Rogue Waves
Grabbing facts and theoretical considerations
January 27th 2005: the 'Semester at Sea' program of the University of Pittsburgh offers 700
students the opportunity to get on board the 180 m. research ship 'Explorer'. They get the privilege
- as a climax of a week of rough seas in the Northern Pacific - to get a close view of a rogue wave.
But once on sea this wave rises to crash the windows of the bridge and shuts down three of the
four engines. The ship limps into Honolulu harbour for repair on the 31st. One crew member
suffers from a broken arm, another from a broken leg and the students have merely bruises. It's
just one example of a rogue wave
On February 14th 2005, by Beaufort sea 8 in the Mediterranean, a wave smashed the glass canopy of the
Grand Voyager. On board 477 passengers and a crew of 313 were cruising from Tunis to Barcelona.
Water put the control and communications systems out of order. Fortunately, one of the ship's two engines
remained operational and allowed the ship to head for shelter at Cagliari. Concern rose very high, but
passengers suffered 'only' broken limbs and bruises.
Many sailor tales mention such 'rogue waves', 'freak waves', 'extreme storm waves', 'three sisters' and
other 'killer waves'. For many years, those reports were openly ridiculed and mariners were accused of
using them to boast about their bravery or to cover the part of their own mistakes in wrecks.
Grabbing facts
During the 20th century, reports have become more and more reliable and eventually a few precise
measurements could be made. Well-known reports of that period include the encounter by the USS
Ramapo of a 112 feet wave in the Pacific in 1933, or that of the 'Glorious Three' by the French training
cruiser Jeanne d'Arc south-east of Tokyo in 1963. Three exceptionally high waves that the ship cleared
with some difficulty, heeling over about 35°, leading the commander in second to comfort the crew and
cadets by reminding that 40° heel would probably be needed to capsize and that the 'best way yet to avoid
encountering sea events is to remain onshore'.
The next step happened when on 1st of January 1995, during a severe but not exceptional North-Sea
storm where significant wave height was about eleven tot twelve meters, a crest rose unexpectedly to
more than eighteen meters above mean sea level at Draupner E platform. It could be unambiguously
measured by sensors that had been installed to monitor the first winter performance of that platform. A
laser measurement of the time-history of the water surface elevation is thus available for that wave.
Although the crest height itself did not challenge the design conditions used for that platform (design crest
had been computed to be 19.5 m), it was assumed that much higher significant wave height would need to
prevail for such an event to occur. One can thus imagine the doubts that the New Year Wave cast onto
design procedures and assumptions.
Uit schip & werf de zee – april 2005
The hypothesis of a population of freak waves has also often been called upon to explain recent
accidents. Such as the loss of the MV Derbyshire in 1980, the largest ship Britain has ever lost, wave
impacts on floating production units Foinhaven and Schiehallion, or the wreck of the semi-submersible
platform Ocean Ranger with 84 lives. Yet, the New Year Wave had the advantage to provide reliable
measurements of a rogue wave that could be used for scientific studies. Scientific research has been
stimulated by both the concerns. The new data and the last decade has seen on one hand investigations
of the few available observations, trying to understand what really happened, and on the other hand
introduction of theoretical models that can produce waves with the observed characteristics.
Rogueness
Many studies refer only to a wave's height for it to qualify for rogueness. Height is a convenient parameter,
but it may be misleading since danger may be related to other additional characteristics of the wave.
As a matter of fact, designers of fixed offshore platforms are mainly concerned about the crest height
above mean sea level, because of the dramatic increase in wave loading that occurs if a wave rises high
enough to hit the deck. This is by no means nearly as transparent to waves as the lower part of the
platform.
Floating production units and ships are sensitive to the steepness in two of its forms. Firstly, the wave
length, especially when it is close to the length of the ship that may break through hogging or sagging
when she rides the crests. Secondly, the wave front steepness, because of the risk that the ship after
speeding down through that can always be found ahead of the wave itself drive her bow into the wave and
see her foredeck and hatch covers fail to withstand the pressure of the falling water masses. On
passenger ships and in other cases where the bridge is located in the fore part of the ship, additional risk
is incurred of water smashing the windows and disabling the electronic controls.
Smaller crafts are prone to being taken abeam by a wave with a steep front and rolled over, as it
happened during the 1998 Sydney-Hobart race. Though the craft most of the time rights up and survives
the first wave, the next ones usually sink her.
Yet, since buoy-measured heights are available and fairly reliable, whereas pure crests and wave-front
steepness measurements require fixed-platform mounted sensors and are rare, studies concentrate on
unexpectedly high waves. Their detailed properties are to be inferred from theory. One may yet wonder
how good theory is when events are unexpected.
From known world or from nowhere
The question is whether extreme rogue waves are normal, and rare extremes of the normal statistical
population of waves - or 'freaks', the 'ones from nowhere' - that would belong to a different statistical
population with generating mechanisms of its own. That would of course not be correctly accounted for by
conventional theories and design methods for marine structures.
The main difficulty in that problem resides in the rareness of such extreme events. In all cases, if some
difference exists in the occurrence probability of actual extremes with respect to predictions using
conventional theories, it will not show reliably unless one can study several million individual waves. Those
numbers are the order of magnitude of the total that a seafarer encounters during his whole life. To be
Uit schip & werf de zee – april 2005
measured, they require long and costly campaigns, and fail proof sensors to still operate on the only
occasions of interest, i.e. when waves sweep everything away.
Results from conventional theories are recalled in the following table, yet one must be aware that the
actual values exhibit a large variability about the most probable ones. The meaning of the figures in that
table is that if one stays at sea for instance one year, the highest wave relatively to the neighbouring ones
(i.e. to the prevailing significant wave height) will likely be 2.72 times that significant wave height.
It may be noted that there are also some 'not so rare' cases of rogue waves, but then they belong more to
the unaware-ness or the carelessness of seafarers than to the world of unexplained phenomena. A typical
example is the Agulhas current that flows down from the Indian Ocean along the South African coast.
When a storm is located at some distance south of Capetown, it dispatches swell opposing the current.
When they encounter the current, the long crests curve into a crescent shape and focus into pyramidal
breakers that can easily damage a ship. Accidents (as on May 3rd 1973 when ms. Bencruachan was
struck by a freak wave 74 miles SE of Durban sustaining severe bow damage) and wrecks, frequent a few
decades ago, have almost completely disappeared in the last decade since the South African Met-Office
broadcasts warnings to seafarers when the dangerous conditions are met.
However, despite removal from the statistics of those rogue waves that should be expected, a large
number of encounters remains, where no better explanation can be given at present than 'the wrong place
at the wrong time'.
How can they be born?
Two kind of studies are on-going to the aim of at least finding hints about when and where bad luck will
come. On one hand, scientists try to find what conditions lead the equations of the fluid mechanics to yield
waves similar to those that are feared. On the other hand, they analyze the data that could be collected
from field measurements for correlation with some special meteorological or oceanographic features, at
the time-scale of a sea state or of a storm, which could be forecast and used to send out warnings and to
validate one of the proposed theories.
The most popular theories are based on 'non-linear wave focusing'. Wind waves consist of a very large
number of wave components travelling with different velocities and/or in different directions. Individual
waves are constantly appearing, evolving and disappearing as a result of the combination - in phase and
out of phase - of those components. Non-linear wave focusing models represent the interactions between
wave trains as waves propagate and evolve, leading to occurrences of high waves that resemble
observations. The main weakness of those models is that they do neither account for wave generation by
the wind nor for dissipation by wave breaking. It is unlikely that those phenomena will not disturb the
evolution before a high focused wave can occur.
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Likely amplitude
Exposure dration factor at
maximum
20 Minutes 1.52
1 Hour 1.69
3 Hours 1.84
1 Day 2.11
1 Week 2.33
1 Month 2.48
1 Year 2.72
10 Years 2.92
20 Years 2.98
50 Years 3.06
100 Years 3.11
Most probable ratio of the height of the maximum wave to the prevailing significant wave height
Laboratory monsters
It should be emphasized that the proposed theories are fully consistent and that as well numerical
simulations as tests in laboratory flumes confirm that the proposed mechanisms generate rogue waves,
i.e. waves that are unexpectedly high considering the prevailing significant wave height. The remaining
question is however 'does this happen frequently enough in nature that extreme wave statistics are
modified beyond any doubt and that seafarers need to care?' The answer to that question is not simple.
Especially, the choice of initial conditions in a laboratory experiment may easily be believed to represent
adequately the variety of natural conditions, when in practice sufficient knowledge of those natural
conditions is out of our reach.
Scene of the crime
Retrieving good measurements of rare conditions at an offshore location is a challenge. For instance,
sensors such as platform-mounted laser distance meters may fail to operate properly in severe storm
conditions because of spray. Waves may be amplified by run-up effects on the platform or decreased by
sheltering effects behind it. In addition, the natural variability of the sea surface elevation in time and
space is high. Statistical parameters computed from the measurements suffer from estimation biases even
when the sensor is operating properly.
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Satellite-borne synthetic aperture radars that can provide huge volumes of data unfortunately still lack the
necessary accuracy to distinguish between mere high waves and true rogue ones. Very few databases
could be constructed up to now with enough individual waves and reliability to provide insight on extremes
at the levels of probability where conventional theories might fail to explain them all. The most useful ones
were obtained in the North Sea, where some offshore operators routinely run them on their platforms.
As a matter of fact, analysis of those data shows that whatever unexpected the highest waves may be with
respect to the prevailing sea states when they occur, they have not been observed globally more
frequently than could be computed from the use of conventional theories.
Impact
After nearly a decade of questioning, consensus has built up these last months to accept that rogue waves
were not sufficiently more frequent than the expectations to affect design at the targeted levels of safety.
Indeed, there does not seem to be deviations from the conventional predictions up to the yearly probability
of occurrence of 10 to 4 that is to be accounted for when manned or environmental potentially threatening
offshore platforms are considered.
Ships, as opposed to offshore platforms, have the capacity to avoid the worst storms and are thus
designed to 'lower' levels of safety. They also are more numerous. Given a world fleet of 90.000 ships, the
yearly 10 to 4 reliability level means that fatal encounters happen in average once every six weeks. That
may seem rather frequent, but for a given seafarer the odds are only one or two to a thousand that he will
have to face one during his whole career.
Prediction perspectives
The risk of occurrence of South African breakers can now be predicted to a reasonable accuracy, but
extending such forecasts to other areas in the world is not yet possible. On many occasions, those
characteristics of the sea conditions that may have caused a rogue wave are still undetermined.
Apart from a few areas, maps of observed wave accidents only reflect the density of ship traffic along
maritime routes. Met-Offices are working on the definition and forecasting of sea conditions parameters
that would be related to increases in the risk of extreme rogue waves. Those parameters are derived from
the theoretical considerations on possible generating mechanisms. It is probable that those parameters
will take a long time before they can be validated since rogue waves are fortunately rarely observed, and
that seafarers are not likely to expose themselves to dangerous waves for the only sake of sending reports
to scientists.
Survival tips
Though one should expect that rogue waves might occur at any time within a storm, features that might
increase the risk are thought to be:
'Running fetches' (i.e. when the displacement of the storm is swift and synchronized with the group
velocity of the waves);
Arrival of the wave system generated just after a cold front over the existing wave system generated
before the front;
Sudden drop of a very strong wind;
Time close to a storm's maximum.
On meeting a rogue wave, a small craft should try to take it head-on in order to avoid being rolled over. A
larger ship, on the opposite, should aim to steer at some angle to the wave so as to try to limit the bending
moment strains and help the bow ease up. In all cases, seafarers should be aware that the worst wave is
not in a fixed bounded ratio to the ones just previously encountered. And that the one-hundred year wave -
which is bound to happen someday - is as likely to occur in a 'merely severe' storm as to wait for the one-
hundred year storm.
Uit schip & werf de zee – april 2005
