The “Design Wave Philosophy’’ Calculation of the design wave

1. Why, where and when ? 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

2. Why, where and when ?

3. Why, where and when ? • ***** Theories ***** • Statistics of occurrence • Findings as of now • Predictive value of indexes

4. Waves with shorter wave-lengths travel slower. If longer ones (usually higher also) start later on, they catch up with the smaller ones and superimpose. Combination of wave trains with different wave-lengths

5. Combination of wave trains with different wave-lengths

6. The Dysthe form of the non-linear Schrödinger equation When wave trains catch up and some conditions are met, they may interact and make bigger waves than mere superimposition. The non-linear Schrödinger equation describes how the envelope “breathes” in space and time, the same group holding at times 5, 6, 7,… waves and at other times only one or 2.

7. The Dysthe form of the non-linear Schrödinger equation • 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

8. Complex, multiple low pressure meteorological systems The time when a cold front is close ahead Combination of wave trains from different directions

9. Why, where and when ? • Theories • ***** Statistics of occurrence ***** • Findings as of now • Predictive value of indexes

10. High Low Risky areas where not to sail ?

11. Only areas where there are more ships at risk... Risky areas ?

12. Why, where and when ? • Theories • Statistics of occurrence • ***** Findings as of now ***** • Predictive value of indexes

13. Where does it come from ? NORMAL: 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. SOMETIMES NORMAL, SOMETIMES NOT: 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. COMPLEX OUTER SPACE: 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.

14. 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

15. 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 rely on the statistics derived from quasi-linear theory ?

16. 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 ?

17. Database: 20 years of data available from Frigg QP platform in the North Sea

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

19. Database: Hmax and H1/3 retrieved preferably from the time-series when available (7%), from the statistics elsewhen. For storms, missing zero-crossing period information was derived from T1/3 (9.4%) and drawn from the empirical H1/3-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.

20. EKOFISK, operated by ConocoPhillips Laser measurements at the time of the ”Varg incident” Norway North Sea

21. 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 H1/3 in that whole storm rather than to the prevailing H1/3 at the precise instant of Hmax.

22. Storm “freakiness” Storms are defined as durations > 12 hours with H1/3> 5m

23. Storm “freakiness” For each one of the 187 identified storms, 1000 random simulations were made using the database statistical parameters. 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/ H1/3max in the corresponding distribution over the 187 actual storms (empirical) and over the 187000 simulated storms (2nd order theory).

24. Storm “freakiness” QQ-plot of Hmax/ H1/3max = blue dots. H1/3 = green dots Hmax = red dots Apart from a very few ones, storms are less “freaky” than 2nd order theory would predict.

25. Medium term: the sea state time scaleFreaky sea states ? Nerzic & Prevosto (98) proposed a Weibull-Stokes model for the distribution of maximum waves Hmax in a sea state, conditional to H1/3 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.

26. 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 H1/3>5 m.

27. 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 the 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.

28. Kurtosis and Benjamin-Feir instability 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 ?

29. Kurtosis and Hmax Hmax/ H1/3exhibits a clear relationship to kurtosis...

30. Kurtosis and Hmax …but if “kurtosis” is computed with removal of the largest wave’s time-duration, the relationship can no longer be seen.

31. What is there to be seen a few waves ahead ? Instantaneous Benjamin-Feir instability index: nothing. H H1/3 BFI Index

32. What is there to be seen a few waves ahead ? Irregularity factor ( # of crests / # up zero crossings ): nothing. H H1/3 Irr. Fact.

33. What is there to be seen a few waves ahead ? Steepness: let’s have a closer look. H H1/3 Steepness

34. What is there to be seen a few waves ahead ? Crest H1/3 Steepness H H1/3 Steepness NOTHING AGAIN !

35. 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.

36. Why, where and when ? • Theories • Statistics of occurrence • Findings as of now • ***** Predictive value of indexes *****

37. Storm “freakiness” QQ-plot of Hmax/ H1/3max = 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”.

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

39. Mostly based on Benjamin-Feir instability, and we just saw not conclusive. What value in Met’Offices warnings ? 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...

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

41. 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. The tsunami analogy

42. 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 All-time awareness

43. 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 !