Statistical Treatment of Remote Sensing Reflectance from Coastal Ocean Water: Proportionality of Reflectance from Multiple Scattering to Source Function b/a

Abstract

Abstract I treat the reflectance of light from coastal ocean water in terms of diffused volume scattering phase function P(θ) derived from successive products of the normalized volume scattering function β(θ). My results show that the wavelength dependence for backscattering in a multiple scattering process is directly proportional to the angle-independent dimensionless source function b/a, which is the ratio of the total volume scattering coefficient b and the total volume absorption coefficient a. I use this result to produce a statistical formula for remote sensing reflectance (Rrs). The statistical formula shows good agreement with experimental data, and—unlike the standard oceanographic expressions for Rrs given in terms of bb/(a + bb), where bb is the volume backscattering coefficient—the statistical relationship for Rrs accounts for the effects of photon turnaround and reduces to the expected asymptotic limits for diffuse reflectance when a → 0 but bb remains finite and when bb → 0 but a and b rema...