Volume scattering function, average cosines, and the underwater light field

The extent to which the relationship between the apparent optical properties of water bodies K d , , R(0) (vertical attenuation coefficient, reflectance) and inherent optical properties of the water ( a, b, b b ,—absorption, scattering, backscattering coefficients) varies with the shape of the volume scattering function has been investigated via Monte Carlo modeling of the underwater light field for 12 different optical water types. The previously derived equation for the vertical attenuation coefficient of downward irradiance urn:x-wiley:00243590:media:lno19913630455:lno19913630455-math-0001 has been shown to be of general applicability, but the coefficient G ( µ o ) is a function not only of the cosine of the refracted incident photons ( µ o ) but also of a shape factor of the volume scattering function in accordance with urn:x-wiley:00243590:media:lno19913630455:lno19913630455-math-0002 where µ ̄, is the average cosine of scattering derived from the volume scattering function in question, and c t , c 2 , c 3 , and c 4 are numerical constants estimated from the modeling data. The well‐known relationship urn:x-wiley:00243590:media:lno19913630455:lno19913630455-math-0003 between the subsurface irradiance reflectance under zenith sun and the ratio of backscattering coefficient to absorption coefficient is shown to apply satisfactorily to all the water types for b b /a values up to ∼0.25, but is less satisfactory at higher values of this ratio. As the incident beam departs from the vertical, so the reflectance increases to an extent that depends on the shape of the volume scattering function.