Specify the water volume reflectance

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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

  • La=Lsw-Lw is the atmospheric path radiance
  • Lw~=0 in the Red to Nir range of the solar spectrum for clear waters
  • for ETM images, Lwgreen may commonly be set to ~=1.5, depending on the image brightness
  • Lwblue is set using statistics over healthy vegetation in the image
    • by ensuring that the Blue vs Red Soils Line runs through the average vegetation point (blue round point in vegetation.png)
    • its value may be quite high for clear waters
    • it must be properly estimated, as it plays a first order role for dark bottom pixels
  • RLBbg only used when modeling Blue vs Green in BGRN images like Landsat
    • default is 1
    • RLBbg=1.15 here
    • its value is to be estimated using the Z2 vs Z3 process



How to Choose Lw
illustrated using Hyperion image 
EO1H0800592002192110PZ of Tarawa Atoll
Blue=band4      Green=band11     Red=band21
Syntax Lw

  • see the hyperspectral spectral signature of a coconut groove at Tarawa atoll
    • from 400 to 650 nm, normalized Lw shall be required by 4SM to decrease from one band to the next
    • then from 650 to 850 nm, they are set to zero all the way to the NIR/SWIR bands 
    • these are normalized BOA radiances,
    • so a bright sandy beach would plot at 200 for all bands
    • it is seen that the radiances are at the same level in the blue and red bands,
      • while they are much higher in the green bands
  • Lw[blue] is set so that the Soil Line in a Blue vs Red linearized bidimensional histogram fits nicely the scatter of healthy dark vegetation pixels : 
    • where the Soil Line is offset from the diagonal position 
    • by an amount which is determined by the difference Lw[blue]-Lw[red:
      •  X[4]=LN(Ls[4]-Lsw[4])    X[21]=LN(Ls[21]-Lsw[21])    
  • Lw[green] is set so that the Soil Line in a Green vs Red linearized bidimensional histogram fits nicely the outer border of the plot of mostly vegetated dark land pixels 
    • it is seen that Lw[green] is significant
      • so that the Soil Line does not plot in a true diagonal position,
      • but is offset by an amount which is determined by the difference Lw[green]-Lw[red
      • X[11]=LN(Ls[11]-Lsw[11])     X[21]=LN(Ls[21]-Lsw[21])   
  • Lw[red] is set to zero:

Blue vs Red
* the vegetated land pixels display just under the Soil Line
* the Soil Line is a pronounced curve  
Lw[blue]=9.0 Lw[red]=0
Green vs Red
* the vegetated land pixels display on the Green side of the Soil Line
* the Soil Line is just slightly curved

Lw[green]=1.9 Lw[red]=0
Red vs NIR
* the Soil Line strikes in a truely diagonal position

Lw[red]=0   Lw[nir]=0

Some common sense
  • In 4SM, La values for RED to NIR bands are set to be equal to Lsw values provided.
  • Spectral Lw is to be set at a value which results in a satisfactory fit of the Soil Line with the observed pixels.
    • This refers to the so-called " dark pixel correction".
  • La=Lsw in the Red to Nir range (Lw=0).
  • La values for GREEN bands are usually just a little lower than Lsw values.
  • La values for BLUE    bands are usually          much lower than Lsw values.  
  • Note that -dLsw argument is available:
    • Lsw=Lsw+dLsw
  • Spectral Lw values are progressively adjusted so as to obtain a satisfactory fit of the Soil Line with the observed Soil Line.
  • Guidelines are
    • Lw nir=0
    • Lw red=0
    • Lw green is usually just  one to  three DN
    • in the case of a Blue waveband in clear waters, Lw blue  can reach up to 10-20 DN.
  • Atmospheric path radiance La=Lsw-Lw :
    • the difference Lsw-Lw is the atmospheric path radiance:
  • Consistency: the values adopted for spectral Lsw, spectral Lw and therefore spectral La must be internally consistent.
    • any gross inconsistency must be noticed, investigated and corrected:
    • the risk here is badly under/over-estimated computed depths over dark bottom substrates
      • particularly in the case of negative bottom contrast.