Specify the WaveLength in nanometers for all spectral bands in the image
HowTo WaveLengths

As of 2016, see 4SM 2K
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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

  • HYPERSPECTRAL: all wavelengths for narrow hyperspectral bands are set at mid-waveband
    • spectral K values are conveniently interpolated at mid waveband
    • but a -dK... parameter must be applied in the 575 to 600 nm range: this is very sensitive
  • MULTISPECTRAL: all wavelengths for wide multispectral bands are set at mid-waveband
    • but a -dK... parameter must be applied in the 575 to 600 nm range: this is very sensitive

Specify the WaveLength in nanometers for all spectral bands in the image
This is of no interest when using SPOT images:
by default, WL for SPOT images are set at 550, 650 and 850 nm
HowTo WaveLengths

We are talking wavelength in water
Quotation from Kirk, page 5
  • The refractive index of vacuum is 1 by definition. 
    • The refractive index of air is 1.00028. 
    • The refractive index of water may with sufficient accuracy be regarded as equal to 1.33 for all natural waters. 
  • Assuming that the velocity of light in vacuum is 300,000 km/s, the velocity in water is therefore about 225,000 km/s. 
  • The frequency of the radiation remains the same in water,  but the wavelength diminishes in proportion of the decrease in velocity. 
    • WL=c/f with f=frequency and c=velocity of light
  • Any idea what to do with this regarding shallow water modeling?
    • like: forC WL[c]=WL[c]*225000/300000.
  • Should I do that in 4SM?
  • Apparently NO,  otherwise Jerlov would have made a strong statement about it.
Wavelengths in  nanometers may be specified in one of two ways:
  • either : -WL/0490.5/550.8/650.2/850.4.... at mid waveband
  • or.......: -WLm and WLM: the alternative is to specify the waveband
    • -WLm/0452/0529/0624/0776.....Wavelength_Minimum for waveband
    • -WLM/0492/0595/0675/0820.....Wavelength_Maximum for waveband
    • ==> WL=WLmin+(WLmax-WLmin)/2
  • For SPOT XS, wavelengths of 550, 650 and 850 nm are provided internally by default
  • For TM, ETM, OLI, ALI, IKONOS and WV02:  WLmin and WLmax are provided by default

As of 2016,
WL is set at mid-wavelength:
please see 4SM 2K
  • The "effective wavelength" refers to the color of the sea, considering the visible part of the solar spectrum
  • Similarly, we can speak of the "effective wavelength" of a given waveband, as the result of the integration of all radiances captured by the sensor over the span of this waveband
  • Subject to the particular shape of the diffuse attenuation curve for the water type considered,
    • and to the particular waveband considered
    • the "effective wavelength" for that waveband may concievably be offset from the mid-waveband position
    • this apparently is the case for the Green waveband of multispectral imageries
The problem of Wavelength versus Response Curve of Waveband
  • In 4SM, wavelengths have to be specified in nanometers
  • This is necessary in order to use the KiKj ratio observed in the image for deriving spectral K values using Jerlov's data, as we need a seed value for K
  • Wavebands are characterized by their specific response curve
  • One discrete wavelength must be specified to represent that response curve: this is not trivial
The problem
  • Under the "BPL assumption"   in 4SM , i.e.
    • clean homogeneous brightest bottom substrate is present at various depths, if at all as isolated patches,
    • and waters are homogeneous over the study area
  • once satisfied that a consistent set of Ki/Kj ratios among all pairs of bands has been derived from the image data,
  • and because next 4SM accesses Jerlov's data in order to derive spectral K values in units of m-1  in the visible range
    • beware though that Jerlov's data  refers explicitly to clear skies, sun high in the sky
  • we need a specific operational wavelength for each spectral waveband: this is a problem
    • with wideband multispectral imageries
    • with all imageries in the 575-600 nm region of Jerlov's classification of marine waters
  • These questions are under constant scrutiny, and warrant careful R&D
    • detail is wanted in the 575-600 nm range of Jerlov's data
    • more careful seatruthing is wanted with all imageries
    • 4SM computed depths must be multiplied by a final depth correcting factor
How do we choose an operational wavelength from a response curve?
Specific benchmark study cases must be arranged,
using bright imageries
over extensive homogeneous bright/clean sandy/oozy (or maybe ice?)
very gently sloping bottoms
in clear marine/lake waters,
with suitable seatruth.

As of mid-2014

and after considerable efforts to see through
  • All wavelengths are set at mid-waveband
  • Using Ki/Kj ratio observed for bands i and j, all spectral K values are interpolated at mid waveband for all visible bands
  • a -dK... commandline argument is used to tune spectral K - other than Ki and Kj -
    • in order to achieve a strict fit with observed BPL pixels in the optical calibration plots
  • dK is set to 0 in the Blue/Green and Red ranges
    • a good fit must be achieved/observed
  • dK is commonly set to some slightly negative value in the 575 to 600 nm range
    • so as to achieve a good fit :  K=K+dK
  • this practice is derived from consistent evidence when using hyperspectral data
  • anyway     FinalDepth=coefZ * RetrievedDepth - Htide
    • with coefZ and Htide to be derived from some seatruth evidence
  • todate, all seatruth on hyperspectral images yielded coefZ=1.00 for all bands

Sensor Wavebands
EO1 Hyperion
  • In hyperspectral sensors, wavelengths are tightly specified
  •  but a probleme arises in the 575-600 nm region of the spectrum, i.e. for bands at 579.5, 589.6 and 599.8 nm
  • where the attenuation properties are seen to vary very fast
  •  and because Jerlov's data are provided by steps of 25 nm

This is a quite sensitive matter,
even more sensitive with multispectral data

ALI bandset
Landsat TM
Operational wavelength:
Once I used
WLblue...]=486 nm instead of mid-band=485.0 nm
WL[green]=570 nm instead of mid-band=569.5 nm
WL[red...]=660 nm instead of mid-band=658.5 nm
WL[nir....]=830 nm instead of mid-band=840.5 nm

with promising comments from seatruth
computed depths match recorded depths
to satisfaction
Source BEGNI, 1982, from GSFC

with various spectra
WLMin[1]=452;    WLMax[1]=518;    //midband=485.0_ERIM98_486
WLMin[2]=529;    WLMax[2]=610;    //midband=569.5_ERIM98_570
WLMin[3]=624;    WLMax[3]=693;    //midband=658.5_ERIM98_660
WLMin[4]=776;    WLMax[4]=905;    //midband=840.5_ERIM98_830
Landsat ETM+

Operational wavelength:
Once I used
WLblue...]=477.6 nm at mid-band
WL[green]=576.3 nm instead of mid-band=561 nm
WL[red...]=661.3 nm at mid-band
WL[nir....]=834.8 nm at mid-band

with the following comments from Tanzania sea truth

Zrecorded ~= 1.42*Zcomputed - 1


Source: U. of South Florida
WLMin[1]=441.3;        WLMax[1]=513.9;    //midband=477.6
WLMin[2]=519.4;        WLMax[2]=600.7;    //midband=560.1
WLMin[3]=630.6;        WLMax 3]=692.0;    //midband=661.3
WLMin[4]=771.6;        WLMax[4]=898.0;    //midband=834.8

Operational wavelength:
Once I used
WLblue...]=480 nm at mid-band
WL[green]=565 nm instead of mid-band=551 nm
WL[red...]=640 nm instead of mid-band=665 nm
WL[nir....]=805 nm at mid-band

with the following comment from sea truth
"recorded depths are 1.0752 less deep"


Operational wavelength:
I've allways used
WL[green]=550 nm instead of mid-band=542 nm
WL[red....]=650 nm instead of mid-band=630 nm
WL[nir.....]=850 nm instead of mid-band=820 nm
and tested against various seatruth datasets
in French Polynesia
to reasonable satisfaction