Here we implement three rate-based calving laws (VM, EC and PD) and two position-based laws (CD and MT) using a level-set method to track the evolution of the calving front . A positive calving rate value, c, retreats the ice and is applied perpendicular to the calving front (following level-set gradients). We impose a maximum migration rate, M˙max⁡, of 10 kmyr-1 to prevent unrealistic terminus fluctuations during our simulations. This value is consistent with all calving laws, with the exception of PD where M˙max⁡ is used as a tuning parameter.

We calibrate each calving law by running a series of simulations for each glacier for 17 years from 2008 until the end of 2024. The tuning parameter of each law is varied systematically across ranges of values found appropriate in previous studies , at intervals of 10 kPa for σmax⁡, 2.5 m for dw, 0.05 for rc across values of M˙max⁡ between 2 and 10 km at 2 km intervals, and finally 5 m for hmin⁡. For the EC law, it became apparent that we need greatly different tuning values of K for different glaciers. We therefore vary K at intervals of 0.1 × 10⁸ myr for Ryder and 79N, and at intervals of 10 and then 100 × 10⁸ myr-1 for Petermann Glacier. To quantitatively assess the performance of each simulation we compare the area difference between the observed terminus position at the end of 2024 and that produced by the calving law. This area difference is then divided by the length of the 2024 calving front, producing misfit values that are consistent between all three ice shelves of different sizes . We note that this gives an absolute misfit value and does not consider the sign of misfit. For 79N, the quantitative misfit is based on the main eastern terminus.

For each calving law, we select the simulations in which the misfit with the observed calving front is minimised, and continue these experiments from 2025 to 2300. We also conduct additional transient simulations where calving fronts are kept fixed in our model (NO). Our transient simulations do not constitute future projections of the ice shelves, but are instead intended to assess if ice shelf evolution differs between the calving parametrisations under a warming atmosphere or ocean. We first complete a control run, in which SMB and ocean melt forcing remain unchanged from the initial calibration simulations, hereby referred to as the static scenario. We then perform a series of transient runs with perturbed climatic forcings. We begin by varying the atmospheric forcing with a high-emission SMB scenario SSP5-8.5 (CMIP6 forced ensemble mean RACMO ensemble), prescribed at monthly intervals , hereby referred smb8.5. Separately, the ocean melt rate is increased under the ice shelf, which has been the key driver of ice-shelf thinning in recent decades . We perturb ocean melt in accordance with results from ocean modelling simulations at Petermann's ice shelf by , where raising ocean temperatures by 1, 2 and 3 °C results in increased sub-shelf melt by 25, 45 and 70 myr-1, respectively. For our transient runs, we increase ocean melt rates in-line with ocean temperatures being 1 °C warmer by 2100, 2 °C by 2200 and 3 °C by 2300. We apply this increase linearly but through two different experiments. Firstly, to isolate the effects of increased melt near the grounding line, the highest melt rates in the linear depth profile are increased while maintaining zero melt in shallow waters. Secondly, the entire melt profile beneath the shelf is increased uniformly. These scenarios are referred to as oceanGL and oceanFull, respectively (Fig. d and e).

Calibrating each calving law to observations exposes distinct sensitivities to its respective tuning parameters, which can vary between the three glaciers (Table ). Calibration values for EC, MT, and PD are different across the three glaciers, whereas values for the VM and CD laws are similar. Here we examine the sensitivity of simulations to tuning parameters, and further assess the performance of each calving law on a glacier-by-glacier basis using the quantitative misfit values and the qualitative shape of the modelled terminus. As only minor differences in ice shelf and grounding line velocities are observed between the parametrisations (Figs. S1–S3 in the Supplement), ice dynamics are not included in the assessment of each law's performance.

At Petermann Glacier, two large calving events in 2010 and 2012 caused the ice shelf to retreat ∼ 40 km. Modest regrowth by 2024 has left Petermann's ice shelf extending ∼ 60 km from the grounding line, with the final ∼ 15 km of the ice tongue detached from the fjord walls (Figs. a and k). Retreat of the ice front using the VM calving law only occurs with values of σmax⁡ below 300 kPa, and only on the western side of the ice shelf (Fig. a and b), producing an adequate magnitude of ice front change but a poor match to its shape. The EC law struggles to produce the observed retreat the ice front at Petermann, requiring values of K above 300 × 10⁸ myr (Fig. c and d), which is of orders of magnitude larger than for Ryder and 79N (Table ). For MT, the choice of hmin⁡ can cause a substantial advance or retreat of the terminus (Fig. e and f). The shape of the ice front is, however, consistent across all tuning values of MT and, of all calving laws, is most akin to the observed 2024 front. The CD law is especially sensitive to the prescribed water in crevasses (dw), with values above 2.5 m resulting in excessive retreat of the ice shelf (Fig. g and h). No values of dw allow Petermann's shelf to advance. Finally, the PD law is sensitive to both the values of rc and M˙max⁡ (Figs. i, j and S4a), with greater retreat at the edges of the ice shelf compared to the central section.

To simulate a retreating shelf front requires an increased calving flux, and we find that the thresholds to calve for the VM, MT and PD laws are lower than required at the other glaciers (Table ). The smallest quantitative misfits to the observed ice shelf front are simulated using the laws PD (0.6 km) and MT (0.8 km), matching the detached shape of the observed shelf on the eastern fjord wall, although it remains entirely connected to the western fjord wall (Fig. k). This is contrasted by the CD (2.4 km) and VM (2.5 km) laws, which fail to match the shape of Petermann's terminus due to excessive calving on the western side of the ice shelf. Nonetheless, the sensitivity to different tuning values in the VM law is low compared to the other laws. The EC law (1.9 km) is unable to retreat the ice front to Petermann's 2024 position.

Ryder Glacier's ice shelf has terminated at a widening section of Sherard Osborn Fjord for several decades, where it remains connected to the fjord walls on both sides (Fig. b). Both VM and EC laws produce small misfits across our full range of tuning values (Fig. a–d); sensitivity to these tuning parameters is low. The choice of thickness threshold in the MT law again allows for ice front retreat or advance, producing large variability in ice front position across our range of tuning values. Owing to thickness differences at Ryder's shelf the single thickness-to-calve threshold produces an unevenly shaped terminus (Fig. e and f) and a pronounced mismatch from the observed frontal shape. The CD law has the same impact as seen at Petermann Glacier, where only retreat of the ice shelf is simulated and dw values greater than 2.5 m cause excessive retreat (Fig. g and h). The shelf also retreats for all values of rc in the PD law, with lower values promoting retreat on the western side of the shelf after it detaches from the fjord walls (Fig. i and j).

The shape and position of the shelf front is best matched by the EC (0.7 km) and VM (0.8 km) laws (Fig. k), although the latter calves to a greater extent than observed on the eastern side of the terminus. Despite a greater quantitative misfit for the CD law (2.1 km), the simulated ice front is uniform in shape and terminates near the widening of Sherard Osborn Fjord, as observed. The MT law (3.6 km) and PD law (3 km) both fail to match Ryder's 2024 position.

79N's main terminus has remained stable for several decades, grounded on ice rises that act to both stabilise the ice shelf and initiate crevasse propagation. The ice shelf's smaller northern terminus calved away in 2020 (Fig. c). Both the VM and EC laws give small misfits against the 2024 position of 79N across a range of calibration values (Fig. a–d); the performance of VM is near-identical at values of σmax⁡ > 200 kPa. Despite this, neither law produces a retreat of 79N's smaller northern shelf terminus across all calibration values tested here. Using a threshold of hmin⁡ = 90 m for the MT law does cause retreat of the northern terminus, although at the expense of greater retreat of the main terminus away from the bedrock highs (Fig. e and f). Only the CD law captures the retreat of the northern terminus while also maintaining the position of the main shelf edge, yet similar to Petermann and Ryder glaciers, the law is extremely sensitive to dw, with values greater than 2.5 m causing the shelf to collapse (Fig. g and h). For PD, the choice of rc has relatively little impact on the ice front, with a large retreat of up to 10 km occurring across all calibration values (Fig. i and j). This insensitivity is consistent across all M˙max⁡ values (Fig. S4).

The position of the main terminus is best matched using the VM (0.9 km) and EC (1.1 km) laws (Fig. k). Both laws are capable of matching the extent and shape of the ∼ 50 km long main terminus, although they fail to retreat the smaller northern ice front. The position-based MT (2.8 km) and CD (3.0 km) laws also simulate a main terminus that is similar to observations, albeit with exaggerated calving in the southeastern section of the ice shelf which is heavily fractured, resembling a matrix of sea ice and icebergs Fig. c;. The largest misfit comes from the PD law (4.4 km), where the ice shelf retreats at an uneven rate, with large regions entirely detached from the ice rise pinning points and retreated 10 km behind the 2024 position.

We find that, on average across our three glacier experiments, the VM and EC laws produce the smallest quantitative misfit between modelled and observed front positions, with MT, CD and PD all exhibiting slightly larger misfits (Fig. ). However, the performance of these calving laws varies between glaciers. VM and EC produce the smallest misfit at Ryder and 79N yet relatively larger misfits at Petermann Glacier. In contrast, MT and PD performed best at Petermann, while relative misfits for CD were consistent across all three glaciers.

With the five calving laws now calibrated to the recent behaviour of the three ice shelves (Table ), we continue these simulations until the year 2300 to understand if the choice of calving parameterisation impacts future ice shelf evolution and discharge rates, given different climate forcings. Four different transient climate forcings are applied: static, where ocean melt and SMB are kept unchanged from the calibration simulation, smb8.5, where the SMB is perturbed in accordance with the high-emission SSP5-8.5 from the RACMO ensemble , oceanGL, where sub-shelf melt rates are increased only toward the grounding line, and oceanFull, where sub-shelf melt rates rise across the entire melt-profile .

The choice of calving parametrisation produces contrasting calving styles and ice-shelf evolution in transient simulations (Figs.  and S5–S7 in the Supplement). Taking oceanFull forcings simulations as an example (Fig. ), we find that across all three ice shelves the rate-based VM and EC laws consistently produce a smooth shaped ice front that spans the fjord width. The rate of retreat is similar to that in the position-based MT law (Fig. c, h and m). CD and PD laws induce different behaviour of the ice shelf. For CD, the position-based calving style produces irregularly shaped, crenulate termini, with uneven retreat rates across the width of the ice shelf (e.g. i). Furthermore, retreat using CD occurs faster than the aforementioned laws, simulating large calving events that remove substantial parts of the ice shelf (e.g. Fig. n). The PD law produces calving styles and an ice-front shape that are, at some time steps and in some settings, similar to the rate-based VM and EC laws (e.g. Fig. o), and in other intervals comparable to the crenulate shelf front seen in CD (e.g. Fig. j). The PD law also produces the greatest magnitude and speed of retreat.

Despite variations in calving styles and transient ice shelf extents, we find that fluctuations in discharge rates, the flux of ice over the grounding line, and grounding line evolution, are largely dictated by the choice of climate forcing (Figs. , and ). In summary, the static forcing maintains discharge rates at approximately contemporary levels and the grounding line position is mostly stable; smb8.5 drives a decline in discharge rates after 2100 due to ice thinning and a reduction in ice flux across the grounding line, while the grounding line retreats. In both oceanGL and oceanFull scenarios, discharge increases above contemporary levels, with the latter causing the largest increase in discharge rates and the largest ice shelf retreat; both forcings drive modest retreat of the grounding line. Within each climate scenario, while the ice shelf evolution is variable (e.g. Fig. ), the choice of calving law brings only minor differences in discharge rate and grounding line positions.

The different calving laws at Petermann Glacier largely follow the same trend in grounding line behaviour and discharge within each climate scenario, yet there are subtle differences in discharge rates between the position and rate-based laws. The position-based laws (CD and MT) exhibit elevated (10 %–20 %) discharge rates and earlier or faster grounding line retreat. In both cases, we attribute this to detachment of the shelf from the fjord walls and loss of lateral friction, due to excessive calving on the eastern side of Peterman's shelf early in the simulations for CD law (Figs. d, S5d and S6d in the Supplement) or due to calving of thin ice on the shelf edge for MT (Fig. c). Discharge rates are, for the most part, lower for the two rate-based laws (Fig. ), where a connection to both fjord walls is maintained. For EC, ice shelf evolution is inline with our simulations without calving (NO). For VM, the ice shelf calves back either gradually or through larger events (e.g. Fig. g), resulting in a shorter ice shelf compared to EC. Despite the eventual contrasts in shelf length (e.g. Fig. e and g), and while calving events may induce a small immediate response in discharge rates, there is little to no difference in discharge rates between the two laws.

At Ryder Glacier, there is less variation in discharge rates and in grounding line positions between the calving laws than at Petermann Glacier. A step increase in discharge occurs across all climate forcings, from ∼ 3 to at least ∼ 3.5 Gtyr-1 (Fig. a–d), reflecting the retreat of Ryder's grounding line into deeper waters on the western side of the fjord (Fig. k). Thereafter, the trajectories of the discharge rate differ according to climate forcing, whereas the choice of calving law produces even less variation in discharge rates and grounding line position than at Petermann Glacier. This retreat occurs first when using the PD law, followed by position laws CD and MT, and then rate laws VM and EC. The magnitude of grounding line retreat and increase in discharge does not differ between the parametrisations and after 2100 show near-identical trajectories within a given climate scenario, despite contrasting shelf extent.

At 79N, rate-based VM and EC laws as well as position-based MT, produce near-identical discharge rates and grounding line positions under a given climate scenario. The shelf front position is also similar between these laws, whether retreating (smb8.5, oceanFull; Fig. f and h) or stable, grounded on ice rises (static, oceanGL; Fig. e and g). For the most part, the CD law produces similar grounding line responses to the other laws, despite larger calving events and shelf front retreat; there is a minor increase in discharge under oceanGL forcing when the CD law triggers shelf retreat from Hovgaard Island (Fig. c and g).

The only pronounced deviations in discharge trends – in magnitude, timing, and between calving laws – occur in association with major calving events or complete loss of the ice shelf. Such events are rare. Most often, these calving or collapse events occur in the PD law. At Petermann Glacier, simulations using the PD law follow the same behaviour independent of climate forcing, where Petermann's ice shelf retreats at a consistent rate until it is entirely lost shortly after 2100 (Fig. e–h). An acceleration in ice discharge rates occurs only once the shelf is shorter than ∼ 10 km in length. Petermann's ice shelf also collapses under the oceanFull scenario and the VM law, as ice discharge at the grounded front accelerate to ∼ 24 Gtyr-1 (Fig. . Again, discharge rates only diverge from the other calving laws when the shelf is almost lost. At 79N, the PD law produces two large-scale (20–40 km) and abrupt shelf retreats under static and oceanGL scenarios, where the ice shelf detaches from ice rises and from Hovgaard Island (e.g Fig e–g). Retreat from Hovgaard Island under static and oceanGL causes a modest increase in discharge from ∼ 12 to ∼ 14 Gtyr-1.

The current calving laws used in ice-sheet modelling contain a tuning parameter to bridge the gap between simplified models and complex real-world processes that cause calving events. By performing an ensemble of calibration simulations, where each calving law investigated here is tuned to Petermann, Ryder, and 79N's recent behaviour, we complement and expand on previous studies that have assessed the performance of calving laws at marine-terminating outlet glaciers . When assessing a law's performance we have taken into account both the quantitative and qualitative misfits from observations, as well as the law's sensitivity to its respective tuning parameters, which would influence its suitability in large continental-scale ice sheet modelling studies.

The two best performing laws in our quantitative assessment were VM and EC (Fig. ). The former is a common choice in many ice sheet modelling studies e.g., and has performed well in other systematic calving comparison studies, both at grounded Greenlandic outlet glaciers and Antarctic ice shelves . Despite proving functional across a wide range of glacial settings, VM requires tuning on a glacier-by-glacier basis with bespoke values of σmax⁡ needed to achieve optimal performance. This may impede its use in continental-scale ice-sheet studies that often employ uniform calving parameter values e.g.. found values of σmax⁡ required to match recent terminus fluctuations of grounded Greenlandic ice fronts varied from 500–3000 kPa , while find that a narrower range of smaller values between 150–400 kPa were suitable for Antarctic ice shelves. For the three Greenlandic ice shelves explored here, required σmax⁡ values are even more concentrated, between 180–280 kPa (Table ), and the differences in performance across our tested range of VM thresholds are small (Figs. , and ). Therefore, the law appears suitable for continental-scale ice-sheet simulations, provided that the model can discriminate between grounded and floating ice.

The EC law was designed to capture the calving dynamics of large ice shelves that terminate in unconfined embayments . With a first-order dependency on strain rate tensor, the law naturally performed well at Ryder Glacier and 79N, which both have terminated at the head of an embayment for several decades (Figs.  and ). However, at Petermann Glacier, where the importance of lateral strain rates is reduced owing to retreat through a narrowing section of the fjord, the law struggled (Fig. c and d). Our findings align with results from other systematic calving studies. For Antarctic ice shelves, which predominantly terminate at the opening of embayments where lateral support is lost, found the law performed well, requiring values of K between 0.2 and 4 × 10⁸ myr (with the exception of Larsen C that required a K of 300 × 10⁸ myr) in-line with our calibrations at Ryder and 79N (Table ). At grounded Greenlandic glaciers, which have often begun to retreat into confined in narrow fjords where perpendicular strain-rates are small, highlights how the EC law struggles to match terminus position changes. Even though the EC law performed well in our simulations over the tuning period, with future retreat of Ryder Glacier and 79N set to occur in a narrowed fjord environment, akin to Petermann Glacier, the EC parameterisation would likely be unsuitable for Greenlandic ice shelves.

Thin ice at the termini of Greenlandic ice shelves means that the required hmin⁡ threshold in the MT law (40–75 m) is an order of magnitude smaller than that required for the corresponding Antarctic floating ice masses 215–410 m, except 55 m for Shackleton ice shelf;. The law performed best at Petermann Glacier, where ice thickness variations across the shelf produce a terminus shape similar to observations (Fig. ). This spatial variability in ice thickness is driven by a number of sub-shelf melt plumes that produce channels of concentrated high melt rates . A similar melt plume likely exists at Ryder Glacier, reflected by thin ice in the centre of the ice shelf and the presence of a large supra-glacial meltwater stream at the same location (Fig. b). Yet, unlike at Petermann Glacier, the MT law cannot match Ryder's observed terminus shape (Fig. ). Thickness variations at 79N's terminus also cause a mismatch with terminus shape using MT, causing retreat and advance on opposite sides of the shelf. Failure to replicate ice-shelf shape, due to the direct control of ice thickness in the MT law, was similarly found by in their Antarctic study.

The CD calving law performed well at Greenland's three largest ice shelves, but only in the absence of water in surface crevasses (Figs. , and ). This result is consistent, independent of setting, and could indicate the law's suitability for floating ice in continental-scale studies of GrIS. Interestingly, our results contrast other studies in which the CD law under-predicted crevasse depth, thus requiring the additional downward force of water in crevasses , or altering the threshold of crevasse propagation required for a calving event , in order to match observed calving behaviour. Required dw values at grounded glaciers have ranged from 0 to 100 m , with values often diverging from real-world observations of water depth in crevasses, indicating dw is a heuristic parameter . To address this, recent studies have revised the classic implementation of the CD law to account for the concentration of stress in non-fractured ice, which indicates tuning through dw may not be necessary .

For the Greenlandic ice shelves investigated here, the success of the CD law, contingent on there being no additional water pressure in the crevasses, reflects a greater propagation of basal crevasses in floating ice and a shallow free board of the ice shelves. For grounded Greenlandic termini, a greater emphasis is placed on surface crevasse extent, owing to Hab > 0 in Eq. () which limits the extent of basal crevasse propagation. In contrast, Hab = 0 for floating termini means sea water can fully fill basal crevasses and cause these to penetrate further. Furthermore, Greenlandic ice shelves are composed of thin ice, at around 100 m thick near the terminus, which can extend for tens of km toward the grounding line and results in relatively shallow free board compared to grounded termini. As such, values of dw approaching as little as 10 m would result in surface crevasses reaching the water line (Eq. ) and thus result in excessive calving of the ice shelf (e.g. Fig. g and h). To that extent, our results demonstrate extreme sensitivity to the choice of dw, which is echoed by other studies at grounded tidewater margins .

The PD law consistently retreats the three ice shelves across all values of rc and M˙max⁡ tested here (Figs. – and S4). Although this behaviour aids in reproducing the retreat at Petermann Glacier, the law is unable to match the observed ice shelf stability at Ryder and 79N. found similar results when the law was tested on Antarctic ice shelves, where PD often produced the largest misfit due to excessive retreat. These findings likely reflect the law's original purpose; developed out of the need to satisfy palaeo eustatic sea-level high stands through greater retreat of the East Antarctic Ice Sheet that was not possible without additional mass loss mechanisms . Given that the original CD, in our experiments, was able to reproduce contemporary calving behaviour at the ice shelves simply through dry surface crevasses and basal crevasses alone, the explicit inclusion of hydrofracturing, with its heightened influence in Greenland due to greater surface melt than in Antarctica, is likely responsible for the exaggerated retreat seen with the PD law.

While it is possible to tune a calving law on a glacier-by-glacier basis for large ice sheet simulations e.g., it is preferable to use a parameterisation that performs well across different glacial settings with a single, consistent calibration value. For this reason, we would recommend either the VM or the CD calving law. Both performed well in our calibration simulations and can utilise similar tuning values across three remaining Greenlandic ice shelves, assuming that the ice sheet model is able to discriminate between floating and grounded ice.

While our calibrations suggest that one calving law may be better suited than another, different calving laws produce only subtle differences in discharge rates during simulated climate forcing to 2300 (with the exception of the PD law at Petermann Glacier; Figs. –). Instead, ice discharge is largely dictated by the applied climate forcings. Rising sub-shelf melt rates cause an increase in discharge over the grounding line, while greater ablation from SMB processes decrease discharge through ice thinning. Furthermore, large calving (ice-shelf collapse) events are rare, triggering only isolated occurrences of rapid discharge acceleration due to a loss of buttressing from the ice shelf – such as at Petermann Glacier using the oceanFull scenario and the VM calving law (Fig. d and and h). Our transient simulations do not constitute explicit future projections of the three ice glaciers, and should instead be viewed as a sensitivity test of the calving laws under different climate forcings. However, they do raise questions regarding the evolution of Greenlandic ice shelves and our ability to accurately constrain future behaviours. Our transient runs can be interpreted in two ways: (1) Greenlandic ice shelves may continue to provide a buttressing force into the coming centuries despite shelf retreat, suggesting that the role of calving in future ice discharge is limited, and discharge is instead dictated by SMB or ocean melt fluctuations; or (2) our calibrated calving laws, which rely on static tuning parameters, are inadequate when parametrising future ice-shelf evolution and their likely collapse in a warming climate.

Continued buttressing potential of these ice shelves may reflect their inherent characteristics that have, so far, endured climatic changes despite the collapse of other floating extensions in Greenland . Ryder Glacier's ice shelf, for example, has been contained in a bottleneck in Sherard Osborn fjord for a several decades, where the narrowing fjord walls increase lateral friction and stabilise the ice shelf . In our transient simulations, Ryder Glacier's floating extension remains supported by this ∼ 30 km long narrow fjord section until at least 2200 across all calving laws and climate simulations with the exception of oceanFull. This persistent presence of the ice shelf is consistent with the findings of , where numerical simulations of Ryder Glacier under various climate warming scenarios find a continued ice-shelf presence into the coming century, despite specific experiments that increased the calving rate.

Similarly, the ice shelf at 79N, which has remained stable for several decades, is supported by Hovgaard Island and a number of ice rises at the terminus, as well as a fjord bottleneck ∼ 40 km from the grounding that allows the majority of the inner ice shelf to be buttressed . As such, retreat from Hovgaard island and the ice rises does not necessarily stimulate a major acceleration in ice discharge (e.g. CD in Fig. c and g). At Petermann Glacier, where the fjord widens inland of the terminus, modelling studies have shown that the majority of buttressing occurs within 10 km of the grounding line . Our results reinforce this, and highlight that across all three glaciers, ice shelf retreat does not necessarily entail an acceleration in discharge rates if a strong connection between the fjord walls and ice shelf is maintained.

Nevertheless, in calibrating the calving laws against recent observations, we have assumed that the underlying physical processes that govern calving will remain consistent and unchanged. This is unlikely to remain true, and may bias any future evolution to behaviour inherited from the calibration period. Here we have calibrated five calving laws over an observation period from 2008 to 2024, during which Ryder Glacier and 79N maintained stable shelf fronts, while Petermann Glacier retreated by ∼ 20 km. At Ryder and 79N, a higher calving threshold (σmax⁡) for the VM law, compared to Petermann Glacier (Table ), could explain why terminus retreat occurs at the same rates as simulations without calving, controlled instead by surface and ocean ablation (Figs.  and ). In contrast, the lower VM threshold at Petermann Glacier produces a greater realtive retreat of the ice shelf as well as a collapse event in oceanFull scenario (Fig. d and h). Such inherent behaviours are further emphasised in all Petermann simulations using the PD law. Therein a lower critical calving threshold (rc) and higher max migration (M˙max⁡) value (relative to Ryder and 79N) result in continuous ice shelf retreat independent of climate forcings (Fig. ). If the same tuning parameters for PD that suited the stable ice shelves at Ryder and 79N are used, ice shelf evolution and discharge falls in-line with the other calving laws (Fig. S8 in the Supplement).

The often unique tuning parameters required by calving laws to match specific glacial behaviour during a specific time period naturally imply that a static value may not be suitable for prognostic modelling simulations . Future retreat of Greenland's ice shelves will occur into a changing fjord geometry or away from stabilising pinning points, see a decrease in sea-ice that has acted to suppress calving , retreat of the terminus towards thicker ice nearer the grounding line, while also confronted with higher sub-shelf and surface melt rates . As such, the current set of calving laws evaluated here, which rely on static tuning parameters, may become inaccurate to model the future evolution of Greenland's remaining ice shelves. While it is not plausible to expect a calving law to capture all individual calving events, future calving laws should be able parameterise terminus fluctuations at a variety of glacial settings through a single set of parameters . We therefore suggest that Greenland's remaining floating shelves serve as ideal candidates to explore new paramerisations, in order to best constrain future discharge rates from the currently buttressed outlet glaciers.