Specify the water volume reflectance

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HowTo Lw
water leaving reflectance, water volume reflectance


  • 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 
    • 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 over a cocconut groove
are at the same level in the blue and red bands,
while they are much higher in the green bands.

The optimization process in 4SM is based on this observation. 

  • 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.


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