  The last IPCC assessment states that clouds and aerosols remain a challenge
in climate prediction with Global Climate Models. Therefore, NASA's 2017
Decadal Survey has made them, along with convection and precipitation, a
priority target for future missions under the ACCP banner, now Atmospheric
Observing System. Atmospheric science is now more than ever driving renewal in
remote sensing to probe clouds and aerosols more accurately and with improved
sampling. Here, we bring new results that support Differential Optical
Absorption Spectroscopy (DOAS) using oxygen absorption features in the
visible/near-IR spectrum. With known concentration and cross-section, the
remaining unknown in O$_2$ DOAS is the path the light followed through the
absorbing gas. In presence of scattering by cloud or aerosol particles, that
path is broken at each interaction. Cumulative pathlength through the gas is a
random variable, and its probability distribution function (PDF) will contain
desirable information about the clouds or aerosols. Here, we compute
statistical moments of the that PDF, showing that mean and variance convey
different pieces of information, namely, size and opacity of the medium. We
also extend the connection between geometric thickness and mean pathlength in
presence of absorption by the scattering particles. We view pathlength moments
as intermediate products that can be obtained from O$_2$ spectroscopy, and
describe an algorithm to do that. In turn, these moments yield cloud or aerosol
profile parameters of interest: layer geometric and optical thicknesses. One
normally thinks about active sensors, radars and lidars, for such atmospheric
profiling. Here, the profile is parameterized and representative of a
horizontal average determined by multiple scattering. However, there are
advantages in passive vs active instrumentation, starting with the possibility
of imaging over a large swath.
