## 3 Results
### Effects of the Exposed Debris on Glacier Mass Loss  
During 2020-2021, the exposed englacial debris was mainly distributed in five zones (A-E in Figure 4a). The main part of zone E is melt-out debris with a thickness of several centimeters, and this glacial till of sand and gravel debris does not fully cover the ice (Figure S1e). By comparison, the debris is much thicker (more than tens of centimeters) in the other four zones (A-C is in river channels; D is melt-out debris), where the unsorted debris of silt-sized glacial flour to large boulders completely covers the glacier (Figure S1a-d). Supraglacial melting is the main mechanism of ice loss on the Qiyi Glacier, whereas the surface elevation change (SEC; see the Section 2) driven by bottom melting is relatively minor and can be neglected on short timescales. In addition, the difference in the glacier movement-induced SECs within a narrow elevation band is also negligible compared to that of supraglacial melting. Therefore, a comparison of the difference in SECs between the debris-free and debris-covered ice over the same elevation range can be used to analyze the effects of debris cover on glacier mass loss (Figure 4). The relative ice mass loss (RIML) of a given single pixel can be expressed as:  
\[\text{RIML}=\text{SEC}\times A\times 900 \tag{1}\]  
where the SEC is surface elevation change (Unit: m), \(A\) refers to the area of the glacier pixel (m\({}^{2}\)), and 900 represents the density of glacier ice (900 kg/m\({}^{3}\)). By using Equation (1), the ice mass loss of all of the bare ice pixels and debris-covered pixels can be obtained (including A, A_c, B, B_c, C, C_c, D, D_c, E, and E_c). Moreover, a field investigation found evidence of a retreat in channel shoulders where debris emerges along rivers, which occurs due to the higher surface temperature of the debris melting more ice of the surrounding slope. This extra part of mass loss was also taken into account for this type of debris (Figure 4c). Therefore, for the total ice mass loss of three of the debris covers along the river channels, the ice mass losses within the entire channel (zones Ar-Cr encircled by thick dashed lines) were compared with the bare ice at the same elevation band (i.e., Ar_c, Br_c, Cr_c) (Figure 4a). The debris thickness determines whether debris cover mitigates or enhances the glacier melting. For the five debris zones, the ice mass loss of zone E is 35.9% more than that of bare ice at the same elevation band (381 m\({}^{3}\) water equivalent) due to its thin debris cover, whereas the debris in the other four zones (A-D) reduces glacier melting. Compared with \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Distance to Glacier**} & \multicolumn{5}{c}{**Debris Cover Area (m\({}^{2}\))**} \\ \cline{2-6}  & **1972** & **2005** & **2012** & **2020** & **2021** \\ \hline
50 & 1815.26 & 1355.98 & 458.46 & 828.67 & 571.57 \\ \hline
100 & 1000.06 & 2932.51 & 36.88 & 1608.89 & 1796.35 \\ \hline
150 & 0.00 & 586.28 & 424.14 & 1000.19 & 1225.05 \\ \hline
200 & 0.00 & 0.00 & 223.37 & 1569.82 & 1890.57 \\ \hline
250 & 0.00 & 0.00 & 161.62 & 493.53 & 549.43 \\ \hline
300 & 0.00 & 0.00 & 118.42 & 693.17 & 762.75 \\ \hline
350 & 0.00 & 0.00 & 284.43 & 243.01 & 272.46 \\ \hline
400 & 0.00 & 0.00 & 0.00 & 8.18 & 15.64 \\ \hline
450 & 0.00 & 72.24 & 0.00 & 15.06 & 19.85 \\ \hline
500 & 0.00 & 54.46 & 0.00 & 0.00 & 0.00 \\ \hline Total debris cover area & 2815.32 & 5001.47 & 1707.33 & 6460.52 & 7103.67 \\ \hline Annual change rate & - & 66.25 & -470.59 & 594.15 & 643.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The areas of debris cover of different years at various distance to the glacier terminal and their total areas/annual changing rates. bare ice, the net reduction of ice mass loss for all five zones is 4631 m\({}^{3}\) water equivalent (\(\sim\)49.5%).