Model of Randomly Oriented Spheroids for the Retrieval of Non-Spherical Particle Microphysical Parameters from 3 β + 2 α + 3 δ Lidar Measurements, Part 1: Structure and Analysis of the Information Content of a Central Spheroid Look-Up Table
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| Title: | Model of Randomly Oriented Spheroids for the Retrieval of Non-Spherical Particle Microphysical Parameters from 3 β + 2 α + 3 δ Lidar Measurements, Part 1: Structure and Analysis of the Information Content of a Central Spheroid Look-Up Table |
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| Authors: | Kolgotin, Alexei1 (AUTHOR), Müller, Detlef2 (AUTHOR) dgmueller@whu.edu.cn |
| Source: | Remote Sensing. May2026, Vol. 18 Issue 10, p1595. 20p. |
| Subjects: | Particle size distribution, Backscattering, Optical remote sensing |
| Abstract: | Highlights: What are the main findings? Spheroid reference look-up table (RLUT) that contains 64,032 entries of synthetic optical data, i.e., extinction (α), scatter (ζ), total backscatter (β) and cross-polarized backscatter (β⊥) coefficients at wavelengths λ = 355, 532 and 1064 nm is developed. The synthetic optical data are calculated based on a model of randomly oriented spheroids (described by different complex refractive indices) and volume particle size distributions (described by lognormal function for different mean radii and mode widths). Synthetic particle linear depolarization ratios (δ) at 355, 532 and 1064 nm from the RLUT contain significant information about particle size and the particle size distributions (PSDs) themselves. In particular, the δ(λ) spectrum is a function that monotonically decreases (increases) with wavelength in case of fine (coarse) mode particles and it is a function that is shaped convex-downwards (convex-upwards) in the case of a bimodal PSD (submicron mode particles that are intermediate between the fine mode and the coarse mode). What are the implications of the main findings? The unique feature of the interdependency between cross-polarized backscatter-related Ångström exponents ( β ˙ ) at the wavelength pairs 532/1064 nm and 355/532 nm is a hysteresis, i.e., it shows a cycloid-like behavior in the interdependency, which means that the size of the non-spherical particles changes. In the next part of this research work the spheroid RLUT will be involved in the development of the retrieval algorithm that can be used for the inversion of 3β + 2α + 3δ lidar data into particle microphysical parameters. 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | Highlights: What are the main findings? Spheroid reference look-up table (RLUT) that contains 64,032 entries of synthetic optical data, i.e., extinction (α), scatter (ζ), total backscatter (β) and cross-polarized backscatter (β⊥) coefficients at wavelengths λ = 355, 532 and 1064 nm is developed. The synthetic optical data are calculated based on a model of randomly oriented spheroids (described by different complex refractive indices) and volume particle size distributions (described by lognormal function for different mean radii and mode widths). Synthetic particle linear depolarization ratios (δ) at 355, 532 and 1064 nm from the RLUT contain significant information about particle size and the particle size distributions (PSDs) themselves. In particular, the δ(λ) spectrum is a function that monotonically decreases (increases) with wavelength in case of fine (coarse) mode particles and it is a function that is shaped convex-downwards (convex-upwards) in the case of a bimodal PSD (submicron mode particles that are intermediate between the fine mode and the coarse mode). What are the implications of the main findings? The unique feature of the interdependency between cross-polarized backscatter-related Ångström exponents ( β ˙ ) at the wavelength pairs 532/1064 nm and 355/532 nm is a hysteresis, i.e., it shows a cycloid-like behavior in the interdependency, which means that the size of the non-spherical particles changes. In the next part of this research work the spheroid RLUT will be involved in the development of the retrieval algorithm that can be used for the inversion of 3β + 2α + 3δ lidar data into particle microphysical parameters. 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 20724292 |
| DOI: | 10.3390/rs18101595 |
