• GREAT READING indeed
• BOA radiances: the data are expected to be corrected for atmospheric and glint effects
• Their problem : 
  • the log-linear bathymetric inversion -Lyzenga's- can't model in case of negative bottom contrast
    • "The non-linear inversion model -Stumpf's- avoids the problem encountered for dark substrates such as dense macroalgae or sea grass.
    • In those areas with dark substrate where radiance (L) is lower than deepwater radiance
      L∞, depths cannot be derived from the log-linear inversion model"
  • the non-linear bathymetric inversion is too difficult to calibrate
    • "Stumpf et al. (2003) tuned the model parameters manually with several reference points in a trial and error manner, but this method is only possible with a small number of reference depth points. 
    • The low number of reference points reduces the reliability of the calibration and the likelihood that optimal model parameters will be determined"

 The authors set out to map bathymetry and changes of bottom types
at Moreton Bay, Australia, using two Quickbird images

• Flaash atmospheric correction

• Refering to a reliable bathymetry is a desirable component of any bottom typing effort: "The bathymetry field data was used to select training sites of specific cover and albedo at known depths"

• Seatruth data is not tide corrected

• Two bathymetric method were tested

  • Linear inversion method (Lyzenga 1978)

  • Ratio method (Stumpf et al 2003 )

• Ratio method impossible to calibrate in this environment

• None was found satisfactory over seagrass

• No deglinting was performed
• Green band only was used in Lyzenga's method : this is the "one band case"
• Blue and green bands were used in Stumpf's method
• None of these two bathymetric methods account for water column reflectance
• This explains why "There was no linear relationship between water depth and observed reflectance over seagrass cover type"
• See 4SM seatruth at Lee Stocking Island
• 4SM calibration is NOT site-dependent
•  

Jeremy KERR is with NOOA's NCRI in Florida
WV2 : Jeremy KERR at Florida keys, with SHOALS seatruthdata

This is DigitalGlobe's 8-bands challenge
"Worldview-02 offers new capabilities for the monitoring of threatened coral reefs"

• First removes the sea-surface glint

• Then converts "at-sensor radiance values to at-sensor reflectance" through a complex process which involves "the corrected extraterrestrial irradiance at the top of the atmosphere", a wavelength-dependent parameter which is integrated over the waveband width using
  • "the extraterrestrial irradiance at the top of the atmosphere",
  • "the sun azimuth angle",
  • Julian day,
  • etc

• Then performs a "deep-water correction for atmospheric effects" : an "image statistic- based" dark-body correction method to remove path radiance, which, as opposed to established "algorithms and modules for atmospheric correction that rely upon radiative transfer theory", only requires
  • "the apparent reflectance"
    • this was derived through the previous step
  • "the water-surface reflectance", alias sky and sun glints, which must be removed
  • the sea water reflectance : "the sea water reflectance, as described by Morel and Prieur (1977) was used for this value" (how they do that in practical terms???)
    • this is the water volume reflectance generated through backscatter by the water column, in order words the color of the sea, at each waveband
    • "deep waters can be assumed to have a seafloor reflectance equal to zero at all wavelengths, allowing an image subset over deep-water to be used in estimating atmospheric reflectance"
    • ==> this sounds weird to me, as "an image subset over deep-water" exhibits  a radiance which equals the sum of the water volume radiance and the path radiance and the sea surface radiance
    • ==> this sounds like
      • the color of the sea in the blue-green region of the solar spectrum is ignored,
      • and the path radiance is overestimated accordingly, which, as I view it, can only result in over-correcting the Green wavebands, and most importantly the Blue wavebands
    • ==> I'm getting confused here
    • ==> If the water-volume reflectance is not correctly accounted for in the inversion, then there is a risk of over-estimating the water depths over the darker bottoms, and under-estimating the water depth over the brighter bottoms in fairly clear waters : this is a characteristic of Stumpf's method

• Then used Stumpf's band ratio method, modified and expanded to 63 band ratio combinations among visible bands: Stumpf's method becomes a multiple linear regression
  • Use existing depth data for calibration (mind you : SHOALS!)
  • Comprehensive statistical study, in search for optimal preprocesing and optimal model: more bands in WV2 result in improved performances
  • RMSE = 0.77 m for the full model using all visible bands available:
    • this markedly improves on the simple band ratio of Stumpf's method, particularly over bright substrates
  • Overestimation of Z at very shalow depth and  underestimation of Z deeper than 10 m
  • THIS METHOD DOES NOT ACHIEVE WATER COLUMN CORRECTION FOR BOTTOM TYPING
    • 4SM does: this provides an opportunity for the practioner to identify areas where results might be faulty 

• Rick Stumpf is with NOAA
• Jeremy Kerr's work at NOAA's NCRI uses and generalises Stumpf et al.'s method for deriving estimated shallow depth using a WorldView 2 image
• NCRI is NOAA
• ==> NOAA have devised and used Stumpf et al.'s log ratio method for extensive use in their shallow-water benthic habitats mapping programme throughout the Pacific
  • this probably represents thousands of high resolution BGRN images 
• in other words, NOAA's log ratio method has been proved to work to satisfaction!
• still it has its own flaws and limitations
  • systematic, but progressive, bias on computed depth:
    • depths over bright bottoms tend to be  under-estimated
    • depths over dark   bottoms tend to be    over-estimated
  • field data are required for calibration
  • no water-column correction is performed

• turbid waters
• atmospheric correction  by the "cloud shadow method" to above-surface reflectances
• bathymetry by Stumpf's Linear Ratio Model
• spectral look-up tables
• use existing depth data for calibration
• Linear Band algorithm is modified
• study limited to depth < 2 m

• GREAT READING, the underwater optics are nicely rounded up in simple terms
• Landsat and WV2 images are used, atmospheric correction using FLAASH
• The authors investigate the diffuse attenuation coefficients and the bottom albedo in melt water ponds on Greenland's ice shelf,
  • with a view to computing water depths and monitoring volumes of melt waters in the perspective of Climate Change
  • based on Philpot's (1989) simplified radiative transfer equation, which is most similar to Maritorena et al's (1994) RTE that 4SM operates
• They seem to operate the "one-band case", using their measurements of bottom albedo at null depth and of diffuse attenuation coefficients denoted g
• They state state that they "plan to use a more sophisticated model of the water column (Lee, 1999), in which depth estimations can be made with a fully physical model of water constituents"

• in fig 3,  parameter g values denote the two-ways diffuse attenuation coefficients
  • 0.0233 m-1 for the blue band and 0.24 m-1  for the green band stand for very clear waters in Jerlov's terms
  • 0.812 m-1 for the red bands stand for a much less clear water, but scattering might be to be blamed, as the content in chlorophyll can't explain that
  • this dataset provides an opportunity to investigate the question of operational wavelengths for Landsat's wide wavebands, and quite a number of aspects of what 4SM does

see 4SM results in Greenland using Landsat, ALI and HYPERION images
I wish I was given the opportunity
to demonstrate 4SM results using this WV2 image
and depth soundings for seatruth

• derive water-column corrected spectral bands, using
  • an Ikonos image,
  • underwater measurements to derive attenuation coefficients,
  • and complete existing co-registered DTM,
• for the purpose of bottom typing

• No need for any existing depth
• No need for underwater measurements to estimate attenuation coefficients 
• to get the same results, plus the attenuation coefficients, plus the shallow DTM
• using 4SM
• in just a fraction of the time
   

• Atmospheric correction
• Lidar depth coverage is used to derive water optical properties, and then map water column corrected bottom reflectance
• Bottom classification in the Baltic, using WV2 image