Stories about monster waves, called rogue waves, have been the lore of sailors for centuries. But when a 26-metre-high rogue wave slammed into the Norwegian oil platform Draupner in 1995, digital instruments were there to capture and measure the North Sea monster. It was the first time that a rogue had been measured and provided scientific evidence that abnormal ocean waves really do exist.

Since then, these extreme waves have been the subject of much study. And now, researchers from the University of Copenhagen’s Niels Bohr Institute have used AI methods to discover a mathematical model that provides a recipe for how — and not least when — rogue waves can occur.

With the help of enormous amounts of big data about ocean movements, researchers can predict the likelihood of being struck by a monster wave at sea at any given time.

“Basically, it is just very bad luck when one of these giant waves hits. They are caused by a combination of many factors that, until now, have not been combined into a single risk estimate. In the study, we mapped the causal variables that create rogue waves and used artificial intelligence to gather them in a model which can calculate the probability of rogue wave formation,” says Dion Häfner.

Häfner is a former PhD student at the Niels Bohr Institute and first author of the scientific study, which has just been published in the journal Proceedings of the National Academy of Sciences (PNAS).

Rogue waves happen every day

In their model, the researchers combined available data on ocean movements and the sea state, as well as water depths and bathymetric information. Most importantly, wave data was collected from buoys in 158 different locations around US coasts and overseas territories that collect data 24 hours a day. When combined, this data — from more than a billion waves — contains 700 years’ worth of wave height and sea state information.

The researchers analyzed the many types of data to find the causes of rogue waves, defined as being waves that are at least twice as high as the surrounding waves — including extreme rogue waves that can be over 20 meters high. With machine learning, they transformed it all into an algorithm that was then applied to their dataset.

“Our analysis demonstrates that abnormal waves occur all the time. In fact, we registered 100,000 waves in our dataset that can be defined as rogue waves. This is equivalent around 1 monster wave occurring every day at any random location in the ocean. However, they aren’t all monster waves of extreme size,” explains Johannes Gemmrich, the study’s second author.

Artificial intelligence as a scientist

In the study, the researchers were helped by artificial intelligence. They used several AI methods, including symbolic regression which gives an equation as output, rather than just returning a single prediction as traditional AI methods do.

By examining more than 1 billion waves, the researchers’ algorithm has analyzed its own way into finding the causes of rogue waves and condensed it into equation that describes the recipe for a rogue wave. The AI learns the causality of the problem and communicates that causality to humans in the form of an equation that researchers can analyze and incorporate into their future research.

“Over decades, Tycho Brahe collected astronomical observations from which Kepler, with lots of trial and error, was able to extract Kepler’s Laws. Dion used machines to do with waves what Kepler did with planets. For me, it is still shocking that something like this is possible,” says Markus Jochum.

Phenomenon known since the 1700s

The new study also breaks with the common perception of what causes rogue waves. Until now, it was believed that the most common cause of a rogue wave was when one wave briefly combined with another and stole its energy, causing one big wave to move on.

However, the researchers establish that the most dominant factor in the materialization of these freak waves is what is known as “linear superposition.” The phenomenon, known about since the 1700s, occurs when two wave systems cross over each other and reinforce one another for a brief period of time.

“If two wave systems meet at sea in a way that increases the chance to generate high crests followed by deep troughs, the risk of extremely large waves arises. This is knowledge that has been around for 300 years and which we are now supporting with data,” says Dion Häfner.

Safer shipping

The researchers’ algorithm is good news for the shipping industry, which at any given time has roughly 50,000 cargo ships sailing around the planet. Indeed, with the help of the algorithm, it will be possible to predict when this “perfect” combination of factors is present to elevate the risk of a monster wave that could pose a danger for anyone at sea.

“As shipping companies plan their routes well in advance, they can use our algorithm to get a risk assessment of whether there is a chance of encountering dangerous rogue waves along the way. Based on this, they can choose alternative routes,” says Dion Häfner.

Both the algorithm and research are publicly available, as are the weather and wave data deployed by the researchers. Therefore, Dion Häfner says that interested parties, such as public authorities and weather services, can easily begin calculating the probability of rogue waves. And unlike many other models created using artificial intelligence, all of the intermediate calculations in the researchers’ algorithm are transparent.

“AI and machine learning are typically black boxes that don’t increase human understanding. But in this study, Dion used AI methods to transform an enormous database of wave observations into a new equation for the probability of rogue waves, which can be easily understood by people and related to the laws of physics,” concludes Professor Markus Jochum, Dion’s thesis supervisor and co-author.

A Northwestern University-led team of astrophysicists has just analyzed the first results from the CECILIA (Chemical Evolution Constrained using Ionized Lines in Interstellar Aurorae) Survey, a program that uses NASA’s James Webb Space Telescope (JWST) to study the chemistry of distant galaxies.

According to the early results, so-called “teenage galaxies” — which formed two-to-three billion years after the Big Bang — are unusually hot and contain unexpected elements, like nickel, which are notoriously difficult to observe.

The research will be published on Monday (Nov. 20) in The Astrophysical Journal Letters. It marks the first in a series of forthcoming studies from the CECILIA Survey.

“We’re trying to understand how galaxies grew and changed over the 14 billion years of cosmic history,” said Northwestern’s Allison Strom, who led the study. “Using the JWST, our program targets teenage galaxies when they were going through a messy time of growth spurts and change. Teenagers often have experiences that determine their trajectories into adulthood. For galaxies, it’s the same.”

One of the principal investigators of the CECILIA Survey, Strom is an assistant professor of physics and astronomy at Northwestern’s Weinberg College of Arts and Sciences and a member of Northwestern’s Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA). Strom co-leads the CECILIA Survey with Gwen Rudie, a staff scientist at Carnegie Observatories.

‘Chemical DNA’ gives insight into galaxy formation

Named after Cecilia Payne-Gaposchkin, one of the first women to earn a Ph.D. in astronomy, the CECILIA Survey observes spectra (or the amount of light across different wavelengths) from distant galaxies. Strom likens a galaxy’s spectra to its “chemical DNA.” By examining this DNA during a galaxy’s “teenage” years, researchers can better understand how it grew and how it will evolve into a more mature galaxy.

For example, astrophysicists still don’t understand why some galaxies appear “red and dead” while others, like our Milky Way, are still forming stars. A galaxy’s spectrum can reveal its key elements, such as oxygen and sulfur, which provide a window into what a galaxy was previously doing and what it might do in the future.

“These teenage years are really important because that’s when the most growth happens,” Strom said. “By studying this, we can begin exploring the physics that caused the Milky Way to look like the Milky Way — and why it might look different from its neighboring galaxies.”

In the new study, Strom and her collaborators used the JWST to observe 33 distant teenaged galaxies for a continuous 30 hours this past summer. Then, they combined spectra from 23 of those galaxies to construct a composite picture.

“This washes out the details of individual galaxies but gives us a better sense of an average galaxy. It also allows us to see fainter features,” Strom said. “It’s significantly deeper and more detailed than any spectrum we could collect with ground-based telescopes of galaxies from this time period in the universe’s history.”

Spectra surprises

The ultra-deep spectrum revealed eight distinct elements: Hydrogen, helium, nitrogen, oxygen, silicon, sulfur, argon and nickel. All elements that are heavier than hydrogen and helium form inside stars. So, the presence of certain elements provides information about star formation throughout a galaxy’s evolution.

While Strom expected to see lighter elements, she was particularly surprised by the presence of nickel. Heavier than iron, nickel is rare and incredibly difficult to observe.

“Never in my wildest dreams did I imagine we would see nickel,” Strom said. “Even in nearby galaxies, people don’t observe this. There has to be enough of an element present in a galaxy and the right conditions to observe it. No one ever talks about observing nickel. Elements have to be glowing in gas in order for us to see them. So, in order for us to see nickel, there may be something unique about the stars within the galaxies.”

Another surprise: The teenage galaxies were extremely hot. By examining the spectra, physicists can calculate a galaxy’s temperature. While the hottest pockets with galaxies can reach over 9,700 degrees Celsius (17,492 degrees Fahrenheit), the teenage galaxies clock in at higher than 13,350 degrees Celsius (24,062 degrees Fahrenheit).

“This is just additional evidence of how different galaxies likely were when they were younger,” Strom said. “Ultimately, the fact that we see a higher characteristic temperature is just another manifestation of their different chemical DNA because the temperature and chemistry of gas in galaxies are intrinsically linked.”

The study, “CECILIA: Faint emission line spectrum of z~2-3 star-forming galaxies,” was supported by NASA, the Pittsburgh Foundation and the Research Corporation for Scientific Advancement. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute and from the W.M. Keck Observatory.