Aerosol retrieval algorithms used in conjunction with remote sensing are subject to ill-posedness. To mitigate non-uniqueness, extra constraints (in addition to observations) are valuable for stabilizing the inversion process. This paper focuses on the imposition of an empirical correlation constraint on the retrieved aerosol parameters. This constraint reflects the empirical dependency between different aerosol parameters, thereby reducing the number of degrees of freedom and enabling accelerated computation of the radiation fields associated with neighboring pixels. A cross-pixel constraint that capitalizes on the smooth spatial variations of aerosol properties was built into the original multi-pixel inversion approach. Here, the spatial smoothness condition is imposed on principal components (PCs) of the aerosol model, and on the corresponding PC weights, where the PCs are used to characterize departures from the mean. Mutual orthogonality and unit length of the PC vectors, as well as zero sum of the PC weights also impose stabilizing constraints on the retrieval. Capitalizing on the dependencies among aerosol parameters and the mutual orthogonality of PCs, a perturbation-based radiative transfer computation scheme is developed. It uses a few dominant PCs to capture the difference in the radiation fields across an imaged area. The approach is tested using 27 observations acquired by the Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) during multiple NASA field campaigns and validated using collocated AERONET observations. In particular, aerosol optical depth, single scattering albedo, aerosol size, and refractive index are compared with AERONET aerosol reference data. Retrieval uncertainty is formulated by accounting for both instrumental errors and the effects of multiple types of constraints.
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