The governing equations are developed for the marine asymptotic daylig
ht field in the scalar approximation, including the effects of inelast
ic processes-Raman scattering and chromophoric dissolved organic matte
r fluorescence. The governing equations are solved numerically and com
pared with Monte Carlo simulations. It is found that these solutions a
re the actual radiance distributions approached by the asymptotic fiel
d in the Monte Carlo simulations. Sample solutions are provided to sho
w the sensitivity of the light held to the various parameters of the m
edium. For certain values of the parameters, inclusion of inelastic pr
ocesses can drastically alter the radiance distribution, e.g., from a
near-Dirac delta function in the absence of inelastic processes to a n
ear-isotropic distribution in their presence. The results suggest that
in a real ocean, the asymptotic (and near-asymptotic) radiance distri
bution will tend to become more uniform as the wavelength increases be
yond similar to 500 nm. Finally, it is shown that even for depths far
from the asymptotic regime, the radiance distribution of the inelastic
component of the light field can be well approximated by the asymptot
ic theory developed here for inelastic processes. Two exact analytical
solutions to the governing equations are also provided.