1 - NO NEED for field data, nor for atmospheric correction
2 - this is demonstrated in this website, using a variety of hyper/multi spectral data
 
Requirements are
1 - homogeneous water body and atmosphere
2 - some coverage of optically deep water
3 - some coverage of dry land
 
Problems are
1 - the precision on estimated depth is found wanting, because the noise-equivalent change in radiance  of accessible data is too high for shallow water column correction work 
2 - radiance data should be preprocessed by the provider at level 1 in order to improve S/N ratio
3 - exponential decay: the deeper/darker the bottom, the poorer the performances
 
So
I keep digging
until suitable data
become available
 
This series of thesis undertakings shows that the School definitely
aims at servicing the Navy's needs for shallow water bathymetry,
water quality and bottom typing, 
using existing and affordable data and techniques.

In spite of more than 30 years of continued efforts by NSF, NRL, NASA, NOAA,
and the scientific community at large, 
the situation now is that there is no sign
of an acceptable operational solution to this problem.

 

In my view,
and after studying hundreds of multispectral and hyperspectral images
and used limited seatruth datasets
for eighteen years,

I have come to the following conclusions:

 
  • 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.
This yields:
  • 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
Please note:
  • 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


Use the PANchromatic band as an additional MULTI band