Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageries
Optical Calibration
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The optical calibration process aims at specifying all parameters
which are needed to process raw data into usefull output.

It is a complex process which involves the practitioner's expertise
and a reasonable background in atmospheric and underwater optics.

In other words, it is not a "push-button" process:
the practitioner must take responsibility .


The final set of modeling parameters is a trade-off of between

  • a simplified radiative transfer equation (or model)

  • the realities of a remote sensing image.

It is effectively observed that
the simplified radiative transfer equation (RTE)
fits RS radiances to reasonable satisfaction in most cases


Calibration diagrams are at the heart of the 4SM process.
They use only a selection of raw (or smoothed) pixels of the image
and also Jerlov's optical classification of marine water types worlwide.

We have observed that
Jerlov's table of diffuse attenuation coefficients
for downward irradiance of CASE_1 marine waters worldwide Kdwl
fits effective two-ways attenuation coefficients
of remote sensing shallow water radiance Kwl ~=2Kdwl
to reasonable satisfaction,

subject to a satisfactory choice of wavelengths


Optical calibration involves the interpolation of an intermediate curve
among Jerlov's familly of curves of diffuse attenuation coefficients
for downwelling irradiances.

This intermediate curve (see below)
is then assumed to describe the spectral operational K values
that shall be applied to the water column correction
of the shallow areas of the remote sensing image under study.

This requires the choice of spectral wavelengths Syntax WL
and sound specification of the BPL model


Bad calibration pixel for the red band

  • Application of Kblue/Kgreen=0.48 entails a Jerlov water type OIB+0.45: the red intermediate curve
  • A bad choice has been made for the red band in the -CP argument, as it clearly implies a K red value lower than K red for pure water!
  • This must sound physically unacceptable to the practitioner - 4SM detects such situations and aborts
    • and shall be taken care of by adjusting the -CP argument accordingly

Good calibration pixel for the red band


  • The -CP argument has been modified for the red band
  • Now spectral K values are fully specified into a physically consistent system for all visible wavebands.




Is the BPL assumption trustworthy?



  • Under the BPL assumption,
    • the linearized BPL pixels display as a straight line.
  • The slope of this straight line is the ratio Ki/Kj
    • for all pairs of wavebands i and j with wavelengths WLi and WLj.
  • This series of ratios for all pairs of wavebands in the spectral image
    • forms a physical system where one must be satisfied
    • that Ki/Kj = (Ki/Kk) / (Kj/Kk) for all wavebands i, j and k.
  • Any seed Ki value may now be entered in order to specify spectral K using these ratios:
    • this shall allow to compute a spectral water column corrected image of the shallow areas of the image
    • but water depth values are still not really calibrated in meters.
  • Wavelengths then must be specified for all wavebands,
    • so that spectral K may be derived
    • from Jerlov's classification of optical properties of marine oceanic and coastal waters worldwide.
  • The final result is spectral K values, which allow to compute water depths in meters, together with the spectral water column corrected bottom reflectance, for each shallow pixel of the spectral image.
  • Ideally, after water column correction, all spectral BPL pixels should display over the LsM point on the Soil Line in a plot of Lsi vs Lsj.
    • These water column corrected BPL bottom reflectances should be spectrally absolutely neutral, as we can expect for clean and bright sands like coral sand/ooze or quartz sand: this is the case at Tarawa atoll.
  • This is far from being the general case though
    • o as even very shallow pixels often tend to be spoiled by some kind of vegetation or micro-algae activity,
    • o in which case even the supposedely "cleanest and brightest" bottoms happen to be spectrally contrasted to some extent: this is the case at Caicos Bank.


Tarawa atoll is the showcase for a trustworthy BPL with Green, Red and NIR bands.


Very bright and clean coral ooze sloping extremely gently towards the inner lagoon.
Operational wavelengths for a SPOT XS wavebands have been shown
to be at 550, 650 and 850 nanometers. Please refer to ERIM98.

Using these wavelengths and Jerlov's data, one gets trustworthy spectral K:
the water depth image is fully calibrated in meters , with no need for any field data.

Here is the winner Landsat calibration
with Blue, Green, Red and NIR


Here  is the winner CASI calibration with 17 bands


Knir at ~4.45 m-1 seems to fit all as a first order estimate?



Casi imagery at Porquerolles Island, French Riviera, yields the best calibration in town!
Here at 508, 585, 644 and 845 nanometers, pixel size: 1 meter

If/when you loose faith, please remember this: the BPL concept works fine!

Path radiance: see in particular that it is very clear how the atmospheric path radiance
is determined by use of the Soils Line by NIR here.

See that wavelengths adopted for this CASI bandset at Porquerolles fits well an intermediate curve
of Jerlov's classification of marine waters

The best CASI calibration in town






like here at Caicos Bank, Bahamas,
where the tmnov subset is too small with too wide pixels
to allow for a correct estimation of the BPL

The practitioner must exercise much care!

View the location of BPL calibration pixels for the tarawa-subset image



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