Our study area comprises various spatial domains (Fig. 1). The larger Himalaya domain is defined here as the region spanning ∼1500 km (∼76 to 92∘ longitude and ∼26 to 34∘ latitude), covering areas from the Himachal/Jammu and Kashmir border in the west to the Bhutan Himalaya in the east (Fig. 1). Glaciers in this area have been in a state of negative mass balance in the last decades, with accelerating trends in the 2000 to 2010 decade (Bolch et al., 2019; Brun et al., 2017; Kääb et al., 2012; Maurer et al., 2019). We developed our method in the glacierized Khumbu region of Nepal, which we refer to hereafter as the “Khumbu domain”, although it also includes glaciers north of the divide (Fig. 2). Glaciers in the Khumbu region have been well studied in terms of glacier mass balance using the traditional glaciologic method (Wagnon et al., 2013), the geodetic method (Bolch et al., 2008; Nuimura et al., 2012; Brun et al., 2017; Bolch et al., 2011; Rieg et al., 2018), energy balance models (Rounce and McKinney, 2014; Rounce et al., 2015; Kayastha et al., 2000), debris cover characteristics (Iwata et al., 1980; Watanabe et al., 1986; Nakawo et al., 1999; Iwata et al., 2000; Casey et al., 2012; Takeuchi et al., 2000) and surface velocity (Quincey et al., 2009). Rates of change of the debris-covered glacier areas in the Khumbu region vary from -0.12±0.05 % a-1 from 1962 to 2005 (Bolch et al., 2008) to -0.27±0.06 % a-1 from 1962 to 2011 (Thakuri et al., 2014). Supraglacial ponds cover ∼0.3 % to 7 % of the glacierized area in the Khumbu region based on high-resolution Pléiades data (Watson et al., 2017a; Kneib et al., 2020; Salerno et al., 2012); ice cliffs cover between 1 % and 9.2 % of the glacier areas (Brun et al., 2018; Watson et al., 2017a; Kneib et al., 2020).

To examine and highlight regional differences in the composition of the debris-covered surfaces, we use four sub-regions selected across monsoonal gradients as defined in the literature, corresponding to the Landsat scenes (∼ 32 919 km2) shown on Fig. 1 (Bookhagen and Burbank, 2010; Thayyen and Gergan, 2010; Barros and Lang, 2003). The Lahaul–Spiti region in the western Himalaya is in the monsoon-arid transition zone, characterized by monsoon precipitation during the summer and precipitation from the westerlies in the winter (Thayyen and Gergan, 2010). The Manaslu and Khumbu regions in the central Himalaya, and the Bhutan region in the eastern Himalaya, are all under the influence of the Indian summer monsoon, which brings large amounts of precipitation during the summer months (June to September) (Barros and Lang, 2003; Bookhagen and Burbank, 2006) (Fig. 1).

To validate the performance of the spectral unmixing as a basis for estimating pond coverage, we used debris-covered glacier zones at three validation sites (700–1150 km2), selected across the wider Himalaya domain from the Khumbu, Langtang and Lahaul–Spiti regions (Fig. 1). Supraglacial ponds on these glaciers were mapped using OBIA methods on high-resolution imagery (Sect. 2.6).

The satellite data used for spectral unmixing comprise of 13 Landsat 8 OLI images covering the Himalaya domain (Fig. 1 and Table 1). Characteristics of these images are given in Table 1. These were top-of-atmosphere registered, radiometrically calibrated and orthorectified imagery (level L1TP -T1), available at 30 m spatial resolution in the visible to short-wave infrared since 2013 (Wulder et al., 2019; USGS, 2015). We selected scenes from the post-monsoon period only (September to November) in order to minimize cloud and snow cover occurrence (Bookhagen and Burbank, 2006). In addition, Landsat scenes across the domain were selected around the same date as much as possible to minimize seasonal differences in surface conditions, notably seasonal changes in pond occurrence (Miles et al., 2017b). All chosen images were acquired around the same time of the day (05:00 UTC time), with similar solar azimuth (∼143∘) and zenith angle (∼30∘). This is important in order to ensure that differences in surface conditions were minimal. Where the 2015 images had too much cloud or snow, we selected images for the same season in 2014 and 2016 (Table 1). We acknowledge that this choice may introduce some uncertainties due to the temporal difference, which we discuss later (Sect. 4.6). The Landsat 8 OLI scene from the Khumbu domain (30 September 2015) was chosen as reference for method development and testing. We also performed a second spectral unmixing on an additional 2016 Landsat 8 OLI scene for the Lahaul–Spiti domain in the western Himalaya (Table 1) in order to have an analysis that was coincident with the high-resolution data used to validate the supraglacial pond mapping within this region.

For calibration and validation of the spectral unmixing products at specific locations, we used a combination of high-resolution optical imagery from Pléiades and Planet (Table 1). The Pléiades 1A satellite sensor acquires tri-stereo high-resolution data (0.5 m spatial resolution in the panchromatic band and 2 m in the multispectral bands, blue to near-infrared), with 20 km image swath at nadir (Table 1). Three Pléiades scenes from 2015 (7, 19 and 20 October) covered the north, north-east, and south-east parts of the Khumbu domain (Fig. 1) (Rieg et al., 2018) and offered the closest match to the date of the reference Landsat image (30 September 2015); these Pléiades scenes were cloud-free and snow-free over the debris-covered part of the glaciers. The scenes were provided as three sets of triplets of primary data (1A) and were orthorectified in the Leica Photogrammetry Suite in ERDAS Imagine 2013 (ERDAS, 2010) using the Pléiades Rational Polynomial Coefficient model and the Pléiades DEM (1 m) previously generated using semi-global matching (Rieg et al., 2018). The individual image scenes were mosaicked to a single image using nearest neighbour at 2 m spatial resolution. In addition, a RapidEye level 3A analytic ortho-tile from 9 October 2015 from Planet (Planet Team, 2017) was used in addition to Pléiades in the Khumbu domain in order to cover a wider region to better overlap the Landsat scene. This RapidEye scene consists of orthorectified, surface reflectance data at 5 m spatial resolution and five multispectral bands, projected to UTM coordinates. A PlanetScope ortho-tile from 19 October 2016 (3 m spatial resolution, 4 multi-spectral bands) was used in the Lahaul–Spiti area to validate the ponds resulting from unmixing the 2016 Landsat 8 scene for this region (Table 1). Both RapidEye and PlanetScope tiles obtained from Planet were mosaicked to single scenes using nearest neighbour. These have a stated positional accuracy of <10 m, reported as root mean square error, RMSE (Planet Labs, 2021).

We co-registered all high-resolution images and the corresponding Landsat 8 OLI images using the Co-registration of Optically Sensed Images and Correlation (COSI-Corr) routine (Leprince et al., 2007) implemented in ENVI 5.5 Classic (L3Harris Geospatial, Boulder CO). For the Pléiades image, after co-registration with 20 tie points and a second-order polynomial transformation (RMSE = 1.3 m), image displacements were -0.16 m in the E/W direction and 0.12 m in the N/S direction. The Planet RapidEye and PlanetScope scenes were co-registered on the Landsat 8 OLI with 15 and 10 tie points (RMSE = 5 and 1.6 m, respectively), yielding offsets of ∼1.1 to 1.7 m in the E/W direction and 0.09 to 0.5 m in the N/S direction after co-registration. These offsets were below the spatial resolution of all scenes (2–5 m).

All Landsat 8 OLI scenes were corrected to minimize atmospheric effects due to scattering or absorption from atmospheric gases, aerosols and clouds. We used the open-source Atmospheric and Radiometric Correction of Satellite Imagery (ARCSI v 3.1.6) routine based on the 6S algorithm (Vermote et al., 1997). We applied the STDSREF option in ARCSI with the shadow option, which provided standardized surface reflectance products for all the scenes; deep shadows were masked out as NoData. ARCSI allows for global and local viewing and solar geometries using physically based illumination and reflectance corrections based on topographic data (Shepherd and Dymond, 2003), a specified atmospheric profile, an aerosol optical thickness (AOT) value and sensor geometry. These settings are important for minimizing differences in surface conditions among the various scenes. The AOT value was automatically derived in ARCSI by a numerical inversion of the surface reflectance on an image basis using the simple dark object subtraction technique (DOS) from the blue band, yielding an AOT of 0.05 for the 30 September 2015 Khumbu scene. To validate the performance of the DOS technique for the atmospheric profile representation in our study area for this date, we validated the estimated AOT against level 1.5 data at reference wavelength of λ=500 nm aerosol size from AERONET (https://aeronet.gsfc.nasa.gov/, last access: 20 September 2021) (Giles et al., 2019) and against daily forecast global reanalysis of total optical depth at multiple wavelengths from the Copernicus Atmospheric Monitoring Service (CAMS) (https://atmosphere.copernicus.eu/catalogue#/, last access: 20 September 2021). The AOT values obtained using the DOS method (0.05) were consistent with the ones calculated from AERONET and CAMS (0.07 and 0.05, respectively). In the Himalaya, we can generally assume relatively clean atmospheres and thus consider that low AOT values are reasonable (Peter Bunting, Aberystwyth University, personal communication, February 2021). Our choice of a constant AOT value in high environments is in line with findings from other studies (Gillingham et al., 2013; Matta et al., 2017). Surface topography used for the atmospheric and topographic corrections was based on the ALOS Global Digital Surface Model (AW3D30 version 2.2, at 30 m) (JAXA, 2019), constructed from data acquired from 2006 to 2011. The vertical accuracy of ∼10 m in eastern Nepal (Tadono et al., 2014) is superior to that of Shuttle Radar Topography Mission (SRTM) DEM (23.5 m, reported by Mukul et al., 2017), because it contains fewer data voids and provides better shadow rendering in our area.

In this study, we constrained our analysis over supraglacial debris surfaces, extracted from the database of global distribution of supraglacial debris cover (Scherler et al., 2018) and referred to hereinafter as the “SDC”. Debris-covered glacier outlines in this dataset were derived from Landsat 8 OLI and Sentinel-2 data using automated approaches on Google Earth Engine by excluding clean ice and snow from glacier areas within the limits of the Randolph Glacier Inventory (RGI v.6) (RGI Consortium, 2017). Outlines span the period 1998 to 2001 for the central and eastern Himalaya, the year 2002 for the western Himalaya (monsoon-dry transition zone) and mostly the year 2010 for glaciers in China. In this study, the outlines obtained from the SDC dataset required pre-processing because supraglacial ponds along with other surfaces such as nunataks were represented as “holes” in this dataset. This caused “NULL geometry” errors due to unclosed polygons, duplicated vertices, etc. We fixed these errors in the SDC polygons using the Repair Geometry command in ArcGIS v10.8., in order to “fill” the holes so that these were included in the SDC polygons. For the test Khumbu area, we removed supraglacial debris polygons with an area less than 0.01 km2, which proved to be erroneous areas upon visual examination, i.e. sliver polygons or isolated bare land pixels. Such unwanted small polygons typically result from polygon overlays and do not represent a physical entity on the ground (Delafontaine et al., 2009).

In remote sensing, the reflectance spectrum of any image pixel represents an average of the materials on the ground, present in various proportions within that pixel (Keshava and Mustard, 2002). These “mixed pixels” are a common occurrence and are especially a concern in low- to medium-resolution imagery, including Landsat. In the case of debris-covered glacier tongues, constituent materials include various types of rock debris and/or ice cliffs, supraglacial ponds, and vegetation in various proportions (Rounce et al., 2018). Spectral unmixing techniques serve to quantify mixed spectra and to decompose each pixel into its constituent materials based on their characteristic, distinct spectral signatures. These materials are referred to as “pure” endmembers (Painter et al., 2009; Keshava and Mustard, 2002) and are either extracted from the image itself before unmixing using unsupervised techniques or supplied by the user using a priori knowledge (Painter et al., 2009; Keshava and Mustard, 2002; Dixit and Agarwal, 2021). The relationship between the fractional abundance of each material and its spectra is most often defined as a linear combination of the spectral reflectance of the distinct constituent materials. This is implemented as linear mixing models (LMMs), used for example to distinguish among vegetation, rock or different snow grain sizes (Painter et al., 2009). LMMs are easy to implement and are therefore widely used (Dixit and Agarwal, 2021; Keshava and Mustard, 2002). In contrast, nonlinear mixing models take into account multiple scattering between surfaces and are used in forested areas where canopy height or particulate mineral mixtures are in close association (Roberts et al., 1993). They are more realistic but are also more difficult to implement (Dixit and Agarwal, 2021).

To yield physically meaningful results, fractions obtained from spectral unmixing should ideally comply with two major constraints: (a) the non-negativity (or positivity) constraint (i.e. fractions should not be negative) and (b) the sum to unity (i.e. for each pixel, fractions should add up to 1) (Keshava and Mustard, 2002). The non-negativity condition is recommended because negative reflectance values have no physical meaning, and the sum-to-unity constraint is recommended when very dark endmembers such as shadows are targeted or for unmixing radiance or thermal infrared emissivity. Models that comply with both conditions (called “fully constrained models”) are difficult to achieve because they require perfect knowledge of the system, which is rarely feasible. Furthermore, fully constrained models have been shown to produce unrealistic fractions in poorly defined areas or areas of low illumination (Cortés et al., 2014). In this study, we applied a LMM with endmembers extracted from the Landsat 8 OLI image itself, and we constrained our analysis over the supraglacial debris cover only to reduce model complexity. We used the LMM implementation in the ENVI 5.5 software (L3Harris Geospatial, Boulder CO).

We validated the performance of the spectral unmixing for supraglacial pond areas on the basis of high-resolution imagery for 6 to 7 debris-covered glacier extents at each of the three sites shown in Fig. 1. For the Khumbu and Lahaul–Spiti glaciers, supraglacial pond areas were mapped from Pléiades and PlanetScope imagery, respectively (Table 1), using OBIA techniques (Blaschke et al., 2014) implemented in the ENVI Feature Extraction Module (Harris Geospatial, 2017). In the Khumbu region, the Pléiades images were acquired several weeks apart from the date of the Landsat scene in some parts of the region (see Table 1), but we assume minimal lateral expansion between the two dates, as discussed by Watson et al. (2018). For the Langtang region, we validated our LMM-derived pond areas with those reported for seven glaciers based on SPOT7 satellite imagery in Steiner et al. (2019). The OBIA method used for the Khumbu and Lahaul–Spiti regions consisted in a segmentation-only extraction workflow on the visible bands of Pléiades and/or PlanetScope, with an edge algorithm (to delineate the pond segments), a fast lambda setting (to merge adjacent segments with similar colours and borders) and a texture kernel size of 3 pixels (suitable for segmenting small areas). The scale and merge levels were adjusted against colour composites to prevent over-segmenting and to combine different segments into single ponds. The resulting polygons were further manually corrected (split, merged or digitized) for any missing and/or shaded areas beneath ice cliffs as described in Watson et al. (2017a). Our aim was not to construct a sophisticated OBIA classification scheme but rather to use the feature extraction module as a time-saving strategy and to add objectivity to the manual digitization.

We explored the dependency of the resulting supraglacial pond cover incidence on topographic variables: elevation bands above the termini, slope and aspect of the debris cover areas. These were calculated over the debris-covered parts of the glaciers on the basis of the AW3D30 DEM (30 m). Only glacier polygons with area larger than 1 km2, resulting in a subset of 408 glaciers, were selected from the SDC database over the Himalaya domain for an in-depth glacier-by-glacier analysis. The area threshold was applied in order to remove spurious small bare land patches or isolated debris pixels present in the SDC database. While the vast majority of glaciers in the Himalaya are smaller than 1 km2, these are mostly clean glaciers (Racoviteanu et al., 2015). In addition to the glacier-by-glacier basis analysis, we also binned the topographic variables, i.e. 100 m elevation, 2∘ slope and 45∘ aspect, and summarized the pond incidence in each bin.

We explored spatial patterns in the pond incidence and supraglacial vegetation with respect to regional climate gradients, average glacier mass balance and average surface velocity. Climate data (total precipitation and average temperature) were obtained from ERA5-Land, which provides gridded monthly average means at 0.1∘ × 0.1∘ of land surface properties (Muñoz-Sabater, 2019). Gridded glacier elevation change data at 30 m resolution for the period 2000–2019 were obtained from Shean et al. (2020). Glacier surface velocities for the period 2013–2015 based on Landsat data were obtained from Dehecq et al. (2015). All topo-climatic variables were binned and averaged over a 1∘ × 1∘ grid as in other studies (e.g. Brun et al., 2017; Dehecq et al., 2019) to explore the topo-climatic controls on pond and vegetation incidence.

Here we present results of the unconstrained LMM, because this had a lower RMSE (0.6 %) compared to the partially constrained model run (RMSE of 1.5 %). The normalized fractional maps of the six surface types are presented in Fig. 5; fractional values ranged from 0.004 to 1. Fractional water values greater than 0.5 correspond to supraglacial ponds, visible for example at the termini of Ngozumpa and Khumbu glaciers (Fig. 6a and b). Light debris and dark debris were identified with a threshold of 0.25 and 0.40, respectively, defined visually on the basis of the Pléiades image. Dry vegetation patches generally exhibited pixel fractions greater than 0.65. Pixels with abnormally high positive fractional vegetation values were found in areas of healthy green vegetation and/or bare terrain, which should not be part of the debris-covered tongues, as will be discussed later (Sect. 4.5). Cloud pixels display fractional values greater than 0.45, although some pixels were mixed with debris, particularly at cloud shadow areas. For clean ice, fractional values were rather low (0.20) and ranged from 0 (areas which might have some degree of dirty, dark ice with a lower albedo) to 1 (small number of clean ice pixels found in the upper areas of supraglacial debris).

Accuracy measures presented in Table 2 for the Khumbu domain show that errors were not evenly distributed among classes. For the water and vegetation classes, recall score was 0.83 to 0.84, respectively, with a precision of 0.94 and 0.93, respectively (Table 2). For these classes, the LMM achieved a balance of precision and recall metrics, with a high F score of ∼0.9 indicating an accurate model. For the debris classes, the model was reasonable but not outstanding, with an F score of ∼0.7 and lower precision score for dark debris (0.56) compared to light debris (0.72) (Table 2). This suggests that in the case of dark debris, the LMM model was less accurate than light debris, because pixels from other classes (clean ice, water and light debris) got mistakenly assigned to this class. Clouds were classified with low precision and low recall scores (F score of ∼0.5), which means that the LMM performed relatively poorly for this class and it also missed 50 % of the cloud pixels. There was confusion between clean ice and cloud pixels, i.e. clean ice pixels were mistakenly included in the cloud class. Clean ice was the most poorly classified, with a recall score close to 0 and F score of 0.13; one ice pixel was correctly identified, but other surfaces were confounded with ice. We attribute this to the poorly defined ice class in the model data (i.e. limited number of pure ice pixels used to extract the spectral signature). Based on these measures, we note that overall the LMM most accurately classified the water and vegetation classes, with reasonable performance for the light debris class but poor performance for clean ice and clouds. The overall accuracy of the LMM-based classification of the six surfaces was 75 %; however, this is a rather coarse metric, and it does not indicate the specific performance of the model for each class, so we do not use this here as evaluation of the accuracy.

The sensitivity analysis of the pond areas obtained from LMM fractional maps with various thresholds (Table 3) indicates that there was up to 40 % variability in total pond area when compared to Pléiades-based ponds, depending on the glacier. A threshold of 0.5 applied to the water class (fractional water >0.5= supraglacial ponds) yielded the best agreement with the total pond areas for the seven glaciers, obtained from OBIA mapping on the Pléiades image (1.0 km2 compared to 1.1 km2 for the total coverage, respectively, or a 9 % difference) (Table 4). For the Khumbu Glacier, LMM with a threshold of 0.5 yielded a pond area of 0.20 km2 versus 0.23 km2 from Pléiades (Table 4), which is in agreement with the area reported by Watson et al. (2017b) (0.24 km2) using the same Pléiades image (7 October 2015).

In the Lahaul–Spiti region, for the seven glaciers we investigated, LMM yielded a total pond area of 0.14 km2 (0.31 % of the total debris-covered area of the glaciers). The area mapped from PlanetScope image from the same date (19 October 2016) using OBIA yielded 0.10 km2 (0.22 % of the debris-covered area) (Table 4).

In the Langtang region, for the six glaciers investigated in Steiner et al. (2019), our LMM-derived pond areas yielded a total of 0.17 km2 pond area (0.64 % of the debris-covered area). Steiner et al. (2019) obtained a total pond area of 0.21 km2 (0.86 % of the debris-covered area) for the same glaciers based on manual digitization by multiple analysts from SPOT7 data for the same date as the Landsat. LMM underestimated the pond area by 0.05 km2 (19 %), which is within the uncertainty range (21 %) reported for the ponds in the Langtang area by Steiner et al. (2019).

Visually, in the Khumbu region, the spectrally unmixed pond pixels correspond well with the validation dataset (Fig. 6a and b), although there is a difference in the representation of the pond surfaces due to the spatial resolution (30 m Landsat vs. 2 m Pléiades). Similarly, in the Lahaul–Spiti region, locations of the supraglacial ponds correspond well between LMM and PlanetScope on Bara Shigri Glacier (Fig. 6c), but the small ponds are not identified using the water threshold of 0.5, which assumes that more than 50 % of the pixel area is covered by water.

While supraglacial ponds are the focus of this study, we mention that LMMs can also be parameterized to map other lakes, by masking the debris-covered glacier areas and replacing the turbid water endmember with the clear water endmember, which has a lower spectral signature (Fig. 4a). This is beyond the purpose of this study, but we provide an illustration of such an output for the terminus of Ngozumpa Glacier in Fig. 7. We present the ponds and lakes on the debris cover and outside it for comparison with two existing glacial lake databases constructed from the same year (2015 Landsat): the HMA v.1 lake dataset, derived using a normalized difference water index (Shugar et al., 2020), and HI-MAG constructed using a modified NDWI and manual corrections (Chen et al., 2021). A comparison with other global databases such as the Global Surface Water dataset (Pekel et al., 2016) was not undertaken here, as this has already been shown to underestimate the water occurrence over most of the Himalaya by Chen et al. (2021). With regards to HMA v.1 and HI-MAG datasets, Fig. 7 shows that the lake outlines obtained from spectral unmixing for the supra-glacier ponds at the terminus of Ngozumpa Glacier and the Gokyo Lakes outside the glaciers are outperforming both of the existing databases in this area. Our lake extents are consistent with the HMA v.1 lake extents outside debris cover (Fig. 7), and the surface area estimates agree quite well; for example, we calculated a difference of 5 % in the summed pond area over the three Gokyo Lakes (1.15 km2 in our estimates vs. 1.09 km2 in HMA v.1). The slight underestimate in the latter is due to simplification of the raster edges in the vector conversion process, visible in the lake extents. With regards to supraglacial ponds, for example Spillway Lake at the terminus of Ngozumpa Glacier, our spectral unmixing technique maps most of these lakes, while both HMA v.1 and the HI-MAG datasets fail to detect all the supraglacial ponds. The HI-MAG detects more of the surface of Spillway Lake compared to HMA v.1, but the outlines are simplified and lack precision with respect to Landsat pixels (Fig. 7). We did not simplify the lake and pond polygons, as this can introduce significant area errors.

The 408 debris-covered glacier tongues selected from the SDC dataset for the in-depth analysis (Sect. 2.7) ranged in area from 1 to 37 km2, with an average area of 3.9 km2 and a mean slope of 12.7∘. The supraglacial pond and vegetation coverage of these glaciers shows heterogeneous patterns (Fig. 11a and b). Both supraglacial ponds and vegetation cover a relatively small percent of the debris-covered glacier areas in the western Himalaya (0 % to 2.5 %) compared to the central and eastern parts. We note some clusters of higher percentage occurrence of both ponds and vegetation in these two regions (7.5 %–10 % for ponds and 20 %–40 % for vegetation, respectively) (Fig. 11a and b). The glacier-by-glacier analysis of pond coverage with respect to minimum debris-covered glacier elevation did not yield a clear trend, suggesting that ponds do not occur necessarily on glaciers situated at lower altitudes. Similarly, supraglacial vegetation coverage did not display significant dependencies on either average slope or minimum elevation of the debris-covered tongues.

The analysis of pond coverage per 100 m elevation bands over the entire range, however, shows clearer patterns than the glacier-by-glacier results: 77 % of the pond area coverage occurs within 10 % elevation from the glacier termini, and then pond density decreases exponentially towards the upper part of the debris-covered tongues (0.1 % of pond coverage at 75 % elevation upwards from the termini) (Fig. 12a). We note from Fig. 12a that the largest concentration of ponds does not occur directly at the glacier termini but rather within 2 % of the elevation from the terminus, i.e. within 100 m above the minimum elevation. The exponential fit shown in Fig. 12a could have useful predictive power but misses the peak pond coverage that is typically found near the glacier terminus, where ponds coalesce into large terminal lakes. This implies that the exponential fit is useful for capturing the ponds perched found above the terminus on thicker ice but likely does not capture the water level representing the hydrological base level in the depressions found in thinner ice at the terminus (Benn et al., 2012; Miles et al., 2017a).

The analysis of pond incidence with regards to slope (Fig. 12b) shows that 38 % of the total pond area occurs on 0 to 10∘ slope bins, with the maximum pond area coverage found at slope bins averaging 4 to 6∘ (9 % of the pond area). The pond incidence increases initially and then drops on slopes >8∘ (Fig. 12b), which is to be expected because at steeper slopes meltwater can drain away (Reynolds, 2000). This is consistent with findings from a previous study (Scherler et al., 2011), which found that slope areas with gradients less than 8∘ were associated with stagnant ice at the terminus regions of debris-covered glaciers over the Himalaya. With respect to glacier aspect, we found that the maximum pond coverage occurs on slopes with an eastern orientation (22.5 to 67.5∘, 15.6 % of the pond area) and south-eastern orientation (67.5–112.5∘, 14.2 % of the pond area), with less pond incidence (∼9 %) on northern-facing slopes (Fig. 12c). Although the differences in pond incidence in the different aspect bands are only within 4 %, this seems to support the fact that southern- and eastern-facing slopes receive more insolation, thus favouring ice melt and formation of ponds.

Here we present the large-scale patterns of pond and vegetation occurrence on debris-covered glacier tongues over the Himalaya domain with respect to topo-climatic variables averaged and binned at 1×1∘ (∼111 km) (Fig. 13).

Binned supraglacial ponds and vegetation over the Himalaya domain exhibit clear spatial patterns (Fig. 13a and b). With regards to geographical location, the pond coverage in the western Himalaya is rather homogenous (ranging from 0.1 % to 1.5 % of the debris-covered areas) and is more pronounced and variable in the eastern Himalaya (2.4 % to 4.3 % of the debris-covered area) (Fig. 13a). Pond incidence exhibits a strong positive correlation with longitude (r=0.82, p<0.01) and a strong negative correlation with latitude (r=-0.72, p<0.01) (Table 7). Supraglacial vegetation incidence is less pronounced in the north-western part of the domain (Fig. 13b) and increases significantly with longitude (r=0.40, p<0.10) and decreases with latitude (r=-0.28, p<0.10) (Table 7). The surface trend analysis of pond and supraglacial vegetation incidence shows that these increase in the east–west direction at the rate of +0.23 % and +0.72 % per degree longitude, respectively.

Pond occurrence is positively correlated with average temperature (r=0.40, p<0.1) and with precipitation (r=0.53, p<0.05). Furthermore, pond occurrence is negatively correlated with glacier thickness change (r=-0.37, p<0.10) (Table 7). We did not find significant correlations of pond and vegetation occurrence with supraglacial debris cover, glacier termini elevation or average glacier velocity (Table 7). Supraglacial vegetation had a weak non-significant positive correlation with precipitation and termini elevation.

The topo-climatic conditions for the occurrence of supraglacial ponds on the surface of debris-covered glaciers have been addressed in previous studies (e.g. Sakai, 2012; Sakai and Fujita, 2010), but supraglacial vegetation and its controls have rarely been addressed. Previous studies showed that both ponds and vegetation tend to develop on stagnant, low-angle slopes of the debris-covered tongues (Sakai and Fujita, 2010; Reynolds, 2000; Quincey et al., 2007). Furthermore, we would expect to find more ponds and lakes on debris-covered glaciers situated at lower elevations, which experience increased temperature and therefore enhanced surface melt. However, our analysis on a glacier-by-glacier basis did not yield significant spatial trends in pond and vegetation occurrence with respect to these controls. This implies that at the mountain-range scale, the distribution of supraglacial features may be governed by more complex factors, such as geomorphologic, glaciologic and climatic patterns. Here we discuss the occurrence of supraglacial ponds and vegetation in light of regional topo-climatic conditions averaged over 1×1∘ cells.

A first observation is that supraglacial debris covers a larger part of the glacierized areas in the central and eastern Himalaya compared to the western extremities (Fig. 13c). Supraglacial debris decreases linearly from the south-west to north-east, and it is significantly correlated with latitude (p=0.47, p<0.05). At the same time, the elevation of the debris-covered glacier termini increases northwards towards the Tibetan Plateau (+354 m per degree latitude) and to a lesser extent from west to east (+114 m per degree longitude) (Fig. 13d, Table 7). The increasing trends in both pond and vegetation coverage towards the eastern Himalaya noted earlier (Fig. 13a, b) are consistent with the presence of lower glacier termini and higher rates of debris in the eastern part compared to the western part. Overall, debris-covered glacier tongues descend to lower elevations in the central and eastern Himalaya regions (∼3700 to 4400 m) compared to the western part (∼4700 to 4900 m). Our results show that glacier termini elevation exhibits only a very weak negative control on pond occurrence (Table 7) and a slightly larger but not significant control on vegetation coverage. It appears that the elevations at which supraglacial debris is found do not significantly influence pond occurrence vegetation growth on these tongues.

Development of supraglacial vegetation (mostly shrubs) has been noted on stagnant, thick debris-covered tongues in various areas of the world (Xie et al., 2020; Tampucci et al., 2016). Increasing trends in supraglacial vegetation in other glacierized areas such as the Alps are a consequence of climatic change (Vezzola et al., 2016). As supraglacial vegetation typically only develops on stagnant surfaces that are no longer undergoing substantial gravitational reworking, its presence may also constitute an indication of glacier inactivity and later stages of decay. The increased vegetation occurrence towards the eastern Himalaya observed in this study (Fig. 13b) coincides with a clear west-to-east pattern in negative glacier surface elevation changes based on Shean's et al. (2020) dataset (Fig. 13e). Glacier surface changes become increasingly more negative towards the east at the rate of 0.02 m per degree longitude. Spatial patterns in glacier surface thinning and the resulting mass balance is consistent with the eastward increase in both pond and vegetation incidence observed in this study. In this study, however, the direct dependence of supraglacial vegetation on glacier thinning patterns is rather weak (Table 7).

In addition, the eastward decrease in average glacier velocities (-0.2 m a-1 per degree longitude and -0.1 m a-1 per degree latitude), based on the trend analysis of 2013–2015 datasets from Dehecq et al. (2015) (Fig. 13f), shows a tendency for stagnating debris-covered glacier tongues towards the north and towards the east. Stagnant glaciers were reported for the northern parts of the central Himalaya (Scherler et al., 2011) and were attributed to topographic differences, i.e. low slope angles on the northern slopes of the range promoting development of stagnant ice. Such patterns are in contrast with more rugged, steeper terrain of the southern slopes, which favours more dynamic glacier environments (Scherler et al., 2011). The stagnating trends coupled with a higher percentage of supraglacial debris correlate with the higher incidence of vegetation towards the east (Fig. 13b), supporting the idea that debris cover of sufficient stability favours plant colonization (Fickert et al., 2007). Such patterns point to a potential transition of debris-covered glaciers in certain areas towards vegetated glaciers as noted in other studies (Fickert et al., 2007). It has been noted in recent studies that supraglacial ponds can enhance local ablation rates by up to 3 times (Brun et al., 2016; Miles et al., 2018; Irvine-Fynn et al., 2017). The slightly more negative mass balances and lower surface velocities towards the east may indicate the transition of debris-covered glaciers to inactive debris-covered glacier tongues or rock glaciers in this part of the Himalaya (Jones et al., 2019; Monnier and Kinnard, 2017).

Climate factors (i.e. higher temperatures and precipitation) induce more dynamic environments and could favour increased surface melt and pond formation (Herreid and Pellicciotti, 2020). In the case of the Himalaya, we observed a significant south-west-to-north-east decreasing trend in gridded average temperatures, with a stronger decrease in the south-to-north direction (-2.3 ∘C per degree latitude) (Fig. 13g and Table 7). Total gridded precipitation for the same month increases in the eastern direction at the rate of -0.06 mm per degree latitude and significantly decreases towards the drier, colder regions of the Tibetan Plateau with a stronger gradient northward (-0.23 mm per degree latitude) (Fig. 13h and Table 7). On the contrary, the warmer and wetter areas of the eastern Himalaya seem to favour higher pond coverage, as also suggested in other studies (Herreid and Pellicciotti, 2020). At larger scales, it has been shown that certain conditions related to topography and lithology could offset this dependency, but at the range of the Himalaya, this climatic dependency holds. Climatic conditions and glacier characteristics in the western Himalaya are more similar to those in the Karakoram, where glaciers have undergone less shrinkage (Brun et al., 2017; Kääb et al., 2012; Gardelle et al., 2013), than those in the central and eastern, monsoon-influenced parts of the Himalaya, which exhibit higher temperatures and larger precipitation amounts.

The controls on debris-covered glacier surface evolution are a complex combination of the cumulative debris-supply, mass-balance condition, debris cover expansion, stagnation and total lowering. Studies have noted that surface types are related to the evolutionary stage of a debris-covered glacier (Thompson et al., 2016), in that debris thickness variability, local topography, degree of downwasting, and glacier tongue slope are all potentially, at least partially, related to the time lapsed since debris cover formation (Sakai and Fujita, 2010; Nicholson et al., 2018). Relatedly, Herreid and Pellicciotti (2020) introduce the term of debris-covered glacier stage ranging from 0 to 1 as a percentage of the full, 2D debris cover carrying capacity of a glacier, such that if 100 % of the ablation zone is debris-covered, then the debris-covered area cannot expand further without up-glacier migration of the equilibrium line. Further analysis is needed to accurately capture the complex combination of topographic and climatic factors that contribute to the development of ponds and vegetation on supraglacial debris cover using the most recent publicly available and corrected datasets (Herreid and Pellicciotti, 2020) and a carefully quality-controlled output of the method proposed here. A full understanding of the occurrence of surface features also requires knowledge of the transient co-evolution of glacier extents and debris cover. This would allow us to quantify better the controls on pond formation and vegetation growth in specific catchments as the debris cover and glacier geometry develop over time.

Our analysis of surface composition of the debris-covered glacier tongues is subject to several limitations related to the spectral and spatial resolution of the input Landsat data. While linear spectral unmixing is a relatively straightforward routine to implement once the endmembers and their spectra are selected, using Landsat data has several limitations due to their spatial resolution and spectral dimensionality. While Landsat 8 is superior to the previous Landsat missions in terms of its calibration, geometry and radiometric resolution (Irons et al., 2012), its spectral dimensionality remains an issue, particularly with respect to mapping of the various types of debris material and/or supraglacial ponds with various degrees of turbidity. Previous studies in the Himalaya (Casey and Kääb, 2012; Casey et al., 2012; Matta et al., 2017) suggest that the spectral dimensionality of these two surfaces is greater than the dimensionality of the Landsat 8 OLI bands available for unmixing. Landsat has limited spectral resolution data (7 bands available for unmixing) compared to hyperspectral data (e.g. AVIRIS, 224 bands). Both the partially constrained and the unconstrained LMMs yielded negative abundances in our study, with larger positive values (>3) especially for the vegetation class. Since our fractions did not satisfy the sum-to-unity condition, normalization of the classes was necessary, which may have introduced further uncertainty in our results because some classes had higher positive values than others. However, previous studies showed that these negative values do not necessarily affect the ability to discriminate between surfaces (Klein and Isacks, 1999).

Limitations posed by the spatial resolution of Landsat data (30 m) affected the accuracy of the selected endmembers. While we used the pixel purity index to automate the selection of endmembers, we acknowledge that some mixture may still occur at 30 m spatial resolution. Furthermore, the 30 m spatial resolution does not allow us to detect supraglacial features such as ice cliffs or small ponds which can span only a few square metres. Improvements envisioned here include applying the spectral unmixing Sentinel-2 imagery, which has a better spectral, spatial and temporal resolution (13 bands in the visible to short-wave infrared, 10–20 m, 5 d revisit time) compared to Landsat (7 bands in the visible to short wave, 30 m, 16 d revisit time). This would allow for better definition of endmembers, facilitating more accurate and repeated mapping in the future.

Furthermore, the 30 m spatial resolution of the DEM does not allow us to infer the precise control of topographic factors such as slope and aspect on pond formation or a full quantification of the small-scale controls of pond incidence but only provides a mountain-range scale of the pond distribution.

In this study, we utilized the maximum number of endmembers (n=6) allowed by the spectral resolution of the Landsat 8 OLI data (7 bands), in an attempt to capture the variability of the system and to avoid high RMSE of the model which may occur due to missing classes. The main difficulty here consisted in capturing the wide variability of the materials present across the mountain range, for example different lithologies, while ensuring a “valid” LMM. This is defined as one where fractional values do not exceed 1.01 (under strict constraint rules) or 2.01 (under looser rules) and where RMSE is less than 2.5 % (Painter et al., 2009). Our choice of debris endmembers was limited to light and dark debris, and these may not cover the wide spectrum of lithology present across the Himalaya. With regards to the on-the-ground spectral characteristics of the debris material in the Khumbu region, Casey et al. (2012) showed that these vary due to the presence of various of minerals, notably distinct granitic (lighter) vs. schistic (darker) debris types with different compositions. However, spectral differences in these two classes can also be related to debris water content especially on very thin debris (as for thinly-debris-covered ice cliffs) and are associated with grain size, i.e. fine-grained sediments which have a greater capacity for water retention (Juen et al., 2013; Collier et al., 2014). We also noted such differences in the spectra for wet fine debris and dry coarse debris with large grain sizes on Mer de Glace (Fig. 4b); however, the limited Landsat spectral resolution implies that we could not define separate endmembers for each. Using only two endmembers for debris cannot capture the various types of debris with different mineral and geochemical composition, nor can it distinguish between debris with various degrees of water content, which has a different spectral signature compared to dry debris (Fig. 4b). Furthermore, we could not take into consideration bare illuminated non-glacierized surfaces including nunataks, which were occasionally mistakenly included within the polygons in the SDC dataset. As a result, these areas were also associated with some high positive fractional values, which might have affected the overall RMSE of our model and particularly the sum-to-unity condition.

Although we defined the water endmember on the basis of turbid water (greyish-blue ponds), supraglacial ponds of various turbidity levels are present across the mountain range, due to various degrees of suspended sediments. The colour of these ponds can range from grey to turquoise and reddish shades in various proportions (Matta et al., 2017) to small clear water supraglacial ponds (Takeuchi et al., 2012; Giardino et al., 2010), as observed in the field (Fig. 3e). Each type of pond has different spectral signatures, but the limited spectral resolution of Landsat does not allow us to use concomitantly both a clear and a variable turbid water endmember in the spectral unmixing. Nevertheless, as shown in Fig. 7, the majority of the turbid supraglacial ponds are connected to the exposed ice and glacier drainage network (hence larger suspended sediment), are expected to be most relevant to glacier evolution and may be of concern for outburst flood potential. Our algorithm parameterized for clear water nicely picks out the small number of isolated non-turbid ponds at the terminus of the Ngozumpa Glacier (Fig. 7), highlighting the success of different endmember selection for addressing other scientific questions. With further testing, fractional water maps obtained from spectral unmixing techniques can be used to characterize the state of lakes and ponds in terms of their turbidity (Matta et al., 2017; Giardino et al., 2010), i.e. by quantifying the fraction of a pixel covered by water, light and/or dark debris. In this regard, repeated monitoring of pond turbidity using these combined tools allows changes in suspended sediment load to be tracked over time, as direct indicators of glacier wasting processes and glacier–lake interaction (Giardino et al., 2010). This aspect is not fully explored in this study but can be further investigated by combining LMMs with field spectra of ponds and lakes to characterize the various degrees of turbidity across the mountain range. Since lake turbidity is temporally highly variable and since our current dataset is a snapshot of pond density, it cannot be used to infer any variability in sediment concentration, but it provides the basis for tracking changes in glacier area for further applications.

Similarly, we could not define a healthy vegetation endmember whose spectral signature (not shown here) differs from that of the dry vegetation endmember we selected. However, small amounts of healthy vegetation do occur on debris-covered glaciers in the eastern part of the Khumbu region, and these were indeed detected by the LMM (Fig. 10).

The cloud and clean ice detection based on LMM was not accurate in this particular configuration. While some isolated pixels were classified as clouds, others pixels were confounded with other types of surfaces, notably debris (Table 2). While the cloud distribution noted in this study corresponds to local meteorology, i.e. more frequent cloud cover in the eastern Himalaya until later fall months compared to the western part (Thayyen and Gergan, 2010), we are less confident in the actual estimations of the cloud cover areas, so we do not wish to over-interpret these. Applying algorithms such as Fmask (Zhu et al., 2015) to mask the clouds resulted in misclassification of the entire glacierized surface as cloud, which is a well-documented issue (Stillinger et al., 2019), so we could not mask the clouds prior to the spectral unmixing.

Likewise, clean ice was poorly classified, mostly likely due to its poor representation in the dataset (i.e. limited number of clean ice pure pixels). While our results hint at the presence of ice to some extent, we are not confident about these results. Some pixels correspond indeed to location of ice cliffs which were perhaps exposed at the end of the ablation season (Fig. 9); others correspond mostly to clean ice patches at the upper limit of supraglacial debris included in the input data, which dated from previous years, or seasonal snow. While we chose our images at the end of the ablation season, post-monsoon snow cover is usually minimal, but early snowfalls can occur. Other features such as the ice sails (Evatt et al., 2017) may not be extracted at the spatial resolution of the Landsat imagery, since these features often span only several square metres. At the same time, the LMM algorithm in its current parameterization cannot detect ice cliffs dusted with fine debris, which have a lower albedo than clean ice (Naegeli et al., 2015). Targeting exposed but dusted ice features within the debris cover in addition to clean ice would need some refinement of the algorithm using Sentinel-2 imagery with better spectral resolution and better parameterization (Kneib et al., 2020), optical thresholding of band ratios using high-resolution imagery (Anderson et al., 2021) and/or feature detection based on OBIA (Kraaijenbrink et al., 2016; Watson et al., 2017a; Mölg et al., 2019).

Selection of the thresholds used to classify the fractional maps to obtain the final maps of each surface is another source of uncertainty in our method. Previous spectral unmixing studies (Hall et al., 2002; Rittger et al., 2013) justified using a threshold of 0.5 for the classifying fractional maps for various types of surfaces, while they also tested thresholds as low as 0.15 (Rittger et al., 2013). While we applied a threshold of 0.5 and 0.65 to our water and vegetation classes, respectively, for the other classes the fractional thresholds were ultimately determined using visual inspection, which introduced a certain degree of subjectivity into our study.

Due to the spectral limitations of Landsat, in this study we applied the unmixing only to the debris-covered areas of glaciers to reduce model complexity. Therefore, model performance is to some extent subject to the quality of the input dataset. At the onset of our study, the only global database of supraglacial debris was the SDC dataset (Scherler et al., 2018), and although Herreid and Pellicciotti (2020) provide updated supraglacial debris outlines, these were not available at the onset of our study and are not currently incorporated in the standardized RGI dataset. Debris outlines in the SDC dataset constitute a multi-time stamp dataset, based on data spanning 1998 to 2015, while our Landsat data were based primarily on 2015. This may introduce uncertainties in the calculation of pond coverage. For example, we assumed that any changes at the termini of the debris-covered areas would have occurred within these older outlines, since surge-type glaciers and hence apparent glacier advance are rare or non-existent in the Himalaya region, contrary to the Karakoram (Sevestre and Benn, 2015). However, recent studies have reported an upward expansion of the debris cover in the Himalaya (Xie et al., 2020; Thakuri et al., 2014; Bhambri et al., 2011b; Kamp et al., 2011), which we do not account for here. As such, in these areas, our pond density may be underestimated, and this would need a more in-depth analysis requiring the use of multi-temporal supraglacial debris datasets. Furthermore, our study revealed some important issues with the input SDC dataset used to constrain the spectral unmixing, particularly the inclusion of patches of healthy vegetation and bare bright steep terrain. The spurious vegetated areas present within the debris cover outlines (Fig. 10b) may have affected to some extent the quality of the spectral unmixing, i.e. the non-negativity and the sum-to-unity conditions, because it produced large negative and positive fractional vegetation values. We were able to identify theses as being healthy vegetation on non-glacierized terrain. On the other hand, some of the high percentage of supraglacial vegetation in some of the eastern parts is attributed to errors in the input supraglacial dataset, and we are hesitant to over-interpret the vegetation analysis. However, we note the potential of the fractional vegetation maps for identifying mapping errors in the SDC dataset. Because these abnormal values served to identify errors in the existing SDC dataset, they constitute a valuable tool to correct and refine these global databases.

In this study we demonstrated the transferability of a method developed on a single region for the year 2015 (Khumbu) by applying it to a Landsat 8 OLI scene from a different area (Lahaul–Spiti) for the same season (post-monsoonal) but a different year (2016) and validating the ponds with PlanetScope data. In the light of the spatial and spectral limitations of Landsat data discussed above, the applicability of our approach for multitemporal analyses requires careful considerations. When transferring methods from one scene to others, illumination differences and shadow effects across the scenes need to be resolved, particularly if the scenes are not acquired on the same date. In this study, we attempted to minimize these effects by applying atmospheric and topographic corrections and implicitly assumed that the set of endmembers defined for the Khumbu region could be applied to the entire Himalaya. However, in some areas, some spectral differences may remain, leading to confusion between the water/light debris/ice classes and hence some overestimation of the pond coverage, particularly in some areas of the western Himalaya. While these pond areas require further quality control prior to their inclusion in regional datasets, they are within the uncertainties reported at other sites, for example the Langtang region (Steiner et al., 2019). Furthermore, if the approach is used over the same area for multi-temporal pond or vegetation analysis, the geolocation accuracy of the Landsat can be a concern, because the pixels can be slightly misaligned from acquisition to acquisition, resulting in potentially very different compositions and unmixing results. This needs to be mitigated by co-registration of the scenes prior to unmixing and performing the change analysis. Further uncertainty is introduced in our study by the fact that for certain areas of the Himalaya, Landsat cloud-free and snow-free scenes were not available for the year 2015, and we used scenes from 2014 and 2016 (see Table 1). We assumed that surface conditions were similar but acknowledge that pond areas are dynamic and can change from year to year. Furthermore, this study does not account for the seasonality of supraglacial ponds but provides a methodological basis for their identification.