# Coherent Backscattering by Large Ice Crystals of Irregular Shapes in Cirrus Clouds

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## Abstract

**:**

## 1. Introduction

## 2. Scattering Matrix for the Models of Ice Crystal Aggregates

**I**= (I, Q, U, V). The incident light

**I**

_{0}is transformed into the scattered light

**I**by the equation [4]:

**n**

_{0}and scattering

**n**directions, and

**Z**is the so-called phase matrix 4 × 4. In the case of randomly oriented particles, the phase matrix reduces to the scattering matrix $F(\theta )$ that has the following view.

## 3. The Scattering Matrixes Calculated in the Physical-Optics Approximation

_{max}= 20 μm where D

_{max}is the maximum distance between two points on the particle surface. The wavelength was equal to 0.532 µm, and the refractive index was assumed as 1.3116.

## 4. The Scattering Matrix for Other Size and Shapes of the Particles

## 5. Grazing-Incidence Trajectories and the Backscattering Peak

## 6. Interference of the Grazing-Incidence Beams

_{max}= 20 μm.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The scattering matrix for the shape 1 of Figure 1.

**Figure 3.**The scattering matrix for the shape 2 of Figure 1.

**Figure 4.**The scattering matrix for the shape 3 of Figure 1.

**Figure 6.**The scattering matrix for particles of Figure 5 with two sizes.

**Figure 7.**Conjugate pair of backscattering beams with grazing-incidence trajectories (

**a**). Shapes of the beams on the exit facets (

**b**) and on a plane perpendicular to the incident direction (

**c**). The line L connects the centers of the beam projections.

**Figure 8.**Distribution of the backscattered intensity over the particle projection obtained in the geometrical optics approximation for the beam trajectories with three (

**a**) and four (

**b**) internal reflections/refraction events averaged for two Euler angles of particle orientations. Here (

**c**) is the average over random orientation.

**Figure 9.**Backscattered intensity ${M}_{11}(n)$ (

**a**) and polarization element $-{M}_{12}(n)$ (

**b**) for two beams of Figure 7 at incoherent summation. The figure centers are the exact backward direction $\theta $ = 180°, the blue color in (

**b**) corresponds to negative quantities.

**Figure 10.**The same as in Figure 9 at coherent summation.

**Figure 11.**Element ${M}_{12}(\theta ,\phi )$ of Figure 10b plotted for: (a) two perpendicular meridians $\phi =0$ (red) and $\phi =\pi /2$ (blue); (b) their average (black), and (c) averaged over $\phi $ (green).

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**MDPI and ACS Style**

Kustova, N.; Konoshonkin, A.; Shishko, V.; Timofeev, D.; Borovoi, A.; Wang, Z. Coherent Backscattering by Large Ice Crystals of Irregular Shapes in Cirrus Clouds. *Atmosphere* **2022**, *13*, 1279.
https://doi.org/10.3390/atmos13081279

**AMA Style**

Kustova N, Konoshonkin A, Shishko V, Timofeev D, Borovoi A, Wang Z. Coherent Backscattering by Large Ice Crystals of Irregular Shapes in Cirrus Clouds. *Atmosphere*. 2022; 13(8):1279.
https://doi.org/10.3390/atmos13081279

**Chicago/Turabian Style**

Kustova, Natalia, Alexander Konoshonkin, Victor Shishko, Dmitry Timofeev, Anatoli Borovoi, and Zhenzhu Wang. 2022. "Coherent Backscattering by Large Ice Crystals of Irregular Shapes in Cirrus Clouds" *Atmosphere* 13, no. 8: 1279.
https://doi.org/10.3390/atmos13081279