Seven models for computing underwater radiances and irradiances by num
erical solution of the radiative transfer equation are compared. The m
odels are applied to the solution of several problems drawn from optic
al oceanography. The problems include highly absorbing and highly scat
tering waters, scattering by molecules and by particulates, stratified
water, atmospheric effects, surface-wave effects, bottom effects, and
Raman scattering. The models provide consistent output, with errors (
resulting from Monte Carlo statistical fluctuations) in computed irrad
iances that are seldom larger, and are usually smaller, than the exper
imental errors made in measuring irradiances when using current oceano
graphic instrumentation. Computed radiances display somewhat larger er
rors.