24 | Engineering Reality Magazine

Understanding tidal mechanisms in Antarctic

ice shelf flowsBy Sebastian Rosier, Northumbria University, UK,

and Andy Bell, MSC Software UK

The continent of Antarctica covers the south pole of our planet, is about the size of Europe, is covered by a vast ice sheet up to 3 miles deep and is one of the most bleak, coldest, and yet beautiful places on Earth. It is home to very few people other than a few thousand engineers and scientists, but it is a relatively pristine, untouched environment that contains many ice records that reflect the atmosphere and the climate of our planet stretching back tens of thousands of years. It is also a bell weather for climate change effects in the world and the sustainability of our complex ecosystems upon which we all depend. We saw this most clearly with the Ozone Layer depletion above Antarctica scare in the 1980s when mankind took urgent action to limit the use of chlorofluorocarbon gases this helping to repair the emerging hole in the atmosphere.

A century on from the heroic age of Antarctic exploration, the Antarctic continent remains one of the most hostile and least accessible places on earth. Sitting atop this hidden continent is the Antarctic Ice Sheet; a vast reservoir of frozen ice up to 4km thick and containing enough water to raise global sea levels by 58m. This landscape, that appears almost entirely flat and dormant from the surface, actually consists of rivers of fast flowing ice, known as ‘ice streams’. These narrow-concentrated regions of ice flow transport ice to the coast where they thin, eventually lifting off the bed under buoyancy and forming the floating ice shelves that fringe most of the continent.

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S ustai n abil it y -St ruct ure s

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Over the last few decades, the Antarctic ice sheet has been rapidly losing mass, largely in response to warming ocean temperatures leading to increased melting of the ice shelves from underneath. Understanding how a changing climate will affect the Antarctic Ice Sheet has become a key question in climate science and yet, despite the important role it plays in the earth system and the potential that a large fraction of the world’s population could be displaced as it melts, our understanding of the physical processes that determine ongoing and future mass loss remains remarkably poor (1).

Perhaps the most fundamental issue for ice science, and the one most problematic for computer modelling efforts, is that we have very little grasp of how ice streams flow rapidly over their beds. Drilling to the base of ice streams to observe this directly is a huge technical challenge and only a few measurements exist. As a result, ice sheet modellers have to resort to parameterisations to describe the numerous possible processes that dictate how quickly an ice stream can slide over, or deform, its underlying sediment; known as the ‘basal sliding law’. Testing how effective these parameterisations are is therefore crucial, but until recently no reliable method existed for doing this. Progress in science is often made through trying to explain observations that do not fit with contemporary understanding and in Antarctica there exists a particularly striking example. In the late 2000s several GPS systems were deployed on the Rutford Ice

Stream, an ice stream in West Antarctica that drains into the large Filchner-Ronne Ice Shelf which itself has an area approximately the size of Sweden (Figure 1).

These GPS systems were far away from the coast, and yet they showed strong variability in the flow speed of the ice stream at ocean tidal frequencies. Even more surprisingly, the strongest tidal component was at a frequency not even measurable in the neighbouring ocean. More recently, we have found that for every ice stream flowing into the Filchner-Ronne Ice Shelf that has been measured, as well as across the entire ice shelf itself, this same phenomenon exists. Here, then, is an observation that can’t be explained by our current understanding of ice stream flows.

In this way, ocean tides and the ice sheet’s response acts as a natural experiment and by filling this knowledge gap we can gain new insights into ice flow that, among other things, will help constrain the form of the basal sliding law.

Until recently, progress in this area has been limited; these tidal processes are occurring at timescales of hours or days and this poses a real problem. Currently, ice sheet models only model the viscous component of ice deformation since ice sheet modelling efforts are largely focused on projections spanning decades to centuries that can safely ignore short-term behaviour. Not only that, but most of them use thin plate type approximations to model ice flow and ignore certain components of stress that are less important for determining ‘secular’ ice flow. Here, the power of non-linear FEA simulations using Marc from MSC Software came into its own we found. With its ability to accurately and rapidly solve the behaviour of nonlinear viscoelastic materials without neglecting any stress terms, it can tackle many problems that would not otherwise be possible to simulate.

Figure 1 : Map showing the Filchner–Ronne Ice Shelf and adjoining ice streams, along with locations of GPS measurements.

Figure 2: Overview of the Marc finite-element model, showing model resolution, the quadratic pentahedral elements used, and a vertically exaggerated oblique view of the model showing modelled mean ice velocity for the default setup experiment.

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In order to explore what was causing these puzzling observations we created a model of the Rutford ice stream in MSC Marc Mentat using the built-in meshing options and forced the model with ocean tides (Figure 2). These tides were found to generate complex flexural and longitudinal stresses at the hinge line where the ice stream meets the ocean. These stresses are transmitted upstream through interactions with the underlying sediment.

What we found through these simulations was that it was remarkably difficult to replicate both the amplitude of the observed signal and the distance it travels upstream from the coast. In fact, this was only possible with the inclusion of a highly conductive drainage system beneath the ice stream. Drainage systems such as these, through which melt water is transported to the coast, are readily observed in the smaller Greenland Ice Sheet but very little evidence exists for them in Antarctica and they are rarely included in large scale model simulations. Our results suggest not only that they should be included, but that we can infer their hydraulic conductivity using tidal observations such as these.

The other enigma that has confounded Antarctic ice scientists is that the horizontal flow of the ice shelf itself is strongly modulated by ocean tides. In fact, this is so strong that in some places the tidal variation in flow causes the ice shelf to periodically

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flow backwards! Ice shelf flow is generally thought to be more well understood than that of ice streams, since these regions float on the ocean and the complication of unseen processes at the bed can be neglected. How, then, do tides that cause floating ice to move vertically translate to a horizontal motion? Once again, MSC Marc has enabled us to address this question. By creating a model of the entire Filchner-Ronne Ice Shelf, including all major ice stream that drain into it, we were able to make great leaps forward in our understanding of the entire coupled system.

It turns out that from our simulations, the answer is two-fold for the Antarctic ice shelf in question. Firstly, spatial variations in tidal amplitude and phase leads to a slight tilting of the ice shelf, generating sufficient elastic strain to account for some of the high frequency large scale motion. Secondly, the margins of the ice shelf move as the tides lift and drop the ice onto the bed below. For this second mechanism, the advanced contact capabilities of MSC Marc were indispensable, allowing us to accurately model the tidal migration of the point at which the ice loses contact with the bed and how the contact stresses evolve over time. These modelling efforts have led to a better understanding of the rheology

of ice over large spatial scales and processes in the hinge zone - a particularly crucial part of the ice sheet system.

Many aspects of these remarkable observations remain unexplained and there is no doubt that MSC Marc will continue to play an important role in helping us to understand these processes. Complicating factors such as ice damage and temperature variation, which are largely overlooked in the current generation of ice sheet models, can easily be added into our model to hopefully answer some of the remaining open questions. As the Antarctic continent and the surrounding ocean continues to warm, the need to reduce uncertainty in our projections of the future evolution of the ice sheet grows increasingly urgent.

Conclusion

Until our study, no computer model has yet been able to reproduce the quantitative aspects of observed tidal modulation across the entire Filchner–Ronne Ice Shelf in Antarctica. The cause of the tidal ice flow response has, therefore, remained an enigma, indicating a serious limitation in science’s current understanding of the mechanics of large-scale ice flow on the continent. A further limitation of previous studies is that they have all

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Reference

1. “Exploring mechanisms responsible for tidal modulation in flow of the Filchner–Ronne Ice Shelf”, S. H. R. Rosier & G. H. Gudmundsson, Department of Geography and Environmental Sciences, Northumbria University, UK, The Cryosphere Journal, 14, 17–37, 2020, https://doi.org/10.5194/tc-14-17-2020

focused on isolated regions and interactions between different areas have, therefore, not been fully accounted for. In our study we have conducted the first largescale ice flow modelling study (using MSC Marc) to explore these processes using a viscoelastic rheology and realistic geometry of the entire Filchner–Ronne Ice Shelf, where the best observations of tidal response are available. We evaluated all relevant mechanisms that have hitherto been put forward to explain how ocean tides might affect ice shelf flow and compared our results with observational data. We concluded that, while some models are able to generate the correct general qualitative aspects of the tidally induced perturbations in ice flow, most of these mechanisms must be ruled out as being the primary cause of the observed long-period response. We find that only tidally induced lateral migration of grounding lines can generate a sufficiently strong long-period Msf tidal frequency response on the ice shelf to match observations. Furthermore, we showed that the observed horizontal short-period semidiurnal tidal motion, causing twice daily flow reversals at the ice front, were generated through a purely elastic response to basin-wide tidal perturbations in the ice shelf slope. Our simulation model has allowed us to quantify the effect of tides on mean ice flow and we found that the Filchner–Ronne Ice Shelf flows, on average, were 21% faster than they would in the absence of large ocean tides. We have therefore found MSC Marc to be a very powerful tool that is well suited to studying processes at shorter timescales where ice behaves viscoelastically. This area of research has important implications for climate science in terms of predicting the future contribution of Antarctica to global sea level rise.