INDIVIDUAL WAVE HEIGHT FROM SAR

W. Rosenthal(1), S.Lehner(2) (1), GKSS, D 2102 Geesthacht, Email:Wolfgang.Rosenthal@gkss.de (2), DLR, D82234 Wessling, , Email:Susanne.Lehner@dlr.de

ABSTRACT Safety of shipping is an ever growing concern. In a summary on shipping safety Douglas Faulkner investigates the causes of shipping casualties [1] and concludes that the number of unexplained accidents are far too high in comparison to other means of transport. From various sources, including insurers data over 30% of the casualties are due to bad weather ( a fact that ships should be able to cope with) and a further 25% remain completely unexplained. The European project MAXWAVE aimed at investigating ship and platform accidents due to severe weather conditions using different radar and in Situ sensors and at suggested improved design and new safety measures. Two methods to derive two dimensional sea surface elevation fields from space borne synthetic aperture radar (SAR) data are discussed and used to explain individual extreme ocean wave events. Two offshore platform accidents that occurred in the North Sea are analyzed and explanations for the events are given..

Fig.1: The photograph is taken from the bridge at the rear of the ship. The foremast of the ship is visible and the travel direction of the ship coincides with the direction of the general sea state seen in front of the ship. The rogue wave floods the ship from a completely different direction and damaged the hull seriously. INTRODUCTION Rogue waves have been seen and described by seafarers from ancient times on. In the last century

there have been photographs (Fig.1) and visual observations yielding an estimation of height. A first measurement by a conventional instrument (Fig 2) has been made on January, 1st at the Norwegian platform Draupner located in the North Sea at 58,11N; 2,28E (Fig.9). The systematic search for rogue waves started within the MaxWave-Project [2] (w3g.gkss.maxwave.de). It could be shown that the ESA radar satellites ERS and Envisat are capable to detect large individual waves on the ocean as shown in Fig 3a,b.

Figure 2 : wave elevation at the Draupner field on Jan. 1., 1995 15:20 UTC Significant Waveheight 11.9m Peak Period 16.7 sec Maximum crest Height 18.5 m Adjacent trough -7.1m and –6.5m Depth 70m

Figure 3a : A grey scale coded sea surface elevation field derived from an ERS 2 SAR image, acquired on Jan.1. 1995 at 11:20 UTC, 50 km east of Draupner. The surface elevation along the two red lines in the image is given in Fig.4.

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Proc. ‘Envisat Symposium 2007’, Montreux, Switzerland 23–27 April 2007 (ESA SP-636, July 2007)

Fig 3b: The vertical displacement along the lines in Fig.3a. A follow-up project named WaveAtlas was set up between DLR and ESA to investigate ERS images from the years 1999 and 2000 for the occurrence of rogue waves, see Lehner et al., this issue. In previous research on ocean wave detection by imaging space radars, starting with Seasat in 1979, the measurement of the two-dimensional wave spectrum (power spectrum) was in the center of interest. For that purpose the raw radar data were cleaned of speckle noise and image distortions were corrected for. Next the image spectra were derived by Fourier transform and the Fourier coefficients were considered as the Fourier coefficients of the surface wave field, multiplied by so called transfer functions, [3].

1. REMARKS ON THE INVERSION OF OCEAN WAVES The transfer function of a real aperture radar (RAR) is dependent on 1. the variable tilt of the wave field, 2. the hydrodynamic interaction of the Bragg-scatterers and the long wave field and 3.the image distortion by the varying distance for three dimensional targets (range bunching).

Theoretically derived transfer functions for the three imaging mechanisms are given in Fig 4.

Fig 4 : SAR forward mapping. The Tk for the velocity bunching is scaled for very strong orbital velocities of the total wave field. An additional physical effect that contributes to imaging is present for a Synthetic Aperture Radar (SAR). This is the displacement of targets which have a velocity component in the direction towards and from the radar antenna. The displacement d for a target with line of sight velocity u is given by

d= R/V · u (1) where R is the distance from the antenna and V is the satellite velocity. For ERS and ENVISAT the ratio is R/V= 108 seconds. With a significant wave height Hs the maximum orbital velocity uorb can be estimated to be on the average: u=0.25 · � · Hs. (2) � = radial frequency For an individual wave with wave number k sin� in azimuth the connected phase shift in azimuth is

Xa = k · sin� · d (3) � = angle of k, relative to azimuth

Brüning and Alpers [4] assumed that waves with phase shifts

Clin = k·d (4) larger than 30° are not retrievable from the image. This parameter Clin defines a cut-off wave number in azimuth, above which the wave spectrum can not be inverted. In range direction the cut-off wavelength is determined by about four times the resolution length in range. The spectral areas inside the cut-off frequencies are not retrievable to include them in the spatial sea surface wave field.

Modulation Transfer Function for a RAR T = TTilt + Trb + Thydr

MTFs, after Alpers, Brüning, Hasselmann, 1979

SAR - additional motion effects

2. INVERSION SCHEMES FOR INDIVIDUAL OCEAN WAVE HEIGHT An improvement of the concept of transfer functions is possible, if we consider the dependency of the backscatter intensity on the tilt (inclination in the look direction of the antenna) of the ocean surface and consider all other modulation processes as small against tilt modulation.

Fig5: Wind Field Algorithm CMOD4 for different Wind Speeds, after (Lehner et al [8]).

Fig 5 gives the respective diagram for the backscatter intensity of the satellite scatterometer. The vertical axis is in decibel so that the dependence is exponential, that means it is a non linear dependence. Although the footprint of the satellite scatterometer is much larger than the resolution cell of a SAR, we may assume the same exponential dependence of the backscatter coefficient from the tilt angle of the ocean surface. Because of this non-linear dependence, the transfer function of each Fourier component is dependent on the entire sea state of the area. A possible extension of the concept of spectral transfer functions has been developed at DLR [5]. In that concept an explicit dependence of each transfer function on statistical sea state parameters is realized, in which all modulation processes are included.

Another inversion of the SAR image has been reported in [6], for which the local tilt of each pixel was determined using the scatterometer algorithm CMOD5, similar to the RAR algorithm derived in [7]. The Scat algorithm CMOD gives the relationship between backscattered intensity and tilt, depending on wind speed and look angle of the radar relative to wind direction. From the so derived tilt the surface topography can be computed by spatial integration along the range direction.

Fig. 6 shows a scatter diagram for about 10 000 comparisons between Hs derived from SAR-imagettes by this CMOD-method and Hs, taken from collocated ECMWF-hindcasts. The left hand scale shows the wave height resulting from the simple application of the CMOD-algorithm. If we use a calibration constant to achieve the best performance of the algorithm we end up with the right hand scale.

Figure 6: Scatter diagram for SAR inversion using CMOD4. 3. INVESTIGATING ROGUE WAVES IN THE NORTH SEA BY ERS2, ENVISAT ASAR AND MERIS In the following two events of extreme waves are described by combining satellite measurements and in-situ data. The Allerheiligenstorm The offshore platform FINO is located ca. 45 km north of the German island of Borkum at latitude N 54° 0,86‘ and longitude E 6° 35,26‘. It was hit by a rogue wave between 4.00 and 6.00 o’clock in the morning of November, 1st, 2006. From the damages at the platform and the time series measured by a wave sensor a crest to trough wave height of 25 m or more is estimated. ENVISAT data from the sensors MERIS and ASAR are available at 10:26 UTC. The weather situation was dominated by a cold air inflow from the north. The MERIS image in Fig.8 shows a very regular pattern of open cloud cells which suggest downdrafts in the open parts and updrafts with cloud formation around the open cells. The resulting strong wind fields can be observed on the ASAR images as light areas on the front side of the open cells. A more extended description is given in the paper of S. Brusch, this issue.

As an explanation for the extreme we suggest, that phase locked wave groups travel together with the open cells of high wind regions. Thus the ocean waves grow to larger heights than would be expected from a random phase distribution. In such a case we may expect more than one rogue wave. A high energy wave field travelling with the meteorological open cells would exist, in which rogue waves would grow and decay.

Fig.7: The lower part of the FINO platform. Damages were found at 17.5 m above mean HW.

Fig. 8:MERIS and ASAR data from 10:26 UTC on 1.Nov. 2006 The New Year Storm Another rogue wave event passed the location of FINO probably 11 years ago, when on January 1st 1995 at the Draupner platform an extreme wave, more than 25 m high, was measured and about seven hours later again

an extreme wave hit a Search and Rescue Vessel, the Alfried Krupp, near to the island of Borkum. We may conclude that these two events belong to the same high energy wave field that was triggered by an observed small scale front of high wind speed that propagated within the large scale flow to the south. FINO was not yet built at that time, but the high energy wave field must have passed the FINO vicinity so that there were at least two rogue wave events within 11 years at the FINO location. 4. STATEMENT ON THE VALIDITY OF THE RAYLEIGH-DISTRIBUTION IN THE GERMAN BIGHT There were two rogue wave events within 11 years near to the location of the FINO 1 platform in seastates with Hs ~ 10 m . Both rogue waves had a crest height above 15 m and the total wave height had been above 25 m. Based on a Rayleigh distribution we estimate the statistical return period for a rogue wave of an individual Hmax > 20 m to be above 40 years. It follows from the two events happening within 11 years, that the validity of Rayleigh statistics for abnormal individual waves should be reconsidered.

5. CONCLUSION

The analysis of SAR-data from ERS and from ENVISAT gives new insight in the size and in the formation and the

Draupner 58,11 N / 2,28 E

FINO 54°0,86‘N 6°35,26‘E

properties of rogue waves. The medium scale wind fields from the SAR together with the collocated optical images from Meris of the cloud structure has lead to a new hypothesis for the generation of rogue waves. ACKNOWLEDGEMENTS The ERS and ENVISATSAR raw data were kindly provided by ESA in the framework of the data AO WAVEATLAS and WINDFARM. The ERA 40 data were downloaded from the web page of the ECMWF.

REFERENCES 1. Faulkner, D., Shipping safety. A matter of

concern, Ingenia, 13, Marine matters, August 2002

2. Lehner S., W. Rosenthal, OMAE 2006 – 92414, Investigation of Ship and Platform Accidents Due to Severe Weather Events: Results of the MAXWAVE Project.

3. Hasselmann, K., and Hasselmann, S., On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum, J. Geophys. Res., pp. 10713-10729, 1991.

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