Introduction

The Tibetan Plateau (TP), often referred to as the “Asian water tower”, constitutes a critical component of the global climate system. Its vast glaciers and snowpacks serve as the primary freshwater source for millions of people across Asia1,2. However, observational records reveal glacial retreat and negative mass balance throughout the TP over the past two decades3,4, with an estimated total glacial mass loss of approximately 340 Gigatons from 2000 to 20184. As the headwaters region for Asia’s major rivers systems, this sizeable solid water storage loss poses imminent threats to water security, particularly for downstream populations in the Indus and Ganges–Brahmaputra river basins that rely heavily on glacier meltwater5,6.

Emerging research identifies black carbon (BC) aerosol, a short-lived climate forcer from incomplete combustion of carbon-containing fuels, as a key driver accelerating the glacial retreat7,8. These light-absorbing particles predominantly originate from anthropogenic sources in South Asia9,10, with the TP’s geographical proximity making it particularly vulnerable to transboundary BC transport11,12. BC is an anthropogenic atmospheric radiative forcing component parallel to greenhouse gases, influencing the radiation balance of the surface–atmosphere system and can modify atmospheric circulation patterns13,14. Furthermore, BC deposition on snow/ice has been observed to reduce surface albedo, increasing the absorption of solar radiation and accelerating melting15,16,17.

While the direct effects of BC on the TP glacier mass balance have been studied on point-based observational analysis18,19,20, its region-scale impact on glacial mass as well as broader hydrological consequences for downstream populations remains uncertain. Meanwhile, South Asian BC has indirectly influenced the TP’s glacial retreat by reducing precipitation and subsequent deposition on the glaciers9. Whereas previous studies have primarily focused on the direct radiative effects of black carbon, our study is first to systematically integrate both direct melting (albedo reduction) and indirect precipitation reduction effects on glacier mass balance, seeking to quantify its contribution to the reduction of solid water storage over the TP.

Our analysis integrates in-situ and satellite observations, reanalysis datasets, numerical simulation experiments, as well as statistical analyses. We aim to provide a clearer understanding of the extent of BC’s influence on the TP’s cryosphere. Our findings have significant implications for climate change mitigation and adaptation strategies, especially for water management in downstream regions that depend on the meltwater from the TP glaciers.

Results

Glaciers mass loss over the TP

Geodetic measurements have revealed an accelerating rate of glacial mass loss across the TP during the 21st century4. We employed the method proposed by Brun21 to calculate glacial mass change, using digital elevation models (DEMs) that cover the period from 2001 to 2016. The Brun method, which is fully automated, calculates DEMs from available ASTER optical satellite stereo pairs (see Supplementary Text 1.1 for further details). Figure 1a illustrates that the extent of glacial mass loss generally decreases from the Himalayas towards the continental interior and is least pronounced in the northwestern aspects of the TP. Our results show good agreement with prior researches4,22 in terms of glacier mass change in magnitude, particularly in spatial pattern. A positive mass change of up to 0.3 m water equivalent per year (m w.e. a−1) is observed in the Kunlun Mountains align, while the largest glacial mass loss is found in the southern TP and in the Nyainqentanglha mountain range, with a variability of –0.53 m w.e. a−1.

Fig. 1: Spatial distribution of glacial mass change as well as its climate drivers for the Tibetan Plateau between 2001 and 2016.
figure 1

a Annual mean glacial mass balance derived from digital elevation models (Supplementary Text 1.1). Glacial mass change due to (b) air temperature and c annual precipitation, based on an empirical model (Supplementary Text 1.2) that considers the synchronous change of temperature and precipitation. Unit of change is meters water-equivalent per annum (m w.e. a−1).

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In addition to calculating glacial mass changes, we investigated mass balance sensitivities to temperature and precipitation using an empirical model (see Supplementary Text 1.2 and 1.3 for details). Sensitivities were calibrated with mass balance observations from 45 glaciers across the TP using the optimization procedure of Radić and Hock23. The results (Supplementary Fig. S1) reveal distinct sensitivity profiles for precipitation and temperature. As precipitation perturbations range from −30% to 30% and temperature perturbations vary from −6 to 6 Kelvin (K), the change in mass balance demonstrates a linear increase with increasing precipitation perturbations, while the relationship is non-linear for temperature perturbations.

Next, we used the aforementioned empirical model to compute the annual mean glacial mass transformation due to a warming environment as well as the precipitation regime for the 2001–2016 time period: Fig. 1b and c show the glacial mass change over the TP as driven, respectively, by the temporal temperature and precipitation regimes. Specifically, precipitation contributes to glacial mass growth in the southern aspects of the TP, particularly in the Himalayas (Fig. 1c). On the other hand, temperature-induced glacial mass change shows a significant decline from the Pamir Mountain range to the southern aspects of the TP in the Himalayas (Fig. 1b).

We also examined summer precipitation over a longer period, i.e., from 1981 to 2016. The results (Supplementary Fig. S2) indicate that mean annual glacial mass change due to summer precipitation was relatively diminutive compared to the annual precipitation. Notably, the Pamir Mountain range stands out as an outlier with less contribution from summer precipitation to glacial mass; this region is primarily influenced by westerly flow rather than southerly flow, which originates from the Indian subcontinent and is directed towards the southern aspects of the TP.

A time series analysis of glacial mass balance for the TP and the Himalayas, as forced by climate drivers of air temperature and precipitation, is outlined in Supplementary Fig. S3. The analysis corroborated that of Fig. 1b, indicating that air temperature dominates glacial mass loss. Although the contribution of precipitation to glacial mass accumulation remains unchanged over the time period studied (Supplementary Fig. S3a), the fluctuations observed in the Himalayas (Supplementary Fig. S3b) suggest distinct years of intermittent decline. Moreover, summer precipitation in the Himalayas (Supplementary Fig. S3b) accounted for a larger proportion of the annual precipitation compared to the same for the TP (Supplementary Fig. S3a). This disparity underscores the regional differences in precipitation patterns and their impact on glacial mass balance.

Accelerated glacial melt due to South Asian BC

BC from South Asia is transported to the TP via several pathways: (i) westerly winds, (ii) the South Asian monsoon24, (iii) mesoscale convective systems25, and (iv) mountain peak-valley winds26. Some of these pathways allow BC to cross the Himalayas and reach the inland areas of the TP27. By conducting the Weather Research and Forecasting with Chemistry (WRF-Chem) model (see the “Methods” section and Supplementary Text 3 for details) simulations from 2007 to 2016, we found that South Asian BC emissions significantly contribute to BC concentrations across the TP. The details are indicated in Fig. 2a which shows a generally decreasing contribution ratio from the marginal southern regions to farther inland. Notably, the southern aspects of the TP and the central Himalayas exhibit the highest contribution ratio, surpassing 80%; this can be attributed to the transport of South Asian BC through south–north oriented valleys, where it is uplifted over the Himalayas24. In essence then, Fig. 2b confirms a considerably higher deposition of BC in the marginal southern regions of the central Himalayas.

Fig. 2: South Asian black carbon cross-border transport and deposition onto the Tibetan Plateau derived through WRF-Chem modeling for the 2007–2016 period.
figure 2

a The contribution ratio (%) of South Asian emissions to surface black carbon concentrations over the Tibetan Plateau and b South Asian black carbon deposition rate over the Tibetan Plateau in milligrams per meter per day (mg m−2 day−1).

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BC deposited on the snow/ice induces positive radiative forcing by darkening the snow/ice, thereby reducing the surface albedo. This positive feedback accelerates glacial melt and shortens snow cover duration16. We calculated the albedo change on glaciers by using the Snow Ice and Aerosol Radiation (SNICAR) model (see the “Methods” section for details). The spatial distribution of albedo reduction ratios on the glaciers (Fig. 3a) generally aligns with the spatial variation of South Asian BC deposition derived from the WRF-Chem model (ref., Fig. 2b). As expected, higher albedo reduction ratios (up to 18%) occurred in the southern TP, while diminishing towards the western part, and decreasing further northward—particularly evident in the eastern part of the TP. The average albedo reduction on the glaciers was ~8.1%, resulting in average radiative forcing over glaciers on the order of 5.2 W m−2 with maximum radiative forcing values reaching 14 W m−2 (Fig. 3b). These radiative forcing estimates are stunning, given that mean values of 0.04 W m−2 (range being 0.02–0.09 W m−2) are typically quoted for global assessments of land snow/ice28. The findings align closely with existing literature19,20, although we observed slight underestimation in the northeastern TP, which we attribute to our study focus on South Asian BC emissions which less transporting to the northeastern TP.

Fig. 3: South Asian black carbon direct effect on the glacier melt during 2007–2016.
figure 3

a Glacial surface albedo decrease due to South Asian black carbon, given as percentage (%), (b) Surface radiative forcing due to South Asian black carbon in watts per square meter (W m−2), and c the extent of glacial melt due to South Asian black carbon over the period in meters water-equivalent per annum. WRF-Chem simulations calculated the black carbon deposition flux on snow/ice, radiation components, sensible and latent heat fluxes, and combined with the SNICAR model towards the simulation of the snow/ice albedo change, then driving the glacier energy model to calculate the glacier melting.

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Finally, we quantified the impacts of South Asian BC deposition on glacial melt through the application of the glacier energy and mass balance model, as introduced in “Methods” section. As shown in Fig. 3c, South Asian BC induced greater glacier melt in the southern TP, reaching up to 0.12 m w.e. a−1 along the Himalayas, associated with the highest BC deposition (reg., Fig. 2b). For instance, in Nyainqentanglha, South Asian BC was responsible for more than 0.07 m w.e. a−1 glacial mass loss. Overall, the southwest to northeast transect confirms a decreasing trend in glacial melt rates. The smallest glacier melt rate (below 0.03 m w-e.a−1) was observed in the Qilian Mountain range. These findings provide further evidence of the significant influence of South Asian BC deposition on glacial melt dynamics in the region.

Reduced precipitation for glacier mass gain due to South Asian BC

In addition to its significant direct impact on glacial melt, atmospheric BC also indirectly affects the precipitation patterns and moisture transport to the TP, thereby further influencing glacier mass balance16. The TP undergoes one of the most active hydrological cycles globally, with large amounts of water flowing away from the TP while simultaneously generating a substantial water vapor supply, crucial for maintaining the water balance budget29. The primary source of moisture to the TP is the South Asian summer monsoon1,30. It has been established (Supplementary Fig. S4) that there is a reduction in the incoming moisture flux at the southern boundary of the TP. In spite of this, numerous studies indicate that BC aerosols induces convective instability and water vapor convergence at the lower middle troposphere over South Asia31,32, which influences long-range moisture transport to the TP and, consequently, the precipitation process there.

Based on a series of numerical sensitivity simulation experiments using WRF-Chem spanning 10 years, we found that South Asian BC led to an overall increase in annual precipitation in the Indian subcontinent, but a decreased annual precipitation over the southern aspects of the TP (Fig. 4a). The reversal in precipitation trend since the 21st century over the southern TP as well as in South Asia were also confirmed by the analysis of Climatic Research Unit (CRU) reanalysis data (Supplementary Fig. S5). The modeled annual large-scale precipitation change highlights a significant reduction in precipitation over the southern aspects of the TP (Supplementary Fig. S6a), indicating that BC emissions in South Asia are an appreciable factor when it comes to the long-distance transmission of moisture headed for the TP. Prior studies also reported that BC emissions in South Asia can alter regional circulation patterns and reduces moisture transport toward the TP33,34. Importantly, BC predominantly influences the summer (June-September) precipitation regime (Supplementary Fig. S6b); this accounts for the bulk of annual precipitation (ref., Fig. 4a) occurring during the summer monsoon35,36,37.

Fig. 4: South Asian black carbon indirect precipitation effect on glacial mass gain during 2007–2016.
figure 4

a Annual change in precipitation due to South Asian black carbon, in millimeters (mm), derived using WRF-Chem modeling. b Glacial mass gain change due to South Asian black carbon, derived from the InVEST modeling scheme combined with WRF-Chem simulated precipitation change.

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As previously established9, BC emissions over South Asia enhance the cyclonic circulation of water vapor in eastern India and the Bay of Bengal during the summer, thus diminishing water vapor input to the TP (Supplementary Fig. S7). The strong absorption of BC leads to tropospheric warming (Supplementary Fig. S9), increasing the meridional temperature gradient, which in turn intensifies zonal wind vertical shear and cyclonic circulation. Additionally, BC influences cloud microphysics by increasing cloud condensation nuclei (CCN) concentrations (Supplementary Fig. S8b), enhancing localized precipitation over the Indian subcontinent. Consequently, these augmented atmospheric dynamic processes result in enhanced water vapor convergence and depletion (i.e., more precipitation) over the Indian subcontinent, thus less moisture transportation towards to the TP (Fig. S7). A reduction in precipitation inevitably reduces glacial mass gain and so, is inherent in the diminution of glacial mass balance that is most prominent in the southern parts of the TP.

We applied the InVEST model (see Supplementary Text 4) to estimate the impact of annual precipitation mass gain on various glaciers across the TP. The model results (Fig. 4b) reveal that BC emissions in South Asia led to overall reduction of glacier mass, with the exception of some places in the northern TP. Specifically, large reductions of annual mass gain were concentrated in the southern aspects and within the central region, with the largest reduction observed in the Himalayas (−156 mm a−1). It is not coincidental that these regions are home to a significant number of glaciers (ref., Fig. 1), with 6860 and 6072 glaciers existing respectively in the Nyenchen Tanglha Mts., and the Himalayas38. In the innermost parts of the TP, such as the Tanggula Mts., the glacial mass gain was relatively smaller, ranging from −10 to −30 mm a−1. The smallest mass loss, around 10 mm yr−1, was observed in the Qilian Mts. The decrease in glacial mass loss from the southwestern aspects of the TP towards the northeast can be attributed to a weakened water vapor inflow from South Asia, as observed in Supplementary Fig. S7. Additionally, BC aerosols create a positive temperature anomaly in the atmosphere, particularly over regions with high BC deposition, such as South Asia (Supplementary Fig. S9). Consistent with prior report14,15, the temperature causes a stronger pressure gradient and interacts with other larger-scale atmospheric circulation patterns, i.e., the Indian Monsoon and the Westerlies, which further enhances the strength of westerly winds (Supplementary Fig. S7); this results in increased precipitation which is then translated into more glacier mass gain in the Kunlun Mountain range (Fig. 4b) as described in Li et al. 39.

Discussion

To comprehensively assess the influence of South Asian BC on the TP’s glacial mass, we selected areas marked as boxes I–VI in Fig. 5a. The categorization was premised on a representative geographic distribution of the glaciers, i.e., two in the center and four at the margins (southeast, northeast, northwest, and the Himalayas), also taking into account those that have been the focus of recent debates on glacial melt rates40,41. Figure 5a illustrates that the largest glacial mass loss has occurred in the southeastern part of the TP (region I) with a variability of –0.53 m w.e. a−1, while the central Himalayas (region II) experienced the second-largest loss of –0.41 m w.e. a−1, and region V (in the central TP) had a minimum loss of –0.13 m w.e. a−1. However, the mass balance was a positive 0.12 m w.e. a−1 in the west Kunlun Mts (region III), likely due to increased precipitation there2. In addition, we calculated the change in glacial areal extent for each region by utilizing Landsat satellite images from the study by Ye et al. 42 Enumerated in Supplementary Table S2, the Himalayas (regions I and II) exhibited the most dramatic shrinkage of glacial areal extent (−1232.6 km2) over the period from 1976 to 2013, followed by the west Kunlun Mountain range (region III, (−894.2 km2)) where glacial decline took place at the smallest rate (0.13% yr−1). An increase of glacial decline is distinguishable from northwest to the southeast, increasing from 0.13% yr−1 in region III, to 0.20% yr−1 region V, and to 0.24% per yr−1 in region I. In summary, spatial heterogeneity of glacial decline is evident with a south-north disparity, where larger glacial mass loss has occurred over the southern TP compared to that over the north of the plateau.

Fig. 5: Glacial mass change due to South Asian black carbon split into six regions of interest.
figure 5

a Indicates glacial change for the six regions in terms of areal retreat ratio as percentage per year (% yr−1) along with the mass balance (meters water-equivalent per annum (m w.e. a−1)). b Shows the contributions attributed to the South Asian black carbon’s direct and indirect effects to glacier mass change as noted in the text.

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South Asian BC causes direct glacial melt (i.e., decreasing albedo) while at the same time indirectly through less precipitation; the contribution ratios of the two is particularly marked over the TP. We calculated the respective contribution ratios of South Asian BC direct and indirect effects on glacial mass change in the six aforementioned regions. In general, for the TP as a whole, South Asian BC’s direct influence through accelerating glacial melt accounts for 7.5% of glacial mass loss, while the indirect effect, through precipitation falloff, is on the order of 6.1%; respective contributions for the six regions are presented in Fig. 5b. Breaking it down, South Asian BC’s direct and indirect effects accounts for, respectively, 8.9% and 3.6% of glacier mass balance in region I. Due to being further away from BC emission sources as well as being disconnected from the South Asian monsoon, region IV experiences a lower contribution of 5.8% glacial mass loss. The leading glacier mass loss (33.7%) was observed in the Himalayas (region II), i.e., 21.9%/11.8%, respectively, indirect/direct effects. These outcomes emphasize that precipitation mass gain change plays a far greater role in the Himalayas and over the southern TP; this subsequently enhances spatial imbalances in solid water resources that have implications for future downstream water supplies, particularly in densely populated areas of South Asia. Continued trends in glacial mass loss and altered water availability have the potential to impact water resources in these regions.

The TP’s water storage servers as a crucial buffer for downstream water resources, providing a supply of glacial meltwater during the warm season or in dry years4,43. However, compared with the satellite retrieval glacial mass change (Fig. 1a), BC from South Asian has led to a 13.6% glacial mass loss over the entire TP. This loss is due to both direct effects that accelerate glacial melting and indirect effects that redirect and reduce precipitation in the region, particularly over the southern TP, leading to significant terrestrial water storage declines43.

By analyzing the annual terrestrial water storage change during 2002‒2017, as documented in Li et al. 43, we further calculated its change due to glacial mass loss ascribed to South Asian BC in all of the basins within the TP (Supplementary Table S3). The ratio is determined by the glacier changes induced by BC divided by the total change in terrestrial water storage. Results revealed that South Asian BC accounts for larger portion of the terrestrial water storage decrease in the basins within the southern TP, particularly in the endorheic basins such as the Indus and Ganges–Brahmaputra. As outlined in Fig. 6, South Asia BC led to an 18.9% decline in total water storage in the glacier-dominated Indus basin, predominantly due to enhanced glacial melt. Meanwhile, a 25.7% decline in total water storage in the Ganges-Brahmaputra basin has a sizeable indirect signature. These results highlight the significant and varied consequences of South Asian BC on water resources. The findings underscore the importance of addressing BC emissions to preserve these critical water resources.

Fig. 6: Terrestrial water storage change (TWS) due to South Asian black carbon.
figure 6

It includes direct melting and indirect mass gain effects on glaciers for key basins in the Tibetan Plateau (TP) for the 2007–2016 period—units are gigatons per year (GT/yr).

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The Ganges–Brahmaputra basin currently has sufficient natural water supply capacity (precipitation minus actual evapotranspiration) to meet the total water demand in downstream locations43. However, the situation is different for the Indus basin, as it heavily relies on upstream water storage/resources. Therefore, the Indus basin is more vulnerable to glacial mass loss. This circumstance has the potential to amplify future water crises in the Indus River basin, given the existing acceleration in population growth, large groundwater depletions, and considerable hydro-political tensions. Furthermore, glacial melting-related disasters like ice–rock avalanches, glacier collapse, glacial debris flows and glacial lake outburst floods have been occurring more frequently in the Himalayas over the past two decades44,45,46. Thus, the effects of South Asian BC on glacial decline need serious attention for the TP, not only to maintain sustainable and viable water availability, but also to reduce the risk of glacial-related hazards.

Conclusions

In this comprehensive study, we first systematically assesses the BC direct melting and indirect precipitation mass gain effects on glaciers for the 2007-2016 period, and scrutinized its potential influences on the water resources and demand. We observed that BC originating in South Asia has resulted in a greater decrease in ice mass over the southern aspects of the TP, especially in the Himalayas (33.7%). The key takeaway is the discovery of a modification of the atmospheric dynamics in the Indian subcontinent that has altered the precipitation regime in the region. This adds another component to the already established understanding that atmospheric warming and associated changes in energy fluxes are the dominant factors affecting the intensive glacier shrinkage over the Himalayas. Himalayan glaciers provide meltwater to densely populated catchments in South Asia such as the Indus and Ganges–Brahmaputra basins. Glacial mass decline due to South Asian BC can affect downstream water demand in these two endorheic basins. Therefore, there was a negative feedback between South Asian human emissions and the TP cryosphere advocates for BC mitigation to ensure future water resource stability and societal well-being. The specific actionable strategies for reducing BC emissions such as promoting cleaner energy technologies, improving fuel quality, and implementing stricter emission standard, will contribute to the potential socioeconomic benefits of BC emission reduction, including improved public health outcomes, enhanced agricultural productivity, and climate co-benefits.

Methods

WRF-Chem simulations

The Weather Research and Forecasting with Chemistry (WRF-Chem) model is a sophisticated modeling system that incorporates both complex physical and chemical processes47. The WRF-Chem model has been widely used for regional air quality modeling studies in the TP and adjacent regions, demonstrating its effectiveness27,38,48. For this study, the WRF-Chem v3.9.1 simulation experiments were performed at a horizontal resolution of 25 km, covering the TP and adjacent regions (see Supplementary Fig. S11). The model domain consisted of 222 grid cells in the west-east direction and 176 grid cells in the west-east direction, utilizing a Lambert projection, centered at 80°E, 26°N. Various physical schemes were employed, including the Lin et al. microphysical parameterization, the RRTMG radiation schemes, the Noah-MP land surface model, and the Yonsei University (YSU) planetary boundary layer scheme. In terms of chemical mechanisms, the gas-phase chemical reactions were represented by the Carbon Bond Mechanism Version Z (CBMZ)49, while the aerosol reactions were modeled using the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC)50. The options of physical and chemical schemes adopted was on basis of the performance of various model configurations (Supplementary Text 3). Additionally, an analysis of the uncertainties associated with the WRF-Chem simulations was conducted (Supplementary Text 3.4). In addition, based on our prior work51, we used the subgrid-scale orography parameterization scheme and updated the land use and leaf area index dataset in the region to improve the simulation accuracy over the TP, despite the challenges posed by its complex terrain and limited data availability.

The initial and boundary meteorological conditions for the WRF-Chem model simulations were obtained from the National Centers for Environmental Prediction Final (NCEP FNL) analysis data, which has a horizontal resolution of 1° × 1° and is available at 6-hour time intervals. The anthropogenic emissions, including CO, SO2, NOX, VOC, BC, OC, PM2.5 and PM10, were based on the Intercontinental Chemical Transport Experiment Phase B (INTEX-B). Biogenic emissions were determined using the Model of Emissions of Gases and Aerosols from Nature (MEGAN)52. Open biomass burning emissions were obtained from the fire inventory from the National Center for Atmospheric Research (NCAR) known as FINN, which utilizes satellite observations53. Additionally, the initial and lateral boundary chemical conditions were updated in real-time using the output of the Model for OZone and Related chemical Tracers (MOZART)54 at 6-hour resolution.

To investigate the mechanism of the climate influence of South Asia BC over the TP, two WRF-Chem experiments were conducted from 2006 to 2016. In the baseline simulations, the original values of BC were retained, while in the sensitivity simulations, the anthropogenic BC emissions originating from South Asia were set to zero. The simulations for the year 2006 served as a model spin-up period. The difference between the baseline and sensitivity (zero anthropogenic BC) simulation experiments was therefore utilized to indicate South Asian BC’s effects on the TP climate.

Calculation of surface albedo and radiative forcing induced by BC

Albedo reduction caused by BC was calculated by the SNICAR model, which utilizes the two-stream radiative transfer solution49. The SNICAR simulator provides hemispheric reflectance of snow for unique combinations of impurity content (BC, dust, and volcanic ash), snow grain size and incident solar flux characteristics55. Based upon observations56, the effective snow grain radius ranged from approximately 100 to 1500 µm for different snow samples, and snow density ranged from 150 to 400 kg m−3.

In terms of the albedo calculation, surface radiative forcing (RF) due to BC was obtained by using the following equation:

$${{R}}{{F}}={{S}}{{W}}(1-\alpha )+{{G}}{{W}}-5.6704\cdot {10}^{-8}\cdot {{{T}}{{S}}{{K}}}^{4}\cdot {{E}}{{M}}{{I}}{{S}}{{S}},$$

where α is the surface albedo with or without BC; SW is downward shortwave flux at the ground surface; GW is downward longwave flux at the ground surface; TSK is surface skin temperature; EMISS is surface emissivity. Except for α with BC, other variables were outputted by the WRF-Chem simulation.

Calculation of glacier melting due to South Asian BC

In this study, WRF-Chem simulations calculated the BC deposition flux on snow/ice, radiation components, sensible and latent heat fluxes, and combined with the SNICAR model (Snow-Ice-Aerosol-Radiative, http://snow.engin.umich.edu/) towards the simulation of the snow/ice albedo change, then driving the glacier energy model to calculate the glacier melting.

The effect of BC on glacier’s surface energy balance was estimated using the following equation:

$${Q}_{{{M}}}={{S}}{{i}}{{n}}(1-\alpha )+{L}_{{{i}}{{n}}}-{L}_{{{o}}{{u}}{{t}}}+H+{{L}}{{E}}+{Q}_{{{P}}}+{Q}_{{{G}}},$$

where QM represents the glacier’s energy balance and includes the following components: absorbed solar radiation (α is albedo, Sin is incoming shortwave radiation), incoming (Lin) and outgoing (Lout) longwave radiation, and the turbulent fluxes of sensible heat (H) and latent heat (LE). These radiation components, sensible and latent heat fluxes are derived from the WRF-Chem simulations. QP represents heat from precipitation and QG is the heat flux from ice.

Finally, based on the energy balance (QM) calculated above, the glacier mass balance was determined using the following equation:

$${MB}=\int \left(\frac{{Q}_{M}}{{L}_{m}}+\frac{{LE}}{{L}_{v}}+{C}_{{en}}+{P}_{{snow}}\right){dt},$$

where MB is mass balance (mm w.e. a−1) and Lm is latent heat of ice with the default value equal to 3.34 × 105 J kg−1. Lv is evaporation heat (2.51 × 105 J kg−1) or sublimation heat (2.85 × 105 J kg−1). Cen represents the mass from meltwater refreezing and PSnow is solid precipitation. This process allows for estimating the influence of BC deposition on glacier mass loss and the overall glacier energy balance.