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

 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

 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 TOA Ls=Lsw+ (LsB-Lsw)/exp(2K*Z) BOA L =Lw  + (LB -Lw  )/exp(2K*Z) this is a much discussed simplification: see Maritorena et al. 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!

 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/users would agree loudly! See comment by Jerlov.

 Bad fit Good fit bad fit : coefK=0.0 good fit: coefK=1.0 bad fit : coefK=0.0 good fit : coefK=1.0
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
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HICO at Lee Stocking Island
WV2 at Princess Cays

 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

 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 using UKHO's MBES DTM 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

 HICO at Bahrain HICO at La Parguera

 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.

 "AOPs Are Not Additive: On the Biogeo-Optical Modeling of the Diffuse Attenuation Coefficient" by Zhongping Lee et al., 2018 Front. Mar. Sci., 30 January 2018 | https://doi.org/10.3389/fmars.2018.00008   Commonly we see the diffuse attenuation coefficient of downwelling irradiance (Kd) expressed as a sum of the contributions of various constituents. We show here that, both theoretically and numerically, because Kd is an apparent optical property (AOP), this approach is not consistent with radiative transfer. We further advocate the application of models of Kd developed in past decades that are not only consistent with radiative transfer but also provide more accurate estimates, in particular for coastal turbid waters.