Water depth inversion from satellite dataset

Abstract

Within an effort to estimate near-shore bathymetry from satellite scenes, a method based on wave celerity and wavelength estimation is developed. These wave characteristics are extracted from SPOT-5 panchromatic and multispectral scenes. The method allows us to associate the wavelength and the celerity of the same detected wave and to estimate the water depth from the dispersion relation. This technique is tested on Saint Pierre area (La Reunion Island). Results are compared to in-situ measurements and show a reasonable agreement in terms of morphology and a mean absolute bathymetric error inferior to 30 % in intermediate depths (5-30 m range).

Water Depth Inversion From a Single SPOT-5 Dataset

“…In this paper, Fourier-filtered subscenes are not used to compute celerity, as in [13] or [14]. Indeed, the spatial resolution given by the Fourier transform subscenes is too coarse to isolate dominant wavelength λ n as determined by the wavelet analysis, particularly for the largest wavelengths.…”

“…To tackle the issue of estimating bathymetry using two images only, a method based on cross correlation and wavelet analysis is proposed that exploits the spatial and temporal characteristics of the SPOT-5-like dataset to extract bathymetry. The proposed method combines the spaceborne direct c measurement method presented in [13] with an original wavelet-based adaptive λ estimate [14] to retrieve a spatially dense series (clouds) of (λ, c) couples that are then used to estimate water depth using dispersion relation (1).…”

Radon-Augmented Sentinel-2 Satellite Imagery to Derive Wave-Patterns and Regional Bathymetry

“…An RT-filter was applied every 50 m in x and y direction, (∆x and ∆y = 50 m), in other words, the depth estimation results have a horizontal resolution of 50 m. The windowing sub-domain for this real-world case is currently set to 30 × 20 pixels which practically relates to 300 × 200 m and an amplification factor (κ) is applied as a function of the distance (D in km) from the coastline κ = 1 + 0.3D. The size of the sub-sample domain is in a similar order compared to [15,17,18], and relates mostly to the stochasticity of the sub-sampled wave pattern. In other words, to apply typical methods such a wavelet or DFT analysis, more than a single wavelength should be sub-sampled, the same holds here.…”

“…The lack of temporal information limits depth estimations from space-borne imagery to the determination of spatial wave characteristics (k or L). Most commonly applied 2D-discrete fast-Fourier transform (DFT) or wavelet analyses require sub-domains with the size of a few wavelengths to overcome wave-stochasticity issues [15][16][17][18], which on its own leads to significant spatial smoothing. To a certain degree, these mathematical applications depend on image resolution and visibility of the wave pattern.…”

Satellite derived bathymetry using deep learning

“…These models are strongly dependent on and largely bounded by the maximum penetration depth of sunlight which varies according to different seasons, locations and bottom reflectance. Alternatively, depth inversion approaches based on wave kinematics have been applied to a variety of data-types, collected from different remote sensing tools, ranging from modelled analysis [Bergsma and Almar, 2018], laboratory experiments [Catalán and Haller, 2006] to local shore-based analysis using time-series data [Stockdon and Holman, 2000, Plant et al, 2008, Almar et al, 2009, Holman et al, 2013, airborne video data [Bergsma et al, 2019a, Brodie et al, 2019 and ultimately space-borne sensors including the IKONOS satellite [Abileah, 2006], SPOT5 [de Michele et al, 2012, Poupardin et al, 2014, Sentinel-2 [Bergsma et al, 2019b] and Pleiades . Wave kinematic approaches exploit temporal information embedded in (satellite) images, in order to extract wave characteristics such as wavenumber and wave celerity that are then used to invert water depths.…”