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Rogue waves (also known as freak waves or killer waves) are large and unpredictable that can be extremely dangerous to ships and isolated structures such as lighthouses. They are distinct from , which are long wavelength waves, often almost unnoticeable in deep waters and are caused by the displacement of water due to other phenomena (such as ). A rogue wave at the shore is sometimes called a sneaker wave.
In oceanography, rogue waves are more precisely defined as waves whose wave height is more than twice the significant wave height ( H or SWH), which is itself defined as the mean of the largest third of waves in a wave record. Rogue waves do not appear to have a single distinct cause but occur where physical factors such as high winds and strong currents cause waves to merge to create a single large wave. Research published in 2023 suggests sea state crest-trough correlation leading to linear superposition may be a dominant factor in predicting the frequency of rogue waves.
Among other causes, studies of nonlinear waves such as the Peregrine soliton, and waves modeled by the nonlinear Schrödinger equation (NLS), suggest that modulational instability can create an unusual sea state where a "normal" wave begins to draw energy from other nearby waves, and briefly becomes very large. Such phenomena are not limited to water and are also studied in liquid helium, nonlinear optics, and microwave cavities. A 2012 study reported that in addition to the Peregrine soliton reaching up to about three times the height of the surrounding sea, a hierarchy of higher order wave solutions could also exist having progressively larger sizes and demonstrated the creation of a "super rogue wave" (a breather around five times higher than surrounding waves) in a Wave tank.
A 2012 study supported the existence of oceanic rogue holes, the inverse of rogue waves, where the depth of the hole can reach more than twice the significant wave height. Although it is often claimed that rogue holes have never been observed in nature despite replication in wave tank experiments, there is a rogue hole recording from an oil platform in the North Sea, revealed in Kharif et al. The same source also reveals a recording of what is known as the 'Three Sisters'.
Once considered mythical and lacking hard evidence, rogue waves are now proven to exist and are known to be natural ocean phenomena. Eyewitness accounts from mariners and damage inflicted on ships have long suggested they occur. Still, the first scientific evidence of their existence came with the recording of a rogue wave by the Gorm Field in the central North Sea in 1984. A stand-out wave was detected with a wave height of in a relatively low sea state. However, what caught the attention of the scientific community was the digital measurement of a rogue wave at the Draupner platform in the North Sea on January 1, 1995; called the "Draupner wave", it had a recorded maximum wave height of and peak elevation of . During that event, minor damage was inflicted on the platform far above sea level, confirming the accuracy of the wave-height reading made by a downwards pointing laser sensor.
The existence of rogue waves has since been confirmed by video and photographs, satellite imagery, radar of the ocean surface, stereo wave imaging systems, pressure transducers on the sea-floor, and oceanographic research vessels. In February 2000, a British oceanographic research vessel, the RRS Discovery, sailing in the Rockall Trough west of Scotland, encountered the largest waves ever recorded by any scientific instruments in the open ocean, with an SWH of and individual waves up to . In 2004, scientists using three weeks of radar images from European Space Agency satellites found ten rogue waves, each or higher.
A rogue wave is a natural ocean phenomenon that is not caused by land movement, only lasts briefly, occurs in a limited location, and most often happens far out at sea. Rogue waves are considered rare, but potentially very dangerous, since they can involve the spontaneous formation of massive waves far beyond the usual expectations of , and can overwhelm the usual capabilities of ocean-going vessels which are not designed for such encounters. Rogue waves are, therefore, distinct from . Tsunamis are caused by a massive displacement of water, often resulting from earthquake of the ocean floor, after which they propagate at high speed over a wide area. They are nearly unnoticeable in deep water and only become dangerous as they approach the shoreline and the ocean floor becomes shallower; therefore, tsunamis do not present a threat to shipping at sea (e.g., the only ships lost in the 2004 Asian tsunami were in port.). These are also different from the wave known as a "hundred-year wave", which is a purely statistics description of a particularly high wave with a 1% chance to occur in any given year in a particular body of water.
Rogue waves have now been proven to cause the sudden loss of some ocean-going vessels. Well-documented instances include the freighter MS München, lost in 1978. Rogue waves have been implicated in the loss of other vessels, including the Ocean Ranger, a semisubmersible mobile oil platform that sank in Canadian waters on 15 February 1982.Royal Commission on the Ocean Ranger Marine Disaster (Canada) (1985). 9780660118277, The Commission. . ISBN 9780660118277 In 2007, the United States' National Oceanic and Atmospheric Administration (NOAA) compiled a catalogue of more than 50 historical incidents probably associated with rogue waves.
Since the 19th century, oceanographers, meteorologists, engineers, and ship designers have used a statistical model known as the Gaussian function (or Gaussian Sea or standard linear model) to predict wave height, on the assumption that wave heights in any given sea are tightly grouped around a central value equal to the average of the largest third, known as the significant wave height (SWH). In a storm sea with an SWH of , the model suggests hardly ever would a wave higher than occur. It suggests one of could indeed happen, but only once in 10,000 years. This basic assumption was well accepted, though acknowledged to be an approximation. Using a Gaussian form to model waves has been the sole basis of virtually every text on that topic for the past 100 years.
The first known scientific article on "freak waves" was written by Professor Laurence Draper in 1964. In that paper, he documented the efforts of the National Institute of Oceanography in the early 1960s to record wave height, and the highest wave recorded at that time, which was about . Draper also described freak wave holes.
This work highlighted that in cases of crossing waves, wave steepness could increase beyond usual limits. Although the waves studied were not as extreme as rogue waves, the research provided an understanding of how multidirectional wave interactions could lead to extreme wave heights - a key concept in the formation of rogue waves. The crossing wave phenomenon studied in the Delft Laboratory therefore had direct relevance to the unpredictable rogue waves encountered at sea.
Research published in 2024 by TU Delft and other institutions has subsequently demonstrated that waves coming from multiple directions can grow up to four times steeper than previously imagined.
At 15:24 UTC on 1 January 1995, the device recorded a rogue wave with a maximum wave height of . Peak elevation above still water level was . The reading was confirmed by the other sensors. In the area, the SWH at the time was about , so the Draupner wave was more than twice as tall and steep as its neighbors, with characteristics that fell outside any known wave model. The wave caused enormous interest in the scientific community.
The first scientific study to comprehensively prove that freak waves exist, which are clearly outside the range of Gaussian waves, was published in 1997. Some research confirms that observed wave height distribution, in general, follows well the Rayleigh distribution. Still, in shallow waters during high energy events, extremely high waves are rarer than this particular model predicts. From about 1997, most leading authors acknowledged the existence of rogue waves with the caveat that wave models could not replicate rogue waves.
Statoil researchers presented a paper in 2000, collating evidence that freak waves were not the rare realizations of a typical or slightly non-gaussian sea surface population ( classical extreme waves) but were the typical realizations of a rare and strongly non-gaussian sea surface population of waves ( freak extreme waves). A workshop of leading researchers in the world attended the first Rogue Waves 2000 workshop held in Brest in November 2000.
In 2000, British oceanographic vessel RRS Discovery recorded a wave off the coast of Scotland near Rockall. This was a scientific research vessel fitted with high-quality instruments. Subsequent analysis determined that under severe gale-force conditions with wind speeds averaging , a ship-borne wave recorder measured individual waves up to from crest to trough, and a maximum SWH of . These were some of the largest waves recorded by scientific instruments up to that time. The authors noted that modern wave prediction models are known to significantly under-predict extreme sea states for waves with a significant height (Hs) above . The analysis of this event took a number of years and noted that "none of the state-of-the-art weather forecasts and wave modelsthe information upon which all ships, oil rigs, fisheries, and passenger boats relyhad predicted these behemoths." In simple terms, a scientific model (and also ship design method) to describe the waves encountered did not exist. This finding was widely reported in the press, which 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 ESA MaxWave project identified more than 10 individual giant waves above in height during a short survey period of three weeks in a limited area of the South Atlantic. By 2007, it was further proven via satellite radar studies that waves with crest-to-trough heights of occur far more frequently than previously thought. Rogue waves are now known to occur in all of the world's oceans many times each day.
Rogue waves are now accepted as a common phenomenon. Professor Akhmediev of the Australian National University has stated that 10 rogue waves exist in the world's oceans at any moment. Some researchers have speculated that roughly three of every 10,000 waves on the oceans achieve rogue status, yet in certain spotssuch as coastal inlets and river mouthsthese extreme waves can make up three of every 1,000 waves, because wave energy can be focused.
Rogue waves may also occur in . A phenomenon known as the "Three Sisters" is said to occur in Lake Superior when a series of three large waves forms. The second wave hits the ship's deck before the first wave clears. The third incoming wave adds to the two accumulated backwashes and suddenly overloads the ship deck with large amounts of water. The phenomenon is one of various theorized causes of the sinking of the on Lake Superior in November 1975.Wolff, Julius F. (1979). "Lake Superior Shipwrecks", p. 28. Lake Superior Marine Museum Association, Inc., Duluth, Minnesota. .
A 2012 study reported that in addition to the Peregrine soliton reaching up to about 3 times the height of the surrounding sea, a hierarchy of higher order wave solutions could also exist having progressively larger sizes, and demonstrated the creation of a "super rogue a breather around 5 times higher than surrounding wavesin a water tank. Also in 2012, researchers at the Australian National University proved the existence of "rogue wave holes", an inverted profile of a rogue wave. Their research created rogue wave holes on the water surface in a water-wave tank. In maritime folklore, stories of rogue holes are as common as stories of rogue waves. They had followed from theoretical analysis but had never been proven experimentally.
"Rogue wave" has become a near-universal term used by scientists to describe isolated, large-amplitude waves that occur more frequently than expected for normal, Gaussian-distributed, statistical events. Rogue waves appear ubiquitous and are not limited to the oceans. They appear in other contexts and have recently been reported in liquid helium, nonlinear optics, and microwave cavities. Marine researchers universally now accept that these waves belong to a specific kind of sea wave, not considered by conventional models for sea wind waves. A 2015 paper studied the wave behavior around a rogue wave, including optical and the Draupner wave, and concluded, "rogue events do not necessarily appear without warning but are often preceded by a short phase of relative order". Predictability of Rogue Events, Simon Birkholz, Carsten Brée, Ayhan Demircan, and Günter Steinmeyer, Physical Review Letters 114, 213901, 28 May 2015
In 2019, researchers succeeded in producing a wave with similar characteristics to the Draupner wave (steepness and breaking), and proportionately greater height, using multiple Wave packet meeting at an angle of 120°. Previous research had strongly suggested that the wave resulted from an interaction between waves from different directions ("crossing seas"). Their research also highlighted that wave-breaking behavior was not necessarily as expected. If waves met at an angle less than about 60°, then the top of the wave "broke" sideways and downwards (a "plunging breaker"). Still, from about 60° and greater, the wave began to break vertically upwards, creating a peak that did not reduce the wave height as usual but instead increased it (a "vertical jet"). They also showed that the steepness of rogue waves could be reproduced in this manner. Lastly, they observed that optical instruments such as the laser used for the Draupner wave might be somewhat confused by the spray at the top of the wave if it broke, and this could lead to uncertainties of around in the wave height. They concluded, "... the onset and type of wave breaking play a significant role and differ significantly for crossing and noncrossing waves. Crucially, breaking becomes less crest-amplitude limiting for sufficiently large crossing angles and involves the formation of near-vertical jets". Laboratory recreation of the Draupner wave and the role of breaking in crossing seas – McAllister et al – Journal of Fluid Mechanics, 2019, vol. 860, pp. 767–786, pub. Cambridge University Press,
[[File:Rogue waves breaking behavior at different crossing angles, McAllister 2019.png|thumb|600px|centre|Images from the 2019 simulation of the Draupner wave show how the steepness of the wave forms, and how the crest of a rogue wave breaks when waves cross at different angles. (Click image for full resolution)
The Ucluelet event generated controversy. Analysis of scientific papers dealing with rogue wave events since 2005 revealed the claims for the record-setting nature and rarity of the wave to be incorrect. The paper Oceanic rogue waves by Dysthe, Krogstad and Muller reports on an event in the Black Sea in 2004 which was far more extreme than the Ucluelet wave, where the Datawell Waverider buoy reported a wave whose height was higher and 3.91 times the significant wave height, as detailed in the paper. Thorough inspection of the buoy after the recording revealed no malfunction. The authors of the paper that reported the Black Sea event assessed the wave as "anomalous" and suggested several theories on how such an extreme wave may have arisen. The Black Sea event differs in the fact that it, unlike the Ucluelet wave, was recorded with a high-precision instrument. The Oceanic rogue waves paper also reports even more extreme waves from a different source, but these were possibly overestimated, as assessed by the data's own authors. The Black Sea wave occurred in relatively calm weather.
Furthermore, a paper by I. Nikolkina and I. Didenkulova also reveals waves more extreme than the Ucluelet wave. In the paper, they infer that in 2006 a wave appeared in the Pacific Ocean off the Port of Coos Bay, Oregon, with a significant wave height of . The ratio is 5.38, almost twice that of the Ucluelet wave. The paper also reveals the incident as marginally more extreme than the Ucluelet event. The paper also assesses a report of an wave in a significant wave height of , but the authors cast doubt on that claim. A paper written by Craig B. Smith in 2007 reported on an incident in the North Atlantic, in which the submarine Grouper was hit by a 30-meter wave in calm seas.
The spatiotemporal focusing seen in the NLS equation can also occur when the non-linearity is removed. In this case, focusing is primarily due to different waves coming into phase rather than any energy-transfer processes. Further analysis of rogue waves using a fully nonlinear model by R. H. Gibbs (2005) brings this mode into question, as it is shown that a typical wave group focuses in such a way as to produce a significant wall of water at the cost of a reduced height.
A rogue wave, and the deep trough commonly seen before and after it, may last only for some minutes before either breaking or reducing in size again. Apart from a single one, the rogue wave may be part of a wave packet consisting of a few rogue waves. Such rogue have been observed in nature. Frederic-Moreau. The Glorious Three, translated by M. Olagnon and G.A. Chase / Rogue Waves-2004, Brest, France
Rogue waves in other media appear to be ubiquitous and have also been reported in liquid helium, in quantum mechanics, in nonlinear optics, in microwave cavities, in Bose–Einstein condensate, in heat and diffusion, and in finance.
This section lists a limited selection of notable incidents.
In 1980, the MV Derbyshire was lost during Typhoon Orchid south of Japan, along with all of her crew. The Derbyshire was an ore-bulk oil combination carrier built in 1976. At 91,655 gross register tons, she remains the largest British ship ever lost at sea. The wreck was found in June 1994. The survey team deployed a remotely operated vehicle to photograph the wreck. A private report published in 1998 prompted the British government to reopen a formal investigation into the sinking. The investigation included a comprehensive survey by the Woods Hole Oceanographic Institution, which took 135,774 pictures of the wreck during two surveys. The formal forensic investigation concluded that the ship sank because of structural failure and absolved the crew of any responsibility. Most notably, the report determined the detailed sequence of events that led to the structural failure of the vessel. A third comprehensive analysis was subsequently done by Douglas Faulkner, professor of marine architecture and ocean engineering at the University of Glasgow. His 2001 report linked the loss of the Derbyshire with the emerging science on freak waves, concluding that the Derbyshire was almost certainly destroyed by a rogue wave.
Work by sailor and author Craig B. Smith in 2007 confirmed prior forensic work by Faulkner in 1998 and determined that the Derbyshire was exposed to a hydrostatic pressure of a "static head" of water of about with a resultant static pressure of . This is in effect of seawater (possibly a super rogue wave) flowing over the vessel. The deck cargo hatches on the Derbyshire were determined to be the key point of failure when the rogue wave washed over the ship. The design of the hatches only allowed for a static pressure less than of water or , meaning that the typhoon load on the hatches was more than 10 times the design load. The forensic structural analysis of the wreck of the Derbyshire is now widely regarded as irrefutable.
In addition, fast-moving waves are now known to also exert extremely high dynamic pressure. Plunging or breaking waves are known to cause short-lived impulse pressure spikes called Gifle peaks. These can reach pressures of (or more) for milliseconds, which is sufficient pressure to lead to brittle fracture of mild steel. Evidence of failure by this mechanism was also found on the Derbyshire. Smith documented scenarios where hydrodynamic pressure up to or over 500 metric tonnes/m2 could occur.
In 2004, an extreme wave was recorded impacting the Alderney Breakwater, Alderney, in the Channel Islands. This breakwater is exposed to the Atlantic Ocean. The peak pressure recorded by a shore-mounted transducer was . This pressure far exceeds almost any design criteria for modern ships, and this wave would have destroyed almost any merchant vessel.
Rogue waves present considerable danger for several reasons: they are rare, unpredictable, may appear suddenly or without warning, and can impact with tremendous force. A wave in the usual "linear" model would have a breaking force of . Although modern ships are typically designed to tolerate a breaking wave of 15 t/m2, a rogue wave can dwarf both of these figures with a breaking force far exceeding 100 t/m2. Smith presented calculations using the International Association of Classification Societies (IACS) Common Structural Rules for a typical bulk carrier.
Peter Challenor, a scientist from the National Oceanography Centre in the United Kingdom, was quoted in Susan Casey's book in 2010 as saying: "We don't have that random messy theory for nonlinear waves. At all." 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."
In 2006, Smith proposed that the IACS recommendation 34 pertaining to standard wave data be modified so that the minimum design wave height be increased to . He presented analysis that sufficient evidence exists to conclude that high waves can be experienced in the 25-year lifetime of oceangoing vessels, and that high waves are less likely, but not out of the question. Therefore, a design criterion based on high waves seems inadequate when the risk of losing crew and cargo is considered. Smith also proposed that the dynamic force of wave impacts should be included in the structural analysis.
The Norwegian offshore standards now consider extreme severe wave conditions and require that a 10,000-year wave does not endanger the ships' integrity. W. Rosenthal noted that as of 2005, rogue waves were not explicitly accounted for in Classification Society's rules for ships' design. As an example, DNV GL, one of the world's largest international certification bodies and classification society with main expertise in technical assessment, advisory, and risk management publishes their Structure Design Load Principles which remain largely based on the Significant Wave Height, and as of January 2016, still have not included any allowance for rogue waves.
The U.S. Navy historically took the design position that the largest wave likely to be encountered was . Smith observed in 2007 that the navy now believes that larger waves can occur and the possibility of extreme waves that are steeper (i.e. do not have longer wavelengths) is now recognized. The navy has not had to make any fundamental changes in ship design due to new knowledge of waves greater than 21.4 m because the ships are built to higher standards than required.
The more than 50 classification societies worldwide each has different rules. However, most new ships are built to the standards of the 12 members of the International Association of Classification Societies, which implemented two sets of common structural rules - one for oil tankers and one for bulk carriers, in 2006. These were later harmonised into a single set of rules.
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Extreme rogue wave events
On 17 November 2020, a buoy moored in of water on Amphitrite Bank in the Pacific Ocean off Ucluelet, Vancouver Island, British Columbia, Canada, at recorded a lone tall wave among surrounding waves about in height. The wave exceeded the surrounding significant wave heights by a factor of 2.93. When the wave's detection was revealed to the public in February 2022, one scientific paper and many news outlets christened the event as "the most extreme rogue wave event ever recorded" and a "once-in-a-millennium" event, claiming that at about three times the height of the waves around it, the Ucluelet wave set a record as the most extreme rogue wave ever recorded at the time in terms of its height in proportion to surrounding waves, and that a wave three times the height of those around it was estimated to occur on average only once every 1,300 years worldwide.
Causes
Because the phenomenon of rogue waves is still a matter of active research, clearly stating what the most common causes are or whether they vary from place to place is premature. The areas of highest predictable risk appear to be where a strong ocean current runs counter to the primary direction of travel of the waves; the area near Cape Agulhas off the southern tip of Africa is one such area. The warm Agulhas Current runs to the southwest, while the dominant winds are westerlies, but since this thesis does not explain the existence of all waves that have been detected, several different mechanisms are likely, with localized variation. Suggested mechanisms for freak waves include:
Research efforts
A number of research programmes are currently underway or have concluded whose focus is/was on rogue waves, including:
Other media
Researchers at UCLA observed rogue-wave phenomena in microstructured near the threshold of soliton supercontinuum generation and characterized the initial conditions for generating rogue waves in any medium. Research in optics has pointed out the role played by a Peregrine soliton that may explain those waves that appear and disappear without leaving a trace.
Reported encounters
Many of these encounters are reported only in the media, and are not examples of open-ocean rogue waves. Often, in popular culture, an endangering huge wave is loosely denoted as a "rogue wave", while the case has not been established that the reported event is a rogue wave in the scientific sense – i.e. of a very different nature in characteristics as the surrounding waves in that sea state] and with a very low probability of occurrence.
19th century
20th century
(2025). 9780711033665, Ian Allan Publishing. ISBN 9780711033665
21st century
Quantifying the impact of rogue waves on ships
The loss of the in 1978 provided some of the first physical evidence of the existence of rogue waves. München was a state-of-the-art cargo ship with multiple water-tight compartments and an expert crew. She was lost with all crew, and the wreck has never been found. The only evidence found was the starboard lifeboat recovered from floating wreckage sometime later. The lifeboats hung from forward and aft blocks above the waterline. The pins had been bent back from forward to aft, indicating the lifeboat hanging below it had been struck by a wave that had run from fore to aft of the ship and had torn the lifeboat from the ship. To exert such force, the wave must have been considerably higher than . At the time of the inquiry, the existence of rogue waves was considered so statistically unlikely as to be near impossible. Consequently, the Maritime Court investigation concluded that the severe weather had somehow created an "unusual event" that had led to the sinking of the München.
Design standards
In November 1997, the International Maritime Organization (IMO) adopted new rules covering survivability and structural requirements for bulk carriers of and upwards. The bulkhead and double bottom must be strong enough to allow the ship to survive flooding in hold one unless loading is restricted.
See also
Notes
Further reading
External links
Extreme seas project
MaxWave report and WaveAtlas
Other
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