556 



from three sets of pictures, each containing ten 

 stereo pairs. These sets were chosen on two bases. 

 One is the photographic quality which was judged by 

 photograminetric experts, the other is the scientific 

 interest. In this stage of the study it was felt 

 that wave fields generated by off-shore winds would 

 be of most interest because the boundary conditions 

 are well defined. Also, results of past investiga- 

 tions of wave generation [Hasselmann et al. (1973) , 

 Hasselmann et al. (1976)] suggests that observations 

 in these conditions may be extrapolated to more com- 

 plex conditions . 



The first set of pictures which was analyzed was 

 taken in September 1973 during almost "ideal" off- 

 shore wind conditions in the area just west of the 

 German island of Sylt. These observations were 

 carried out in the framework of an international 

 oceanographic project known as the Joint North Sea 

 Wave Project (JONSWAP) which is concerned with the 

 study of wave generation and prediction. A variety 

 of articles directly related to JONSWAP has been 

 published and more are being prepared for publica- 

 tion. Some references are: Hasselmann et al . (1973), 

 Spiess (1975), Hasse et al . (1977), and Huhnerfuss 

 et al (1978) . The two other sets of pictures were 

 taken in March and November 1976 in the area west of 

 Holland near the town of Noordwijk, also in off- 

 shore wind conditions . Wave observations at sea 

 level during the first and last flights are avail- 

 able and these have been used for comparison with 

 the stereophotogrammetric results. 



2. STEREOPHOTOGRAMMETRY OF THE SEA SURFACE 



When an object is photographed from two slightly 

 different positions, the imagery in the .two pictures 

 will also be slightly different. The differences 

 depend upon the geometry of the object. By measur- 

 ing the differences , the elevation of the surface 

 relative to an arbitrary plane of reference can be 

 determined. The conventional technique of analysis 

 requires human interpretation of the pictures and 

 complicated stereoscopic viewing devices. More ad- 

 vanced procedures , which have only recently been 

 developed, use a computer to carry out a correlation 

 between the images to arrive at the same results 

 [e.g. , Crawley (1975) ] . 



In the conventional geodetic aerial survey the 

 pictures are taken vertically in sequence from an 

 airplane and the interval is chosen such that the 

 pictures overlap in the area directly under the 

 line of flight. An obvious condition is that the 

 object does not change between exposures. In land 

 survey this poses no problem since the ground sur- 

 face does not move. The sea surface, however, 

 changes very rapidly. To limit the distortions be- 

 tweeen two successive pictures to an acceptable 

 level , they should be taken within an interval of 

 1 - 5 ms. The airplane cannot possibly fly from 

 one required point of photography to the other within 

 this time lapse. The consequence is that not one but 

 two cameras are needed which take the pictures "simul- 

 taneously," that is, within an interval of 1 - 5 ms 

 and that two aircraft are needed to position the two 

 cameras. Apart from these technical differences in 

 obtaining the stereo pairs, the methods and pro- 

 cedures used in this study are standard in geodetic 

 survey and they have been used in the past by various 

 oceanographic investigators. A well publicized ef- 

 fort is the Stereo Wave Observation Project [SWOP, 



Cote et al. (I960)] and the present system is es- 

 sentially a revised version of the system used in 

 SWOP. 



It will suffice here to comment only briefly on 

 the operational system. Actually two independent 

 systems were built. One is based on Hasselblad 

 cameras and has been described in detail elsewhere 

 [Holthuijsen et al. (1974)]. The other is an almost 

 exact copy of that system except that the Hasselblad 

 cameras were replaced by UMK cameras of Jenoptik 

 which are superior in optical and metrical aspects. 

 The Hasselblad system was used for observations in 

 the area off Sylt and the UMK system was used in 

 the area off the coast of Holland. Synchronization 

 of the cameras was achieved by using a radio signal 

 that triggered a command pulse which was manipulated 

 electronically in such a way that it complied with 

 the timing characteristics of the receiving camera. 

 The synchronization error for the Hasselblad system 

 was less than 1 ms for all of the analyzed stereo 

 pairs and for the UMK system the synchronization 

 error was less than 5 ms . To position the cameras 

 two Alouette III helicopters were used. These heli- 

 copters had a drop-door over which the cameras could 

 be mounted. The distance between the helicopters 

 was estimated during the flight through a range 

 finder which was imposed on the viewer of a third 

 camera which looked from one helicopter to the other. 

 It took a picture of the other helicopter every time 

 the downward looking cameras were activiated. From 

 these photographs the distance between the helicop- 

 ters could be computed and the scale of photography 

 could be determined. 



The specification for the helicopter formation 

 during a photographic sortie were largely based on 

 photogrammetric requirements . Only the altitude 

 was based on the anticipated sea state since the 

 noise and resolution in the spectrum are directly 

 related to the altitude of photography. The upper 

 limit of the altitude was based on noise considera- 

 tions . The standard deviation of the measurement 

 error is estimated to be 0.03% of the altitude 

 [Holthuijsen et al. (1973)]. Taking a noise to 

 signal variance ratio of 1:10 as an acceptable upper 

 limit, it can be shown that the altitude should be 

 less than 1,000 times the standard deviation of the 

 instantaneous sea surface elevation (or 250 times 

 the significant wave height) . The lower limit of 

 the altitude is directly related to the resolution. 

 If a resolution in the spectrum is required equiva- 

 lent to \, of the peak wave number or better, it 

 appears that for the Hasselblad system the altitude 

 should be higher than 6.7 times the reciprocal of 

 the peak wave number. For the UMK system the fac- 

 tor is 4.0. For most "young" sea states these upper 

 and lower limits are not in conflict. The final 

 choice of the altitude was confined to multiples of 

 250 ft for the pilot's convenience. 



The size of the sea surface covered in stereo in 

 one stereo pair is usually too small to produce suf- 

 ficient data for a reliable estimate of the two- 

 dimensional spectrum. To increase the amount of 

 data more pictures were taken in sequence with a 

 space interval sufficiently large to ensure photog- 

 raphy of non-overlapping sea areas . The correspond- 

 ing time interval between the exposures would be 

 typically between 4 s and 20 s (depending on camera 

 type, ground speed, and altitude). The photographic 

 operation to obtain this sequence is called a sortie. 



In principle , the pictures can be analyzed with 

 recently developed, fully automated processes. The 



