Radiation transfer in ocean water: Average penetration depth of a photon flux in a fixed time interval

Abstract

It has been shown that for a set of photons emitted, initially as a parallel flux, within the water, the average distance traversed along the original direction by the surviving photons in time interval Δt is Δ̄r = d exp(- bd) ∑∞n=0 (bd)n/(n+1)! [∑ni=0 μ̄si] or, Δ̄r = d F(b, μ̄s, d) where d is cwΔt (cw being the speed of light in water), b is the scattering coefficient, μ̄s is the average cosine (or asymmetry factor) of the scattering phase function and F(b, μ̄s, d) may be referred to as the penetration function. The average depth traversed in time interval Δt by those photons which are emitted from a thin layer of the ocean at depth z, but not absorbed, is Δ̄z = cwΔt F(b, μ̄s, cwΔt) μ̄(z) where μ̄ (z) is the average cosine of the light field at that depth. Computer calculations based on these equations can readily be implemented, and the validity of the calculations has been confirmed by Monte Carlo modeling. Copyright 2007 by the American Geophysical Union.