Rogue Wave Prediction

[GordMay]

New Study* Finds Rogue Waves Far More Common Than Previously Thought
➥ https://www.theinertia.com/environme...ously-thought/

Ocean Measurements Detect Conditions for Giant Waves ➥ https://physics.aps.org/articles/v17/61

* “Observations of Rogue Seas in the Southern Ocean” ~ by A. Toffoli, et al
➥ https://journals.aps.org/prl/abstrac...ett.132.154101

In the largest study [1] of its kind, scientists analysed 20 years of observations from buoys situated along America's western seaboard.
They found that, between 1994 and 2016, rogue waves decreased slightly in frequency, but increased [1% year on year] in height.
The researchers also found that rogue waves varied over the seasons, being more frequent, and extreme, in winter.

More about: “Rogue waves in the ocean are much more common than anyone suspected, says new study”
➥ https://findanexpert.unimelb.edu.au/...says-new-study

“... Our results show young waves display signs of self-amplification and an increased likelihood of rogue waves. We recorded waves twice as high as their neighbours once every six hours.

This mirrors what lab models have reported: sea conditions theoretically more prone to self-amplification would produce more rogue waves.

In contrast, mature seas don’t show an increased probability of rogue waves. We detected none under those conditions ...”

[1] “Seasonal intensification and trends of rogue wave events on the US western seaboard” ~ by A. D. Cattrell et al
➥ https://www.nature.com/articles/s41598-019-41099-z

“... Rogue wave occurrence displays a mostly decreasing trend, but the relative height – or severity – of the waves is increasing. We also identify seasonal intensification in rogue waves with increased rogue wave occurrence, of higher severity, in the winter than in the summer ...”

Using 700 years’ worth of wave data, from more than a billion waves, scientists have used artificial intelligence to find a formula [2] for how to predict the occurrence of rogue waves.
They registered 100,000 waves, in their dataset, that can be defined as rogue waves. This is equivalent to around one monster wave, occurring every day, at any random location in the ocean.

[2] “Machine-guided discovery of a real-world rogue wave model” ~ by Dion Häfner et al
➥ https://www.pnas.org/doi/10.1073/pnas.2306275120


The exact way that rogue waves form is still being studied, but, there are two three prominent hypotheses:

1. Constructive Interference
In the open-ocean, wave sets often intersect, cutting across each other. The wave patterns produced when two or more wave sets intersect are called interference patterns. Interfering wave sets can produce exceptionally high waves and very deep wave troughs form when two waves come together. This combining is called wave reinforcement. Interference patterns formed by two sets of waves can be seen on a small scale by tossing two pebbles close together into a pond and watching how the waves intersect.

2. Focusing of Wave Energy
Another hypothesis for how rogue waves form involves the interaction between waves and current. When the current is pushing against storm waves, the current shortens the wave frequency, which can cause the storm waves to join together and create rogue waves.

3. Self Amplification
When waves are steep, and most of them have a similar amplitude, length, and direction, another mechanism can trigger the formation of rogue waves.
This mechanism involves an exchange of energy, between waves, that produces a ‘self-amplification, where one wave grows disproportionately, at the expense of its neighbors.
Basically, the mere existence of a series of large waves, can allow one of those waves, to cannibalize energy from its sisters, and become a rogue wave.

[lestersails]

Originally Posted by Tillikum

I see you make no "hillbilly" remarks this time; got that impulse wrestled down I suppose, lest it reveal too much??

What you perceive as "ridicule" is merely a healthy degree of common sense and skepticism in most cases. Certainly those who have been harmed or had family members harmed by the advice or direction of so-called experts might be expected to engage in ridicule at the very least, but happily I am not one of those.

The real problem is the monumental self-conceit of "experts" and their wonderful ability to imagine themselves as the Don Quixote's of knowledge when the oldest profession is usually a more apt metaphor. A trend which parallels the decline in public and private morality and indeed in the existence of moral sense all. The contempt if not actual hatred often displayed for the "others" of humanity speaks volumes.

That is moral sense as in founded on a set of moral values rather than what is now mostly confused with it: a contemptible conformity and mob mentality which has never in all human history been associated with any kind of intellectual, moral or "scientific" advancement, and is in fact the polar opposite of it. A fact so obvious that the current blithe indifference to it is probably enough to charge if not convict as a group those who should be the most aware of it.

Those who cannot stomach criticism or are hyper-sensitive to it are the emotionally fragile. Those whose self-esteem is founded on their purported expertise and little else, naturally react violently to whatever their perceive as an attack on it as their whole self-image is often at stake. Used to the deference of perceived inferiors such people often come to match quite closely the psychological profile of the classic narcissist.

And history certainly shows what they are capable of.

Nice try. It is all about the insecurities of people who feel threatened by those with superior knowledge and expertise. The world is more complicated than it used to be and a larger and larger proportions of things are harder to understand because so much of it is based on expert knowledge. Anyone with honesty and integrity has to admit that they don't fundamentally understand many things that they interact with every day. A microprocessor, a weather model, quantum computing, etc. To carp that "the experts aren't always right" is to express a profound ignorance of the process of moving towards better knowledge. They aren't always right, but they actually do know more than us about some things and if it hurts our feelings, gee, that's really too bad.

[wholybee]

Originally Posted by El Pinguino

Rouge waves are quite common in the Red Sea.

The average punter sailing downwind in the trades won't be bothered by them.. OK so with a wave train of say 2 metres a 4 metre jobby come rolling through it isn't exactly the end of life as we know it.

I've only encountered one, south of Mar del Plata, poking along to windward under reduced canvas, just back from the mast having tucked another reef in.
Swept the deck clean, lucky it didn't take me as well.

Dunno how that would have been forecast .

The conditions where serious 'rogue wave' conditions exist - the western approaches to Europe , Bass Strait, Chile, etc, in winter tend to be places where sensible sailors aren't sailing anyway

What I am postulating is that a 4 meter wave that rolls through every 8 hours (or whatever the interval) when the SWH is only 2 meters is not a rogue wave because:

1. It does not EXCEED 2xSWH
2. It is at a regular interval, not an unexpected wave that comes out of nowhere.
3. It is the same direction and part of the regular recurring pattern.

If waves of 2xSWH are regular occurrences in the Red Sea, then they are not rogue waves because a requirement (in addition to > 2xSWH) is that they are unexpected.

As a comparison, a friend of mine lost his vessel hit by a rogue wave. He was a few hundred miles from a hurricane. (his navigational error and error in deciding to depart when he did) He had 48 hours of good conditions, was sailing comfortable will following seas. Then out of nowhere a wave rose up, hit his beam (90 degrees from the swell direction) and rolled his boat and ripped it apart.

That wave was a true rogue wave. It was > 2xSWH. It was not regular or repeating at any interval. It was the ONLY wave of that size. And, it was coming from a different direction from the swell.

Even using the example of a 2m SWH. If you are sailing downwind with a 2 meter swell, and a 4 meter wave rises and breaks on your beam, that is a serious (and rare) event. A sailboat can be capsized and rolled 360 with a breaking wave 1/4 of it's LWL. So for any sailboat less than 12 meters, a rouge wave of 4 meters on it's beam is a big deal. Conversely, in the same conditions, a 4 meters swell in the normal wave pattern that comes every 8 hours is NOT a rogue wave, and because it is following, not a big deal at all.

I think a deciding factor, which is still being studied and not fully understood, is how the waves form. For waves in the normal pattern, waves form by wind, and by predicable addition and stacking. Sometimes there will be a wave 2xSWH because that is just how they add up. But for rogue waves the formation is more chaotic. While the physics may still be the addition of waves of lessor height, the directions and intervals of the waves are more complicated and the results much more rare.

[Lee Jerry]

A question, and I think contributing to confusion, is how rare or regular are waves twice the significant wave height? I hope we are all already aware that when we receive a weather report that includes wave height, that waves twice the significant height are possible.

But, I don't think they are frequent.

The short answer is about 1 in 3000 waves.



The (abbreviated) nerdy answer is:

Wave heights follow a Rayleigh distribution (Longuet-Higgins,1952).

The probability of a wave exceeding some value is the area under the spectrum to the right of that value. Using the RMS (root mean square) wave height, Hrms, that gives:


Note, the significant wave height, Hs, is the square root of 2 times the Hrms, or 1.414Hrms.

Therefore, the probability of a wave being 2x Hs is:
Q(H) = e^(-2Hs/Hrms)^2 = e^(-2(1.414Hrms)/Hrms)^2 = e^(-8) = 0.0003355

Or, taking the inverse, 1 in 2981 waves will exceed 2x the significant wave height.

Also note that the probability function is far from linear. Some notable values:
> 1.5x Hs, Q(H) = 0.0111 ---> or 1 in 90 waves
> 1.75x Hs, Q(H) = 0.00219 ---> or 1 in 457 waves
> 2.25x Hs, Q(H) = 0.0000401 ---> or 1 in 25,000 waves
>2.5x Hs, Q(H) = 0.00000373 ---> or 1 in 268,000 waves
>3x Hs, Q(H) = 0.0000000152 ---> or 1 in 65,700,000 waves


Another useful relationship from the statistics is for the maximum height. If J, is the number of waves, then:


So for 3000 waves:
Hmax= 0.707 * (ln 3000)^0.5 * Hs = 2.0 * Hs

I'll leave it for you to calculate other values.

[lestersails]

Originally Posted by Lee Jerry

The short answer is about 1 in 3000 waves.



The (abbreviated) nerdy answer is:

Wave heights follow a Rayleigh distribution (Longuet-Higgins,1952).

The probability of a wave exceeding some value is the area under the spectrum to the right of that value. Using the RMS (root mean square) wave height, Hrms, that gives:
Attachment 292434

Note, the significant wave height, Hs, is the square root of 2 times the Hrms, or 1.414Hrms.

Therefore, the probability of a wave being 2x Hs is:
Q(H) = e^(-2Hs/Hrms)^2 = e^(-2(1.414Hrms)/Hrms)^2 = e^(-8) = 0.0003355

Or, taking the inverse, 1 in 2981 waves will exceed 2x the significant wave height.

Also note that the probability function is far from linear. Some notable values:
> 1.5x Hs, Q(H) = 0.0111 ---> or 1 in 90 waves
> 1.75x Hs, Q(H) = 0.00219 ---> or 1 in 457 waves
> 2.25x Hs, Q(H) = 0.0000401 ---> or 1 in 25,000 waves
>2.5x Hs, Q(H) = 0.00000373 ---> or 1 in 268,000 waves
>3x Hs, Q(H) = 0.0000000152 ---> or 1 in 65,700,000 waves


Another useful relationship from the statistics is for the maximum height. If J, is the number of waves, then:
Attachment 292440

So for 3000 waves:
Hmax= 0.707 * (ln 3000)^0.5 * Hs = 2.0 * Hs

I'll leave it for you to calculate other values.

This is interesting - I had not heard of the Rayleigh distribution. The number at the top seems a bit high to me. Currently, the wave period in the Atlantic north of Puerto Rico is about 6 seconds. Given that, one would encounter 10 waves per minute, 600 waves per hour and 14,400 waves per day. That would predict I would, on average, experience 4-5 waves a day that are twice as high as the average. My experience is that I encounter quite a bit fewer than that. Is my math correct? Maybe I am just not a good observer.

[bdgWesternMass]

Originally Posted by lestersails

Nice try. It is all about the insecurities of people who feel threatened by those with superior knowledge and expertise. The world is more complicated than it used to be and a larger and larger proportions of things are harder to understand because so much of it is based on expert knowledge. Anyone with honesty and integrity has to admit that they don't fundamentally understand many things that they interact with every day. A microprocessor, a weather model, quantum computing, etc. To carp that "the experts aren't always right" is to express a profound ignorance of the process of moving towards better knowledge. They aren't always right, but they actually do know more than us about some things and if it hurts our feelings, gee, that's really too bad.

I agree with everything you said. My complaint about experts is the tunnel vision it creates. Some experts get so framed in by the context they work in that they can't take in a wider view of solutions.

[Tillikum]

Originally Posted by lestersails

Nice try. It is all about the insecurities of people who feel threatened by those with superior knowledge and expertise.

Repeating things over and over does not make them true, despite what Dr. Goebbels said. Clearly this is a paradigm very dear to your heart: “superior knowledge and expertise”. You might have said “greater knowledge” or “more in-depth knowledge”, but no, as per your previous implication that those who don’t agree with you are “hillbillies”, you like the word “superior”. Vanity, one of the perpetuals of human nature and the more otherwise unbalanced or inadequate a person, physically or socially, the greater the compensatory vanity.

Originally Posted by lestersails

The world is more complicated than it used to be and a larger and larger proportions of things are harder to understand because so much of it is based on expert knowledge. Anyone with honesty and integrity has to admit that they don't fundamentally understand many things that they interact with every day. A microprocessor, a weather model, quantum computing, etc. To carp that "the experts aren't always right" is to express a profound ignorance of the process of moving towards better knowledge. They aren't always right, but they actually do know more than us about some things and if it hurts our feelings, gee, that's really too bad.

The world is more technologically complex and the mechanisms of control have become more complex, and effective, but human nature has not changed in the slightest, despite you or one of you confreres here stating in a previous exchange that it had done so since the case of Dr. Semmelweis in the 19th Century no less. How very “scientific” to assert that humanity had evolved in a century or so!

“Experts” are like tradesman: very useful in their fields; essential to humanity’s technological progress and therefore our standards of living, comfort and convenience, but sadly high intelligence or high qualification does not confer common sense, moral courage, breadth of vision, or human decency. In fact quite often the reverse as such people tend to come to see themselves as “special” and “entitled”; “superior” to use your term.

It would be an interesting field of research to investigate the extent to which such attitudes pervade the higher percentiles of intelligence and then to determine the extent to which such attitudes originate in upbringing, education, inherited personality or acquired self-perception in adult-hood. That “genius is next to madness” is a byword, but the association of high intelligence with other personality defects such as psychopathy, sociopathy, narcissism, etc. would be worthy of investigation. Of course the highly intelligent subjects of such study would be difficult to assess given their greater talent for deception of themselves and others.

And so while “experts” often at least cordially despise the rest of humanity and think themselves more valuable, they remain of course as eager to profit and prosper as anyone else, often more so in fact as Mr. Expert having invested his time and money, not to mention his ego, in his specialized career path or rarefied area of study, must prosper in his field or start again at nothing; an inconceivable disaster once his career is well advanced.

Rockefeller for example, was one of the pioneers at selecting and grooming rising academics in the pedagogy field in the late 19th century, for his declared purpose of changing in the average American into a more compliant creature than he then was; and his success is all around us today. This “science” has far advanced since then.

Those who hold real power in this world, that is those who control the money system and supply, can easily make or break the careers of such “experts” and do. By spreading around billions of dollars of public money and a concerted campaign in our ludicrously concentrated mass media a story-line has been established in various fields, which the vast majority of the “experts” eagerly embrace, the better to get slice of the money pie and the career-boosting publicity that also comes to those who toe the party line.


Many know the story lines are in many respects fraudulent, but why buck the system when almost all your peers are going along for the ride? Who wants to be an outcast? The more they know of the fraud, the more violently anyone who points it out is attacked as the quislings know very well that their credibility will be gone if the truth should out. And so we all produce our little papers on the Emperor’s magnificent attire, and natter back and forth at conferences about it, and the show goes on.

Such people are often highly dangerous to the common good. In exchange for a little preference and profit they at best create and maintain the mechanisms of control and at worst conspire at the oppression and even destruction of whole groups of people. Or have you forgotten recent history - or perhaps you don’t read much of it?

There are of course a small minority of experts who cannot accept self-delusion or the conscious deception of others, and these are the outcasts of every age and level of human knowledge. Their outraged and insulted peers attack them violently, but those of us with some common sense realize that those willing to sacrifice career and profit to what they believe is the truth are very likely to be telling it, in contrast to the rest who go along so as to get along in every age.

[boatman61]

^^^My Hero^^^

[MicHughV]

I'm somewhat confused with the word " prediction", which by definition, is essentially a statement about what you think will happen in the future.

Every Tom, Dick and Harry have their " predictions" about all sorts of things...who wins the big game in sports....the weather....lotto numbers....etc, etc, ad nauseam.

That a so-called " rogue wave" happens from time to time is, I believe, indisputable, but "predicting" when it might happen is a toss of the dice.

Furthermore, the likelihood of witnessing one means you are sailing somewhere in the high southern or northern latitudes, where wave heights have an opportunity to grow.

On any given day, I suspect that the number of sailors sailing in these areas can probably be counted on one hand. Even during the round-the-world races, the number of sailors in these neck of the woods is probably a dozen or less.

Elsewhere, you'd have to be in an area with prolonged winds of 60 knots plus.

So then, it's an event most likely to be witnessed by crew on a ship, and odds are they don't post here.

So "predicting" when a rogue wave might appear would appear to be a bit of a stretch of the imagination.

My 2c for the day.

[GordMay]

Tillikum [#37] raises some interesting points, and opinions, about how personality and intelligence* relate to each another.

An enormous new [publicly available] dataset [1] establishes hundreds of reliable relationships, between dozens of personality traits, and cognitive abilities [intelligence].
It contains 79 personality traits, and 97 cognitive abilities, from 1,300 studies, from over 50 countries, including over 2 million participants.
An early meta-analysis [2], published in the Proceedings of the National Academy of Sciences, shows that personality and intelligence relate, in some surprising ways.

[1]“Meta-Analyses of Personality Traits and Cognitive Abilities” ~ by Kevin C. Stanek & Deniz S. Ones
➥ https://www.pnas.org/doi/full/10.1073/pnas.2212794120

Originally Posted by Stanek & Ones

“... Neuroticism facets (e.g., suspiciousness, depression) were negatively related to most cognitive abilities including non-invested (e.g., fluid reasoning) and invested abilities (e.g., knowledge). Extraversion’s activity facet had sizable, positive relations with several non-invested (e.g., retrieval fluency and processing abilities) and invested abilities. Conscientiousness’ industriousness and agreeableness’ compassion aspects positively related to most invested abilities. Previous focus on high-level relations obscured understanding of individual differences and their applications...”

[2] “Meta-analytic relations between personality and cognitive ability” ~ by Kevin C. Stanek et al
➥ https://www.pnas.org/doi/10.1073/pnas.2212794120

See also ➥ https://stanek.workpsy.ch/interactivewebtool/

* Personality describes how someone generally thinks, feels, and behaves. It is made up of five major independent traits, per the “Revised NEO Personality Inventory” [AKA: NEO PI-R, or the “Big 5”]:
neuroticism, extraversion-introversion, conscientiousness, openness to experience, and agreeableness.
Stanek and Ones’ dataset also incorporates six aspects and facets [sub-categories], that make up each of the Big 5 traits, like depression and suspiciousness for neuroticism, and politeness and empathy for agreeableness.

Intelligence [cognitive ability] describes how well someone can understand, and apply, information. Intelligence can be split into two kinds. Acquired knowledge, also called invested abilities, refers to specific skills and knowledge. Non-invested knowledge refers to all other cognitive abilities. Like personality, these two types of intelligence can be broken into facets like working memory, pattern recognition, and verbal ability.
The links between these nuanced traits are what make us individuals.

[lestersails]

Originally Posted by bdgWesternMass

I agree with everything you said. My complaint about experts is the tunnel vision it creates. Some experts get so framed in by the context they work in that they can't take in a wider view of solutions.

Really appreciate your post. Might amend it to say "...the tunnel vision it can create." Your next sentence "Some experts..." kind of does that. I am a bit tetchy on this topic as there is an effort underway to universally deride "experts", which are sometimes called "elites". It is related to the idiotic phrase of "alternative facts". This philosophy is extraordinarily dangerous for all of civilization and is a ploy by demagogues to rule with absolute power.

What you said is deserved criticism of a few. There are some behaviors of experts that are really annoying. But if they are shouted down into obscurity, it will be worse. Guaranteed. A revival of the dark ages would not be fun.

[wholybee]

Originally Posted by lestersails

This is interesting - I had not heard of the Rayleigh distribution. The number at the top seems a bit high to me. Currently, the wave period in the Atlantic north of Puerto Rico is about 6 seconds. Given that, one would encounter 10 waves per minute, 600 waves per hour and 14,400 waves per day. That would predict I would, on average, experience 4-5 waves a day that are twice as high as the average. My experience is that I encounter quite a bit fewer than that. Is my math correct? Maybe I am just not a good observer.

It is interesting and I believe it to be correct. I believe I do encounter that. But something I have noticed is that in along line of swells, they step up and down. So, the 2xSHW wave will follow a 1.5xSWH swell, with little So, they don't always look very large. In fact, any swell is very difficult to measure or estimate from a boat. You just never have a reference to see the lowest and highest point at the same time.

[alitaptap]

Well, when all is said an done, since 1991 when I started offshore sailing, I have only ever encountered one wave that I would call “rouge”. About 180NM SSE of Hong Kong at about 3am, under a full moon, we encountered a monster – way more than “2xSWH”. I was at the helm of a 47 foot ferro-cement yacht, returning to Hong Kong from Philippines in December 1996, and the wave looked taller than the mast. Up to that point we had been generally experiencing 4-8 foot waves on the starboard beam, driven by a persistent NE monsoon, Beaufort 6-7.

We had previously discussed (for the sake of discussion only, we thought) what you should do when encountering a rouge wave, and the consensus was: if not breaking then angle 45deg up the face, if breaking then run before it.

When we did encounter the “rogue”, I steered up the face because it was not breaking but then it broke before we reached its zenith. As I turned the wheel to run before the breaking wave it caught the hull broadside – the port spreader touched the lower face of the wave – through the companionway I saw the book-shelf empty itself across the cabin, the skipper who (had positioned himself to rest, starboard-side, perpendicular to the engine housing amidships) found himself standing on the engine housing as we were pushed down the wave face sideways for maybe 200 meters – middle of the night so difficult to judge distance. The wave subsided, the yacht righted herself but we had lost all forward motion so no response from the rudder – I though we had lost the rudder.

Breeze continued, sails filled, forward motion and steerage restored. Skipper pocked his head out of the companionway and asked: WTFWT?

I would wish that somehow I had had 5 five minute warning (a challenge in the 1990s) but . . . we did what we did and I am here to write about it . . .

I have not experienced a repeat episode in the 28 years that have followed, although I have since heard that “rogues” are “1 in every 3000”, on average. My guess is that this particular one was a “super-rouge” . . . what do the math gurus offer for super-rouge statistics?

[GordMay]

Originally Posted by alitaptap

Well, when all is said an done, since 1991 when I started offshore sailing, I have only ever encountered one wave that I would call “rouge”...
... I have not experienced a repeat episode in the 28 years that have followed, although I have since heard that “rogues” are “1 in every 3000”, on average. My guess is that this particular one was a “super-rouge” . . . what do the math gurus offer for super-rouge statistics?

I wouldn’t even begin to know [nor understand] how to calculate/predict the likelihood of a moving vessel, being struck by a [moving] rogue wave, at any given time & place.
Several studies have calculated the probability of rogue wave formation, but, those are generally for static [buoy] locations.

Researchers, from the University of Copenhagen's Niels Bohr Institute, have used AI methods to discover a mathematical model [A], that provides a recipe for how, and not least when, rogue waves can occur. The scientific study [A], has been published in the journal Proceedings of the National Academy of Sciences [PNAS].
I don’t understand, much of the study content.

A 2019 study [1], published in Scientific Reports, that utilized data from the US coastline, from 1994 to 2016, suggests that rogue waves might become less frequent, but more extreme [higher], due to climate change.
They also identify seasonal intensification in rogue waves, with increased rogue wave occurrence, of higher severity, in the winter, than in the summer.

The US National Weather Service [NWS], through NOAA/NCEP, is working on an hourly forecast, for potentially hazardous ocean conditions, called WAVEWATCH III. [2]
(WAVE-height, WATer depth and Current Hindcasting)

[A] “Machine-guided discovery of a real-world rogue wave model” ~ by Dion Häfner et al
➥ https://www.pnas.org/doi/full/10.1073/pnas.2306275120

“"Our analysis demonstrates that abnormal waves occur all the time. In fact, we registered 100,000 waves in our dataset that can be defined as rogue waves. This is equivalent to around one monster wave occurring every day at any random location in the ocean. However, they aren't all monster waves of extreme size," explains Johannes Gemmrich, the study's second author.”

[1] “Seasonal intensification and trends of rogue wave events on the US western seaboard” ~ by A. D. Cattrell et al
➥ https://www.nature.com/articles/s41598-019-41099-z

[2] “Wavewatch III” ~ NWS
➥ https://www.weather.gov/sti/coastalact_ww3


See also:

“Waves” ~ NOAA
➥ https://www.noaa.gov/jetstream/ocean/waves

“Rogue Wave Observations Off the US West Coast” ~ by Burkard Baschek and Jennifer Imai
➥ https://tos.org/oceanography/assets/...-2_baschek.pdf

“... The average likelihood of occurrence is 63 per year in coastal waters and 101 per year in the open ocean. An extrapolation to conditions in the world ocean yields an average likelihood of encountering rogue waves along the main shipping routes in the North Atlantic of 0.8–1.2% per day for rogue waves exceeding 11 m in height ...”

https://tos.org/oceanography/article...-us-west-coast


“Real-world rogue wave probabilities” ~ by Dion Häfner et al
➥ https://www.nature.com/articles/s41598-021-89359-1

“... Overall, it is important to keep in mind that our results relate to the rogue wave probability per wave at one given location in space. For extended periods of time and large objects such as oceangoing vessels, the total risk to encounter a rogue wave will be dramatically higher than the probabilities we present here..."

“Rogue waves: rare but damaging” ~ by Dr Johannes Gemmrich, Prof Burkard Baschek, & Prof Chris Garrett
➥ http://web.uvic.ca/~gemmrich/pdf/GBG...ve_Seaways.pdf

“... The likelihood of occurrence of a rogue wave is commonly calculated with the so-called Tayfun distribution. It yields an occurrence rate of 1 in 1.3 x104 waves for a wave with H/Hs ≥ 2.0. With an average wave period of 7.8 seconds, as reported by buoy 46073, thisis equivalent to a return period of only 28 hours ..."

[Thomas1985]

We were heading in earlier this year when a super cell storm hit. We’re motoring along in 3-5 foot chop when all of the sudden about 20 feet off my starboard side this wall of water appeared.

It came totally broadside over my hard dodger, crashed on top of my cabin, and completely filled the cockpit with water.

It wasn’t even like a wave. It was a completely vertical column of water lol