Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageries
WorldView 2 image at Waimanalo Beach, Oahu, Hawaii islands
3289x3241, 2 m ground resolution, courtesy of Ron Abileah

for errors, see also 4SM FAQs 

see also Pollution at  

see paper by DigitalGlobe : 
WorldView-2 bathymetric capabilities

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

July 16th
Sources of errors in 4SM
While shallow water modeling,  the practitioner faces a very wide range of potential errors.
In other words, the simplified Radiative Transfer Equation is actually simplistic,
and the end result can be really nasty.
As a result, the end user must take their share of responsibility, or pay full price for conventional surveying services.
When the image data is of suitable quality,
very attractive and cost effective end products may be derived to cover vast areas,
within a short time and for just a fraction of the cost .
  • system noise  
    • what "Noise Equivalent Change in Radiance" specification is required for shallow water work?
  • glint: bad deglinting, adjacency effect
  • alien: breaking waves, white caps, ship wakes, alien floating objects
  • linearity of the sensor's response  
  • Lsw: estimation of spectral deep water radiance
  • BPL assumption
    • estimation of ratio Ki/Kj
    • estimation of spectral K
    • heterogeneous water quality  
  • SL assumption
  • Lw: estimation of spectral water volume reflectance  

System noise
  • The simplified RTE relies heavily on the estimation of the bottom contrast Ls-Lsw

    • Ls-Lsw= (LsB-Lsw)*exp(K*Z)

    • where LsB represents the bottom albedo

  • System noise affects the estimation of both Ls and Lsw, more so as the measured radiance Ls decreases towards the deep water radiance Lsw,

    • either as the bottom depth increases

    • or as the bottom brightness decreases

    • or both

  • Todate, and with regard to radiometric quality of multispectral data, the only sensors worthy of shallow water work I've had access to are
    • AAHIS (courtesy of Eric Hochberg)
    • SPOT 5 (courtesy of IGN)
    • EOS ALI (courtesy of USGS)
  • Quite many other existing sensor should be added to this short list, that I don't have access to
    • it is a question of "Noise Equivalent change in radiance"
  • Things are improving over time, though, but still at present, most sensors are designed to service land based applications

  • The amount of glint in the measured radiance must be removed 
    • ?or at least the part of it which is modulated by the swell
  • In this WV2 image, we observe that
    • glint in band 8 is reasonably correlated with three other bands
    • glint in band 7 is resonably correlated in the remaining three bands
  • But the very high level of system noise tends to blurr these correlations
    • this results in incomplete glint removal,
    • this warrants a very strong and punishing smoothing
    • this in turn makes a mockery of that 2 m ground resolution

Bad deglinting and high level of system noise are obvious
Linearity of the sensor's response seems questionable


alien features
All sorts of alien features that affect the sea surface shall cause artifacts in the results, like
  • whitecaps
  • floating algae
  • oil smears
  • vessels and their wakes
  • etc


Linearity of sensor response





BPL Assumption
  • The BPL assumption allows for the estimation of the complete series of ratios Ki/Kj among visible bands
    • which in turn allows for the estimation of jerlov's intermediate water type
    • which in turn yields a complete series of diffuse attenuation coefficients 2K in units of m-1
  • the error on the estimation of a suitable ratio Ki/Kj from the image entails

    • an error on the estimation of Jerlov's water type

    • an error on computed depth which increases with depth

Estimation of spectral K in m-1
 operational wavelength and Jerlov's data: Zfinal=Htide+coefZ*ZC

Heterogeneous water quality  

Soil Line Assumption
  • The Soil Line assumption: the spectral properties of the bareland areas in the image, which are at null depth, are used to elaborate a spectral model for water column corrected bottom reflectances
  • The Soil Line  is defined as the straight line that joins the following two points in a biplot of Li vs Lj
    • La: the radiance of a black body
    • LsM: the radiance of a the brightest shallow substrate at null depth
  • The Soil Line represents the continuous series of spectrally neutral substrates from the brightest to the darkest
  • The normalisation is achieved by ensuring that the BOA radiance LsM-La is made to equal a value of 200, by application of a normalization coefficient CN=200/(LsM-La)
    • Therefore, the slope of the normalized Soil Line equals 1
  • In 4SM, all radiances are normalized: Ls=CN*Ls
  • In 4SM, which is a "ratio method", inverse modeling is achieved by increasing Z until the water column corrected spectral bottom signature fits the Soil Line one way or another
  • Ideally, this approach assumes that the bottom exhibits a spectraly neutral signature
    • this suits any substrate whose color is a shade of grey from bright to dark,
    • but it entails substantial error for subturf, and the like: this the main source of error in any ratio method
  • This error shall be of just a very few decimeters at most
    • where the overall bottom  contrast is high, i.e. at shallow depth, even over fairly dark bottoms, where all bands exhibit healthy bottom detection
  • Conversely, this error can exceed several meters
    • over dark bottoms at depths which are optically deep in all but the Blue-Green wavebands
    • or if thresholds have been raised in order to counter artifacts
  • Most shallow substrates shelter some sort of life, which is dependent on the chlorophyll activity and causes them to look greenish
    • this causes an under-estimation of the computed depth
    • this is why, in 4SM, the Soil Line is somewhat re-routed in order to counter this under-estimation,
    • according to our experience, this appears to suit the vast majority of substrates as soon as they depart from the bright and clean sands paradigm
  • But some coral, algae or turf communities exhibit a wide variety of exotic colorations: blueish, brownish, reddish, purplish
    • To-date, it is not possible to account properly for these less frequent cases in 4SM   
  • This error is most obvious is the case in our WV2 image.  It is located in the western part of the image over a field of relatively dark corals (?) which slopes from the fringing reef at ~ 1 m down to 4-5 m: where computed depths are over-estimated by up to 4 meters (red tones).
  • The cause is as follows: subject to the very high thresholds applied, the Red and Yellow bands are disqualified, and modeling only uses bands 1 and 2 versus band 3: -Lm/1/1/1/10/10/255/255/255
  • Then, why disqualify the Red and Yellow bands at that location, so far away of the area affected by "pollution"? For 4SM to yield more acceptable depths, the practioner needs to release the thresholds and run a special processing of the erroneous area: -Lm/1./1/1/1.5/2/255/255/255
  • Lw, the water volume reflectance, is a key element of the simplified RTE,
    • which most existing methods do not bother with.
  • As a result, 4SM is relatively good at processing very dark shallow bottoms,
    • while many express dis-satisfaction at the results they obtain over very dark bottoms: usually badly underestimated computed depths