Volume 49, Issue 5 e2021GL097085
Research Letter
Free Access

Helheim Glacier's Terminus Position Controls Its Seasonal and Inter-Annual Ice Flow Variability

Gong Cheng

Corresponding Author

Gong Cheng

Department of Earth Sciences, Dartmouth College, Hanover, NH, USA

Department of Earth System Science, University of California, Irvine, CA, USA

Correspondence to:

G. Cheng,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Writing - original draft, Writing - review & editing, Visualization

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Mathieu Morlighem

Mathieu Morlighem

Department of Earth Sciences, Dartmouth College, Hanover, NH, USA

Department of Earth System Science, University of California, Irvine, CA, USA

Contribution: Conceptualization, Methodology, Software, Validation, Formal analysis, ​Investigation, Writing - original draft, Writing - review & editing, Supervision, Project administration, Funding acquisition

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Jérémie Mouginot

Jérémie Mouginot

Department of Earth System Science, University of California, Irvine, CA, USA

Institut de Géosciences de l’Environnement, Université Grenoble Alpes, Grenoble, France

Contribution: Data curation, Writing - review & editing

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Daniel Cheng

Daniel Cheng

Department of Computer Science, University of California, Irvine, CA, USA

Contribution: Data curation, Writing - review & editing

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First published: 21 February 2022
Citations: 1


Over the past decade, one of the largest contributors to total ice discharge across the Greenland ice sheet, Helheim Glacier, has experienced large fluctuations in ice velocity. In this study, we simulate the dynamics of Helheim, from 2007 to 2020, using the Ice-sheet and Sea-level System Model to identify the drivers of these large changes in ice discharge. By quantifying the impact of individual external forcing and model parameters on Helheim's modeled velocity, we find that the position of the calving front alone explains the dynamic variability of the glacier, as it has a direct and large impact on Helheim's ice velocity. The seasonal to inter-annual variability of Helheim Glacier is, however, relatively insensitive to the choice of friction law or ice rheology factor. This study shows that more research on calving dynamics and ice–ocean interactions is required to project the future of this sector of Greenland.

Key Points

  • Calving has been controlling Helheim's speed variability since 2007

  • Averaging the calving rate over 60 days does not change the glacier behavior significantly

  • Constraining a calving law is critical to model the future of Helheim's mass balance

Plain Language Summary

At least half of today's mass loss of the Greenland ice sheet is due to the acceleration and retreat of tidewater glaciers. Over the past decade, Helheim Glacier in southeast Greenland has experienced large fluctuations in its flow speed, varying sometimes by more than 2,000 m/yr within a single year. It is still unclear which physical processes are responsible for the fluctuations in ice speed of Helheim Glacier and how much they contribute individually. In this study, we use a novel numerical technique to simulate Helheim Glacier from 2007 to 2020 to investigate the role of some of the physical processes that have been proposed to potentially drive this variability in ice speed. By comparing the solutions of the numerical model to observations of ice speed, we find that the terminus position is the main control of the ice motion at Helheim Glacier.

1 Introduction

The Greenland ice sheet has been losing more than 200 Gt/year during the last two decades and it is currently contributing about one fifth of global mean sea level rise (Group, 2018; Mouginot et al., 2019; Shepherd et al., 2020). Among all Greenland tidewater glaciers, Helheim Glacier has one of the largest drainage areas (∼50,000 km2) and one of the highest total ice discharges since 2010 (Khan et al., 2020; Mouginot et al., 2019). Its terminus is 6 km wide and the average depth of the bed close to the ice front is about 600 m (Figure 1a). The geometry of the bed is prograde close to the ice front (<10 km) but retrograde between 15 and 25 km away from the terminus, with the deepest point about 1,060 m below sea level, which raises concern of marine ice sheet instability (Schoof, 2007) if Helheim starts to retreat inland.

Details are in the caption following the image

(a) Bed topography (Morlighem et al., 2017) of the model domain. The black rectangle indicates the close-up view of the fast-flowing region shown on the right panel. (b) Observed velocity magnitude used for inferring the basal friction coefficients (Joughin et al., 2010). Only the ice covered area is shown, with the ice mask acquired from BedMachine Greenland v4 (Morlighem et al., 2017). The three dashed lines are the northern (N), central (C), and southern (S) flowlines.

While geological evidence suggest that Helheim Glacier has been fairly stable between 1930 and 2000 (Bjork et al., 2018; Khan et al., 2014), its terminus retreated dramatically by 6 km between 2001 and 2005. This retreat of the calving front coincided with an acceleration of Helheim Glacier (Howat et al., 2005). A simple flow-line model showed that the acceleration initiates at the terminus and propagates upstream (Nick et al., 2009). By 2006, the glacier stopped thinning, slowed down, and re-advanced 4 km and has been relatively stable since then.

Since Helheim re-advanced in 2007, its terminus position has been fluctuating by up to ∼5 km and these changes in calving front positions coincide with large variations in surface velocity (up to ∼25%) (Bevan et al., 2015; Khan et al., 2014; Miles et al., 2016; Moon et al., 2014; Vijay et al., 2019). So far, however, this variability has not yet been linked to changes in atmospheric or oceanic forcing (Kehrl et al., 2017; Moon et al., 2014). Previous studies suggest that changes in basal friction or ice rheology could have a strong impact on the variability of Greenland outlet glaciers (Brondex et al., 2019; Khan et al., 20142020; King et al., 2018). Basal conditions are expected to change seasonally due to the production of meltwater at the surface of Helheim in the summer. Surface runoff could also weaken Helheim's shear margins in summer months, and increase ocean undercutting at the terminus. However, numerical models have not yet been able to reproduce this seasonal and inter-seasonal variability in ice front position and surface speed (Choi et al., 2018).

One factor that could explain why ice sheet models have not been able to capture Helheim's seasonal cycle may be related to uncertainty in model parameters and external forcings (An et al., 2021; Moon et al., 2018). The influence of ocean circulation in the fjord, combined with the intermittent presence of a freshwater plume at the ice front is certainly more complex than what existing models are able to capture (Everett et al., 2021; Straneo et al., 2011; Wood et al., 2021). Other factors such as subglacial hydrology (Vijay et al., 2019), iceberg melting in the fjord (Moon et al., 2018) may also play an important role, but these processes remain poorly understood.

In this study, we develop a new numerical model of Helheim Glacier to identify the mechanisms that are responsible for Helheim's variability. Instead of investigating the physical processes involved in Helheim's calving dynamics, we constrain the motion of the model's ice front position using observed terminus positions and compare the model's dynamic response to satellite derived surface velocities collected between 2007 and 2020. This approach allows us to exclude uncertainties in calving dynamics and to focus on the ice dynamics of Helheim Glacier, so that we are able to narrow down the range of possible factors that may be responsible for its variability.

We first present the ice sheet model and the datasets used to constrain the simulations, we then discuss the results of the numerical experiments and analyze the performance of the model in terms of matching Helheim's observed variability using different friction laws and ice rigidity factors. We conclude on future research directions to improve the ability of ice flow models to capture Helheim's variability.

2 Method and Data

2.1 Ice Sheet Model

We use the Shelfy-Stream Approximation (SSA) implemented in the Ice-sheet and Sea-level System Model (ISSM; Larour et al., 2012) to simulate the behavior of Helheim Glacier between 2007 and 2020. While this approximation may not be appropriate close to ice divides, it is an excellent approximation for ice streams where the glacier motion is primarily controlled by basal sliding. A two-dimensional unstructured mesh is constructed on the horizontal plane with a spatial resolution varying from 100 m in the fast flowing region to 1,500 m in the interior part of the domain, requiring a time step of Δt = 1.825 days (0.05 years). The bed topography (Figure 1a), and the initial ice thickness are from BedMachine Greenland v4 (Morlighem et al., 2017).

For a better visualization of the model results, we choose three flowlines distributed across the glacier. These flowlines (northern, central, and southern) are shown as dashed lines in Figure 1b, with observed surface velocity magnitude (Joughin et al., 2010) in the background. The surface mass balance used here is from the Regional Atmosphere Model (MAR; Tedesco & Fettweis, 2020). To constrain the ice rheology factor, B, we assume that the temperature of our model follows the results of the ISSM submission to the initMIP-Greenland benchmark (Goelzer et al., 2018), with an ice temperature uniformly equal to −8°C. In Section 3.2, we investigate the sensitivity of our results to the ice rheology factor by varying the temperature from warmer (−5°C) to colder (−15°C) ice.

2.2 Basal Boundary Conditions

Several friction laws have been proposed in the literature (Brondex et al., 2019; Gillet-Chaulet et al., 2016; Maier et al., 2019). While basal friction has been shown to have a critical influence on ice dynamics (e.g., Brondex et al., 2019; Habermann et al., 2013), it remains unclear which friction law would be best suited for Helheim Glacier and how much the choice of friction law influences future projections (Maier et al., 2021; Shapero et al., 2016).

In this study, we employ three common friction laws: Weertman's law (Equation 1, Weertman, 1957), Budd's law (Equation 2, Budd et al., 1979), and Schoof&Gagliardini's law (Equation 3, Schoof, 2005; Gagliardini et al., 2007):

where τb is the basal shear stress, vb is the basal velocity, CW, CB, and CS are the corresponding spatially variable friction coefficients, m and q are positive exponents and take different values in these three laws, and N is the effective pressure at the base of the glacier. Because we do not use a subglacial hydrology model, we assume here that the effective pressure is computed assuming a perfect hydrological connection between the subglacial drainage system and the ocean (Brondex et al., 2019), such that: urn:x-wiley:00948276:media:grl63800:grl63800-math-0004, where ρi and ρw are the densities of ice and seawater, respectively, g is the gravitational acceleration, H is the ice thickness, zb is the bed elevation with respect to sea level, and min(zb, 0) takes the negative part of zb. In Schoof&Gagliardini's law (Equation 3), Cmax = 0.8 parameterizes Iken's bound (Iken, 1981). For very large effective pressures (N), Equation 3 becomes a Weertman-type friction law, as in Equation 1. For small effective pressures (N → 0), Schoof&Gagliardini's law converges to τb = CmaxN, which is a Coulomb type basal rheology that is consistent with Iken's bound (Brondex et al., 2017).

2.3 Observations

In this study, we use two sets of time dependent observations collected between 2007 and 2020. The first data set consists of surface velocities at 150 m spatial resolution derived from normalized cross-correlation between consecutive passes acquired by either the optical Landsat-8 or the synthetic aperture radar Sentinel-1 (Mouginot et al., 20172019). These surface velocities are, by construction, time-averaged over at least 6 days. The second data set consists of a time series of calving front positions of Helheim Glacier, extracted from satellite images by the Calving Front Machine (CALFIN) a machine learning algorithm (Cheng et al., 2021). From 2007 to 2020, the algorithm identifies 123 distinct ice front positions used in this study. Due to the temporal coverage of the optical Landsat satellite images at Helheim Glacier, these observations are discrete and not equally distributed in time. In order to adapt to the time steps in the numerical experiments, at each of the available time points, the observed calving front positions are converted to signed distance functions and the gaps in the time series are filled using linear interpolations, that is, the modeled ice front moves linearly from one terminus position to the next.

2.4 Experiments

To eliminate the difficulty of modeling calving dynamics, we constrain the calving front position using observations, and split the experiments into two scenarios. We first investigate the sensitivity of the model variability using three friction laws described in Section 2.2 with the ice temperature fixed at −8°C and compare the model results with the observations (see Section 3.1). The friction coefficients of the three friction laws in Equations 1-3 are assumed to be time independent in order to limit the complexity of model, and are individually determined by solving inverse problems to match surface velocities (Joughin et al., 2010) over the whole model domain at the beginning of the simulation. For comparison, a control run is also included with the calving front fixed at its initial position. The goal of this control experiment is to measure the effect of variations in ice front positions.

In a second set of experiments (Section 3.2), we vary the ice rheology factor, B, and run the same experiments with the calving front position constrained by observations. The inversion of friction coefficient is done separately for each of the experiments. The objective of this second set of experiments is to assess the sensitivity of the results to the chosen ice viscosity.

2.5 Frontal Ablation Rate

We describe here how the inferred frontal ablation rate urn:x-wiley:00948276:media:grl63800:grl63800-math-0005 is constructed. In ISSM, calving front dynamics is handled by a level-set function (Bondzio et al., 2016; Morlighem et al., 2016) such that
where vf is the frontal velocity and the zero level-set contour ϕ = 0 defines implicitly the calving front position. A general form for the frontal velocity is

where v is the ice velocity, Ab is the total frontal ablation rate, which includes both ocean undercutting and iceberg calving, and n is the outward-pointing normal vector. For numerical stability purposes, the level-set function, ϕ, is reinitialized as a signed distance function at every time step.

Having a time series of the observed terminus positions, we can infer for the frontal ablation rate Ab by combining Equations 4 and 5 such that
The ice velocity v is first reconstructed from the numerical simulations (see Section 3). Then, Equation 6 is discretized using a Forward Euler scheme:
where the superscript, n, indicates the time step and Δt is the step size.

3 Results

3.1 Observation-Constrained Terminus Position With Different Friction Laws

We first present the results of the first scenario, where different friction laws are applied and the calving front position is directly forced by observed terminus positions.

We compare the transient behavior of the model during 2007–2020 using the three friction laws to the control run for which the ice front is kept fixed (Figure 2a–b, where Figure 2a is the total ice volume estimated over the whole model domain (as shown in Figure 1a), and Figure 2b is the mean velocity along the calving front). We also show the observed frontal velocity averaged over the calving front in Figure 2b.

Details are in the caption following the image

Total ice volume and mean frontal velocity at the calving front. (a)–(b) Friction law experiments. The green dots show the mean observed velocity along the calving front. (c)–(d) Ice rheology experiments. (e)–(f) Inferred ablation rate experiments.

The surface velocity along the central flowline is shown in Figure 3. The velocity magnitude from numerical simulations is resampled according to the temporal coverage of the velocity observation in Figure 3a, and the numerical solutions are not shown for the time periods for which no observation exists within the model domain. The surface velocity from the northern and southern flowlines in Figure 1b are also compared with the observations and the results are shown in Figures S2 and S3 in Supporting Information S1.

Details are in the caption following the image

Hovmöller diagram of ice velocity along the central flowline of the (a) observation, (b) control run with fixed calving front position, (c)–(e) different friction laws, (f)–(j) different ice temperatures, (k)–(o) use inferred ablation rate. The x-axis indicates the distance along the flowline and the y-axis is time.

As shown in Figure 2a, the evolution of the total ice volume for the three friction laws follows the same trajectory, while the control run diverges from the other simulations after 2013. Large variations (∼4,000 m/a) are found in the mean frontal velocity of the three friction law experiments in Figure 2b. After 2014, the maximal mean velocity exceeds 10,000 m/a and the lowest velocity is below 6,000 m/a. By contrast, the mean frontal velocity in the control shows no seasonal cycle throughout the entire period of the experiment and follows the trend of the other three friction law experiments. There are obvious differences in the results between the three friction law experiments and the control run, and this is also confirmed by the surface velocities in Figure 3b–e, where the surface velocities of the three friction law experiments are in good agreement with the observation in Figure 3a. The surface velocities when the front is allowed to move have clear biennial cycles, particularly after 2014. However, there is no such variability in the surface velocity of the control run (Figure 3b), where the terminus is not allowed to move from its initial position. If we compare the modeled velocities to the observed surface velocity, the three friction law experiments show similar variations in time as the observations, but the control run has almost constant surface velocity in time. This is also the case for the northern and southern flowline in Figures S2 and S3 in Supporting Information S1.

3.2 Observation Constrained Terminus Position With Different Ice Rheology

In the second set of experiments, the total ice volume during 2007–2020 are shown in Figure 2c, with ice temperature varying from −5°C to −15°C. We observe the same temporal variations in all five experiments, although the −5°C case has substantially smaller ice volume than the other experiments. We find that the total ice volume gets larger as the ice temperature decreases. On the other hand, the mean frontal velocities, shown in Figure 2d, decreases as the ice gets colder. We also observe the inter-annual variability in the mean frontal velocities. Since 2014, the acceleration and deceleration patterns repeat within a 2-year cycle. We find the same biennial pattern in the surface velocities along the central flowline (Figure 3f–j), and also in the velocity solutions along the other two flowlines in Figure 1b that are shown in Figures S2 and S3 in Supporting Information S1.

4 Discussion

4.1 Choice of the Friction Law

The results in Section 3.1 show that the three friction law experiments have the same transient behavior and the surface velocities are similar to the observations, both in terms of magnitude and timing of variability. By contrast, the control run with a fixed terminus position diverges from the three friction law experiments and there is no obvious seasonal variability in its surface velocity.

To further quantify the misfits between observations and simulated velocities of all the experiments, particularly regarding the seasonal to inter-annual variability in the observations, we compute both the Wasserstein–Fourier (WF) distances (Cazelles et al., 2021) and the temporal correlations between the observed and modeled velocities. The WF distance is a measure of the similarity between different time series in the frequency domain by computing the displacement of the power spectral densities, which ignores time shifts and focuses on the agreement in variability. The smaller the WF distance is, the more similar the two time series are. A brief description of the method is provided in the supplement. The second metric used to compare the models and observations is the temporal correlation, which measures the displacement of the two series in the temporal domain, which quantifies the synchronicity of the two data. Smaller correlation corresponds to larger differences.

We consider the velocity at each node of the mesh as an individual time series. As we are primarily interested in the fast-flowing region (see in Figure 1b), all the nodes of the mesh with mean velocity lower than 5,000 m/a are neglected when computing these WF distances and temporal correlations. The WF distances are shown in Figure S5 in Supporting Information S1. We find that the control run has larger WF distances (with a mean value of 0.020 ± 0.003) than the other three friction law cases, whereas the mean values of the WF distance are 0.017 ± 0.003 for Budd's law, 0.017 ± 0.002 for Weertman's law, and 0.016 ± 0.003 for Schoof&Gagliardini's law. The variability in ice velocity is therefore better reproduced by the runs that account for changes in ice front positions than the control run.

The positive part of the distribution of the correlations are shown in Figure S4 in Supporting Information S1. The middle 80% interval of temporal correlations in the control run is [−0.18, 0.46] with a maximal probability at 0.38. In contrast, the Schoof&Gagliardini's friction law experiment has a middle 80% interval at [0.42, 0.70] and a maximal probability at 0.54. Similar distributions are found for the other two friction laws, which also confirms that all friction laws have stronger correlations to the observation than the control run.

This first set of experiment shows that the choice of friction law does not have a strong influence on Helheim's response to changes in ice front position for the time period that we are considering in this study. Temporal changes in friction coefficients, due for example, to seasonal changes in subglacial hydrology, are therefore not necessary to reproduce the overall variability of Helheim Glacier as long as the motion of the calving front is consistent with observations. We use Schoof&Gagliardini's law hereafter due to its stronger physical basis.

4.2 Influence of Ice Rheology

The results of the ice rheology experiments are very similar to the ones of the first set of experiments described above, especially when for ice temperature between −7.5°C and −12.5°C. For the cases with ice temperature equals −5°C, the model loses more ice than in other cases. As the temperature increases, the ice becomes softer and the velocity increases such that the entire glacier tends to lose more mass. This can also be seen both in the mean frontal velocity in Figure 2d and the surface velocity in Figure 3f. The ice velocity for Tice = −5°C is slightly faster than in other experiments. We find the opposite behavior for colder ice: the case of −15°C tends to give larger ice volume and lower ice velocity.

We compute the WF distances between the observations and simulated velocities, as stated in Section 4.1. The mean values for all the five cases of the ice rheology experiments are the same at 0.016 with a standard deviation between 0.002 and 0.003, which is significantly lower than the control run (0.020 ± 0.003). There is also a trend that the WF distance becomes smaller as the node is closer to the ice front. The complete results of the WF distance are shown in Figure S5 (f)–(j) in Supporting Information S1.

In terms of temporal correlations, these five experiments have almost the same distributions. The middle 80% interval of the temporal correlations at Tice = −5°C is [0.42, 0.66] with a maximal probability at 0.54. For Tice = −15°C, the middle 80% interval of the temporal correlations is [0.42, 0.66] with a maximal probability at 0.58. Indeed, the differences in the temporal correlations among these five cases are insignificant compared to the control run case (Section 4.1). The complete distribution of the temporal correlations is shown in Figure S4 in Supporting Information S1.

4.3 Inferred Frontal Ablation Rate

All the experiments described above show that the ice front position alone explains most of the variability of Helheim Glacier. To further verify this conclusion, we remove the constraints on the terminus positions and apply an inferred frontal ablation rate to the numerical model, thereby indirectly forcing the calving front.

We compute the inferred ablation rate according to Equation 7, using the velocity solutions acquired from Section 3 with the best fitted friction law and ice temperature (see Figure S6a in Supporting Information S1). We apply the inferred ablation rate urn:x-wiley:00948276:media:grl63800:grl63800-math-0010 to the numerical model and let the calving front move accordingly. The numerical solutions of the velocity magnitude along the central flowline are shown in Figure 3k, and remain in good agreement with observations and is similar to the friction law and ice rheology experiments. The WF distance of the velocities between this experiment and the observation is shown in Figure S5k in Supporting Information S1 with a mean value 0.017 ± 0.002, which is similar to the previous experiments of observation-constrained terminus position. The middle 80% interval of the temporal correlations of the inferred ablation rate case is between [0.38, 0.66] with a maximal probability at 0.54 (shown in Figure S4 in Supporting Information S1). The solutions along the other two flowlines (“N” and “S” in Figure 1b) are shown in Figures S2 and S3 in Supporting Information S1.

4.4 Smoothing the Inferred Ablation Rate

There are many relatively rapid changes in the ablation rate in Figure S6a in Supporting Information S1, which coincide with actual calving events. Some of the peak values of these ablation rates exceed 4 × 104 m/a over short time periods, which is difficult to represent in a continuous calving law. It is not clear whether the model needs to capture these ephemeral calving events in order to capture the observed variability. In order to smear out these “discontinuities” in urn:x-wiley:00948276:media:grl63800:grl63800-math-0011 and investigate whether neglecting individual calving events while capturing the overall migration of the terminus has an impact on the model, we apply a moving average filter to the inferred ablation rate. For instance, Figure S6b in Supporting Information S1 shows the 60 days averaging ablation rate at the observed calving front for the same 50 flowlines.

As the level-set function ϕ is defined over the entire catchment of Helheim Glacier, the solution of the inferred ablation rate urn:x-wiley:00948276:media:grl63800:grl63800-math-0012 in Equation 7 is also available everywhere on the model domain. The ablation rate in Figure S6b in Supporting Information S1 is therefore not a direct moving average of the inferred ablation rate at the calving front as in Figure S6a in Supporting Information S1, since the moving average filter is applied to urn:x-wiley:00948276:media:grl63800:grl63800-math-0013 over the entire model domain, not just for the inferred ablation rate shown in Figure S6a in Supporting Information S1.

We further investigate the influence of the choice of the moving average filter on the ice dynamics of Helheim Glacier. The moving average filters can be viewed as a temporal smoothing process of the ablation rate and calving events. The width of the filter varies from 12 days, which is twice of the minimal time period in the observations of surface velocities, and up to 90 days (one season). Figure S6c in Supporting Information S1 shows the mean of the ablation rates (from Figure S6a–b in Supporting Information S1), over the 50 flowlines, together with 12, 30, 60, and 90 days averaging cases.

The results of the velocity magnitudes along the central flowline are shown in Figure 3l–o, where the 90-day averaging case behaves differently from the others. The total ice volume and mean frontal velocity of the 90-day averaging case in Figure 2e–f are also on different trajectories than the other experiments. The WF distances of the 90-day averaging case has a similar pattern and the same mean value (0.020 ± 0.003) as the control run, which is significantly larger than the 12, 30, and 60-day averaging cases, where the mean WF distances are 0.017 ± 0.002, 0.017 ± 0.002, and 0.018 ± 0.002, respectively. The temporal correlation of the 90-day averaging case has a middle 80% confidence interval of [−0.26, 0.46] with a maximal probability at 0.30, whereas the other cases have the interval between [0.41, 0.63] ± [0.06, 0.06] and the maximal at 0.55 ± 0.06, which is in the same range as the inferred ablation rate case. The complete results of the temporal correlation are seen in Figure S4 in Supporting Information S1.

Overall, these results show unequivocally that the calving front position is the main driver of Helheim Glacier's variability and that individual calving events do not need to be captured in order for the model to reproduce this variability. The model suggests that a 60-day averaging is enough to reproduce Helheim's seasonal variability, both in terms of magnitude and timing.

4.5 Outlook

This study shows that the changes in ice speed of Helheim observed over the past 15 years are due to ice–ocean interactions and calving alone. While surface runoff affects the rate of undercutting at the calving front, ice–atmosphere and ice–bed interactions have not played a direct significant role on the glaciers dynamics, in the sense that no change in basal friction is necessary to explain the variability of the glacier. The strong variability of Helheim Glacier shows that even seasonal changes in ocean conditions can affect the glacier discharge significantly. This result is consistent with an analysis of sedimentary deposits from Sermilik Fjord, which suggested that Helheim Glacier responds to short term fluctuations of climate forcing (Andresen et al., 2012).

We attempted to implement different calving laws proposed in the literature, combined with ocean thermal forcing from Estimating the Circulation and Climate of the Ocean (ECCO) project, but we have not been successful in reproducing the ice front motion of Helheim Glacier accurately. We suspect that either the forcings we applied to the model are not accurate enough, or existing calving laws are not sufficiently realistic, or a combination of these two aspects. More research on calving and ice–ocean interactions is therefore necessary in order for models to capture these seasonal and inter-annual variability.

5 Conclusion

We presented a numerical study of the seasonal and inter-annual ice flow variability of Helheim Glacier during 2007–2020. By constraining the calving front position with observations, the model is able to reproduce the surface velocity of Helheim Glacier with high fidelity. After comparing different friction laws and ice temperatures with a control run, we found that the basal friction and ice rheology have only a limited influence on the overall dynamics of Helheim Glacier. We conclude that the calving front position is the main driver of Helheim's variability in the seasonal to inter-annual time scales. With an inversion method, we then reconstructed the inferred frontal ablation rate and showed that the results were unchanged if we smooth the inferred ablation rate by up to 60 days. This experiment shows that Helheim's variability does not depend strongly on individual calving events but on their cumulative effect on the position of the calving front over a monthly averaging. Similar conclusions have been found for Jakobshavn Isbræ (Bondzio et al., 2016), but it remains unclear how widespread across Greenland this behavior is, as some glaciers do show fluctuations in ice speed while maintaining a stable calving front position, such as Upernavik Isstrøm – III (Vijay et al., 2019). Our study highlights the necessity of the development of more realistic calving laws and a better understanding of ice–ocean interactions.


This work was supported by the Heising Simons Foundation grant 2019-1161 and 2021-3059. J. M. acknowledges support from the French National Research Agency (ANR) grant (ANR-19-CE01-0011-01).

    Data Availability Statement

    Data is available through (Mouginot et al., 20172019) and (Cheng et al., 2021). The code of the simulations is available at https://doi.org/10.5281/zenodo.5879143.