Cloud information content in EPIC/DSCOVR's oxygen A- and B-band channels: A physics-based approach

In a companion paper [Davis et al., JQSRT 216, 6-16 (2018)], we used a numerical 1D radiative transfer (RT) model and the statistical formalism of optimal estimation to quantify cloud information content in the O2 A- and B-band channels of the Earth Polychromatic Imaging Camera (EPIC) on the Deep Space Climate ObserVatoRy (DSCOVR) platform that images the Earth's sunlit hemisphere from the vantage of the Lagrange-1 point. These two pairs of “in-band” and nearby “reference” radiances are combined into differential optical absorption spectroscopic (DOAS) ratios for both A- and B-bands, from which one can derive, in principle, both cloud top height (CTH) and cloud geometric thickness (CGT). However, Davis et al. show that under most circumstances, there is much redundancy between the two DOAS ratios and, in practice, only CTH can be reliably and accurately retrieved. Here, we derive a simplified analytical 1D RT model for the DOAS ratios to gain physical insights as well as quantify both the CTH retrieval bias from neglecting in-cloud absorption and the impact of measurement error on CTH and CGT retrievals. Using this alternative approach, we again show that only CTH can be inferred reliably when unavoidable measurement error is factored in. Finally, our new theoretical developments are related to a recently uncovered invariance property of the mean path cumulated by light in arbitrarily-shaped optical media of arbitrary opacity with arbitrary scattering properties, as long as it is conservative.