Surface temperatures
in the western North Atlantic: Most of the North American landmass is
black and dark blue (cold), while the Gulf Stream is red (warm). Source:
NASA
The Gulf Stream is a warm and swift Atlanticocean current that originates in the Gulf of Mexico and flows through the Straits of Florida
and up the eastern coastline of the United States, then veers east near
36°N latitude (North Carolina) and moves toward Northwest Europe as
the North Atlantic Current. The process of western intensification causes the Gulf Stream to be a northward-accelerating current off the east coast of North America. Around 40°0′N30°0′W,
it splits in two, with the northern stream, the North Atlantic Drift,
crossing to Northern Europe and the southern stream, the Canary Current, recirculating off West Africa.
The Gulf Stream influences the climate of the coastal areas of
the East Coast of the United States from Florida to southeast Virginia
(near 36°N latitude), and to a greater degree, the climate of Northwest
Europe. A consensus exists that the climate of Northwest Europe is
warmer than other areas of similar latitude at least partially because
of the strong North Atlantic Current. It is part of the North Atlantic Gyre. Its presence has led to the development of strong cyclones of all types, both within the atmosphere and within the ocean.
History
Benjamin Franklin's chart of the Gulf Stream printed in London in 1769
European discovery of the Gulf Stream dates to the 1512 expedition of Juan Ponce de León, after which it became widely used by Spanish ships sailing from the Caribbean to Spain.
A summary of Ponce de León's voyage log on April 22, 1513, noted, "A
current such that, although they had great wind, they could not proceed
forwards, but backwards and it seems that they were proceeding well; at
the end, it was known that the current was more powerful than the wind."
Benjamin Franklin became interested in the North Atlantic Ocean circulation patterns. In 1768, while in England, Franklin heard a curious complaint from the Colonial Board of Customs:
"Why did it take British packets several weeks longer to reach New York
from England than it took an average American merchant ship to reach Newport, Rhode Island, despite the merchant ships leaving from London and having to sail down the River Thames and then the length of the English Channel before they sailed across the Atlantic, while the packets left from Falmouth in Cornwall?"
Franklin asked his cousin Timothy Folger, a Nantucket Island
whaling captain, for an answer. Folger explained that merchant ships
routinely crossed the current—which was identified by whale behaviour,
measurement of the water's temperature, and changes in the water's
colour—while the mail packet captains ran against it.
Franklin had Folger sketch the path of the current on a chart of the
Atlantic and add notes on how to avoid the current when sailing from
England to America. Franklin then forwarded the chart to Anthony Todd,
secretary of the British Post Office. Franklin's Gulf Stream chart was printed in 1769 in London, but it was mostly ignored by British sea captains.
A copy of the chart was printed in Paris circa 1770–1773, and a third
version was published by Franklin in Philadelphia in 1786.
Properties
The Gulf Stream proper is a western-intensified current, driven largely by wind stress. In 1958, oceanographer Henry Stommel noted, "very little water from the Gulf of Mexico is actually in the stream". The North Atlantic Current, in contrast, is largely driven by thermohaline circulation.
Its carrying warm water northeast across the Atlantic makes Western
Europe and especially Northern Europe warmer and milder than it
otherwise would be.
Formation and behaviour
Evolution of the Gulf Stream to the west of Ireland continuing as the North Atlantic Current
A river of sea water, called the Atlantic North Equatorial Current,
flows westwards off the coast of Central Africa. When this current
interacts with the northeastern coast of South America, the current
forks into two branches. One passes into the Caribbean Sea, while a second, the Antilles Current, flows north and east of the West Indies. These two branches rejoin north of the Straits of Florida.
The trade winds blow westwards in the tropics, and the westerlies blow eastwards at mid-latitudes. This wind pattern applies a stress to the subtropical ocean surface with negative curl across the north Atlantic Ocean. The resulting Sverdrup transport is equatorward.
Because of the conservation of potential vorticity caused by the northward-moving winds on the subtropical ridge's
western periphery and the increased relative vorticity of
northward-moving water, transport is balanced by a narrow, accelerating
poleward current. This flows along the western boundary of the ocean
basin, outweighing the effects of friction with the western boundary
current, and is known as the Labrador Current.
The conservation of potential vorticity also causes bends along the
Gulf Stream, which occasionally break off as the Gulf Stream's position
shifts, forming separate warm and cold eddies.
This overall process, known as western intensification, causes
currents on the western boundary of an ocean basin, such as the Gulf
Stream, to be stronger than those on the eastern boundary.
As a consequence, the resulting Gulf Stream is a strong ocean
current. It transports water at a rate of 30 million cubic metres per
second (30 sverdrups) through the Florida Straits. As it passes south of Newfoundland, this rate increases to 150 sverdrups.
The volume of the Gulf Stream dwarfs all rivers that empty into the
Atlantic combined, which total 0.6 sverdrups. It is weaker, however,
than the Antarctic Circumpolar Current.
Given the strength and proximity of the Gulf Stream, beaches along the
East Coast of the United States may be more vulnerable to large
sea-level anomalies, which significantly impact rates of coastal erosion.
The Gulf Stream is typically 100 km (62 mi) wide and 800 to
1,200 m (2,600 to 3,900 ft) deep. The current velocity is fastest near
the surface, with the maximum speed typically about 2.5 m/s (5.6 mph).
As it travels north, the warm water transported by the Gulf Stream
undergoes evaporative cooling. The cooling is wind-driven; wind moving
over the water causes evaporation, cooling the water and increasing its salinity and density. When sea ice forms, salts are left out of the ice, a process known as brine exclusion.
These two processes produce water that is denser and colder (or more
precisely, water that is still liquid at a lower temperature). In the
North Atlantic Ocean, the water becomes so dense that it begins to sink
down through less salty and less dense water. (The convective action is similar to a lava lamp.) This downdraft of cold, dense water becomes a part of the North Atlantic Deep Water, a southgoing stream. Very little seaweed lies within the current, although seaweed lies in clusters to its east.
In April 2018, two studies published in the British scientific journal Nature found the Gulf Stream to be at its weakest for at least 1,600 years.
Localized effects
The Gulf Stream is influential on the climate of the Florida peninsula. The portion off the Florida coast, referred to as the Florida Current,
maintains an average water temperature of at least 24 °C (75 °F) during
the winter, and often 29 °C (84 °F) in summer and fall. East winds moving over this warm water move warm air from over the Gulf Stream inland, helping to keep temperatures milder across the state than elsewhere across the Southeastern United States during the winter.
The Gulf Stream carries a wide variety of tropical fish and organisms northward along the East Coast from Florida to extreme southeast Massachusetts
in spring and summer. Following the warm waters of the Gulf Stream,
tropical fish are often encountered off the East Coast as they search
for food, including several species of Batoidea, Dolphin, Barracuda, and Triggerfish. The Gulf Stream's proximity to Nantucket, Massachusetts, adds to its biodiversity,
because it is the northern limit for southern varieties of plant life,
and the southern limit for northern plant species, Nantucket being
warmer during winter than the mainland in winter just 30 miles to the north. North of Nantucket Island along the New England coast northward to the eastern Canadian coast the cold Labrador Current is found.
The North Atlantic Current of the Gulf Stream, along with similar warm air currents, helps keep Ireland and the western coast of Great Britain a few degrees warmer than the east. However, the difference is most dramatic in the western coastal islands of Scotland. A noticeable effect of the Gulf Stream and the strong westerly winds on Europe occurs along the Norwegian coast. Northern parts of Norway lie close to the Arctic
zone, most of which is covered with ice and snow in winter. However,
almost all of Norway's coast remains free of ice and snow throughout the
year.
The warming effect provided by the Gulf Stream has allowed fairly large
settlements to be developed and maintained on the coast of Northern Norway, including Tromsø,
the third-largest city north of the Arctic Circle. Weather systems
warmed by the Gulf Stream drift into Northern Europe, also warming the
climate behind the Scandinavian Mountains.
The possibility of a Gulf Stream collapse has been covered by some news publications. The IPCC Sixth Assessment Report
addressed this issue specifically, and found that based on model
projections and theoretical understanding, the Gulf Stream will not shut
down in a warming climate. While the Gulf Stream is expected to slow down as the Atlantic Meridional Overturning Circulation (AMOC) weakens, it will not collapse, even if the AMOC were to collapse.
Nevertheless, this slowing down will have significant effects,
including a rise in sea level along the North American coast, reduced
precipitation in the midlatitudes, changing patterns of strong
precipitation around Europe and the tropics, and stronger storms in the
North Atlantic.
Effect on cyclone formation
Hurricane Sandy intensified as it tracked northward along the axis of the Gulf Stream in 2012
The warm water and temperature contrast along the edge of the Gulf Stream often increase the intensity of cyclones, tropical or otherwise. Tropical cyclone generation normally requires water temperatures in excess of 26.5 °C (79.7 °F).
Tropical cyclone formation is common over the Gulf Stream, especially
in July. Storms travel westward through the Caribbean and then either
move in a northward direction and curve towards the eastern coast of the
United States or stay on a north-westward track and enter the Gulf of Mexico. Such storms have the potential to create strong winds and extensive damage to the United States' Southeast coastal areas. Hurricane Sandy in 2012 was a recent example of a hurricane tracking along the Gulf Stream and gaining strength.
Strong extratropical cyclones have been shown to deepen significantly along a shallow frontal zone, forced by the Gulf Stream, during the cold season. Subtropical cyclones
also tend to be generated near the Gulf Stream. About 75% of such
systems documented between 1951 and 2000 formed near this warm-water
current, with two annual peaks of activity occurring during May and
October.
Cyclones within the ocean itself form under the Gulf Stream, extending
as deep as 3,500 m (11,500 ft) beneath the ocean's surface.
The Gulf Stream periodically forms rings resulting from a meander of
the Gulf Stream being closed off from an alternate route distinctive
from that meander, creating an independent eddy. These eddies have two
types - cold-core rings, which rotate cyclonically
(counterclockwise in the Northern Hemisphere and clockwise in the
Southern Hemisphere), and warm-core rings, which rotate
anticyclonically. These rings have the capacity to transport the
distinct biological, chemical, and physical properties of their
originating waters to the new waters into which they travel.
Rogue waves (also known as freak waves or killer waves) are large and unpredictable surface waves that can be extremely dangerous to ships and isolated structures such as lighthouses. They are distinct from tsunamis,
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 earthquakes). A rogue wave at the shore is sometimes called a sneaker wave.
In oceanography, rogue waves are more precisely defined as waves whose height is more than twice the significant wave height (Hs
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. Recent research 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 water-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'.
Rogue waves are waves in open water that are much larger than surrounding waves. More precisely, rogue waves have a height which is more than twice the significant wave height (Hs or SWH). They can be caused when currents or winds cause waves to travel at different speeds, and the waves merge to create a single large wave; or when nonlinear effects cause energy to move between waves to create a single extremely large wave.
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 platform in the central North Sea in 1984. A stand-out wave was detected with a wave height of 11 m (36 ft) 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 25.6 m (84 ft) and peak elevation of
18.5 m (61 ft). 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 a SWH of 18.5 metres
(61 ft) and individual waves up to 29.1 metres (95 ft).[12] In 2004, scientists using three weeks of radar images from European Space Agency satellites found ten rogue waves, each 25 metres (82 ft) 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 ship designers,
and can overwhelm the usual capabilities of ocean-going vessels which
are not designed for such encounters. Rogue waves are, therefore,
distinct from tsunamis. Tsunamis are caused by a massive displacement of water, often resulting from sudden movements 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 statistical 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 offshore drilling unit that sank in Canadian waters on 15 February 1982. 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.
History of rogue wave knowledge
Early reports
In 1826, French scientist and naval officer Jules Dumont d'Urville
reported waves as high as 33 m (108 ft) in the Indian Ocean with three
colleagues as witnesses, yet he was publicly ridiculed by fellow
scientist François Arago. In that era, the thought was widely held that no wave could exceed 9 m (30 ft). Author Susan Casey wrote that much of that disbelief came because there were very few people who had seen a rogue wave and survived; until the advent of steel double-hulled ships
of the 20th century, "people who encountered 100-foot [30 m] rogue
waves generally weren't coming back to tell people about it."
Pre-1995 research
Unusual waves have been studied scientifically for many years (for example, John Scott Russell's wave of translation, an 1834 study of a soliton
wave). Still, these were not linked conceptually to sailors' stories of
encounters with giant rogue ocean waves, as the latter were believed to
be scientifically implausible.
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 12 m (39 ft), the model suggests hardly
ever would a wave higher than 15 m (49 ft) occur. It suggests one of
30 m (98 ft) 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 20 metres (67 ft). Draper also described freak wave holes.
Research on cross-swell waves and their contribution to rogue wave studies
Before
the Draupner wave was recorded in 1995, early research had already made
significant strides in understanding extreme wave interactions. In
1979, Dik Ludikhuize and Henk Jan Verhagen at TU Delft
successfully generated cross-swell waves in a wave basin. Although only
monochromatic waves could be produced at the time, their findings,
reported in 1981, showed that individual wave heights could be added
together even when exceeding breaker criteria. This phenomenon provided
early evidence that waves could grow significantly larger than
anticipated by conventional theories of wave breaking.
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.
The 1995 Draupner wave
Measured amplitude graph showing the Draupner wave (spike in the middle)
The Draupner wave (or New Year's wave) was the first rogue wave to be detected by a measuring instrument. The wave was recorded in 1995 at Unit E of the Draupner platform, a gas pipeline support complex located in the North Sea about 160 km (100 miles) southwest from the southern tip of Norway.
The rig was built to withstand a calculated 1-in-10,000-years
wave with a predicted height of 20 m (64 ft) and was fitted with
state-of-the-art sensors, including a laser rangefinder wave recorder on the platform's underside. At 3 pm on 1 January 1995, the device recorded a rogue wave with a maximum wave height of 25.6 m (84 ft). Peak elevation above still water level was 18.5 m (61 ft). The reading was confirmed by the other sensors. The platform sustained minor damage in the event.
In the area, the SWH at the time was about 12 m (39 ft), 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.
Subsequent research
Following the evidence of the Draupner wave, research in the area became widespread.
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 29 m (95 ft) 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 21 metres per second (41 kn), a
ship-borne wave recorder measured individual waves up to 29.1 m
(95.5 ft) from crest to trough, and a maximum SWH of 18.5 m (60.7 ft).
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 12 m (39.4 ft).
The analysis of this event took a number of years and noted that "none
of the state-of-the-art weather forecasts and wave models— the information upon which all ships, oil rigs, fisheries, and passenger boats rely— had
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
25 m (82 ft) 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 20 to 30 m (66 to 98 ft) 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 spots— such as coastal inlets and river mouths— these extreme waves can make up three of every 1,000 waves, because wave energy can be focused.
Rogue waves may also occur in lakes. 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 SS Edmund Fitzgerald on Lake Superior in November 1975.
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 wave"— a breather around 5 times higher than surrounding waves— in 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".
In 2019, researchers succeeded in producing a wave with similar
characteristics to the Draupner wave (steepness and breaking), and
proportionately greater height, using multiple wavetrains
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 1.0 to 1.5 m (3 to 5 ft) 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".
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)
In the first row (0°), the crest breaks horizontally and plunges, limiting the wave size.
In the middle row (60°), somewhat upward-lifted breaking behavior occurs.
In the third row (120°), described as the most accurate simulation achieved of the Draupner wave, the wave breaks upward, as a vertical jet, and the wave crest height is not limited by breaking.
Extreme rogue wave events
On 17 November 2020, a buoy moored in 45 metres (148 ft) of water on Amphitrite Bank in the Pacific Ocean 7 kilometres (4.3 mi; 3.8 nmi) off Ucluelet, Vancouver Island, British Columbia, Canada, at 48.9°N 125.6°W recorded a lone 17.6-metre (58 ft) tall wave among surrounding waves about 6 metres (20 ft) 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.
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 10.32 metres
(33.86 ft) 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 21-metre
(69 ft) wave appeared in the Pacific Ocean off the Port of Coos Bay,
Oregon, with a significant wave height of 3.9 metres (13 ft). The ratio
is 5.38, almost twice that of the Ucluelet wave. The paper also reveals
the MV Pont-Aven
incident as marginally more extreme than the Ucluelet event. The paper
also assesses a report of an 11-metre (36 ft) wave in a significant wave
height of 1.9 metres (6 ft 3 in), 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.
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 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:
According to this hypothesis, coast shape or seabed shape directs
several small waves to meet in phase. Their crest heights combine to
create a freak wave.
Focusing by currents
Waves from one current are driven into an opposing current. This
results in shortening of wavelength, causing shoaling (i.e., increase in
wave height), and oncoming wave trains to compress together into a
rogue wave. This happens off the South African coast, where the Agulhas Current is countered by westerlies.
A rogue wave may occur by natural, nonlinear processes from a random background of smaller waves.
In such a case, it is hypothesized, an unusual, unstable wave type may
form, which "sucks" energy from other waves, growing to a near-vertical
monster itself, before becoming too unstable and collapsing shortly
thereafter. One simple model for this is a wave equation known as the nonlinear Schrödinger equation
(NLS), in which a normal and perfectly accountable (by the standard
linear model) wave begins to "soak" energy from the waves immediately
fore and aft, reducing them to minor ripples compared to other waves.
The NLS can be used in deep-water conditions. In shallow water, waves
are described by the Korteweg–de Vries equation or the Boussinesq equation. These equations also have nonlinear contributions and show solitary-wave solutions. The terms soliton (a type of self-reinforcing wave) and breather
(a wave where energy concentrates in a localized and oscillatory
fashion) are used for some of these waves, including the well-studied Peregrine soliton. Studies show that nonlinear effects could arise in bodies of water. A small-scale rogue wave consistent with the NLS on (the Peregrine soliton) was produced in a laboratory water-wave tank in 2011.
Normal part of the wave spectrum
Some studies argue that many waves classified as rogue waves (with
the sole condition that they exceed twice the SWH) are not freaks but
just rare, random samples of the wave height distribution, and are, as such, statistically expected to occur at a rate of about one rogue wave every 28 hours.
This is commonly discussed as the question "Freak Waves: Rare
Realizations of a Typical Population Or Typical Realizations of a Rare
Population?"
According to this hypothesis, most real-world encounters with huge
waves can be explained by linear wave theory (or weakly nonlinear
modifications thereof), without the need for special mechanisms like the
modulational instability. Recent studies analyzing billions of wave measurements by wave buoys demonstrate that rogue wave occurrence rates in the ocean can be explained with linear theory when the finite spectral bandwidth of the wave spectrum is taken into account.
However, whether weakly nonlinear dynamics can explain even the largest
rogue waves (such as those exceeding three times the significant wave
height, which would be exceedingly rare in linear theory) is not yet
known. This has also led to criticism questioning whether defining rogue
waves using only their relative height is meaningful in practice.
Constructive interference of elementary waves
Rogue waves can result from the constructive interference
(dispersive and directional focusing) of elementary three-dimensional
waves enhanced by nonlinear effects.
While wind alone is unlikely to generate a rogue wave, its effect
combined with other mechanisms may provide a fuller explanation of freak
wave phenomena. As the wind blows over the ocean, energy is transferred
to the sea surface. When strong winds from a storm blow in the ocean
current's opposing direction, the forces might be strong enough to
generate rogue waves randomly. Theories of instability mechanisms for
the generation and growth of wind waves – although not on the causes of
rogue waves – are provided by Phillips and Miles.
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 wave groups have been observed in nature.
Research efforts
A number of research programmes are currently underway or have concluded whose focus is/was on rogue waves, including:
In the course of Project MaxWave, researchers from the GKSS Research Centre, using data collected by ESAsatellites,
identified a large number of radar signatures that have been portrayed
as evidence for rogue waves. Further research is underway to develop
better methods of translating the radar echoes into sea surface
elevation, but at present this technique is not proven.
The Australian National University, working in collaboration with Hamburg University of Technology and the University of Turin,
have been conducting experiments in nonlinear dynamics to try to
explain rogue or killer waves. The "Lego Pirate" video has been widely
used and quoted to describe what they call "super rogue waves", which
their research suggests can be up to five times bigger than the other
waves around them.
The European Space Agency continues to do research into rogue waves by radar satellite.
Massachusetts Institute of Technology(MIT)'s
research in this field is ongoing. Two researchers there partially
supported by the Naval Engineering Education Consortium (NEEC)
considered the problem of short-term prediction of rare, extreme water
waves and developed and published their research on a predictive tool of
about 25 wave periods. This tool can give ships and their crews a two
to three-minute warning of a potentially catastrophic impact allowing
crew some time to shut down essential operations on a ship (or offshore
platform). The authors cite landing on an aircraft carrier as a prime
example.
The University of Oxford Department of Engineering Science published a comprehensive review of the science of rogue waves in 2014. In 2019, A team from the Universities of Oxford and Edinburgh recreated the Draupner wave in a lab.
At Umeå University in Sweden, a research group in August 2006 showed that normal stochastic
wind-driven waves can suddenly give rise to monster waves. The
nonlinear evolution of the instabilities was investigated by means of
direct simulations of the time-dependent system of nonlinear equations.
The University of Oslo has conducted research into crossing sea state and rogue wave probability during the Prestige accident;
nonlinear wind-waves, their modification by tidal currents, and
application to Norwegian coastal waters; general analysis of realistic
ocean waves; modelling of currents and waves for sea structures and
extreme wave events; rapid computations of steep surface waves in three
dimensions, and comparison with experiments; and very large internal
waves in the ocean.
Researchers at UCLA observed rogue-wave phenomena in microstructured optical fibers 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.
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.
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.
This section lists a limited selection of notable incidents.
19th century
Eagle Island lighthouse
(1861) – Water broke the glass of the structure's east tower and
flooded it, implying a wave that surmounted the 40 m (130 ft) cliff and
overwhelmed the 26 m (85 ft) tower.
Flannan Isles Lighthouse
(1900) – Three lighthouse keepers vanished after a storm that resulted
in wave-damaged equipment being found 34 m (112 ft) above sea level.
20th century
SS Kronprinz Wilhelm, September 18, 1901 – The most modern German ocean liner of its time (winner of the Blue Riband) was damaged on its maiden voyage from Cherbourg to New York by a huge wave. The wave struck the ship head-on.
RMS Lusitania
(1910) – On the night of 10 January 1910, a 23 m (75 ft) wave struck
the ship over the bow, damaging the forecastle deck and smashing the
bridge windows.
USS Memphis, August 29, 1916 – An armored cruiser, formerly known as the USS Tennessee, wrecked while stationed in the harbor of Santo Domingo, with 43 men killed or lost, by a succession of three waves, the largest estimated at 70 feet.
RMS Homeric
(1924) – Hit by a 24 m (80 ft) wave while sailing through a hurricane
off the East Coast of the United States, injuring seven people, smashing
numerous windows and portholes, carrying away one of the lifeboats, and
snapping chairs and other fittings from their fastenings.
USS Ramapo (1933) – Triangulated at 34 m (112 ft).
RMS Queen Mary (1942) – Broadsided by a 28 m (92 ft) wave and listed briefly about 52° before slowly righting.
SS Michelangelo (1966) – Hole torn in superstructure, heavy glass was smashed by the wave 24 m (80 ft) above the waterline, and three deaths.
SS Edmund Fitzgerald (1975) – Lost on Lake Superior,
a Coast Guard report blamed water entry to the hatches, which gradually
filled the hold, or errors in navigation or charting causing damage
from running onto shoals. However, another nearby ship, the SS Arthur M. Anderson,
was hit at a similar time by two rogue waves and possibly a third, and
this appeared to coincide with the sinking around 10 minutes later.
MS München
(1978) – Lost at sea, leaving only scattered wreckage and signs of
sudden damage including extreme forces 20 m (66 ft) above the water
line. Although more than one wave was probably involved, this remains
the most likely sinking due to a freak wave.
Esso Languedoc (1980) – A 25-to-30 m (80-to-100 ft) wave washed across the deck from the stern of the French supertanker near Durban, South Africa.
Draupner wave (North Sea, 1995) – The first rogue wave confirmed with scientific evidence, it had a maximum height of 26 metres (85 ft)
Queen Elizabeth 2 (1995) – Encountered a 29 m (95 ft) wave in the North Atlantic, during Hurricane Luis. The master said it "came out of the darkness" and "looked like the White Cliffs of Dover." Newspaper reports at the time described the cruise liner as attempting to "surf" the near-vertical wave in order not to be sunk.
21st century
U.S. Naval Research Laboratory ocean-floor pressure sensors detected a freak wave caused by Hurricane Ivan in the Gulf of Mexico, 2004. The wave was around 27.7 m (91 ft) high from peak to trough, and around 200 m (660 ft) long. Their computer models also indicated that waves may have exceeded 40 metres (130 ft) in the eyewall.
Aleutian Ballad, (Bering Sea, 2005) footage of what is identified as an 18 m (60 ft) wave appears in an episode of Deadliest Catch.
The wave strikes the ship at night and cripples the vessel, causing the
boat to tip for a short period onto its side. This is one of the few
video recordings of what might be a rogue wave.
In 2006, researchers from U.S. Naval Institute
theorized rogue waves may be responsible for the unexplained loss of
low-flying aircraft, such as U.S. Coast Guard helicopters during search-and-rescue missions.
MS Louis Majesty (Mediterranean Sea, March 2010) was struck by three successive 8 m (26 ft) waves while crossing the Gulf of Lion on a Mediterranean cruise between Cartagena and Marseille.
Two passengers were killed by flying glass when the second and third
waves shattered a lounge window. The waves, which struck without
warning, were all abnormally high in respect to the sea swell at the time of the incident.
In 2011, the Sea Shepherd vessel MV Brigitte Bardotwas damaged by a rogue wave of 11 m (36.1 ft) while pursuing the Japanese whaling fleet off the western coast of Australia on 28 December 2011. The MV Brigitte Bardot was escorted back to Fremantle by the SSCS flagship, MV Steve Irwin. The main hull was cracked, and the port side pontoon was being held together by straps. The vessel arrived at Fremantle Harbor on 5 January 2012. Both ships were followed by the ICR security vessel MV Shōnan Maru 2 at a distance of 5 nautical miles (9 km).
In 2022, the Viking cruise ship Viking Polaris was hit by a rogue wave on its way to Ushuaia, Argentina. One person died, four more were injured, and the ship's scheduled route to Antarctica was canceled.
Quantifying the impact of rogue waves on ships
The loss of the MS München 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 20 m (66 ft) 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 20 m (66 ft). 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.
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 was— and remains to be— 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 20 m (66 ft) with a resultant static pressure of 201 kilopascals (2.01 bar; 29.2 psi). This is in effect 20 m (66 ft) 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 2 m (6.6 ft) of water or 17.1 kPa (0.171 bar;
2.48 psi),
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 200 kPa (2.0 bar; 29 psi) (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 5,650 kPa (56.5 bar; 819 psi) 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 745 kPa (7.45 bar; 108.1 psi). This
pressure far exceeds almost any design criteria for modern ships, and
this wave would have destroyed almost any merchant vessel.
Design standards
In November 1997, the International Maritime Organization(IMO)
adopted new rules covering survivability and structural requirements
for bulk carriers of 150 m (490 ft) 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.
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 12 m (39 ft) wave in the usual
"linear" model would have a breaking force of 6 metric tons per square
metre [t/m2] (8.5 psi). 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 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 19.8 m (65 ft). He presented analysis that
sufficient evidence exists to conclude that 20.1 m (66 ft) high waves
can be experienced in the 25-year lifetime of oceangoing vessels, and
that 29.9 m (98 ft) high waves are less likely, but not out of the
question. Therefore, a design criterion based on 11.0 m (36 ft) 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 21.4 m (70 ft). 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.
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and, ultimately, for some authors, the entire universe.
Complex systems are systems
whose behavior is intrinsically difficult to model due to the
dependencies, competitions, relationships, or other types of
interactions between their parts or between a given system and its
environment. Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others.
Because such systems appear in a wide variety of fields, the
commonalities among them have become the topic of their independent area
of research. In many cases, it is useful to represent such a system as a
network where the nodes represent the components and links to their
interactions.
The term complex systems often refers to the study of
complex systems, which is an approach to science that investigates how
relationships between a system's parts give rise to its collective
behaviors and how the system interacts and forms relationships with its
environment.
The study of complex systems regards collective, or system-wide,
behaviors as the fundamental object of study; for this reason, complex
systems can be understood as an alternative paradigm to reductionism, which attempts to explain systems in terms of their constituent parts and the individual interactions between them.
Complex systems are usually open systems — that is, they exist in a thermodynamic gradient and dissipate energy. In other words, complex systems are frequently far from energetic equilibrium: but despite this flux, there may be pattern stability, see synergetics.
Complex systems may exhibit critical transitions
Graphical
representation of alternative stable states and the direction of
critical slowing down prior to a critical transition (taken from Lever
et al. 2020).
Top panels (a) indicate stability landscapes at different conditions.
Middle panels (b) indicate the rates of change akin to the slope of the
stability landscapes, and bottom panels (c) indicate a recovery from a
perturbation towards the system's future state (c.I) and in another
direction (c.II).
Critical transitions are abrupt shifts in the state of ecosystems, the climate, financial and economic systems or other complex systems that may occur when changing conditions pass a critical or bifurcation point.
The 'direction of critical slowing down' in a system's state space may
be indicative of a system's future state after such transitions when
delayed negative feedbacks leading to oscillatory or other complex
dynamics are weak.
The components of a complex system may themselves be complex systems. For example, an economy is made up of organisations, which are made up of people, which are made up of cells
– all of which are complex systems. The arrangement of interactions
within complex bipartite networks may be nested as well. More
specifically, bipartite ecological and organisational networks of
mutually beneficial interactions were found to have a nested structure.
This structure promotes indirect facilitation and a system's capacity
to persist under increasingly harsh circumstances as well as the
potential for large-scale systemic regime shifts.
Dynamic network of multiplicity
As well as coupling rules, the dynamic network of a complex system is important. Small-world or scale-free networks
which have many local interactions and a smaller number of inter-area
connections are often employed. Natural complex systems often exhibit
such topologies. In the human cortex for example, we see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions.
May produce emergent phenomena
Complex systems may exhibit behaviors that are emergent,
which is to say that while the results may be sufficiently determined
by the activity of the systems' basic constituents, they may have
properties that can only be studied at a higher level. For example,
empirical food webs display regular, scale-invariant features across
aquatic and terrestrial ecosystems when studied at the level of
clustered 'trophic' species. Another example is offered by the termites in a mound which have physiology, biochemistry and biological development at one level of analysis, whereas their social behavior and mound building is a property that emerges from the collection of termites and needs to be analyzed at a different level.
Relationships are non-linear
In practical terms, this means a small perturbation may cause a large effect (see butterfly effect), a proportional effect, or even no effect at all. In linear systems, the effect is always directly proportional to cause. See nonlinearity.
Relationships contain feedback loops
Both negative (damping) and positive (amplifying) feedback
are always found in complex systems. The effects of an element's
behavior are fed back in such a way that the element itself is altered.
History
In 1948, Dr. Warren Weaver published an essay on "Science and Complexity",
exploring the diversity of problem types by contrasting problems of
simplicity, disorganized complexity, and organized complexity. Weaver
described these as "problems which involve dealing simultaneously with a
sizable number of factors which are interrelated into an organic
whole."
While the explicit study of complex systems dates at least to the 1970s, the first research institute focused on complex systems, the Santa Fe Institute, was founded in 1984. Early Santa Fe Institute participants included physics Nobel laureates Murray Gell-Mann and Philip Anderson, economics Nobel laureate Kenneth Arrow, and Manhattan Project scientists George Cowan and Herb Anderson. Today, there are over 50 institutes and research centers focusing on complex systems.
Since the late 1990s, the interest of mathematical physicists in
researching economic phenomena has been on the rise. The proliferation
of cross-disciplinary research with the application of solutions
originated from the physics epistemology has entailed a gradual paradigm
shift in the theoretical articulations and methodological approaches in
economics, primarily in financial economics. The development has
resulted in the emergence of a new branch of discipline, namely
"econophysics", which is broadly defined as a cross-discipline that
applies statistical physics methodologies which are mostly based on the
complex systems theory and the chaos theory for economics analysis.
The
traditional approach to dealing with complexity is to reduce or
constrain it. Typically, this involves compartmentalization: dividing a
large system into separate parts. Organizations, for instance, divide
their work into departments that each deal with separate issues.
Engineering systems are often designed using modular components.
However, modular designs become susceptible to failure when issues arise
that bridge the divisions.
Complexity of cities
Jane Jacobs described cities as being a problem in organized complexity in 1961, citing Dr. Weaver's 1948 essay.
As an example, she explains how an abundance of factors interplay into
how various urban spaces lead to a diversity of interactions, and how
changing those factors can change how the space is used, and how well
the space supports the functions of the city. She further illustrates
how cities have been severely damaged when approached as a problem in
simplicity by replacing organized complexity with simple and predictable
spaces, such as Le Corbusier's "Radiant City" and Ebenezer Howard's
"Garden City". Since then, others have written at length on the
complexity of cities.
Recurrence quantification analysis has been employed to detect the characteristic of business cycles and economic development. To this end, Orlando et al.
developed the so-called recurrence quantification correlation index
(RQCI) to test correlations of RQA on a sample signal and then
investigated the application to business time series. The said index has
been proven to detect hidden changes in time series. Further, Orlando
et al.,
over an extensive dataset, shown that recurrence quantification
analysis may help in anticipating transitions from laminar (i.e.
regular) to turbulent (i.e. chaotic) phases such as USA GDP in 1949,
1953, etc. Last but not least, it has been demonstrated that recurrence
quantification analysis can detect differences between macroeconomic
variables and highlight hidden features of economic dynamics.
Complexity and education
Focusing
on issues of student persistence with their studies, Forsman, Moll and
Linder explore the "viability of using complexity science as a frame to
extend methodological applications for physics education research",
finding that "framing a social network analysis within a complexity
science perspective offers a new and powerful applicability across a
broad range of PER topics".
Complexity in healthcare research and practice
Healthcare
systems are prime examples of complex systems, characterized by
interactions among diverse stakeholders, such as patients, providers,
policymakers, and researchers, across various sectors like health,
government, community, and education. These systems demonstrate
properties like non-linearity, emergence, adaptation, and feedback
loops. Complexity science in healthcare frames knowledge translation
as a dynamic and interconnected network of processes—problem
identification, knowledge creation, synthesis, implementation, and
evaluation—rather than a linear or cyclical sequence. Such approaches
emphasize the importance of understanding and leveraging the
interactions within and between these processes and stakeholders to
optimize the creation and movement of knowledge. By acknowledging the
complex, adaptive nature of healthcare systems, complexity science advocates for continuous stakeholder engagement, transdisciplinary collaboration, and flexible strategies to effectively translate research into practice.
Complexity and biology
Complexity science has been applied to living organisms, and in particular to biological systems. Within the emerging field of fractal physiology, bodily signals, such as heart rate or brain activity, are characterized using entropy
or fractal indices. The goal is often to assess the state and the
health of the underlying system, and diagnose potential disorders and
illnesses.
Complexity and chaos theory
Complex systems theory is related to chaos theory, which in turn has its origins more than a century ago in the work of the French mathematician Henri Poincaré. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order.
Chaotic systems remain deterministic, though their long-term behavior
can be difficult to predict with any accuracy. With perfect knowledge of
the initial conditions and the relevant equations describing the
chaotic system's behavior, one can theoretically make perfectly accurate
predictions of the system, though in practice this is impossible to do
with arbitrary accuracy.
The emergence of complex systems theory shows a domain between deterministic order and randomness which is complex. This is referred to as the "edge of chaos".
When one analyzes complex systems, sensitivity to initial conditions,
for example, is not an issue as important as it is within chaos theory,
in which it prevails. As stated by Colander,
the study of complexity is the opposite of the study of chaos.
Complexity is about how a huge number of extremely complicated and
dynamic sets of relationships can generate some simple behavioral
patterns, whereas chaotic behavior, in the sense of deterministic chaos,
is the result of a relatively small number of non-linear interactions. For recent examples in economics and business see Stoop et al. who discussed Android's market position, Orlando
who explained the corporate dynamics in terms of mutual synchronization
and chaos regularization of bursts in a group of chaotically bursting
cells and Orlando et al.
who modelled financial data (Financial Stress Index, swap and equity,
emerging and developed, corporate and government, short and long
maturity) with a low-dimensional deterministic model.
Therefore, the main difference between chaotic systems and complex systems is their history.
Chaotic systems do not rely on their history as complex ones do.
Chaotic behavior pushes a system in equilibrium into chaotic order,
which means, in other words, out of what we traditionally define as
'order'.
On the other hand, complex systems evolve far from equilibrium at the
edge of chaos. They evolve at a critical state built up by a history of
irreversible and unexpected events, which physicist Murray Gell-Mann called "an accumulation of frozen accidents".
In a sense chaotic systems can be regarded as a subset of complex
systems distinguished precisely by this absence of historical
dependence. Many real complex systems are, in practice and over long but
finite periods, robust. However, they do possess the potential for
radical qualitative change of kind whilst retaining systemic integrity.
Metamorphosis serves as perhaps more than a metaphor for such
transformations.
Complexity and network science
A
complex system is usually composed of many components and their
interactions. Such a system can be represented by a network where nodes
represent the components and links represent their interactions. For example, the Internet
can be represented as a network composed of nodes (computers) and links
(direct connections between computers). Other examples of complex
networks include social networks, financial institution
interdependencies, airline networks, and biological networks.
