2. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Michel Olagnon IFREMER Brest, France Anne Karin Magnusson MET.NO Bergen, Norway Spectral parameters to characterize the risk of rogue waves occurrence in a sea state

3. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Problem: If some characteristic parameter varies only at the instant of a rogue wave, then it is of no practical use for prediction.

4. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Findings (Isope 2004): Parameters that exhibit sensitivity: 1. Remain within the normal range of aleatory variations. 2. Exhibit a high rate of false alarms.

5. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Conclusions (Isope 2004): It is unlikely that examination of a single parameter at a single time can provide warnings of increased risks of rogue waves. One should thus: – Find out criteria based on combined occurrence of several characteristics, probably including directional ones, or – Find out criteria based on the process or the time-history of characteristics over a whole storm duration.

6. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Underlying idea: “Roguewavy” storms Some storms may be more rogue-wave prone than others. It is a reasonable assumption, since for instance, -damage was also reported on some BP platform on New Year 95, -in 2 cases out of 6 storms where damages were reported (Ersdal and Kvitrud), damage was observed at two different locations

7. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Best candidates parameters related to theoretical explanations put forward for rogue waves occurrence: Benjamin-Feir instability indices Or related to some recurrent meteorological phenomenon: running fetch conditions

8. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Benjamin-Feir instability indices BFI, defined as some measure of steepness divided by some measure of spectral bandwidth. Results reported in Isope paper give little hope … yet it might be because of poor bandwidth estimator BFI Distribution of 200.000 waves Distribution of waves with Crx/Hs > 1 and Crx/Hs > 1.25

9. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Benjamin-Feir instability indices In theory, many authors use a measure of spectral bandwidth based on half-power, i.e. focused on the spectral peak. As Goda (1980) recognizes himself for Qp, the measures of spectral bandwidth that we used up to now are based on spectral moments that are sensitive, at least to some extent, on the tail of the spectrum. We thus used relative height of the peak as a measure of spectral bandwidth.

10. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Benjamin-Feir instability indices Relative height of the peak S(fp)fp/m0 has several advantages: it is not significantly affected by the cut-off frequency or the imperfect knowledge of the shape of the spectrum tail; It can be robustly estimated using weighted averages of the peak and of its 2 neighbors; It allows to define in the same manner a spectral front bandwidth using the restriction of m0 to [0, fp]

11. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Benjamin-Feir instability indices Robust BFI index as defined in Isope paper

12. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Benjamin-Feir instability indices Normalized height bandwidth Crx/Hs

13. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Benjamin-Feir instability indices The use of another measure of bandwidth restores the initial variability of the estimators, but does not change the overall behavior of the index during the storm. We might want to base the index on spectral front bandwidth only as can be seen on the next slide, but note the false alarm at the start of the graph.

14. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Benjamin-Feir instability index based on spectral front bandwidth

15. BREST 2004/10/20-21-22 ROGUE WAVES 2004 History of bandwidth Since no relation was found between steepness and rogue wave occurrence (Van Iseghem & Olagnon, Rogue Waves 2000), we might want to concentrate on bandwidth rather than on the composite BF instability indices. Since running fetch situations might be at the origin of “roguewavy” storms, they might be reflected as changes in the spectral shape and especially the front bandwidth.

16. BREST 2004/10/20-21-22 ROGUE WAVES 2004 History of bandwidth

17. BREST 2004/10/20-21-22 ROGUE WAVES 2004 History of front bandwidth

18. BREST 2004/10/20-21-22 ROGUE WAVES 2004 History of bandwidth On this particular storm, there does not seem to be much to say about the history of bandwidth, apart from its stability during the storm. -> it is necessary to compare histories for a number of storms. We went to the Frigg data base, approximately 8 years of 3-hourly records, and took every storm for which we had data.

19. BREST 2004/10/20-21-22 ROGUE WAVES 2004 History of bandwidth Black line: Hs Black dots: Cmax Blue lines: Bw Green lines: Bwf Red lines: Asymetry

20. BREST 2004/10/20-21-22 ROGUE WAVES 2004 History of bandwidth

21. BREST 2004/10/20-21-22 ROGUE WAVES 2004 Concluding remark We could not find anything in the histories of the spectral parameters that would distinguish “roguewavy” storms from common ones. -> We may even question the validity of assuming that “roguewavy” storms can be characterized from their spectral parameters. -> We may also question the validity of assuming that rogue waves have more chances to occur when some conditions are met.