The technical term is "Rogue wave". You can find numerous paper on their characterization. You can check this review even if it is somewhat dated.

http://www.researchgate.net/publication/234151195_Oceanic_Rogue_Waves/file/3deec527a04af776be.pdf

Article Oceanic Rogue Waves

The technical expression is "freak or rogue" I choose to use "freaque" that combined both. Yes, the review by Dythe et al. is good but does not answer my question about measurement: can it be measured out there in the real ocean? Nonlinear physics and mathematics are not measurement!

It is a problem that we do not agree on what a freaque wave is (let alone the nomenclature). If a freaque wave is a rare wave, then these are measured routinely. I think a more interesting  question is this: what makes rare wave events less rare? And can we take what is measured and make a direct connection to a particular generation theory (i.e. modulation instability, wave-current interaction)? For example, is there something within a time series of a rare wave event that might be a signature of modulation instability or linear dispersive coherence or anything else? What can we learn from single-point time series?

Good point, Clarence, we do not agree on what a freaque wave is mainly because we don't have enough real data to deal with it. You ask what can we learn from single-point time series. That's the key. We can NOT! Single-point time series is not real ocean. For over 70 years, we idealized our understanding of ocean waves by the single point time series and spectrum analysis. The real ocean wave processes out  there remains unexplored. When I asked about measuring freaque waves, I was not at all thinking about single-point time series measurement. We are way into 21st century now, we should not still clinging to the 20th century leftovers!

Hi Paul. It's nice to see you out there stirring up the debate and trying to inspire people. I never told you that, but it is after your talk at a WISE meeting that I looked into stereo video data, and this has been a very nice adventure so far with Alvise Benetazzo and Francesco Fedele. In particular we are now able to separate linear from nonlinear contributions to the wave field.... something you cannot do with a point time series.

The shape of the extreme waves has some nice link to the correlation of the sea surface elevation. Instead of asking whether we can observe special waves that are particularly dangerous, my take on the issue is: are the waves at sea (including the extremes) any different than predicted by a random draw using linear theory with a second order correction (e.g. Tayfun 1981)?

My colleagues that work on ocean engineering tell me that no, the extremes are all in that distribution and that is enough, and by the way the waves with H > 2.2 Hs are not relevant for the extreme value analysis of things like an oil platform (the relevant waves are the H < 2.2 Hs but in very big storms, hence it is most important to get the statistics of storms correct, not so much the statistics of individual waves, for which Tayfun is OK).

Now I also have some other colleagues that try to find special cases of waves in currents (e.g. Janssen and Herbers) or wind blowing over waves (e.g. Kharif and Touboul), where the wave statistics may be different.

Thank you so much, Fabrice, for taking the time answering my question on Research Gate. I'm always wholeheartedly admiring your seemingly exhaustible energy and productivity. I have read your impressive work with Alvise and Francisco. I think that's the direction wave measurement should follow. Regarding measuring freaque waves, however, we still don't know if the area carried by the current stereo measurement is sufficient to accommodate the dynamic movements of a freaque wave since we don't know where, when, how, and why a freaque wave occurs. And we can not define the most perplexing aspect of freaque waves, the unexpectedness. We need more measurements on what is really happening out there, and it is widely open! 

This is a very nice - nearly philosophical - question.

As I have understood your definitions, you name a

* freak or rogue (freaque) wave a 'dangerous' wave and an

* extreme wave a wave which is higher than 2 (or so) * Hs.

We measure waves with Datawell buoys, ADCP from Nortek and RDI, platform-fixed single beam radars and with marine X-band radars. We currently start to try to fumble extreme waves (following your definition) out of our time series. The task now is to discriminate between outliers and extreme waves (see discussion https://www.researchgate.net/post/Does_anybody_know_about_the_discrimination_of_extreme_ocean_waves_and_outliers_derived_from_in_situ_buoy_or_radar_gauge_platform_measurements)

We are now at the point where we try to find features indicating the shape differences between outliers and extreme waves. Aim is a fully automated piece of software.

So we still stick in the era of the 20th century!

If Paul asks for a setup and method for a global approach, there is a group working with satellite SAR image data (http://www.dlr.de/eoc/en/desktopdefault.aspx/tabid-5426/10518_read-23261/)

Beside the advantage of the huge spatial coverage there are up to now two main disadvantages:

* the poor temporal coverage, as a satellite needs some time to come back to the same area (in the order of days)

* the methods are yet not validated.

Therefore my guess is, that the 20th century still will remain our companion for some time.

Nevetheless 'the community' could win some effort by a structured archive of wave raw data and a set of well accepted methods to determine extreme waves from the time series.

For freaque waves (if I understood it right, that the meaning is dangerous waves) the future vision may is not that clear.

Also a nice paper:

Christou, M., and K. Ewans,

Field Measurements of Rogue Waves,

JPO Vol. 44, pp. 2317 - 2335, 2014.

Thanks Christian, for your thoughtful answer to my question.  I am excited to hear about your many enviable measurements. I assume that most of your measurement will resulting in single point time series data.  I agree that it is important to discriminate between outliers and extreme waves. I presume that they are both greater than 2 times the Hs, What I am wondering is if they are appearing to be like Draupner-type waves. I know the draupner-type waves are always greater than 2Hs. But I am not certain that any data with Wave greater than 2Hs will be similar to the Draupner-type waves. Somehow I have no problem regarding a Draupner-type as freaque waves, But I have difficulty to think all wave data with wave greater than 2Hs as automatically a freaque wave. 

Dear Paul,

you are definitely right, the 2 * Hs criterion is not sufficient. This is a very rough data sieve. So following set theory all Hi > Hsj * 2 are obviously all in the set 'extreme waves' but only a subset of freaque waves are extreme waves.

As I mentioned in the discussion

https://www.researchgate.net/post/How_does_one_define_unexpectedness_of_the_occurrence_of_an_unexpected_freak_wave_in_the_ocean

my feeling is, that we still do not know what a freaque wave is. So as it often happens in our business: from one question more questions arise. Here are mine:

* What is a freque wave?

* Is it a dangerous potentially wave?

* Is it a wave which has caused an incident?

* Is it something else?

* Which features characterise a freaque wave, there are some candidates: steepness (assymmetry?) , height (crest, trough) , kurtosis, ...

* Can a wave field be (potentially) 'freaquey'?

* So if we still may not know, what a freaque wave is (or is there anybody here?), how we could calculate its probability of occurence at a specified point (area?) and time (period)?

* What is unexpectedness? a function of probability?

* How to consider spectra and directional spectra (encounter spectra in case of shipping)?

* How remote sensing (ground based, satellite based, ship based) could help?

* How numerical (spectral and operational) models - as from my knowledge they base on linear wave theory with some more or less working nonlinear 'add ons' - could help? Means, if there is a more frequent occurence of suspicious (extreme or freque) waves for a certain type of spectra in the measurement data, a model could act as a harazardous wave warning system.

* If all these and more questions are answered: can an integrated and fully automated system be implemented?

Dear Christian,

I am thrilled that you ask more questions to my questions. Here let me try to answer some of yours:

A freaque wave is an unexpected large wave, we don’t know where, when, how or why it happens, it could be dangerous because mariners were caught by surprise, unprepared. My feeling is that it happens in the world ocean somewhere, sometimes, all the time. But mostly there’s no one around to encounter it, so did it happen? Of course it did, but we don’t know, so while it is being called rare, it is not necessarily so. I don’t think we can find answer from the conventional spectrum analysis of single point measurement. That’s why I asked the first question. I don’t know how to quantify unexpectedness, that’s my other question!

Dear Paul,

So my impression is, if one would like to come to a practical approach, unexpectedness must be translated (or boil down) to probability. Nevertheless, for freaque have we still miss the features to describe a freaque have or a freaque wave field (the sum of waves in a certain area and time)

The question must be answered in between the triangle of remote sensing - in situ - models.

We will need generations of researchers and a global community of operationally measuring institutions to answer your question and a lot of money for the satellites.

I assume that you mean 'Freak' or rogue wave, which as Christian pointed out is the increased sea surface amplitude produced, at one point in time, by at least 2 or more discrete wave trains, with wave periods that are likely to produce both constructive and destructive interference and in an area with deep enough water not to inhibit/attenuate the particle motion. To be able to measure them directly will require constant monitoring of the sea surface when conditions are favorable. 

There is an approach to reconstruct the surface elevation from image sequences acquired by platform based marine X-Band radars, which have a radius of about 1 km to 2 km:

http://www.oceanwaves.de/download/PDF/DETECTION_SINGLE_WAVES.pdf

There are still some doubts about the method, as validation is a difficult task as always, if one tries to validate a surface measurement by in situ point measurements.

Have a look at this: 

http://www.thebrahanproject.com/

This was organised by us and has the ability to monitor up-to 200 km.

Christian, I am a little reluctant to think of unexpectedness in terms of probability. Undoubtedly they are related to some extent. But probability generally applies to expected things. I can't visualize what the probability looks like for unexpected things. That's why I asked the question!