Forecasting the Ice Loss of Greenland’s Glaciers With Viscoelastic Modeling

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To someone standing near a glacier, it may seem as stable and permanent as anything on Earth can be. However, Earth's great ice sheets are always moving and evolving. In recent decades, this ceaseless motion has accelerated. In fact, ice in polar regions is proving to be not just mobile, but alarmingly mortal.

Rising air and sea temperatures are speeding up the discharge of glacial ice into the ocean, which contributes to global sea level rise. This ominous progression is happening even faster than anticipated. Existing models of glacier dynamics and ice discharge underestimate the actual rate of ice loss in recent decades. This makes the work of Angelika Humbert, a physicist studying Greenland's Nioghalvfjerdsbrae outlet glacier, especially important - and urgent.

As the leader of the Modeling Group in the Section of Glaciology at the Alfred Wegener Institute (AWI) Helmholtz Centre for Polar and Marine Research in Bremerhaven, Germany, Humbert works to extract broader lessons from Nioghalvfjerdsbrae's ongoing decline. Her research combines data from field observations with viscoelastic modeling of ice sheet behavior. Through improved modeling of elastic effects on glacial flow, Humbert and her team seek to better predict ice loss and the resulting impact on global sea levels.

She is acutely aware that time is short. Nioghalvfjerdsbrae is one of the last three floating tongue' glaciers in Greenland," explains Humbert. Almost all of the other floating tongue formations have already disintegrated."

One Glacier That Holds 1.1 Meter of Potential Global Sea Level Rise

The North Atlantic island of Greenland is covered with the world's second largest ice pack after that of Antarctica. (Fig. 1) Greenland's sparsely populated landscape may seem unspoiled, but climate change is actually tearing away at its icy mantle.

The ongoing discharge of ice into the ocean is a fundamental process in the ice sheet mass-balance," according to a 2021 article in Communications Earth & Environment by Humbert and her colleagues. (Ref. 1) The article notes that the entire Northeast Greenland Ice Stream contains enough ice to raise global sea levels by 1.1 meters. While the entire formation is not expected to vanish, Greenland's overall ice cover has declined dramatically since 1990. This process of decay has not been linear or uniform across the island. Nioghalvfjerdsbrae, for example, is now Greenland's largest outlet glacier. The nearby Petermann Glacier used to be larger, but has been shrinking even more quickly. (Ref. 2)

Existing Models Underestimate the Rate of Ice Loss

Greenland's overall loss of ice mass is distinct from calving", which is the breaking off of icebergs from glaciers' floating tongues. While calving does not directly raise sea levels, the calving process can quicken the movement of land-based ice toward the coast. Satellite imagery from the European Space Agency (Fig. 2) has captured a rapid and dramatic calving event in action. Between June 29 and July 24 of 2020, a 125 km2 floating portion of Nioghalvfjerdsbrae calved into many separate icebergs, which then drifted off to melt into the North Atlantic.

Direct observations of ice sheet behavior are valuable, but insufficient for predicting the trajectory of Greenland's ice loss. Glaciologists have been building and refining ice sheet models for decades, yet, as Humbert says, There is still a lot of uncertainty around this approach." Starting in 2014, the team at AWI joined 14 other research groups to compare and refine their forecasts of potential ice loss through 2100. The project also compared projections for past years to ice losses that actually occurred. Ominously, the experts' predictions were far below the actually observed losses" since 2015, as stated by Martin Ruckamp of AWI. (Ref. 3) He says, The models for Greenland underestimate the current changes in the ice sheet due to climate change."

Viscoelastic Modeling to Capture Fast-Acting Forces

Angelika Humbert has personally made numerous trips to Greenland and Antarctica to gather data and research samples, but she recognizes the limitations of the direct approach to glaciology. Field operations are very costly and time consuming, and there is only so much we can see," she says. What we want to learn is hidden inside a system, and much of that system is buried beneath many tons of ice! We need modeling to tell us what behaviors are driving ice loss, and also to show us where to look for those behaviors."

Since the 1980s, researchers have relied on numerical models to describe and predict how ice sheets evolve. They found that you could capture the effects of temperature changes with models built around a viscous power law function," Humbert explains. If you are modeling stable, long-term behavior, and you get your viscous deformation and sliding right, your model can do a decent job. But if you are trying to capture loads that are changing on a short time scale, then you need a different approach."

To better understand the Northeast Greenland Ice Stream glacial system and its discharge of ice into the ocean, researchers at the Alfred Wegener Institute have developed an improved viscoelastic model to capture how tides and subglacial topography contribute to glacial flow.

What drives short-term changes in the loads that affect ice sheet behavior? Humbert and the AWI team focus on two sources of these significant but poorly understood forces: oceanic tidal movement under floating ice tongues (such as the one shown in Fig. 2) and the ruggedly uneven landscape of Greenland itself. Both tidal movement and Greenland's topography help determine how rapidly the island's ice cover is moving toward the ocean.

To investigate the elastic deformation caused by these factors, Humbert and her team built a viscoelastic model of Nioghalvfjerdsbrae in the COMSOL Multiphysics software. The glacier model's geometry is based on data from radar surveys. The model solved underlying equations for a viscoelastic Maxwell material across a 2D model domain consisting of a vertical cross section along the blue line shown in Fig. 3. The simulated results were then compared to actual field measurements of glacier flow obtained by four GPS stations, one of which is shown in Fig. 3.

How Cycling Tides Affect Glacier Movement

The tides around Greenland typically raise and lower the coastal water line between 1 and 4 meters per cycle. This action exerts tremendous force on outlet glaciers' floating tongues, and these forces are transmitted into the land-based parts of the glacier as well. AWI's viscoelastic model explores how these cyclical changes in stress distribution can affect the glacier's flow toward the sea.

The charts in Figure 4 present the measured tide-induced stresses acting on Nioghalvfjerdsbrae at three locations, superimposed on stresses predicted by viscous and viscoelastic simulations. Chart a shows how displacements decline further when they are 14 kilometers inland from the grounding line (GL). Chart b shows that cyclical tidal stresses lessen at GPS-hinge, located in a bending zone near the grounding line between land and sea. Chart c shows activity at the location called GPS-shelf, which is mounted on ice floating in the ocean. Accordingly, it shows the most pronounced waveform of cyclical tidal stresses acting on the ice.

The floating tongue is moving up and down, which produces elastic responses in the land-based portion of the glacier," says Julia Christmann, a mathematician on the AWI team who plays a key role in constructing their simulation models. There is also a subglacial hydrological system of liquid water between the inland ice and the ground. This basal water system is poorly known, though we can see evidence of its effects." For example, chart a shows a spike in stresses below a lake sitting atop the glacier. Lake water flows down through the ice, where it adds to the subglacial water layer and compounds its lubricating effect," Christmann says.

The plotted trend lines highlight the greater accuracy of the team's new viscoelastic simulations, as compared to purely viscous models. As Christmann explains, The viscous model does not capture the full extent of changes in stress, and it does not show the correct amplitude. (See chart c in Fig. 4.) In the bending zone, we can see a phase shift in these forces due to elastic response." Christmann continues, You can only get an accurate model if you account for viscoelastic spring' action."

Modeling Elastic Strains from Uneven Landscapes

The crevasses in Greenland's glaciers reveal the unevenness of the underlying landscape. Crevasses also provide further evidence that glacial ice is not a purely viscous material. You can watch a glacier over time and see that it creeps, as a viscous material would," says Humbert. However, a purely viscous material would not form persistent cracks the way that ice sheets do. From the beginning of glaciology, we have had to accept the reality of these crevasses," she says. The team's viscoelastic model provides a novel way to explore how the land beneath Nioghalvfjerdsbrae facilitates the emergence of crevasses and affects glacial sliding.

When we did our simulations, we were surprised at the amount of elastic strain created by topography," Christmann explains. We saw these effects far inland, where they would have nothing to do with tidal changes."

Figure 6 shows how vertical deformation in the glacier corresponds to the underlying landscape and helps researchers understand how localized elastic vertical motion affects the entire sheet's horizontal movement. Shaded areas indicate velocity in that part of the glacier compared to its basal velocity. Blue zones are moving vertically at a slower rate than the sections that are directly above the ground, indicating that the ice is being compressed. Pink and purple zones are moving faster than ice at the base, showing that ice is being vertically stretched.

These simulation results suggest that the AWI team's improved model could provide more accurate forecasts of glacial movements. This was a wow' effect for us," says Humbert. Just as the up and down of the tides creates elastic strain that affects glacier flow, now we can capture the elastic part of the up and down over bedrock as well."

Scaling Up as the Clock Runs Down

The improved viscoelastic model of Nioghalvfjerdsbrae is only the latest example of Humbert's decades-long use of numerical simulation tools for glaciological research. COMSOL is very well suited to our work," she says. It is a fantastic tool for trying out new ideas. The software makes it relatively easy to adjust settings and conduct new simulation experiments without having to write custom code." Humbert's university students frequently incorporate simulation into their research. Examples include Julia Christmann's PhD work on the calving of ice shelves, and another degree project that modeled the evolution of the subglacial channels that carry meltwater from the surface to the ice base.

The AWI team is proud of their investigative work, but they are fully cognizant of just how much information about the world's ice cover remains unknown - and that time is short. We cannot afford Maxwell material simulations of all of Greenland," Humbert concedes. We could burn years of computational time and still not cover everything. But perhaps we can parameterize the localized elastic response effects of our model, and then implement it at a larger scale," she says.

This scale defines the challenges faced by 21st-century glaciologists. The size of their research subjects is staggering, and so is the global significance of their work. Even as their knowledge is growing, it is imperative that they find more information, more quickly. Angelika Humbert would welcome input from people in other fields who study viscoelastic materials. If other COMSOL users are dealing with fractures in Maxwell materials, they probably face some of the same difficulties that we have, even if their models have nothing to do with ice!" she says. Maybe we can have an exchange and tackle these issues together."

Perhaps, in this spirit, we who benefit from the work of glaciologists can help shoulder some of the vast and weighty challenges they bear.

References

1. J. Christmann, V. Helm, S.A. Khan, A. Humbert, et al. Elastic Deformation Plays a Non-Negligible Role in Greenland's Outlet Glacier Flow, Communications Earth & Environment, vol. 2, no. 232, 2021.
2. European Space Agency, Spalte Breaks Up, September 2020.
3. Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Model comparison: Experts calculate future ice loss and the extent to which Greenland and the Antarctic will contribute to sea-level rise, September 2020.