How to estimate
operational spectral attenuation coefficient 2K

for remote sensing radiance in water,
so that: no need for field data for shallow water work!

This page was developped in 2016 after 22 years of experimenting.

Please first get a feeling of 4SM:
peer-reviewed article 2017
 presentation   and   summary 



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

In order to ensure that "no need for field data":
* leave all wavelengths at mid waveband
* apply an image-specific CoefK>=0.0,
or use a -CP...argument.

As of july 2016, I have gathered growing evidence to show that
applying CoefK~=0-2  in the orange-red range
suits most Landsat 8 scenes
possibly related to diffuse atmospheric lightfield

Following Maritorena, Lyzenga, Kirk and Jerlov:
get operational spectral 2K
BPL assumption: in 4SM, we derive operational spectral diffuse attenuation coefficient 2K for remote sensing radiance
  • using Jerlov's table of diffuse attenuation coefficients for downwelling irradiance in water under clear sky conditions, sun high in the sky.
  • See quotations by Jerlov, and by Kirk.
Ki/Kj : for this, we estimate the ratios Ki/Kj from all visible bands i and j in the image, using a protocole slightly modified from Lyzenga.
  • Note that one must ensure that Ki/Kj =(Ki/Kk)/(Kj/Kk).
  • This turns out to be a sensitive requirement over the Yellow-Red range.
The ratio Kblue/Kgreen is then used to interpolate operational spectral K for all visible bands, as suggested by Kirk. Note that one needs to specify the operational spectral wavelength for all visible bands.
Mid-waveband: by default, one commonly uses the wavelength at mid-waveband, although there is room for accounting for the specific radiance response curve of each wideband.
Two-ways : we then use 2K in the simplified radiative transfer equation
So we expect that coefZ~=1   in         FinalZ=coefZ*RetrievedZ - Htide,
  • i.e. no need for field data!
  • wavelenths at mid-waveband
  • coefZ~=1
  • 2K in units of m-1
  • Z   in units of m
  • L, LB and Lw in native image DNs, as this is a "ratio" method:
    • no need to convert into units of reflectance (0-1)
Achieving a good fit in optical calibration diagrams
requires decreasing 2K in the 0-~10 m depth range,
i.e. in the Yellow-Red range
in line with Jerlov's statement
Then maybe: no need for field data!



Evidence 1
bottom detection by OLI's red band at Caicos bank
Deglinted Red band
Landsat 8 OLI Caicos 13 may 2013

Red band at 655 nm
in this image exhibits bottom detection
in excess of 10 m,
as evidenced using BILKO's field dataset
  • This means that operational Kred for remote sensing radiance is distinctly lower in this scene than diffuse attenuation coefficient for downwelling irradiance Kdred of Jerlov.
  • Either we need to shift WLred at an operational wavelength much shorter than mid-waveband, which would only reach down to ~6 m over very bright bottoms.
    • I suppose sensor designers would object loudly!
  • Or , as I realized using HYPERION in 2014, operational  2Kred  for remote sensing radiance is affected by viewing geometrical conditions and/or atmospheric optical properties.
    • I suppose HYDROLIGHT designers would agree loudly!
  • See comment by Jerlov.


Evidence 2
optical calibration using HYPERION at Fakarava atoll

band_4=Blue, band_11=Green, band_21=Red

Bad fit Good fit

bad fit : coefK=0.0
HYPERION Fakarava 21 september 2011

good fit: coefK=1.0
HYPERION Fakarava 21 september 2011


bad fit : coefK=0.0
HYPERION Fakarava 21 september 2011

good fit : coefK=1.0
HYPERION Fakarava 21 september 2011

Spectral CoefK observed for this Fakarava HYPERION image is now hard-coded.
CoefK  may take any value >=0 as required to achieve a good fit.
This is supported by a growing number of study cases:

  HICO at Bahrain coefK=1.9 very dense atmosphere
HICO at Lee Stocking Island 
   WV2 at Princess Cays   

Evidence 3
optical calibration using Landsat 8 OLI at Fakarava atoll 

band_2=Blue, band_3=Green, band_5=Red

Landsat 8 OLI 25 july  2014
Bad fit
Landsat 8 OLI 25 july  2014
Good fit

bad fit : coefK=0.0
Landsat 8 OLI Fakarava 25 july  2014

bad fit : coefK=1.0
Landsat 8 OLI Fakarava 25 july  2014

bad fit : coefK=0.0
Landsat 8 OLI Fakarava 25 july  2014

good fit : coefK=1.0
Landsat 8 OLI Fakarava 25 july  2014


Landsat 8 OLI 22 march 2015
Good Fit

good fit : coefK=1.0
Landsat 8 OLI Fakarava 22 march 2015

Landsat 8 OLI 22 march 2015
Good fit

good fit : coefK=1.0
Landsat 8 OLI Fakarava 22 march 2015


Evidence 4
Optical calibration using WV2 at Princess Cays
A blind WV2 test on Sept 28th 2012 
Sept 28th 2012: first calibration
all wavelengths at mid-waveband
2K    0.091 0.074 0.142 0.535 0.799 3.50 4.490 8.9

[X2-3] vs [X5]: notice the bad fit
Seatruth by Digital Globe October 3rd 2012
 on Sept 28th preliminary work
DG_Morel-Comparison Sept 28th 2012
DG's depths vs DTM         4SM's depths vs DTM

This image, compiled by Gregory Miecznik,
compares results obtained
  • LEFT:   by Gregory Miecznik DG's method
  • RIGHT: by Yann Morel           4SM method
This diagram provides 
a compelling support
to the CoefK proposition.
  • K2/K3=0.52 is appears to be fairly well established
    • this yields K2=0.074 m-1  and K3=0.142 m-1
  • CoefK=0: this entails a bad fit as evidenced by the [X2-3]vs[X5] diagram
  • Applying a CoefK>0 value would have achieved a good fit in the [X2_3] vs [X5] diagram.

This diagram provides
a compelling support 
to our claim that
"no need for field data".
  • 0-8 m depth range: display of 4SM depths
    • applying a CoefK>0 value would have  achieved a diagonal display of 4SM depths.
  • 8-25 m depth range: all 4SM depths are overestimated by ~3.5 m. This means that:
    • slope: K2=0.074 m-1  and K3=0.142 m-1 are correct. No need for field data!
    • offset: the slope of the Soil Line should be distinctly increased in order to get good-looking results over the MBES coverage,   as explained. This is to be done by decreasing LsM for the Green band.
This was in 2012
As of july 2016, I know better

Evidence 5
Optical calibration using HICO

HICO at Bahrain

HICO at La Parguera

Evidence 6
Optical calibration using SPOT
SPOT at Rangiroa
WL at mid-waveband


In order to ensure that "no need for field data":
  • Leave all wavelengths at mid waveband.
  • Apply a image-specific CoefK>=0 in the yellow-red range,
    • or use a -CP...argument.