The study area was located around 35.40∘ N, 74.38∘ E in the mountains and adjacent mountain valleys of the Karakoram and Himalayan region in northern Pakistan (Fig. 1). Snow and ice samples were collected in summer from six glaciers – Passu, Gulkin, Barpu, Mear, Sachin, and Henarche – and in autumn from Gulkin and Sachin (Fig. 1). The Passu and Gulkin glaciers are located very near the Karakoram highway connecting Pakistan with China, and there are a number of small villages (Passu, Hussaini, Gulmit, and others) close by. The Barpu and Mear glaciers are located very close to each other and around 3 km away from the residential area of the Hopar and Nagar valleys. There is a small city (Astore) near the Sachin glacier and some restaurants near its terminus (Muhammad and Tian, 2016). Winter snow samples were collected from mountain valleys near the Passu, Barpu, and Sachin glaciers and three other areas to the west with a number of small villages (Fig. 1). The average elevation of the selected glaciers was quite low compared to the elevation of the glaciers studied for BC, OC, and dust on the Tibetan Plateau by previous researchers. The mountains around the selected glaciers are mostly dry and rocky. The 10-year records (1999–2008) of the two nearby climate stations at Khunjerab (36.83∘ N, 75.40∘ E; 4730 m a.s.l.) and Naltar (36.29∘ N, 74.12∘ E; 2858 m a.s.l.) show mean total annual precipitation values of 170 and 680 mm, respectively. The daily average temperature during winter and the pre-monsoon showed an increasing trend between 1980 and 2014 (Gul et al., 2017). The study area is mostly exposed to the westerlies and emissions from south Asia. Most of the people in the region use wood for cooking and heating.

A total of 50 surface ice and 49 snow samples were collected from the glaciers in summer 2015 and 2016 (Passu – 15; Gulkin – 31; Barpu – 6; Mear – 8; Sachin – 35; Henarche – 4) and 13 (total of ice and snow samples combined) in autumn 2016 (Gulkin – 7; Sachin – 6) at elevations ranging from 2569 to 3895 m a.s.l. (Fig. 1). Eighteen snow samples were collected in winter 2015 and 2016 from nearby mountain valleys at elevations of 1958 to 2698 m a.s.l.; the winter sampling region was divided into six sites (S1 to S6) based on geographical location and elevation (Fig. 1). Samples were collected using the “clean hands – dirty hands” principle (Fitzgerald, 1999). Ice samples were collected from the surface (5 cm depth) at different points on the glaciers. The elevation difference between collection points on the same glacier ranged from 30 to 100 m.

The samples were preserved in ultraclean plastic bags, allowed to melt in a temporary laboratory near the sampling location, and filtered through quartz filters immediately after melting. An electric vacuum pump was used to accelerate filtration. The melted snow/ice volume of the samples was measured using a graduated cylinder. Sampled filters were carefully packed inside petri slides marked with a unique code representing the sample.

The snow density of winter snow samples was measured using a balance, snow/ice grain sizes were observed with an accuracy of 0.02 mm using a hand lens (25×) (Aoki et al., 2011), and snow shape was estimated using a snow card. In the models, we assumed external mixing of snow and aerosol particles and spherical snow grains. Snow grain size and snow texture were the largest sources of uncertainty in albedo reduction (Sect. 3.3). Qian et al. (2015) have summarized the sampling methods available for light-absorbing particles in snow and ice from different regions including the Arctic, the Tibetan Plateau, and midlatitude regions.

Before analysis, sampled filters were allowed to dry in an oven for 24 h and then weighed using a microbalance. The dust mass on the filters was calculated from the mass difference in weight before and after sampling (Kaspari et al., 2014; Li et al., 2017).

There are many methods available for analyzing BC and OC. The three methods considered the most effective for measuring BC and water-insoluble OC concentrations in snow are thermal optical analysis, filter-based analysis, and single-particle soot photometer analysis (Ming et al., 2008). The thermal optical (filter-based) analysis method has been used by many researchers (e.g., Li et al., 2017) and was chosen for the study. This is an indirect method for measuring BC and OC on sampled filters; it follows Beer's law and uses the stepwise combustion of the particles deposited on quartz filters (Boparai et al., 2008), followed by the measurement of light transmission and/or reflectance of the filters. The BC and OC content in the collected samples was measured using a thermal optical Desert Research Institute (DRI) carbon analyzer, similar to the Interagency Monitoring of PROtected Visual Environments (IMPROVE) protocol (Cao et al., 2003). The temperature threshold applied to separate the two species is described in M. Wang et al. (2012). A few (< 10) filters had higher dust loads; for these the method was slightly modified using a 100 % helium atmosphere and temperature plateau (550 ∘C). A very few (< 5) samples with very dense dust concentrations were not properly analyzed by the instrument and were excluded from the results. The extremely high dust value of one sample from Passu (15 times the level in the next-highest sample), which had low values of other pollutants, was excluded as a probable error. In some cases, a single sample was analyzed two or three times to ensure accurate results were obtained.

The CALIPSO models also define multiple aerosol subtypes – clean continental, clean marine, dust, polluted continental, polluted dust, smoke, and other – using the 532 nm (1064 nm) extinction-to-backscatter ratio. The frequency of these different aerosol subtypes in the atmosphere over the study region was investigated using CALIPSO data for the same months in which ice and snow samples were collected, i.e., January, May, June, and December, over the period June 2006 to December 2014. The CALIPSO Level 2 lidar vertical feature mask data product describes the vertical and horizontal distribution of clouds and aerosol layers (downloaded from https://eosweb.larc.nasa.gov/project/calipso/aerosol_profile_table, last access: May 2016). The aerosol subtypes were classified in the downloaded data using the observed backscatter strength and depolarization values. The details of the algorithm used for classification are given in Omar et al. (2009). The percentage contributions of individual aerosol subtypes were plotted using MATLAB (MathWorks, Inc.).

The frequencies of different subtypes were calculated along the specific paths followed by CALIPSO over the study region.

Snow albedo was estimated for each of the 18 winter samples and the average calculated for samples at each of the sites (1 to 6). Albedo from two sites – S1 (Sost), which had the highest average concentration of BC and dust, and S6 (Kalam), which had the lowest average concentration of BC and dust – was further explored using the SNICAR model (Flanner et al., 2007). The aim was to quantify the effect of BC, dust, and mass absorption cross section (MAC) on albedo reduction. Sensitivity model experiments were carried out using various combinations of BC, dust, and MAC values, while other parameters were kept constant (parameters for sites 1 and 6 shown in the Supplement, Table S1). Snow albedo was simulated for different daylight times, with the solar zenith angle (SZA) set in the range 57.0–88.9∘ based on the position of the sun in the sky for the sampling date and locations. The daily mean was calculated from the mean of the albedo values simulated for 24 different SZA values (one per hour) and the daytime mean from the mean of the albedo values simulated for 10 SZA values (one per hour during daylight). The midlatitude winter clear-sky option was selected for surface spectral distribution. The parameters used for sensitivity analysis are shown in Table S1 in the Supplement. MAC values of 7.5, 11, and 15 m2 g-1 were selected based on a literature review (Qu et al., 2014; Pandolfi et al., 2014). In order to reduce the uncertainty, the dust concentration in the samples was divided into four diameter classes (as per the model requirements): size 1 (0.1–1.0 µm) was taken to be 2 %, size 2 (1–2.5 µm) to be 13 %, size 3 (2.5–5 µm) to be 31 %, and size 4 (5–10 µm) to be 54 % of total dust mass present in the sample, based on results published by others (Gillette et al., 1974; Mahowald et al., 2014). Radiative forcing (RF) was estimated for the same samples following Eq. (1): RFx=Rin-short⋅Δαx, where Rin-short denotes incident shortwave solar radiation (daily mean), as measured by the SBDART model, and Δαx denotes the daily mean reduction in albedo, as simulated by the SNICAR model.

Three methods were used to identify the potential source regions of pollutants found at the study site: wind maps, emissions inventory coupled with back trajectories, and a region-tagged chemical transport modeling analysis.

Wind vector maps were prepared using MERRA-2 reanalysis data (available from the National Aeronautics and Space Administration (NASA): https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/docs/, last access: December 2017). The U and V wind components were combined into a matrix around the study area for each individual month and then plotted against latitude–longitude values to show the spatial variance of monthly wind stress at 850 mb using arrows to indicate the direction and intensity of wind.

Air trajectories were calculated backwards from the sampling sites (S1: 36.40∘ N, 74.50∘ E; S6: 35.46∘ N, 72.54∘ E) to identify potential source regions for the pollutants using the web version of the HYSPLIT-4 model (Draxler and Hess, 1998). The HYSPLIT-4 model has been used by others to compute air mass trajectories to identify possible source regions (Ming et al., 2009; Zhang et al., 2013). Reanalysis meteorological data from the same source as the wind data (https://www.esrl.noaa.gov/psd/data, last access: November 2016) were used as input data in the HYSPLIT model for May, June, and December 2015 and January 2016. HYSPLIT was run in a 7-day backward trajectory mode with trajectories initiating every 6 h (0, 6, 12, and 18) on a daily basis from 4 May to 19 June 2015 (77 days during summer) and from 1 December 2015 to 31 January 2016 (62 during winter). The HYSPLIT model results were combined with Representative Concentration Pathway (RCP) emission data for 2010 (available from http://sedac.ipcc-data.org/ddc/ar5_scenario_process/RCPs.html, last access: November 2016; data file <RCPs_anthro_BC_2005-2100_95371.nc>) to identify the source location. This comprises emission pathways starting from an identical base year (2000) for multiple pollutants, including BC and OC; the file description indicates that the inventory includes biomass burning sources. The RCP inventory has the same emissions sectors as the Hemispheric Transport Air Pollution (HTAP) emission inventory used in the modeling approach for identifying source regions (see below), including fuel combustion, industry, agriculture, and livestock, but the HTAP inventory has a higher resolution (0.1 × 0.1∘) than the RCP inventory (0.5 × 0.5∘). Lamarque et al. (2010) give a more detailed discussion of the inventory and sectors (12) used in the base year calibration of the RCP. Monthly CALIPSO satellite-based extinction data from 2006 to 2014 were used to calculate the vertical profile for aerosol extinction over the study region. The CALIPSO extinction profile was constructed for selected months in 2006 to 2014 – May and June for summer and December and January for winter (Fig. S1). The exponential equation X=(log⁡10.46-log⁡(Y))/10.29, where Y is the vertical height of individual trajectories in kilometers and X indicates the extinction against the height of trajectories, was used to calculate the extinction profile for the trajectory heights. The normalized extinction profile was obtained by assuming that surface extinction equals 1 (Fig. S1).

The WRF-STEM model was used as a third approach for identifying the origin (source regions) of air masses carrying pollutants. The WRF-STEM model uses region-tagged carbon monoxide (CO) tracers for many regions in the world to identify geographical areas contributing to observed pollutants (Adhikary et al., 2010). Region-tagged CO tracers are used as a standard air quality modeling tool in various regional and global chemical transport models to identify pollution source regions (Chen et al., 2009; Park et al., 2009; Lamarque and Hess, 2003). The WRF-STEM model domain was centered on 50.377∘ E longitude and 29.917∘ N latitude, with a model horizontal grid resolution of 45 × 45 km with 200 grids in the east–west direction and 125 north–south. The meteorological variables needed for the chemical transport were derived from the WRF meteorological model (Grell et al., 2005) using FNL (Final) data (ds083.2) available from the University Corporation for Atmospheric Research (UCAR) website as input data. The main aim of the simulation was to identify the geographic locations contributing to the observed pollutants at the field sites. The HTAP version 2 emission inventory, which comprises multiple pollutants including BC and OC, was used for the WRF-STEM modeling (available from http://edgar.jrc.ec.europa.eu/htap_v2/, last access: January 2017). This emission inventory includes major sectors, such as energy, industry, transport, and residential, but not large-scale open agricultural and open forest burning. The simulations applied in our study used the anthropogenic emissions from the HTAP inventory. Thus, the results indicate the amount of pollutants reaching the study area from day-to-day planned and recurring activities in domestic, transport, industrial, and other sectors. The model was run for a month prior to the field campaign dates to allow for model spin-up (normal practice for a regional chemical transport model) and then for the months of December, January, and June to match the field campaign dates.

The minimum, maximum, and average concentrations of BC, OC, and dust in the ice and snow samples are given in Table 1. The OC and BC concentration values were blank corrected by subtracting the average value of the field blanks. Blank concentrations were used to calculate detection limits as mean ± standard deviation. The average BC concentration overall was 2130 ± 1560 ng g-1 in summer samples, 2883 ± 3439 ng g-1 in autumn samples (both from glaciers), and 992 ± 883 ng g-1 in winter samples. The average OC concentration overall was 1839 ± 1108 ng g-1 in summer samples, 1423 ± 208 ng g-1 in autumn samples, and 1342 ± 672 ng g-1 in winter samples. There was considerable variation in individual samples, with summer values of BC ranging from 82 ng g-1 (Gulkin glacier) to 10 502 ng g-1 (Henarche glacier), autumn values from 125 ng g-1 (Gulkin glacier) to 6481 ng g-1 (Sachin glacier), and winter samples from 79 ng g-1 (Kalam) to 5957 ng g-1 (Sost).

The lowest BC (82 ng g-1) and OC (128 ng g-1) concentrations were observed in summer samples collected from the Gulkin and Sachin glaciers, respectively. The average values of BC and OC were low in all samples from the Passu glacier, even though it lies close to the Karakoram highway which links Pakistan with China. The low concentrations of BC may have been due to the east-facing aspect of the glacier shielding it from pollutants transported from west to east. Slope aspect of a glacier is known to be important for snow cover dynamics (Gul et al., 2017); dust concentrations are known to vary with slope aspect due to the effects of wind direction on deposition.

The highest average concentration of BC was found in autumn samples from the Sachin glacier and the highest average concentration of OC in summer samples from the same glacier. The average concentration of BC was much greater in autumn than in summer on the Sachin glacier but somewhat greater in summer than in autumn on the Gulkin glacier, indicating highly spatiotemporal patterns in the deposition of particles. The marked difference on the Sachin glacier may have reflected the difference in the direction of air, which comes from Iran and Afghanistan in summer and the Bay of Bengal via India in autumn, with the generally lower deposition on the Gulkin glacier more affected by other factors (such as slope aspect of the glacier and status of local emissions near the glacier). There was no clear correlation between the average BC concentration in glacier samples and glacier elevation. However, winter snow samples showed a weak increasing trend in average BC with site elevation (Table 1, Fig. S3).

Most summer samples were collected from surface ice (Fig. S2a), but a few samples for Gulkin and Sachin were collected from aged snow on the glacier surface (Fig. S2b, c). Dust was visible on the relatively aged snow, and the BC and OC concentrations in these snow samples were much higher than those in ice. The highest average BC values in winter were also observed in aged snow (from Sost) and the lowest in fresh snow (from Kalam) (Table 1). Generally, snow samples collected within 24 h of a snowfall event were considered to be fresh snow.

We analyzed the ratios of OC to BC in the different samples as in atmospheric fractions; this can be used as an indicator of the emission source, although apportionment is not simple and only indicative. The BC fraction is emitted during the combustion of fossil fuels, especially biomass burning in rural areas in winter, and urban emissions from road transport. The OC fraction can be directly emitted to the atmosphere as particulate matter (primary OC) from fossil fuel emissions, from biomass burning, or in the form of biological particles or plant debris; it can also be generated in the atmosphere as gases are converted to particles (secondary OC). In general, lower OC / BC ratios are associated with fossil fuel emissions and higher OC / BC ratios with biomass burning. Overall, there was no clear correlation between BC and OC concentrations in our samples. In most cases, the concentration of OC was greater than the concentration of BC, which might indicate a greater contribution from biomass burning in the emissions, but in a few, the concentration of BC was greater than that of OC, which might indicate a greater contribution from coal combustion. The lowest OC / BC ratio of 0.041 was observed in a summer sample from Henarche glacier and the highest ratio of 5 in a winter sample from Kalam. The higher value at Kalam may indicate greater contributions from biomass burning than from fossil fuel combustion in the region. In summer samples, the average concentration of OC was greater than the average concentration of BC in samples from four of the six glaciers, but it was much lower in Barpu and Henarche. In winter, individual snow samples indicated that the concentration of OC was greater than BC at low-elevation sites and vice versa; the average OC was greater than average BC at all except the highest elevation site (Table 1).

However, these results should be considered with caution. There are a number of factors that can affect the OC / BC ratio in snow and ice samples apart from the concentrations in the atmosphere. Spatiotemporal variability of the OC / BC ratio may indicate the contribution of different sources, seasonal variation, and frequent change in wind direction. In deposited samples, low OC / BC ratios can result from a reduction in OC (Niu et al., 2017), greater contributions from BC enrichment and OC scavenging, and/or the contribution of different emission sectors (including quantity, combustion conditions, and fuel type). Post-deposition processes of scavenging and enrichment, which are influenced by the snowmelt rate, can cause water-soluble OC to be underrepresented as meltwater removes OC but not BC, with OC and BC being redistributed primarily by meltwater rather than by sublimation and/or dry/wet deposition. Thus, the OC / BC ratio often reflects the impact of the dilution of dissolved organic carbon and the enrichment of primary organic carbon during snow/ice melting, with differences in OC / BC ratios reflecting differences in the enrichment process. The low OC / BC ratio in the samples from Henarche, the glacier at the lowest elevation, could, for example, be due to preferential washing out of OC particles with meltwater. Overall, there was a higher positive correlation between BC and dust than with OC, suggesting that for BC and dust, particle precipitation and enrichment processes were similar. The method used for analysis and the amount of dust loading on the sample can also affect the OC / BC ratio, as can the presence of metal oxides and calcium carbonate. High iron oxide concentrations can cause BC to pre-oxidize or drop off the filter, while calcium carbonate can be wrongly identified as BC. Laboratory studies have shown that the presence of metal oxides in aerosol samples can alter the OC / BC ratio either by enhancing OC charring or by lowering the BC oxidation temperature (Wang et al., 2010), while higher fractions of metal oxide can increase BC divergence across the thermal optical protocols (Wu et al., 2016). Dust can lead to a greater decrease in optical reflectance during the 250 ∘C heating stage in the thermal–optical method and thus an incorrect OC / BC ratio (M. Wang et al., 2012). Carbon detected by the flame ionization detector (FID) before the optical signal attains the initial value is defined as OC and that detected after is defined as BC; dust on the filter results in the FID division being postponed or inefficient and thus OC being overestimated and BC underestimated or even negative (M. Wang et al., 2012). M. Wang et al. (2012) provide a more detailed discussion of OC / BC ratios derived using the thermal optical method.

A wide range of values has been reported by different authors for BC concentrations in snow and ice samples from different regions (Table S2). The concentrations of BC in our samples were higher than those reported by many authors (Table S2) but were comparable with the results reported by Xu et al. (2012) in the Tien Shan, by Li et al. (2016) in the northeast of the Tibetan Plateau, by Wang et al. (2017) in northern China, and by Zhang et al. (2017) in western Tien Shan, central Asia. High concentrations indicate high deposition rates on the snow and ice surface, but there are several possible reasons for a wide variation in values apart from differences in deposition rates, including differences in sampling protocols, geographical/sampling location and elevation of sampling site (Qu et al., 2014), and year/season of sampling. The majority of samples were from the ablation zone of the glaciers. Strong melting of surface snow and ice in the ablation zone could lead to BC enrichment and high-BC concentrations, as observed by Li et al. (2017) for glaciers on the southern Tibetan Plateau. The sampling season (May to September in our study) is an important factor because rapid enrichment occurs as snowmelts during the melting season. The peak melting period is May to August/September; thus, the concentration of BC, OC, and dust in our samples would have been increased as melting progressed due to the enrichment in melting snow and scavenging by the melting water. In most cases, snow and ice samples were collected quite a long time after snow fall, and the concentration of pollutants would also have increased in the surface snow and ice due to dry deposition. It seems likely that the pollutants in surface samples would be affected by sublimation and deposition until the next melt season (Yang et al., 2015). In some of the cases in our study, the average concentration of BC, OC, and/or dust for a particular glacier/site was increased as a result of a single highly concentrated sample, reflecting the wide variation that results from the interplay of many factors.

Enrichment is more marked at lower elevations as the temperatures are higher, which enhances melting and ageing of surface snow, while deposition also tends to be higher because the pollutant concentrations in the air are higher (J. Wang et al., 2012; Nair et al., 2013). Previous studies have tended to focus on the accumulation area of glaciers (e.g., ice cores and snow pits), where enrichment influences are less marked, and on high-elevation areas, where deposition is expected to be lower, in both cases leading to lower values. In our study, the majority of samples collected in summer and autumn were collected from the ablation area of debris-covered glaciers where enrichment influences are marked due to the relatively high temperature, and this is reflected in the relatively high values of BC, OC, and dust. Li et al. (2017) showed a strong negative relationship between the elevation of glacier sampling locations and the concentration of light-absorbing particles. Stronger melt at lower elevations leads to higher pollutant concentrations in the exposed snow. Equally, BC may be enriched in the lower-elevation areas of glaciers as a result of the proximity to source areas as well as by the higher temperatures causing greater melting. Thus, the main reason for the high concentrations of BC, OC, and dust in our samples may have been that the samples were taken from relatively low-elevation sites. Human activities near the sampling sites in association with the summer pilgrimage season probably also contributed to an increase in pollutant concentrations. Our results do not necessarily indicate that all the glaciers in the Karakoram region are substantially darkened by BC. The ablation zones of debris-covered glaciers which are at relatively low elevations and near pollution sources may be more polluted than other glacier areas.

The analysis of aerosol types using the CALIPSO data identified smoke as the most frequent aerosol type over the study region in both summer and winter, indicating that biomass burning may be the dominant source of emissions. Figure 2 shows the average frequency of different aerosol types in May–June (summer) and December–January (winter) over the period 2006 to 2014 in the form of a box plot. The frequency of different aerosol subtypes in June from 2006 to 2014 is shown in Fig. S4; smoke had the highest frequency (39 %), followed by dust (21 %), polluted dust (12 %), and other (20 %). This type of aerosol measurement in the atmosphere was useful for our current study because it provides observation-based data over the study region, whereas the other approaches used (such as modeling) were based on interpolation not observation. Pollutant deposition depends on the concentration of pollutants in the atmosphere, and the results are consistent with the high concentration of BC (from smoke) and dust particles in the glacier and snow surface samples.

The albedo of individual winter snow samples was calculated using the SNICAR model and then averaged for each site (S1 to S6). Figure 3a shows the average for each site across the visible and infrared spectrum. Two sites were chosen for further analysis: S1 (Sost), which had the highest average concentration of BC, and S6 (Kalam), which had the lowest average concentration of BC. The albedo was simulated for selected MAC values and SZA for samples at the two sites, as described in Sect. 2.4 (“Methods”). The values for the average albedo of samples from the two sites simulated for MAC values of 7.5, 11, and 15 m2 g-1 and SZA of 57.0–88.9∘ (daytime) under a clear sky ranged from 0.39 (site S1, BC only, midday, MAC 15 m2 g-1) to 0.85 (site S6, dust only, early evening, MAC 7.5–15 m2 g-1). The detailed values are shown in Table S3.

The percentage change in albedo was calculated in absolute terms as the change between albedo values with a pollutant (BC or dust or both) and a reference albedo value with zero pollutants (zero BC and dust concentration). Table 2 shows the calculated percentage reductions in daily minimum, maximum, and mean broadband snow albedo at different MAC values (7.5, 11, 15 m2 g-1) resulting from the average BC, dust, and combined BC and dust concentrations found in samples at each of the sites. The reduction was strongly dependent on BC concentration and almost independent of dust concentration and increased with increasing MAC value. The results suggest that BC was the dominant forcing factor, rather than dust, influencing glacial surface albedo and accelerating glacier melt. BC was found to play an important role in forcing in the northern Tibetan Plateau (Li et al., 2016), whereas in the central Tibetan Plateau and the Himalayas, dust played a more important role (Qu et al., 2014; Kaspari et al., 2014). The MAC value affected the albedo more in the visible range than at 1.2 µm (near-infrared) wavelength (Fig. 3c, d). The combined concentration of BC and dust, or BC alone, strongly reduced the snow albedo for a given combination of other input parameters. The effect at the low-pollutant site (S6) was small: the values for daytime snow albedo at 0.975 µm due to BC, or BC plus dust with different MAC and SZA, ranged from 0.70 to 0.83, with a reduction in daily mean albedo of 1.8 to 2.9 %, and those for dust alone range from 0.79 to 0.85, with a reduction in daily mean albedo of less than 0.1 %. The effect at the high-pollutant site (S1) was much more marked: BC or BC and dust reduced daytime snow albedo to values ranging from 0.39 to 0.64, a reduction in daily mean albedo of 8.8 to 12.0 %, but the effect of dust alone was still low, with values of 0.70 to 0.78, again representing a reduction in daily mean albedo of less than 0.1 %.

Both the snow albedo and the impact of light-absorbing particles depend on a range of factors including the SZA, snow depth, snow grain size, and snow density. For example, the snow albedo reduction due to BC is known to be less in the presence of other light-absorbing particles as these will absorb some of the available solar radiation (Kaspari et al., 2011). The snow albedo calculated for our samples was strongly dependent on the SZA with albedo increasing with decreasing SZA, especially at near-infrared wavelengths (Table S3).

The impact of snow ageing was also investigated. The winter samples from S1 (Sost) were aged snow, whereas those from S6 (Kalam) were fresh snow (Table 1, Fig. S5b, c). Not only was dust clearly visible on the surface of the aged snow, the grain size was large and the snow was dense. The aged snow had a much higher concentration of BC and dust, which reduced the albedo, but the extent of reduction is also affected by other factors. Albedo reduction by BC and dust particles is known to be greater for aged snow than for fresh snow (Warren and Wiscombe, 1985). In our samples, the calculated reduction in snow albedo for high MAC values (15) compared to low MAC values (7.5) was greater in aged snow than in fresh snow (Fig. 3b). The effective grain size of snow increases with time as water surrounds the grains. Snow with a larger grain size absorbs more radiation because the light can penetrate deeper into the snowpack, thus decreasing surface albedo (Flanner and Charles, 2006) . In the melting season, the snowpack becomes optically thin and more particles are concentrated near the surface layer, which further increases the effect on albedo.

The estimated reduction in snow albedo by dust and BC (up to 29 % of the daytime maximum value, Table 2) was higher than that reported by others for high Asia based on farmers' recordings (e.g., 1.5 to 4.6 % reported by Nair et al., 2013) and in the Himalayas (Ming et al., 2008; Kaspari et al., 2014; Gertler et al., 2016). However, although the values were relatively high, they were at the same level or lower than the estimates for an albedo reduction of 28 % by BC and 56 % by dust in clean ice samples and of 36 % by BC and 29 % by dust in aged snow samples, reported by Qu et al. (2014) for surface samples from the Zhadang glacier, China. Simulation results by Ming et al. (2013) showed BC, dust, and grain growth to reduce the broadband albedo by 11, 28, and 61 %, respectively, in a snowpack in central Tibet. Dust was the most significant contributor to albedo reduction when mixed inside the snow and ice or when the glacier was covered in bare ice. In our case BC was a more influential factor than dust during a similar study period to that reported by Li et al. (2017), indicating that BC plays a major role in albedo reduction.

The possible reasons for the relatively high values for albedo reduction in our samples include the lower elevation of the sampling locations, relatively high concentrations of BC and dust, high MAC values, low snow thickness, underlying ground quality, the presence of small and large towns near the sampling sites, and the predominance of aged snow samples. Most of the samples collected in winter were from places with a snow depth of less than 50 cm (Fig. S5a); thus, mud, stones, and clay below the snow layer would be expected to increase the absorption of solar radiation and reduce the albedo.

The high albedo reduction in the visible range of the electromagnetic spectrum could be due to the relatively high concentration of surface snow impurities. The total amount of deposited particles in the surface layer of aged snow was relatively high, indicating a high deposition rate of atmospheric pollutants.

Flanner et al. (2007) reported that BC emission and snow ageing are the two largest sources of uncertainty in albedo estimates. The uncertainties in our estimated albedo reduction include the BC type (uncoated or sulfate coated), the size distribution of dust concentration, the accuracy of snow grain size, snow texture, snow density, and the albedo of the underlying ground. Sulfate-coated particles have an absorbing sulfate shell surrounding the carbon; recent studies confirm that coated BC has a larger absorbing power than non-coated BC (Naoe et al., 2009). We used uncoated black carbon concentration in the SNICAR model, but the pollutants at the remote site are presumed to be mainly from long-range transport; thus, the BC may have gained some coating. The albedo reduction for sulfate-coated black carbon was calculated to be 3–8.5 % higher, depending on the MAC and SZA values, than for uncoated black carbon at the low-concentration site S6 (Fig. S6). The snow grain size (snow aging) and snow texture are also large sources of uncertainty. The effect of snow grain size is generally larger than the uncertainty in light-absorbing particles and varies with the snow type (Schmale et al., 2017). The albedo reduction caused by 100 ng g-1 of BC for an effective snow grain radius of 80, 100, or 120 µm was calculated to be 0.017, 0.019, or 0.021, respectively. The snow grain size was measured with a hand lens with an accuracy of 20 µm; thus, the associated uncertainty in the albedo results was at least 0.002. The snow grain shape was measured with the help of a snow card, but a spherical shape was assumed for snow grains in the (online) SNICAR albedo simulation model. The albedo of nonspherical grains is higher than the albedo of spherical grains (Chen et al., 2016), and the shape of snow grains and/or ice crystals changes significantly with snow age and meteorological conditions during and after snowfall (LaChapelle, 1969). A number of recent studies (e.g., Flanner et al., 2012; Liou et al., 2014; He et al., 2014, 2017) have shown that both snow grain shape and aerosol–snow internal mixing play an important role in snow albedo calculations.

RF is a measure of the capacity of a forcing agent to affect the energy balance in the atmosphere – the difference between sunlight absorbed by the Earth and energy radiated back to space – thereby contributing to climate change. Changes in albedo contribute directly to radiative forcing: a decrease in albedo means that more radiation will be absorbed and the temperature will rise. In snow and ice, the additional energy absorbed by any pollutants present also increases and accelerates the melting rate.

Various authors have described the impact of albedo change in snow and ice on radiative forcing. Zhang et al. (2017) reported that a reduction in albedo by 9 to 64 % can increase the instantaneous radiative forcing by as much as 24.05–323.18 W m-2. Nair et al. (2013) estimated that in aged snow a BC concentration of 10–200 ng g-1 can increase radiative forcing by 2.6 to 28.1 W m-2, while Yang et al. (2015) reported radiative forcing of 18–21 W m-2 for aged snow in samples from the westernmost Tibetan Plateau. The authors used different atmospheric conditions in the forcing estimates: Zhang et al. (2017) used midlatitude winter with a clear sky and a cloudy environment, Nair et al. (2013) midlatitude winter, and Yang et al. (2015) clear-sky and cloudy conditions.

We calculated the radiative forcing in the samples assessed for daytime albedo and daily (24 h) mean albedo. The radiative forcing at different daylight times caused by BC deposition varied from 3.93 to 43.44 W m-2 (3.93–11.54 W m-2 at the low-BC site and 20.88–43.45 W m-2 at the high-BC site) and that cause by dust from 0.16 to 2.08 W m-2 (0.16–0.30 W m-2 at the low-BC site and 1.38–2.08 W m-2 at the high-BC site) (detailed values given in Table S4), indicating that BC was the dominant factor. The radiative forcing due to combined BC and dust was very similar to that for BC alone. In contrast, studies by others have shown higher forcing by dust than by BC based on the optical properties and size distribution of dust particles (Qu et al., 2014). In our study, the increase in daily mean radiative forcing ranged from 0.1 % for dust only at the low-pollutant site to 14.9 % for BC at the high-pollutant site. However, dust forcing varies strongly with dust optical properties, source material, and particle size distribution. The properties for dust are unique in each of the four size bins used in the SNICAR online model. These size bins represent partitions of a lognormal size distribution. We used an estimated size of dust particles and generic dust properties in the model, but some dust particles can have a larger impact on snow albedo than the dust applied here (e.g., Painter et al., 2007).

Both radiative forcing and albedo reduction increased with decreasing daytime SZA, indicating higher melting at midday compared to morning and evening. Figure 4 shows the daily mean albedo reduction and corresponding radiative forcing caused by BC for fresh (low-BC) and aged (high-BC) snow with different MAC values. Snow aging (snow grain size) plays an important role in albedo reduction and radiative forcing. According to Schmale et al. (2017) the effect of snow grain size is generally larger than the uncertainty in light-absorbing particles, which varies with snow type. Snow aging reduces snow albedo and accelerates snowmelt, but the impact of snow aging on BC in snow and the induced forcing is complex and includes spatial and seasonal variation (Qian et al., 2014).

An increase in MAC value from 7.5 to 15 led to an increase in radiative forcing by 1.48 W m-2 in fresh snow and 4.04 W m-2 in aged snow. This suggests that when the surface of snow, ice, and glaciers experiences strong melting, enrichment with BC and dust could cause more forcing. Previous studies of ice cores and snow pits probably underestimated the albedo reduction and radiative forcing in glacier regions as samples were taken from high-elevation areas where there is less ageing and melting and thus lower surface enrichment of BC and dust than at lower elevation. Our results are higher than those reported in other studies on the northern slope of the Himalayas (Ming et al., 2012), on the western Tibetan Plateau (Yang et al., 2015), and the Tien Shan (Ming et al., 2016). However, they are comparable to values for radiative forcing reported more recently by others, for example for the Muji glacier (Yang et al., 2015), Zhadang glacier (Qu et al., 2014), in high Asia (Flanner et al., 2007; Nair et al., 2013), and in the Arctic (Wang et al., 2011; Flanner, 2013). The results suggest that the enrichment of black carbon (in our case) and mineral dust (other authors) can lead to the increased absorption of solar radiation, exerting a stronger effect on climate and accelerating glacier melt.