Rewriting equations for ice deformation and flow in watery glaciers

When Neil Iverson was asked to explain a research paper on ice flow in glaciers that had just been published in Science, he started with two lessons in ice physics.

First, the distinguished professor emeritus of Iowa State University’s Department of Earth, Atmosphere, and Climate stated that there are many different types of ice within glaciers. Some of the glaciers are at pressure-melting temperatures and are soft and watery.

The temperate ice is similar to ice cubes left on a kitchen counter, with melted water collecting between the ice cubes and the countertop. Temperate ice has been difficult to study and characterize.

Second, other parts of the glacier have cold, hard ice, like the ice cubes that are still in your freezer. This is the type of ice that is typically studied and used as the basis for glacier flow models and predictions.

A new research paper, “Linear viscous flow in temperate ice,” deals with the former, said Iverson, co-author and project supervisor.

In this paper, the standard values ​​in “Empirical Foundations of Glacier Flow Modeling” (an equation known as Glenn’s flow law, named after the late British ice physicist John W. Glenn) are: We describe laboratory experiments and resulting data that suggest that this should be the case. Changed to temperate ice.

Using this new value in the flow laws “tends to predict much smaller increases in flow velocity in response to increased stresses caused by ice sheet shrinkage as the climate warms,” ​​Iverson said. he said. That means models predict less glacial flow into the ocean and less sea level rise.

There is an urgent need to consider warm glacier ice.

Open the walk-in freezer in Iverson’s campus lab and you’ll see a nine-foot-tall ringshear device that has been simulating the forces and motion of glaciers since 2009.

At the center of the device is a ring of ice approximately 3 feet in diameter and 7 inches thick. Below the ring is a hydraulic press that can apply up to 100 tons of force to the ice, simulating the weight of an 800-foot-thick glacier. The ice ring is surrounded by a bath of circulating fluid that controls the temperature of the ice to the hundredth of a degree. An electric motor attached to a plate with grippers above the ice ring can rotate the ice at speeds of 1 to 10,000 feet per year.

For this project, the researchers modified the device by adding another gripper to the bottom of the ice ring, so that the rotation of the top gripper sheared the ice below.

Colin Schon, a former master’s student at Iowa State University and now a geologist with the Chicago-based BBJ Group and lead author of the group’s latest research paper, used a modified device to A series of six experiments were conducted, each lasting approximately six times. A few weeks. The experiment also included measuring the liquid water content of the ice, an experiment of this kind that had not been done since the 1970s.

“These experiments involved deforming the ice at melting temperatures and various stresses,” Schon said.

Iverson likened the experiment to grabbing the top and bottom of a bagel, twisting the two halves together and spreading cream cheese in the middle.

Iverson said experimental data showed that ice deforms at a rate linearly proportional to stress. Under conventional thinking, researchers expected that increasing stress would cause the ice to soften, so the velocity would increase more and more as stress increased.

Why is this important?

The ice is temperate near the bottom and edges of the fastest-flowing parts of the ice sheet, and in fast-flowing mountain glaciers, both of which shed ice into the ocean and affect sea levels. “Therefore, there is a pressing need to accurately model and predict ice flow on warm glaciers,” the authors write.

reset n to 1.0

Glenn’s flow law is written as ε ̇ = Aτn.

This equation relates the stress on the ice, τ, to its deformation rate, ε ̇. where A is a constant for a given ice temperature. The results of the new experiment show that the value of the stress index n is 1.0 instead of the normally assigned values ​​of 3 or 4.

The authors conclude that “Over many generations, based on Glenn’s original experiments and many subsequent experiments, primarily in cold ice (below -2°C), the value of the stress exponent n in the model is 3.0. It has been thought that there is. (They also write that other studies on “cold ice in ice sheets” have set even higher values ​​of 4.0.)

Part of the reason is that “experiments with ice at melting temperatures that are pressurized are difficult,” says study co-author and former postdoctoral fellow and dean of the Department of Geosciences at Iowa State University. said Lucas Soet, Associate Professor L. Morgridge. at the University of Wisconsin-Madison. Zort, who co-supervised the project, built a slightly smaller version of the ring shear device with transparent walls for the laboratory.

However, data from large-scale shear deformation experiments performed in Iverson’s laboratory raised questions about the value assigned to n. Temperate ice is linearly viscous (n = 1.0) “over the typical range of liquid water content and stress expected near glacier beds and at the edges of ice streams,” the authors write.

They proposed that the cause is melting and refreezing along the boundaries of individual ice grains on the millimeter to centimeter scale, and that this should occur at a rate linearly proportional to stress.

This new data will allow modelers to “build ice sheet models based on the physical relationships demonstrated in the laboratory,” Zoet said. “The more we understand, the more accurate our predictions will be.”

Obtaining data to support new values ​​of n required some patience.

“We’ve been working on this project for years,” Sean said. “It was really hard to make this work.”

Ultimately, Iverson said, “This was about a 10-year process considering all the failures and developments.”

Researchers say the long process is essential for more accurate models of temperate glacier ice and more accurate predictions of glacier flow and sea level rise.