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Math vs. the Volcano: Mitigating an Eruption’s Aftermath

By: Kathleen Tuck   Published 4:14 pm / September 25, 2014

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Few forces in the universe rival that of an erupting volcano. And while the tremendous power unleashed in that event can devastate massive mountains, the damage caused by an ensuing ash cloud can bring nations to a halt.

Take for example the 2010 eruption of Iceland’s Eyjafjallajökull volcano, which released more than 9 billion cubic feet of ash over the course of months. The initial ash cloud led to airport closures across Europe, stranding millions of passengers and leading to billions of dollars in lost revenue.

A Boise State mathematician thinks that’s unacceptable.

Donna Calhoun

Donna Calhoun

Backed by a three-year, $194,000 National Science Foundation grant, Donna Calhoun is reimagining the algorithms currently used to predict where ash will collect in the atmosphere following an eruption. The grant is titled “A parallel algorithmic framework for flexible time discretization adaptive Cartesian grids.”

Together with collaborators from the U.S. Geological Survey’s Cascade Volcanic Observatory, the King Abdullah University of Science and Technology in Saudi Arabia, and University of Bonn in Germany, she is developing a new code she calls “ForestClaw” to provide better real-time ash cloud modeling.

“The model used following the Iceland volcano was not accurate enough,” Calhoun said, noting that many air corridors were closed despite the fact that ash accumulation in those areas was mild or non-existent.

Coarse imaging (top), fine mesh imaging (center) and Calhoun's target (bottom).

Coarse imaging (top), fine mesh imaging (center) and Calhoun’s target (bottom).

That’s because low-resolution simulations essentially “fill in the gaps” for geographic points not included in the algorithm, thus forming a fuzzy model where clear areas may appear as though they are congested with ash.

“This new model will use the same level of computing power, but provide a much higher resolution, allowing us to see open space better.”

ForestClaw will be able to accurately track a thin filament of volcanic ash using adaptive mesh refinement (AMR) to update high-resolution regions of the simulation domain and follow the ash plume as it meanders through the atmosphere. The program won’t waste computational resources in areas of the globe where no ash has arrived.

Using more data grid points to “focus” the numerical prediction of where the ash will move will provide aviation officials with a more accurate picture of ash movement.

“I love the idea of creating software that can make someone’s life easier,” said Calhoun, noting that there are about 60 volcanic eruptions worldwide each year. “This [an adaptive mesh refinement code] is numerically challenging to develop but once it is done, others can put their existing code into an adaptive framework to solve larger challenges. I find that extremely satisfying.”

This work follows in the footsteps of Calhoun’s post-doc advisor, Marsha Berger at NYU, who almost 30 years ago developed the first AMR code, used at that time to accurately track shock waves.

Calhoun came to Boise State after living for several years in France, where she worked for the Atomic Energy Commission on projects dealing with nuclear related hazards.

This material is based upon work supported by the National Science Foundation under Grant No. DMS 1419108 to Boise State University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.