A THEORETICAL DERIVATION OF THE DEPENDENCE OF THE REMOTELY-SENSED REFLECTANCE OF THE OCEAN ON THE INHERENT OPTICAL-PROPERTIES

An expression for the ratio of the upwelling nadir radiance L(pi, z) a nd the downwelling scalar irradiance E(od)(Z) is derived from the foll owing equation of radiative transfer. This expression is given by RSR( z)=[L(pi, z)]/E(od)(z) = [f(b)(Z)b(b)(z)]/2 pi[k(pi, z) + c(z) - f(L)( z)b(f)(z)], where b(b)(z) is the backscattering coefficient, k(pi, z) is the vertical attenuation coefficient of the nadir radiance, c(z) is the beam attenuation coefficient, and f(b)(z) and f(L)(z) are shape p arameters that depend on the shape of the volume scattering function a nd the radiance distribution. Successive approximations are subsequent ly applied to the above exact equation. These are f(b)(z) = [2 pi beta (pi - theta(m), z)]/[b(b)(z)], where beta(pi - theta(m), z) is the vol ume scattering function at 180 degrees minus the zenith angle of the m aximum radiance, and k(pi, 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 sa me inherent optical properties, a is the absorption coefficient, and b /c is the single scattering albedo. Together with f(L)(z) = 1.05 and a pplication of Gershun's equation, it is shown that for nearly all ocea nic cases RSR(z) = L(pi, z)/E(od)(z) = [beta(pi - theta(m), z)]/{a(z)[ 1 + m(z)]}.