et al. [22] calculated the glacier elevation change rate in 2003–2019 using the ICESat-1&2 data. Brun et al. [17] and Shean et al. [10] calculated the glacier elevation change rates in 2000–2016 and 2000–2018 using ASTER data in 2016/2018 and SRTM DEM data in 2000, respectively. Kääb et al. [58] calculated the glacier elevation change rate in 2003–2008 using ICESat-1 data. The error bars are the standard deviation of spatial glacier elevation change rate calculated by Equation (6) at 1σ level.

Existing studies have shown that the glacier thinning rate based on ICESat-1&2 data is greater than that based on stereo pair data in the Nyainqentanglha region [22,59]. However, with the exception of Nyainqentanglha region, the difference between our results in 2003–2020 and the results of Brun et al. [17] and Shean et al. [10], both using stereo pair data, is very small (within two standard deviations), indicating that our results of glacier elevation change rate are within an acceptable range.

### 5.1.2. Comparison of Intra-Annual Glacier Elevation Change

The results of this study are basically consistent with the existing studies (Table 2) on intraannual variation of glacier elevation. In general, glaciers in the marginal regions of the HMA (the Tienshan Mountains, Spiti Lahaul, etc.) thicken in winter. However, similar to existing studies, the glaciers in Bhutan and Nepal have an obvious thickening trend in summer. This may be due to the accumulation of water vapor in the whole Tibet Plateau mainly in summer. The southern slopes of Bhutan and Nepal are affected by the strong monsoon from the Indian Ocean and the Bay of Bengal, with the most precipitation in summer [60]. The impacts of precipitation outweigh the impacts of temperature, leading to summer replenishment of glaciers in Himalayas. However, there are also large fluctuations in glacier elevation changes in Bhutan and Nepal. Our findings show that in 2019 the glaciers generally accumulated between January and June, while in 2020 the opposite was true, although the months with the highest glacier elevation were all in July. Kansakar et al. [61] found large variation in precipitation patterns in Nepal suggesting that there may be large differences in glacier elevation changes in the Himalayas Mountain, which is consistent with studies by Maussion et al. [30] and Wang et al. [31]. Similarly, the greater variability in the glacier elevation change in the Nyainqentanglha Mountains may be partly due to the influence of hydrothermal conditions, because the inter-annual variability of precipitation due to abnormal anticyclones in the northern Indian subcontinent and the Bay of Bengal varies greatly [62,63]. Different from the existing research, in the Tienshan Mountains, our results showed a clear trend of glacier thickening in autumn, although the glacier elevation in autumn was the lowest. This is mainly due to the large glacier loss from July to September. However, looking at the monthly distribution, we found a slight increase in autumn during the two-year period (September to December). The same phenomenon occurred in Nyainqentanglha, Pamir and Hindu Kush. This is also an advantage of our study based on monthly data from ICESat-2, as we could highlight the details between seasons. In short, using the ICESat-2 data, we can more precisely monitor the intra-annual changes in glacier elevation. However, when the analysis is carried out on a monthly/seasonal scale, the amount of data is reduced, which also affects the accuracy of regional results. For example, some glaciers may have only a few hundred points in a month, which may be the reason for the large fluctuations in glacier elevation change in some areas. Nevertheless, our method is a direct calculation of glacier elevation change that can represent the intra-annual variation pattern of glacier elevation. With the continuous observation by ICESat-2 satellite, we will obtain more accurate monthly/seasonal variation characteristics of glacier in the future.

**Table 2.** The period of glacier accumulation in the sub-regions of the HMA from this study and the comparison with previous studies.


*5.2. Factors Controlling Glacier Elevation Change*

5.2.1. Factors Controlling Inter-Annual Glacier Elevation Change Rate

Previous studies have shown that the sensitivity of glaciers to climate is the main controlling factor of the HMA glacier change [64]. The rate at which a glacier melts is related to the energy gain or loss on the glacier surface. The main factors affecting glacier changes include temperature and precipitation. Warmer temperatures will lead to accelerated glacier loss [65], while increased precipitation will compensate for glacier mass loss. To explore the factors affecting the changes of

glacier thickness, we calculated the change of glacier elevation change rate from 2003 to 2020 and from 2003 to 2008 (Figure 8a), and used the ERA5 data to investigate the average temperature and precipitation changes in autumn in the HMA from 2003 to 2020 and from 2003 to 2008 (Figure 8b,c).

**Figure 8.** Difference between 2003–2020 and 2003–2008 (in autumn) in: (**a**) glacier elevation change rate, (**b**) mean temperature, and (**c**) mean precipitation.

The result showed strong warming in the central and southeastern regions of the HMA, while the temperature decreased in the western, northwestern and southwestern regions. The precipitation in the HMA generally showed an overall increasing trend, but the increased precipitation was mainly concentrated in the Tienshan Mountains in the northwest of the HMA, the western part of the HMA, parts of the central HMA and southern edge of the HMA. Our study revealed that in the context of global warming, most glaciers in the HMA experienced accelerated mass loss. Spatially, the change of glacier elevation change rate in the Tienshan Mountains is consistent with the change in precipitation, indicating that the change of glaciers in the Tienshan Mountains may be more affected by precipitation. However, the rate of glacier thinning in the southwest of HMA has slowed down. Guo et al. [66] found that, compared with the warming trend (+0.18 ◦C/decade) of the Tibetan Plateau since 2001, the temperature in the southwest of the Tibetan Plateau decreased by 0.15 ◦C/decade, and we found that Pamir and Hindu Kush also appeared to have a similar pattern. Overall, a decrease in temperature (Figure 8b) and an increase in precipitation (Figure 8c) explained the slowing of glacier mass loss in the west HMA region. The analysis of climatic factors of precipitation and temperature showed that the regional pattern of glacier elevation changes was consistent with the patterns of precipitation and temperature. Existing studies showed that for every 1 degree increase in temperature, precipitation needs to increase by 25 −35% to compensate for the impact of temperature on glaciers [67]. Both temperature and precipitation within the HMA are increasing overall, and while more precipitation can compensate for the mass loss of the glaciers, it is still far from being able to compensate for the overall melting of glaciers caused by the increase in temperature, which contributes to the accelerated glacier mass loss in most parts of the HMA.

### 5.2.2. Factors Controlling Intra-Annual Glacier Elevation Variation

The glaciers in the HMA region have multiple types of accumulation and ablation patterns, which are largely related to precipitation [68,69]. This study analyzed the monthly/seasonal variations in temperature and precipitation from January 2019 to December 2020. In all regions of the HMA, the temperature throughout the year showed a trend of first rising and then falling. The changes in precipitation can explain the characteristics of intra-annual glacier elevation variations (Figure 9).

**Figure 9.** Monthly temperature and precipitation from January 2019 to December 2020 in each sub-region of the HMA. The red line (left *Y*-axis) represents the monthly temperature, and the blue column (right *Y*-axis) represents the monthly precipitation.

For example, precipitation in the Himalayas has a clear upward trend in summer, which explains the accumulation of its glaciers in summer. In the Nyainqentanglha Mountains, the thickening of the glaciers in spring is attributed to that the concentration of about 20−40% of the precipitation in spring [70]. The strength and nature of the coupling between the monsoon system and the westerly system are important factors that cause precipitation changes. Glaciers in Pamir, Hindu Kush and Spiti Lahaul, located at the intersection zones of westerly and monsoon air flows, may be more sensitive to changes in weather and atmospheric circulation [30]. Compared with other regions, Spiti Lahaul and Pamir have significantly more precipitation in winter and spring, which is the reason for the thickening of glaciers here. April in particular is the rainiest month in Pamirs and in Spiti Lahaul from November to March, while the rest of the HMA is around July. As shown in Section 4.3, the overall trend of glacier elevation changes in Karakoram is similar to that in Pamir and Hindu Kush, except in July 2019, which may be due to less precipitation in July 2019. Existing studies have shown that in areas affected by the westerly climate, the precipitation in winter is more than that in summer [71]. At the same time, affected by the atmospheric circulation and the deviation of the earth's rotation, the Tienshan Mountains, Pamir and Hindu Kush are mainly affected by the Atlantic southwesterly wind. Coupled with the barriers of mountains, the westerly wind in spring will bring sufficient precipitation here and reduce the mass loss of glaciers. For example, in Pamir and Hindu Kush, the glacier elevation is highest in spring, due to the continuous thickening of the glaciers from October to March. There is less glacier mass loss in spring as precipitation remains high from March to May. In conclusion, the difference of precipitation can explain the difference in the glacier accumulation in different regions of the HMA.

#### *5.3. Advantages and Disadvantages of ICESat-1&2 Data in Estimating Glacier Elevation Change*

The ICESat-1&2 data have high vertical detection accuracy, and their applications in the cryosphere will be worth exploring. The emergence of ICESat-1&2 data allows us to obtain a large amount of data every year or even every month, which provides us with an opportunity to understand the glacier changes at higher temporal resolutions (monthly/seasonal), which is of grea<sup>t</sup> significance to disaster prevention and rational use of water resources [24,72]. For example, the ICESat-2 data are observed more frequently and therefore have more data points in space, providing a new perspective for the monitoring changes in glacier elevation. Its main disadvantage is that the large orbital spacing in the middle latitudes [73]. As shown in Figure 2, the ICESat-1 GLAS data have less data density. Although the amount of ICESat-2 ATLAS data and glacier coverage have been greatly improved, it still cannot cover all glaciers completely, which is an unavoidable problem when using ICESat-1&2 data in mid latitudes. The number and spatial distribution of data points will directly affect the accuracy of the results. In some regions, the reduction in data volume can increase the uncertainty of the results. For example, in the monthly analysis in Section 4.3, there were only a few hundred points per month in some regions, resulting in large fluctuations in annual performance. The spatiotemporal sampling of the data will affect the accuracy of the results, especially the ICESat-1 data with a small amount of data. There is no doubt that the more complete the data points, the more reliable the results will be. In future study, systematic analysis should be carried out to explore the impact of the spatial distribution of the ICESat-1&2 data points on the accuracy of the results. The second disadvantage is that the orbital revisit positions of ICESat-1&2 are not constant, so the observation points of each orbit do not repeat at the same position. While the track crossing method or plane fitting method can help reduce uncertainty, these methods are mostly applicable to polar regions [74] and are not reliable in mid-latitudes. The method proposed in this paper can better calculate the glacier elevation changes, but the uncertainty of the ICESat-1&2 data itself cannot be eliminated compared with studies based on stereo image pairs.

It should be noted that the data record of ICESat-1&2 is short (2003–2008 & 2018-onwards), making it is difficult to draw ultimate and firm conclusions about the trend in glacier elevation changes. With more ICESat-2 data becomes available over time, the glacier thickness change and seasonal dynamics can be monitored with longer record and data of better quality.

### **6. Conclusions**

This study applied the "elevation-aspect bin analysis method" to ICESat-1&2 data to estimate glacier elevation changes in the HMA region and explored the inter-annual and intra-annual changes of glacier elevation in the HMA. The main conclusions of this study are as follows: (1) The "elevationaspect bin analysis method" can efficiently capture the glacier elevation change and reduce the uncertainty caused by uneven spatial distribution of data points of ICESat-1&2 observations. (2) The result of the inter-annual rate of change in glacier elevation in the HMA showed spatial heterogeneity. The glacier elevation in the marginal regions of HMA declined more (i.e., thinned faster), while the elevation of the glaciers in West Kunlun rose. The declined rate of glacier elevation in the HMA in 2003–2020 ( −0.26 ± 0.11 m/year) was faster than that in 2003–2008 ( −0.21 ± 0.12 m/year). Glacier retreat is accelerating in all regions of the HMA except in the western part of the HMA. The regional variability of the glacier elevation change rate from 2003 to 2020 was large, ranging from −1.12 ± 0.13 m/year in the Nyaingentanglha Mountains to +0.18 ± 0.11 m/year in the West Kunlun Mountains. (3) For the intra-annual variation of glacier elevation, the results show that glacier elevation change has spatial heterogeneity, and the glacier thickening period is gradually delayed from the marginal regions to inner regions of the HMA. The glaciers in the Spiti Lahaul (December to March) and the Tienshan Mountains (September to April) tend to thicken during winter to spring, while glacier elevation in the Tienshan Mountains tends to rise slightly in autumn. The glaciers in Pamir and Hindu Kush (October to March) and Karakoram (October to January) thicken during winter. The glaciers in Nyainqentanglha thicken during spring (October to April or June). The glaciers in West Kunlun, Inner TP and Bhutan and Nepal thicken in spring and summer. West Kunlun has two accumulation periods (March–June and July–September). The glaciers in the Bhutan and Nepal (February to July) thicken in spring and summer, with elevation peaking in July. The glacier elevation in Inner TP reaches the highest level in June or July, but the accumulation trend is not obvious. In addition, the factors affecting glacier elevation changes are analyzed and the results indicate that the inter-annual and intra-annual changes in glacier elevation are consistent with the changes in air temperature or precipitation patterns.

**Author Contributions:** Conceptualization, C.S. and L.J.; methodology, C.S., L.J. and S.R.; software, C.S.; validation, C.S. formal analysis, C.S. and L.J.; investigation, C.S. and L.J.; resources, L.J. and C.S; data curation, C.S., L.J.; writing—original draft preparation, C.S.; writing—review and editing, C.S., L.J. and S.R.; visualization, C.S.; supervision, L.J.; project administration, L.J.; funding acquisition, L.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded jointly by the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (grant no. 2019QZKK0103); the projects of National Natural Science Foundation of China (grant no. 91737205, 42171039); the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDA19070102); the MOST High-Level Foreign Expert program (grant no. GL20200161002).

**Conflicts of Interest:** The authors declare no conflict of interest.
