4SM for dummies

Deal or NoDeal?

It shall be seen that an acceptable calibration which yields acceptable results
- is a fuzzy concept in respect of the many parameters involved
- even though we are using a simplified radiative transfer model
What is important is NOT
- that a physically exact calibration has been achieved
- leave that for the big boys at NRL, or EOMAP, or CSIRO
Rather what is important to us
- is that a coherent set of calibration parameters be assembled
- so that an acceptable and usefull result be produced : DTM and bottom type classification
- using only the image
4SM offers an integrated set of ergonomic tools to achieve that
- within a short time frame

Dummies please

Where is the competition?

Basic equation

L = Lw + (LB-Lw)/exp(K*Z)

LB = Lw + (L - Lw) * exp(K*Z)

Now, suppose

we have a clean BOA spectral image,
- after removal of glint and path radiances,
- with wavebands of increasing wavelengths labelled i, j, k, ...,n
and effective wavelengths WLi, WLj, WL..., WLn are known for each waveband
and BOA spectral L and Lw are estimated from the image
and BOA spectral LM radiances are estimated for bright bareland in the image
and the complete series of Ki/Kj ratios are estimated from the image for all pairs of bands

Then the water column correction
of the shallow marine area may be performed

At this stage, the product is comprised of

Retrieved depth: a map of the water depth for the shallow marine area in arbitrary units
Bottom typing: a map of the BOA water column corrected spectral bottom reflectance in units of image DNs, ready for bottom type classification

If a seed value for K is derived using Jerlov's data
then then K is specified for all visible wavelengths

Retrieved depth: at this stage, the above map of the water depth becomes a provisory bathymetric map in units of meters
Bottom typing: this does not affect the water column corrected bottom reflectances, though

When suitable field data become available

Final bathymetric map: then a final retrieved Z may be computed:
- a final coefficient may be estimated and applied to all retrieved depths
- the tide correction may be applied to retrieved depths
- so that the provisory bathymetric map becomes the final bathymetric map
Habitat map: the bottom types may be given an appropriate habitat label
- the bottom type classification becomes a habitat map

BOA Soil Line

Suppose the various ratios LBi/LBj for non-contrasted shallow bottom signatures at null depth
- like clean bright to dark sands, muds, clean rocks and gravels, bare soils
- are known for all pairs of wavebands i and j from some bareland areas in the image
Then in a bi-dimensional histogram of BOA radiances for the pair i and j, this Soil Line
- extends as a straight line scatter
- from a maximum=LM, the radiance of the brightest shallow bottom type
- to a minimum= 0, the radiance of a black body at the base of the atmosphere

Normalization of the data
arrange for all ratios LMi / LMj = 1
(this assumes a "flat" non-contrasted bottom signature)

Normalize all BOA radiances LM, L, and Lw,
- so that the various ratios LMi/LMj now equal 1
For all non-contrasted shallow pixels at depth Z=0
- Li = LBi
- Lj = LBj
For all shallow pixels at depth Z>0
- Li<LBi
- Lj<LBj
- Li>Lj because Kj>Ki

Now compute Z and spectral LB all at once

for a pair of bands i and j, increase Z in the inverted model
- until the ratio LBi/LBj reaches 1
  - because Kj>Ki, LBj increases faster than LBj
  - LBi/LBj decreases from being >1 to a value of 1 when correct Z is applied
for bands i, j, k, ..., n, increase Z in the inverted model
- until the ratio average(LBi,...,LBm)/LBn equals 1

Bias on Z and spectral LB

Two bands case: of course, only non-contrasted shallow bottom signatures resort to such simplification when using a pair of bands i and j
- for a contrasted shallow bottom signature like seagrass, corals, etc, true Z may not be reached: such simplification entails a -potentially severe- bias on computed depth
- unless the concept of the Soils Line is modified for BGRN multispectral bands, as demonstrated in this website's tutorials
N bands case: when using wavebands bands i, j, k, ..., n,
- this bias can be reduced to considerable extent
- and contrasted spectral LB signatures may be obtained for bottom typing , like if at low tide

You're done

Go for it! write an image for Z and a spectral image for LB