Using the Panchromatic band for water column correction to derive water depth and spectral bottom signature: Landsat 8 OLIP bandset used for this work Purple=1, Blue=2, Green=3, PAN=4, Red=5, NIR=6 and SWIR1=7 
Collaboration with Fabio Favoretto, Ph.D Student, Coralline Algae Ecology Grupo Interdisciplinario de Ciencia Ambiental, Universidad Autonoma de Baja California Sur Carretera al sur km 5.5  La Paz favorettofabio@gmail.com 
Using pan sharpened images in this study Pan sharpening using Rstudio with Brovey method 

Once the shallow areas in a scene have been correctedd for the diffuse attenuation effects of the water column,
For this purpose, various sources/methods can be used.

The Spectral Angle is defined as the ratio Blue/Green of reflectances,

In 4SM, the Spectral Angle is computed as the ratio (Coastal+Blue)/(2*Green) of water column corrected reflectances.

Coral sands have the following reflectances for OLIP bands (from Maritorena) 0.550 is estimated for the Panchromatic band 0.310, 0.380, 0.440, 0.550, 0.560, 0.670, 0.700 This yields SAcoralsand=0.784 so, in theory, this should be the maximum SA value for shallow substrates 
My own estimation from processing images in the Bahamas Caicos LSI are quite close to Maritorena's estimation 
Now, how do I set a color table for displaying images of SA? SAM2 color palet is for CoralSand reflectances 
Now, The brightest shallow bottom at San Lorenzo Channel yields SA~=0.59 This is at the intertidal sand flats of Bahia San Gabriel (figure 4 of Halfar et al, 2000) where low sandy dunes may be assumed to be devoid of any greenish material (do you concur?) Type10 signature below is used as a local reference for SAM It is sampled at a depth of ~1,52 m Calibration of the Soil Line for this scene is fine tuned so as to obtain this result. 
"The advantage of SAM is that it uses only the direction of the spectra, and not their length, and hence the method is insensitive to the unknown gain factor, and all possible illuminations are treated equally." 
"This method is insensitive to illumination since the SAM algorithm uses only the vector direction and not the vector length. " 