The meteorological forcing data included the near-surface air temperature, total precipitation, downward shortwave and longwave radiation, wind speed, surface pressure, and specific humidity. For the historical period (1995–2014), except for the precipitation data, the data for the meteorological variables were obtained from the China Meteorological Forcing Dataset (CMFD), which has a high spatiotemporal resolution (3 h and 0.1∘) from 1979 to 2018 and has been widely used in hydrometeorological research because of its good applicability (He et al., 2020). To better evaluate the applicability of four reanalysis precipitation products – the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth-generation reanalysis data product (ERA5), the Global Land Data Assimilation System (GLDAS) product, version 2 of the Modern-Era Retrospective Analysis for Research and Applications (MERRA-2) product, and the Multi-Source Weighted-Ensemble Precipitation (MSWEP) product (Beck et al., 2017) – in the USR, we mainly used several statistical indices to evaluate the products based on the meteorological observation data in this work, including correlation coefficients (CCs), mean bias (MB), and the root-mean-square error (RMSE). Moreover, the probability of detection (POD), the false alarm ratio (FAR), the missing alarm rate (MAR), and the critical success index (CSI) were calculated to check the capture capability of rainfall events from reanalysis products (Ebert et al., 2007; Tian et al., 2009). It can be seen from Figs. S1 and S2 that, except for GLDAS, the statistical indicators of other precipitation products are relatively consistent; however if the international exchange station is excluded (Naqu and Dingqing), ERA5 and MSWEP have good performance (CC is about 0.5). In addition, ERA5 has a higher POD (average of about 0.97) and a lower FAR (average of about 0.44) as a whole, which is also shown in the CSI (average of about 0.56), implying that ERA5 has better characterization of rainfall events. Therefore, we selected ERA5 based on its 1 h and 0.25∘ resolutions from 1979 to the present, its better spatiotemporal distribution, and the fact that it has been widely used in hydrological simulations of high mountainous regions (Hersbach et al., 2020; Yang et al., 2021). The projected climate forcing variables used in the hydrological model were obtained from the Inter-Sectoral Impact Model Intercomparison Project 3b (ISIMIP3b) (Lange and Büchner, 2021), of which four GCMs (GFDL-ESM4, IPSL-CM6A-LR, MPI-ESM1-2-HR, and MRI-ESM2-0) that have a consistent experimental protocol (historical, SSP126, and SSP585) and atmospheric climate variables (spatial and temporal resolutions of 0.5∘ and 1 d, respectively) were selected as the model input. The ISIMIP3BASD (v2.4.1) method was used for the bias adjustment and statistical downscaling of these variables to ensure their consistency with the long-term statistics of the observation reference dataset, i.e., W5E5 v2.0 (WFDE5 v0.1 over land merged with ERA5 over the ocean) (Lange, 2019, 2021a, b; Cucchi et al., 2020). To maintain the relative and absolute trends in these variables during the historical and future periods at the basin scale, we further corrected these variables on the monthly scale using the delta method (a simple linear bias correction method), which has been widely used and can effectively avoid a large model bias (Cuo et al., 2011; Su et al., 2016); the reader is referred to the bias correction methods in the Supplement for details. The historical and future meteorological forcing data were interpolated to the model's resolution (5 km) via bilinear interpolation. The time downscaling method used for the daily forcing data was consistent with that used by Song et al. (2020).

A digital elevation model (DEM) was used to extract the basin's boundary and calculate the topographic parameters. The DEM was the National Aeronautics and Space Administration (NASA) Shuttle Radar Topography Mission (SRTM) DEM with a spatial resolution of 90 m. The soil type and land use maps with a spatial resolution of 1 km used to calculate the soil hydraulic parameters and land use types were obtained from the Food and Agriculture Organization (FAO, 2003) and the U.S. Geological Survey (USGS) (Fig. 1a, b), respectively. The fraction of photosynthetically active radiation (FPAR) and the leaf area index (LAI) used to calculate the vegetation dynamics were downloaded from the Global Land Surface Satellite (GLASS) datasets, both with respective temporal and spatial resolutions of 8 d and 0.05∘ (Xiao et al., 2014). The second glacier inventory of China was provided by the National Tibetan Plateau Data Center (Guo et al., 2015). These data were resampled to the model's resolution (5 km).

The daily observed discharge data at the outlet (JYQ) of the USR basin were obtained from the National Hydrology Almanac of China and were used to calibrate and validate the hydraulic parameters of the hydrological model during 1981–1987. There are six meteorological stations within the basin. Among them, Naqu and Dingqing stations are the international exchange stations (Fig. 1a). The meteorological observation data used to evaluate the precipitation products were obtained from the China Meteorological Administration (CMA). The land surface temperature (LST) data were obtained from the MODIS and MOD11A2 products, with respective spatial and temporal resolutions of 1 km and 8 d from 2001 to 2018 (Wan et al., 2014). The SC data were obtained from an improved Terra–Aqua MODIS snow cover and Randolph Glacier Inventory 6.0 combined product (MOYDGL06∗) for high-mountain Asia with respective temporal and spatial resolutions of 8 d and 500 m from 2002 to 2018, which can be accessed from PANGAEA (Sher and Amrit, 2019).

First, the model parameters were calibrated using the daily observed discharge data measured at JYQ station from 1981 to 1983, which mainly included the following soil hydraulic parameters: the saturated soil moisture content (θs=0.48), the residual soil moisture content (θr=0.07), the hydraulic conductivity anisotropy ratio (anik = 2.17), the van Genuchten parameter (α=0.014, n=2.385), the saturated hydraulic conductivity for soil surface (Ksat1=141.45 mm h-1), the saturated hydraulic conductivity for unsaturated areas (Ksat2=21.22 mm h-1), and the hydraulic conductivity for an unconfined aquifer (Kg=0.7 mm h-1). Then, the daily observed discharge data for 1984–1987 (observations for 1986 were missing) were used to validate the calibrated hydrological model. The results are shown in Fig. 2. The time series of the simulated discharge matched the observations during 1981–1987 well and can capture the daily and monthly changes in the observed discharge, especially in the dry season. The values of the evaluation criteria during the calibration and validation period were determined to be as follows: 0.7 (NSE), 0.75 (R2), 0.84 (KGE), and 3.18 % (RB) for calibration, and 0.79 (NSE), 0.81 (R2), 0.88 (KGE), and 3.29 % (RB) for validation (Fig. 2a). The monthly simulated and observed discharge were in better agreement during the peak flow (Fig. 2b), accurately reproducing the inter-annual and intra-annual variations in the discharge at JYQ station, although there were overestimates and underestimates during the wet seasons in some years.

Due to the lack of observed discharge data from 1988 to the present, remote sensing data (MODIS LST and snow cover) were used to further validate the performance of the hydrological model at the basin scale. Figure 3 shows the comparison of the results for the basin-averaged time series between the simulated and MODIS LST values at daytime (10:30 LT, local time) and nighttime (22:30 LT) during 2001–2018. The results show that the simulated LST is in good agreement with the MODIS LST at daytime (R2=0.69) and nighttime (R2=0.91). The simulated nighttime LST has a higher R2 value and lower MB value, but the RMSE is better than that of the daytime LST, which indicates that the LST is mainly affected by the incoming solar radiation and land surface absorption during the daytime and is affected very little at night.

From the perspective of the spatial distribution patterns (Fig. 4), the simulated multiyear seasonal average LST during the daytime and nighttime were similar to those of the MODIS LST from 2001 to 2018. Similarly, the simulated nighttime LST was better than the simulated daytime LST. The basin-average value of simulated seasonal LST during the nighttime was closer to the MODIS LST (December–January–February, DJF: MB =-2.25 K; June–July–August, JJA: MB = -1.07 K; March–April–May, MAM: MB =-1.5 K; September–October–November, SON: MB =-0.66 K) than that at daytime, and the simulated seasonal LST during the daytime was underestimated in winter (MB =-5.38 K), spring (MB =-7.24 K), and autumn (MB =-2.76 K), and it was slightly overestimated in summer (MB = 0.86 K). The reason for this difference between the daytime and nighttime LST simulations may be that the complex interactions of the surface energy balance during daytime are also one of the reasons that the simulated LST at the nighttime is closer to MODIS LST than that at daytime. The LST is controlled by solar radiation absorbed by the surface canopy and the ground during daytime, and these factors lead to greater uncertainty in the simulated daytime LST, whereas the solar radiation can be ignored at nighttime, and the LST is mainly affected by the downward longwave radiation (Xue et al., 2013; Zhou et al., 2015; Zhong et al., 2021). In addition, the complex terrain and strong convective activities (clouds) in the USR basin may also affect the accuracy of satellite observations (clouds and terrain may lead to increased missing observations) and the reanalysis products (complex terrain may lead to lapse rate errors in reanalysis products and affect temperature calculations).

The fraction of simulated snow-covered area (FSCA) was also verified using the MOYDGL06∗ FSCA data at the basin scale from 2003 to 2019 at 8 d and monthly temporal scales (Fig. 5). As shown in Fig. 5a, there was a good correlation between the simulated 8 d FSCA and the MOYDGL06∗ 8 d FSCA (CC = 0.73). It can be seen from Fig. 5b that the simulated FSCA was overestimated, except for in October and November, especially in summer (by almost 100 %). Of course, this could reflect the intra-annual changes in the MOYDGL06∗ FSCA values at the basin scale. Figure 5c illustrates the good agreement between the simulated and MOYDGL06∗ FSCA at a monthly temporal scale during 2003–2018 (R2=0.56), which generally reflects the inter-annual changes in the MOYDGL06∗ FSCA in the USR basin.

As can be seen from Figs. 6 and S3, the simulated SC reproduced the spatial distribution of the seasonal evolution of the SC in the USR basin, and it also captured the snow ablation (April–August) and accumulation (September–March) processes well. Moreover, the simulated SC also reflected the rapid melting of snow after 2 June and the rapid accumulation of snow after 8 October, but there was a difference on some days – that is, the SC was overestimated in the high mountains in summer and underestimated in the low valleys in winter. If the uncertain grids in MOYDGL06∗ were considered (red grids), the difference would be smaller. The differences in some months may partly be caused by the bias in the forcing data, especially the biases in the temperature and precipitation. In addition, the resolution of MOYDGL06∗ (500 m) is not consistent with that of the hydrological model (5 km), which may also lead to differences in the calculation of the average SC for the entire basin.

Overall, the verification results show that the simulation results of the hydrological model are reasonable and can be used to simulate the historical and future snow and hydrological processes in the USR basin.

Due to the systematic bias and coarse spatial resolution of the GCM, there was great uncertainty in using it directly to drive the hydrological model at the basin scale (Zhang et al., 2016; Liu et al., 2018). Thus, it was necessary to evaluate these data before conducting the hydrometeorological analysis. Four GCM datasets with bias adjustment conducted using the delta method were used as the meteorological forcing data to drive the WEB-DHM-sf hydrological model; the results are shown in Fig. 7. Although the simulated values of the single GCM in the wet season were overestimated (GFDL-ESM4 and IPSL-CM6A-LR) or underestimated (MPI-ESM1-2-HR and MRI-ESM2-0), the daily simulated discharge of each GCM was relatively consistent with the inter-annual variations in the observations during 1981–1987 (Fig. 7a). Moreover, the daily hydrograph curve of the multi-GCM ensemble mean (MEM) reproduced the discharge at JYQ well, with reasonable NSE (0.61), KGE (0.77), R2 (0.64), and RB (-9.62 %) values. The monthly hydrograph curve of the MEM and observed data exhibit a good overall agreement (NSE = 0.78, KGE = 0.77, R2=0.79, and RB = -9.7 %) during 1981–1987 (Fig. 7b), and the intra-annual changes in the discharge at JYQ station were captured. In summary, the MEM was better than the single GCM; thus, the MEM was used in the analysis of the snow-related hydrological processes in the USR basin.

As shown in Table S1, the temperature exhibits significant growth trends under SSP126 (0.2 ∘C per decade) and SSP585 (0.7 ∘C per decade) during 1995–2100. It also shows a consistently increasing trend during the different periods, except in the long term for SSP126 (during which time a slightly significant decrease occurs). In addition, precipitation also exhibits growth trends throughout the entire study period under SPP126 (5 mm per decade) and SSP585 (27.8 mm per decade) as well as an increasing trend in the near term, midterm, and long term, except during the reference period when it exhibited an obvious decreasing trend (-5.8 mm per decade for SSP126 and -9 mm per decade for SSP585). The climate in the USR generally undergoes a warming and wetting trend in the future under these scenarios. For the different periods, both the warming and wetting trend of the basin gradually slow down under SSP126, whereas they become much stronger under SSP585.

Figure 8 and Table S2 show the relative changes in the annual precipitation and mean annual temperature in the USR during 1995–2100, with 1995–2014 as the baseline, under SSP126 and SSP585. Compared with the reference period, the warming amplitude increases in the near, mid- and long-term periods, but the rate of increase slows down and does not exceed 2 ∘C at the end of this century under SSP126. However, warming exceeds 2 ∘C in the future in the midterm and reaches about 6 ∘C by the end of this century under SSP585 (Fig. 8a). The annual precipitation increases by 4.64 %–5.57 % under SSP126 and by 1.34 %–26.99 % under SSP585 during the different periods (Fig. 8b).

The seasonal cycles of the projected temperature and precipitation in the USR exhibit different changes under different scenarios (Fig. 9). Intense warming occurs in all of the seasons under SSP126 and SSP585. Compared with the reference period, the changes in the seasonal warming rates for each period are relatively small under SSP126, but these changes are greater under SSP585, with a distinct gradient. The warming rates during each season do not exceed 2 ∘C in the near term, and the smallest change occurs in spring under all of the scenarios; however, it exceeds 4 ∘C in the long term under SSP585 (Fig. 9a, b). As can be seen from Fig. 9c and d, the precipitation in the other periods (compared to the reference period) is projected to increase from April to September and to decrease from October to March under all of the SSPs, and its growth amplitude gradually increases from the near term to the long term. The above results indicate that the USR is a typical monsoon region that will become warmer and wetter in the monsoon season and warmer and dryer in the non-monsoon season in the future.

There is a significant decreasing trend in the annual snowfall and the snow / precipitation ratio (Snow / Pre) in the USR under all of the SSPs during 1995–2100 (Fig. 10a, b). The rate of decrease in snowfall under SSP585 (-13.6 mm per decade) is much faster than that under SSP126 (-4.2 mm per decade). In the near term, snowfall is projected to decrease by more than 13 % under SSP126 and by 16 % under SSP585. By the end of the century, snowfall is reduced to about 118 mm under SSP585, which is less than half of the snowfall in the reference period, while snowfall decreases by approximately 16 % under SSP126. Similarly, Snow / Pre exhibits changes similar to those of the snowfall, and Snow / Pre is projected to decrease to approximately 10 % under SSP585 and to 20 % under SSP126 by the end of the century.

Figure 10c and d show the changes in the monthly snowfall and rainfall at the basin scale. The rainfall mainly occurs from May to October (monsoon season), accounting for more than 70 % of the total annual precipitation, and the changes in rainfall and the pattern of rainfall in the future are similar to those of the total precipitation. However, snowfall exhibits a distinct bimodal pattern, with the first peak appearing in May (accounting for about 21 % of the annual snowfall) and the second occurring in October (accounting for about 14 % of the annual snowfall). Snowfall is projected to decrease by less than 10 % from November to April compared with the reference period, and there will likely be no snowfall in July and August after the midterm. Moreover, the projected Snow / Pre exhibits a consistent decrease in all of the months compared with the reference period (Fig. 10e, f). Further analysis of the seasonal variations in snowfall revealed that snowfall would be the heaviest in spring, and it is projected to decrease by about 30 % (1 %) under SSP585 (SSP126) by the end of the century. The largest reduction in snowfall occurs in the summer and autumn seasons under all of the SSPs, and it is likely to decrease by approximately 85 % (44 %) and 60 % (21 %) in these respective seasons under SSP585 (SSP126) by the end of the century (Table 1). The above results indicate that precipitation in the USR is less likely to occur in the form of snow in the future under climate warming.

The trends and relative changes in the annual FSCA at the basin scale under the different SSPs during 1995–2100 are shown in Fig. S4 and Table S3. The annual FSCA exhibits a significantly decreasing trend at the basin scale during 1995–2100, and this trend is more obvious under SSP585 (-0.42 % yr-1). Compared with the reference period, the annual FSCA is projected to increase by 4.9 % in the near term and to decrease by 8.59 % and 2.77 % in the midterm and long term, respectively, under SSP126. In contrast, the annual FSCA is projected to drastically decrease under SSP585, and it will be less than 40 % by the end of the century according to this scenario compared with the reference period. Moreover, it should be noted that the SC will continue to decrease from the near term to the midterm under SSP126, but it will begin to increase in the long term, which is significantly different from the pattern under SSP585. This indicates that future SC in the USR will decrease further under climate warming, and the severe warming projected under SSP585 would cause the SC to melt rapidly.

The results obtained from the analysis of the monthly-scale decadal FSCA from 1995 to the 2090s are shown in Fig. 11a and b. Figure 11 shows that the cycle of accumulation and ablation of the FSCA increases gradually from September to March and decreases rapidly from April to August. Under SSP585, the FSCA is projected to decrease in almost all months. However, the FSCA increases in June–November and decrease in December–April under SSP126. This pattern also occurs for the monthly-scale FSCA during the different periods (Fig. 11c, d). Similarly, the changes in the FSCA are more pronounced under SSP585 than under SSP126. For example, compared with the reference period, the FSCA becomes snow-free from July to September by the end of the century under SSP585.

Figure 11e and f and Table S4 present the change trends in the seasonal FSCA, i.e., in spring (MAM), summer (JJA), autumn (SON), and winter (DJF). The results show that there is a decrease in all of the seasons during 1995–2100, but the decrease is more significant in winter and spring. Compared with the reference period, the FSCA is projected to decrease most (by about 61 % on average) in winter and spring under SSP585. Even under SSP126, the FSCA will decrease by about 15 % on average in winter and spring. However, there are differences between SSP126 and SSP585 in summer and autumn. From the near term to the long term, the FSCA is projected to increase in summer and autumn under SSP126, but this would not offset the large losses in spring and winter. This shows that the reduction in the SC in winter and spring would cause a reduction in the annual SC, which may further lead to a decrease in the snow storage in the basin, thereby affecting the amount of snowmelt during the ablation period.

From the perspective of different elevations, the SC is mainly distributed at middle–high elevations (≥4500 m), accounting for about 44 % of the basin area during the reference period, whereas less than 7 % of the SC is located at low elevations (<4500 m) (Table S3, Fig. 12). During 1995–2100, the annual FSCA at all elevations (3500–6000 m) significantly decreases under all of the SSPs, except in the area above 5500 m a.s.l. under SSP126, where no change occurs (Fig. S4). Further analysis revealed that the rate of decrease in the FSCA is faster at middle–high elevations (4500–5500 m) than at low elevations. However, the magnitude of the decrease in the FSCA is much greater at low elevations than at middle–high elevations in all of the periods compared with the reference period. For example, the FSCA in the low-elevation areas is projected to decrease by about 78 % under SSP585 and by 14 % under SSP126 by the end of the century. This illustrates that the amount of SC lost at middle–high elevations will be much greater than that lost at low elevations throughout the 21st century, but the response of the SC to climate warming at low elevations will more rapid and pronounced.

Further statistical analysis of the monthly-scale FSCA at all elevations during all of the periods revealed that there is a consistent decrease in the FSCA at all elevations compared with the reference period (1995–2014), except in areas with elevations of 4500–5500 m a.s.l. in the near term under SSP126 (Table S3, Fig. 12). Under all of the SSPs, the FSCA at middle–high elevations (≥4500 m) is projected to decrease in almost all months from the midterm to the long term. At low elevations (<4500 m), the FSCA decreases by approximately 25 % from December to April under SSP126 by the end of the century, whereas there is a slight increase in the FSCA during June–November (with no snow cover in July and September). However, the FSCA is projected to decrease by approximately 80 % in almost all months under SSP585 by the end of the century. Moreover, the decrease in the FSCA is more pronounced in winter and spring at low elevations than at high elevations under all of the SSPs, and it further strengthens towards the end of the century. Remarkably, we found that the snowmelt starts earlier at high elevations than at low elevations under SSP585 by the end of the century. This was confirmed at elevations of 4500–5500 m a.s.l., where the starting time of the decrease in the FSCA shifts from May to March, and it continues until the end of August Correspondingly, the FSCA in this elevation range also decreases by more than 60 %. In addition, there is almost no snow at elevations below 5000 m from July to September, and the snow is very sparse and broken at high elevations. For all of the SSPs, the projected climate would not be conducive to the occurrence and development of SC.

Figure 13 and Table 2 show the monthly- and seasonal-scale changes in the SWE in the different periods under SSP126 and SSP585. Compared with the reference period, the SWE is projected to decrease by about 39 % in the near term and midterm, and it slightly rebounds in the long term (about 31 %) under SSP126. However, there is a clear decrease in the SWE from the near term to the long term under SSP585, and the SWE decreases by more than 85 % by the end of the century. Similarly, the characteristics of the abovementioned changes are also reflected in the seasonal changes in the SWE (Fig. 13c, d). The SWE in the USR is the highest in spring and the lowest in autumn. Further analysis of the data revealed that the SWE decreases in all of the seasons and all of the periods under all of the SSPs, and the largest decrease occurs in summer and autumn, with a decrease of more than 91 % (30 %) under SSP585 (SSP126) by the end of the century. Furthermore, the peak in the SWE shifts from June to May under SSP585 by the middle of the century, and the SWE is almost zero from July to September. However, this does not occur under SSP126. Moreover, it can be seen that the peak in the SWE after the near term shifts from June to May under SSP585, whereas it remains in June under SSP126, and the peak value of the SWE weakens after the reference period.

The trends in the annual total runoff, total snowmelt, and snowmelt runoff during 1995–2100 are shown in Fig. S5. The total runoff increases under all of the SSPs, and it is faster under SSP585 (4.4 mm yr-1) than under SSP126 (0.31 mm yr-1). However, the total snowmelt, including the snowmelt runoff and snowmelt that seeps into the soil, significantly decreases under SSP585 (-1.04 mm yr-1) and SSP126 (-0.34 mm yr-1). The snowmelt runoff changes very slightly and insignificantly under SSP126, whereas it significantly decreases (0.56 mm yr-1) under SSP585. During the reference period, the snowmelt runoff (0.1 mm yr-1) and its contribution to the total runoff significantly increased (0.3 % yr-1), but the total runoff exhibited a nonsignificant downward trend (-0.13 mm yr-1). The trends in the total runoff, snowmelt runoff, and the contribution of snowmelt runoff in the midterm and long term are the inverse of those during the reference period under all of the SSPs, except in the long term under SSP126 (Fig. 15). This indicates that the snowmelt and snowmelt runoff likely peak in the near term (2021–2041).

Table S5 presents the changes in the annual total runoff, total snowmelt, and snowmelt runoff from the near term to the long term under SSP126 and SSP585. In the near term, the total runoff slightly increases under SSP126 (1.07 %) and SSP585 (1.40 %). In the midterm, the total runoff increases by twice as much under SSP585 (22.86 %) compared with SSP126 (10.4 %). By the end of the century, the total runoff is projected to increase by 112.29 % under SSP585 compared with the reference period (341.0 mm), whereas there is only a small increase under SSP126 (4.7 %). The total snowmelt consistently decreases from the near term to the long term under all of the SSPs. The reduction in the snowmelt remains below 20 % under SSP126, whereas it decreases by 22.5 % and 43.01 % in the midterm and the long term under SSP585, respectively. The snowmelt runoff increases in the near term and long term and decreases in the midterm (by -20.3 %) under SSP126, while the snowmelt runoff decreases significantly from the near term to the long term under SSP585, and the projected decrease is about 75 % in the long term.

The intra-annual changes in the total runoff are very similar to those of the precipitation, and the hydrograph remains largely consistent in all periods under SSP126 and SSP585, with 60 % of the annual total runoff occurring in summer and the peak flow occurring in July (Fig. 14a–h). There is a very obvious change in the total snowmelt – that is, the peak snowmelt shifts from July to June after the reference period (Fig. 14i–p). The snowmelt runoff in summer is the largest compared with the other seasons, accounting for about 65 %–85 % of the annual snowmelt runoff, and it sharply increases in May, with a peak in June (Fig. 14i–p). From Table 3, compared with the reference period, it can be seen that there is a consistent decrease in the spring and winter total runoff in the future periods under all of the SSPs, except in the long term for SSP585, whereas total runoff increases in summer and autumn in all of the periods. The snowmelt consistently increases in winter and spring in the future periods under all of the SSPs, whereas it markedly decreases in summer and autumn. Similarly, the snowmelt runoff in spring is projected to increase in all of the periods under all of the SSPs, whereas it decreases in summer and autumn, except in the near term and long term under SSP126.

Table  S6 and Fig. 15 show the contributions of the multiyear average and seasonal snowmelt runoff to the annual total runoff (SR / TR) in all of the periods under SSP126 and SSP585. The SR / TR was about 17.6 % in the reference period, and this value reaches about 19 % by the end of the century under SSP126. However, the SR / TR constantly decreases in all periods under SSP585, reaching about 2 % by the end of this century. Compared with the reference period, the SR / TR in spring was projected to increase in all of the periods, except in the long term under SSP585. Although the SR in summer contributes the most to the TR at the annual scale, the spring SR contributed the most to the spring TR at the seasonal scale, which is more obvious after the midterm under all of the SSPs due to climate warming. (Table S7). At the monthly scale (Fig. 14a–h), the SR / TR was the largest in June during the reference period, while it gradually shifted to May after the near term under SSP585 and SSP126. In short, the abovementioned results indicate that change in the SR under all of the SSPs is not the primary reason for the increase in the annual total runoff, but its contribution cannot be ignored.