Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageriesbusy? see 4SM slides

Empirical vs Analytical
Further to Lyzenga and Maritorena:
a "ratio method" in three steps
BPL: concept of the Brightest Pixels Line
  • Get an estimate of deep water radiance in the image: spectral TOA Lsw.
  • Start with the radiance of a clean fine grained sand/mud on a beach in the image: spectral TOA LsM.
  • Choose a set of spectral diffuse water attenuation coefficients: spectral K (clear homogeneous waters).
  • Use the simplified radiative transfer equation to operate the exponential decay on LsM, by increasing Z from Zero until extinction.
  • In a bidimensional histograms of linearized TOA radiances:
  1. you get a conceptual model of the spectral Brightest Pixels Line: its slope is the ratio Ki/Kj for bands i and j
  2. just you need to use the real spectral K that applies to the image.
SL: concept of the Soil Line
  • Start with the radiance of a clean fine grained sand/mud in the image: spectral LsM. 
  • Darken all spectral bands, until pitch black (dark body).
  • In a bidimensional histograms of natural TOA radiances, this runs as a straight line from LsM to spectral La, the atmospheric path: this is the spectral Soil Line
Now, knowing that Lwnir=0,  
you can estimate the spectral water volume reflectance Lw=Lsw-La (homogeneous atmosphere):
no atmospheric correction needed.
Ztrue=offset + slope*Zretrieved   in meters
Now your conceptual model is complete, just you need to calibrate it
  1. Extract bareland pixels from the image, from bright to dark: they sample the Soil Line 
    1. this is where Z is null in the image for non-vegetated substrates.
    2. this is your zero-depth TOA spectral radiance reference
    3. offset=0
  2. Extract BPL pixels from the image over the whole depth range:
    1. this is where shallow bottom substrate is brightest over the whole depth range
    2. then you can measure the ratios Ki/Kj for all pairs of bands i and j in the image
    3. chose one of them, like Kblue/Kgreen at operational wavelengths WLblue and WLgreen
    4. use Jerlov's data to interpolate spectral K for all operational visible wavelengths, in m-1
      1. adjust wavelengths so as to achieve reasonably tight fits
    5. slope=1: this might still need to be fine-tuned using field data
You're done
Your simplified RTE is fully specified, it may now be "operated"
Results are retrieved depth and spectral water column corrected radiance for each shallow pixel

read more


Brightest Pixels Line      and          Soils Line


  • "4SM" stands for     "Self-calibrated Spectral Supervised Shallow-water Modeler"
    • 4SM is an implementation of the principles of passive multispectral bathymetry modeling.
    • It caters for multi/hyperspectral imagery, up to several tens of wavebands.
    • For the calibration of the optical model, 4SM only uses dry land and marine areas in the imagery itself along with Jerlov's table of spectral attenuation coefficients of marine waters worldwide.
    • Therefore, in most cases, field data are neither required nor used.
  • "RSP" stands for  "Remote Sensing Production"
    • Same Day: we want that the water column correction of a worthy 4-bands image should be achieved same day: operationality and ergonomy are wanted
    • RSP Ltd:   if/when appropriate, I should establish a place of business to be called something like RSP Ltd, in order to manage licensing fees
4SM is original
in that it uses only the image itself, as it is in raw DNs,
to "frame" the optical properties of the shallow water body.    
This means that no field data are needed.
  • All shallow pixels lie between"Brightest Pixels Line" and the "Soils Line".
  • This allows to compute depth and spectral bottom reflectance of shallow pixels.
  • Using a value Ki/j observed in the image,  operational two-way spectral attenuation coefficients are interpolated from Jerlov's table of diffuse attenuation coefficients for downwelling irradiance: this allows to compute depths in meters.
  • All this can be done ahead of any field work.
  • For a proper "finish", all computed depths then need to be multiplied   by a final adjustment factor which can only be derived from some sea truth when available, while spectral bottom reflectances remain unaffected.
The 4SM process is a "ratio method"
derived from the concepts behind "passive multispectral bathymetry modeling"
  • Passive refers to natural sun light.
  • Multispectral refers to RS imagery comprised of N wavebands in the visible range (N>=2).
  • Modeling refers to the estimation of the desired information using simplifying assumptions in order to operate the very complex physical model of radiative transfer of light through water for an applied purpose.
  • Although modeling may not be presented in simple plain terms,
    • it is necessary to present its nature and detail its limitations in respect of the services offered.
A summary of the 4SM process

4SM is an existing operational radiative transfer model process which
  • uses multispectral or hyperspectral remote sensing imagery
  • to achieve water column correction of spectral radiance (~="a low tide view ")
  • and yield an estimate of water depth (="a digital terrain model ") at each shallow pixel ,
  • without the use of any field data.  
Applications to Remote Environment Assessment and Coastal Zone Management.

Simplified RTE
A widely accepted simplified operational radiative transfer model
for a shallow bottom is
  • ..................................... Ls= La + Lw - Lw/ exp (KZ) + LB/ exp(KZ)    top    of the atmosphere (TOA )
  • which may be rewritten   L = Lw + (LB-Lw)/exp(KZ)                              base of the atmosphere (BOA)
  •  where, at any given wavelength in the visible to near infra-red range,
    • La                     is the atmospheric path radiance
    • Lw                    is the BOA water volume backscattering radiance over optically deep water
    • Lsw=Lw+La   is the TOA radiance over optically deep water
    • K(in m -1)         is an operational two-way attenuation coefficient for remote sensing radiance
    • Z(in m)             is the depth of the shallow bottom
    • L                        is the BOA radiance for the shallow bottom at depth Z
    • Ls=L+La          is the TOA radiance for the shallow bottom at depth Z
    • LB                     is the BOA water column corrected radiance for the shallow bottom (i.e. if Z=0)
    • LsB=LB+La     is the TOA water column corrected radiance for the shallow bottom (i.e. if Z=0)
Please note
  • Physical units of radiance
    • Radiance terms in this model do not need to be specified in physical units of radiance. Radiances may be raw digital numbers.
  • Atmospheric correction to BOA reflectance
    • If   K, La and Lsw are assumed to be constant over the remote sensing scene and may be estimated from the image,  then the image does not need to be corrected to BOA reflectance for atmospheric path radiance
  • Ratio method
    • Using a band ratio method to derive both Z and spectral LB only requires that spectral LB meets a certain condition.

Like most existing operational propositions,
the 4SM process assumes that
the deep water radiance Lsw
may be estimated from the imagery itself.

Unlike all current methods,
the calibration of the optical properties of the model in  4SM
  • accounts for the color of the water column,
  • and does not need or use any field data. 
In an innovative approach in 4SM:  
  • SL: the concept of the "soil line"
    • uses the bare land areas of the image to derive an average spectral model of the desired water column corrected image: a spectral bottom reflectance reference model at null depth. 
    • This shall be used to specify the above mentioned required condition on spectral LB,
      • which, among other things, eliminates the need for a spectral library of bottom type end-members to be collected on site.
    • This is a distinct improvement  of Polcyn et al.'s work (1970).
  • La: estimating the atmospheric path radiance
    • The soil line also allows for the estimation of the spectral atmospheric path radiance La,
    • and therefore of the spectral water volume backscattering radiance Lwin Lsw=La+Lw, 
    • thus permitting a first order atmospheric correction of the imagery at the base of the atmosphere.
    • This is a distinct improvement  of Polcyn et al.'s work (1970).
  • BPL: the concept of the "brightest pixels line" 


Calibrating spectral K in units of m-1
  • Using one of these ratios and Jerlov's published data on marine optics (1976),  
  • and in line with Kirk's statement that "a family of curves, of progressively changing shape, determined mainly by phytoplancton concentration, is observed. Thus, for any given oceanic water, specification of the ratio of radiances or radiance reflectances at any two wavelengths should, in effect, specify the whole radiance reflectance curve, and therefore the optical character of the water ",
    • one then derives one seed K value, either  Ki or Kj ,
    • which then is enough for specifying all required spectral K values across the whole visible range (400-700 nm).
  • This avoids the need for field calibration data,
    • and is enough to "ballpark" the optical calibration very closely.
  • Interestingly, the estimated spectral K values are very close to sea-truth derived values.
  • To this extent, it means that 4SM is NOT site-specific
  • Still, the spectral bottom reflectances only depend on the series of ratios
    • as seed value only needs to be realistic for computing shallow water depth in meters

  Now that all model parameters are specified
  • Z and spectral LB are then derived  at each shallow pixel in the image by inversion of the above model ,  assuming that, for the assumed depth Z, the average spectral water column corrected  bottom signature LB must approximately match the spectral soil line.
  • The output are
    • a DTM of the shallow water area,
    • and also " a low-tide view of the scene in units of radiance" ready for shallow bottom typing by current thematic classification methods.
  • Quite close: interestingly, the estimated spectral K values are very close to sea-truth derived values.
  • Some sea-truth data is needed though for fine-tuning the estimation of Z,
    • while the "low tide view of the shallow bottom" remains unaffected.
 This method was presented by Morel and Lindell (1998)  
and is illustrated on the Internet at https://www.watercolumncorrection.com/

It is very close to – but much more comprehensive than- the method used
by Malthus and Karpouzli (2003) who relied heavily on field data
both for atmospheric correction and for optical calibration.

It is distinctly different from -and much better than-
NOAA's "Log ratio method" by Stumpf and Holdereid (2003).

An example of the results of the optical calibration is presented in table 1 below.

Table 1 :  Optical calibration of the shallow water body 
at Mahone Bay,   Nova Scotia, Canada,  
as estimated from CASI imagery (2001).

Water type was found to be approximately JERLOV type OIII+0.12 
for an observed ratio K 490/K 654=0.286.

(1): the CASI image has 17 wavebands
(2): wavelengths are in units of nanometers
(3): two-ways operational attenuation coefficients are in units of m -1
(4): maximum depth of bottom detection Zmax over bright bottom is in meters


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