OII+0.26; coefWL[green]=0.740
This calibration picks up the optical properties
of open oceanic waters for this ETM image

 OII+0.64;  coefWL[green]=0.755
This calibration is expected to pick up
the optical properties of  lagoon,
which is wide open to the ocean
on its western side
Tarawa is the capital island of Kiribati,
 The atoll is wide open to the ocean to the west.
Maximum tide height is approx ~1.5 m
Over 30,000 persons live on the southerm atoll rim.

OII+0.64; coefWL[green]=0.755

computed depths
are far too shallow inside the lagoon

average bottom reflectance is most questionable

This result is most questionable:
the average lagoon bottom cannot be so dark.
We must suspect that the above calibration
depicts the clear oceanic waters along the west side
rather than the murky waters in the lagoon.
.
Notice that the island is surrounded
by foul waters which would appear
to reach to Marakei atoll in the green band
I think there must be a body
of foul waters inside the lagoon.
Nothing 4SM can do about it!