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Journal of Offshore Mechanics and Arctic Engineering | Volume 135 | Issue 3 | research-article
Research Papers: Ocean Engineering

The Andrea Wave Characteristics of a Measured North Sea Rogue Wave

[+] Author and Article Information
Anne Karin Magnusson

Norwegian Meteorological Institute,
Bergen, 5007Norway
e-mail: anne.karin.magnusson@met.no

Mark A. Donelan

University of Miami,
Miami, FL 33149-1098 
e-mail: mdonelan@rsmas.miami.edu

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 28, 2012; final manuscript received February 8, 2013; published online June 12, 2013. Assoc. Editor: R. Cengiz Ertekin.

J. Offshore Mech. Arct. Eng 135(3), 031108 (Jun 12, 2013) (10 pages) Paper No: OMAE-12-1062; doi: 10.1115/1.4023800 History: Received June 28, 2012; Revised February 08, 2013
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Wave profiles have been measured with a system of four Optech lasers mounted on a bridge at the oil production site Ekofisk in the central North Sea since 2003, operated by ConocoPhillips. A double rogue wave was measured on Nov. 9, 2007 in a storm crossing the North Sea and named Andrea following a forecasting procedure between the Norwegian Meteorological Institute and ConocoPhillips. This wave, named here the “Andrea wave,” is comparable in height and characteristics to the well known Newyear wave (or Draupner wave) measured in 1995 by Statoil. Front steepness is higher. That the same profile is measured by all four lasers is a good indication that the shape of the wave has been captured correctly, but one may still ask if this crest is that of blue, green, or white water. That is, how much of the height is related to presence of foam or sea spray? We attempt to answer this using the information of intensity of the return signals, which has been related to wave breaking and sea spray in recent studies by Toffoli et al. (2011, “Estimating Sea Spray with a Laser Altimeter,” J. Atmos. Oceanic Technol., 28(9), pp. 1177–1183). Measurements of the average intensity of the return signal do not indicate presence of sea spray in the incoming part of the wave, but high intensity of return after the passage of the crest indicates presence of sea spray or foam on the parts of the waves exposed to winds. Cameras following the sea surface at measuring position with information on the return signal as given here would most probably increase our understanding of what is measured. Exceedance probability of crests and heights show a deviation from the second order distribution as given by Forristall (2000, “Wave Crests Distributions: Observations and Second-Order Theory,” J. Phys. Oceanogr. 30(8), pp. 1931–1943) for the one percent highest waves in an apparently stable 3 h period including the Andrea wave. The deviation already starts at crest/Hs factors around 1.0.
Copyright © 2013 by ASME
Topics: Lasers , Waves , Seas , North Sea
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References

1
Jenkins, A. D., Magnusson, A. K., Hagen, Ø., Bitner-Gregersen, E., Monbaliu, J., and Trulsen, K., 2002, Met. No Research Report No. 138, Bergen, Norway.
2
Magnusson, A. K.Bitner-Gregersen, E., and Nieto-Borge, J. C., 2003, “Analysis of Extreme Waves in the Maxwave Database,” Proceedings of the MAXWAVE Final Meeting, Geneva, Switzerland.
3
Bitner-Gregersen, E., and Magnusson, A. K., 2004, “Extreme Events in Field Data and in Second Order Wave Model,” Proceedings of the Rogue Waves 2004 Workshop, M.Olagnon and M.Prevosto, eds., Brest, France, Oct. 20–22.
4
Krogstad, H. E., Barstow, S. F., Mathiesen, L. P., Lønseth, L., Magnusson, A. K., and Donelan, M. A., 2008, “Extreme Waves in the Long-Term Wave Measurements at Ekofisk,” Proceedings of the Rogue Waves 2008 Workshop, M.Olagnon and M.Prevosto, eds., Brest, France, Oct. 13–15, pp. 23–33.
5
Kharif, C., Pelinovsky, E., and Slunyaev, A., 2009, Rogue Waves in the Ocean. Advances in Geophysical and Environmental Mechanics and Mathematics, Springer-Verlag, Berlin-Heidelberg.
6
Haver, S., and Anderson, O. J., 2000, “Freak Waves: Rare Realisations of a Typical Population or Typical Realisations of a Rare Population?” Proceedings of the 10th International Offshore and Polar Engineering Conference and Exhibition, ISOPE2000, Seattle, May 28–June 2.
7
Skourup, J. K., Andreassen, K., and Hansen, N. E. O., 1996, “Non-Gaussian Extreme Waves in the Central North Sea,” Proceedings of the 1996 OMAE, Vol. I, Part A., ASME, New York.
8
Mori, N., Liu, P. C., and YasudaT., 2002, “Analysis of Freak Wave Measurements in the Sea of Japan,” Ocean Eng., 29(2002), pp. 1399–1414. [CrossRef]
9
Magnusson, A. K., 2008, “Forecasting Extreme Waves in Practice,” Proceedings of the Rogue Waves 2008 Workshop, M.Olagnon and M.Prevosto, eds., Brest, France, Oct. 1–15, pp. 261–281.
10
Hjorteland, K. M., Mes, J., and Magnusson, A. K., 1999, “Ekofisk Observed Weather Compared With Weather Predictions,” Proceedings of the Offshore Technology Conference in Houston, TX, May 3–6, Paper No. OTC 10768.
11
Toffoli, A. A., Babanin, V., Donelan, M. A., Haus, B. K., and Jeong, D., 2011, “Estimating Sea Spray With a Laser Altimeter,” J. Atmos. Oceanic Technol., 28(9), pp. 1177–1183. [CrossRef]
12
Reistad, M., Breivik, Ø., Haakenstad, H., Aarnes, O. J., Furevik, B. R., and Bidlot, J.-R., 2011, “A High Resolution Hindcast of Wind and Waves for the North Sea, the Norwegian Sea and Barents Sea,” J. Geophys. Res., 116, C05019. [CrossRef]
13
Magnusson, A. K., 2009, “What is True Sea State,” Proceedings of the 11TH International Workshop on Wave Hindcasting and Forecasting and Coastal Hazard Symposium. JCOMM Halifax, Canada, Oct. 18–23, 2009. Technical Report No. 52, WMO/TD-No. 1533, IOC Workshop Report No. 232.
14
Donelan, M. A., and Pierson, W. J., 1983, “The Sampling Variability of Estimates of Spectra of Wind Generated Gravity Waves,” J. Geophys. Res., 88(C7), pp. 4381–4392. [CrossRef]
15
Forristall, G. Z., 2000, “Wave Crests Distributions: Observations and Second-Order Theory,” J. Phys. Oceanogr, 30(8), pp. 1931–1943. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Location of AlwynNorth, Draupner, Ekofisk and Gorm in the North Sea where rogue waves have been recorded. Approximate water depths from north to south at the locations: 130, 70, 70, and 50 ms.

+Location of AlwynNorth, Draupner, Ekofisk and Gorm in the North Sea where rogue waves have been recorded. Approximate water depths from north to south at the locations: 130, 70, 70, and 50 ms.
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Location of AlwynNorth, Draupner, Ekofisk and Gorm in the North Sea where rogue waves have been recorded. Approximate water depths from north to south at the locations: 130, 70, 70, and 50 ms.
Grahic Jump Location
Fig. 2

Wave sensors at the Ekofisk complex (56.3'N, 3.2’E) in central North Sea. Picture from before 2003. The LASAR array is mounted on the bridge connecting the two platforms at upper left.

+Wave sensors at the Ekofisk complex (56.3'N, 3.2’E) in central North Sea. Picture from before 2003. The LASAR array is mounted on the bridge connecting the two platforms at upper left.
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Wave sensors at the Ekofisk complex (56.3'N, 3.2’E) in central North Sea. Picture from before 2003. The LASAR array is mounted on the bridge connecting the two platforms at upper left.
Grahic Jump Location
Fig. 3

Wind and waves measured at Ekofisk on Nov. 8 to 9, 2007 (12 to 00 UTC). Wind direction and speed (top two panels) are from sensor A (70 m) and B (110 m), both 10 min average and reduced to 10 m. Wave significant height and peak period (lower two panels) from Waverider (blue line; Buoy). LASAR downsampled to 2 Hz (red line; K-B Laser), and a Miros Range Finder (black line; FS-MRF).

+Wind and waves measured at Ekofisk on Nov. 8 to 9, 2007 (12 to 00 UTC). Wind direction and speed (top two panels) are from sensor A (70 m) and B (110 m), both 10 min average and reduced to 10 m. Wave significant height and peak period (lower two panels) from Waverider (blue line; Buoy). LASAR downsampled to 2 Hz (red line; K-B Laser), and a Miros Range Finder (black line; FS-MRF).
View Large  |  Save Figure  |  Download Slide (.ppt)
Wind and waves measured at Ekofisk on Nov. 8 to 9, 2007 (12 to 00 UTC). Wind direction and speed (top two panels) are from sensor A (70 m) and B (110 m), both 10 min average and reduced to 10 m. Wave significant height and peak period (lower two panels) from Waverider (blue line; Buoy). LASAR downsampled to 2 Hz (red line; K-B Laser), and a Miros Range Finder (black line; FS-MRF).
Grahic Jump Location
Fig. 4

Hindcast fields of wind, surface pressure, and waves from the NORA10 database (Reistad et al. [12]). Left: maps of mean sea level pressure with wind arrows and color coded wind speed. Right: fields with significant wave height and arrows for wave mean direction. Thick lines for Hs = 5 and 10 ms. From top to bottom: maps valid on Nov. 8, 2007 at 12 UTC, 18 UTC and on Nov. 9 at 00 UTC.

+Hindcast fields of wind, surface pressure, and waves from the NORA10 database (Reistad et al. [12]). Left: maps of mean sea level pressure with wind arrows and color coded wind speed. Right: fields with significant wave height and arrows for wave mean direction. Thick lines for Hs = 5 and 10 ms. From top to bottom: maps valid on Nov. 8, 2007 at 12 UTC, 18 UTC and on Nov. 9 at 00 UTC.
View Large  |  Save Figure  |  Download Slide (.ppt)
Hindcast fields of wind, surface pressure, and waves from the NORA10 database (Reistad et al. [12]). Left: maps of mean sea level pressure with wind arrows and color coded wind speed. Right: fields with significant wave height and arrows for wave mean direction. Thick lines for Hs = 5 and 10 ms. From top to bottom: maps valid on Nov. 8, 2007 at 12 UTC, 18 UTC and on Nov. 9 at 00 UTC.
Grahic Jump Location
Fig. 5

Wave profile time series as measured by the first laser during 20 min with 5 Hz sampling frequency, starting at 00:40 UTC on Nov. 9, 2007. Abscissa, nb, is sample number within the 20 min series.

+Wave profile time series as measured by the first laser during 20 min with 5 Hz sampling frequency, starting at 00:40 UTC on Nov. 9, 2007. Abscissa, nb, is sample number within the 20 min series.
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Wave profile time series as measured by the first laser during 20 min with 5 Hz sampling frequency, starting at 00:40 UTC on Nov. 9, 2007. Abscissa, nb, is sample number within the 20 min series.
Grahic Jump Location
Fig. 6

Crest of the Andrea wave as measured by all four lasers

+Crest of the Andrea wave as measured by all four lasers
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Crest of the Andrea wave as measured by all four lasers
Grahic Jump Location
Fig. 7

A blow-up of the spike-like wave seen in Fig. 5: the Andrea wave has a crest height of 15 m in a sea state with Hs = 9.2 m (crest factor Crx/Hs = 1.63). Time range on the x-axis is 40 s.

+A blow-up of the spike-like wave seen in Fig. 5: the Andrea wave has a crest height of 15 m in a sea state with Hs = 9.2 m (crest factor Crx/Hs = 1.63). Time range on the x-axis is 40 s.
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A blow-up of the spike-like wave seen in Fig. 5: the Andrea wave has a crest height of 15 m in a sea state with Hs = 9.2 m (crest factor Crx/Hs = 1.63). Time range on the x-axis is 40 s.
Grahic Jump Location
Fig. 8

The Draupner wave, with a crest height 18.5 m in Hs = 11.9 m, (crest factor Crx/Hs = 1.56) measured on Jan. 1, 1995. Time and height scales are identical to Fig. 7. Time range on x-axis is 40 s.

+The Draupner wave, with a crest height 18.5 m in Hs = 11.9 m, (crest factor Crx/Hs = 1.56) measured on Jan. 1, 1995. Time and height scales are identical to Fig. 7. Time range on x-axis is 40 s.
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The Draupner wave, with a crest height 18.5 m in Hs = 11.9 m, (crest factor Crx/Hs = 1.56) measured on Jan. 1, 1995. Time and height scales are identical to Fig. 7. Time range on x-axis is 40 s.
Grahic Jump Location
Fig. 9

Time series of distance to water surface from each of the four lasers at Ekofisk. Top Panel: Nov. 8, 2007 at 00 UTC. Bottom Panel: Nov. 9 at 00 UTC. Time series are 20 min. From top to bottom within each panel: Laser numbers 1 to 4. Lines connecting the values are discontinuous when there are default values in between. Number of default values, percentage of nondefault values, Hs, Skewness, and Kurtosis of nondefault values are given in each graph.

+Time series of distance to water surface from each of the four lasers at Ekofisk. Top Panel: Nov. 8, 2007 at 00 UTC. Bottom Panel: Nov. 9 at 00 UTC. Time series are 20 min. From top to bottom within each panel: Laser numbers 1 to 4. Lines connecting the values are discontinuous when there are default values in between. Number of default values, percentage of nondefault values, Hs, Skewness, and Kurtosis of nondefault values are given in each graph.
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Time series of distance to water surface from each of the four lasers at Ekofisk. Top Panel: Nov. 8, 2007 at 00 UTC. Bottom Panel: Nov. 9 at 00 UTC. Time series are 20 min. From top to bottom within each panel: Laser numbers 1 to 4. Lines connecting the values are discontinuous when there are default values in between. Number of default values, percentage of nondefault values, Hs, Skewness, and Kurtosis of nondefault values are given in each graph.
Grahic Jump Location
Fig. 10

Measurements through Nov. 8 and 9, 2007. From top to bottom: wind speed (m/s, 10 m level), significant wave height from the four lasers (Hs = 4*std(x(t)), Average Intensity of Good Returns (AIGR) in each 20 min sequence, standard deviation of AIGR within each 20 min time series, and Number of Good Returns (NGR) in a 200 ms sample, with maximum = 80.

+Measurements through Nov. 8 and 9, 2007. From top to bottom: wind speed (m/s, 10 m level), significant wave height from the four lasers (Hs = 4*std(x(t)), Average Intensity of Good Returns (AIGR) in each 20 min sequence, standard deviation of AIGR within each 20 min time series, and Number of Good Returns (NGR) in a 200 ms sample, with maximum = 80.
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Measurements through Nov. 8 and 9, 2007. From top to bottom: wind speed (m/s, 10 m level), significant wave height from the four lasers (Hs = 4*std(x(t)), Average Intensity of Good Returns (AIGR) in each 20 min sequence, standard deviation of AIGR within each 20 min time series, and Number of Good Returns (NGR) in a 200 ms sample, with maximum = 80.
Grahic Jump Location
Fig. 11

Measurements through Nov. 8 and 9, 2007. From top to bottom, Hs from the four lasers (=4*std(x(t)), Kurtosis, Skewness, number of spikes (spike limit = 7.0, see text), and percentage of good returns in a 20 min record. Thick blue line is for sensor number 1 (see legend in the bottom panel for other colors).

+Measurements through Nov. 8 and 9, 2007. From top to bottom, Hs from the four lasers (=4*std(x(t)), Kurtosis, Skewness, number of spikes (spike limit = 7.0, see text), and percentage of good returns in a 20 min record. Thick blue line is for sensor number 1 (see legend in the bottom panel for other colors).
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Measurements through Nov. 8 and 9, 2007. From top to bottom, Hs from the four lasers (=4*std(x(t)), Kurtosis, Skewness, number of spikes (spike limit = 7.0, see text), and percentage of good returns in a 20 min record. Thick blue line is for sensor number 1 (see legend in the bottom panel for other colors).
Grahic Jump Location
Fig. 12

Time series of wave height from Laser number 1 including the Andrea wave (top panel), and simultaneous measurements of Average Intensity of Good Returns (AIGR)

+Time series of wave height from Laser number 1 including the Andrea wave (top panel), and simultaneous measurements of Average Intensity of Good Returns (AIGR)
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Time series of wave height from Laser number 1 including the Andrea wave (top panel), and simultaneous measurements of Average Intensity of Good Returns (AIGR)
Grahic Jump Location
Fig. 13

Time series of wave profile from Laser number 1 including the Andrea wave (top panel). Panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.

+Time series of wave profile from Laser number 1 including the Andrea wave (top panel). Panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.
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Time series of wave profile from Laser number 1 including the Andrea wave (top panel). Panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.
Grahic Jump Location
Fig. 14

Time series of wave profile (top panel) from Laser number 1 including the second highest wave measured within UTC 00:40 to 01:00. Four panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.

+Time series of wave profile (top panel) from Laser number 1 including the second highest wave measured within UTC 00:40 to 01:00. Four panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.
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Time series of wave profile (top panel) from Laser number 1 including the second highest wave measured within UTC 00:40 to 01:00. Four panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.
Grahic Jump Location
Fig. 15

Time series of wave profile from Laser number 2 (top panel) including the highest wave measured within 00:20 to 00:40. Four panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.

+Time series of wave profile from Laser number 2 (top panel) including the highest wave measured within 00:20 to 00:40. Four panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.
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Time series of wave profile from Laser number 2 (top panel) including the highest wave measured within 00:20 to 00:40. Four panels below: Average Intensity of Good Returns (AIGR) from all four lasers. Thin lines: 5 Hz samples, thick line: running average over five points.
Grahic Jump Location
Fig. 16

The wave profile as measured by laser number 1 during 3 h just previous to culmination. Inserted in figures: Significant wave heights from 20 min periods (below) and from 30 min periods (above).

+The wave profile as measured by laser number 1 during 3 h just previous to culmination. Inserted in figures: Significant wave heights from 20 min periods (below) and from 30 min periods (above).
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The wave profile as measured by laser number 1 during 3 h just previous to culmination. Inserted in figures: Significant wave heights from 20 min periods (below) and from 30 min periods (above).
Grahic Jump Location
Fig. 17

Probability of exceedance of individual wave crest heights during the 3 h previous to the Andrea wave and including it. Cyan dots: normalized to 20 min Hs. Red dots: normalized to 30 min Hs. Blue line: Forristall [15] crest distribution for long crested sea (Forristall [15]) using the 3 h significant wave height and mean wave periods. Black line: Rayleigh distribution.

+Probability of exceedance of individual wave crest heights during the 3 h previous to the Andrea wave and including it. Cyan dots: normalized to 20 min Hs. Red dots: normalized to 30 min Hs. Blue line: Forristall [15] crest distribution for long crested sea (Forristall [15]) using the 3 h significant wave height and mean wave periods. Black line: Rayleigh distribution.
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Probability of exceedance of individual wave crest heights during the 3 h previous to the Andrea wave and including it. Cyan dots: normalized to 20 min Hs. Red dots: normalized to 30 min Hs. Blue line: Forristall [15] crest distribution for long crested sea (Forristall [15]) using the 3 h significant wave height and mean wave periods. Black line: Rayleigh distribution.

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