Rogue wave

• 1. Introduction

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  A rogue wave was measured by an instrument for the first time at 15:24 UTC on the 1st of January 1995. The place was Unit E of the Draupner platform, a gas-pipeline support complex in the North Sea. It stands about 100 miles southwest of the southern tip of Norway. A laser pointed down at the water recorded a maximum wave height of 25.6 m. The peak rose 18.5 m above still water level. The sea around the platform had a significant wave height of about 12 m, the usual yardstick for how big a sea is. That made the giant more than twice as tall and steep as its neighbors. The other sensors confirmed the reading, and minor damage far above the waterline on the platform backed up the laser. The wave fell outside every known wave model, and it caused enormous interest among scientists. Why had so many experts refused to believe such waves existed? What lets the ocean pile ordinary swell into a single wall of water? And what happens to a ship or a platform that meets one?

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• 2. Defining The Wave

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  Oceanographers set the bar at twice the significant wave height, a figure that is itself the mean height of the largest third of waves in a record. Any wave that clears that bar counts as rogue. The same thing goes by the names freak wave, monster wave and killer wave. These are large, unpredictable surface waves, and they can be extremely dangerous to ships and to isolated structures such as lighthouses.

  A tsunami is a different animal. Tsunamis are long-wavelength waves, caused by a massive displacement of water, often from a sudden movement of the ocean floor such as an earthquake. In deep water they are almost unnoticeable. They turn dangerous only as the seabed rises toward the shore. For that reason tsunamis do not threaten ships at sea, and the only ships lost in the 2004 Asian tsunami were in port.

  The hundred-year wave is another term that is easy to confuse with a rogue wave. It is a purely statistical description of an unusually high wave, one with a 1% chance of occurring in any given year in a particular body of water.

  A rogue wave, by contrast, is a natural ocean phenomenon that is not caused by land movement. It lasts only briefly, appears in a limited location, and most often forms far out at sea. Rare as it is, it can form spontaneously at sizes far beyond what ship designers expect. Ocean-going vessels are not built to handle such encounters. Where one of these waves reaches the shore, it is sometimes called a sneaker wave.

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• 3. Years Of Disbelief

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  In 1826, the French scientist and naval officer Jules Dumont d'Urville reported waves as high as 33 m in the Indian Ocean, with three colleagues as witnesses. A fellow scientist, François Arago, ridiculed him in public. At that time, many people held that no wave could rise higher than 9 m. The author Susan Casey later argued that the disbelief had a grim cause. Until steel double-hulled ships arrived in the 20th century, she wrote, "people who encountered 100 ft rogue waves generally weren't coming back to tell people about it."

  From the 19th century onward, oceanographers, meteorologists, engineers and ship designers predicted wave heights with a statistical tool called the Gaussian function. It is also known as the Gaussian Sea or the standard linear model. It assumes that wave heights cluster tightly around the significant wave height. In a storm sea with a significant wave height of 12 m, it says a wave above 15 m would hardly ever appear. A 30 m wave could occur, but only once in 10,000 years. Everyone acknowledged this was an approximation. Even so, it was the sole basis of virtually every text on the subject for a century.

  Oddities existed at the margins. John Scott Russell studied his wave of translation, a soliton wave, in 1834. Nobody connected it to sailors' stories, because those stories were believed to be scientifically implausible. The first known scientific article on freak waves came from Professor Laurence Draper in 1964. He described efforts by the National Institute of Oceanography in the early 1960s to record wave heights. The highest wave logged at that time was about 67 ft. Draper also described freak wave holes.

  In 1979 at TU Delft, Dik Ludikhuize and Henk Jan Verhagen generated cross-swell waves in a wave basin. Only monochromatic waves, meaning waves of a single frequency, could be produced then. Their 1981 report showed that individual wave heights could add together even beyond the breaker criteria. Where waves crossed, steepness could rise past the usual limits. These waves were far from rogue size, but the work showed how waves from several directions could reach extreme heights. Research published in 2024 by TU Delft and other institutions found that waves coming from multiple directions can grow up to four times steeper than previously imagined.

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• 4. Instruments Settle It

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  The Gorm platform in the central North Sea gave the first scientific hint in 1984. It detected a stand-out wave of 11 m in a relatively low sea state. A study published in 1997 was the first to comprehensively prove that freak waves exist outside the range of Gaussian waves. From about 1997, most leading authors accepted that rogue waves were real, with the caveat that wave models could not replicate them. In 2000, researchers from Statoil presented a paper arguing that freak waves are not rare draws from an ordinary sea. They are typical draws from a rare, strongly non-Gaussian population of waves. In November 2000, leading researchers gathered in Brest for the first Rogue Waves 2000 workshop.

  In February 2000, the British research vessel RRS Discovery was sailing in the Rockall Trough, west of Scotland. A severe gale was blowing, with winds averaging 21 m/s. The ship's instruments logged a significant wave height of 18.5 m and individual waves up to 29.1 m from crest to trough. These were the largest waves ever recorded by scientific instruments in the open ocean up to that time. The authors noted that modern prediction models significantly under-predict extreme seas above 12 m of significant height. The analysis took years. The press reported that "according to all of the theoretical models at the time under this particular set of weather conditions, waves of this size should not have existed".

  In 2004, the European Space Agency's MaxWave project studied three weeks of radar images from a limited area of the South Atlantic. It found ten or more giant waves above 25 m. By 2007, satellite radar studies showed that waves 20 to 30 m from crest to trough occur far more often than anyone had thought. Rogue waves are now known to appear in every ocean, many times each day. Professor Akhmediev of the Australian National University has said that 10 of them exist in the world's oceans at any moment. Some researchers speculate that roughly three of every 10,000 waves reach rogue status. In coastal inlets and river mouths, where wave energy can be focused, the figure may be three in 1,000. In 2002, the Great Lakes Environmental Research Laboratory published work dispelling the long-held view that rogue waves were rare.

  On the 17th of November 2020, a buoy moored in 45 m of water on Amphitrite Bank, 7 km off Ucluelet on Vancouver Island, recorded a lone 17.6 m wave. The waves around it stood about 6 m high. That put the wave at 2.93 times the surrounding significant wave height. When the reading became public in February 2022, one scientific paper and many news outlets called it the most extreme rogue wave event ever recorded. They also called it a "once-in-a-millennium" event, since a wave three times the height of its neighbors was estimated to occur only about once every 1,300 years worldwide.

  A review of papers published since 2005 showed those claims to be incorrect. The paper Oceanic rogue waves, by Dysthe, Krogstad and Muller, describes a Black Sea event in 2004. A Datawell Waverider buoy recorded a wave 3.91 times the significant wave height, in relatively calm weather. Inspection of the buoy afterward showed no malfunction. A paper by I. Nikolkina and I. Didenkulova inferred a 21 m wave off Coos Bay, Oregon, in 2006, when the significant wave height was 3.9 m. That ratio of 5.38 is almost twice the Ucluelet figure. In a 2007 paper, Craig B. Smith reported that the submarine Grouper was hit by a 30-meter wave in calm seas in the North Atlantic.

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• 5. Causes And Experiments

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  Cape Agulhas, off the southern tip of Africa, is among the areas of highest predictable risk. The warm Agulhas Current runs to the southwest, while the dominant winds are westerlies. Waves driven into an opposing current shorten in wavelength, which raises their height and squeezes oncoming wave trains together. This does not explain every wave that has been detected, so researchers think several mechanisms operate, with local variation. Naming the most common cause is, by the field's own account, premature.

  Diffraction focusing is one candidate. The shape of a coast or a seabed steers several small waves so that they meet in phase, and their crests add up. Constructive interference is a close relative. In it, elementary three-dimensional waves focus by dispersion and direction, and nonlinear effects enhance the result.

  The nonlinear explanation is the most dramatic. In the nonlinear Schrödinger equation, a perfectly ordinary wave begins to soak up energy from the waves just ahead of it and behind it. It reduces them to ripples, grows into a near-vertical monster, and collapses soon after. That equation works in deep water. In shallow water, the Korteweg-de Vries and Boussinesq equations take over, and they also have nonlinear parts. A soliton is a self-reinforcing wave. A breather is a wave in which energy concentrates in a localized, oscillating way. The Peregrine soliton is the best-studied example.

  Some studies argue that most waves labeled rogue are not freaks at all. If the only test is twice the significant wave height, such waves are statistically expected about once every 28 hours. This is framed as a question: are freak waves rare realizations of a typical population, or typical realizations of a rare one? Studies of billions of buoy measurements find that linear theory explains ocean rogue wave rates once the finite bandwidth of the wave spectrum is counted. Whether weakly nonlinear dynamics can explain the largest waves, those above three times the significant wave height, is not yet known. That uncertainty has led critics to ask whether defining rogue waves by relative height alone is meaningful. Research published in 2023 suggests that crest-trough correlation, leading to linear superposition, may be a dominant factor in predicting how often they occur.

  Wind alone is unlikely to produce a rogue wave. Strong storm winds blowing against an ocean current might, together with other mechanisms, be enough to generate one at random. In 2005, R. H. Gibbs analyzed rogue waves with a fully nonlinear model. He found that a typical wave group focuses into a wall of water at the cost of reduced height. A rogue wave and its deep trough may last only minutes before breaking or shrinking. Rogue waves can also arrive as a packet of a few, and such groups have been observed in nature.

  A small-scale Peregrine soliton was produced in a laboratory water-wave tank in 2011. A 2012 study reported that this kind of wave can reach about three times the height of the surrounding sea. It also pointed to a hierarchy of higher-order solutions of progressively larger size. In a tank, the researchers created a "super rogue wave", a breather about five times higher than the waves around it. A video known as Lego Pirate has been widely used to show these super rogue waves. The work came from the Australian National University, in collaboration with Hamburg University of Technology and the University of Turin.

  Also in 2012, researchers at the Australian National University proved the existence of rogue wave holes, the inverted profile of a rogue wave, by creating them on the surface of a tank. The depth of a hole can reach more than twice the significant wave height. Maritime folklore holds stories of holes as common as those of waves, yet they had never been shown experimentally. Claims that holes were never seen in nature are not quite right. Kharif and colleagues reveal a recording of one from an oil platform in the North Sea. The same source reveals a recording of the "Three Sisters", three successive large waves.

  A 2015 paper studied wave behavior around a rogue wave and concluded that "rogue events do not necessarily appear without warning but are often preceded by a short phase of relative order". In 2019, researchers produced a wave with the steepness and breaking of the Draupner wave, and proportionately greater height. They used multiple wavetrains meeting at an angle of 120°. Below about 60°, the crest broke sideways and downwards as a plunging breaker. From about 60° upward, it broke vertically upwards in a near-vertical jet, which raised the wave instead of lowering it. Spray from a breaking crest could also confuse an optical instrument such as the Draupner laser, leaving uncertainties of around 1.0 to 1.5 m in the measured height. That same year, a team from the Universities of Oxford and Edinburgh recreated the Draupner wave in a lab.

  Rogue waves are not confined to water. Researchers at UCLA observed them in microstructured optical fibers, near the threshold of soliton supercontinuum generation. Research in optics points to the Peregrine soliton as a possible explanation for waves that appear and vanish without a trace. Similar waves have been reported in liquid helium, microwave cavities, quantum mechanics, Bose-Einstein condensates, heat and diffusion, and even finance.

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• 6. Ships Lost

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  The MS München was a state-of-the-art cargo ship, with multiple watertight compartments and an expert crew. She was lost in 1978 with everyone aboard, and her wreck has never been found. The only physical evidence was her starboard lifeboat, recovered from floating wreckage some time later. Lifeboats hung from forward and aft blocks 20 m above the waterline. The pins had been bent back from forward to aft, showing that a wave had run along the ship and torn the lifeboat away. To exert such force, that wave must have been considerably higher than 20 m. At the time, rogue waves were considered so statistically unlikely as to be near impossible. The Maritime Court investigation therefore concluded only that severe weather had somehow created an "unusual event".

  The Ocean Ranger, a semisubmersible mobile offshore drilling unit, sank in Canadian waters on the 15th of February 1982. Rogue waves have been implicated in her loss. In 2007, the United States' National Oceanic and Atmospheric Administration compiled a catalog of more than 50 historical incidents probably associated with rogue waves.

  The MV Derbyshire was lost in 1980 during Typhoon Orchid, south of Japan, along with all of her crew. Built in 1976, she was an ore-bulk oil combination carrier of 91,655 gross register tons. She remains the largest British ship ever lost at sea. Her wreck was found in June 1994, and a remotely operated vehicle photographed it. A private report published in 1998 prompted the British government to reopen a formal investigation. The Woods Hole Oceanographic Institution took 135,774 pictures of the wreck during two surveys. The formal investigation concluded that the ship sank from structural failure, and it absolved the crew of any responsibility. A third analysis came from Douglas Faulkner, professor of marine architecture and ocean engineering at the University of Glasgow. His 2001 report linked the loss to the emerging science of freak waves, and concluded that a rogue wave almost certainly destroyed the ship.

  Craig B. Smith's 2007 work confirmed Faulkner's earlier forensic findings. He calculated that the Derbyshire faced about 20 m of seawater flowing over her, a static pressure of 201 kPa. The deck cargo hatches were the key point of failure. Their design allowed for less than 2 m of water, or 17.1 kPa, so the typhoon load was more than 10 times what they were built to bear. The forensic structural analysis of the wreck is now widely regarded as irrefutable.

  Fast-moving waves add a second danger. Plunging or breaking waves cause short-lived pressure spikes called Gifle peaks. These can reach 200 kPa or more for milliseconds, enough to fracture mild steel by brittle fracture, and evidence of this was found on the Derbyshire. Smith documented scenarios with hydrodynamic pressure up to 5650 kPa, or over 500 metric tonnes per square meter. In 2004, a shore-mounted transducer at the Alderney Breakwater in the Channel Islands recorded a peak pressure of 745 kPa from an extreme wave. That pressure would have destroyed almost any merchant vessel.

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• 7. Notable Encounters

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  When the Queen Elizabeth 2 met a 29 m wave in the North Atlantic in 1995, it was during Hurricane Luis. The master said the wave "came out of the darkness" and "looked like the White Cliffs of Dover." Newspaper reports at the time described the liner as trying to "surf" the near-vertical wave to avoid sinking. Many such stories reach the public only through the media, and in popular culture any huge wave is loosely called a rogue wave. Scientifically, a rogue wave must differ in character from the surrounding sea and have a very low probability of occurring.

  The Eagle Island lighthouse, in 1861, had the glass of its east tower broken and the tower flooded. That implies a wave that climbed a 40 m cliff and overwhelmed a 26 m tower. At the Flannan Isles Lighthouse in 1900, three keepers vanished after a storm, and wave-damaged equipment was found 34 m above sea level. The Fastnet Lighthouse was struck by a 48 m wave in 1985.

  The liner SS Kronprinz Wilhelm, the most modern German ocean liner of its time and winner of the Blue Riband, was damaged on its maiden voyage from Cherbourg to New York. A huge wave struck the ship head-on on the 18th of September 1901. On the night of the 10th of January 1910, a 75 ft wave hit the RMS Lusitania over the bow. It damaged the forecastle deck and smashed the bridge windows. In 1916, Sir Ernest Shackleton met a wave he called "gigantic" while piloting the lifeboat James Caird from Elephant Island to South Georgia. That year on the 29th of August, three successive waves, the largest estimated at 70 ft, wrecked the armored cruiser USS Memphis in the harbor of Santo Domingo, with 43 men killed or lost.

  The RMS Homeric was hit by an 80 ft wave in a hurricane off the East Coast of the United States in 1924. Seven people were injured, and one lifeboat was carried away. In 1942, a 92 ft wave broadsided the RMS Queen Mary, and she listed about 52° before slowly righting. In 1966, a wave 80 ft above the waterline tore a hole in the superstructure of the SS Michelangelo and killed three people. In 1980, a wave of 25 to 30 m washed across the deck of the French supertanker Esso Languedoc near Durban, South Africa.

  On Lake Superior in November 1975, the SS Edmund Fitzgerald was lost. A Coast Guard report blamed water entering the hatches, or navigation errors that put her onto shoals. Another nearby ship, the SS Arthur M. Anderson, was hit at a similar time by two rogue waves and possibly a third. That appeared to coincide with the sinking, around 10 minutes later. A pattern called the "Three Sisters" is said to occur on that lake. The second wave hits the deck before the first clears, and the third adds to the two accumulated backwashes, suddenly overloading the deck with water. It is one of several theorized causes of the loss.

  In 2004, ocean-floor pressure sensors of the U.S. Naval Research Laboratory detected a freak wave caused by Hurricane Ivan in the Gulf of Mexico. It was around 27.7 m from peak to trough and around 200 m long. Computer models suggested that waves may have exceeded 40 m in the eyewall. In 2005, footage from an episode of Deadliest Catch showed a wave of about 60 ft striking the Aleutian Ballad in the Bering Sea at night. The vessel tipped briefly onto its side. In 2006, researchers from the U.S. Naval Institute theorized that rogue waves may explain the unexplained loss of low-flying aircraft, such as Coast Guard helicopters on search-and-rescue missions.

  In March 2010, the MS Louis Majesty was crossing the Gulf of Lion on a cruise between Cartagena and Marseille. Three successive waves of 8 m struck without warning, and the second and third shattered a lounge window. Flying glass killed two passengers. On the 28th of December 2011, the Sea Shepherd vessel MV Brigitte Bardot was damaged by an 11 m wave off the western coast of Australia. It had been pursuing the Japanese whaling fleet. Its main hull cracked, and its port pontoon was held together by straps. The MV Steve Irwin escorted it to Fremantle. In 2019, the extratropical remnant of Hurricane Dorian generated a 100 ft wave off the coast of Newfoundland. In 2022, the cruise ship Viking Polaris was hit on its way to Ushuaia, Argentina. One person died and four were injured, and the scheduled route to Antarctica was canceled.

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• 8. Designing For Giants

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  In November 1997, the International Maritime Organization adopted new rules on survivability and structural strength for bulk carriers of 150 m and upwards. Their bulkhead and double bottom must be strong enough for the ship to survive flooding in hold one, unless loading is restricted.

  The numbers explain why rogue waves worry designers. A 12 m wave in the usual linear model has a breaking force of 6 MT per square meter. Modern ships are typically designed to tolerate a breaking wave of 15 t per square meter. A rogue wave can dwarf both figures, with a breaking force far exceeding 100 t per square meter. Craig B. Smith presented calculations on this using the Common Structural Rules of the International Association of Classification Societies, applied to a typical bulk carrier.

  In 2006, Smith proposed changing IACS recommendation 34, on standard wave data, so that the minimum design wave height rose to 65 ft. He argued there was enough evidence that 66 ft waves can be met in the 25-year lifetime of an ocean-going vessel. Waves of 98 ft are less likely but not out of the question. A design criterion based on 36 ft waves therefore seemed inadequate. He also proposed including the dynamic force of wave impacts in structural analysis.

  The Norwegian offshore standards now consider extreme severe wave conditions, and they require that a 10,000-year wave not endanger the ship's integrity. W. Rosenthal noted that as of 2005, rogue waves were not explicitly accounted for in classification society rules. DNV GL's Structure Design Load Principles remained largely based on significant wave height, and as of January 2016 they still made no allowance for rogue waves.

  The U.S. Navy historically took the position that the largest wave likely to be met was 21.4 m. Smith observed in 2007 that the Navy now believes larger waves can occur, including steeper ones that do not have longer wavelengths. The Navy has not needed fundamental design changes, because its ships are built to higher standards than required. Worldwide, more than 50 classification societies exist, each with its own rules. Most new ships follow the standards of the 12 members of the IACS. In 2006 it implemented two sets of common structural rules, one for oil tankers and one for bulk carriers, later harmonised into one.

  Peter Challenor of the National Oceanography Centre in the United Kingdom was quoted in Casey's 2010 book. "We don't have that random messy theory for nonlinear waves. At all," he said. He added, "People have been working actively on this for the past 50 years at least. We don't even have the start of a theory."

  Prediction offers one practical hope. Two MIT researchers, partially supported by the Naval Engineering Education Consortium, developed a tool for short-term prediction of rare, extreme water waves. It looks ahead about 25 wave periods. That gives ships and their crews a two- to three-minute warning of a potentially catastrophic impact, enough time to shut down essential operations on a ship or offshore platform. The authors cite landing an aircraft on a carrier as a prime example of such an operation.

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