Hunting the Elusive Rogue Wave

In 1942, the ocean liner Queen Mary was in use as a troop ship, ferrying American soldiers across the Atlantic to fight the war in Europe. During one such week-long voyage in December, while fighting a gale near the British Isles, the hearts of the crew suddenly sank. An enormous wave, measured from the bridge at 92 feet (28 meters) appeared off the ship's beam. The ship took its full force broadside. Her decks awash as she emerged onto the wave's back side, she had rolled a full 52°, making the bulkheads closer to level than the decks. Ballast, men, furniture, and countless tons of fuel oil flooded to the lee, and it was nearly a full minute before the great ship slowly righted herself. It was one of the most dramatic encounters on record between a ship and what we now refer to as a rogue wave. However, if you pick up any book or article on these maritime leviathans, you'll learn that only recently did scientists accept that rogue waves are real, and not just cooked-up old sailors' yarns. The story of rogue waves is presented as a classic evolution of a scientific field; from dismissal, to shaky evidence, to better evidence, to adaptation of the theories and finally to acceptance. Today we're going to find out if this is indeed the way this story should be told.

Rogue waves, it should be noted, are distinct from waves that may be caused by an earthquake, volcano, landslide, or other impact or explosive event. Those would not be rogues; they are expected. Rogue waves are those generated only by the wind, like the majority of ocean waves, except that they break out of the mold of how big waves in their conditions are supposed to get. If they are twice as high (or more) than the biggest waves should be, and if they are separate from those around them, then and only then do we call them rogue waves. It's a high bar to clear, so it shouldn't be surprising that scientists may have been dubious about them until we got that Eureka moment of evidence.

Let us begin with that moment. It came on the afternoon of January 1, 1995 at the Norwegian Draupner natural gas platform. A laser rangefinding wave sensor affixed to the bottom of the platform recorded a single wave with a height of 25.6 meters (84 feet), which was more than twice as high as the normal biggest waves that day. We call it the significant wave height, defined as four times the standard deviation from sea level of the waves, and it's approximately equal to the mean wave height of the biggest one-third of the waves. When any given single wave is more than twice as high as the significant wave height, it meets the definition for what we now term a rogue wave. The Draupner wave, as it has since been dubbed, was the first concrete proof of a rogue wave; and it was from this moment on back that everyone says scientists previously did not accept the concept.

The alleged old-time belief that waves couldn't get very big is found throughout the modern literature. One interesting example is its inclusion in the 2019 book Ball Lightning by physicist Herbert Boerner, which is a subject that for sure has little to no consensus support for its existence — see the full Skeptoid episode #192 on ball lightning for more on that tenuous subject. Boerner wrote:

Another example is rogue waves. For many years mariners have reported huge waves, much larger than normal waves. Since the theory of water waves did not allow for such large waves, scientists simply did not believe these reports. Given the reputation sailors have of telling incredible yarns, they might perhaps be forgiven.

Even the Wikipedia article on rogue waves repeats this same assertion. In the section "History of rogue wave knowledge," it alludes to the 1826 account from the French research vessel Astrolabe which reported a storm in which the waves were "at least 80 to 100 feet" in height, and goes on to state "In that era it was widely held that no wave could exceed 9 metres (30 ft)." As a source for that, Wikipedia gives two books: The Power of the Sea (2012) by Bruce Parker, and Oceanography in the Days of Sail (2008) by Ian and Joyce Jones.

Oceanography in the Days of Sail is Wiki's source for the story of the Astrolabe. In that book, it says:

In an era when opinions were being expressed that no wave would exceed 30 feet, Dumont d'Urville's [the captain of the Astrolabe] estimations were received, it seemed, with some scepticism. No one was more outspoken in his rejection than François Arago...

However the authors gave no citation or reference at all for their assertion that "opinions were being expressed that no wave would exceed 30 feet." Arago has written that sailors' imaginations and tendency to exaggerate tall tales were responsible for fantastic wave reports, but nowhere in any of his publications could I find a mention of a limit of 30 feet. So far as I could find, this assertion is purely a modern ex post facto.

The other source given by Wikipedia, The Power of the Sea, attempts to explain why scientists were dubious of the reports:

That skepticism was primarily due to the scientists' own inability to mathematically determine how such huge waves could exist. And since they could not understand the physics of how such monstrous waves could be created, many decided there must be something wrong with each rogue wave account, no matter how reliable the person reporting.

He's speaking of 20th century events in this section of his book, so we are to assume he's saying 20th century scientists did not have the math to support the existence of rogue waves. Unlike the other authors, Parker does add at least a footnote to his statement, referring to them by their older name freak waves:

A few oceanographers did believe freak waves were real. See: Draper, L., 1964. "Freak Ocean Waves," Oceanus, vol. 10, no. 4, pp. 13-15.

In Draper's article, he gives many example accounts, including the one he considered most reliable, from the US Navy ship Ramapo in 1933 which made a conservative calculation of the height of an observed wave at 112 feet. Draper, an oceanographer at Woods Hole, explained that waves of different speeds could catch up to one another and become monsters:

The life of such a wave is only a transient one, being not much more than a minute or two. Because each wave component is travelling at its own characteristic speed, the faster ones will escape from the others and the monster wave will die just as surely as it was born.

So this was probably not the best citation for Wikipedia to use to support its statement that scientists didn't think waves could exceed 30 feet.

In fact, from my own survey of 20th century oceanographic literature, sound theoretical support for the existence of giant rogue waves was the rule, not the exception. Writing in the Journal of Marine Research in 1952 (12 years before Draper), English mathematician and oceanographer Michael Longuet-Higgins published a comprehensive series of statistical and physics equations describing "the root-mean-square wave-height, the mean height of the highest one-third (or highest one-tenth) waves and the most probable height of the largest wave in a given interval of time," and found that his predictive equations had "close agreement with observation," contradicting Parker's assertion that the physics of rogue waves were not understood. On the subject of the very largest freak waves — though he did not use that term — Longuet-Higgins did find a very small probability for them that seems to be in proportion to the rarity with which we observe them today:

Table II shows that even in a time interval containing 100,000 waves, which for 10-second waves would be about 11 1/2 days, the most probable value of the highest wave is less than 3 1/2 times the root-mean-square value... Equation (73) also shows that there is an extremely small chance that the most probable [maximum wave height] will be greatly exceeded.

We could follow these threads all day, but I'll just summarize by pointing out that each of these articles from a scientific journal includes citations and references, and by following those we can see that any number of other oceanographers and mathematicians were theorizing the presumed existence of enormous rogue waves going all the way back to the 1930s.

So I am going to strike the Skeptoid gavel and state that at least as far as the 20th century is concerned, scientists neither doubted the existence of rogue waves, nor were they unable to account for them mathematically. And so far as I can tell, the notion that scientists thought waves couldn't get bigger than 30 feet is the invention of modern authors seeking to make rogue waves seem even more fantastical and shocking.

Soon after the Draupner wave, three Danish authors published a study of freak waves intended to find the safest height for drilling platforms above sea level. The title of their paper, published in the Journal of Offshore Mechanics and Arctic Engineering, was "Non-Gaussian Extreme Waves in the Central North Sea." What did they mean by "non-Gaussian"? For much of this history we've been covering, most researchers believed that wave heights in a given place over a given period of time, if plotted on a chart, would fall into one of two distributions: Gaussian or Rayleigh. A Gaussian curve is what we typically think of as a bell curve: it's symmetric with a long tail on both ends. Most waves would fall into that meaty thick part of the curve, with progressively fewer very small waves and very large waves, represented by the long tails of the curve. A Rayleigh distribution is different: it starts at zero, jumps up way high very quickly, and curves back down more gradually, fading off into a very long tail that would represent the very small number of the largest waves. Looking at either curve, it's possible to pinpoint the most probable wave height (which is the highest point on the curve), the significant wave height, the means and medians, the tallest third and the 90th percentile, and so on. The Danish authors found that the rogues waves recorded — by now they had some 400 in their database — did not conform to either model. And this is basically where the science remains today. We do not have a perfect theory to account for rogue waves; consequently it is an exciting and active area of research.

What we do have, however, is a lot more data. We have satellites recording wave height and spotting rogue waves every day; there appear to be an average of about ten rogue waves on the world's oceans at any given moment in time. They are more common in some places than others, especially at places where waves converge and their collective energy is focused on a particular spot. They tend to be short-lived, as Draper said way back in 1964. We know lots of other stuff too.

Where you should be skeptical turns out to be the surprising part in this story. The scientists of old were not all as cynical or disbelieving — or as ignorant of statistics and distributions — as some of today's authors would have you believe. They may not have the laser rangefinders or the satellites, but for having little more to work from than old sailors' yarns, I think they did a pretty good job with rogue waves.

Correction: An earlier version of this, in the dramatic opening narrative of the RMS Queen Mary being struck by a rogue wave, I carelessly said that "coal" tumbled to the lee. The Queen Mary's boilers were fired with fuel oil, not coal. —BD

By Brian Dunning
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