The assumptions commonly used in operational shallow water modeling are the following.
  • Simplified RTE: shallow water modeling is only possible because the very complex radiative transfer equation of sun and sky light through atmosphere and water has been extensively simplified for sake of operationality.
  • Homogeneity: the optical properties of the atmosphere column and of the water column are assumed to be horizontally homogeneous.
  • Operational K: the various specific diffuse attenuation coefficients for downwelling and upwelling irradiances, Kup and Kdown, which compound into the depth-dependent diffuse attenuation coefficients for irradiance Kd are conveniently rounded up into an effective two-way diffuse attenuation coefficient for near-nadir radiances, denoted K, for sake of operationality.
  • Multiple scattering in the water column is neglected, as is multiple reflection at the water-air interface.
  • Dark target assumption: in 4SM, the radiance measured in the imagery at the longer wavelength available (possibly a NIR -or Red- band) over an optically deep water area is assumed to be representative of the radiance of the atmospheric path at that wavelength.
  • For all these reasons, bathymetry modeling is best conducted using images, or part of them, which exhibit a very high radiometric quality standard, and it should be considered a safe precaution that certain images or part of them may not be used for this specific purpose.

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