# Effect of Polygonal Agglomerated Ice Crystals on Laser Scattering

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## Abstract

**:**

## 1. Introduction

## 2. DDA Method and Agglomeration Model

#### 2.1. Discrete Dipole Approximation (DDA)

#### 2.2. Agglomeration Structural Model

#### 2.3. Calculation of Scattering Characteristics

## 3. Results and Analysis

#### 3.1. Effect of Effective Size on Extinction, Absorption and Scattering Efficiencies of Agglomerated Ice Crystal Particles

#### 3.2. Effect of Ice Crystal Particle Size on Laser Scattering Intensity

#### 3.3. Influence of Ice Crystal Particle Shape on Mueller Matrix Elements

#### 3.4. Influence of Spatial Orientation of Agglomerated Ice Crystals on Scattering

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Complex ice crystal particles with a modest magnification of 250–4500 times. (

**a**) bullet rosette and unclassified compact convolution ‘singular polyhedron’; (

**b**) rhomboid and prismatic linear coarser crystals with discrete adhesion spots on the surface; (

**c**) rosette mixed crystals; (

**d**) irregular cross section of the base, geometrically stratified and hollow columnar, a highly coarser crystal [10].

**Figure 2.**Ice crystal particle model with agglomerated structure. (

**a**) sphere–sphere; (

**b**) sphere–ellipsoid; (

**c**) sphere-hexagonal prism; (

**d**) sphere-hexagonal plate.

**Figure 3.**Variation of the extinction efficiency, absorption efficiency, and scattering efficiency of agglomerated ice crystal particles with effective size for the different agglomeration models [8]. (

**a1**–

**a3**) changes in extinction efficiency; (

**b1**–

**b3**) changes in absorption efficiency; (

**c1**–

**c3**) changes in scattering efficiency.

**Figure 4.**Influence of the shape of the ice crystals with aggregated structures on the laser scattering intensity [8]. (

**a1**–

**a3**) effective radius $0.1\lambda $ µm; (

**b1**–

**b3**) effective radius $\lambda $ µm; (

**c1**–

**c3**) effective radius $10\lambda $ µm.

**Figure 5.**Influence of shapes of ice crystals with aggregated structures on Mueller matrix elements [8]. (

**a1**–

**a3**) ${S}_{11}$; (

**b1**–

**b3**) ${S}_{12}/{S}_{11}$; (

**c1**–

**c3**) ${S}_{33}/{S}_{11}$; (

**d1**–

**d3**) ${S}_{34}/{S}_{11}$.

**Figure 6.**Target orientation in the laboratory frame coordinate system [13].

**Figure 7.**Visualization of the near-field electric field distribution of the four clustered particle models. (

**a1**) sphere–sphere $\Theta ={0}^{\circ}$; (

**a2**) sphere–sphere $\Theta ={90}^{\circ}$; (

**b1**) sphere–ellipsoid $\Theta ={0}^{\circ}$; (

**b2**) sphere–ellipsoid $\Theta ={90}^{\circ}$; (

**c1**) sphere-hexagonal prism $\Theta ={0}^{\circ}$; (

**c2**) sphere-hexagonal prism $\Theta ={90}^{\circ}$; (

**d1**) sphere-hexagonal plate $\Theta ={0}^{\circ}$; (

**d2**) sphere-hexagonal plate $\Theta ={90}^{\circ}$.

**Figure 8.**The relative errors of extinction efficiency, absorption efficiency, and scattering efficiency of ice crystal particles at $\Theta ={0}^{\circ}$ and $\Theta ={90}^{\circ}$ spatial position. (

**a**) relative error of extinction efficiency; (

**b**) relative error of absorption efficiency; (

**c**) relative error of scattering efficiency.

**Figure 9.**The relative errors of the Mueller matrix elements of ice crystal particles at $\Theta ={0}^{\circ}$ and $\Theta ={90}^{\circ}$. (

**a**) relative error of ${S}_{11}$; (

**b**) relative error of ${S}_{12}/{S}_{11}$; (

**c**) relative error of ${S}_{33}/{S}_{11}$; (

**d**) relative error of ${S}_{34}/{S}_{11}$.

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**MDPI and ACS Style**

Ren, S.; Gao, M.; Nan, Z.; Wang, M.; Li, Y.
Effect of Polygonal Agglomerated Ice Crystals on Laser Scattering. *Atmosphere* **2022**, *13*, 369.
https://doi.org/10.3390/atmos13030369

**AMA Style**

Ren S, Gao M, Nan Z, Wang M, Li Y.
Effect of Polygonal Agglomerated Ice Crystals on Laser Scattering. *Atmosphere*. 2022; 13(3):369.
https://doi.org/10.3390/atmos13030369

**Chicago/Turabian Style**

Ren, Shenhe, Ming Gao, Ze Nan, Mingjun Wang, and Yan Li.
2022. "Effect of Polygonal Agglomerated Ice Crystals on Laser Scattering" *Atmosphere* 13, no. 3: 369.
https://doi.org/10.3390/atmos13030369