Moments of Sunlight Pathlength in Water and Aerosol Clouds from O$_2$ Spectroscopy: Exploitable Parameter Sensitivities

According to the latest IPCC assessment, clouds and aerosolsremain a major challenge in future climate prediction using Global ClimateModels (GCMs). Consequently, NASA's 2017 Decadal Survey has made them,along with convection and precipitation, a high priority by calling them outas Designated Observables for future coordinated missions under the "ACCP"banner, now known as the Atmospheric Observing System. Atmosphericscience is now more than ever driving a renewal in remote sensing techniquesthat can probe clouds and aerosols more accurately and with improvedsampling. Herein, we bring new theoretical results that support a special formof Differential Optical Absorption Spectroscopy (DOAS) that uses oxygenabsorption features in the visible/near-IR (VNIR) spectrum where there isan abundance of sunlight. Having known concentration and cross-section,the remaining unknown in O2 DOAS (DO2AS) is the path that the light hasfollowed through the absorbing gas. In the presence of scattering by cloudand aerosol particles, that path is broken at each interaction. Cumulativepathlength through the well-mixed O2 gas thus becomes a continuous randomvariable, and its probability distribution function (PDF) will contain desirableinformation about the clouds and aerosols such as top and bottom altitudesof the layer they occupy as well as its optical thickness. In this study, webuild on previous work to compute statistical moments of the pathlengthPDF. Specifically, we show that mean and variance of the pathlength insidethe scattering particulate medium convey different pieces of information,namely, size and opacity of the optical medium, hence geometric and opticalthicknesses in the case of plane-parallel layers. We also extend, with denseaerosol plumes in mind (e.g., wildfire smoke, volcanic ash, elevated dust),the mean pathlength's close connection between geometric thickness andmean pathlength in the presence of absorption by the scattering particlesthemselves. In summary, we view pathlength moments as intermediate DO2ASproducts that can be obtained from O2 spectroscopic data, and we describe apreliminary algorithm to do just that. In turn, these moments yield cloudor aerosol profile parameters of high interest: layer geometric and opticalthicknesses. One normally thinks about active sensors, radars and lidars, todo such atmospheric profiling. In this case, the profle is parameterized andrepresentative of some kind of horizontal average determined by the multiplescattering. However, there is a clear advantage in using passive over activeinstrumentation, starting with the possibility of imaging over a large swath.