**4. Results**

This study analyzed the change in glacier elevation from two perspectives, inter-annual and intra-annual. In the first part, we investigated the change in glacier elevation at different altitudes and slope aspects (Section 4.1) and analyzed the spatial differences in the inter-annual rate of change in glacier elevation (Section 4.2). In the third part, we conducted monthly/seasonal study by analyzing the 24-month pattern of glacier elevation changes from January 2019 to December 2020 (Section 4.3).

### *4.1. Glacier Elevation Change in Different Elevations and Slope Aspects*

Firstly, we analyzed the glacier elevation changes between 2000 (from SRTM DEM data) and 2020 (from ICESat-2 data) in different elevations and slope aspects in the HMA sub-regions according to the regional division of Brun et al. [17], as shown in Figure 1a. Overall, the glacier elevation changes (i.e., the glacier thickness change) between 2000 and 2020 decreased with increasing altitudes in all sub-regions of the HMA (Figure 4a), which is consistent with the findings of Ragettli et al. [56]. In addition, the accumulation and melting characteristics of glaciers also varied in different slope aspects (Figure 4b). In general, in most sub-regions, the glacier elevation changes on the southern slope decreased more than that on the northern slopes from 2000 to 2020, because the southern slopes received more solar radiation, resulting in more melting of the glaciers. However, different features were found in the Nyainqentangla Mountains, Bhutan, Nepal and the Tienshan Mountains. In the Nyainqentangla Mountains, the glaciers thinning on the northern slopes thinned more than that in the southwestern slopes. Additionally, in Bhutan, the glacier on the northern slopes thinned more than that on the eastern and southwestern slopes. The reason might be that these regions were strongly influenced by monsoon which brings abundant precipitation and leads to less reduction in glacier thickness on the windward sides [57]. In Nepal, for example, the southern slopes of the mountains are windward, and the glaciers on the southern slopes were replenished by precipitation from the Indian monsoon, resulting in less reduction in glacier thickness. Similarly, in the Tienshan Mountains, under the influence of the westerly winds, the glacier thickness on the southwestern slopes (windward) decreased less than that on the northeastern slopes. To sum up, the water vapor carried by monsoon will affect the melting rate of the glaciers in the HMA region, resulting in a large difference in the glacier elevation changes on different slope aspects, especially in the areas greatly affected by the monsoon.

**Figure 4.** Glacier elevation change between 2000 and 2020 in each sub-region of the HMA in: (**a**) different elevations, and (**b**) different slope aspects. (The sub-regions were defined in Figure 1a).

### *4.2. Inter-Annual Change Rate of Glacier Elevation*

### 4.2.1. Spatial Pattern of Annual Glacier Elevation Change Rate

To calculate inter-annual rate of change in glacier elevation, ICESat-1&2 data in autumn months (September–November) from 2003 to 2008 and from 2018 to 2020 were selected (procedure described in Section 3). Autumn was chosen for the annual trend analysis because the ICESat-1&2 and SRTM observations are less influenced by snow cover in this season [35,54]. The year 2009 was not included in the trend analysis due to too little data available in autumn to ensure reliable results (ICESat-1 eventually ceased work in 2010). Figure 5 showed the spatial distribution of the annual rate of change in glacier elevation in the HMA region from 2003 to 2008 and from 2003 to 2020, respectively. The detailed annual changes in glacier elevation and the respective error information were shown in Table A1. The results showed that the spatial variation of glacier elevation change rate in the HMA was very significant, and the change rate was very different in some areas between 2003– 2008 and 2003–2020. The glacier elevations have thinned across much of the HMA region. For the entire HMA, the annual rate of change in glacier elevation from 2003 to 2008 and from 2003 to 2020 were −0.21 ± 0.12 m/year and −0.26 ± 0.11 m/year, respectively, indicating a faster thinning rate in recent years. In Nyainqentanglha, the annual glacier elevation change rate increased from −0.81 ± 0.15 m/year in 2003–2008 to −1.12 ± 0.13 m/year in 2003–2020, which is the region with the fastest glacier loss. The annual glacier change rate in the Tienshan Mountains increased from −0.27 ± 0.13 m/year in 2003–2008 to −0.33 ± 0.11 m/year in 2003–2020. In contrast, the rate of glacier thinning decreased significantly in the west HMA. For example, in the Pamir, the glacier

elevations decreased by 0.22 m/year in 2003–2008 and 0.13 m/year in 2003–2020, indicating a slowing down trend in glacier thinning rate. Although the elevation of most glaciers generally decreased between 2003–2020, some glaciers in the inner region of HMA showed an increase in elevation. Previous studies found that glaciers in the West Kunlun was thickening [17]. Our results showed that in West Kunlun, the glacier elevation change rate was 0.18 ± 0.11 m/year in 2003–2020 and 0.10 ± 0.13 m/year in 2003–2008. As a summary of our results, the glacier thinning rate across the entire HMA is gradually accelerating, except for the West Kunlun, Karakoram, Pamir and Hindu Kush.

**Figure 5.** Glacier elevation change rate in the HMA in 2003–2008 (**a**) and in 2003–2020 (**b**) (Statistics in 1◦ × 1◦ grids).

### 4.2.2. Glacier Elevation Change Rate in Basin Scale

The melting of the HMA glaciers has an important impact on the changes in river flow and water resources in the HMA and its downstream regions. Therefore, obtaining information on glaciers changes in different basins of the HMA is of grea<sup>t</sup> significance for understanding the changes of water resources in the HMA and its surrounding areas. We estimated the glacier elevation change rate in each basin of the HMA during 2003–2008 and 2003–2020 (Table 1) (method described in Section 3.3).

**Table 1.** The rate of change in glacier elevation in the basins of the HMA in 2003–2008 and 2003–2020. The errors are given at the 1σ level calculated by Equation (6).


Due to the differences in temperature, precipitation, evapotranspiration and other factors in different basins, rates of changes in glacier elevations varied greatly in time and space (Table 1). The results in Table 1 showed that from 2003 to 2020, the glacier elevations in almost all basins of the HMA showed a decreasing trend, except for Tarim. From 2003 to 2020, the Mekong River basin experienced the fastest thinning of glaciers, followed by the Salween and Brahmaputra basins. However, we found that the rate of thinning of glaciers in the Indus, Syr Darya and Amu Darya river basins slowed down. We will analyze the reasons for this phenomenon in Section 5.2.1.

### *4.3. Intra-Annual Change of Glacier Elevation*

The period of thickening or thinning of glaciers varied in different regions of the HMA due to climate and topography. In this section, the HMA was divided into eight sub-regions to explore the monthly/seasonal characteristics of the glacier elevation changes in the HMA caused by differences in glacier accumulation and melting over time. The eight sub-regions are Spiti Lahaul, Bhutan and Nepal, Nyainqentanglha mountain, West Kunlun, Pamir and Hindu Kush, Tienshan mountain, Karakoram and Inner TP (Tibetan Plateau). The ICESat-2 monthly data in 2019–2020 were used for monthly/seasonal analysis.

In this study, we found that the period of glacier thickening from the marginal regions of the HMA to the interior HMA was gradually delayed from autumn to summer. The results in Figure 6 revealed that in Pamir and Hindu Kush and Karakoram, glaciers showed similar seasonal changes in thickening in autumn (SON: September–October–November) or winter (DJF: December–January– February). In Pamir and Hindu Kush, although the glaciers were at their highest elevations in spring, significant glacier thickening occurred mainly in October–March, followed by a significant thinning period. The glaciers in Karakoram had almost the same seasonal variation as in Pamir and Hindu Kush, except for a sudden drop in elevation in July 2019, which might be attributed to relatively low precipitation and warmer temperatures in July 2019 (see the discussion in Section 5.2.2). In West Kunlun and Bhutan and Nepal, the glaciers exhibited similar seasonal thickening variation in spring (MAM: March–April–May) or summer (JJA: June–July–August). The glaciers in West Kunlun Mountains showed two accumulation periods with obvious thickening, i.e., in March–June and in July–September. In the Bhutan and Nepal regions, the month with the least glacier elevation decline in 2019–2020 occurred in July. In the inner TP, the glaciers did not show an obvious consistency of accumulation (or melting) in the two years, although the months with the highest glacier elevations

appeared in the summer of the two years. In the Tienshan Mountains, the glacier elevations fluctuated greatly, the glacier thickening time was mainly concentrated from December to April, and there was a weak thickening trend from September to December. In Spiti Lahual, the southwest of the HMA, the glacier thickening period was mainly concentrated in winter and spring, with thinning in summer. The glacier elevations in the Nyainqentanglha Mountains reached their highest points in spring.

**Figure 6.** The monthly change of glacier elevation in different regions of the HMA from January of 2019 to December of 2020. The red line (left *Y*-axis) represents the glacier elevation difference between the ICESat-2 data in 2019–2020 and the SRTM DEM data in 2000, the blue column (right *Y*-axis) represents the number of ICESat-2 data points in each month. The error bars are the values of standard deviation of spatial glacier elevation difference in the corresponding months calculated by Equation (5) at 1σ level.
