What is a Rogue Wave The Design Wave

What is a Rogue Wave ? The “Design Wave Philosophy’’ Calculation of the design wave Wave forces on semi-submersible platforms Wave forces and bending moments in FPSO-ships Platform movements in large waves Examples of heavy weather damage ***** What is a Rogue Wave ? ***** Why, where and when ? Shall we design against Rogue and Freak Waves ? What can a platform master do against Rogue and Freak Waves ? Remote-sensing of sea conditions Search And Rescue and emergency operations Decision making in an emergency Trondheim Tekniske Fagskole

What is a rogue wave ? Trondheim Tekniske Fagskole

What is a rogue wave ? • The various definitions • What are the problems for design ? • What are the problems for operations ? • What are researchers working on ? Trondheim Tekniske Fagskole

What is a rogue wave ? Let’s start with “What is a Wave ? ” Trondheim Tekniske Fagskole

What is a rogue wave ? In practice, you know it was a rogue wave once you saw it. Trondheim Tekniske Fagskole

What is a rogue wave ? A good excuse when crew failed to install port hole storm covers ? Trondheim Tekniske Fagskole

What is a rogue wave ? A 15° roll of the camera angle ? Trondheim Tekniske Fagskole

What is a rogue wave ? Just something that happens ? Trondheim Tekniske Fagskole

What is a rogue wave ? In physics and/or statistics, there are several definitions: Trondheim Tekniske Fagskole

What is a rogue wave ? Some say a wave that is more than twice the significant wave height, but that may not be a reliable definition. Trondheim Tekniske Fagskole

What is a rogue wave ? If significant wave height was constant and equal to 10 meters, one would encounter a wave of: • 18. 5 m every 3 hours • 21. 5 m every day • 25. 0 m every month • 27. 5 m every year • 30. 0 m every 20 years • 31. 5 m every 100 years • 33. 1 m every 1000 years • 34. 8 m every 10000 years The maximum in one day is also the maximum in the 20 minutes or 3 hours surrounding it, so twice the significant wave height is by no means abnormal: it happens every day ! Trondheim Tekniske Fagskole

What is a rogue wave ? One of those waves in a [large] set of a given height that make the set more numerous than it should be from conventional theory. Trondheim Tekniske Fagskole

What is a rogue wave ? From the figures above, theory states that there should be 500 waves above 2 Hs in a year. If one measures 1000 of them, they are rogue waves: about 500 freak and 500 normal extremes and of course we can’t distinguish easily which are which. Trondheim Tekniske Fagskole

What is a rogue wave ? A wave of unexpected severity given the prevailing sea conditions at the time it occurs Trondheim Tekniske Fagskole

What is a rogue wave ? A wave of unexpected severity given the prevailing sea conditions at the time it occurs. Unexpected: A good deal of damage can be avoided if those exposed are fully aware there and then. Severity: Steepness, Front steepness and other characteristics may be more damaging than mere height. Trondheim Tekniske Fagskole

What is a rogue wave ? The famous “Draupner wave” Reconstructed water surface elevations over a 1000 m span, from T-30 s (blue) to T (red) for the New Year Wave. Trondheim Tekniske Fagskole

Where does it come from ? Georg tells us (Lindgren, 1970) that if it comes from the normal gaussian process, it is a wave that looks in retrospect like the autocorrelation function of the water surface elevation signal. Sverre (Haver, 2000) states that it is a freak wave if it represents an outlier when seen in view of the population of events generated by a piecewise stationary and homogeneous second order model of the sea surface process, otherwise “only” rogue. Miguel and Al (Onorato & Osborne, 2005) tell us that according to the Schrödinger equation, it sucks energy from its neighbors and thus it is a freak invader from an outer statistical population. Trondheim Tekniske Fagskole

It is nice to be able to recognize a Freak or Rogue Wave in the statistics after it occurred. . . For various reasons, a much nicer ability would be that of being successful when speculating that approaching waves are not rogue waves, or even that they are. ‘‘ When a woman at a party asks me what I do, I invariably say «I ’m just a speculator. » The encounter ’s over. The only worse conversation stopper is «I ’m just a statistician. » ’’ Victor Niederhoffer, The Education of a Speculator, Wiley, 1997 Trondheim Tekniske Fagskole

Where does research stand with regards to rogue waves : recent studies. A wave is coming. In order to predict its rogueness, should we use quasi-deterministically the non-linear Schrödinger equation or merely on the statistics derived from, for instance, Slepian processes ? Trondheim Tekniske Fagskole

Discriminating questions: 1. Do we have more high waves than our conventional long-term statistical models predict ? 2. When we do have high waves, do other characteristics of the whole storm, of the sea state, or of the few previous waves look different from those of other storms, sea states, or sets of a few consecutive waves ? 3. Especially, do characteristics related to theoretical deterministic constructions of rogue waves exhibit statistical evidence of predictive power ? Trondheim Tekniske Fagskole

Database: 20 years of data available from Frigg QP platform in the North Sea Trondheim Tekniske Fagskole

Database: 1979 -1989: mostly 3 -hourly measurements, many time-series available. 1991 -1999: mostly 20 -minute statistics, only reduced parameters Trondheim Tekniske Fagskole

Database: Hmax and H 1/3 retrieved preferably from the time-series when available (7%), from the statistics elsewhen. For storms, missing zero-crossing period information was derived from T 1/3 (9. 4%) and drawn from the empirical H 1/3 -Tz distribution when no information at all was available (1. 7%). The final database consists of 265147 statistical records, it is thus equivalent to nearly 9 years of continuous measurements. Trondheim Tekniske Fagskole

EKOFISK, operated by Conoco. Phillips Laser measurements at the time of the ”Varg incident” Norway North Sea Trondheim Tekniske Fagskole

Storm “freakiness” We (Olagnon & Prevosto, 2005, Olagnon & Magnusson, 2004) tried to investigate the widest time-scale: the whole storm. Especially, the maximum wave expected in a storm is a more useful forecast to seafarers than the maximum wave in some particular 1 - or 3 -hour duration sea state of that storm. It may thus appear natural to relate the maximum wave in a storm to the maximum predicted H 1/3 in that whole storm rather than to the prevailing H 1/3 at the precise instant of Hmax. Trondheim Tekniske Fagskole

Storm “freakiness” Storms are defined as durations > 12 hours with H 1/3 > 5 m Trondheim Tekniske Fagskole

Storm “freakiness” For each of the 187 identified storms, 1000 random simulations were made using the database statistical parameters and a Jonswap wave spectrum with gamma=3. Second order correction was then applied to all computed Hmax values. Freakiness of a storm is defined as the quantile rank of that storm’s observed Hmax/ H 1/3 max in the corresponding distribution over the 187 actual storms (empirical) and over the 187000 simulated storms (2 nd order theory). Trondheim Tekniske Fagskole

Storm “freakiness” QQ-plot of Hmax/ H 1/3 max = blue dots. H 1/3 = green dots Hmax = red dots Apart from a very few ones, storms are less “freaky” than 2 nd order theory would predict. Trondheim Tekniske Fagskole

Storm “freakiness” QQ-plot of Hmax/ H 1/3 max = blue dots. Mean storm BFI = red dots Benjamin-Feir instability at the time-scale of a storm can only be very weakly related to its “freakiness”. Trondheim Tekniske Fagskole

Storm “freakiness” Expectations based on experience rather than theory would be definitely too low: An explanation for so many freak waves reported ? Trondheim Tekniske Fagskole

Medium term: the sea state time scale Freaky sea states ? Nerzic & Prevosto (98) proposed a Weibull-Stokes model for the distribution of maximum waves Hmax in a sea state, conditional to H 1/3 and Tz of the sea state. They used a 7% subset of the Frigg database, without any special emphasis on extremes, to derive their model. We use the full database to study how the model performs with long-term extremes. Trondheim Tekniske Fagskole

Distribution of maximum wave heights No underestimation by model ! Again, an appropriate transformation, limited to taking into account standard non-linearities up to second order, is sufficient to explain the observed extremes Comparison of empirical distribution of Hmax with Nerzic & Prevosto model for H 1/3>5 m. Trondheim Tekniske Fagskole

Kurtosis and Benjamin-Feir instability “When a similarity connection is achieved between two objects to 20 decimal places, the greater will move to the lesser” A. E. Van Vogt, The World of Null-A, 1945 Even though conventional Hmax models seem acceptable for long-term distributions, it might be possible to predict when the extremes in the distribution are most likely to occur : at those times, the similarity between the actual world and theoretical deterministic world of non-linear Schrödinger equation may be such that we can apply the rules of the latter for some limited time-space window. In that latter world, extremes are governed by Benjamin-Feir instability. Trondheim Tekniske Fagskole

Kurtosis and Benjamin-Feir instability, i. e. the ratio of steepness to bandwidth, and signal kurtosis are strongly related (Mori & Janssen 2005). . . … but are kurtosis (BFI) excursions away from regular values the cause of freak waves, or a mere consequence of their observation ? In other words, is kurtosis (BFI) a predictor or only a detector ? Trondheim Tekniske Fagskole

Kurtosis and Hmax/ H 1/3 exhibits a clear relationship to kurtosis. . . Trondheim Tekniske Fagskole

Kurtosis and Hmax …but if “kurtosis” is computed with removal of the largest wave’s timeduration, the relationship can no longer be seen. Trondheim Tekniske Fagskole

What value in Met’Offices warnings ? Mostly based on Benjamin-Feir instability, and we just saw not conclusive. Difficult to assess how good the chosen omens are. Difficult to find volunteers to go into the worst areas of storms and validate the forecasts. . . Trondheim Tekniske Fagskole

What is there to be seen a few waves ahead ? Instantaneous Benjamin-Feir instability index: nothing. H H 1/3 BFI Index Trondheim Tekniske Fagskole

What is there to be seen a few waves ahead ? Irregularity factor ( # of crests / # up zero crossings ): nothing. H H 1/3 Irr. Fact. Trondheim Tekniske Fagskole

What is there to be seen a few waves ahead ? Steepness: let’s have a closer look. H H 1/3 Steepness Trondheim Tekniske Fagskole

What is there to be seen a few waves ahead ? Crest H 1/3 Steepness H H 1/3 Steepness NOTHING AGAIN ! Trondheim Tekniske Fagskole

Conclusions so far • Extreme waves are not found more frequently than conventional long-term distribution models predict. • When extremes are observed, no abnormal characteristic can be found in non-directional parameters at the time scale of the whole storm, of the sea state or of a set of a few consecutive waves. There is nothing more in rogue waves than what we can see in the statistics. Trondheim Tekniske Fagskole

Associated risks A small ship usually climbs up the wave. . . Trondheim Tekniske Fagskole

Risks for small ships …but may get rolled over or caught from the back. Trondheim Tekniske Fagskole

Risks for small ships Flooding of the bridge or control room Trondheim Tekniske Fagskole

Risks for larger ships Get green water in addition to white on the foredeck. . . Trondheim Tekniske Fagskole

Risk for larger ships …and water weighs a lot ! “for a while until they got it squared away, we launched them sailing backwards…” Trondheim Tekniske Fagskole

Risks for larger ships Breaking of the structure due to sagging or hogging, in the trough or on the crest. Trondheim Tekniske Fagskole

Risky areas where not to sail ? Trondheim Tekniske Fagskole

Risky areas ? Only areas where there are more ships at risk. . . Trondheim Tekniske Fagskole

The wrong place at the wrong time Except if you are named Hosukai, of course. . . Trondheim Tekniske Fagskole

Offshore platforms Cannot avoid bad weather areas. The deck has to be high enough to let the waves pass by in the “transparent” part. Trondheim Tekniske Fagskole

How the offshore industry deals with the risk. Reliability targets of 10 -4 yearly. On one hand, 10000 years from now, the North Sea may well be a desert, on the other hand, risks associated with waves are at least one order of magnitude lower than those of blast, fire, human errors, etc. The idea is to keep the metocean risk at that relative level. Trondheim Tekniske Fagskole

How the offshore industry deals with the risk. Design methods were questioned for a while, because of the possibility of some phenomenon different from the ones that had been used to derive theories that led to design values. Experience and studies have shown that there was no problem with those theories onto the 10 -4 limit. To some extent, the shipping industry uses a similar approach, but less openly. To the shipowner, the risk of a rogue wave is an acceptable one, as we would say for the risk of a car accident when driving to work. Trondheim Tekniske Fagskole

The tsunami analogy When you go to Hawaii, there is no sign, to be seen on the real estate near the beaches, that they could be washed away by a tsunami at any moment. Yet, if a tsunami occurs in Hawaii, there will be loss of property, but likely no loss of lives: those subject to the risk are properly trained, know the ominous tokens and what to do then. Rogue waves can be considered in the same fashion: they may happen, one should just train not to be caught unprepared in that case. Trondheim Tekniske Fagskole

The 3 Rules for survival: Training, training and training What should you watch for ? • Complex, multiple low pressure meteorological systems • Pressure lows traveling at the same speed as the waves they create (“running fetch”) • A sea state easier to handle than could have been expected from the wind’s strength • The time when the storm’s maximum is close ahead • The time when a cold front is close ahead Trondheim Tekniske Fagskole

Perspectives • Design: Rogue waves understanding is now far from being a priority, but they do occur (as statistically expected), and should not be neglected. • Forecast (the priority): No automatic rules, but … it may not be impossible to train super-expert meteorologists to estimate the risks with good chances of success. NOT A MET’OFFICE ACCEPTED PRACTICE HOWEVER ! Trondheim Tekniske Fagskole

Freak events do happen The death of Aeschylus was not of his own will; […]. Having come out of the place where he lived in Sicily, he sat under the sun. An eagle carrying a tortoise happened to fly above him. Mistaken by the whiteness of his bald head, it let the tortoise fall on to it, as it would have done to a stone, in order to break it and eat its flesh. The blow took his life away from the poet who first gave the most perfect form to tragedy. Valerius Maximus, Factorum ac dictorum memorabilium, IX 12, ca. 30 AD THAT’S LIFE ! Thank you. Trondheim Tekniske Fagskole