4SM 2K Jerlov

see some most interesting reading
about Secchi depth and Jerlov's optical classification of marine water types:
A New Algorithm to Estimate Diffuse Attenuation Coefficient
from Secchi Disk Depth, 2020

The Effect of Optical Properties on Secchi Depth
and Implications for Eutrophication Management, 2019

Influence of the vertical distribution of cyanobacteria
in the water column on the remote sensing signal, 2008

**Conclusion** But wait!
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 evidence_1: red band OLI evidence_2: red-orange range HYPERION evidence_3: red-orange range OLI evidence_4: red-orange range WV2 evidence _5: red-orange HICO evidence _6: red band SPOT

**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.
K_i/K_j : for this, we estimate the ratios K_i/K_j from all visible bands i and j in the image, using a protocole slightly modified from Lyzenga. Note that one must ensure that K_i/K_j =(K_i/K_k)/(K_j/K_k). This turns out to be a sensitive requirement over the Yellow-Red range.
Jerlov's optical classification of marine waters The ratio K_blue/K_green 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(2KZ) BOA L =Lw + (LB -Lw )/exp(2KZ) this is a much discussed simplification: see Maritorena et al.
So we expect that coefZ~=1 in *FinalZ=coefZRetrievedZ - 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 K_red for remote sensing radiance is distinctly lower in this scene than diffuse attenuation coefficient for downwelling irradiance Kd_red of Jerlov. Either we need to shift WL_redat 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 2K_red 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.

**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	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 g
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
see also Landsat 8 OLI at BahiaSanJuanico
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 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

**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

Conclusion
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.

But wait: AOPs are not additive!
"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.