• The basics of shallow water modeling using the simplified radiative transfer equation may be tested using SPOT and Landsat images
  • the simplified RTE adequately accounts for first order physics, in particular for the all-important water volume reflectance (i.e. the color of the water)
• Adequate expert knowledge of underwater realities allow the practioner to tune the optical calibration of shallow radiances in units of DN, with no need for any field data
• Assumptions: this is subject to the following assumptions and uses only the image itself -not even any metadata!
  • glint and haze in the data has been removed from marine areas
  • SL : for any pair of bands i and j, the non-vegetated pixels in the image, from the brightest on the beach to the darkest in shadowed areas, allows the practioner to formulate a model of what an acceptable water column corrected spectral bottom signature may look like: 
  • this is the equivalent of the agronomer's Soils Line, with which the atmospheric path radiance La is estimated
  • this allows for a very simple first order atmospheric correction : at the base of the atmosphere L =Ls - La
  • this correction is just as good as most current corrections reported by authors (and the practioner is in control to prevent negative radiances...)
• Lsw and Lw : the water bodies in the image are reasonably homogeneous radiance over optically deep waters Lsw must be estimated from the image
  • Lw: the water volume reflectance Lw = Lsw - La is estimated from the image
• BPL : for any pair of visible radiances i and j, the ratio Ki/Kj of effective diffuse attenuation coefficients may be derived from the shallow areas in the image 
  • for this, we introduce the concept of the brightest Pixels Line, with which to estimate ratios Ki/Kj of diffuse attenuation coefficients
• Spectral K from Jerlov : for each visible waveband, the effective wavelength in nanometers must be known or assumed so that the spectral values Ki, Kj, K..., Kn, in meters-1 for all visible bands may be derived using Jerlov's table of diffuse attenuation coefficients for marine water worldwide
• ==> As a consequense, any shallow spectral signature may be reverse modeled by increasing Z until the water column corrected spectral bottom signature is observed to fit the spectral Soil Line within reasonable limits, ahead of any field work.

• a raster image of shallow depths in meters, which now may be turned into a bathymetric map
• a spectral water column corrected image of the shallow areas (like if at low tide), which now may be classified into a map of bottom types
• an insight on the water quality, through spectral K values in m-1, which may be commented in terms of underwater visibility

• no need for calibration of DNs into physical units of radiance, as this is a "ratio method"
• no need for formal atmospheric correction, as long as the deep water radiance may be estimated form some coverage of optically deep waters in the imager; that's until adjacency effect may be corrected for using affordable techniques
• no need for seatruth until next and final step

S/N ratio:

• because of the exponential nature of the attenuation of light in water, the performances shall depend on the S/N ratio (the so called Noise Equivalent Change in Radiance): it must be stated here that 
  • the dramatic -and much wanted- reduction of the footprint of the pixel has been obtained at the expense of any significant improvement of the S/N ratio 
  • the community at large shall not be satisfied by forthcoming progresses in shallow water modeling until the S/N ratio has improved as needed: QuickBird and now WorldView2 are clear examples of poor S/N ratio

Once suitable seatruth becomes available,

• Final_Z = coefZ * Computed_Z - TideToDatum
• The map of bottom types may be labeled into a habitat map