Introduction

Disregarding glaciers and ice caps at the ice-sheet peripheries, the Southern Hemisphere accommodates about 6% of the global glacier-ice volume1,2. This fraction has the potential to raise global mean sea-level by about 15 mm. It is remarkable that 80% of this volume is stored in only two ice bodies in the Southern Andes - the Patagonian icefields (PIs). The Southern Patagonian Icefield (SPI) is about three times larger than the Northern Patagonian Icefield (NPI). In 2000, the combined ice masses of the PIs covered a surface comparable to the metropolitan area of Paris (~16,000 km2)3,4, and showed average thickness values that exceed 250 m. This implies that PI glaciers are typically five times thicker than their European counterparts. In total, they store forty times more ice volume than glaciers in the European Alps. The Patagonian climate is characterised by westerly winds impinging on the Andean Cordillera resulting in a unique atmospheric gradient from super-humid conditions in the west to arid conditions in the east5. Prolific moisture transport results in inimitable amounts of annual precipitation6,7,8,9,10. High mass turn-over of glacier ice is the consequence, with maximum flow speeds reaching several kilometres a year11. Such velocity magnitudes are comparable to the largest outlet glaciers in Greenland and Antarctica12,13,14,15. Moreover, gravimetry measurements indicate that the vast ice plateau of the interior shows thickness values that exceed 1000 m16. Again, this is exceptional for glacierised regions outside the large ice sheets.

In the recent past, we have observed widespread thinning over the PIs. Specific ice-loss rates not only exceed values observed in nearby regions17,18 but are also elevated as compared to other mountain ranges around the globe19,20. The primary reason for this exceptional mass loss is controversial. The dominant driver is either direct climatic forcing or ice-dynamics. The former relates to mass gain and loss at the glacier surface, i.e. the surface mass balance (SMB). Ice-dynamic losses exclusively occur at marine- and lake-terminating (MALT) ice fronts. The ice-dynamic losses are typically subsumed under frontal ablation, which comprises iceberg calving and subaqueous melting. A final judgement of the dominant mass-loss term remains evasive because of the poorly constrained SMB processes6,8 as well as the little knowledge of ice thickness near the glacier snouts21. The reasons for this are the strong climate gradients in the region, the temperate nature of glacier ice as well as the general inaccessibility of the MALT glacier trunks (remoteness, crevassing, etc.).

Many attempts have been made to estimate how much ice is stored in the PIs and how it is distributed. Recent studies with a global focus1,2 relied on principles of mass conservation, the shallow ice approximation or a combination of the two. These studies were calibrated with measurements in the Glacier Thickness Database (GlaThiDa)22,23. Up to its latest version, GlaThiDa3.1.0, no direct measurements were included for either icefield in Patagonia. Therefore, the quality of these thickness maps ultimately depends on the transferability of these approaches between regions. Thickness reconstructions with a regional focus on South America16,24,25 are based on the yield-stress assumption or on gravimetric inversions. These studies attempted to constrain the thickness map with available measurements. Often this meant using selected survey campaigns on the low-elevation trunks of just a few glaciers. For gravimetric inversions16,25, abundant measurement records were available over the plateau areas. However, coverage of the elongated glacier trunks is poor. In summary, available thickness maps are largely unconstrained and often ignore the region-specific climatic, ice-dynamic and geometric setting. Moreover, thickness maps are particularly unreliable along the low-elevation outlet-glacier trunks.

Apart from the mere interest in the ice volume or its spatial distribution, glaciers are key elements with socio-economic and ecological importance26,27,28,29,30. In terms of natural resource, they act as natural water reservoirs. In this role, questions arise such as when peak water is reached under future warming27 and to what extent glaciers continue to buffer fresh-water shortage during dry seasons31. Such questions rely on future glacier projections. Their reliability is ultimately tied to the knowledge of present-day ice thickness32,33. As glaciers retreated in recent decades, new pro-glacial lakes formed while others expanded34. Although such lakes are potential sites for future hydro-power generation29, they also pose a threat to downstream communities, if dams break. In a review of glacier related hazards for Chile and Argentina35, the authors appeal for a research intensification in mountainous regions on the influence of cryospheric changes on slope failures and on outburst floods. The basis for such research is solid knowledge on the basal topography beneath the ice cover. Finally and on global scales, there is evidence that glacier retreat impacts positively on biodiversity28. This idealistic picture is moderated by the fact that particular species, adapted to glacial conditions, are often losers under these changes. In Tierra del Fuego, phytoplankton biomass reduction was observed in fjord systems as glacier retreated36. For further details, we refer the interested reader to a recent overview of the environmental impacts of glacier changes in Chile37. In summary, glacier thickness mapping is relevant far beyond the mere interest in sea-level relevant melt volume.

The primary objective of this study is to compile available thickness surveys, many of which were not considered previously. In addition, multi-temporal remote sensing of glacier elevation and outline changes is used to infer past thickness values in areas that have become ice free. This glacier retreat information represents additional near-front data. All thickness observations are assimilated with a state-of-the-art reconstruction approach for mapping glacier ice thickness that combines two methods. One method makes use of the principles of mass conservation38,39 and converts ice flux to thickness values using the shallow-ice approximation (SIA)40. The other method relies on the perfect plasticity assumption (PPA) for describing the ice rheology (for details see Data & Methods). Thickness results from both methods are updated in regions of fast ice flow according to velocity observations and subsequently combined into a multi-model reconstruction. The chosen reconstruction approach will thereby account for model-based SMB estimates, reflecting the climatic state, as well as remotely sensed information on the geometric setting, recent elevation changes and the ice-dynamic conditions. Apart from targeting a multi-model thickness map for both icefields, a primary motivation is to better constrain the dominant drivers for recent mass loss.

Results and discussion

The multi-model reconstruction approach provides a distributed field of ice thickness, together with associated uncertainties and the underlying bedrock topography (Fig. 1). The thickness map has a timestamp of 2000 stemming from the reference geometric state as defined by the digital elevation model (DEM) from the Shuttle Radar Topography Mission (SRTM)41. Contemporaneous glacier outlines are taken from the Randolph Glacier Inventory version 6.0 (RGI6.0)3,4. The maps are presented on a 200-m resolution. Direct and indirect thickness information is imprinted (cf. Data and Methods, Supplementary Fig. S5).

Fig. 1: The ice-free topography beneath the Patagonian icefields.
figure 1

a Overview panel for icefield locations. b NPI basal topography. c SPI basal topography in metres above sea level (ma.s.l.). The magenta lines delineate areas below sea- or lake level per adjacent glacier drainage basin. Coordinates: UTM 18S in kilometres. Background: SRTM hillshade.

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Ice volume

By integrating the ice-thickness maps, ice volumes of 1156 ± 398 and 4195 ± 1362 km3 are computed for NPI and SPI (Table 1), respectively. On the one hand, the NPI volume is at the lower end of previous estimates but agrees within ~10% considering temporal differences. On the other hand, the SPI volume is at the upper end and the disagreement to previous estimates increases to 25%. Ignoring the low-biased consensus estimate1, the agreement values reduce again to the same level as for NPI.

Table 1 Icefield volume estimates
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Concerning the associated volume uncertainties, we find relative values above 30% for both icefields (Table 1). All previous volume estimates fall into these ranges. Most previous studies were more optimistic about their uncertainty assessments. We are surprised that our approach produces higher errors, compared to these other studies, because a substantially larger amount of thickness measurements were considered. When averaging the relative measurement error of the thickness observations themselves (cf. Data & Methods), we obtain a mean value of 28% (standard deviation 16%). Admittedly, this average can only serve as a loose orientation and the final volume error will depend on the specific spatial distribution of these measurements. However, we assume that it is unlikely that a much lower relative volume error can be achieved, and values below 20% do not seem justifiable for the PIs.

Frontal areas & outlet glaciers

Knowing the thickness distribution and the basal topography, we can infer the volume fraction of glacier ice that lies below flotation (BF), i.e. not contributing to sea-level when melted. For both icefields only a small fraction (1–2%) is situated below flotation (Table 1). This ice is located in a confined area of 189 km2 on NPI and 445 km2 on SPI, representing about 4–5% of the total icefield extent. Considering the current areal retreat rates of 0.2–0.5% yr−1 for NPI and 0.2% yr−1 for SPI, this area is imminently at risk. This is certainly the case for SPI, where half of the mass loss occurs as frontal ablation at the ice fronts of MALT glaciers21. Except for the low-biased consensus estimate1, previous thickness maps often suggest more than twice as much BF ice. The moderate BF-volume reported here is somewhat in contrast to our high-end estimate of the total SPI volume. This contrast is a first indication that outlet glaciers tend to be thinner than previously thought.

The new PI bedrock maps show many glaciers with deeply incised troughs that lie below sea- or lake-level (Fig. 1). With respect to depth and areal extent, the most prominent incisions are found for Glaciar San Quintín in NPI and Glaciar Upsala in SPI. For the former glacier, the bed over-deepening reaches almost 20-km inland - a potentially susceptible setup for future retreat. This susceptibility assessment is based on paleo-evidence from an Arctic outlet glacier42 as well as centennial glacier retreat in Patagonia and Tierra del Fuego43,44,45,46,47,48. Episodes of fast retreat of MALT glaciers preferentially occurred along over-deepened bed sections. Further over-deepened sections beneath the NPI are found for Grosse and Exploradores glaciers in the north and Glaciar Nef in the east. At Glaciar Upsala in the SPI, frontal bathymetry locally exceeds 700 m below present lake level (179 m a.s.l.). However, the bed topography is prograde, certainly from its current front, that is to say it increases upglacier. This implies a more stable setup under retreat. Prograde bed topographies seem more characteristic for glacier fronts of SPI. A prominent exception is Glaciar Perito Moreno, for which the bedrock topography reaches up to 300 m below the lake level some 4 km from the ice-front. Near the ice-front, values range between 30 and 140 m, which is small compared to direct bathymetric measurements of up to 160 m in the adjacent lakes themselves49,50. Further north, the marine-terminating Glaciar Pío XI - the largest glacier in SPI - drains more than 10% of the ice field area into Eyre Fjord. Its trunk thickness is unsurveyed. Our approach suggests that the bathymetry is rather shallow near the front (<100 m) and in vast areas the bed remains above sea-level. This is in accordance with aerial images from the 1940s (Fig. 2), which show a much receded glacier front compared to its present-day position. An exposed outwash plain is visible in the area currently covered by the northern glacier branch and an ice-dammed proglacial lake. For further discussion of selected glacier examples, we point the interested reader to Supplementary Section S3. The identification of over-deepened bed sections can only be the first step to point out susceptible glacier setups. Yet, the pre-conditioning, the onset and the duration of phases of fast retreat is complex as they not only depend on the exact bedrock details. These phases are additionally controlled by the general ice-flow regime32, the thermal and circulation conditions in the pro-glacial water body21,51,52,53, the climatic or SMB history54,55 as well as glacier response times56.

Fig. 2: Aerial photograph of Glaciar Pío XI.
figure 2

The photo was taken on February 15, 1945 at 10:48am by the US Air Force using a trimetrogon camera74,75. The glacier calves into Eyre Fjord (centre left). Towards the north (centre, right), a large outwash plane is seen in areas which are now covered by the glacier itself or Lago Greve. The blue hatching loosely follows the fjord outlines as well as the outwash plane that are now covered by Glaciar Pío XI. Photo courtesy: Geographical Military Institute (IGM) of Chile.

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Thickness distribution and aggregated performance

Here, the analysis will focus on the thickness distribution and its comparison to independent observations and other map estimates (Fig. 3). In the interior, our reconstructed thickness field agrees well with the gravimetry inversion25 (Fig. 3c). The reason is that values of the latter inverted map were used as an input to this study along the actual flight-lines of the underlying gravity survey (Supplementary Fig. S5). Two more recent map estimates (Fig. 3d, e and Supplementary Fig. S1d, e), based on a global multi-model consensus or velocity observations, appear somewhat shallower in the interior. Close to ice-free areas and nunataks, thickness values increase much quicker with distance as compared to some of the previous maps (Fig. 3a, d, e). The resultant steeper mountain flanks are more consistent with the surrounding ice-free high-relief topography. This has important consequences for slope stability assessments26. Further discussion on the valley shape is presented in Supplementary Section S3.

Fig. 3: NPI thickness distribution for various reconstructions.
figure 3

Distributions are shown for a this study and b the perfect plasticity estimate24, c the gravimetry-based25, d the global consensus1 and e the global velocity-based estimates2. Background: SRTM hillshade.

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The participant approaches in the consensus estimate1 often pursue the reconstruction along flow lines or elevation bands and the final map interpolation depends on local slopes1,57,58. This dependence introduces a patchy pattern in the ice thickness distribution. On NPI, San Rafael and San Quintín glaciers are prime examples (Fig. 3d). Also the velocity-based approach (Fig. 3e) shows this erratic pattern because it relies on the SIA, which is equally sensitive to surface slope. Our estimate is less affected (Fig. 3a). The reason is that for the fast-flowing glacier units, it exclusively builds on mass conservation and is thereby independent of local slope magnitudes.

We aggregate the differences between modelled and observed values of ice thickness from each measurement location into scalar metrics (Fig. 4, Supplementary Fig. S4). These metrics serve as an overall evaluation for the various thickness maps. On NPI, mean and median differences are considerably smaller than in previous studies. This is less clearly expressed for SPI. Standard deviations, as a measure of the scattering of these differences, are lower for our approach on both icefields. This primarily reflects our systematic assimilation of ground-truth data. More details on these metrics are discussed in Supplementary Section S3. In summary, we are convinced that our thickness maps show improved quality mainly along fast-flowing outlet glaciers, as these areas are ideally suited for our method and because direct thickness measurements are concentrated there (Supplementary Fig. S5b, d).

Fig. 4: Observed vs. reconstructed ice thickness.
figure 4

The comparison distinguishes between NPI and SPI. For the point-by-point comparison, respective thickness maps are bi-linearly interpolated to the measurement locations. For this figure, the measurement record only comprises borehole, seismic and GPR measurements. Thickness comparison is conducted for the map products from a this study, b the perfect-plasticity24, c the global consensus1, d the gravimetry-based25 and e the global velocity-based estimates2. Values for mean (μ), median (M) and standard deviations (σ) are given.

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Frontal ice discharge

For the remainder of this section, we will focus on frontal ablation or more specifically on the frontal ice discharge (cf. Data & Methods). It is computed along flux gates (FG) using our thickness map, 2004 velocity information11 and a down-glacier correction for apparent mass balance. For NPI, the total discharge of 1.61 ± 0.29 km3 yr−1 is ~40% smaller (Fig. 5) than inferred in a recent FG study21. Also for SPI, we find a value which is about 25% lower than the aforementioned study, i.e. 16.48 ± 2.56 km3 yr−1. Part of these differences are certainly explained by glacier retreat, which is neglected in our study. However, the discrepancy mostly arises from just a few glaciers. For NPI, Glaciar San Quintín is found to export less than one third of the ice than previously thought. The remaining difference in total ice discharge stems from some other MALT glaciers being prolific (e.g., Acodado, Steffen, Nef, Leones). For Glaciar Nef, the low value is well constrained by extensive thickness surveys. In the case of Glaciar San Rafael, frontal thickness has been known for a long time and good agreement is seen between the various discharge estimates. Turning to SPI, a similar picture of reduced discharge arises. The prime example is Glaciar Pío XI, which we find to discharge about half as much ice, i.e. 1.48 ± 0.21 km3yr−1. The main reason is that its front is significantly thinner than in previous estimates. Together with four other prominent glaciers, i.e. Penguin, Europa, HPS31 and O’Higgins, most of the reduction in the total discharge is explained. None of the discharge values of these glaciers are well constrained in terms of direct observations (Supplementary Fig. S5). More glacier examples are discussed in Supplementary Section S3. In summary, distinctly reduced frontal discharge values imply that climatically controlled surface processes must explain a larger share of the past ice loss.

Fig. 5: Frontal Ice Discharge and Frontal Ablation.
figure 5

Values are given for the largest MALT glaciers in anticlockwise direction starting in the north of the icefields. Icefield-wide values and associated uncertainties (top right numbers) are given for NPI and SPI both for this study (blue) as well as for the most recent FG estimate21. For this study, individual discharge values are given for the most prominent MALT glaciers (numbers ± uncertainties, blue bars). Whiskers indicate associated uncertainties, partitioned into the contribution from the thickness uncertainty (yellow), the velocity error (black) and the integration of the apparent mass balance error (pink). Values from two other recent flux gate (FG) studies8,21 (green and purple bars) are provided together with independent estimates from mass budgeting (MB) for some individual glaciers6,8 (red bars). These studies reported on their uncertainties (grey whiskers). For all predecessor studies, some glaciers of SPI (i.e., Bernardo, Témpano, Occidental and Greve) have been aggregated into compounds. For compounds, combined discharge values are represented by bars with dashed outlines and light shading. Note that all estimates have distinct time coverage.

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Considering relative uncertainties in total ice discharge (Fig. 5), we find 18% and 16% for NPI and SPI, respectively. The previous study respectively reported 21% and 8%21. The lower relative uncertainty for SPI is surprising because much less is known about glaciers there, as compared to the NPI. An 8% discharge uncertainty appears, however, irreconcilable with typical errors of thickness measurements. Errors stemming from thickness mapping are the unequivocal and dominant source for uncertainties in frontal ablation (yellow whiskers in Fig. 5).

Independent estimates for frontal ablation are available from mass budgeting (MB) by differencing the integrated information on total geodetic mass change and SMB. The comparison with MB estimates of frontal ice discharge6,8 reveals two aspects. First, mass budgeting suggests larger values for most outlet glaciers. The differences are important for SPI. Second, reported MB errors appear small as compared to the FG methods. Turning to icefield-wide scales, recent studies report an almost balanced SMB (±0.6 km3 yr−1) for NPI6,9 (1975–2009) and +27.7 (1975–2000), +40.1 km3 yr−1 (2000–2011) or +29.9/31.5 km3 yr−1 (1975–2011) for SPI8,9. Another SMB study7, which admits to not fully resolve melting along the narrow outlet glaciers, suggests even higher positive values of about +9 and +55 km3 yr−1 (2000–2012) for NPI and SPI, respectively. Total mass-change values inferred by geodetic techniques using different satellite sensor systems agree well17,18. They amount to about −4.5 ± 0.2 and −13.5 ± 0.8 km3 yr−1 for NPI and SPI, respectively. The time period for the latter is about 2000 to 2012–2015. The residual between integrated values of the total mass change and the SMB (i.e., mass budgeting) gives information on ice loss across the lateral margin, i.e. frontal ablation. For both icefields, the differences are very large. The MB technique indicates a discharge value of over 40 km3 yr−1 for both NPI and SPI together. This value is twice as large than reported in this study. Neither the uncertainty associated to the geodetic method nor the conservative uncertainty estimates of our FG estimates allow a reconciliation with the SMB modelling efforts. Even the previous FG estimates for frontal ablation21, which are somewhat larger, cannot close the mass budget. However, it is known that the SMB estimates suffer from the poorly quantified precipitation amounts over the Patagonian Andes59. Reasons are the sparse station network, which does not allow an adequate sampling and quantification of the singular zonal gradients in the atmopshere and of the extreme precipitation rates, especially at high elevation5. Moreover, existing SMB estimates remain to this day controversial and they likely suffer from overestimated precipitation amounts from regional climate models10. Precipitation amounts have been found to not be reconcilable with regional moisture availability in the atmosphere.

Let us turn to changes in the PI mass budget. Between 2000 and 2020, frontal ablation was virtually constant over the NPI6 - a period in which total mass loss increased by ~1.8 km3 yr−118. For SPI, frontal ablation was reduced by about ~4 km3 yr−121. Yet mass loss rates only decreased by ~2.0 km3 yr−118. For both icefields, the discrepancy between changes in mass loss and frontal ablation requires a decreasing SMB. Again, the climatic influence seems to have had a more dominant control on past and recent ice loss from the PIs - and more so, than suggested in previous studies, considering the distinctly lower discharge estimates presented here.

Conclusions

This study is the first to compile and exploit available thickness surveys to estimate the ice-volume distribution of the two icefields in Patagonia in 2000. First, we suggest an upper-end ice volume estimate for Patagonia. The main reason is that the SPI likely stores 10% more ice than previously thought. Nonetheless, previous estimates remain within associated uncertainties. Despite making dedicated use of ground-truth data, this study cannot reduce and rather continues to produce large relative volume uncertainties exceeding 30%. These values ultimately stem from non-negligible errors inherent in the observations. The largest asset of this multi-model thickness map is that an abundant record of direct and indirect measurements is imprinted. In terms of thickness distribution, we are therefore convinced that the new basal topography represents an important quality increase, certainly along the many elongated outlet glaciers. Prominent examples are Glaciar San Quintín in NPI and Glaciar Upsala in SPI, two outlet glaciers, for which the trunk geometries are for the first time informed by direct measurements. We also find that our multi-model estimate appears beneficial in unsurveyed areas (e.g., Pío XI in Fig. 2). In summary, our basal topography map is key to reliably project future changes of the mountain cryosphere in Patagonia32. Such projections will present a solid basis to assess changes in regional fresh-water availability27, hydrological turnover, biodiversity28 and natural hazards35. Apart from the timing of future glacier retreat, the high quality of this map allows an improved identification of future lake formation - i.e., potential sites for hydro-power production29.

Considering that the Patagonian icefields show elevated ice-loss rates in recent decades, it is a pressing task to partition the mass change into frontal ablation and surface mass balance. Assuming that the presented basal topography is more reliable along the MALT glaciers, frontal ice discharge estimates become more robust. For NPI and SPI, we find icefield-wide values of 1.6 and almost 16.5 km3 yr−1, respectively. For this 2000–2004 estimate we ignored glacier retreat. Previous discharge estimates diverge dependent on the underlying methodology. As compared to a recent study21, ice-discharge values are lowered by more than 20%. This implies that surface processes, and with them the climatic influence, are likely more dominant drivers for mass loss from the Patagonian icefields, certainly when considering the discrepancy between recent changes in frontal ablation and total mass change18,21.

In any case, there remains a very large discrepancy in frontal ablation with respect to residual estimates from mass budgeting, which involves integrated values of SMB and geodetic mass change. This discrepancy is actually an overestimation by mass budgeting, which is not covered by our conservative uncertainty estimate for frontal ablation. If we confide in the small uncertainties reported along geodetic mass changes, it appears that an adequate description of the surface mass balance conditions of the icefields remains, to this day, evasive. This is substantiated by a typical overestimation of precipitation amounts by regional climate models in this area10. Moreover, because of the year-round strong westerly winds, snow-drift is a key process in redistributing mass input over the large plateau areas and between the various drainage basins of the icefields. On icefield-wide scales, an appropriate quantification of both precipitation and snow drift continues to be a key challenge in Patagonia.

Data & methods

Reconstruction approaches

For reconstructing 2D maps of basal topography, we rely on a two-step mass-conserving approach38, which readily assimilates available thickness measurements on regional scales1,39. In the first step, we employ two strategies to infer basin-wide thickness fields without using velocity observations. The first strategy is the classical iterative method, which casts the problem with respect to the ice-flux. The flux is subsequently converted into a thickness field by relying on the shallow ice approximation (SIA)40. This conversion relies on a spatially variable viscosity field B, which is determined where thickness observations are available. This classical method has further been updated with a viscosity re-scaling that improves the thickness distribution away from observations60. The second strategy is a 2D adaptation of a PPA approach61. It assumes that the local driving stress τd equals a material-specific yield stress τ0. Similar to above, τ0 is estimated where thickness measurements are available and subsequently interpolated. To accommodate for non-local stress coupling62, the driving stress field is spatially smoothed as described in the original first-step approach38. This smoothing initially uses a constant radius and is updated once. The thickness field from each strategy independently serves as boundary conditions for the second-step reconstruction, which directly updates the ice thickness in a sub-domain where surface velocities exceed 100 m yr−1. The two thickness maps are then averaged to infer a multi-model estimate. Model parameters are given in Supplementary Table S3. The triangular model mesh has target resolution of 400 m, which is refined near the measurements (~200 m). For the final thickness map, results are interpolated to a 200 m rectangular grid.

Data

Glacier outlines

Two glacier inventories are consulted for outline information. Reference outlines are taken from the Randolph Glacier Inventory version 6.0 (RGI6.0)3,4. For this data base, glacier extents have been manually mapped from Landsat images in March 200163,64. This reference extent serve as a basis for the thickness mapping of ice-covered areas. A more recent inventory was required to delineate glacier retreat. It has a 2016 timestamp and was digitised from multiple Landsat scenes47.

Surface elevation & elevation changes

The reference digital elevation model (DEM) from February 2000 is based on the C-band 30-m product of the Shuttle Radar Topography Mission (SRTM, v2.1)41. Remaining voids in steep slope terrain were filled with the 2010 Global multi-resolution terrain elevation data65. The SRTM vertical accuracy is smaller than 9m. To determine elevation-change rates after 2000, we rely on the TerraSAR-X-Add-on for DigitalElevation Measurements (TDX)66. Elevation change rates have been inferred for both icefields from TDX imagery acquired between 2011 and 201617,67. A second DEM with a more specific time stamp was inferred from TDX coverage in 2019.

Surface mass balance

A combination of dynamical and statistical downscaling techniques were used to infer high-resolution climatic conditions for 1975–2011 from NCEP-NCAR atmospheric reanalysis data68 over the NPI6 and the SPI8. On this basis, the glacier SMB was estimated using an enhanced temperature index model accounting for cloud-cover corrected potential incoming radiation. From a comparison between geodetic mass changes17,67 and SMB values over drainge basins of land-terminating glaciers, we infer a specific uncertainty of ~1 myr−1 in water equivalent (w.e.). This value comprises both the uncertainty in the elevation change observations as well as in the SMB model estimate. It therefore serves as the input uncertainty for the apparent mass balance.

Thickness observations

Despite the multitude of survey campaigns on the Patagonian Icefields (Supplementary Table S1), no single point measurement of ice thickness is included in the current version 3.1.0 of the global Glacier Thickness Database (GlaThiDa)22,23. Here we compile thickness information on 1,475,054 point measurements from two primary sources. The first source comprises direct measurement from ground penetrating radar (GPR), seimsics surveys and a borehole (463,822) as well as gravimetry inferred thickness values (489,194). The second source is indirect thickness values inferred from glacier retreat since February 2001. The retreat area is defined by 2016 outline information with respect to RGI6.0. For retreat on land, we estimate past thickness by DEM differencing against SRTM on 30-m resolution (459,442). For marine retreat, available bathymetric measurements were used and added to the SRTM DEM (62,596). For more details on the considered survey campaigns please refer to the Supplementary Material (Section S1).

Experimental design

The timestamp of the pursued thickness reconstruction is tied to the reference SRTM DEM and thus February 2000. The reason for this is that SRTM serves as the geometric input and is key to determine the retreat thickness information (cf. Supplementary Section S1). Unfortunately, we cannot provide a second thickness map for a more recent period. An option would be the 2011–2015 Copernicus DEM69. However, the somewhat contemporaneous national glacier inventories of Argentina70 and Chile71 show incomplete coverage. For 2000, we first produce two thickness maps, one building on the SIA and the other on the PPA. Both maps are updated in a second step according to the observed velocity field while thickness observations are assimilated. Gravimetric measurements show a very dense coverage. Where they overlap with other measurements, we often observe an underestimation by gravimetry. We therefore introduce a down-weighting of gravimetric measurements at lower elevation (Supplementary Section S2) in order to give priority to other measurements, where available. In a final step, the SIA and PPA thickness maps are distilled into a multi-model map by simple averaging. We thereby follow the advises from the Ice Thickness Models Intercomparison eXperiment (ITMIX) phases 1 & 272,73, that multi-model estimates show improved performance.

Frontal ablation & frontal ice discharge

Flux gates (FG) were placed close to the present ice-fronts of all MALT glaciers, acknowledging the quality of the available velocity field at the glacier surface11. The ice flux across these gates is computed as the product of the ice thickness and the surface velocity component perpendicular to these gates. In this way, we assume plug flow and negligible vertical shearing near the ice-fronts. To compute frontal ablation, these flux values are corrected by the integrated apparent mass balance field over the tongue area downstream of the FGs. The apparent mass balance is the difference between the SMB and geodetic elevation changes, with the latter being subtracted. Thereby, we deliberately ignore effects from glacier retreat or basal mass balance. We refer to this flux as the frontal ice discharge. Uncertainties in this quantity are computed by linear error propagation using the error map of our thickness product as well as the largest error of the used multi-sensor surface velocity map, which is reported to be ~52 myr−111.