Michel Olagnon IFREMER Brest, France

1. Rogue Waves: What risks ? Michel Olagnon IFREMER Brest, France

2. Outline • Statistics: What is a rogue wave ? • Definition • Examples • Occurrence probabilities • Reliability: What are the associated risks ? • Small ships • Large ships • Offshore platforms • Humanity: How should we deal with those risks ? • The offshore industry method • The tsunami analogy • Perspectives

3. What is a rogue wave ?

4. What is a rogue wave ?

5. What is a rogue wave ?

6. What is a rogue wave ? A wave of unexpected severity given the prevailing sea conditions at the time it occurs

7. 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.

8. 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 • Twice the significant wave height is thus by no means abnormal

9. What is a rogue wave ? A good excuse when crew failed to install port hole storm covers ?

10. What is a rogue wave ? A 15° roll of the camera angle ?

11. What is a rogue wave ? Just something that happens ?

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

13. 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.

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, for instance, Slepian processes ?

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 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/ 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. 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”.

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

27. 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.

28. 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.

29. 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.

30. 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 ?

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

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

33. 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...

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

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

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

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

38. 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.

39. A small ship usually climbs up the wave... Associated risks

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

41. Flooding of the bridge or control room Risks for small ships

42. Get green water in addition to white on the foredeck... Risks for larger ships

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

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

45. Risky areas where not to sail ?

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

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

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

49. 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 keepthe metocean risk at that relative level. How the offshore industry deals with the risk.

50. Design methods were questioned for a while, because of the possibility of some phenomenon different from the ones that had been used to derive the 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. How the offshore industry deals with the risk.