Individual Wave Height from Sar

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. _____________________________________________________ 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