4SM reflectance of shallow water bottoms

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

WV2 data

CASI at Heron Island

-WL439.0/459.4/478.8/498.4/516.1/531.1/547.1/564.0/574.4/596.0/610.0/624.5/643.5/661.0/675.0/690.0/705.0
-RM/0.567/0.614/0.656/0.691/0.727/0.737/0.783/0.805/0.817/0.813/0.796/0.795/0.795/0.750/0.717/0.761/0.769_Roelsfema

I have drawn the figure below from Roelsfema et al's data.

Optically deep water volume reflectance R_rs
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 Rw_red~=0
Most often I seem to observe Rw_coastal>Lw_blue

Analytical modeling the water volume reflectance R_rs

Satellite-sensor calibration verification with the cloud-shadow method. Reinersman, Carder, Chen · Applied Optics A MOST INTERESTING READING	So 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.