In this study we analyze the results of our classification algorithm using a suite of 40 Landsat Thematic Mapper (TM), ETM+ and Optical Land Imager (OLI) images (1998–2013) across a spatially and topographically diverse set of study sites comprising eight Landsat footprints (Path/Row combinations: 144/30, 145/30, 147/31, 148/31, 149/31, 151/33, 152/32, 153/33) along a ∼ 1500 km profile from the central Pamir to the central and central-eastern Tien Shan (Fig. , Table 1).

The study area contains a wide range of glacier types and elevations, with both small and clean-ice-dominated glaciers, as well as large, low-slope, and debris-covered glaciers. The diversity in glacier types in the region provides an ideal test area – particularly in mapping glaciers with long and irregular debris tongues, such as the Inylchek and Tomur glaciers in the central Tien Shan .

The wintertime climate of the study area is controlled by both the winter westerly disturbances and the Siberian High, which dominate regional circulation and create strong precipitation gradients throughout the range, which extends from Uzbekistan in the west through China in the east (Fig. ) . The western edges of the region tend to receive more winter precipitation in the form of snow, with precipitation concentrated in the spring and summer in the central and eastern reaches of the range .

Our glacier mapping algorithm is based on several data sets. The Landsat 5 (TM), 7 (ETM+), and 8 (OLI) platforms were chosen as the primary spectral data sources, as they provide spatially and temporally extensive coverage of the study area (Table 1). ASTER can also be used as a source of spectral information, but here we chose to focus on the larger footprint and longer time series available through the Landsat archive. In addition to spectral data, the 2000 Shuttle Radar Topography Mission V4.1 (SRTM) digital elevation model (DEM) (∼ 90 m, void-filled) was leveraged to provide elevation and slope information . The SRTM data and its derivatives were downsampled to 30 m to match the resolution of the Landsat images using bilinear resampling. The USGS HydroSHEDS (Hydrological data and maps based on SHuttle Elevation Derivatives at multiple Scales) river network (15 s resolution, ∼ 500 m) was also used as an input data set .

For accurate glacier delineation, we primarily used Landsat images which were free of new snow, and had less than 10 % cloud cover. However, we have also included scenes with limited snow and cloud cover in our analysis to understand their impacts on our classification algorithm. We find that the presence of fresh snow in images tends to overclassify glacier areas and classify non-permanent snow as glaciers. Additionally, cloud-covered glaciers cannot be correctly mapped by the algorithm . We use the USGS Level 1T orthorectified Landsat scenes to ensure that the derived glacier outlines are consistent in space .

The algorithm uses Landsat imagery, a void-filled DEM, a velocity surface derived from image cross-correlation, and the HydroSHEDS 15 arcsec river network (buffered by 200 m and converted to a raster) as the primary inputs (steps 1a, 1b). The algorithm generates a slope image from the DEM and rectifies additional input data sets described below for processing by resampling and reprojecting each data set to the same spatial extent and resolution (30 m to match the Landsat data) (steps 1d, 1e). Although the current algorithm leverages a few proprietary Matlab commands, we will continue to update the code with the goal of using only open-source tools and libraries in the future.

Calculations are performed on rasterized versions of each input data set, which have been standardized to the same matrix size. The first step in the classification process leverages Landsat 7 bands 1, 3, and 5 (Step 2a). For Landsat 8 OLI images, a slightly different set of bands is used to conform to OLI's modified spectral range. For simplicity, bands referenced in this publication refer to Landsat 7 ETM+ spectral ranges. The ratio of TM3 / TM5 (value ≥ 2), with additional spectral information from TM1 (value > 25) has been used in previous research as an effective means of delineating glacier areas e.g., but is not effective in delineating debris-covered glacier areas (Fig. a). In our algorithm, we use a threshold of TM3 / TM5 ≥ 2 and TM1 > 60 to map clean glacier ice. While these thresholds perform well over many scenes, using thresholds which are not tuned to specific scene conditions can generate large errors, particularly in shadowed areas . Here we choose fairly conservative threshold values to ensure that we do not remove clean glacier ice. We find that increasing the TM1 threshold results in tighter classification of debris-covered glacier tongues but also removes some areas properly classified as glacier, particularly in steep areas of the accumulation zone. Thus, we err on the side of overclassification with our delineation of clean glacier ice. The end result of this step is the spectrally derived (clean-ice) glacier outlines, which are later integrated back into the workflow before statistical filtering (Fig. a).

Manual control data sets encompassing ∼ 750 glaciers (∼ 11 000 km2) were created to test the efficacy of the glacier mapping algorithm. These data sets were digitized from Landsat imagery in a GIS and then corrected with higher-resolution imagery in Google Earth. The data sets are coherent in space but cover two different times (∼ 2000 and ∼ 2011, depending on the dates of the available Landsat scenes). The bulk of the manually digitized glaciers fall within the boundary of Landsat Path/Row combination 147/031, as this is the most heavily glacierized subregion of our study area. However, we have digitized glaciers throughout the eight Path-Row combinations to avoid biasing our statistics and algorithm to one specific scene extent. We have also considered a wide range of size classes in our manual data set (<0.5 km2 to 500+ km2), as well as both clean-ice and debris-covered glaciers. We note that although the manual data sets here are considered “perfect”, there is inherent error in any manual digitization in a GIS e.g.,. Due to the lack of ground truth information, we have estimated the overall uncertainty of the manual data set to be 2 % based on previous experiments . Figure  shows the size–class distribution of the manual control data set, with logarithmic area scaling.

Before any comparisons between glaciers can be performed, glacier complexes must be split into component parts. A set of manually edited watershed boundaries, derived from the SRTM DEM, were used to split both the manual and algorithm data sets into individual glacier areas for analysis. In this way, the diverse data sets and classified glacier areas can be split into the same subset areas for statistical comparison.

A subset of 215 glaciers from the manual control data sets of varying size and topographic setting was chosen for more detailed analysis. The unedited, algorithm-generated glacier outlines were compared against spectral outlines, which only classify the glacier areas via commonly used spectral subsetting (using TM1, TM3, and TM5, produced in Step 2b), the manual control data sets, and the CGI v2. Figure a shows the bulk elevation distributions across 215 glaciers for each data set in 10 m elevation bins.

There is some apparent bias in our algorithm towards low-elevation areas, which represent the debris-covered portions of glaciers and are the most difficult areas to classify. This bias also stems from misclassified areas in shadows, particularly in north-facing glaciers. There is also a bias in our control data set towards underclassifying the high-elevation areas, which we attribute to user bias in removing isolated rock outcrops within glaciers, as opposed to simply defining accumulation areas as a single polygon. In general, the algorithm and the control data set are well-matched below 4000 m; above this, the spectral data set and the algorithm data set begin to align closely and generally follow the manually digitized data. This threshold represents the general transition from debris-covered glaciers to clean glacier ice in the study area. Our algorithm output is also well-matched with the CGI v2, except at very high elevations where it overclassifies some areas as compared to the CGI v2.

In order to examine inherent bias throughout the algorithm classification, under- and overclassified areas were examined for a subset of the control data set. To determine areas of overclassification (underclassification), the manually (algorithm) generated data set was subtracted from the algorithm (manual) data set, leaving only pixels that were overclassified (underclassified). Figure b shows the elevation distributions of under- and overclassified areas. The algorithm tends to consistently overclassify areas across the range of glacier elevations, which we attribute here to differences in manual and algorithm treatment of steep and de-glacierized areas within glacier accumulation zones. Importantly, the algorithm underclassifies a much smaller number of pixels, generally corresponding to areas below 4000 m, where debris tongues are dominant. The majority of these pixels are along the edges of debris-covered glacier tongues, which are removed by the algorithm due to their low relative velocity. It is also possible that some of these pixels are “dead ice”, which is difficult to differentiate from debris tongues by visual inspection. The total misclassification of algorithm-derived outlines against two independent manual control data sets is 2 and 10 % respectively, which represents a significant improvement from a pure spectral delineation approach.

To investigate sampling bias in our analysis, we used 465 GLIMS glacier identification numbers (centroids, point features) that overlapped with the manual control data sets. A random subset of 100 of these points was chosen for this analysis. As can be seen in Fig. c, similar patterns emerge between the randomly sampled glaciers and the sampling used in other sections of this paper. There is evidence of more noise in the random sample, as some glaciers which we avoided due to closeness to wet sand/or other hard-to-classify areas were chosen during the random sampling. However, the relationship between the algorithm and the manual data sets remains significant (Kolmogorov–Smirnov test passes at 99 % confidence interval).

To capture changes in the shape of the glacier outlines between the initial spectral classification and the final algorithm output, we computed the distance between pairs of glacier vertices. We first reduced our manual control data set to a set of X/Y pairs for each component vertex, which were then matched to the closest vertex in the resulting spectral and final algorithm polygons, respectively (Fig. ).

The distance distribution for the algorithm data set shows generally close agreement between the algorithm and manual control data sets. The spectral data set also contains a large percentage of vertices close to a 1:1 agreement with the manual control data set, which are primarily the vertices at the upper edges of glaciers or from small, debris-free glaciers. The difference in these two distributions is attributed to the increased precision with which the algorithm maps debris-covered glacier outlines. Both data sets were normalized by their whole-data-set maximum distances.

Several authors have presented alternative debris-covered glacier classification methods and schemes using thermal and spectral data , topographic and neighborhood analysis , clustering of optical and thermal data , maximum likelihood classification , slope and curvature clustering combined with thermal data , decision tree classification and texture analysis, and object-based classifications . While all of these methods present improvements over basic clean-ice delineation as proposed by , they each have shortcomings that limit their range of use. Table 2 shows a comparison of these different methods alongside the algorithm presented in this study.

Our study improves on previous work in three main ways: (1) reduced computational intensity, (2) greater diversity of study area, and (3) increased temporal range of our data set. The methods proposed in this study, excepting the generation of a velocity field, require very little processing power. Once initial input data sets (velocity surface, rasterized river network) have been created, a Landsat scene can be processed in 3–5 min (Ubuntu 14.04, 8 cores (3.6 GhZ), 16 GB RAM). When this is compared with the training data set creation, computationally expensive classification schemes, and neighborhood analyses employed by other studies, there is a clear improvement in efficiency. Secondly, we analyze a significantly larger glacier area than any of the previous studies, which has helped us generalize our algorithm and methods to a wide range of topographic and land cover settings. Finally, we process a multi-year data set, encompassing 40 Landsat scenes with varying land cover and meteorological settings. This has allowed us to further generalize our algorithm to be effective beyond a single scene or small set of scenes, and to remain effective across a wide spatial and temporal range. The time-dynamic aspect of our algorithm can also complement time-static wide-area data sets, such as the RGI v4.0, the CGI v2, and the forthcoming GAMDAM data sets . While these data sets may provide higher-quality manually digitized outlines for specific glaciers, they only provide a single snapshot in time and are limited to a specific area of coverage.

Two additional topographic indices – spatial fast Fourier transforms (FFTs), also known as 2-D FFTs, and ASTER surface roughness measurements – were tested during the development of the algorithm, although neither provided significant improvement. We attempted to derive frequential information from several Landsat and ASTER bands, with limited success. Some glaciers exhibit a unique frequency signature when analyzed using spatial FFTs, although these were not consistent across multiple debris-covered glaciers with differing surface characteristics. Additionally, the FFT approach was tested against a principal component analysis (PCA) image derived from all Landsat bands, without significant improvement to the algorithm.

We also attempted to integrate surface roughness measurements using the ASTER satellite, which contains both forward looking (3N – nadir) and backwards looking (3B – backwards) images, primarily intended for the generation of stereoscopic DEMs. The difference in imaging angle provides the opportunity to examine surface roughness by examining changes in shadowed areas . We found that there are slight surface roughness differences between terrain on and off glaciers; however, these differences are not significant enough to use as a thresholding metric. Furthermore, the nature of the steep topography limits the efficacy of this method, as valleys which lie parallel the satellite flight path and those which lie perpendicular to the flight path show different results. Thus, the algorithm relies on the velocity and slope thresholds to characterize the topography of the glacier areas.

The glacier outlines provided by the algorithm are a useful first-pass analysis of glacier area. It is often more efficient to digitize only misclassified areas, as opposed to digitizing entire glacier areas by hand . also note that for clean ice, automatically derived glacier outlines tend to be more accurate, and it is only in the more difficult debris-covered and shadowed areas that manual digitization becomes preferable. In the algorithm presented here, clean-ice thresholding was implemented using TM1, TM3, and TM5. However, because the algorithm operates primarily on “potential debris areas”, any clean-ice classification scheme could be used. For example, in other study regions or for different satellite sensors, other schemes, such as the normalized difference snow index , may outperform clean-ice classification as implemented in this study.

The algorithm moves a step further than spectral-only classification and attempts to classify glacier areas as accurately as possible, including debris-covered areas. As can be seen in Fig. , the algorithm compares well with both the control data set and the CGI v2 – a high-fidelity, manually edited, data set – across a range of glacier types (Step 2a) . However, the algorithm outlines do not perfectly align with either data set. In Fig. , a tendency to remove pixels along the edge of debris-covered glacier tongues can be observed, which we attribute to the fact that the center of debris tongues often move faster than the edges. Furthermore, both the algorithm results and the manual control data set underestimate glacier area as compared to the CGI v2, due to the removal of non-clean-ice pixels at high altitudes or high slopes, which are generally within the accumulation area of a glacier but are not always covered by permanent ice. These two types of classification bias are easily rectified with minimal manual intervention. Some biases between the manual or algorithm data sets and the CGI v2 can also be attributed to the difference in time; while the manual and algorithm data sets share an image date, the CGI v2 was digitized on top of multiple images that may not match up perfectly in time with our data sets. Despite these misclassified areas, the raw algorithm output effectively identifies the furthest reaches of the glacier tongues in most cases, as can be seen in three long debris tongues shown in Fig. .

Without post-processing, these raw glacier outlines can be used to analyze regional glacier characteristics, such as slope, aspect, and hypsometry. Even if glacier outlines are not perfectly rectified in space, at the scale of watersheds, satellite image footprints, or mountain ranges, errors of under- and overclassification even out, yielding valuable regional statistics (Fig. a). As the method can be easily modified to fit the topographic and glacier setting of any region, it is a powerful tool for analyzing glacier changes over large scales for the period of Landsat TM, ETM+ and OLI coverage. While the algorithm has yet to be applied to large and slow-moving debris-covered glaciers in the Himalaya, a wide range of glacier size classes, speeds, and topographic settings are well-classified by the algorithm. For example, even small glacier changes are captured by the algorithm, as can be seen in Fig. .

Figure  also illustrates some potential errors in the algorithm where river sand is sometimes delineated as glacier area. In many cases, the same areas are captured across different time periods, as the topographic and velocity data used to define “potential debris areas” are mostly static in time, excepting the distance-weighting steps. However, these areas are easily removed during manual inspection of results.

The second use case for the algorithm is as a substitute for simple spectral ratios. Manual digitization of glacier tongues is time consuming, particularly in regions with numerous debris-covered glaciers. Our algorithm provides a robust baseline set of glacier outlines that can be corrected manually, with minimal extra processing time. As generating the input velocity surfaces can take longer than processing glacier outlines from dozens of Landsat scenes, efficiencies are gained when Landsat scenes are processed in bulk. The algorithm as presented in this paper takes ∼ 3–5 min of actual processing time once the base data sets have been created. For a single Path/Row combination, the time to set up the input data sets (velocity surface, manual debris points) is ∼ 4 h. Once the initial setup has been completed for a given Path/Row combination, any number of Landsat scenes can be processed very quickly.

Although the algorithm represents a step forward in semi-automated glacier classification, there are several important caveats to keep in mind. (1) Lack of data density and temporal range limits the efficacy of individual glacier analysis; the algorithm presented in this paper was not designed with individual glacier studies in mind, and in many cases, such as in mass balance studies, more accurate manual glacier outlines are necessary. Furthermore, (2) the algorithm relies on manual intervention to separate individual glaciers which are connected through overlapping classified areas or which are part of glacier complexes. Finally, (3) the algorithm relies heavily on the fidelity of the Landsat images provided, in that glacier outlines on images with cloud or snow cover are less likely to be well-defined. This creates a data limitation, as many glacierized areas are subject to frequent cloud and snow cover and thus have a limited number of potentially useful Landsat images for the purpose of this algorithm.