A fissure on Kilauea’s East Rift Zone contunued to erupt on July 22, 2018 during the 3-month eruption. The aerial image shows the erupting vent and near-vent part of the channel, which sends lava toward the coast and ocean. / Courtesy of United States Geological Survey

The active Kilauea Volcano on the island of Hawaii erupted nearly continuously from 1983 until April 30, 2018. The 35-year-long eruption ended when the volcano’s Pu’u ‘O’o crater collapsed. Days later, on May 3, the eruption patterns changed when fissures appeared in a flank area of the volcano known as the East Rift Zone. Magma then migrated to this spot, more than 40 kilometers from Kilauea’s summit.

The magma reservoir drained, and the surface of an active lava lake at the volcano’s summit fell by over 1,000 feet. The resulting caldera, or volcanic crater formed as magma withdrew from a major storage reservoir, collapsed. Over the three-month eruption, the caldera continued to expand with a total collapse area of around 5 km2.

By the time the volcanic activity stopped on Aug. 4, over 700 homes had been destroyed and thousands had been evacuated. It was Kilauea’s largest eruption in over 200 years.

Scientists’ understanding of collapsing volcanic calderas had been severely limited by poorly-documented caldera-forming eruptions up until this 2018 outburst. With an extensive monitoring network and direct visual observations, they were able to closely track the events of Kilauea’s caldera collapse.

Outlined in a paper published in Science, researchers, including Mengyang Gu, an assistant professor in UC Santa Barbara’s Department of Statistics and Applied Probability, investigated various volcanic conditions to evaluate how they related to Kilauea’s caldera collapse.

One of the study’s goals was to determine the geometry of the magma reservoir.

As a statistician, Gu helped run computer coding to combine the various types of data that were tracking the small ground changes leading up to the eruption, including Interferometric Synthetic-Aperture Radar (InSAR). The researchers also used GPS to track the directional changes of the ground at various locations.

“We have two data which evaluate the derivative of the ground changes,” Gu explained. “We needed to combine those data and then try to make an inference of quite a few problems, like where the magma chamber is, how large it is, what is the geometric shape of it and how fast the magma outflow [related to] pressure changes [affects the caldera collapse].”

Gu also lent his expertise in constructing the team’s physical model that linked the data to what was occurring underneath the earth’s surface in order to understand the physical process that led to the caldera collapse. In addition to writing code to form a more complete picture of the data, Gu helped analyze the results using Bayesian statistics, which are used to predict the probability of an event.

Even after much analysis, the scientists found that there were still numerous unresolved, confounding issues. For example, in trying to figure out the geometry of the magma chamber, the researchers drew two potential possibilities from the data. The reservoir was either a smaller, shallower one of perhaps 1,000 kilometers in diameter or a deeper, larger chamber that was more than 2,000 kilometers wide.

“We think from the data it is like a large chamber with a small volcano and a little deeper, not a shallow, very small chamber … [But] this type of confounding is well known in mathematical statistics, and we need to use some method to solve it. This is still an open issue.”

The study’s exploration may provide scientists with the insight necessary to extrapolate about Kilauea’s future eruptions.

“People also care about forecasting when it will erupt. It’s a hard question, forecasting, but it also depends on what kind of forecasting. Something like Kilauea — because it keeps erupting — we want to predict how much it will erupt [in terms of] magma and the size,” Gu said.

Forecasting is especially imperative in this active volcano’s case, as it’s a matter of when and not if, according to Gu.

The study concluded that a caldera collapse can occur after only a small fraction of stored magma has receded.

“People feel that [eruptions] may stop, that all the magma has already erupted or more than half of it has. But actually, from our inference, it’s only like 4 to 5 percent of the magma that has erupted. There’s still quite a bit of magma underneath the crater,” Gu stated.

The statistical techniques used to process the data from the 2018 eruption can be applied to other similar studies, Gu mentioned, such as in estimating the location of a magma chamber as well as the critical pressure change rate that precedes a caldera collapse.

“This can be used in not only volcanoes but other things, probably, because many data like InSAR radar imaging is also used for earthquakes quite a lot,” he pointed out.

The sole statistician among a group of volcanologists, Gu said, “I hope there will be more collaborations like this. As a statistician, I need to talk to [other collaborators]. These topics are really useful to me. And then [they need] my knowledge [of] how to combine this data properly, how to address those biases and how to, for example, how to make their model fast, doable … Collaboration makes these things work.”

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