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Paper title Extraction of wave characteristics from optical satellite imagery. Application to the production of coastal bathymetry from Sentinel-2 data.
Authors
  1. Rana El Arayeh BRGM Speaker
  2. Marcello de Michele BRGM - Bureau de Recherches Géologiques et Minières
  3. Daniel Raucoules BRGM (French Geological Survey)
  4. Romain Abraham Institut Denis Poisson, CNRS UMR 7013, Université de Tours, Université d’Orléans
Form of presentation Poster
Topics
  • A8. Ocean
    • A8.14 Remote-sensing of Ocean Waves and their Applications
Abstract text Detailed knowledge of the shape of the seafloor is crucial to humankind. In an era of ongoing
environmental degradation worldwide, bathymetry data (and the knowledge derived from it) play
a pivotal role in using and managing the world’s oceans. Bathymetric surveys are used for many
research fields including flood inundation, the contour of streams and reservoirs, water-quality studies,
planning the coastal reservoir, and many other applications.
However, the vast majority of our oceans is still virtually unmapped, unobserved, and unexplored.
Only a small fraction of the seafloor has been systematically mapped by direct measurement.
For understanding changes of the underwater geomorphology, regional bathymetry information is
paramount. This sparsity can be overcome by space-borne satellite techniques to derive bathymetry.
With the development of new missions in open-access, space-borne sensors now represent an attractive
solution for a broad public to capture local-scale coastal impacts at large scales.
Only from intermediate water until shore, the linear dispersion relation (1) can be used to estimate
a local depth.
c² =g/h tanh( h/λ ) ⟺ h = λ atanh( c²/gλ ) (1)
in which c is wave celerity, g represents the gravitational acceleration, and λ is the wavelength.
Studies, for example [2], show that wave pattern can be extracted using a Radon transform then they
obtained physical wave characteristics (λ, c) using a 1D-DFT for the most energetic incident wave
direction in Radon space (sinogram).
In this work, we seek a thorough research in signal processing that is contained in Sentinel-2 (ESA/
Copernicus spaceborne optical sensor) images and optimization of this signal. This work is carried out
in the perspective of the production of differential bathymetry, with interest for detection / evaluation
of changes on underwater geomorphology. Identification of such changes has potential applications
in risk analysis related to seismotectonics, submersion, submarine gravitational movements and morphodynamics,
littoral dynamic-related seasonal or extreme event, among others.
Here, regional bathymetries are derived at the test-site of Arcachon, France.
Our approach is based on the calculation of the gradient around each point of the image. This approach
will be a source of improvement of the method [2, 4] and will give us a better estimation of
wave propagation direction and the possibility of dealing with two wave regimes which overlap.
When analyzing directional data, it is often appropriate to pay attention only to the direction of
each datum, disregarding its norm. The von Mises–Fisher (vMF) distribution is the most important
probability distribution for such data[3].
With this novel technique, we extract the wave direction by estimating the parameters of Von Mises-
Fisher distribution from local gradients around each point[1]. Therefore, Sentinel-2 imagery derived
wave characteristics are extracted using a unidirectional radon transform. A discrete fast-Fourier
(DFT) procedure in Radon space (sinogram) is then applied to derive wave spectra. Sentinel-2
time-lag between detector bands is employed to compute the spectral wave-phase shifts. Finally, we
estimate depth using the gravity wave linear dispersion equation (1).
In conclusion, the development of the theoretical model based on von Mises–Fisher(vMF) distribution
is an alternative way to carry out the processing in order to produce coastal bathymetry suggesting
potential improvements respect to previous approaches. Ultimate goals are to be able to make accurate
developments of our approach with the intention of improving the method to detect mixture of
von Mises-Fisher distributions.

Keywords— bathymetry, signal processing, spaceborne imagery

References
[1] Akihiro Tanabe, Kenji Fukumizu, Shigeyuki Oba, Takashi Takenouchi, and Shin Ishii. 2007. ”Parameter
estimation for von Mises–Fisher distributions” Computational Statistics 22(1), 145-157.
[2] Bergsma, Erwin W.J., Rafael Almar, and Philippe Maisongrande. 2019. ”Radon-Augmented Sentinel-2 Satellite
Imagery to Derive Wave-Patterns and Regional Bathymetry” Remote Sensing 11, no. 16: 1918.
[3] Lu Chen, Vijay P. Singh, Shenglian Guo, Bin Fang, and Pan Liu. 2012. ”A new method for identification of
flood seasons using directional statistics” Hydrological Sciences Journal 58(1), 1–13.
[4] Marcello de Michele, Daniel Raucoules, Deborah Idier, Farid Smai, and Michael Foumelis. 2021. ”Shallow
Bathymetry from Multiple Sentinel 2 Images via the Joint Estimation of Wave Celerity and Wavelength”
Remote Sensing 13, no. 12: 2149.