Model of Randomly Oriented Spheroids for the Retrieval of Non-Spherical Particle Microphysical Parameters from 3β + 2α + 3δ Lidar Measurements, Part 1: Structure and Analysis of the Information Content of a Central Spheroid Look-Up Table

We developed a reference look-up table (RLUT) of particles of spheroidal shape. This RLUT will be used in our lidar-data inversion algorithm we have developed in the past 25 years for the retrieval of microphysical parameters of non-spherical particles from 3β + 2α + 3δ optical datasets measured with Raman/HSRL lidar. The optical datasets are described by particle backscatter coefficients (β) at three wavelengths λ = 355, 532, and 1064 nm, particle extinction coefficients (α) at two wavelengths λ = 355 and 532 nm, and particle linear depolarization ratios (PLDRs, δ) at three wavelengths λ = 355, 532, and 1064 nm. The RLUT contains 64,032 synthetic 3β + 2α + 3δ—datasets calculated on the basis of a light-scattering model of randomly oriented spheroids and spheroid particle size distributions described by different particle complex refractive indices (CRIs) and lognormal functions with different Gauss parameters such as mean radius (μ) and standard deviation (σ). We investigate major features of the RLUT such as information content encoded in the 3β + 2α + 3δ datasets, conditionality, determinacy and the sensitivity of the retrievals to the underlying measurement errors. We find that major features of the sphere and spheroid RLUTs are similar; however, extra information is encoded in the PLDRs. The PLDR spectrum on the domain λ ∈ [355; 1064] μm contains significant information about the size of spheroid particles. The analysis of the information content is more productive if we use the cross-polarized backscatter-related Ångström exponent (CrPBAE) at the wavelength pairs 355 and 532 nm [β˙⊥(355/532)] and the wavelength pairs 532 and 1064 nm [β˙⊥(532/1064)]. In particular, the cycloid-like behavior of the interdependency β˙⊥(355/532) versus β˙⊥(532/1064), i.e., hysteresis, means that non-spherical particle size changes.