The melting of glaciers and ice caps accounts for about one-third of current sea-level rise1,2,3, exceeding the mass loss from the more voluminous Greenland or Antarctic Ice Sheets3,4. The Arctic archipelago of Svalbard, which hosts spatial climate gradients that are larger than the expected temporal climate shifts over the next century5,6, is a natural laboratory to constrain the climate sensitivity of glaciers and predict their response to future warming. Here we link historical and modern glacier observations to predict that twenty-first century glacier thinning rates will more than double those from 1936 to 2010. Making use of an archive of historical aerial imagery7 from 1936 and 1938, we use structure-from-motion photogrammetry to reconstruct the three-dimensional geometry of 1,594 glaciers across Svalbard. We compare these reconstructions to modern ice elevation data to derive the spatial pattern of mass balance over a more than 70-year timespan, enabling us to see through the noise of annual and decadal variability to quantify how variables such as temperature and precipitation control ice loss. We find a robust temperature dependence of melt rates, whereby a 1 °C rise in mean summer temperature corresponds to a decrease in area-normalized mass balance of −0.28 m yr−1 of water equivalent. Finally, we design a space-for-time substitution8 to combine our historical glacier observations with climate projections and make first-order predictions of twenty-first century glacier change across Svalbard.
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The 1936/1938 Svalbard glacier inventory presented here consists of raster DEMs and orthophotos (5 m resolution), and vector outlines of glacier extents (Extended Data Fig. 3). All data are publicly available on the NPI website (https://www.doi.org/10.21334/npolar.2021.f6afca5c) and on Zenodo (https://doi.org/10.5281/zenodo.5806388). In these repositories, we also provide the raw (unprocessed) 3D point clouds as .laz files and a spreadsheet (.xlsx file) containing glacier-by-glacier estimates of area, volume, hypsometry, ∆h/∆t, bed slope, DEM uncertainty and climate fields (mean annual temperature, mean summer temperature, PDDs, precipitation as snow and total precipitation). The original 1936/1938 aerial images and their locations can be viewed at https://toposvalbard.npolar.no/. The 5 m regional DEMs from the 2008–2012 survey33 are available as .tif files from https://publicdatasets.data.npolar.no/kartdata/S0_Terrengmodell/Delmodell/ and the associated 50 cm orthophotomosaic is available as a WMTS layer from https://geodata.npolar.no/#basemap-data.
The code developed to analyse the 1936–2010 mass balance data and implement the space-for-time substitution is available on Zenodo (https://doi.org/10.5281/zenodo.5643856).
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We thank F. Simons, C.-Y. Lai, P. Wennberg, P. Moore, B. Dyer, G. Moholdt, R.A. Morris, E. Isaksson, A. Schomacker, C. Nuth, E. Schytt Holmlund and B. Geyman for conversations that improved the manuscript. W.J.J.v.P. acknowledges funding from the Swedish National Space Agency (project 189/18). E.C.G. was supported by a Daniel M. Sachs Class of 1960 Global Scholarship at Princeton University, a Svalbard Science Forum Arctic Field Grant, and the Fannie and John Hertz Foundation.
The authors declare no competing interests.
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Extended data figures and tables
The x-axis represents the total ice loss, expressed in terms of mm of global sea level equivalent (SLE). The SLE is normalized to a 100-yr period to facilitate comparison between historical observations of varying length and projections for the 21st century. For the historical models that only simulate climatic mass balance19, we added a calving flux86 of −6.75 ± 1.7 Gt yr−1 to estimate the total mass balance and facilitate comparison with the geodetic and gravimetric observations. Since the data are compiled from many sources2,3,4,–5, 12,13,14,15,16,–17, 85, 87,88,89,90,91,92,93,94,95,96,97,–98, 103, the error bars represent different quantities. In most cases, the shaded bars represent the reported ± 1σ uncertainty. For Marzeion et al. (2012), the bars represent the range of results from different ensemble runs, and for ‘This study’, the bars represent the range from using the 5th to 95th percentile of future precipitation estimates (Fig. 4). The 21st century projections for this study are broken into 3 groups: (1) those based on the 1936-2010 mass balance observations using mean summer temperature as the explanatory variable for ice loss (†; Figs. 3–4), (2) those based on the 2000-2019 satellite era observations4 using mean summer temperature (∗; Extended Data Fig. 10), and (3) those based on the 1936-2010 observations using positive degree days (‡; Extended Data Fig. 9). All three methods produce similar estimates for 21st century ice loss. The predictions begin to diverge under the most extreme warming scenario (RCP8.5)6, with the space-for-time substitution based on the positive degree day (PDD) approach (Extended Data Fig. 9) producing the highest estimates of sea level rise. Note that the total ice volume of Svalbard is estimated59 to be ∼6,199 km3 which is equivalent to 15 mm of sea level rise. Thus, the 21st century predictions exceeding 15 mm of SLE87,88,89 are not feasible.
(a-c) The 1,888 glaciers in Svalbard span an elevation range38 of >1,200 m, a mean annual temperature range of >10 °C, and a >4-fold change in precipitation (<0.5 to 2.0 m.w.e. yr−1). The elevation map in (a) uses the Norwegian Polar Institute S0 terrain model33, and the mean annual air temperature (b) and mean annual precipitation (c) estimates use the downscaled NORA10 dataset5 (1 km resolution, 1957-2018). (d-i) Glacier-averaged summer temperature (d-f) and solid precipitation estimates (g-i) for 2010-2100 from Arctic CORDEX under the RCP2.6, RCP4.5, and RCP8.5 scenarios6. The color bar for the mean summer temperature (Ts) maps in (d-f) is centered on the upper bound of the 1936-2010 Ts (95th percentile = 2.2 °C; Fig. 3). Thus, brown colors indicate that, in the space-for-time substitution in Fig. 4, we are predicting glacier behavior in response to temperatures that rise higher than those in the observational data that calibrate the model.
Extended Data Fig. 3 An overview of the 1936/1938 aerial survey7 and the new datasets available from this study.
(a) Locations of the 5,507 high-oblique aerial photographs acquired during the mapping campaigns7 of 1936 and 1938. The coordinates are displayed in WGS84 / UTM zone 33N. (b) We divided the images into 17 groups with convergent camera geometries for SfM reconstruction in Agisoft Metashape (Extended Data Fig. 4). We provide the Svalbard-wide (c) 1936 orthophotomosaic, (d) 1936 digital elevation model (DEM), and (e) 1936-2010 elevation change (∆h) at 20 m and 50 m resolution. We also provide the 1936-2010 ∆h datasets at 5 m resolution, although, because of file size constraints, these data are divided into 8 files for each of the Svalbard zones depicted in Fig. 2d. The unprocessed point clouds from the 17 regional SfM reconstructions in (c) are available as .laz files. In addition to the raster datasets in (c-e), we provide a .shp file inventorying the 1936 extents of Svalbard glaciers and a spreadsheet recording statistics such as ∆h/∆t, ∆M/∆t, DEM uncertainty, and NORA10 climate fields5 (mean summer temperature, precipitation as snow, etc.). See Data availability.
Extended Data Fig. 4 An overview of the image pre-processing and structure from motion (SfM) pipelines.
To improve feature selection during the SfM reconstruction, we enhance the digitized images by increasing contrast through histogram stretching and sharpening features using the Dehaze Tool in Adobe Lightroom. This radiometric enhancement step improves photogrammetric reconstructions over ice and snow, which tend to be lower contrast than the surrounding land. Finally, since scanning does not preserve the internal geometry (images can be rotated, translated, and warped), we locate the four fiducial marks on the edges of each image and apply a projective transformation that maps the images to a standardized internal geometry. Owing to the large number of images in the dataset, we use an automated pipeline for fiducial mark identification. We convolve the edges of the image with an idealized fiducial template to identify target regions. Next, inside the target regions, we convolve the image with a Laplacian of Gaussian filter to locate the fiducial spot. We process the aerial photographs in a standard photogrammetric workflow in Agisoft Metashape 1.6.0. In brief, we first extract up to 40,000 keypoints from each image. Keypoint matching across all the images provides the constraints to solve for the unknown parameters, including the relative camera locations/orientations and the camera distortion parameters. Adding ground control points (GCPs), with specified (x,y,z) positions, enables the absolute georeferencing of the model. Finally, a multi- view stereo (MVS) reconstruction converts the sparse 3D model to a dense 3D point cloud. We perform the MVS reconstruction with a Dense Quality of Medium (meaning that depth maps are generated at 1/4 the image resolution) and Dense Filtering at Moderate to Aggressive.
(a) Austre/Vestre Brøggerbreen, (b) Midtre/Austre Lovénbreen, (c) Grønfjordbreen, (d) Tungebreen, (e) Gløttfjellbreen, (f) Pedâsenkobreen. Glacier volume decreased by 11% across Svalbard during the interval 1936-2010 (Fig. 2). The 2008-2011 models use the NPI 5 m regional DEMs33 and associated 50 cm orthophotos (https://geodata.npolar.no/).
(a) Black areas denote regions with 3D photogrammetric (SfM) constraints from the 1936/1938 aerial images (Fig. 1) and white regions denote void areas infilled with the GP regression (Methods). The SfM-generated point clouds have void areas because of occlusion and poor feature matching in low-contrast areas. There is no reconstruction for the eastern portion of Austfonna (Fig. 2), since no photographs of that region were acquired during the 1936/1938 expeditions7 (Extended Data Fig. 3a). (b-e) An illustration of the void filling procedure, applied to Oscar II Land in western Svalbard. To fill the holes in the 1936 DEM, we first compute the ∆h map, differencing the ∼2010 reference DEM to the 1936 reconstruction (b). Next, we train a GP regression to estimate the ∆h values in the void areas. The GP regression is trained using x, y, and z (the 2010 elevation) as predictor variables to infer ∆h as the response variable, and thereby incorporates both the spatial information in (a) and the elevation-dependence of ∆h illustrated in (c). (d) The error of the GP-regression-infilled values is estimated on random subsets of data points (60%) held-out from model training. Finally, subtracting the infilled ∆h map in (e) from the 2010 reference DEM yields the 1936 surface (Extended Data Fig. 3d).
(a-b) Temperature control on ice loss. The scatter plots in (a-b) show a similar relationship as Main text, Fig. 3f-g (Ts vs. ∆h/∆t), except the y-axis in (a-b) also includes the solid precipitation component. Specifically, Fout = Psolid − b, where Psolid is extracted from the downscaled NORA10 dataset5, and b is ∆h/∆t converted to m.w.e. yr−1 using a density57 of 850 kg m−3. Since the glacier-specific precipitation estimates are noisy, the plots in (a-b) show considerably more scatter than those in Main text, Fig. 3f-g. The advantage of examining the data in terms of Fout is that it enables us to extract the physical quantity k1, which describes the expected increase in ice loss (m.w.e. yr−1) for each 1 °C rise in mean summer temperature. The gray bands in (a-b) depict the 25th–75th percentile uncertainty envelopes of the Ts vs. Fout regressions (all glaciers). Note that the ice loss in marine-terminating glaciers is regulated not only by air temperature driving Fmelt, but also by fjord temperature, bathymetry, and circulation controlling Fcalving31,73,99. We take a first-order approach and fit different k constants to land- vs. marine-terminating glaciers. In both (a-b), the k1 coefficients are larger in land-terminating glaciers than marine-terminating glaciers. This observation of a weaker sensitivity of Fout to air temperature is consistent with the Fout in marine-terminating glaciers being driven partly by fjord processes that are decoupled from air temperature. Since the satellite-era observations (b) represent a shorter interval and therefore the ∆h/∆t data are more influenced by annual variability100 and surge cycles101, we only fit glaciers with ∆h/∆t within the 10th–90th percentile range. Glaciers outside this range are depicted with gray dots. Note that the estimated k1 coefficients from the 1936-2010 observations (a) and satellite-era datasets4 (b) are within uncertainty of each other. (c-d) Glacier slope modulates sensitivity to warming. (a) Simple theoretical glacier models79 predict that glaciers with steeper slopes should be less sensitive to temperature rise. The rationale is that, for a lower-slope glacier, a given ELA rise of x meters will transfer a larger fraction of the glacier’s area from the accumulation zone to the ablation zone38, causing a more substantial decrease in glacier-averaged ∆h/∆t. (b) We test whether there is evidence for a bed-slope control on glacier sensitivity to temperature rise79 in our 1936-2010 dataset (Fig. 2) by estimating the relationship between Ts and ∆h/∆t for low, medium, and high slope glaciers. The bed slope is calculated as ∆z/∆x of the bed topography59 along each glacier’s centerline56. The distributions in (b) represent the regression slopes derived from weighted total least squares regressions on repeated random 50% subsamples of the dataset.
Extended Data Fig. 8 Visual and quantitative comparison of the regional Ts vs. ∆h/∆t behavior of Svalbard glaciers.
(a-b) A visual comparison between glaciers in (a) NE Spitsbergen and (b) Edgeøya near the end of the 2020 melt season. Note that, in contrast to the glaciers in (a), the glaciers in (b) have no remaining winter snow, as evinced by the darker, debris-rich ice exposed even at the highest reaches of the glaciers. In other words, 100% of the glacier surface lies within the ablation zone. The Sentinel-2 imagery is from August 01, 2020 and the coordinates are in UTM zone 33N. (c-d) Glacier extents in 1936 and 2010. (e-i) Searching for evidence of threshold behavior in the Svalbard-wide 1936-2010 dataset. (e-f) If a strong tipping point already had been reached, such that, at high Ts, glaciers diverged from the linear behavior in Fig. 3, one might expect a Ts vs. ∆h/∆t relationship like that depicted in (f). However, (e) does not show strong support for the model in (f). Next, we look for a regional signal in the Ts vs. ∆h/∆t relationship. We divide the Svalbard-wide dataset into the 8 regions shown in (h), each of which has a different average Ts (g) and ∆h/∆t. (i) For each region, we study the residual between the Svalbard-wide linear Ts vs. ∆h/∆t (e) and the regional observations. The residuals are computed as predicted minus observed, so negative values indicate that the observed mass balance is more negative than the predictions. The regions in (i) are ordered according to the region-averaged glacier bed slope (Extended Data Fig. 7c), from smallest to largest. The glaciers like those in (b) that are committed to a path of pure melting (no accumulation) appear to follow similar Ts vs. ∆h/∆t relationships as the healthier (close to balance) glaciers in (a).
Extended Data Fig. 9 Glacier sensitivity to warming and 21st century predictions based on positive degree day (PDD) estimates.
(a-g) An analogous figure to Fig. 3, except using positive degree days (PDDs) to model the ice loss flux (eqns. 12–13) rather than mean summer temperature. In (g), only bins representing n ≥ 20 glaciers are shown. (h-k) PDDs are a non-linear function of mean summer temperature. For each glacier, we use the 1957-present daily temperature time series5 (h) to understand the relationship between mean summer temperature and PDDs (k). Specifically, we iteratively shift the time series in (h) up at 0.5 °C steps and compute the new number of PDDs. The red dashed line in (k) depicts what the PDD estimate would be if the melt season didn’t get any longer, which is analogous to what the Ts model does (Figs. 3–4). As illustrated in (j), the number of PDDs increases not only because the mean summer temperature rises, but also because the duration of the melt season increases. The plots in (h-k) are for the glacier Bungebreen (76.814◦N, 16.097◦E). We repeat the analysis for all glaciers on Svalbard to produce glacier-specific relationships between mean summer temperature and PDDs (k). (l) We test the PDD-based space-for-time substitution using 1936-1990 data to calibrate the model, and then compare predictions for the 1990-2010 interval to independent DEM-derived mass balance estimates. We find excellent agreement between the model and observations. Next, we use the model to predict 21st century (2010-2100) mass balance. (m-n) The predictions using the PDD method are nearly identical to the predictions using mean summer temperature (Fig. 4) under the RCP2.6 (m) and RCP4.5 (n) scenarios. However, the PDD method produces more negative mass balance estimates under RCP8.5, because of the divergence of the PDD curve from a simple linear function at higher summer temperatures (k). The brackets in (m-o) show results from simulations using the 5th and 95th percentiles of predicted winter precipitation6.
Extended Data Fig. 10 Temperature control on glacier mass balance in the satellite era4 (2000-2019).
An analogous figure to Figs. 3–4, but using 2000-2019 ∆h/∆t derived from ASTER DEMs4. The mean summer temperature values are extracted from the downscaled NORA10 dataset5. (c) The very negative ∆h/∆t at Basin-3 on Austfonna represents an ongoing surge there with an estimated calving flux102 of 4.2 ± 1.6 Gt yr−1, which represents about a quarter of the Svalbard-wide ice loss103. (e-g) To reduce the influence of outliers in the regression analysis, we only include the glaciers that have mean summer temperature and ∆h/∆t values that fall within the 10th to 90th percentiles of the Svalbard-wide dataset. (e) As in Fig. 3e, the distribution of regression slopes from the bootstrap resampling scheme does not overlap 0 m yr−1 °C−1, indicating a significant temperature dependence of ∆h/∆t. The estimated regression slope is −0.28 [−0.36, −0.22] m yr−1 °C−1 (median with 25-75th percentile range), which is slightly less negative, but still within the uncertainty envelope of the value estimated in Fig. 3 (−0.37 [−0.43, −0.29] m yr−1 °C−1). (h) To test whether the 2000-2019 observations4 are sufficiently long to characterize the temperature and precipitation control on ice loss (Extended Data Fig. 7), we train a space-for-time substitution using the 2000-2019 observations and the NORA10 temperature and precipitation estimates5 for 1936-1990 to estimate mass balance during the period 1936-1990. Comparison with the independent, DEM-derived observations of ∆h/∆t indicates that the space-for-time estimates have an error of 0.05 m yr−1. The simulated 1936-1990 mass balance in (h) may have a larger spread than the observed mass balance due to the somewhat more noisy (affected by surges, interannual variability100, etc.) satellite-era data used to calibrate the model. (i-k) We use a space-for-time substitution, trained using the 2000-2019 observations4 to predict 21st century Svalbard-wide ∆h/∆t under the same three climate scenarios6 as in Fig. 4b-d. The brackets show the model runs with the 5th and 95th percentiles of modeled winter precipitation6.
Additional clarification and details about the methodology. The code and the associated datasets required to reproduce the space-for-time analysis can be downloaded from https://doi.org/10.5281/zenodo.5643856. The full dataset of 1936/1938 3D glacier reconstructions can be downloaded from https://doi.org/10.5281/zenodo.5644415.
Glacier-by-glacier statistics such as ice loss, climate parameters and twenty-first century predictions.
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Geyman, E.C., J. J. van Pelt, W., Maloof, A.C. et al. Historical glacier change on Svalbard predicts doubling of mass loss by 2100. Nature 601, 374–379 (2022). https://doi.org/10.1038/s41586-021-04314-4