Molecular line absorption in a scattering atmosphere. Part I: Theory

This paper revisits the classical problem of particle scattering-gaseous ab sorption and considers the extent to which the growth of absorption lines o f a known gas can be used to obtain information about the scattering partic les, The focus of the study is directed toward interpretation of the reflec tion spectrum of the O-2, A band located in the spectral region between 0.7 59 and 0.771 mu m and the results provide a theoretical foundation for the retrieval of particle information described in a related study. This study demonstrates that there are six main properties that affect the absorption and reflection spectra: the optical depth of the cloud or aerosol, the pres sure level of the top of this layer, the (pressure) thickness of the layer, the scattering phase function, the particle single-scatter. albedo, acid t he surface albedo, Measured quantities, such as the spectral radiance or th e ratio of in-absorption to continuum radiances ale shown to be st sensitiv e to these parameters in a manner that varies according to the O-2 optical depth. This variation sensitivity offers a way of separating the dependence of the measurements on these parameters, thereby providing some basis for their retrieval with suitable spectral measurements that resolve a sufficie nt range of O-2, optical depth. Specifically, it is shown that radiances re flected from thin layers are sensitive to optical depth and phase function whereas the radiance ratio is sensitive to layer height. For thick layers, the sensitivity to optical depth diminishes leaving primarily a sensitivity to bull information about the scattering phase function. By measuring radi ances as a function of changing O-2 absorption, it is possible to distingui sh optically thin layers above brighter lower reflecting surfaces, providin g an ability to distinguish high-level thin cloud over brighter lower-level clouds or reflecting surfaces. The effects of 3D geometry on the spectral radiances is also considered in the context of photon path. it is shown how the spectral radiances provide some insight on 3D effects and the probable importance of these 3D effects on the retrievals. The equivalence theorem is illustrated and is used to provide line-by-line simulations of the refle ction spectrum from hypothetical 3D clouds. A method to identify the nature of the 3D bias on retrievals of optical depth is discussed.