Molecular Line Absorption in a Scattering Atmosphere. Part I: Theory

Abstract

This paper revisits the classical problem of particle scattering?gaseous absorption and considers the extent to which the growth of absorption lines of a known gas can be used to obtain information about the scattering particles. The focus of the study is directed toward interpretation of the reflection spectrum of the O2 A band located in the spectral region between 0.759 and 0.771 ?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 pressure level of the top of this layer, the (pressure) thickness of the layer, the scattering phase function, the particle single-scatter albedo, and the surface albedo. Measured quantities, such as the spectral radiance or the ratio of in-absorption to continuum radiances are shown to be sensitive to these parameters in a manner that varies according to the O2 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 sufficient range of O2 optical depth. Specifically, it is shown that radiances reflected 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 bulk information about the scattering phase function. By measuring radiances as a function of changing O2 absorption, it is possible to distinguish optically thin layers above brighter lower reflecting surfaces, providing 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 reflection spectrum from hypothetical 3D clouds. A method to identify the nature of the 3D bias on retrievals of optical depth is discussed.