Unveiling the topography beneath the world’s glaciers
Since direct observations of glacier bed elevations are only available for ~2% of glaciers globally23, spatially complete subglacial topography must be inferred through inversion methods constrained by surface data. We have compiled a comprehensive dataset from publicly available sources for the > 200,000 glaciers in the globally complete Randolph Glacier Inventory v6.0 (RGI)24,25, including digital elevation models (DEMs)26, glacier outlines24,25, surface elevation changes27, ice flow velocities14,28, and modeled specific mass balances1, alongside frontal ablation estimates for marine-terminating glaciers in the Northern Hemisphere29 and Patagonia30. This data feeds into an iterative inversion workflow that matches observed and modeled surface elevation changes, previously validated on synthetic glaciers22 and successfully applied on regional scales19,31. In the algorithm, IGM runs for at least 2000 model years per glacier—an effort computationally prohibitive with traditional models of comparable complexity at global scale, now enabled by GPU acceleration (Methods)21. Glaciers that share boundaries are treated as a single entity to avoid artificial discontinuities in bed topography observed in previous products13. In fast-flowing sectors of marine-terminating glaciers, a spatially distributed friction parameter is inverted to ensure consistency between modeled and observed ice flow velocities and prevent unrealistic thicknesses22. Automatic Bayesian calibration of model parameters32 against all > 3,800,000 point observations of ice thickness in the Glacier Thickness Database v4-beta (GlaThiDa)23,33 for each of the 19 RGI glacier regions with available data, ensures that region-wide parameters yield the best inversion performance.
Bed topographies for all glaciers on Earth
The details of our new global subglacial topography dataset cannot be adequately visualized here, so we refer to the openly available dataset at https://doi.org/10.6084/m9.figshare.2994093234 and showcase here only example outputs of a valley glacier and an ice cap (Fig. 1). The modeled topographies (100—400 m resolution) align with our expectations of subglacial morphology, revealing characteristic features such as U-shaped valleys, glacial cirques, and overdeepenings. Similarly, well-known features of marine-terminating glaciers, such as retrograde bed slopes and deep basins below sea level, are well represented, for example, in the Arctic, Antarctic, and Patagonia. These glaciers currently comprise ~ 60% of the global ice volume (see below) despite accounting for < 2% of the glacier count. Given that their retreat is highly sensitive to bed geometry35,36, our new topographies are expected to substantially improve future sea-level projections.
a, c Modeled ice thickness draped over present-day surface topography; b, d glacier-free topography with future lakes. Topographies in all plots are shown as hillshades.
The strength of TOPO-DE lies in its physical consistency, achieved through a higher-order representation of ice flow dynamics combined with an inversion method based on mass conservation. Error metrics against observed thicknesses indicate improved skill compared to previous studies (Fig. S1, S2), although these metrics should be interpreted with caution because a shared, independent validation dataset across studies is lacking (Supplementary Discussion). Importantly, TOPO-DE substantially reduces systematic biases found in earlier thickness estimates which tended to overestimate thin and underestimate thick ice (Fig. 2). This has important implications for accurate glacier projections: With TOPO-DE, thinner glaciers with smaller initial thickness will disappear faster under future warming compared to using previous (greater) thickness estimates. Thicker glaciers, by contrast, are expected to survive longer. These biases would naturally also affect the mapping of potential future lakes. For example, unrealistically smooth beds may be caused by underestimating thickness variability within individual glaciers, which could imply that the potential for lakes is underestimated.
Horizontal orange lines represent the median and triangles the mean misfit, the box represents the interquartile range (Q1–3), the whiskers 1.5 times the interquartile range and orange dots represent fliers. Note that the thickness classes differ slightly due to the different spatial coverage of the products. The same analysis with uniform classes yields the same patterns (not shown).
TOPO-DE also visibly improves the realism of glacier beds (Figs. S3, S4). Previous reconstructions frequently produced features that are physically implausible—such as “walls” between individual outlet glaciers of ice caps, highly irregular beds in slow-flowing areas, “stripes” perpendicular to the flow direction or flat beds under ice caps (Supplementary Discussion). Such erroneously mapped features can have significant practical implications. For instance, they can prevent the correct delineation of emerging watersheds as glaciers retreat, and/or induce numerical stability issues in future glacier simulations. In contrast, our results are consistent with our physical understanding of subglacial morphology (Figs. S3, S4). Moreover, when paired with geological maps of surrounding unglaciated terrain, our glacier bed maps provide valuable insights into subglacial geology. For instance, a sequence of resistant and weak rocks mapped outside a glacier in the Canadian Arctic37 can now be traced in detail beneath the ice, whereas the same formations were weakly expressed or absent in previous products (Fig. 5). This highlights the potential of TOPO-DE to aid geological mapping of currently ice-covered landscapes.
Nevertheless, TOPO-DE inevitably contains inaccuracies arising from input data errors, physical shortcomings, and solution equifinality inherent to underconstrained ice thickness inversions (Supplementary Discussion). Biases in surface elevation change, mass balance, glacier outlines, velocities, and DEMs can locally affect inferred thickness and bed geometry22,38. Meanwhile, the use of higher-order ice-flow physics substantially reduces physical shortcomings compared to SIA-based approaches13,14. Errors are expected to be elevated for surging glaciers39, in regions with few thickness and mass balance observations40,41, and for bed features smaller than approximately one ice thickness, which are fundamentally unconstrainable42,43,44. More ice thickness observations are critical to improve glacier bed inversions further, specifically in data-sparse regions such as High Mountain Asia, the Russian Arctic, and Subantarctic & Antarctic Islands. Our input-preparation and data-assimilation framework effectively minimizes and balances error sources, but residual artifacts naturally remain and can propagate into modeled lake locations and volumes. At large scales we expect errors to average out, but localized applications should evaluate bed shape, ice thickness and potential lake locations in light of these uncertainties. Importantly, the data assimilation framework used here makes TOPO-DE particularly well-suited to be refined by future improvements in input datasets.
Detecting potential future lakes
Leveraging the physically realistic bed shapes, we predict the locations and volumes of new lakes that would form if all glacier ice was to melt. This is done by mapping overdeepenings in the modeled subglacial topographies and calculating their volume up to the height at which water would overflow to adjacent grid cells. For simplicity, we assume no modification of bed shape by future geomorphic processes, a simplification which likely renders our areas and volumes upper-bound due to dam breaches and sediment infill that reduce the initial lake potential over time12. In addition, unresolved small-scale topography may include drainage pathways not represented here.
Globally, we estimate a potential for 56,659 new lakes (≥0.05 km2) with an area of 40,647 km2 (Fig. 3, Table 1). Lakes would cover ~ 6% of the newly deglaciated landscape—approximately three times the proportion of lake cover on global present-day non-glacierized land (2%45). In the Alps, refs. 46,47 observed lake covers of 0.5% (Austria) and 0.9% (Switzerland) on land that became ice-free since the Little Ice Age. We estimate a potential future lake coverage of 0.9% in Central Europe, closely aligned with these historic values. For comparison, ref. 48 modeled a potential future lake area of 45.2 km2 in the Swiss Alps, corresponding to a coverage of 4.7%, about four times higher than the historical reference. In Svalbard, ref. 49 showed an increase in ice-marginal lakes of 72 km2 between the 1930s and ~2010 while 2144 km2 land became ice-free50 (3.3% lake coverage). Here, our estimate is 5.6% (including not only ice-marginal, but also proglacial lakes). The lakes would globally be capable of holding 3138 km3 of water (Fig. 3, Table 1). Considering only the volume above sea level, the lakes would lower the potential sea-level contribution of complete global glacier melt by 7 mm (2%). This amount is double the sea-level equivalent stored in present-day glacial lakes (defined as lakes hydrologically connected to a glacier and within 10 km of the RGI outline)51. The global mean depth of the potential lakes is 77 m, the mean lake surface elevation is 711 m above sea level, and the average overlying ice thickness is 410 m—approximately twice the mean global ice thickness (see below).
Shaded polygons show Randolph Glacier Inventory glacier regions. Glacier cover is indicated in light grey.
The largest potential lake volumes are found in Alaska (854 km3), the Southern Andes (408 km3), and Arctic Canada North (436 km3), regions that are already known to host many glacial lakes today12. The first two regions also show the largest mean lake depths (117 and 124 m, respectively). In this regard, Arctic Canada North (mean depth: 60 m) is more similar to other high-latitude regions such as Greenland, Svalbard, Subantarctic & Antarctic Islands and Arctic Canada South, where the mean depths range between 60 and 75 m (Table 1). The deep lakes found in Alaska and the Southern Andes, but also in Iceland (mean depth: 97 m) and New Zealand (mean depth: 96 m), coincide with maritime conditions in these regions. Maritime temperate glaciers have a large erosional potential, thus efficiently creating bedrock overdeepenings and tall moraines capable of damming lakes52. New Zealand has potential for ~ 5.5 times more new lake volume than the more continental region of Central Europe, despite the latter having roughly twice the ice volume and glacierized area (Fig. 3). The largest mean lake areas are found in Iceland (2.73 km2), the Russian Arctic (1.17 km2), and Alaska (1.12 km2) whereas North Asia and Low Latitudes—both home to small mountain glaciers—exhibit the on average smallest lakes (0.10 km2). In terms of lake density per glacierized area, we establish a link to current glacier geometries. Excluding tidewater glaciers, we find that regions with steeper glacier surfaces have smaller potential lake volumes per glacierized area than regions with gentler slopes (r = −0.65, p < 0.05; Fig. S6). High-latitude regions with often thick glaciers extending to sea-level show smaller surface slopes and correspondingly larger potential lake volumes per area. Conversely, the glacierized mountains of the mid-latitudes in North America, Europe and Asia are characterized by steep surface topography and comparatively small lake volumes per area. Despite this relative sparsity of lakes in High Mountain Asia, the mean lake depth there (51 to 79 m) is comparable to flatter polar regions and considerably greater than in other steep mountain regions (Table 1). A likely explanation are tall moraines due to the extensive debris cover of many glaciers53 that allow deep lakes to form.
We find the largest potential lake volumes in High Mountain Asia in the lowermost parts of the glaciers (Fig. 4). Although our bed maps do not indicate dam types and materials, this suggests that a large proportion of potential lakes in High Mountain Asia is moraine-dammed, as are many present-day proglacial lakes in the region54. By number of individual lakes, we do not see a similar concentration at low elevations, indicating that the low-elevation lakes have above-average volumes. This makes them susceptible to generating large and potentially devastating GLOFs12. Similar lake distributions as in High Mountain Asia are found in Alaska and New Zealand (Fig. 4). Both regions are known to feature large proglacial lakes today55, such as the proglacial lake of Tasman glacier, which we estimate has the potential to expand further by 17 km2 [from 7 km2 in 201455]. Other regions dominated by valley glaciers (such as Central Europe, Caucasus & Middle East, and Low Latitudes) also show a concentration of large lakes relatively close to the glacier fronts, albeit to a somewhat lesser degree. This pattern likely results from the joint presence of lakes in bedrock and sediment along low-sloping glacier tongues in major valleys, and of moraine-dammed lakes. Meanwhile, polar regions such as Arctic Canada N, Greenland, Russian Arctic and Subantarctic & Antarctic Islands show more uniform lake distributions over the glacier altitudinal range. This is because beds of tidewater glaciers below sea level will not form lakes, and also likely due to the overall flatter topography, which is more prone to overdeepening anywhere along the glacier than in steep mountains (Fig. S6). In Scandinavia, Greenland and the Russian Arctic, lake volumes are comparatively more pronounced at higher relative elevations. Under hypothetical globally uniform relative glacier retreat rates, this implies that it would take the longest in these regions until the regional majority of potential lake volumes is realized. In the upper third of the glacier altitudinal range in most regions, we find numerous lakes though smaller volumes, likely reflecting the widespread presence of small lakes in glacial cirques (Fig. 4).
Number of lakes (blue) and lake volume (orange) in 30 elevation bins, with the y axis normalized to the largest bin. The normalized glacier altitudinal range represents a scale from 0 (lowest) to 1 (the highest point of a glacier). Each lake’s location on that scale is computed by normalizing the mean glacier surface elevation under which the lake is located. Blue and orange numbers in each subplot show the mean normalized altitude of the lake counts (μC) and volumes (μV), respectively.
Historically, roughly one third of GLOFs were caused by drainage of moraine- or bedrock-dammed lakes that we can identify in TOPO-DE, with the other two thirds resulting from ice-dam failure12. In High Mountain Asia, catastrophic GLOF events from moraine-dammed lakes have occurred frequently and human exposure to GLOF impacts is the highest globally12,56,57. Although so far reporting biases preclude the detection of significant positive GLOF trends related to glacier retreat12, the future presence of large lakes near the glacier margins strongly suggests that GLOF hazard from moraine-dammed lakes will increase58. Moreover, future hazards will likely also increase from emerging bedrock-dammed lakes which are less vulnerable to dam failure, and thus historically have caused fewer GLOFs, yet may release large volumes of water due to displacement waves from mass movements into the lakes12. Recent studies indicate increasingly unstable mountain flanks due to permafrost thaw and consequently more frequent mass movements, underscoring and exacerbating the substantial hazard emanating from all emerging lakes59.
In High Mountain Asia, we find a total potential lake volume of 141 km3 (Table 1), roughly consistent with 120 km3 estimated by ref. 60. However, our estimate is around 2.5 and three times higher than estimates by ref. 61 (60 km3) and ref. 62 (50 km3), respectively, with both previous analyses relying on the bed topographies of ref. 13. References 61, 62 applied morphological criteria such as surface slope thresholds in addition to a sink-fill algorithm to identify potential future lakes, naturally rendering their estimates more conservative than ours47. However, the known artifacts in ref. 13 dataset and its possible tendency to exhibit overly smooth beds (see above and ref. 19) may have led to an underestimation of potential lake volumes, and thus GLOF hazard. This highlights the importance of utilizing realistic bed shapes for lake mapping and hazard assessments. A priority for future studies on GLOF hazards (e.g.63) should be to synthesize and validate different available lake products on the local scale, thus increasing confidence in modeled lake locations and volumes, and ultimately enabling effective mitigation measures57.
Beyond hazards, emerging lakes may support water storage, tourism64, and hydropower generation9. For instance, a recently emerged proglacial lake in a glacier-carved overdeepening at Trift glacier, Switzerland, has become a popular tourist attraction and is a suggested site for hydropower production65. For the sustainable development of each site, case-specific opportunities and constraints must be carefully assessed, taking into account various factors including technological feasibility, environmental vulnerability, and social acceptance58,65.
Global and regional ice volumes
Knowledge of subglacial topography combined with surface DEMs directly yields ice volumes, here aggregated regionally, globally, and by latitude for approximately the year 2013 (Fig. 5, Table S1). We find a global glacier volume Vtotal = 149.41 ± 29.28 × 103 km3, corresponding to a SLE of 308 ± 60 mm accounting only for ice volume above flotation, and a mean thickness of 212 ± 41 m. This estimate agrees well with the two most recent independent studies13,14 and consequently further constrains global glacier volume (Fig. 6). Earlier estimates were higher by up to a factor of two due to considerably simpler methodological approaches and a lack of high-quality input data, and now appear increasingly unlikely15,18,66,67,68,69,70.
Dashed circles indicate volume uncertainties, and dark shaded pies the volume stored in marine-terminating glaciers (as defined in the Randolph Glacier Inventory; in Subantarctic & Antarctic Islands, also including shelf-terminating). Shaded polygons show Randolph Glacier Inventory glacier regions. Glacier cover is indicated in light grey. The blue shaded bar to the right indicates the share of global glacier volume by latitude (5∘ bins).
Regionally, our results show marked differences from the most recent previous studies13,14. In the largest RGI region, Subantarctic & Antarctic Islands, our volume of 50.57 ± 8.34 × 103 km3 closely matches the 46.47 ± 12.06 × 103 km3 reported by ref. 13, but exceeds that of ref. 14 (35.10 ± 9.10 × 103 km3) by > 40%. The considerable disagreement with ref. 14, where uncertainties barely overlap, may be a result of ref. 14 predominantly relying on BedMachine71 in this region, which likely produces too thin ice in poorly observed valley glaciers, as previously shown for the Antarctic peninsula72. In contrast, for the Greenland Periphery, our volume (12.46 ± 0.94 × 103 km3) is nearly identical to that of ref. 14 (12.54 ± 3.95 × 103 km3), but ~ 20% lower than the 15.69 ± 4.07 × 103 km3 estimated by ref. 13, with their central estimate outside our uncertainty range. Reference 13 is biased by ~90 m to thickness observations in this region, whereas our results are almost bias-free (4 m, Fig. S1). These examples from two regions highlight how our results provide much-needed clarification where the two previous estimates diverged. Overall, our volumes agree more closely with ref. 14 than with ref. 13 in the majority of regions. In High Mountain Asia, where glaciers act as critical water buffers5, ref. 14 reported a volume 37% higher than ref. 13, suggesting that this would delay peak water by several decades. In contrast, we find a volume of 6.39 ± 1.64 × 103 km3, even ~ 9% lower than ref. 13. However, this region remains highly uncertain, with thickness observations available for only 16 out of >70,000 glaciers23,41. Future field campaigns are therefore critical to obtain more thickness observations for calibration and uncertainty reduction. In Arctic Canada North and the Russian Arctic, our volumes are between 12% and up to 30% lower than previous estimates, despite being negatively biased or unbiased relative to thickness observations (Fig. S1). This may directly reflect the difference between a higher-order and an SIA model, the latter requiring manual corrections in flat areas of ice caps (Fig. S3). However, the presence of numerous surging glaciers in the Northern Canadian Arctic introduces uncertainties in both approaches.
Implications and future perspectives
The new subglacial topographies provide critical data for a wide range of disciplines, including glaciology, hydrology, ecology, geology, and geomorphology. As glaciers retreat in a warming climate, improved knowledge of emerging landscapes and lakes is essential for land management, hydropower planning, safety in glacier tourism, as well as hazard and ecosystem change assessments. TOPO-DE offers substantial opportunities for further characterization of the subglacial landscape, which warrant dedicated investigation in future studies. Our large-scale analysis highlights major GLOF hazards associated with potential future lakes in steep mountain terrain, particularly large moraine-dammed lakes in High Mountain Asia. More detailed, localized investigations will be essential to further refine this picture and to generate actionable data for mitigating such mountain hazards under climate change. Future glacier simulations based on the new bed product will be instrumental in constraining the timing of glacier retreat and the associated emergence of proglacial lakes. Together with the revised ice-volume estimates, which diverge substantially from previous studies across many glacier regions, future glacier projections based on TOPO-DE are expected to reveal new regional patterns of deglaciation with associated improved estimates of sea level rise.
More broadly, our results underscore the value of computationally efficient, higher-order ice-flow models in inversion frameworks that exploit the growing availability of high-resolution remote sensing data, paving the way for global glacier modeling beyond the era of shallow ice flow physics and one-dimensional flow-line models.
