A finite-strain logarithmic viscoelastic model for Antarctic ice shelves based on an additive split

The floating edges of Antarctica's massive ice sheets are not static walls of ice; they are dynamic, breathing structures that constantly shift, bend, and eventually break apart. These floating extensions, known as ice shelves, act as crucial buttresses, holding back the vast glaciers behind them. When they break, a process called calving, they release icebergs into the ocean, a primary way these ice sheets lose mass. For decades, scientists have tried to predict exactly when and where this breaking happens. To do this, they rely on computer models that simulate how ice moves and deforms under its own weight and the pressure of the ocean. However, these models have traditionally treated ice in one of two ways: either as a solid that snaps back instantly when pushed (elastic), or as a thick, slow-moving fluid that flows over years (viscous). In reality, ice shelves experience forces that act on both timescales simultaneously. Tides and ocean waves push and pull the ice over hours, while the slow creep of the glacier happens over decades. A model that ignores the quick, spring-like bounce of the ice might miss the cracks that form during a storm, while a model that ignores the slow flow might fail to predict the shelf's long-term shape.

To solve this, a team of researchers has developed a new way to simulate the behavior of these ice shelves that captures both the quick bounce and the slow flow at the same time, even when the ice has changed its shape significantly over time. They created a mathematical framework that treats the ice as a material that can stretch and bend in complex ways, yet still remembers its original form. This approach allows them to track how the ice responds to the immediate stress of a rising tide while also accounting for the years of slow stretching that happen between tidal cycles. By focusing on the specific geometry of the ice shelf's edge, where it meets the open ocean, they found that the shape of the cliff and the way the ice is layered inside it play a decisive role in where the ice is most likely to crack. Their work suggests that the interplay between the ice's ability to bounce back and its tendency to flow slowly creates a specific pattern of tension near the front, which controls how and when the ice breaks off.

The researchers built their model on a concept called a "Maxwell" system, which is a standard way to describe materials that act like both a spring and a thick fluid. Imagine a spring connected in a line with a piston moving through honey; if you pull on them, the spring stretches instantly, and the honey slowly drags along. In their simulation, the spring represents the ice's immediate elastic response, while the honey represents the slow, viscous flow that follows Glen's flow law, a rule that has long been used to describe how ice moves over centuries. The innovation in this study lies in how they handle the math when the ice stretches a lot. Previous models often struggled when the ice changed its shape significantly, requiring complex calculations that were difficult to run on computers. This new approach uses a specific type of measurement called logarithmic strain, which allows the team to split the total movement of the ice into its elastic and viscous parts in a straightforward, additive way. This means they can add the two types of movement together without needing to track a separate, invisible "intermediate" shape of the ice, making the calculations much more efficient and easier to integrate into existing climate models.

To test if their new method worked, the team first ran a simulation of a vertical column of ice supporting its own weight, comparing their results against a well-established, more complex model. The results matched almost perfectly. After a year and a half of simulated time, the new model predicted the ice would sink and bulge out by amounts that differed from the complex model by only a few centimeters. The stress levels inside the ice were also nearly identical, differing by less than one kilopascal in most areas. This confirmed that their simplified, additive approach could accurately reproduce the behavior of the ice without the heavy computational cost of the older methods. However, the researchers were careful to note where their method might fail. They found that if the ice were subjected to a specific type of twisting motion, known as simple shear, where layers slide past each other like a deck of cards, their model would start to diverge from the more complex one. In those extreme twisting scenarios, the new model would predict the ice unloading or relaxing too quickly. Fortunately, the researchers determined that the ice shelves they are studying do not experience this kind of extreme twisting. Instead, the ice near the front is primarily being stretched and bent by gravity and buoyancy, a type of movement where their new model remains highly accurate.

With the model verified, the team applied it to an idealized ice tongue, a long strip of ice floating on the ocean, to see how different shapes and internal properties affect the stress at the front. They included realistic details, such as the fact that ice is denser at the bottom than at the top due to compression, and that it flows more easily when it is warmer. They also tested different cliff shapes, including some with a submerged "foot" of ice and others with an undercut base. The simulations revealed that the shape of the cliff dramatically changes where the tension builds up. A submerged foot can actually reverse the direction of the bend, reducing the stress at the surface and potentially making the ice more stable. Conversely, an undercut face concentrates the tension and shifts the most dangerous stress point further inland. The study also showed that the temperature and density variations through the thickness of the ice create their own internal bending forces, independent of the cliff's shape. These findings highlight that the risk of calving is not just about the total weight of the ice, but about the precise balance of forces created by the ice's geometry and its internal structure.

The ultimate goal of this research is to provide a more reliable tool for predicting the future of Antarctica's ice shelves. By capturing both the rapid elastic response to tides and waves and the slow viscous creep over years, this new model offers a clearer picture of the stress fields that lead to calving. The researchers emphasize that while their method is not a universal replacement for all types of ice modeling, it is particularly well-suited for the specific conditions found at the edges of ice shelves. It allows scientists to simulate the complex, finite changes in the ice's shape over decades without losing the ability to see the immediate effects of short-term events. This capability is crucial for understanding how ice shelves might react to a changing climate, where the frequency of storms and the rate of ocean warming could alter the delicate balance of forces that hold these massive structures together. The work does not claim to solve the mystery of calving entirely, but it provides a robust, efficient, and physically consistent way to explore the mechanics of the ice front, offering a clearer view of the forces that drive the breaking of ice.