Ice shelves are the floating expanses that form when the ice sheets of Greenland and Antarctica flow into the surrounding ocean. These ice shelves ultimately break up and form icebergs in a process called “calving”.

To date there hasn’t been a law based on physical principles that explains ice-shelf calving, which has made it tricky to model ice-sheet behaviour. Predicting the future of the ice sheets under global warming is of considerable interest to scientists and therefore a physical model of calving would be very welcome.

Now Richard Alley of Pennsylvania State University and colleagues at five other academic institutes in the US have come up with a simple law that explains much calving behaviour (Science 322 1344).

Earthquake prediction comes to mind, or guessing whether a tea cup pushed off the table will break or bounce Richard Alley, Pennsylvania State University

“Fracture-mechanics problems are invariably difficult,” explained Alley. “Earthquake prediction comes to mind, or guessing whether a teacup pushed off the table will break or bounce upon hitting the floor. With the teacup, a drop from 1 mm high won’t break it, and a drop from 100 m almost surely will — one term, the height of the drop, explains a whole lot of the behaviour. Our hope was to find such a dominant term in calving of bergs from ice shelves.”

### Surprisingly simple hypothesis

And indeed, that’s what the researchers managed to do. “Our first hypothesis was that spreading is required to open a crack that isolates a new iceberg, so the spreading tendency in the direction of ice and berg motion should play the role of the height of your teacup,” explained Alley. “Almost surprisingly, this simple hypothesis explains most of the variance in a data set we assembled to test [it].”

The team’s basic equation for ice calving is the rate of spreading times the width of the shelf times thickness multiplied by a constant. For narrow shelves between two ridges, the sides hold back the ice, slowing the overall movement and making it harder to break the ice. And thicker ice shelves tend to spread more quickly.

“The spreading rate can be calculated from ice thickness and a few other things that are already solved for in numerical models, so we have provided a practicable calving law,” said Alley. “At present, models rarely if ever calculate physically where the ice ends, instead stopping the model before the ice ends or using some other relation that is not fully physical.”

### Pinning points

According to Alley, in its simplest implementation this calving law requires a “pinning point” such as an island to stabilize an ice shelf. “And we typically see such pinning points,” he said. “Without such stabilization, the law almost always produces unstable shelves, that either elongate greatly or calve back rapidly. We believe this is an interesting line of inquiry to be followed.”

The team used both new and previously published data, putting together a data set for a representative range of ice shelves.

Now the team plans to follow the discussion that emerges following publication of their work and to “make sure that new data sets coming in remain consistent with our results”. The researchers are also implementing the law in models to further understand the implications. “We believe this matters for understanding the history and projecting the future of ice shelves,” said Alley.