RES surveys were conducted on MG, SG, RG, and RIV during 2024–2025, using a Blue System Integration ice penetrating radar (v3), towed behind a snowmobile (Table ). This portable impulse radar hardware comprises a 1–200 MHz transmitter, digitizer, computer, and a GPS receiver . The GPS receiver is a Garmin OEM18x, with a positioning accuracy of 15 m and an update rate of 5 Hz . RES data were collected in an in-line antenna configuration, with antenna separation of 15 m, operating at a central frequency of 10 MHz and a receiver sampling rate of 125 MHz or 250 MHz (Table ). The snowmobile was driven at a steady speed of 4–6 m s⁻¹. The RES signals were stacked 512 times during acquisition, resulting in a trace spacing of 4–6 m during steady driving.

RES surveys were conducted at high spatial density, covering most of each glacier's surface. The greatest distance between any location on each glacier and the nearest known ice-thickness point (RES measurements or glacier outline) is within 210 m. Data acquisition was restricted in the upper accumulation zone of SG (near its western boundary) and in the northeastern upper accumulation zone of RG due to steep surface slope and avalanche risk (Fig. d, e). Surveys were not carried out in the southern and southeastern parts of RG because of the rockfall risk. RES profiles were planned along a regular grid, however, field conditions (e.g., crevasses and moulins) resulted in some deviations. The grid spacing varies between 20 and 300 m. The survey trajectory was tracked by the GPS receiver integrated into the RES system. The total length of RES surveys is 249.5 km (Table ).

The subglacial ice-bed interface, i.e., the glacier bed, is a strong electromagnetic reflector because of the dielectric contrast between ice and bedrock or ice and sediment . As a result, it appears as a distinct reflection in radargrams. In polythermal glaciers, the cold layer has few reflectors or scatterers, making it relatively transparent in radargrams . In contrast, water-filled temperate ice, which is at the pressure melting point, exhibits increased scattering and attenuation due to its different dielectric properties. As a result, it appears opaquer in radargrams, which can lead to ambiguous bed detection (Fig. a). RES data were post-processed using the ReflexW module for 2-D data analysis . The data processing workflows for valley glaciers MG (Fig. ), SG (Fig. ), and RG (Fig. ) are designed to enhance bed reflections and include the following steps: dewow, time-zero correction, dynamic correction to account for the 15 m antenna separation, topography correction, signal divergence compensation, 2-D filtering to remove horizontal banding, Butterworth bandpass filtering to retain low-frequency signals (1–5 MHz), and Kirchhoff migration. For RIV, which contains relatively shallow ice, a simplified processing flow comprising time-zero correction, dynamic correction, topography correction, 2-D filtering, and Kirchhoff migration was applied (Fig. ). The radargrams (Figs. , –) were rescaled using GPS-recorded positions to account for variable trace spacing caused by changes in acquisition speed, ensuring that the horizontal axis represents true distance.

For polythermal glaciers, the glacier bed is generally picked manually from radargrams , as strong signal scattering in the temperate ice can complicate automatic or semi-automatic bed identifications (e.g. Fig. a). However, manual picking is time-consuming and prone to subjective bias. Therefore, here we combined both automatic and manual approaches for bed identification, to achieve a balance between efficiency, objectivity, and accuracy. The preliminary glacier bed picks, expressed in units of two-way travel time (TWT), were obtained automatically through batch analysis in ReflexW and MATLAB following this workflow: (a) the Hilbert transform was applied to generate the signal envelope of the fully processed data using trace analysis in ReflexW. The resulting envelope data were then imported into MATLAB; (b) the maximum reflection was identified in each trace and interpreted as the bed; (c) static traces (where GPS trace spacing <1 m) were removed; (d) adjacent bed picks with large TWT difference were taken as potential erroneous picks and removed; and (e) outlier picks were further filtered using a move median filter, thereby removing surface maximum picks (likely caused by crevasses) as well as other unreliable picks (Fig. a). The automatic preliminary bed picks were used to evaluate the data quality and rapidly generate preliminary ice thickness and bed topography maps. The preliminary automatic bed picks were then imported into ReflexW for further manual refinement, where misidentified bed picks were repicked. For manual repicking, the bed reflections were first traced on radargrams that were not bandpass filtered, where the bed reflections not covered by temperate ice were clearly visible. Subsequently, filtered radargrams retaining only the low-frequency components were used in areas where the bed reflections were ambiguous or not visible in the unfiltered radargrams. This process allows bed identification while minimizing inaccurate interface tracking caused by filter-induced pulse broadening. In addition, weak bed reflections caused by steeply dipping reflectors or reflectors at great depth, and multiple basal reflectors were unpicked to improve the accuracy of the overall data interpretation (Fig. b).

We calculated point ice thickness (H) from the TWT of bed picks (t) using a constant radio-wave velocity of 168 m µs⁻¹ in ice (v), the same value was used previously for SG and other glaciers : 1H=tv2.

We assessed the within RES dataset consistency by comparing ice thicknesses at intersection points, i.e., crossovers between survey lines. RES data points from different survey directions less than 5 m apart (the average trace spacing) were considered as crossovers. Ice thicknesses at crossovers exhibit small absolute misfits but larger relative misfit for RIV and near glacier boundaries, primarily affected by the relatively shallow ice in these areas (Table ). Crossover analysis shows some significant inconsistencies along or near valley walls, and during sharp turns. We accordingly unpicked those bed reflectors to limit the influence of out-of-plane reflections and incomplete extension of the antennas. In total, 38 205 point values of RES-measured ice thickness were presented for the four reference glaciers (Table ).

Whilst crossover analysis can reveal inaccurate bed picks by comparing discrepancies between RES measurements, it does not quantify ice-thickness uncertainty for each RES data point. We therefore calculated the uncertainty using standard analytical error propagation methods . The total uncertainty ϵH includes contributions from RES measurement uncertainty ϵHRES and from uncertainty in the positioning of data points ϵHxy: 2ϵH=ϵHRES2+ϵHxy2. Applying error propagation to Eq. (), RES measurement uncertainty ϵHRES is a function of radio-wave velocity v, TWT t, their errors ϵv and ϵt: 3ϵHRES=12v2ϵt2+t2ϵv2. Note that radio-wave velocity v varies spatially, as it is influenced by the density and water/air content of snow, firn, and cold/temperate ice layers. Assuming a constant v for all RES data points (168 m µs⁻¹) can result in biased ice thickness estimates, e.g. overestimations in the ablation zone and underestimations in the accumulation zone. proposed that uncertainties in v vary from ∼1% to ∼5%, for polythermal glaciers. In our study, we used 5 m µs⁻¹ as ϵv following . We used range resolution of the RES data as ϵt, which represents how precisely the reflections can be identified. Range resolution is generally evaluated between one-quarter and half the RES wavelength, corresponding to 4.2–8.4 m for our unprocessed dataset. Considering the additional uncertainties introduced by data processing and manual interpretation, ϵt values of 80, 150, and 250 ns (representing 6.7, 12.6, and 21 m in the ice) were assigned to bed reflections of varying identification quality.

We estimated the positioning-related ice-thickness uncertainty ϵHxy, as the maximum discrepancy in ice thickness between a RES data point and its adjacent points located within ϵxy, which represents the positioning uncertainty: 4ϵxy=ϵxyGPS2+ϵΔxy2, ϵxy has two components, ϵxyGPS is horizontal positioning accuracy of the GPS, and ϵΔxy represents the displacement of the RES system occurring within the time lag between the GPS coordinate update and the trace recording (ϵT): 5ϵΔxy=vRESϵT, where vRES is the travel speed of the RES system, which in our case equals the snowmobile driving speed of 5 m s⁻¹. ϵT is estimated as the GPS update period.

Due to the ground-based nature of the surveys, RES profiles could not be conducted over areas with moulins, large crevasses, and steep ice surface slopes. We interpolated and extrapolated RES-measured ice thickness to obtain continuous ice thickness distribution (hereafter referred to as “distributed ice thickness” to distinguish them from RES-measured ice thickness) using a model-based approach. Based on who compared the performance of different ice thickness models, we selected the Glacier Thickness Estimation algorithm (GlaTE) , which performs well where observation data coverage is relatively high. GlaTE is based on mass conservation, apparent mass balances, and Glen's ice flow law. It considers both constraints from RES data and glaciological modelling in inversion.

We input glacier surface elevation, glacier outlines, as well as RES-measured ice thicknesses and their associated uncertainties to GlaTE. ArcticDEM strips acquired closest in time to the RES data acquisition were used as surface elevations. They were acquired in 1 October 2022 (MG), 5 October 2024 (SG), 5 October 2024 (RG), and 17 May 2024 (RIV), respectively, thus ranging from more than 1.5 years before (MG) to a few weeks after (RIV) RES data acquisition in the field. For MG, RG, and RIV, the ArcticDEM elevations were corrected using vertical offsets of -1.7, 2.5, and -0.1 m based on dGNSS point elevations (Table ) measured in 2 April 2024 (MG), 21 April 2025 (RG), and 25 March 2024 (RIV), respectively (the dates closest to the RES data acquisition). The -1.7 m adjustment for MG represents cumulative surface elevation changes during the period autumn 2022 to spring 2024, whereas the 2.5 m adjustment for RG captures substantial snow accumulation during the winter 2024/2025. The relatively small correction value for RIV is explained by the temporal proximity of the ArcticDEM strip and the RES survey. The ArcticDEM elevation was not corrected for SG because of the lack of dGNSS measurements in 2024. Latest glacier outlines identified from 2024 Sentinel-2 imagery were selected as input for the model, and used to adjust ice thickness at the glacier boundary to zero. RES-measured ice thicknesses and their uncertainties were used to constrain the modelled ice thickness in GlaTE. In the model, we assigned apparent mass balance gradients for the accumulation/ablation zones of MG, SG, RG, and RIV as 0.0056/0.0069, 0.0045/0.0067, 0.0053/0.0063, and 0.00054/0.00098 m w.e. m⁻¹ yr⁻¹, respectively, based on mass balance surveys conducted over the most recent three years . We finally obtained distributed ice thickness maps for four reference glaciers with a spatial resolution of 10 × 10 m. It should be noted that this does not represent the realistic spatial resolution away from the RES survey lines. This is because GlaTE relies on surface information, which physically limits the spatial detail that can be resolved in the modelled bed, i.e. bed features smaller than at least one ice thickness cannot be recovered .

We repeated the modelling using the maximum and minimum RES-measured ice thickness within the ϵH range, the absolute difference between distributed ice thickness was taken as the uncertainty of distributed ice thickness. This estimate represents a lower bound of the true uncertainty, as it does not include uncertainty contributions from the interpolation method and from the surface elevation dataset used. The interpolation uncertainty is related to multiple mechanical and smoothing parameters, while the surface elevation uncertainty depends on data resolution and acquisition time, both of which are difficult to quantify explicitly. The misfit between the distributed ice thickness and RES-measured ice thickness was calculated along RES survey lines.

Bed topography was calculated by subtracting distributed ice thickness datasets from the calibrated surface elevation for each glacier. Our final bed topography products were smoothed using a Gaussian filter with a spatial smoothing scale of approximately 60 m and calibrated to the geoid using geoid model SWEN17_RH2000 .

The RES-measured ice thicknesses were compiled in a similar format as “Table TTT. Glacier thickness: Point measurements” in GlaThiDa to ensure the data accessibility and reusability . The along track ice thickness data are provided in a CSV (comma-separated values) table containing the following fields: glacier name (GLACIER_NAME), survey date (SURVEY_DATE), RES profile identifier (PROFILE_NAME), RES point identifier (POINT_ID), latitude and longitude of each RES point (POINT_LAT and POINT_LON), calibrated surface elevation (ELEVATION), ice thickness (THICKNESS), and corresponding ice-thickness uncertainty (UNCERTAINTY).

For MG, thickest ice (241 m) is located in the northwestern part. The southern section of the glacier also has relatively thick ice (Fig. a). For SG, the thickest ice is found in the central section, where the glacier narrows and then widens into the central plateau region, reaching a maximum of 225 m. In the western accumulation zone there is relatively thick ice of ∼200 m (Fig. b). For RG, the maximum measured ice-thickness is 158 m in the centre of the glacier after ice converges from the northeastern and southeastern accumulation areas. The northeastern part has relatively thick ice of ∼150 m (Fig. c). For RIV, the maximum measured ice thickness is 88 m in the northern part of the glacier. Relatively thick ice on RIV is found in its middle-north section (Fig. d). Overall, MG is the thickest among the four reference glaciers, followed by SG and RG, while RIV is relatively shallow compared with the other three glaciers (Table ).

Larger ice-thickness uncertainty related to RES measurement (ϵHRES) are found where the ice is thicker or the bed is harder to identify in radargrams (Fig. a–d). In contrast, ice-thickness uncertainty related to positioning error (ϵHxy) shows a relatively uniform distribution, with larger values in areas of steeper slopes (Fig. e–h). Overall, the total ice-thickness uncertainties (ϵH) are primarily related to ϵHRES (Fig. e–h). Compared with the other three glaciers, RIV has substantially smaller ice thickness and ice-thickness uncertainty (Table ).

Distributed ice thickness maps exhibit the continuous ice thickness variations over each glacier (Fig. a, d, g, j). By integrating the ice thickness over the glacier area, we obtained ice volume estimates of 0.32 (MG), 0.25 (SG), 0.23 (RG), and 0.10 km³ (RIV), respectively.

Consistent with RES observations, MG contains the thickest ice (∼ 240 m) among four reference glaciers (Table ). MG, SG, and RG exhibit different ice-thickness patterns. The thickest ice at MG is within its accumulation zone, whereas SG and RG have the thickest ice in the central sectors, where ice converges from different accumulation areas. The thicker ice at RG extends to the lower ablation area. The differences between the glacier ice thicknesses is likely related to the glacier geometries (Fig. c–d) and bed topography. At RIV, the thickest ice (∼ 80 m) displays a saddle-shaped pattern in the northern sector, which is consistent with earlier observations by . The ∼ 20 m difference between our maximum ice thickness and the previous estimates can be explained by mass loss over the past 28 years.

The mean uncertainties of distributed ice thickness are 27.0 (MG), 24.7 (SG), 21.3 (RG), and 12.9 m (RIV) for the four glaciers (Fig. a–d). Overall, larger distributed uncertainties concentrate in the thicker, interior regions of the glaciers. Misfits between distributed ice thickness and RES-measured ice thickness are larger near the ice margins, where the model assumes zero ice thickness based on the glacier outlines. This occasionally contradicts the RES measurements, primarily due to temporal asynchrony between the RES surveys and the satellite images from which the glacier outlines were extracted (Fig. e–h).

We compared our distributed ice thickness of four Swedish reference glaciers with those from previous studies (Fig. , Table ). estimated the ice thickness of Scandinavian glaciers using the Instructed Glacier Model , which is based on a higher-order ice flow approximation. Their approaches incorporated surface elevation and its rate of change , mass balance , and glacier outlines corrected by them from RGI 6.0 to address systematic misalignment with topography. Additionally, previous bed elevation for SG was used for ice-thickness calibration. The mean absolute ice-thickness misfits between their study and ours are 36, 31, 21, and 72 m for MG, SG, RG, and RIV, respectively (Fig. b, e, h, k). provided a consensus estimate of global ice thickness using an ensemble of up to five models considering surface characteristics. Their estimates were based on RGI 6.0 and thus exhibit misaligned glacier outlines (Fig. c, f, i, l). estimated global ice volumes and ice thicknesses based on high-resolution mapping of ice motion during the period 2017–2018, using glacier outlines from the RGI 6.0. Compared with our results and the other two modelled estimates, these ice thicknesses are clearly overestimated. This discrepancy is likely related to the model's strong dependence on surface flow velocity, which is relatively low (0–18 m yr⁻¹ in 2022 reported by ) and thus difficult to constrain accurately for the four Swedish reference glaciers (Table ). Therefore, we do not include this study in further comparative analyses.

Previous studies for the four reference glaciers are based on observational input data obtained in the past, e.g., glacier outlines obtained around 2001–2002 . Thus their ice-thickness estimates correspond to an earlier time period than ours. Given the observed ice losses in the recent years, which are quantified as 0.030 (MG), 0.019 (SG), 0.029 (RG), and 0.026 km³ (RIV) during 2017–2024 based on continuous annual mass balance records and glacier area records (Table ), the previous studies should show larger ice volumes and ice thicknesses relative to this study. However, presented smaller mean ice thicknesses for MG, SG, and RG, indicating an underestimation of their results. reported larger ice volumes and mean ice thicknesses for SG, MG, and RG than our study, which are likely related to glacier mass and area losses between their research period and ours. suggested that their estimates correspond approximately to the year 2010. Assuming similar mass loss rates during 2010–2017 as observed for 2017–2024, their results would slightly underestimate ice volume for MG by ∼ 2.7 %, while overestimating ice volume for SG and RG by ∼ 7.1 % and ∼ 4 %, respectively. For RIV, both and significantly overestimated ice thickness and ice volume as they both relied on the RGI 6.0 glacier outline. This outline corresponds to approximately twice the current RIV area (Fig. j–l), directly affecting the ice volume calculation. Moreover, ice-free terrain included within the overly large outline violates a key requirement for meaningful ice thickness inversions, which generally rely on a glacier mask to define the modelling domain. As a result, the modelled thicknesses in such areas are unreliable.

There are also notable differences in spatial ice-thickness distributions between previous studies and our work (Fig. ). For MG, our RES measurements indicate the thickest ice in the northwest, whereas and both reported thicker ice in the south and in the central section while both underestimated ice thickness in the northwestern part (Fig. b–c). This underestimation may result from inaccuracies in the mass balance data used in the modelling, as both and rely on elevation-dependent gradients, but could also arise from assumptions regarding sliding and ice viscosity, surface elevation data input, or incomplete representation of ice flow physics. For SG, both and derived the thickest ice in the central glacier (Fig. e–f). Similar to our results, also obtained relatively thick ice in the northwestern part of glacier, while underestimated the ice thickness there. For RG, and showed ice-thickness patterns broadly consistent with our results, i.e. thick ice in the central and northeastern glacier (Fig. h–i). underestimated the ice thickness near to the glacier terminus. For RIV, the ice-thickness distributions from and do not agree with our result (Fig. k–l), primarily due to inaccurate glacier outlines. Overall, and captured the broad patterns of the ice-thickness distribution for MG, SG, and RG. However, tended to underestimate ice thickness in accumulation zones, whereas systematically underestimated ice thickness across the glaciers. Although these global and regional studies often rely on coarser data, trading spatial resolution for broader coverage, this comparison still highlights the importance of RES measurements for accurately mapping ice-thickness distributions, both for Swedish glaciers and for other glaciers across the world.

At MG, the subglacial topography reveals a depression in the eastern part of the glacier, with the lowest elevation ∼ 1300 m above sea level (a.s.l., referenced to the geoid model SWEN17_RH2000). The bed gradually rises towards the glacier boundary surrounding this depression, reaching elevations up to ∼ 1800 m a.s.l. along the northwestern and southern margin (Fig. a). At SG, an elongated trough is situated in the central-eastern part, containing two depressions at ∼ 1150 m a.s.l. The bed elevation increases towards the glacier boundary in the southwest, reaching a maximum of ∼ 1700 m a.s.l. In the northwestern part, there is a depression with an elevation of ∼ 1400 m a.s.l., before the bed rises to ∼ 1900 m.a.s.l. in the uppermost accumulation zone (Fig. b). At RG, there is a pronounced deepening along the central section and towards the glacier terminus, where the bed elevation reaches a minimum of ∼ 1100 m a.s.l. The bed rises towards the three accumulation areas of RG, approaching a maximum elevation of ∼ 1900 m a.s.l. near the southeastern glacier boundary (Fig. c). Each of these three glaciers is associated with a trough along its central section, through which ice flows. Unlike the three valley glaciers, the glacier bed at RIV does not vary substantially in elevation. Instead, the bed gradually descends from a maximum elevation of ∼ 1430 m a.s.l. in the west to a minimum elevation of ∼ 1200 m a.s.l. in the east (Fig. d).

To visualize the topographic variations, we have plotted the bed elevation and surface elevation of selected profiles for four reference glaciers (Fig. ). In MG (Fig. a), a small depression in bed topography in the northwestern section (500–1200 m) corresponds to locally thicker ice in the upper glacier. In contrast, SG (Fig. b) and RG (Fig. c) show a more continuously descending bed, which is associated with thicker ice along the central flowline, extending towards the central and lower parts of the glaciers. The bed descends by only ∼ 120 m along the centreline across RIV, it shows no clear relationship with ice thickness (Fig. d).

Our results and previous RES-derived bed topography of SG and RG show good consistency in both values and patterns (Fig. ). Both our and previous maps of SG reveal two depressions in the central-eastern section with an elevation of ∼ 1150 m a.s.l., as well as a smaller depression at ∼ 1400–1450 m in the northwestern part. Both maps of RG reveal the deepening along the central section towards the terminus. With denser and more modern RES measurements, our high-resolution maps reveal small-scale undulations of bed topography. Moreover, our digital maps enable reusability in the future.

Currently, no point measurements of ice thickness from Swedish glaciers are included in the global ice-thickness database GlaThiDa , our datasets fill this gap and have considerable value across a wide range of disciplines.

The newly obtained ice thickness measurements can contribute to improving ice-thickness modelling for Swedish glaciers by constraining modelling parameters (such as ice viscosity). For example, we calibrated global model parameters using RES-measured ice thicknesses and repeated the experiment described in for MG. The model estimates more accurate ice thickness in the northwestern and central section (Fig. ). The mean absolute misfit between the updated modelled ice thickness and our result is 31 m, representing a 20 % reduction compared with their original modelled misfit.

Our bed topography maps provide essential boundary conditions for numerical modelling. They can be used for future studies of glacier evolution to improve projections of the remaining lifetimes of these glaciers . They can also support simulations of future hydrological changes within glacier catchments of four reference glaciers, e.g., determining water routing and locating future glacier lakes .

Annual ice volumes of the four reference glaciers can be quantified by combining our bed topography maps with annual high-resolution surface DEMs, which can be acquired using uncrewed aerial vehicles. Furthermore, bed topography maps reveal characteristics of the landscapes that will be exposed during the future post-glacial time (Fig. ). They provide insights into the potential geohazards (e.g. landslides, debris flows, and rockfalls) which might occur as landscape stability changes during glacier retreat.

The above predictions are crucial for local policymaking during glacier retreat and in the post-glacial future, when formerly glacier-covered areas become ice-free. This is particularly relevant for tourism planning, infrastructure development, and the sustainable livelihoods of Indigenous communities who rely on natural environments .