Unraveling shallow-water tsunami waves in reverse

This week, scientists from the University of Alaska Fairbanks are presenting their work alongside thousands of colleagues from around the world at the 2023 American Geophysical Union fall meeting. Some of their discoveries are featured here. You can also find out more about UAF at AGU by searching for #UAFxAGU on social media platforms.

Knowing how a tsunami wave will behave in shallow water is important in determining how far inland water will flow during a tsunami event. Being able to calculate this in real time, after the wave has been generated, is a long-time goal for UAF mathematics and statistics professor Alexei Rybkin.

“Tsunami inundation waves are governed by extremely complicated equations,” Rybkin said, “solving them requires hours of computations, and tsunami waves travel faster than our computers can process.” 

What is needed is a rapid yet accurate method for doing these calculations. Rybkin and his colleague Efim Pelinovsky, with the Institute of Applied Physics in Russia, have been mentoring students tackling the complex mathematics needed to solve this problem.

They are now approaching the problem in reverse. They use measurements from the shoreline from previous tsunami events to mathematically determine the tsunami’s source, water displacement and other wave characteristics. This information can then be used to more accurately estimate how future tsunami waves will behave. 

On Friday, Dec. 15, Oleksandr Bobrovnikov, UAF mathematics graduate student, will present the current phase of the project to tsunami researchers at the American Geophysical Union fall meeting. Fellow UAF graduate student Noah Palmer and students from Northwestern University and the University of San Francisco are co-authors.

“I’ve found it interesting seeing all of these mathematical connections develop, math that hadn’t yet been systematized,” Bobrovnikov said. “I’ve enjoyed the pure mathematics of it, but it’s nice that there are applications for it.”