• 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.

• 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 calibrated BOA reflectances
• 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 K_BLUE/K_GREEN  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 K_BLUE/K_GREEN  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.

•  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

4SM modeling performances

TechWorksMarine:
Improving Satellite-derived Bathymetry Using Spatial Regression Algorithms