Michel Olagnon IFREMER Brest, France

1. Spectral parameters to characterize the risk of rogue waves occurrence in a sea state Michel Olagnon IFREMER Brest, France Anne Karin Magnusson MET.NO Bergen, Norway

2. Problem:If some characteristic parameter varies only at the instant ofa rogue wave, then it is of no practical use for prediction.

3. Findings (Isope 2004): Parameters that exhibit sensitivity: 1. Remain within the normal range of aleatory variations. 2. Exhibit a high rate of false alarms.

4. 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.

5. 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

6. 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

7. 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 Distribution of 200.000 waves Distribution of waves with Crx/Hs > 1 and Crx/Hs > 1.25 BFI BFI

8. 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.

9. 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]

10. Benjamin-Feir instability indices Robust BFI index as defined in Isope paper

11. Benjamin-Feir instability indices Normalized height bandwidth Crx/Hs

12. 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.

13. Benjamin-Feir instability index based on spectral front bandwidth

14. 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.

15. History of bandwidth

16. History of front bandwidth

17. 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.

18. History of bandwidth Black line: Hs Black dots: Cmax Blue lines: Bw Green lines: Bwf Red lines: Asymetry

19. History of bandwidth

20. 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.