## 4 Results  
### Estimation of Glacier Size  
Following the method outlined in Section 3.1, recovering the valley indices of four typical glacial valleys in the Tianchi area was conducted using the GlaRe tool [[https://github.com/cageo/pellitero-2015](https://github.com/cageo/pellitero-2015)]([https://github.com/cageo/pellitero-2015](https://github.com/cageo/pellitero-2015)) (accessed on 19 December 2023). The F-values of the XipotingChechang Valley ranged from 0.34 to 0.53 (Figure 3a), with a mean value of 0.43. The F-values of the Songjianghe Valley ranged from 0.36 to 0.52 (Figure 3b), with a mean value of 0.40. The F-values of the Heifengkou Valley were in the range of 0.35-0.64 (Figure 3c), with a mean value of 0.49. And the F-values of the Erdaobaiahe Valley were in the range of 0.38-0.57 (Figure 3d), with a mean value of 0.47. In addition, the shear stress in the XipotingChechang Valley ranged from 60 to 95 kPa (Figure 4a), with a mean value of 77.50 kPa. In the Songjianghe Valley, the shear stress ranged from 50 to 100 kPa (Figure 4b), with a mean value of 69.15 kPa. The shear stress in the Heifengkou Valley ranged from 50 to 140 kPa (Figure 4c), with a mean value of 114.09 kPa. And the shear stress in the Erdaobaiahe Valley ranged between 50 and 80 kPa (Figure 4d), with a mean value of 62.17 kPa. For valley glaciers, shear stress is usually in the range of 50-150 kPa [61]. The mean shear stress values at the bottom of each valley's paleogalcier calculated in this study are therefore within this range. We reconstructed the paleogalcier surfaces and thicknesses of typical glacial valleys on the outer slopes of the volcanic cone of the Tianchi caldera (i.e., the XipotingChechang, Songjianghe, Heifengkou and Erdaobaiahe valleys) (Figure 5). The altitude of the paleogalcier's surface in the XipotingChechang Valley ranged from 2096 to 2562 m asl (Figure 4a), with a mean value of 2401 m asl. The maximum glacier thickness was calculated to have been 113 m (Figure 5b), with a mean value of 85 m. The surface area of the paleogalcier was reconstructed as 0.47 km\({}^{2}\), and its volume was 0.04 km\({}^{3}\). The altitude of the paleogalcier's surface in the Songjianghe Valley ranged from 1850 to 2520 m asl (Figure 5c), with a mean value of 2195 m asl. The maximum glacier thickness was reconstructed as 132 m (Figure 5d), with a mean value of 103 m. The area of the paleogalcier's surface was reconstructed as 3.72 km\({}^{2}\), and its volume was 0.39 km\({}^{3}\). The altitude of the paleogalcier's surface in the Heifengkou Valley was in the range of 1952-2492 m asl (Figure 5e), with a mean value of 2247 m asl. The maximum glacier thickness was reconstructed as 134 m (Figure 5f), with a mean value of 84 m. The paleoglacier's surface area shows as 0.88 km2, and the volume of the paleoglacier was 0.07 km3. The altitude of the paleoglacier's surface in the Erdaobaihe Valley was in the range of 1856-2040 m asl (Figure 5g), with a mean value of 1967 m asl. The maximum thickness of this paleoglacier is shown to be 119 m (Figure 5h), with the mean value of 91 m. The paleoglacier's surface area was shown to be 1.24 km2, and its volume was 0.11 km3. The results of the glacier size reconstruction revealed that the total glacial coverage of the four glacial valleys on the outer edge of the caldera was reconstructed as 6.31 km2 during the LGM, with a total volume of 0.61 km3. Figure 4: The shear stress of four typical glacial valleys. The figure shows the specific values and changes in shear stress in different valleys from upstream to downstream. (**a**) Xipotingchechang Valley, (**b**) Songjianghe Valley, (**c**) Heifengkou Valley, (**d**) Erdaobaihe Valley. Figure 3: The F-values of four typical glacial valleys. The figure shows the specific values and changes in the F-values from upstream to downstream for different valleys. (**a**) Xipotingchechang Valley, (**b**) Songjianghe Valley, (**c**) Heifengkou Valley, (**d**) Erdaobaihe Valley.