Two weeks before Christmas in 1978, the cargo ship MS München encountered a fierce storm in the North Atlantic. Although the captain couldn’t evade it, the forecasted waves and winds should have posed no threat to the 261-meter-long ship. At midnight, just three hours earlier, an operator had radioed out to a cruise ship, “Have a good trip and see you soon.” Now came a distress call from the München — then silence. The West German vessel and its 28-person crew vanished, leaving behind just four lifeboats, three shipping containers, and a handful of flotation devices.

One clue in particular stumped investigators. A recovered lifeboat — originally bolted to the München about 20 meters above the water — appeared to have been ripped from its perch by a tremendous force hurtling toward the ship’s stern. Rumors circulated that a monstrous wave had crashed onto the deck from above, but such a swell was, at the time, unthinkable. West Germany’s Maritime Board of Inquiry eventually declared it “impossible to explain the cause of the sinking.”

Mariners have known for centuries what researchers have documented only in recent decades: The ocean is a far more dangerous place than common sense would suggest. Data-driven researchers long struggled to square sailors’ tales of monstrous “rogue” waves with the expectation that wave heights vary like human heights — clustering around an average with a few outliers dotting the thin tails of a bell curve. Sure, you might get a wave twice as tall as its neighbors in theory, but you’d have to watch the seas for a long time.

That skepticism changed on New Year’s Day in 1995, when a rogue wave struck the Draupner oil installation in the Norwegian North Sea. Equipped with a downward-pointing laser, the platform recorded a 26-meter wave spiking out of a sea filled with 11.8-meter waves — a nautical Bigfoot caught in a high-resolution snapshot. This hard evidence turned maritime myth into fact. Researchers have since determined that rogue waves probably claimed 22 supercarriers and more than 500 lives in the second half of the 20th century alone.

The Draupner wave spurred physicists to understand exactly how these solitary behemoths might arise. Researchers have since come up with two main theories. Each can describe how large waves form in laboratory wave pools. But debate rages as to which matters more in the ocean.

Now, a group of applied mathematicians reports that they’ve found a way to sidestep the fight over the specific mechanism and focus on predicting the outcome — paving the way for machinery that could, for instance, scan the ocean and notify ship captains that they face a 13% chance of running into a 30-meter wave in the next 15 minutes. The work implies that “impossible” waves of all flavors may share a unified fundamental character.

“You could imagine that a rogue wave of 30 meters in the ocean could happen in many different ways,” said Eric Vanden-Eijnden, an applied mathematician at New York University’s Courant Institute of Mathematical Sciences who helped develop the statistical framework. “But the answer is no.”

Wave Addition

In Draupner’s wake, two schools of thought surfaced regarding how monstrous waves could develop.

The first is the simplest. It starts with the observation that swells travel at different speeds. When one overtakes another, the two are combined. If a number of swells happen to overlap at the same place at the same time, a rogue wave results, but the component waves always act completely independently of each other. Francesco Fedele, an ocean engineer at the Georgia Institute of Technology, describes this so-called linear addition mechanism as “fortune playing dice with the ocean.”

Oceanographers have long used this approach to calculate the chance that a wave of a given height will arise, but that forecasting method remains controversial, as it seems to underestimate the likelihood of monsters like Draupner.