This study had strict requirements for glacier outlines, and therefore, all glacier complexes were divided into individual glaciers prior to the centerline extraction. However, because of the limited semi-automatic glacier segmentation approach (Kienholz et al., 2013) and the high-priority strategy of completeness of coverage adopted by RGI v6.0 (RGI Consortium, 2017), some glaciers were not supported by our algorithm. These unsupported glaciers included three categories, namely glacier complexes with/without inaccurate segmentation (Fig. 3a–b), erroneous glacier outlines (Fig. 3c) resulting from the vectorization, and flawed glaciers (Fig. 3d–f) generated by the automatic extraction algorithm. For the third category, we designed an identification algorithm to mark and screen them (described in the last paragraph of this section). The flaws in these glacier outlines were mainly caused by topological errors of polylines/polygons, such as unclosed, sawtooth, and overlapping polygons. The first two categories did not affect the algorithm's normal operation; however, the extraction accuracy is not always guaranteed. We could not identify the source of the problem at the time of the study, and a solution is needed to improve the quality of the global glacier inventory.

In this study, we defined the external contour of a glacier (Pgec), namely the polygon corresponding to the longest closed polyline of the glacier, to reduce the storage of DEMs and improve the efficiency of batch processing. The buffer masks of all glaciers (buffer distance of approximately 100 m) were generated by their Pgec to meet the requirement for the extent of input DEMs to be slightly larger than the Pgec. The buffer masks generated initially were partially broken because there were overlaps or gaps between adjacent polygons of the buffer zone; thus, polygons with a perimeter of less than 12 times the buffer mask distances of each region were removed.

The third category of flawed glaciers (Fig. 3d–f) was identified by obtaining Pgec. The most common error type was a glacier outline with two or more closed polylines with the same endpoint. These flawed glacier outlines were identified by assessing whether there were multiple polylines sharing endpoints after converting the glacier from a polygon to a polyline. However, these outlines did not include the unclosed types. There were a few glacier outlines that appeared to be closed polylines but had geometric flaws such as non-coinciding head and tail endpoints of the polylines.

All the data associated with the dataset production were processed in units of first-order glacier regions. The input glacier outlines excluded all the defective glacier outlines. Similarly, the nominal glaciers (represented by an ellipse) and ice caps remarked in RGI v6.0 were also treated, which were distinguished by two attributes, i.e., status (nominal glacier) and form (ice cap). The inspection of glacier outlines show that there are 10 764 defective glacier outlines (FGODS) in RGI v6.0, accounting for approximately 4.97 % of the total (216 502; Table 2). After excluding nominal glaciers (461) and ice caps (7174), 198 646 glaciers remained as input glacier outlines (IGODS), accounting for 91.75 % of the global mountain glaciers.

The Pgec of all glaciers in RGI v6.0 comprises the global glacier external contour dataset (GGECDS), which generated the global mountain glacier's buffer mask dataset (GGBMDS). The collected DEMs were extracted using GGBMDS, and 43 035 DEM tiles were generated. They were then mosaicked according to different first-order glacier regions to generate a global glacier elevation dataset (GGEDS). The details of the two input datasets are presented in Table 2.

Glacier centerlines and lengths were automatically extracted with the GlacierCenterlines_Py27 (update to version 5.2.1) tool, which is based on the axis concept and Euclidean allocation (Zhang et al., 2021). The principle is briefly explained as follows: the highest and lowest points of the external outline of a glacier were extracted as two endpoints that divide the glacier outline into two parts. In the glacier polygon, points that have the equal shortest distances to the two parts were identified as other vertices. The line formed by two endpoints and these other vertices was regarded as the glacier centerline. The maximum length of glaciers was calculated using an algorithm similar to the critical path. The updated contents focused on formulating the parameterization scheme (Appendix A; Table A1) for extracting global glacier centerlines and repairing some newly discovered bugs, such as a dead cycle in the process of auxiliary line extraction. All glacier outlines included in the IGODS were divided into 10 levels based on the proportion of cumulative area after ranking the area of all input glacier polygons from small to large (Table 3). The Albers projection (see the Supplement for detailed parameter files) with WGS1984 was used as a unified projection coordinate system for each glacier region. The empirical values of the other parameters were determined in repeated attempts, and their values were significantly correlated with the glacier scale. The generated glacier centerlines were merged according to the glacier regions. Then, the graphics and attribute information of glacier length were exported as corresponding independent Esri shapefiles. In addition, other data associated with the dataset production were exported, such as the segmentation results of glacier outlines, the lengths in the accumulation and ablation region of each glacier, the lowest points, the local highest points (Pmax), the extracted failed glacier outlines, and logs.

A random assessment was prioritized to assess the accuracy of the extracted centerlines. We randomly selected 100 glaciers in each of the 19 glacier regions, obtaining a total of 1900 glacier centerlines. These glacier centerlines were divided into three first-level categories (Zhang et al., 2021), namely correct (I), inaccurate (II), and incorrect (III). Type II mostly contained glaciers with accurate glacier maximum lengths but missing, redundant, or unreasonable branches of glacier centerlines. When calculating the dataset accuracy, types I and II were regarded as correct, and only type III was considered incorrect. Finally, the proportion of type III glaciers in the sample was counted, and the valuation result (R) was calculated using Eq. (1): 1R=∑i=119Si×NTiNG, where NG is the total number of glacier centerlines, and Si and NTi are the verification accuracy and the number of glaciers in the ith glacier region (i=1, 2, 3, …, 18, 19), respectively.

This study's maximum glacier lengths (GLmax) were compared with the Lmax (Machguth and Huss, 2014) in RGI v6.0 using linear correlation and ratio analysis. The correlations between GLmax and Lmax were established according to different glacier regions and glacier levels, and the length ratio Rr (Eq. 2) was calculated as follows: 2Rr=GLmax⁡Lmax⁡. In addition, considering the differences between the graphics, we also collected the graph data of the glacier length extracted by Machguth and Huss (2014). Considering the limited availability of the data (obtained R13–R15), we only compared two glacier-covered regions in the Himalayas, namely Mount Qomolangma and Kangchenjunga (the world's third-highest mountain) and their surrounding areas.

The evaluation results using random samples from the glacier centerline dataset suggested that the average verification accuracy of the glacier centerline dataset was 89.68 %. There were significant differences across the accuracies of the 19 glacier regions around the world (Fig. 5). Among them, R11, R15 and R10, R09, and R19 had the highest (98 %), second highest (95 %), second lowest (78 %), and lowest (50 %) accuracies, respectively. In terms of types, the average proportions of types I and II were 83.53 % and 6.16 %, respectively. The proportions of type I in R07 and R09 were relatively low, at 79 % and 73 %, respectively, and the lowest in R19 was only 50 %. Type II had the highest proportion in R19 at 16 %, followed by R07 (10 %). Moreover, type II accounted for more than 5 % in seven regions, including R11, R13, R17, R18, R16, R01, and R06.

The above results indicate that, in addition to the three glacier regions of R07, R09, and R19, the random samples of the glacier centerline dataset show excellent performance in terms of accuracy, particularly in R02, R12, and R14. The unmarked ice cap and local low-quality DEM were the main reasons for the poor quality of the glacier centerlines in R07 and R09. Owing to glacier complexes and low-altitude differences in low-quality DEMs at the glacier tongues, the glacier centerlines obtained in R19 were of poor quality but were included for completeness.

We compared the glacier lengths (GLmax) automatically obtained in this study with those (Lmax) obtained by Machguth and Huss (2014; Fig. 6). After eliminating 5408 glaciers with the Lmax value of -9 (missing value), the length values of the other 192 728 glaciers in the global glacier length dataset were compared directly. The GLmax and Lmax were generally comparable (Fig. 6a). The glaciers in grades L4–L10 showed excellent agreement, while those of L1–L3 determined the linear correlation coefficient owing to their large number. There were approximately 35 000 glaciers with a length ratio (Rr) between GLmax and Lmax that was greater than 1.55, and these were excluded from the histogram in Fig. 6b because there was a high probability that the length of at least one of the two datasets was wrong. The peak value of the histogram of Rr is in the interval 1.05–1.15, and Rr in the interval 0.95–1.25 accounts for 64.55 % (Fig. 6b). The glacier length GLmax determined in this study was generally 10 % longer than Lmax, which suggests that the glacier centerline lengths were probably underestimated in previous studies. In addition, the length ratio of glacier L1 was the highest, and the median value was high (Fig. 6c). The Rr values of glaciers L4–L10 fluctuated greatly. The Rr distributions of glaciers L2 and L3 were relatively concentrated. The reason for this is that the length of glacier L1 was affected by the DEM, while glaciers L4–L10 were mainly impacted by differences in glacier scale and the accuracy of the auxiliary line.

Comparisons between GLmax and Lmax for each first-order glacier region and all random samples are shown in Appendix B. The fit between GLmax and Lmax was better in seven glacier regions, including R01, R04, R07, and R12–R15, in which the R2 was larger than 0.95 (Fig. B1). The Rr in R17 (R2=0.8174), R05 (R2=0.8136), and R03 (R2=0.6311) were lower, whereas that in R19 (R2=0.5487) was the worst. The R2 values of the other eight glacier regions were between 0.85 and 0.95. The histograms (Fig. B2) suggest that GLmax and Lmax fitted well in R04, R06, R07, R09, and R12–R15 because they had recognizable single peak values. The peak values of R03, R05, R17, and R19 were not prominent, and the proportion of glaciers with Rr>1.55 was extremely high, further increasing the uncertainty in glacier length estimates in these four regions. R01, R07, R08, R11–R15, and R18 performed well in the box plot (Fig. B3), whereas the results for R09 were not good. Moreover, the fit of all random samples was poor (Fig. B1; R2=0.7547), the peak value was more prominent (Fig. B2), and the length ratio distribution of glaciers of different grades was relatively scattered (Fig. B3). In general, the glacier lengths of R07 and R12–R15 were the closest, while there were significant differences in R03, R05, R17, and R19.

Furthermore, the graphic results, which were collected for the maximum length of glaciers in parts of HMA (Machguth and Huss, 2014), were used to compare with those in this study. There were two parts of R15 shown, which were Mount Qomolangma and its surrounding area (Fig. 7a) and Kangchenjunga and its surrounding area (Fig. 7b). A visual comparison suggested that the extraction approach used in this study was robust (Fig. 7a) and that its sensitivity to topography was lower than that of Machguth and Huss (2014; Fig. 7b). Large differences in glacier length extraction schemes are present only in a few glaciers or in certain types of glaciers, such as slope glaciers and ice caps.

Although we compared the two current global length datasets, it is still difficult to accurately characterize the dataset's quality in this study. For glaciers for which centerlines were not provided in this dataset, users need to update the corresponding glacier outlines and could use the automatic extraction tool provided in this study to generate their centerlines, including the defective glacier outlines (FGODS), nominal glaciers, and ice caps of the RGI v6.0. Specifically, the centerlines of the FGODS rely on the glacier outlines that meet the requirements of this study. These glacier outlines include glacier inventory data from other sources or the FGODS that were repaired by some algorithm or manual process. Nominal glaciers are similar to FGODS and also require users to obtain corresponding glacier outlines. Automatic approaches to dividing ice caps from glacial complexes into individual glaciers are currently limited, and data users can only use their own criteria to separate the ice caps and then use our tool to generate the centerlines. In addition, prioritizing the coverage of this dataset, we designed a geometry-based algorithm to repair FGODS and provided users with their centerlines in the form of a supplementary dataset. Corresponding codes and results can be seen in sub-datasets CODES and SUP_220707.

The automatic extraction algorithm in this study is more suitable for single-outlet glaciers, particularly valley glaciers; it is not suitable for ice caps, flat-top glaciers, and tidal glaciers, which tend to be widely distributed in the Antarctic, Subantarctic, and northern Canadian Arctic, among other areas. In short, the uncertainties in this dataset probably come from the centerlines of some slope glaciers and the ice caps that are not identified in RGI v6.0 or a few centerlines with unpredictable quality due to the input data, such as the incorrect glacier polygons and erroneous DEMs. In future work, improved glacier inventories and more accurate DEMs will contribute to improving centerline quality. Furthermore, optimizing the automatic glacier segmentation approach, the DEM-based extraction algorithm of glacier feature lines, and the centerline tradeoff algorithm will also likely further improve the accuracy of glacier centerlines. In addition, centerline accuracy will probably benefit from further improving the classification type of each glacier in the glacier inventory.