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

Stumpf's non-linear inversion
Stumpf et al 2003
Lyons, Phinn & Roelfsema 2011
Bramante et al
Tedesco & Steiner 2011
Malthus & Karpouzli at Eriskay Sound, Scotland
Tulldahl et al: bottom typing in the Baltic


"Determination of water depthwith high-resolution satellite imagery
over variable bottom types"
  • "an empirical solution using a ratio of reflectances"
  • the most widely used operational method
  • developped and used extensively by NOAA for coastal mapping of remote areas in the US
    • because the standard linear transform approach (Lyzenga's) cannot process extremely low-albedo bottom features and requires the -all too uncertain- estimation of deep water reflectance
  • uses BGRN images (Ikonos, Quickbird,...)
  • is more robust than the standard linear transform approach (less prone to light water turbidity)
  • Requires BOA radiances, i.e. real atmospheric correction
  • Requires existing depth measurements coefficients m0 and m1 in equation 1
  • Does not yield a watercolumn corrected image
  • Ignores totally the physics of the underwater light field
  • For a comparison, see https://www.watercolumncorrection.com/sld082.php
    • 4SM does not need formal atmospheric correction
    • 4SM does not need existing depth measurements for the calibration of the optical model
    • 4SM processes extremely low-albedo bottom features
    • 4SM yields both a bathymetric map and a watercolumn corrected image in units of image's DN, ready for bottom typing


  • 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"

Lyzenga's own method
the log-linear bathymetric inversion for dummies
  • this model fails to account for the fact that the water volume reflectance Lw is equal to Lsw-La after glint removal
  • because the data now are BOA radiances
    • La now equals 0 for all bands
    • Lw now equals Lsw, and decreases as wavelength increases, with Lw=0 in the Red to Nir range of the solar spectrum
"Assuming that the ratio of bottom reflectance between two spectral bands is constant for all bottom types within a given scene..."
  • Well, this amounts to assuming a Soils Line in a scatterplot of Lbi vs Lbj natural data!
  • coefficients must be estimated using existing seatruth data which need to sample the whole depth range over the whole range of bottom reflectance in a faithfull manner (NOT a common situation!)
    • a0 is an offset in meters
    • coefficients ai are weights which incorporate gi
"In areas with dark substrate where radiance (L) is lower than deepwater radiance L∞, depths cannot be derived from the log-linear inversion mode"
How about 4SM? ==>YES we can!



Stumpf's own method, extended by the authors
the non-linear automated calibration for dummies

"Calibration of Non-linear Inversion Model Based on Levenberg-Marquardt Method"
  • done with the Lsw deep water radiance term: too uncertain
  • only uses the Blue and Green pair of bands
"SHOALS system for ground-truth depth points with which to calibrate and compare the performance of the two
bathymetric inversion models"
  • coefficients m0 and m1 must be estimated using existing seatruth data
  • Mind you: SHOALS Lidar seatruth data!
  • How about 4SM? ==> NO we dont need seatruth data to calibrate the model
"the non-linear inversion model is more robust and accurate than the the conventional log-linear inversion model for relatively deep areas"
  • I suppose that this is because the red band is NOT used at all, therefore cannot warp the results over "relatively deep areas"
"As shown in our assessment, the predicted-depth accuracy from IKONOS satellite images is about 1–2 m for shallow (0–15 m deep) substrates and about 3 m for deeper (15– 20 m deep) substrates. This level of vertical accuracy is generally considered inadequate for navigational purposes in shallow waters. However, the derived bathymetric information is useful for many scienti?c and practical coastal management applications."
  • How about 4SM ==> the predicted depth accuracy is significantly better than that
    • in waters less than ~4-5 m because 4SM uses all visible band
    • in general because the log-linear method entails 



Lyons, Phinn & Roelfsema 2011

 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

I wish I'd be viven the opportunity
to show what 4SM can do
on your WV2 image of Heron Island



World View 2

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
==> same process as in 4SM
  • 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
==> this is a pain; can't we avoid that please, for sake of operationality? YES we can in 4SM
  • 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
I wish I'd be given the opportunity to process this image using 4SM

  • 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

Bramante et al

"Derivation of bathymetry from multispectral imagery in the highly turbid waters of Singapore’s south islands: A comparative study"
  • 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


 Tedesco & Steiner 2011

"In-situ multispectral and bathymetric measurements over a supraglacial lake
in western Greenland using a remotely controlled watercraft
  • 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


Malthus & Karpouzli at Eriskay Sound, Scotland

  • 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

Tulldahl et al: bottom typing in the Baltic
  • 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


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