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Bathymetry from inverse wave refraction

Bathymetry of area of investigation acquired by multibeam echosounder.

It is possible to determine the bathymetry of a certain area using radar data. On the Island of Sylt at the German Bight Coast, measurements are done during storm conditions. This data is processed based on inversion of the non-linear and linear wave theory. More about the area of investigation, data processing, result and discussion of the results can be found in the article.

The determination of the bathymetry in coastal environments by utilizing the ocean wave-shoaling photographic imagery, and the observed reduction of ocean wave phase speed with decreased water depth, is used since the WW-II (Williams 1946)[1]. The last decade, with the expansion of different ground based instrumentations, mainly radar and video imagery, for the observation of the sea surface and the exponential increase of the computational power, several methodologies for the bathymetry reckoning have been published, e.g. Bell 1999[2], Seemann et al. 1999[3], Stockdon and Holman 2000[4], Dankert 2003[5], Bell et al. 2004[6], Catalan and Haller 2008[7], Senet et al. 2008[8]. The core of the previously mentioned methods is the inversion of the wave characteristics by assuming the validity of linear or non-linear models for the propagation of the wavefield over uneven sea bottom.

In the present investigation, twelve hourly radar datasets acquired during storm conditions are analyzed by two methods: The non-linear method of Bell et al. 2004[6] (henceforth BW04), which is based on the inversion of the non-linear wave dispersion equation of Hedges (1976)[9] and the Dispersive Surface Classificator (henceforth DiSC08), Senet et al. 2008[8], which is based on the inversion of the linear wave theory. The results are validated as bathymetric retrieving instruments and the two wave propagation theories are compared about their sensitivity to the local bathymetric relief. The two methods are compared under the assumption of fundamentally similar implemented algorithms.
  1. Williams, W.W. 1946, The determination of gradients of enemy-held beaches. Geographical Journal 107, 76–93.
  2. P. Bell 1999, Shallow water bathymetry derived from an analysis of x-band radar images of waves, Coastal Engineering 3-4, pp. 513-527.
  3. Seemann J., C. Senet, H. Dankert, Hatten, H., Ziemer, F. 1999, Radar image sequence analysis of inhomogeneous water surfaces, in proc. of the SPIE'99 Conference - Applications of Digital Image Processing XXII. vol. 3808, pp. 536-546.
  4. Stockdon, H.F., Holman, R.A. 2000, Estimation of wave phase speed and nearshore bathymetry from video imagery. Journal of Geophysical Research 105 (C9), pp. 22015–22033.
  5. Dankert, H. 2003, Retrieval of Surface-Current Fields and Bathymetries using Radar-Image Se-quences, International Geoscience and Remote Sensing Symposium, Toulouse, France.
  6. 6.0 6.1 Bell, P., J. Williams, S. Clark, B. Morris and A. Vila-Concejo 2004, Nested Radar Systems for Remote Coastal Observations, Journal of Coastal Research SI39, pp. 483-487.
  7. Catalan, P.A. and Haller, M.C., 2008, Remote sensing of breaking wave phase speeds with ap-plication to non-linear depth inversions. Coastal Engineering, 55(1), pp. 93-111.
  8. 8.0 8.1 Senet, C. M., J. Seemann, S. Flampouris, F. Ziemer 2008, Determination of Bathymetric and Current Maps by the Method DiSC Based on the Analysis of Nautical X–Band Radar-Image Se-quences of the Sea Surface, IEEE Transaction on Geoscience and Remote Sensing 46(7), pp.1-9.
  9. Hedges, T.S. 1976, An empirical modification to linear wave theory, Proc. Inst. Civ. Eng., 61, pp. 575-579.