Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageries
Busy? 4SM in 10 lines
Review of some papers collected on the net

This review shows how hot this area of R&D still is!  

return to 4SM Study Cases

As it turns out, this review shows that most of those
go through formal atmospheric correction and  calibration  to reflectance 4SM does not
are mostly stuck with either Lyzenga's model or Stumpf's model 4SM innovates
need existing depth sounding to yield water depth 4SM does not
don't even mention water column correction and bottom typing 4SM does it all

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
I keep digging
until suitable data
become available



Jupp's DOP zones
Deidda and Sanna, 2012 using WV2

Bierwirth et al 1993
see ETM at  Hamelin Pool
  • BOA data: RE = (e-2kZ)Rb + (1 -e-2kZ)Rw??
    • Bierwirth's method requires atmospheric correction to BOA data
  • It can be noted that pixels display as linear clouds for the Blue and Green bands, but not quite so for the Red band
    • measuring 2Kblue and 2Kgreen is straightforward
    • measuring 2Kred in impossible
  • Bierwirth's Kred=0.194 m-1 ==> 2Kred=0.392 m-1 at Hamelin Pool is physically un-acceptable:??
    • the red band would show bottom detection down to (ln(200)-ln(1))/0.392~=13.5 m over a very bright shallow bottom in a bright Landsat TM image, whereas it seldom exceeds ~6-7 m!
    • 2Kred actually varies in the range of 0.6 m-1 to 1.0 m-1 in Jerlov's clear waters (two-ways) for in TM/ETM images
  • with Kblue/Kgreen=0.85
    • the measured slopes of 2Kblue=0.20 m-1 and 2Kgreen=0.26 m-1 are quite obvious from looking at Fif. 4
      • although I measure 2Kblue=0.25 m-1 and 2Kgreen=0.30 m-1 with Kblue/Kgreen=0.83
    •  Hamelin Pool's surface waters from 0 to 4 m would have water type ~OII+0.5 of Jerlov
  • with Kgreen/Kred=0.68, Hamelin Pool would have water clearer than OI of Jerlov?
    • Oceanic I of Jerlov is Sargasso sea
  • with Kblue/Kred=0.53, Hamelin Pool would have water type ~Coastal 4 of Jerlov?
    • we observed 2Kred~=0.8 m-1 in Hamelin Pool in 2000
  • All this is definitely inconsistent
  • As for M=0, well what can I say?
    • M=0 "standardizes the geometric mean of substrate reflectance for every pixel" Hmmmf... quite a fuzzy concept
    • in equation 14, for each band i with bottom detection at the current pixel, ln(Rbi)/2Ki equals the maximum detectable depth. Therefore M is the average of all these maximum detectable depths at that current pixel
    • in equation 15, we see that M is a depth offset which is specific to the actual bottom reflectances of the current pixel
    • "It is important to note that, in applying the constraint which standardizes the sum of the logarithms of band substrate reflectances, we introduce errors in depth determinations. These errors are greatest for dark substrates which will resolve as deeper than true." This is particularly obvious at Hamelin Pool over the area where a dark diatom rich ooze is reported.

  • Seatruth
    • First source of systematic error in so-called linear methods:
      • bright and dark shallow bottoms shall get an underestimated Z
      • while other pixels shall conversely get an overestimated Z
    • Second source of systematic error in so-called linear methods:
      • Offset: this an offset which may be viewed as needing a tide height correction (~3.5 m here)
    • Third source of error in so-called linear methods:
      • Slope: K values may have been mis-estimated, hence a possible slope not being equal to 1 in the seatruth regression
    • Fourth source of error with all methods:
      • Bottom detection limit: clearly visible here: if the Red band is used beyond its bottom detection limit (at most ~6-7 m, for a very bright bottom in very clear waters), things happen!
      • Bottom contrast:
        • for 8 bits DNs, bottom contrast=Ls-Lsw
        • bottom contrast of at least 1 DN, but quite often much more where the S/N ratio of the data is poor, is needed for a band to be enabled in the computations.
  • The authors refer to clearer waters at depth for a possible explanation of the change in slope beyond seatruth depth ~4 m in this regression plot
    • in other words, depths are underestimated because 2K are overestimated


Huguenin et al 2004
  • A special version of the Subpixel Classifier in ERDAS Imagine, by Applied Analysis Inc.
  • "It uses Image Calibrator to automatically convert the detected water spectrum to units of apparent re?ectance, utilizing image data alone and requiring no ground truth or external information"
  • This method sits somewhere between "empirical methods" and "semi-analytical methods"
    • uses " a four-dimensional re?ectance look-up table" 
  • Oddly, this commercial method does not seem to be cited in the literature,
    • although it has a lot to offer
  • I say : try it, if you want, you should not be deceived provided you can master the beast
    • I'm not sure whether the LUT is site specific or not
  • But make sure first that 4SM can't meet your needs while providing an acceptable level of control
I wish I was given the opportunity to show
what 4SM can do using these Ikonos images



  • An even grander approach for the military
  • Here we get MonteCarlo simulation
    • for computing shallow water depth and water column corrected bands
    • using airborne hyperspectral data

Neural network
quite effective; training requires adequate depth soundings though
Neural network in Turkey          Turkey    
Remote Sens. 2013, 5, 2746-2762; doi:10.3390/rs5062746
 NRL : Sandige et al 1998
SPC Magron