Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageries
Reflectance of the brightest shallow bottoms in coral reef environments
estimated using 4SM

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

Landsat 8 data
WV02 data
CASI data

Water volume reflectance

Landsat 8 OLI data

  • Conversion into TOA reflectance: Landsat 8 spectral images can easily be converted into Top Of Atmosphere reflectance, using the metadata provided in the _MTL.txt text file: please refer to "Using the USGS Landsat 8 Product".
  • Conversion into BOA reflectance
    • normally, one would have to perform a formal atmospheric correction, like using TAAFKA or the like: see for example University of California at Berkeley: this is a very complex and time consuming process, and we hear of artifacts caused by "over-correction".
    • in 4SM, we use the deep water radiance Lsw and an estimate of the water volume reflectance Lw to derrive La=Lsw-Lw in units of DNs for all wavebands of Landsat 8 data.
      • there is enough information in the multispectral image to do so, and the result is -to say the least- as usefull as that of a formal atmospheric correction over shallow water areas.
      • with Landsat 8 data, there is even enough information to convert La and Lw in units of reflectance. This provides good control on the physical consitency of th values obtained.
  • Water column correction
    • normally, one would need BOA reflectances as the input to any inversion of the radiative transfer equation, whether simplified or not.
    • in 4SM, water column correction is achieved using spectral BOA radiances in units of DNs: L=Ls-La-Lglint: this yields water column corrected spectral bands in units of DNs at the Base Of Atmosphere, which may then be converted into units of reflectance (scaled from 0 to 1), for the purpose of bottom typing and coastal monitoring.

work in progress


work in progress:
more data shall be added to these plots using Landsat 8 images of
  • Andros and Caicos islands, Bahamas
  • Marawaah island, UAE
  • La Parguera, Puerto Rico
  • Perth, Marmion and SharkBay, Western Australia
  • Rangiroa, Tuamotu Archipelaago
  • Tarawa, Kiribati
  • and more: images courtesy of USGS
I have drawn the figure below from Roelsfema et al's data.

Optically deep water volume reflectance  Rrs  
 for Landsat 8 OLI's  coastal, blue, green and PAN bands
see Water Leaving Reflectance Algorithm Theoretical Basis Document:  HyspIRI  VSWIR, NRL Washington

This is in poor agreement with the work illustrated below:
How does the radiance collected by the sensor's very narrow near-nadir viewing FOV
correlate with the "Remote sensing reflectance" analyzed below?

Most often I seem to observe Rwred~=0 
Most often I seem to observe

Analytical modeling the water volume reflectance  Rrs
Satellite-sensor calibration verification
with the cloud-shadow method.

Reinersman, Carder, Chen · Applied Optics
  • OLI_Rw655 is >=0.01
  • OLI_Rw480 ~= OLI_Rw560
  • OLI_Rw440 is less than OLI_Rw480
Cloud 1
OLI_Rw440    0.028
OLI_Rw480   0.038
OLI_Rw560   0.036
OLI_Rw655   0.009
Cloud 2
OLI_Rw440    0.034
OLI_Rw480   0.044
OLI_Rw560   0.048
OLI_Rw655   0.017

I suspect the water volume reflectance in the case of a Lambertian sky
is heavily dependent on
  • the bidirectional distribution of the light field: the most famous cosine of the irradiant light field
  • the sensor's viewing angle, which is commonly near-nadir
 I need to oppose situations of dense atmosphere with situations of clear skies.