### Abstract:

An expression for the ratio of the upwelling nadir radiance L(π, z) and the downwelling scalar irradiance Eod(Z) is derived from the following equation of radiative transfer. This expression is given by RSR(z)=[L(π, z)]/Eod(Z) = [fb(z)bb(z)]/2π[k(π, z) + c(z) – fL(z)bf(z)], where bb(z) is the backscattering coefficient, k(π, z) is the vertical attenuation coefficient of the nadir radiance, c(z) is the beam attenuation coefficient, and fb(z) and fL(z) are shape parameters that depend on the shape of the volume scattering function and the radiance distribution. Successive approximations are subsequently applied to the above exact equation. These are fb(z) = [2πβ(π – θm, z)]/[bb(z)], where β(π – θm, z) is the volume scattering function at 180° minus the zenith angle of the maximum radiance and k(π, z) = am = c[1 – 0.52 b/c – 0.44 (b/c)²], where m is a parameter that is numerically equal to the inverse of the average cosine of the asymptotic light field for a medium with the same inherent optical properties, a is the absorption coefficient, and b/c is the single scattering albedo. Together with fL(z) = 1.05 and application of Gershun’s equation, it is shown that for nearly all oceanic cases RSR(z) ≡ L(π, z)/Eod(z) = [β(π – θm, z)]/{a(z)[1 + m(z)]}.