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
add the PANchromatic band to the multispectral bands YES: 4SM does it
       Your comments are invited                   See you on 4SM blog    

4SM errors
4SM conclusions

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


from Hydro-International 2015

Satellite Derived Bathymetry Migration 
From Laboratories to Chart Production Routine

Two SDB Methods in a Nutshell

  • Empirical    methods    explore    the    statistical relationships    between    image    pixel    values    and    field    measured    water    depths.
  • Analytical    approaches    rely    on    the    general    principle    that    sea    water    transmittances at    near-visible    wavelengths    are    functions    of    a    general    optical    equation    dependent on the intrisinc optical properties of sea water. A number of external factors  affect    the    accuracy    of    the    depth    calculation,    including    the    spatial    and    spectral resolution    of    the    imagery,    the    viewing    angle    of    the    satellite,    the    solar    illumination angle,    atmospheric    effects,    sunlight,    tide    level    and    submerged    vegetation.    Careful selection    of    satellite    imagery    and    subsequent    image    processing    can    mitigate    some of    these    effects.
Anything in between?
YES, see 4SM
4SM is an empirical  "ratio method" operating a radiance inversion approach
which does not need any 
field  measured water depths for calibration
  • which relies on an understanding of the physics behind
  • which requires the practioner to maintain physical consistency among parameters
    • rather than rely on existing depth measurements and multiple regressions
  • which assumes homogeneous atmospheric and water optical properties
  • which, being a ratio method, does not  need conversion of TOA DN radiances into BOA reflectance
  • which uses bareland pixels in the image to specify the agronomer's Soil Line concept
    • as a spectral reference for shallow pixels pixels at null depth
    • this then leads to approximate estimation of the spectral atmospheric path radiance: no need for formal atmospheric correction,
    • uses the "dark pixel" assumption
  • which requires proper removal of sea-surface clutter (glint)
  • which relies on the estimation  of spectral opticaly deep water radiance from the image
  • which relies on measuring the ratio KBLUE/KGREEN  from shallow areas of the image, as proposed by Lyzenga        
  • which uses Jerlov's table of diffuse attenuation coefficients of marine waters for specifying spectral K in the visible range as a function on the ratio KBLUE/KGREEN  observed for the shallow areas of the image, as observed by Kirk.
  • which uses a visual display of the optical calibration diagram as a powerful tool to ascertain physical consistency of all parameters
  • which then uses the inverted simplified radiative transfer equation (RTE) proposed by Maritorena et al 1994
    • to optimize the estimation of derived depth which results in an acceptable fit of the water column corrected spectral bottom signature of each shallow pixel with the Soil Line
    • although contrasted bottom signatures entail potentially severe bias on retrieved depth
  • which then uses the image metadata to convert spectral water column corrected bottom signatures into calibrated reflectances (0-1), ready for bottom typing and time series studies.
  • operational 2K~=2*a over the 0-10 m depth range
  • this results in satellite derived depths calibrated in meters without the need/use of any field data for calibration purpose.
  • this has been verified against many seatruth datasets, using SPOT, Landsat, IKONOS, WV2, QUICKBIRD, CASI, HYPERION and HICO.
Processing a time series of images results in
a plain DTM of shallow areas devoid of cloud/shadow artifacts
where outliers like NoData 
and transient situations
like discoloured waters or turbid plumes 

have been excluded from average combined depth

4SM in a nutshell:
  •  4SM operates the "simplified radiative transfer equation" as suggested by Maritorena, Morel and Gentilly, 1994, under the proviso that both atmosphere and water column are homogeneous over the ROI, vertically ans spatially, and that sea-surface clutter has been removed (sun/sky glint).
  • this means that most of the atmospheric/water_column complexities involved in analytical methods are rounded up into two variables:
    • a TOA spectral Lsw deep water radiance term or a BOA Lw deep water radiance term
    • a spectral two-ways diffuse attenuation coefficient 2K term in units of 1/m
  • therefore, the spectral TOA signal is  Ls=Lsw+LsB-Lsw)/exp(2K_Z) in units of image DNs
  • therefore, the spectral BOA signal is  L =Lw  +LB  -Lw )/exp(2K_Z) in units of image DNs
  • where
    • Lsw=La+Lw,
    • La is the atmospheric path radiance,
    • Lsw is the TOA deep water radiance (backscatter light flux)
    • Lw  is the BOA deep water radiance (backscatter light flux)
    • BOA=base of atmosphere,
    • TOA=top of atmosphere,
    • "spectral" means "for all visible operational wavelengths in the image"
  • operating the simplified RTE (aka "inverting the model") is done by increasing water depth Z in units of meters: LB=Lw+(LB-Lw)*exp(2K*Z)
    • until the BOA LB spectrum is deemed to match closely the Soil Line that has been observed over bare dryland in the image
    • this is an optimization process
  • this requires knowledge of applicable spectral 2K in units of 1/m
    • this is gained by estimating the ratio Ki/Kj for all pairs of visibles bands in the image, as directed by Lyzenga
    • then interpolating Kblue and Kgreen using Jerlov's table of diffuse attenuation in water for downwelling sun light
    • then using Kblue or Kgreen to interpolate all Ki for visible bands
  • because 4SM is a "ratio method", radiance terms need not to be specified in units of calibrated reflectance,
    • therefore there is no need for formal atmospheric correction
    • nor for conversion of the water leaving signal into calibrated reflectance.
  • 4SM does not require a LUT of bottom substrate endmembers
  • 4SM runs 40 times faster than the fastest ALUT method, while yielding similar results
Note from Sachak Pe'eri, NOAA, 2015 
"For an algorithm that can be used by the hydrographic community on a COTS GIS software, a ratio transform algorithm based from an optimization approach provides a robust solution that does not require to sample the environment or generate a database. "
this applies to 4SM

Jupp's DOP zones
    Bierwirth's approach
Fancy methods
Lyzenga's log-linear inversion
Stumpf's non-linear inversion
(semi)analytical methods
reviews and comparisons
US Naval PostGraduate School

4SM modeling performances

Dec 2013: I give up reporting, this is red hot!
Just see HYPHOON and join the crowd
SDB: satellite derived bathymetry is now at the forefront
useful and practical, even if lacking required hydrographic accuracy
In short, SDB has been confirmed; not as an overrated exploration tool,
but as a new sensor capable of providing calibrated and validated depths to the marine cartographer.

IHO              NOAA presentation        IHO-IOC GEBCO Landsat 8 cookbook 2015

Fugro International


Improving Satellite-derived Bathymetry Using Spatial Regression Algorithms

Busy? 4SM in 10 lines