In future simulations, the models for ice dynamics (Sect. ) and SMB (Sect. ) are two-way coupled at yearly intervals. Thereby, we account for the feedback between SMB and the changing glacier-surface elevation over time. At the end of each year, the modelled ice-surface topography is used as input for the downscaling routine described below. SMB is downscaled to the updated ice-surface topography on a monthly basis for the subsequent year, in 100 m resolution. The obtained 100 m SMB is then interpolated onto the mesh of the ice-flow model, which then simulates ice-cap evolution over the following year.

We distinguish between different representations of SMB, to isolate the effects and feedbacks with SMB involved. The reference-surface mass balance, SMB_static, refers to the SMB on an unchanging reference geometry (no elevation or area changes) and serves as a direct indicator of climatic variations . The conventional surface mass balance, SMB_transGeom, is produced with the coupling procedure described above and accounts for the dynamic adjustment of both ice-surface elevation and glacier area to the SMB forcing. To isolate the SMB-elevation feedback from the effect of glacier area changes, we also evaluate SMB_transArea, which is SMB for an evolving area, but without elevation changes.

To provide high-resolution distributed SMB to the ice-flow model we downscale the modelled SMB from the 1 km DTM of the seNorge_2018 dataset to 100 m resolution using the elevation-dependent downscaling procedure of . This algorithm downscales SMB from a coarse to a high-resolution DTM grid based on linear regression to determine local SMB gradients. We apply the algorithm on a monthly time scale to retrieve monthly fields of SMB at 100 m resolution. First, for each grid cell of the 1 km DTM the local SMB gradient (slope of the regression) is computed using the 1 km SMB and elevation of the given cell and the adjacent cells. The intercept of the regression in the given cell is then found using the 1 km SMB and elevation and the local SMB gradient. Secondly, the 1 km regression coefficients (slope and intercept) are bilinearly interpolated to the 100 m DTM to retrieve 100 m regression coefficients. Finally, SMB is computed in each 100 m grid cell using the 100 m regression coefficients and elevation in the given cell.

To simulate SMB over the period 2021–2100, we construct time series of daily mean temperature and precipitation using a combination of daily variability in historical data (seNorge_2018) and future trends from regional and global climate model (RCM/GCM) projections (Table ). The general procedure is based on the approach of and can be outlined as follows: (1) we detrend daily temperature and precipitation in seNorge_2018 for a 20-year historical reference period (2001–2020) by subtracting monthly linear trends in daily temperature and precipitation over the reference period from the historical data, (2) for each combination of climate model and future emission scenario (eight in total) we compute monthly linear trends for 20-year periods (2021–2040, 2041–2060, 2061–2080 and 2081–2100), and establish piece-wise linear functions for future changes in temperature and precipitation, and (3) we superimpose the piece-wise linear functions on the detrended reference data, repeated for each future 20-year future period.

The basis for future trends in temperature and precipitation are 1 km downscaled and bias-corrected daily resolution temperature and precipitation fields based on four EURO-CORDEX GCM/RCM combinations and two Representative Concentration Pathway (RCP) emission scenarios that have been used to assess climate change impacts in Norway see Table . The original 12.5 km resolution GCM/RCM fields have been re-gridded to 1 km resolution and bias-corrected (see for details) using 1 km resolution temperature and precipitation fields from the seNorge dataset version 1.1;.

When detrending precipitation, the monthly trends and intercepts are distributed evenly over each day of the month. This results in some days having negative precipitation values, even after the addition of future monthly trends. Where this occurs, daily precipitation is set to zero. This means that the number of wet/dry days in future periods is not necessarily consistent with the reference period. We judge this to be of minor importance since repeating past variability may not be fully representative of future conditions. Capping negative values at zero may also result in deviations between future precipitation sums and computed trends. However, since precipitation generally increases in future projections, large differences are unlikely to occur.

After ensuring that the model can satisfactorily reproduce recent glacier changes and dynamics, we conduct a suite of experiments of future evolution of the ice cap (Table ). These simulations are grouped into four categories: “Future”, “Commit”, “Reverse” and “Regrow”. Below we describe each group of experiments in more detail.

“Future” simulations (Sect. ) are run from 2021–2100, using SMB based on climate forcing from the four GCM/RCM combinations, and for RCP4.5 and RCP8.5 emission scenarios. Each of these simulations, eight in total, start from the transient model state at the end of the `Historical' simulation. This ensures consistent internal model dynamics and, crucially, that future simulations account for the time-lagged ice-cap response to recent climate forcing. We specifically designed an experiment called “CommitNow” to assess this aspect, where we let the historical simulation continue until 2300, using the mean annual SMB of 2001–2020 as a constant forcing.

The modelled ice cap in 2100 produced using the ECEARTH/CCLM model combination is used as the initial state for the “Commit”- and “Reverse”-experiments (Sect. ; ). This model combination was chosen because it renders a mid-range volume evolution across the four climate model combinations (Sect. ). The Commit experiments quantify mass losses “in the pipeline” by 2100, without any further climate change taking place. They thus shed light on the long-term response of the ice cap to climate change. In these simulations, the ice cap evolves for another 200 years until 2300, using mean annual SMB from 2081–2100 as a constant forcing. Meanwhile, Reverse experiments explore the potential to undo the modelled 21st-century evolution of the ice cap (Reverse4.5 and 8.5). To this end, mean annual SMB of 2001–2020 is used as forcing from 2101 until 2300.

Finally, we assess whether Jostedalsbreen ice cap can regrow from ice-free ice conditions in the present or future climates (Sect. ). These experiments run for 1000 years and use mean annual SMB for the present-day (2001–2020, RegrowNow) or end-of-the-century climate (2081–2100, Regrow4.5 and 8.5). SMB and ice dynamics are coupled every 20 years in these simulations, as opposed to every year in the other future runs. The longer coupling interval for “Regrow” experiments saves computation time and has here negligible effect compared to coupling every year, due to the relatively slow dynamics involved when growing Jostedalsbreen from no ice.

Future SMB simulations reveal that substantial changes in SMB forcing (SMB_static) on Jostedalsbreen can be expected over the coming century (Figs.  and ). Moreover, differences between climate model combinations and emission scenarios are striking (Fig. c). The majority of climate models result in cumulative mass losses of around -25 m w.e. over the next 30–40 years, with relatively low variation between the RCP4.5 and 8.5 scenarios. After around year 2050, models show a larger spread with cumulative mass losses up to around -150 m w.e. by the end of the century. Note that this mass loss is for an SMB over a fixed geometry (SMB_static), that is, before considering the effects of future area changes and the SMB-elevation feedback (see Sect.  and Fig. ). One model combination stands out from the rest: MPI/CCLM shows a large mass increase under the high-emission scenario (Fig. c). This is a result of rapid and extreme (unrealistic; Sect. ) gains in future winter precipitation, along with mainly negative winter temperature and little change in summer temperature (Fig. ), which renders a positive cumulative SMB_static over the course of the 21st-century (Fig. ). The near balance with ECEARTH/HIRHAM under a medium-emission scenario is a result of similar, but less extreme, mechanisms.

Our simulations indicate an increase in the frequency and magnitude of negative SMB throughout the century, under both medium- and high-emission scenarios (Fig. a and b, respectively). Under high-emission scenarios, ice-cap wide mass losses can reach SMB magnitudes similar to those seen only for the low-lying tongues of Jostedalsbreen today e.g. around -6 to -7.5 m w.e. on the lower tongue of Nigardsbreen in 2023;. Our results also indicate that, under both emission scenarios, years with positive ice-cap wide SMB can occur far into the 21st century, although this occurs significantly less often during the second half of the century. Uncertainties in future SMB are greater for high-emission scenarios, mainly due to the substantial spread between climate model projections (see Sect. ).

Considering the mid-range climate forcing ECEARTH/CCLM, before considering the SMB–elevation feedback (Fig. ), the ice cap will retain a substantial accumulation area at high elevations in the South and Central parts for RCP4.5 by the end of the 21st century (Fig. a), while annual SMB rates in the North will be mainly negative. For RCP8.5, SMB rates remain positive only for smaller parts on the central plateau (Fig. c), with a large reduction in SMB rates over the entire ice cap compared to present day (Fig. d). The greatest reduction in SMB occurs on low-lying glacier tongues and along ice-cap margins (Fig. b and d). However, the South part, which has shown mostly positive SMB rates over the historical period 1960–2020;, also displays large negative changes in SMB by the end of the 21st century for this scenario.

Our dynamical model simulations reveal that Jostedalsbreen stays in near balance until year 2040. Thereafter, the ice cap is projected to lose half (two-thirds) of its ice volume under medium (high) emissions until the year 2100 (Fig. d and b). These results are obtained with the ECEARTH/CCLM climate forcing, which gives an ice-volume loss that is mid-range across the four climate model combinations (Fig. ; cf. Table ). Model simulations forced by the full ensemble of climate models suggest that, until the year 2100, Jostedalsbreen will lose 10 %–75 % of its present-day volume under medium emissions (Fig. f). Meanwhile, for high emissions, future volume evolution ranges from 75 % loss (CNRM/CCLM) to 17 % gain (MPI/CCLM) by 2100. The latter unexpected future increase of volume with MPI/CCLM under high emissions is a result of positive SMB. While we include these results for completeness, we deem this climate projection unrealistic (Sect. ). If we exclude the MPI/CCLM results, the projected future mass loss is 12 %–74 % for medium emissions, and 53 %–74 % under high emissions (Fig. f).

In our experiments of future evolution until 2100, Jostedalsbreen splits up into three separate ice caps both under medium and high emissions (ECEARTH/CCLM, RCP4.5 and 8.5; Fig. ). With medium emissions, North separates from the rest of the ice cap in the 2070s, while South becomes a separate ice cap in the 2090s (see Supplement video 1). Meanwhile, under high emissions, these breakups occur around 10–20 years earlier; in the 2050s for North, and in the 2080s for South (see Supplement video 2). However, it is important to note that these separations and other small-scale details include a high degree of uncertainty. They can vary by several decades due to differences in the future climate projections (Sect. ), underlying model limitations (Sect. ) and local mismatches between the modelled and real-world geometry. For example, the model mesh is too coarse (Fig. ) to resolve a few small ice-free patches (100–200 m across) which currently partly separate the southern and central parts (cf. Fig. ). Modelled contemporary ice thickness is 20–50 m in this area, while the measured ice thickness is less than 25 m . This suggests that a separation may occur several decades before the 2080s. The North part of Jostedalsbreen, with its plateau situated ca. 100–300 m lower than the Central ice cap (Fig. ), is simulated to decline most strongly. The modelled future thinning here is 20 %–100 %, and total volume loss 74 %–93 %, depending on emissions (Fig. ). This is already the area of the ice cap where current mass loss is greatest .

Regardless of emission pathway, most of the volume loss is driven by strong thinning of 20–200 m at the ice-cap margins (Fig. ), with less pronounced thinning of 20–100 m on the plateau. This results in frontal retreat and an overall steepening of the ice cap's outlet glaciers (Fig. a, b). These patterns can be explained by a SMB_transGeom that, over the course of the century, becomes increasingly negative in ablation zones, while net annual SMB on the plateau remains positive for many of the years in the coming decades (Fig. c, d, f). Annual SMB on the plateau is in fact rather similar between the medium and high emissions, which is likely due to similar precipitation amounts (see Sect. ). Meanwhile, SMB along the margins of key outlet glaciers such as Nigardsbreen and Tunsbergdalsbreen is 3–8 m w.e. more negative than at present (Fig. c, d). This corresponds to typical annual SMB values of -12 to -18 m w.e. at the frontal regions, which presently are located at 300–700 m a.s.l.

Depending on the emission scenario, terminus retreat for Nigardsbreen and Tunsbergdalsbreen is simulated to be ca. 2.5–5 and ca. 5–10 km, respectively (ECEARTH/CCLM; Fig. ab). Because mass loss at the high-lying plateau here is rather subdued, these glaciers still retain around half of their volume by the year 2100, even under high emissions (Fig. ). Similarly, Austerdalsbreen loses the entire glacier tongue below its ice fall under RCP4.5, but two-thirds of the ice volume remains by 2100. To reiterate this point: Tunsbergsdalsbreen retreats 10 km under high emissions (Fig. b), yet by the end of the century still hosts large upper areas with ice more than 500 m thick (Fig. d). As we will see in Sect. , this is the most resilient part of the ice cap.

Our simulations show that the ice cap is in strong disequilibrium with the current climate. If the climate of the last 20 years (2000–2020) would persist into the future, almost half (47 %) of the ice-cap volume would be lost (CommitNow; Figs. b and a). Under the medium-emission scenario RCP4.5, Jostedalsbreen loses around half of its present-day volume by 2100. Similarly, about one-third of the ice volume remains by 2100 under the high-emission scenario RCP8.5 (Fig. b). However, this is only half of the story, since Jostedalsbreen will not have reached a steady-state in 2100. Further mass loss is “in the pipeline”, as the ice cap undergoes additional dynamic adjustments and continues to thin due to the effective SMB-elevation feedback. In the high-emission case, our simulations show that the ice cap is committed to vanish completely by around 2200, even without any post-2100 climate warming (Commit8.5; Figs.  and b). Similarly, with moderate 21st-century emissions (RCP4.5), the ice cap is committed to lose 90 % of its present-day volume by 2300 (Commit4.5). Upper Tunsbergsdalsbreen and the nearby high-elevation areas to the north (upper Brenndalsbreen and southwest corner of upper Nigardsbreen) is the part of the ice cap that is most likely to survive the longest. Another resilient high-lying ice complex appears to be upper Fåbergstølsbreen and nearby areas along the local ice divides (Fig. b, c).

Our Reverse experiments test whether the ice cap can recover if the climate is reversed back to present immediately at the year 2100. That is, instantly resetting the climate forcing to an SMB associated with the prevailing climate of 2000–2020. We find that such hypothetical time travel leads to barely any recovery (Fig. b). The inability to recover holds regardless of whether emissions are moderate or high before the reversal. The main reason for the failure to recover is that the ice cap is currently strongly out of balance with the prevailing climate. In other words, resetting the climate of year 2100 to the climate of 2000–2020 means aiming for an ice-cap that is considerably smaller than that of the present-day. The CommitNow experiment illustrates this, where Jostedalsbreen's volume is halved by the year 2300 (Fig. b). Indeed, by 2300, the Reverse4.5 and Reverse8.5 simulations would reach steady-state volumes similar to that of the CommitNow experiment, if the simulations are allowed to continue for another 100 years (ca. 30–35 km³; Fig. b). Another aspect preventing recovery may be that by 2100, the ice cap is on the course to an even lower ice volume (cf. Commit4.5 and Commit8.5 experiments; Fig. b). Therefore, any ice-cap growth due to a more favourable SMB, will in fact compete with ongoing dynamic adjustments and associated SMB-elevation feedback working towards a smaller ice cap.

The found failure to recover, as well as the difficulty to regrow the ice cap (Sect. ), is also an aspect of the hysteresis effect . This hysteresis is particularly strong for ice caps and ice sheets , since a large part of their area is concentrated within a small elevation range. These ice masses can be maintained as long as sufficiently large areas with positive SMB persist. If the ELA rises above such flat high-elevation areas, mass loss quickly accelerates and becomes difficult to reverse .

The majority of our simulations suggest that Jostedalsbreen will experience a substantial mass loss over the course of the 21st century (Fig. ). At the same time, modelled SMB based on the ensemble of climate models leads to a large spread of possible future ice-cap evolution. This suggests both substantial variations between projected temperature and precipitation changes between climate models (Fig. ) and a strong sensitivity to choice of climate model and scenario. Medium and high emission scenarios show a mean annual temperature increase over Jostedalsbreen (2019 area) of 1.8 and 3.4 °C, respectively, by the end of the century. The mean increase in annual precipitation sums for the respective scenarios is 27 % and 65%, with an increase of 30 % and 67 % in winter (Fig. c). However, for a given emission scenario there are considerable differences between the models. For example, projected change in summer (May–September) temperature varies from -0.3 to +2.7°C under RCP4.5, and +0.2 to 3.0°C under RCP8.5 (Fig. b). The spread in winter (October–April) temperature is smaller, around 1.2 and 1.9 °C for RCP4.5 and 8.5, respectively (Fig. a). Differences in precipitation between climate models and scenarios are even more striking, with models projecting winter precipitation changes between -14 % and +72 % for RCP4.5 and between +39 % and +80 % for RCP8.5 (Fig. d). Moreover, the timing of precipitation changes also varies across the climate models, both in terms of the time of year and the evolution throughout the century.

Our simulations allow us to assess future changes in seasonality and magnitudes of ablation and accumulation for Jostedalsbreen. With the ECEARTH/CCLM projections, the largest changes in the SMB for the transiently evolving Jostedalsbreen can be expected in autumn and summer under medium and high emissions, respectively (Fig. ). Under an RCP4.5 scenario, the ablation season is prolonged by approximately a month, from mid-September to mid-October, with an equivalent shortening of the winter accumulation period (Fig. a). Meanwhile, ablation magnitudes at the peak of summer change relatively little. This contrasts with high emissions, where strong summer melt intensifies and is more prolonged between June to September (Fig. b). These differences reflect both differing warming and precipitation trends between climate projections (Fig. ), and variations in which seasons and months such changes are projected to occur. While both ECEARTH/CCLM scenarios render relatively strong winter warming (Fig. a), temperature increase in summer is smaller (Fig. b). Moreover, there are variations between the projections within seasons. For example, warming is stronger in October for RCP4.5 than RCP8.5, which could explain why autumn SMB changes are less pronounced for the latter. However, it should be noted that the future monthly SMB in Fig.  not only reflects climatic changes but also accounts for the feedback of glacier retreat and surface-elevation lowering (SMB_transGeom).

Most climate models show that precipitation gains increase with elevation. This explains why the models indicate larger precipitation increases over Jostedalsbreen than for western Norway in general . This may be a natural consequence of increasing and intensifying precipitation; precipitation amounts on Jostedalsbreen are likely substantially affected by orographic uplift e.g.. However, the large precipitation increase over Jostedalsbreen may also be a result of how climate models are downscaled and bias-corrected to the seNorge version 1.1. dataset , which relies on precipitation lapse rates to extrapolate precipitation to higher elevations . The large projected increases in precipitation, and differences between climate models and scenarios, highlight the considerable uncertainty in future temperature and precipitation in mountainous regions, and the sensitivity of glacier projections to climate model input. For glaciers with a substantial mass turnover and likely large future accumulation area, such as Jostedalsbreen, our results highlight that future glacier evolution strongly depends on future precipitation changes, and that projections of future glacier change remain uncertain due to the (in)ability of climate models to capture these changes.

In future SMB simulations there are two competing feedbacks between SMB and glacier geometry changes at play . The first is the retreat feedback, which contributes to a more positive SMB_transArea, relative to the reference SMB_static, as the glacier retreats to higher elevations where ablation is smaller. The elevation feedback acts in the opposite direction, contributing to a more negative SMB_transGeom as the glacier surface is lowered to elevations where ablation is higher . To quantify the relative and net impacts, we computed the transient SMB in Megatonnes (Mt) across the entire ensemble of climate model combinations (Fig. d). This analysis shows that, for most climate models, the total mass balance SMB_static becomes very negative towards the end of the century, since it ignores the two feedbacks. Meanwhile, the positive retreat feedback, which includes area changes, makes the SMB_transArea ca. 0.5–2.5 Mt less negative than SMB_static. Note that the glacier is still losing mass overall for all scenarios with this feedback included. Including also the elevation feedback, where glacier geometry and SMB is fully coupled (SMB_transGeom), shifts the total mass balance 0.1–0.6 Mt more negative compared to SMB with the retreat feedback only (SMB_transArea). Simulation of long-term glacier evolution thus requires careful consideration of the mass-balance elevation feedback. If not, a strong positive bias in modelled SMB can be expected (Fig. ).

A pertinent question is whether Jostedalsbreen can regrow from no ice to its current size under contemporary or future climate conditions. The answer is no, neither in the current climate, nor in a warmer future one, at least not using the chosen main climate model combination ECEARTH/CCLM. If Jostedalsbreen disappeared tomorrow, the present-day climate (2000–2020) would render a much smaller ice cap than the present-day Jostedalsbreen, with a 59 % smaller ice volume (29 km³), 30 % smaller area (317 km² and 60 % thinner ice [mean ice thickness of only 91 m]; Fig. ). This implies 60 % thinner ice on average than for the present-day . The modelled volume of this regenerated ice cap is similar to present-day Søndre Folgefonna 30 km³;, Norway's third largest ice cap by area, and around three times larger than the present-day Hardangerjøkulen (ice volume of 9.3 km³, area of 71 km², max ice thickness ca. 350 m), one of the most well-studied ice caps in Norway . Meanwhile, we barely produce any glacier ice when trying to grow Jostedalsbreen from no ice using an SMB (2081–2100) associated with medium 21st-century emissions, and no ice at all with a high-emission climate (experiments Regrow4.5 and Regrow8.5). For Hardangerjøkulen, similarly found that a small negative SMB anomaly relative to the present-day would render a regrowth from no ice impossible. These findings collectively imply that if two of the largest Norwegian ice caps would melt away, a recovery appears very difficult, and would require a colder and/or wetter climate than the present one.

Regional studies of Scandinavian glaciers have shown that Jostedalsbreen will lose 35 % (RCP4.5) to 50 % (RCP8.5) of its area and volume by 2100 . This is slightly lower mass loss than estimated by the current study (49 % for RCP4.5, 63 % for RCP8.5; Fig. ). Meanwhile, suggested that Nigardsbreen would lose 64 % (RCP4.5) to 85 % (RCP8.5) of its present-day volume, which is roughly 50 % more mass loss than our mid-range results for Nigardsbreen from ECEARTH/CCLM (Fig. ). More broadly, estimates for 21st-century mass loss for Scandinavian glaciers and ice caps as a whole range from  40 %–80 % (RCP4.5) and 70 %–100 % RCP8.5; e.g.. These large-scale studies may perform well on regional scales, but their estimates for individual ice masses are not directly comparable with those of a detailed study like ours. As emphasised in Sect. , regional studies treat connected glacier units separately, use crude ice-flow dynamics, and have not benefitted from such detailed ice-thickness data and surface mass balance simulations as we have in the current study. The methods, scales and implementations thus differ greatly compared to the detailed, higher-order, high-resolution, spatially continuous modelling approach presented here.

For high-emission scenarios, some studies of other ice caps in Norway suggest almost complete disappearance by the year 2100 or soon thereafter, including Hardangerjøkulen Table ;, and Spørteggbreen ice cap, ca. 15 km east of Jostedalsbreen . Our findings suggest that Jostedalsbreen will be more long-lasting, and retain one-third to half of its present-day ice volume at the end of the 21st-century, depending on emissions (Fig. b). Not only does Jostedalsbreen contain more ice – its particular resilience is likely also related to the vast plateau being at high elevations, and relatively large precipitation amounts, which will increase even more in the future. Even so, an extrapolation of the high-emission modelled rate of mass loss by 2100 suggests a complete disappearance in the late 22nd-century, if emissions are not curtailed. While our Commit-experiments do not explicitly test this, they illustrate that by 2100, Jostedalsbreen may be committed to a complete disappearance 200 years later.

simulated future evolution of Nigardsbreen (cf. Fig. ) using a 1d-flowline model. For a warming of 1 °C and +10 % precipitation, Nigardsbreen was projected to lose 24 % of its present-day (AD 1950) volume, while for a 2 °C-warming and +20 % increase in precipitation, Nigardsbreen's modelled future volume loss was 58 %. This is comparable to our modelled 40 %–56 % volume loss for Nigardsbreen for RCP4.5 and RCP8.5, respectively (Fig. ). However, the thickness data, models and future climate projections used by the current study and differ significantly.

The impact of future warming on Briksdalsbreen has previously been modelled using a flowline model together with a degree-day model for surface mass balance . While they did not provide volume projections, they estimate 21st-century frontal retreat of 2.5 to 5 km under scenarios similar to RCP4.5 and RCP8.5 used here. A similar retreat is simulated in the current study, along with a volume loss of 33 % (RCP4.5) and 46 % (RCP8.5) for the glaciers terminating in Oldedalen, using the ECEARTH/CCLM climate (Fig. ).

Results from Søndre Folgefonna indicate that for RCP4.5 and RCP8.5 about 43 % and 92 %, respectively, of the ice cap will have melted away by the year 2120 . The northern parts of the ice cap are more vulnerable than the southern parts. Søndre Folgefonna's current ice volume is 28 km³ , around 40 % smaller than the ice volume of Jostedalsbreen. Considering its smaller size, Søndre Folgefonna is surprisingly resilient to future warming. The knowledge of the bed topography underneath Søndre Folgefonna is perhaps the only one in Norway that matches the level of detail in the newly-mapped topography under Jostedalsbreen , and maximum ice thicknesses are similar, with areas of ice more than 500 m thick existing for both ice caps. Some outlet glaciers from Folgefonna are known to have reached their Little Ice Age maximum extent as late as in the 1940s , and has not retreated much since, which may explain the relative resilience to warming. Folgefonna is also a more maritime ice cap than Jostedalsbreen, with its surface mass balance heavily controlled by high winter snowfall . This may buffer Folgefonna from future warming, and perhaps also the western outlets of Jostedalsbreen. Such snowfall buffering however has its limits. As climate warms, more precipitation falls as rain rather than snow, which, for example, has been found to diminish the buffering of Patagonian glaciers located in a similar maritime climate .

The gridded observation-based ice-thickness dataset is based on measured ice-thickness point data combined with an ice-thickness model based on inversion (Sect. ; see for details). Despite the unprecedented level of detail in this dataset, the uncertainties in areas without thickness observations are estimated to be up to 50–100 m, but in practice likely smaller, particularly close to radar survey lines . An overestimated (underestimated) observation-based thickness will affect modelled ice-flow and render a too slow (too fast) future mass loss and retreat. Meanwhile, present-day thickness and ice-cap margins are overall well reproduced by the historical simulations, yet there are some mismatches at the end-of-historical state (Fig. ). These differences for individual glaciers will propagate into the future, affecting the timing of retreat. For example, the front positions of the steep Briksdalsbreen and Brenndalsbreen outlets are ca. 700 and 1200 m too advanced, respectively, for the present-day (cf. Figs.  and a). This disagreement likely propagates several decades into the future simulations. This means that future modelled frontal positions for these glaciers are likely located several hundred metres further downvalley compared to reality. Meanwhile, the fronts of these and other outlet glaciers with steep ice falls (e.g. Austerdalsbreen) are thin and may disconnect from the upper glacier. This is modelled for Brenndalsbreen (Fig. b) and illustrated for similar ice masses . In this case, the disconnected tongue will lose its ice supply from the upper glacier, and quickly melt away.

The future projections presented here rely on the model geometry and dynamics of the historical simulations 1960–2020. In turn, the historical experiments are influenced by the initial ice-cap state of the 1960s, obtained through model spinup (Sect. ). The spinup uses the 1966 ice-surface topography as a target, and assumes that the ice cap was in steady-state in the 1960s. We also tested to obtain the initial historical geometry without a steady-state assumption, starting from the 1966 surface DEM and running a relaxation for only a few years. While ice-surface data artifacts dissipated, this approach resulted in unrealistic model drift of the ice-surface topography during the historical simulation. We therefore switched to the practical steady-state assumption. An inverse approach to find the ice thickness could also have been considered, yet here we take advantage of the detailed newly collected thickness dataset from . In reality, the ice cap will have experienced ongoing adjustments to climate variations occurring between the Little Ice Age maximum in the 1800s up until the 1950s. Indeed, several records of frontal variations of Jostedalsbreen's outlet glaciers show retreat in the 1930s through 1960s https://glacier.nve.no/viewer/CI/en/, last access: 3 October 2025;. Such adjustments are not accounted for in the historical simulations. This may partly explain why the model underestimates the reconstructed ice volume in 1966 (Fig. a), and partly why a relatively modest historical retreat and volume loss is simulated – although we emphasise that there are also underlying uncertainties in the observation-based ice thickness dataset . Regardless, not accounting for the real-world ongoing decline could have resulted in chosen model parameters being biased towards too positive SMB.

Historical and future ice cap evolution is strongly controlled by the SMB forcing (Figs.  and ), which is subject to its own limitations, in addition to the uncertainty in climate forcing. There are several features that our SMB model does not explicitly account for, including spatially variable processes such as redistribution of snow by wind and avalanching, and differences in incoming solar radiation with different aspects and topographic shading. However, some of these characteristics could be accounted for by the spatially variable model parameters (see for a detailed discussion). We have also assumed that parameter values in the SMB model are constant over time, including in a changing future climate. Some studies indicate that this may cause an oversensitivity to temperature change , although it is unclear if more physically-based approaches improve the performance when detailed meteorological data is lacking . Nevertheless, the above discussion in Sect.  illustrates that modelled future SMB, and thus ice-cap evolution, strongly depends on the choice of climate model, where especially precipitation is uncertain. Thus, the uncertainty in future climate forcing, illustrated by the large spread in future projected temperature and precipitation (Fig. ), likely outweighs the uncertainty associated with SMB model parameter values. In our Commit-experiments, the mean SMB 2081–2100 is used as a constant climate forcing. Other time periods could be considered to represent the end-of-the-century climate, but the mean SMB over two decades was chosen in order to be consistent with the two-decade mean for present-day SMB in the CommitNow experiment.

Modelled ice dynamics is heavily influenced by the representation of basal friction e.g.. Here we have taken advantage of a global velocity dataset for the fastest outlet glaciers. The velocity data appears to be of good quality for the large outlet glaciers (Sect. ), and more uncertain for small and narrow glaciers. Comparison against the global velocity dataset suggests that several model glaciers are less dynamic compared to observations (Fig. d). Given accurate velocity data, this could partly explain why historical outlet-glacier retreat is underestimated in a few cases (e.g. steep glaciers such as Briksdalsbreen and Brenndalsbreen; Fig. ). It follows that more dynamic outlet glaciers would render faster frontal retreat than what we have projected here.

The global velocity dataset used does not come without issues, as highlighted in Sect. . We illustrated a hybrid approach to mediate this, with inversion for the largest and most dynamic glaciers, where we judge the velocity data quality to be highest. While the quality of the velocity data varies spatially, it also provides limited temporal information. This means that friction coefficients are uncertain over the modelled historical timespan, let alone in future simulations. Like virtually all previous model studies, we keep the friction parameters fixed in time, ignoring any feedbacks between increased meltwater supply and friction, which in a future warmer climate may accelerate mass loss further e.g..

Several alternative approaches to basal friction were tested. We tried a transient inversion of the friction field, where ice thickness was allowed to evolve using a constant SMB, and the friction parameter adjusted at regular intervals (10–50 years) depending on local thickening or thinning, following . Despite theoretical promise, this approach resulted in large unrealistic drift of the ice-cap geometry during spinup, and was therefore abandoned. Moreover, we also tested a spatially uniform friction parameter, an elevation-dependent friction parameter everywhere (Eq. ), as well as imposing the friction inversion everywhere (Eq. ). All of these approaches rendered poorer results (higher RMSEs) than our approach outlined in Sect. . For example, using a friction inversion for the entire ice cap (Eq. ; Sect. ), increases the mismatch with present-day observed ice volume from 0.4 % using the current hybrid approach to 3.5 % using the inversion everywhere.

The spatially variable friction field obtained aims to represent the bulk effect of all interactions between ice, water, rock and sediments at the ice-bed interface. Still, friction parameter adjustments are essentially also compensating for potentially missing physics and uncertainties in the bed topography, ice-flow physics and surface mass balance forcing. In this light, we expect and accept some mismatches between the modelled and observation-based thickness, as well as between modelled glacier fronts and their observed historial and present-day positions.