Modeling the Response of Nioghalvfjerdsfjorden and Zachariae Isstrøm Glaciers, Greenland, to Ocean Forcing Over the Next Century

Abstract

Recent studies have shown that the Northeast Greenland Ice Sheet region has been undergoing significant acceleration and dynamic thinning since 2010, and these changes are closely related to regional atmospheric and oceanic warming. Here we model the response of Nioghalvfjerdsfjorden (79North) and Zachariae Isstrøm (ZI) to ocean forcing to investigate their evolution over the coming decades. Our model suggests that 79North will retreat slowly over the next century, whereas ZI will lose its floating ice tongue completely and retreat rapidly for 70 years. After 70 years, ZI will stabilize 30 km upstream of its current position on a topographic ridge. Frontal melt rates need to reach 6 m/d in the summer to dislodge the glacier from this ridge. ZI will then continue a fast and unstoppable retreat, contributing more than 16.2 mm to global sea level rise by 2100.

Key Points

• Nioghalvfjerdsfjorden and Zachariae Isstrøm are committed to contribute at least 2.8 mm to global sea level rise by the end of the century
• Zachariae Isstrøm is in a state of irreversible retreat and will continue to lose mass until it stabilizes on a ridge 30 km upstream
• In high-end scenarios, Zachariae Isstrøm will retreat past its ridge and contribute 16.2 mm to global sea level rise by 2100

1 Introduction

The Greenland ice sheet has significantly contributed to global sea level rise over the last two decades (Khan et al., 2014) and is currently contributing to sea level at a rate of ∼0.8 mm/yr (van den Broeke et al., 2016; Forsberg et al., 2017; Rietbroek et al., 2016). Dynamic thinning of marine terminating glaciers along coastal Greenland accounts for a large portion of its mass loss (e.g., Pritchard et al., 2009). As glacier termini are exposed to warmer ocean currents and enhanced subglacial water discharge, ocean-induced melt at calving faces and under floating ice increases, which may lead to glacier retreat and ice flow acceleration (Holland et al., 2008; Jenkins, 2011). Assessing the vulnerability of individual glaciers to ocean forcing along the coast of Greenland is necessary to determine the regions that are most likely to change in the coming decades.

Nioghalvfjerdsfjorden (79North) and Zachariae Isstrøm (ZI) are two major marine terminating glaciers of the Northeast Greenland Ice Sheet (NEGIS) region, which drain about 12% of the Greenland ice sheet surface area (Rignot & Mouginot, 2012) and have the potential to raise sea level by 1.1 m (Mouginot et al., 2015). The 79North glacier forms a long (80 km) floating ice shelf confined in a wide (20 km) valley (Khan et al., 2014; Mouginot et al., 2015) (Figure 1). It exhibits high flow speeds (∼1.4 km/yr) near the grounding line and slows down near its terminus because of the presence of several islands and ice rises. The bed is 600 m deep at the grounding line and reaches a depth of 900 m below sea level under the floating tongue (Mayer et al., 2000). The bathymetry rises to 200 m below sea level near the ice front (Mouginot et al., 2015). ZI is more exposed to the ocean, with an almost 30 km wide ice front that is not protected by islands or ice rises. Its velocity was 2 km/yr near its floating calving front in 2015 (Mouginot et al., 2015). The seafloor is almost 900 m deep under the remnant part of its floating ice tongue and gradually rises inland for 30 km upstream where a ∼200 m high ridge is formed. Inland of this ridge, the bed remains between 300 and 500 m below sea level (Figure 1).

Figure 1

(a) Ice surface velocity from 2008 to 2009 with white contours (Mouginot et al., 2015). The black line is the ice edge, and the dashed black lines show the flow lines used in Figure 2. (b) Bed topography (white contours) inferred from mass conservation (beneath grounded ice) and gravity inversion (beneath floating ice and open ocean) (Morlighem et al., 2017) and grounding lines (GL) from 1996 to 2014.

The calving front of ZI has retreated 7–9 km between 2009 and 2014 (Mouginot et al., 2015). The rate of grounding line retreat increased from 230 m/yr to 875 m/yr after 2011. The ice surface velocity tripled compared to 2000–2012, and the thinning rate doubled from 2.5 ± 0.1 m/yr to 5.1 ± 0.3 m/yr during 1999–2014. These changes led to an increase in ice discharge of about 50%, from 10.3 ± 1.2 Gt/yr in 1976 to 15.4 ± 1.7 Gt/yr in 2015 (Mouginot et al., 2015). ZI has lost almost all of its floating ice and only 5% of the ice shelf remains compared to 2002. The 79North glacier has not experienced such dramatic changes, but its ice shelf near the grounding line lost 30% of its thickness from 1999 to 2014, which led to an increase in ice discharge by 8% during 1976–2015 (Mouginot et al., 2015).

In situ measurements show that the mean temperature of Atlantic Water (AW), transported from the North Atlantic toward the Arctic Ocean, has increased by 1°C over the last decade (Holliday et al., 2008; Mouginot et al., 2015). Although more observations are needed to investigate its transport, warm AW has been observed at the 79North ice shelf (Schaffer et al., 2017; Wilson & Straneo, 2015). Recent studies suggest that AW may be responsible for the fast retreat of the calving front of ZI and enhanced basal melting under the ice shelf of 79North (Khan et al., 2014; Mouginot et al., 2015). It is therefore essential to address the effect of ocean thermal forcing on the dynamics of this region.

Currently, the role of ocean forcing in these observed changes is not well understood, and it remains unclear whether NEGIS will continue to accelerate and retreat over the coming decades. Here we model NEGIS using a three-dimensional (3-D) ice sheet numerical model to improve our understanding of this region and investigate its sensitivity to ocean forcings. First, we model the past 6 years of NEGIS to calibrate our calving law (Morlighem et al., 2016); we then make projections based on different ice/ocean interaction scenarios. We discuss the impact of ocean forcing on ice dynamics of each glacier and conclude on the potential future contribution of NEGIS to sea level rise.

2 Data and Method

We use the Ice Sheet System Model (ISSM, Larour et al., 2012) to model 79North and ZI glaciers. We rely on a 3-D higher-order model (Blatter, 1995; Pattyn, 2003), with subelement grounding line parameterization (Seroussi et al., 2014) and level set-based moving boundaries (Bondzio et al., 2016). The mesh resolution varies between 200 m in the vicinity of the grounding line to 10 km inland. The mesh is vertically extruded into 12 layers and comprises about 340,000 prismatic elements.

To initialize the model, we infer the basal friction coefficients under grounded ice and ice viscosity parameters on floating ice through inversions following Morlighem et al. (2013) based on 2008–2009 surface velocities derived from Landsat and satellite interferometry (Mouginot et al., 2015). These inferred fields are assumed to be constant during the simulations. The bed and surface topography are from BedMachine Greenland version 3 (Morlighem et al., 2014). We force the model using the surface mass balance (SMB) from the regional atmospheric model RACMO2.3 (Lenaerts et al., 2012). We keep the SMB constant during the simulations, as we focus only on the effect of the ocean. All of our simulations start in 2008 and run for 100 years under different ocean forcings described below, using a time step of 7.3 days that satisfies the Courant-Friedrichs-Lewy condition. More details about the model are provided in supporting information Text S1 (Cuffey & Paterson, 2010; Frey, 2001; Glen, 1955; Hecht, 2006; MacAyeal, 1992).

We model calving front dynamics in the 3-D model by relying on the level set method and assuming that the calving front remains vertical (Bondzio et al., 2016; Morlighem et al., 2016). At each time step, the ice front moves at a velocity

(1)

where v is the ice horizontal velocity vector, c is calving rate, is the melting rate at the calving front, and n is a unit normal vector pointing outward (supporting information Text S1).

We apply the calving law from Morlighem et al. (2016), which depends on tensile stresses:

(2)

where is von Mises tensile stress and σ_max is a stress threshold (SI Text S1; Benn et al., 2007). To calibrate the stress threshold, we run the model from 2008 to 2014 with σ_max varying from 100 kPa to 1.5 MPa. We compare the modeled ice front evolution to Landsat derived data and find a best match with σ_max= 1 MPa for grounded ice, which is the same value as the one used in Morlighem et al. (2016) and is consistent with ice tensile strength measurements (Petrovic, 2003), and σ_max= 150 kPa on floating ice (SI Text S1). We attribute the lowering in the stress threshold over floating ice to crevassing and damage, which generally form at the grounding line and weaken the ice, lowering its resistance to effective tensile stresses. One of the limitations of this approach is that we have a discontinuity in the stress threshold across the grounding line, which should be improved in future modeling studies.

We ignore the frontal melt rates of floating termini due to its shallow depth and relatively cold water near the ocean surface. Yet frontal melting needs to be accounted for once the glacier loses its floating extension and becomes a tidewater glacier. Once the terminus of the glacier is grounded, the calving face becomes exposed to strong melt rates due to subglacial freshwater discharge (Jenkins et al., 2010; Straneo et al., 2010; Xu et al., 2012, 2013). Following Morlighem et al. (2016), the melt rate at the ice front, , is parameterized using a sine function to represent a seasonal variability, with a maximum melt rate, , in the summer and no melt in the winter:

(3)

This melt is applied uniformly along the calving face where it is grounded and where the glacier base is deeper than 300 m below sea level to account for the depth of warm AW (Straneo et al., 2010). For the control experiment, we do not apply frontal melting. However, we apply and increase the maximum summer melt rates to investigate the sensitivity of glaciers to frontal melting in our sensitivity experiments.

We also need to model basal melting under ice shelves. In this study, we use a simple parameterization to model basal melting following Favier et al. (2014). In this parameterization, basal melting rates increase linearly with depth between the top-water (−100 m) and the deep-water elevation (−450 m). No basal melting is applied if the bottom of ice shelf is greater than the top-water elevation, and the highest melt rate, 30 m/yr, is applied below the deep-water elevation (SI Text S1). We calibrate these parameters by comparing the parameterized spatial pattern of basal melt rates to the one derived from mass conservation (SI Text S1). For our forcing experiments, we change the maximum basal melt rate at depth to assess the response of glaciers to ocean forcings.

Based on our model calibrated with the past 6 years of observations, we run the model forward over next 100 years to see if the grounding line retreat of 79North and ice front retreat of ZI continue without any further forcings. Then, to test the sensitivity of NEGIS to ocean forcings, we set up two sets of experiments to test the response of the glaciers to basal melting of floating extensions and frontal melting of grounded termini. In each experiment, we increase ocean forcing parameters (e.g., basal melt rates of floating ice and frontal melt rates of grounded ice) to determine the threshold necessary to trigger dramatic changes, so that we assess how vulnerable this region is to an increase in ocean forcing in the future.

3 Results

The control experiment with unperturbed melt rates (Figure 2 and Movie S1) shows that 79North does not change significantly, with only a marginal advance in ice front position. The grounding line retreats inland about 7–8 km compared to its current position but stops migrating when it reaches higher bed topography (Figure 1) after 80 years. Although 79North does not retreat significantly during the simulation, the ice shelf velocity near the grounding line increases in response to thinning, and this acceleration propagates up to 150 km upstream (Figure 2b). The ice front of ZI, on the other hand, continues to retreat steadily and loses its floating extension after 70 years, becoming a grounded tidewater glacier. The ice front stabilizes after 70 years 30 km upstream, where a 200 m step in bed topography prevents further retreat. ZI also speeds up near the terminus as it retreats, but the velocity stabilizes as the ice front reaches this topographic ridge. Combined, the two glaciers lose about 1,110 km³ of their volume above floatation (VAF) over the course of the simulation, equivalent to 2.8 mm of sea level rise, and about 60% of this loss comes from ZI.

Figure 2

(a) Modeled ice front positions from 2014 to 2100 and modeled 2100 grounding line overlaid on a Google Earth image, and modeled ice velocity of (b) 79North and (c) ZI from 2014 to 2100 along the flow line shown in Figure 1a.

In our first set of sensitivity experiments, we increase the maximum ice shelf basal melt rates from 30 m/yr up to 90 m/yr without frontal melting. In all cases, the pattern of ice front and grounding line retreats is similar to the control experiment with the basal melt rates modulating the rate of retreat (Figures 3a and 3b). In all scenarios, the ice front of 79North remains stable with the same amount of grounding line migration as the one of the control experiment. Notably, the increase in basal melting induces an acceleration of its ice shelf, especially near the grounding line, which causes a local increase in the driving stress, but the glacier nonetheless remains stable. For ZI glacier, higher basal melt rates accelerate the retreat rate of its calving front and grounding line. The accelerated retreat of the grounding line yields to a larger ice shelf: the differences in stress regimes are such that the grounding line retreats faster than the ice front compared to the control experiment. The ice front, however, stabilizes at a similar position as the one of the control experiment. The loss of VAF from two glaciers is slightly larger: 1,200–1,250 km³ over the coming century (Figure 4).

Figure 3

Modeled ice front positions between 2014 and 2100 and modeled 2100 grounding line under different melting scenarios overlaid on a Google Earth image. (a) Maximum basal melt of 60 m/yr, (b) maximum basal melt of 90 m/yr, (c) maximum summer frontal melt of 3 m/d, and (d) maximum summer frontal melt of 6 m/d.

Figure 4

Changes in ice volume above floatation (VAF) of two glaciers and their sea level equivalent between 2014 and 2100 under different melting scenarios. The inset shows a zoom in shaded area of the main plot.

In our second set of experiments, we investigate the response of the system to increased frontal melting at the grounding termini (Figures 3c and 3d and Movie S2). Since frontal melt is assumed to be 0 when the ice front is floating, the ice shelf of 79North is not sensitive to these experiments. The future of ZI, on the other hand, is strongly dependent on these frontal melt rates: the speed of ice front retreat increases with the summer maximum melt rate, . We increase from 0 m/d with increments of 1 m/d leaving basal melt rates at the same value as the control experiment. For all melt rates below 6 m/d, the ice front of ZI does not retreat beyond the 200 m step during the simulations. A 6 m/d maximum frontal melt rate is necessary for the model to be dislodged from this step over the course of the century. Under this scenario, the glacier retreats faster and then remains stable for about 25 years on this ridge. After 25 years, however, the northern part of the glacier continues to retreat and destabilizes the southern part of the glacier. The glacier is dislodged from the step and starts a fast retreat inland where the bed topography is retrograde. During the simulation, the velocities dramatically increase over the entire region in response to ice front retreat, and the VAF would decrease by about 6,400 km³, which would raise global sea level by 16.2 mm by 2100 (Figure 4).

4 Discussion

The model suggests that 79North remains relatively stable under all forcing scenarios. Although some scenarios seem extreme, it has been suggested that warm Atlantic Intermediate Water could reach the ice tongue of 79North by making its way through the deep trough, which could result in a significant increase in melting rates in the near future (Schaffer et al., 2017). ZI, however, retreats steadily about 30 km upstream and loses its floating extension, even with the ocean forcing turned off (i.e., no melt applied at the base or at the front; SI Figure S7). These results confirm the analyses of Khan et al. (2014) and Mouginot et al. (2015): ZI will become a grounded tidewater glacier as a result of the complete collapse of its floating part. A pronounced step in the bed topography about 30 km upstream stabilizes the ice front and prevents further retreat of the glacier. To dislodge the glacier from this ridge over the course of the coming century, our model suggests that the maximum summer melt at the ice front must reach 6 m/d. This melting rate would require an increase of 0.8–3.0°C in ocean thermal forcing, together with an increase in subglacial discharge by a factor of 2 to 10 within this century (SI Text S2 and Figure S11) (Fettweis et al., 2013; Holland et al., 2008; Rignot et al., 2012; Rignot et al., 2016; Xu et al., 2013). While significant, compared to other observed frontal melt rates (∼4 m/d) from west and south Greenland (Carroll et al., 2016; Rignot et al., 2016; Truffer & Motyka, 2016; Xu et al., 2013), these changes remain within the range of possible scenarios in this region (Fettweis et al., 2013; Straneo et al., 2013; Yin et al., 2011).

In the sensitivity experiments, in which frontal melting is applied to grounded termini, we find that ZI glacier is more sensitive to frontal melting than basal melting (Figure S8). Although an increase in basal melting does not considerably affect calving dynamics, frontal melting causes faster retreat, which further increases ice surface velocity and destabilizes the glacier. The velocity of the ice front (v_front in equation 1 is indeed directly controlled by frontal melting rate ( ), which explains faster retreat as frontal melting increases. Fast ice front retreat substantially increases ice surface velocity at the termini and that acceleration propagates upstream over the entire model domain.

Our results show that the bed topography plays a critical role in determining stable positions of grounding lines and ice fronts in response to increased melt rates, which confirms the conclusions of earlier studies (e.g., Morlighem et al., 2016; Pattyn et al., 2013; Schoof, 2007; Weertman, 1974). The ice fronts and grounding lines of 79North and ZI stop retreating once they reach a step in the bed topography. Since the bed topography controls the glacier retreat and basal melting pattern, it is therefore critical to have an accurate bed topography, especially including small ridges or depressions, to understand the glacier behavior and make reliable projections.

The two glaciers have a different response to enhanced ocean forcings mainly because their geometrical settings are different. Near the calving front of 79North, islands and ice rises act as pinning points and stabilize the ice front, which is not undergoing significant tensile forces (Favier et al., 2016). On the other hand, the terminus of ZI does not have any pinning point and is exposed to ocean water. Tensile stresses are therefore stronger at the calving face, and the glacier is more susceptible to retreat, according to our calving law. Additionally, the bed slope near the current grounding line slows down the retreat of 79North while ZI could retreat about 30 km along the deep seafloor until it reaches a ridge in the bed topography.

It is important to notice that ZI glacier is already in a stage of retreat and will continue to lose mass until it reaches a new state of equilibrium, 30 km upstream from the current calving front position. The glacier will continue to retreat for 70 years even with no further ocean forcing or faster for stronger ocean forcings. Our sensitivity study shows that ice mass loss from this region is not sensitive to ocean forcings unless the melt rate along the calving front increases to 6 m/d, at which point the glacier retreats beyond its stabilizing ridge rapidly in a region of retrograde bed (Figure 4). Ice mass loss from the unforced experiment (with ocean forcings turned off) is considered as a committed loss due to the current state of NEGIS (Goldberg et al., 2015; Price et al., 2011), and this is the minimum contribution of this region to global sea level by 2100. While the grounding line and ice velocity are stable once the ice reaches its stabilizing sill, the glacier does not reach the steady state (Figure 4) and still loses mass over the entire duration of the simulation. It is therefore not clear whether or when the glacier will eventually retreat farther inland on a longer time scale.

In this study, we apply a simple parameterization in order to model frontal melt rates. In reality, summer frontal melt rates are 2–3 times higher compared to winter depending on subglacial water discharge and thermal forcing, and the seasonal variability of observed melt rates is not sinusoidal (Rignot et al., 2016). To better model frontal melting, we need to modulate melt rates by subglacial discharge, thermal forcing, and water depth. In this study, however, we simplify the seasonal variability using a sine function and only increase the maximum melt rates for the sensitivity experiments, as we do not have ocean temperature data in front of ZI glacier.

Another limitation of this study is the basal melting under the floating ice tongue, which is based on a depth-dependent parameterization. Although the model with this method reproduces a pattern of grounding line retreat that is in good agreement with observations (Figure S6), it does not account for changes in amplitude or specific spatial patterns. Basal melt rates vary with time and space depending on the shape of the sub-ice shelf cavity, ice/ocean interactions, and ocean water circulation (Wilson & Straneo, 2015). To reproduce basal melting more accurately, ocean circulation models with an accurate bathymetry is essential. Moreover, more realistic ways to parameterize the transition between basal and frontal melt as ice fronts ground could further improve the model. We also do not account here for some physical processes that may enhance the retreat rate, such as the effect of surface runoff on crevasse propagation, damage, and calving. These processes could potentially decrease the threshold of 6 m/d, as it has been shown that meltwater runoff could be multiplied by a factor of 10 by the end of the century (Fettweis et al., 2013) and the effect of runoff on ice discharge remains poorly known.

5 Conclusion

We model two major glaciers of NEGIS using a 3-D ice sheet model, which includes a tensile stress-based calving law, to assess their response to ocean thermal forcing under different warming scenarios. Under these scenarios, our model suggests that 79North will not change significantly over the next century, even with a strong increase in basal melt rates. ZI will continue to retreat 30 km upstream and become a grounded tidewater glacier, until it reaches a stabilizing ∼200 m step in bed topography. Our simulations show that ZI is in a state of unstoppable retreat that does not depend significantly on ocean forcing but is due to its current internal dynamics, which is mainly controlled by the bed topography. This retreat will stop once the ice front reaches this stabilizing ridge in the bed topography. An increase in the frontal melt rate up to 6 m/d in the summer would be necessary in order to trigger a farther retreat inland, and this amount of oceanic forcing, while significant, remains within the range of possible scenarios. Future model studies will need to improve model and climate forcing parameterization with more ocean data to overcome the limitations of this study and improve future projections.

Acknowledgments

This work was performed at the University of California, Irvine under a contract with the National Science Foundation's ARCSS program (1504230) and the National Aeronautics and Space Administration Cryospheric Sciences Program (NNX15AD55G). The data used are listed in the references and are freely available at the National Snow and Ice Data Center. ISSM is an open-source software available at https://issm.jpl.nasa.gov.