Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageries
busy? see 4SM slides
4SM advantages, pluses, musts, and challenges

compared to NOAA's most widely used method worldwide
also compared to Digital Globes's own solution
4SM summary        4SM FAQs        4SM Blog      4SM conclusions

4SM goes as far as possible to "operate" the simplified radiative transfer equation (RTE),
as it was confirmed to be "safe to use" in 1994 by Maritorena, Morel and Gentilli.
  • This should satisfy the needs of most potential users,
  • until the likes of SAMBUCA and EOMAP semi-analytical methods can actually take over for all practical purposes.
    • In my view, this shall happen in a few decades, as they require a world of integration of countless parameters which are simply not accessible to the    -often lonely- lay practitioner
      • using commercialy available spaceborne high resolution multispectral imageries 
      • and comprehensive commercialy available software packages
      • with a reasonable workflow
      • far away from any cutting edge R&D support
      • at a reasonable cost
      • under reasonable time constraints.
This leaves us with 4SM for decades to come
  • for a comprehensive water column correction method,
    • including NOAA's extended log ratio method as a backup as desired for water depth only, 
  • both with their own flaws, which now need to be fully documented and exposed thoroughly by independent investigators.

VNC : let's work together live!

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
Busy? 4SM in 10 lines
The Self-calibrated Spectral Shallow-waterSupervised Modeler


4SM : advantages
4SM : pluses
4SM : requirements
4SM : challenges

4SM : where's the catch?
4SM : errors
4SM: conclusions

please also refer to CSIRO's SAMBUCA   and to Heege's EOMAP

4SM advantages over other "empiric" methods         
4SM advantages

No need for conversion of raw image DNs to apparent reflectance in units of reflectance using image metadata

  • this is the priviledge of a "ratio method", as all computations are performed using data in units of DN!!!!!!!!!!!!!

No need for a formal atmospheric correction

  • the spectral path radiance and the water volume reflectance are estimated through the calibration processand this has shown to be satisfactory for a lightweight method

No need for existing depth points to achieve the optical calibration   Best seatruth in town

  • this yields an insight on water quality: the spectral diffuse attenuation coefficients

  • this is a legacy of Jerlov's outstanding work on the optical properties of marine waters worldwide

  • this would appear to be the case for WV2 wavebands, just like for CASI, SPOT and IKONOS wavebands

  • as per my own 4M experience up to now, the only exception seems to be Landsat and ALI wavebands, for which a -often quite significant- depth correcting factor must be estimated using some seatruth and applied to all computed depths

    • even this exception might give way to a process in 4SM to account for it: I'm still working on it!

Calibration makes great use of a graphical plot of the simplified radiative transfer equation applied to the specifics of the current study case

  • unlike all other empirical ratio methods, which rely on statistics of seatruth data and tend happily to forget about the physical realities behind what they are doing

Water column correction of the image is performed in the same process: this yields a "low tide" view of the shallow areas of the scene, "on the fly" along with a DTM

  • this is an exclusivity of 4SM, apart from semianalytical methods

  • it  provides a very sensitive means for the practioner to locate areas where conspicuous results 
    • either warrant further revision of modeling conditions 
    • or must be flagged as lousy
  • bottom typing may then be performed through common classification schemes

4SM can make good use of a panchromatic band along standard spectral bands

  • This is exclusive: only 4SM does that

  • In practise, it more than doubles the range of shallow depths which can be computed for SPOT archive images, and extends  significantly the range of shallow depths which can be computed for high resolution BGRN images

All this same day if required, ahead of any field work

4SM pluses

Accounts for the water volume reflectance

Reads form the raw image in PCIDSK format, then proceeds to writing a segmentation mask, extracting of calibration data, then to calibrating the optical model

  • then once optical calibration is achieved to satisfaction, proceeds to deglinting, smart-smoothing, model inversion to yield and write images of
    • computed depth , ready for seatruthing
    • AND
    • spectral water column corrected signature of the bottom reflectance , ready for bottom typing
  • in the unfolding of this process, the practioner can/must see for him(her)self whether or not the result seems acceptable: the inspection of the water column corrected signature is of great help in this regard
    • this is exclusive to 4SM

All computations are performed using data in units of DN!!!!!!!!!!!!!

All this ahead of any field work!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

4SM has processed a wide range of multi/hyper spectral imageries, up to ~20 spectral bands

4SM is  ~50,000 lines of dense C code by an amateur programer; it includes tools for

  • importing raw data from a PCIDSK formated image

  • writing to (using OpenEV) and reading from shapefiles

  • seatruthing

  • combining depth results obtained from a time series of co-registered images

  • bottom typing

  • writing a variety of Postscript formated graphic illustrations, like the most precious calibration diagram and various types of profiles and regressions

  • processing a subset of the current image

  • once calibration is achieved to satisfaction without the need for any field data, and if desired, Stumpf's method may be used straight away for computing shallow depths

  • and more

A one-stop workshop :
all this ergonomy for sake of operationality


4SM requirements
For operating 4SM, the following are required

4SM needs some coverage of optically deep waters, like all other empirical ratio methods apart from  Stumpf's log ratio method

4SM needs some coverage of bare dryland as well, but still can do without any

4SM requires a seasonned practioner, well versed in things optical and underwater

4SM is a supervised process: the practitioner is in command and takes full responsibilities, while  ensuring that the basics of radiative transfer theories are accounted for : garbage in -> garbage out   Disclaimer

  • 4SM operates various thresholds with a view to preventing/suppressing the most obvious artifacts

4SM does not require the use of any proprietary software, and reads/writes from/to PCIDSK image format

For operating 4SM, the above are required
All this on a low-cost open source workstation

4SM challenges
4SM faces many challenges

Contrary to widely accepted views expressed by respected gurus, it is demonstrated in this website that there is NO NEED for

  • conversion to calibrated reflectances

  • formal atmospheric correction

  • field data

On top of it, 4SM performs the water column correction of spectral  shallow bottom signatures, while computing depth in meters

  • this is well documented to be a much desirable prerequisite for anyone who wants to map shallow bottom type

Apart from quite some SPOT archive images, and  also CASI datasets, most images processed todate are Landsat, ALI and HYPERION

  • hardly a way to broaden the 4SM audience!

Propper working conditions imply a team work, where the practioner can interact in-house with knowledgeable colleagues

  • not an easy prerequisite until the market actually demands it!

4SM uses the Linux/bash open source environment and has no graphical user interface

  • hardly worth mentioning for the vast majority of potential users who are MS and GUI addicts

4SM code in C MUST be recoded by professionals, into a cross-platform open source application with suitable GUI

  • not a simple thing to achieve within a reasonable time, while protecting intellectual property rights

We are talking big $$$

Once acknowledged sometime in the (near!) future, 4SM shall become the ultimate craze for a few decades, until semi-analytical methods take over for dual use operational purposes

Universities shall set out to research, experiment and teach the 4SM method, and set networked R&D groups for the purpose of thorough cal/val activities

Research funding agencies shall want to see through  

Government organisations shall progressively want to use it for themselves

Inter-governmental organisations shall want to follow suite, by devising large projects for tender and also training programmes

Hydrographic and defense services shall want to use 4SM on their own

  • for updating nautical charts

  • and for remote environment assessment (REA)      

RS consulting firms shall be hard-pressed to compete for sizeable tenders based on the use of 4SM and imageries like Ikonos, Quickbird, and now WV2, SPOT6 or Pleiades

Vendors of RS image processing packages shall need to offer their own version of 4SM

Vendors of RS imageries might even want to try and sell 4SM results along with the raw data

4SM conclusions
also compare with Digital Globes's own solution

In my view,
and after studying hundreds of multispectral and hyperspectral images
and used limited seatruth datasets
for eighteen years,

I have come to the following conclusions:

  • the basics of shallow water modeling using the simplified radiative transfer equation may be tested using SPOT and Landsat images

    • the simplified RTE adequately accounts for first order physics, in particular for the all-important water volume reflectance (i.e. the color of the water)

  • adequate expert knowledge of underwater realities allow the practioner to tune the optical calibration of shallow radiances in units of DN, with no need for any field data

  • this is subject to the following assumptions and uses only the image itself (not even any metadata!)

    • glint and haze in the data has been removed from marine areas

    • SL : for any pair of bands i and j, the non-vegetated pixels in the image, from the brightest on the beach to the darkest in shadowed areas, allows the practioner to formulate a model of what an acceptable water column corrected spectral bottom signature may look like:

      • this is the equivalent of the agronomer's Soils Line, with which the atmospheric path radiance La is estimated

      • this allows for a very simple first order atmospheric correction : at the base of the atmosphere L =Ls - La

      • this correction is just as good as most current corrections reported by authors (and the practioner is in control to prevent negative radiances...)

    • Lsw : the water bodies in the image are reasonably homogeneous radiance over optically deep waters Lsw must be estimated from the image

      • the water volume reflectance Lw = Lsw - La is estimated from the image

    • BPL : for any pair of visible radiances i and j, the ratio Ki/Kj of effective diffuse attenuation coefficients may be derived from the shallow areas in the image

      • for this, we introduce the concept of the Brightest Pixels Line, with which to estimate ratios Ki/Kj of diffuse attenuation coefficients for all pairs of visible bands

    • K from Jerlov : for each visible waveband, the effective wavelength in nanometers must be known or assumed so that the spectral values Ki, Kj, K..., Kn, in m-1 for all visible bands may be derived using Jerlov's table of diffuse attenuation coefficients for marine water worldwide

  • ==> as a consequense, any shallow spectral signature may be reverse modeled by increasing Z until the water column corrected spectral bottom signature is observed to fit the spectral Soil Line within reasonable limits.


Z_final = Z_estimated * CoefZ  - Htide
still, two final corrections must be applied : 

only the use of seatruth data shall allow for estimating

CoefZ : depth correction factor :  a final depth correction factor coefZ

  • whenever the effective wavelengths for visible wavebands is precisely known, CoefZ proved to be equal to 1.00

  • in other words: no need for field data

Htide : tide correction factor : tide height to datum

  • This yields
    • Z : a raster image of shallow depths in meters, which now may be turned into a bathymetric map
    • spectral LB : a spectral water column corrected image of the shallow areas (like if at low tide), which now may be classified into a map of bottom types
    • water quality : an insight on the water quality, through spectral K values in m-1, which may be commented in terms of underwater visibility
  • Please note that:
    • no need for calibration of DNs into physical units of radiance, as this is a "ratio method"
    • no need for formal atmospheric correction, as long as the deep water radiance may be estimated from some coverage of optically deep waters in the image; that's until adjacency effect may be corrected for, using affordable techniques
    • no need for seatruth until next and final step
  • S/N ratio: because of the exponential nature of the attenuation of light in water, the performances shall depend on the S/N ratio (the so called Noise Equivalent Change in Radiance): it must be stated here that
    • the dramatic -and much wanted- reduction of the footprint of the pixel has been obtained at the expense of any significant improvement of the S/N ratio
    • the community at large shall not be satisfied by forthcoming progresses in shallow water modeling until the S/N ratio has improved as needed: QuickBird and now WorldView2 are clear examples of poor S/N ratio
  • Once suitable seatruth becomes available,
    • Final_Z = coefZ * Computed_Z - TideToDatum
    • The map of bottom types may be labeled into a habitat map
Busy? 4SM in 10 lines
4SM summary