In the atmosphere, the dust shapes are various, and a single model is difficult to represent the complex shapes of dust. We proposed a tunable model to represent dust with various shapes. Two tunable parameters were used to represent the effects of the erosion degree and binding forces from the mass center, respectively. Thus, the model can represent various dust shapes by adjusting the tunable parameters. To evaluate the applicability of the single spheroid model in calculating the optical properties of single dust with irregular shapes, the aspect ratios of spheroids were retrieved by best fitting the phase function of dust with irregular shapes. In this work, the optical properties and polarimetric characteristics of irregular dust with a diameter range of 0.2–2.0

Dust particles, as a main atmospheric aerosol in the Earth system, play an important role in climate forcing

Remote sensing, as an effective tool for monitoring Earth, has been applied to retrieve the aerosol properties

Polarization is more sensitive to the atmosphere and less disturbed by surfaces than radiation

In most remote sensing algorithms, aerosol shapes were commonly assumed to be spherical, and the optical properties can be calculated using Mie theory. However, transmission electron microscopy (TEM) and scanning electron microscope (SEM) images have shown that most aerosols exhibit distinct non-spherical shapes

Some modeling work has been conducted to investigate the optical properties of more irregular dust, and they have shown that the optical properties of dust are significantly affected by their shapes

Could the single spheroid with a best-fitted aspect ratio reproduce the single-scattering properties of a single dust particle with more complex shapes?

Could the single spheroid with a best-fitted aspect ratio reproduce the polarimetric characteristics of a single dust particle with more complex shapes?

How do the dust shapes affect the scattering properties and polarimetric characteristics?

In the atmosphere, the dust shapes are various, and a single model is difficult to represent the complex shapes of dust, so we need to develop dust models which can represent various shapes. In principle, in order to reproduce the scattering properties of dust, ensembles of spheroidal particles should be used (i.e., with a distribution of sizes and aspect ratios). However, as a first step towards exploring the applicability of spheroidal shapes for reproducing the scattering properties of dust, we just consider single particles in this work, and further investigations for ensembles of dust particles should be investigated in the future. To answer the above questions, we proposed a tunable model to represent the dust with various morphologies, and the scattering properties were calculated using discrete dipole approximation (DDA) methods. Then, we retrieved the aspect ratio that best fits the phase function of dust with complex morphologies using the spheroid model, and the scattering matrices of dust with complex morphologies and best-fitted spheroids were compared. Besides, the radiance and polarization were calculated using a vector radiative transfer (VRT) code based on plane-parallel successive order of scattering (SOS), and the capabilities of spheroids for representing the radiance and polarization of irregular dust were evaluated.

To model the dust with irregular shapes, we proposed a model based on the physical process. To evaluate the applicability of spheroids as dust turns more irregular, we assumed that the ideal dust particles are spheroids, but they could become more irregular in the atmosphere. We assumed that the evolution of dust shapes is mainly affected by two factors. On the one hand, the dust could be eroded under the effects of external forces, such as wind, water, etc. Due to erosion forces acting on the particles, part of the dust mass would be lost in the form of dust granules leaving the particle surface. However, the binding force from the particle center of mass could constrain this loss. We have generated various dust shapes based on the above mechanisms.

Figure

The generation of irregular dust.

We first sort the

The typical morphologies of simulated dust.

The normalized scattering matrix, extinction cross-section (

The first element of the scattering matrix

In this work, we mainly focus on the polarization of the dust particles, so the vector radiative transfer equations need to be considered, and the complete Stokes scattering matrix was inputted into the radiative transfer equations. The real part of the dust was assumed to be 1.52 based on the study by

The T-matrix method has great advantages in calculating the optical properties of symmetrical particles

As shown in Fig. S1 in the Supplement, the difference of the scattering matrix of spherical particles calculated using DDSCAT is below 1 %, which is much smaller than the difference caused by the dust shapes. Thus, the accuracy of DDSCAT is acceptable.

In this work, we attempt to find spheroids that best fit the phase function of irregular dust particles. Firstly, the scattering matrix of dust with irregular shapes was calculated using DDSCAT; then the spheroid model was used to retrieve the aspect ratio by minimizing the following function:

A successive-order-of-scattering (SOS) vector radiative transfer (VRT) code was employed to calculate the radiance and polarization

Similar to the radiance, the polarized bidirectional reflectance factor (PBRF) was also investigated. PBRF is defined as the normalized polarized intensity, can be expressed as the following

Another important parameter (DoLP), which characterizes the ratio of radiance to polarized intensity, was also used in polarimetric remote sensing. DoLP is defined as the following

Table 1 shows the input parameters adopted in this work for radiative transfer calculations.

Input parameters for radiative transfer calculation.

The scattering matrices of dust with different irregular shapes and the corresponding spheroids that best fit the phase function are shown in Figs.

The scattering matrix of dust with irregular shapes, where the aspect ratio is

Similar to Fig.

Similar to Fig.

From the comparisons of Figs.

Similar to Fig.

Similar to Fig.

The imaginary parts of refractive indices of dust particles can vary in a relatively wide range. Figure

Similar to Fig.

From Figs.

With a large particle size, the scattering matrix differences between dust with irregular shapes and best-fitted spheroids become rather obvious. Figures S4–S5 show that the absolute

Figures

Figures

Table

The scattering or extinction cross-section of dust with irregular shapes.

Figure

To investigate the effects of dust shape on the polarized remote sensing signal, the normalized radiance (

The polarimetric characteristics of dust with irregular shapes, where the aspect ratio is

Similar to Fig.

Similar to Fig.

Nevertheless, with the particle size increasing, the erosion degree has more obvious impacts on the normalized radiance (

With a

The effects of

Figure

The polarimetric characteristics of dust with irregular shapes, where the aspect ratio is

Figure

The relative difference of normalized radiance between dust with irregular shapes and best-fitted spheroids, where the aspect ratio is

As the particle diameter increases to 0.8

As

The spheroid model can also provide inaccurate estimations for PBRF. As shown in Fig.

The difference of PBRF between dust with irregular shapes and best-fitted spheroids, where the aspect ratio is

Figure

Similar to Fig.

Figure

The difference of polarimetric characteristics between dust with irregular shapes and best-fitted spheroids, where the aspect ratio is

Spheroidal shapes are commonly used to reproduce the scattering properties of dust, although their applicability is still unclear. To calculate the scattering properties of dust, we proposed a tunable model to represent dust with various shapes. We assumed that the dust shapes are mainly affected by two factors: (1) the dust shape can vary with erosion by external force, which can lead to loss of mass, and (2) the binding force from the center of mass can prevent the loss of dust mass. We proposed an algorithm with two tunable parameters to simulate the effects of these two factors, and various complex dust shapes were generated. As we used tunable parameters to represent various dust shapes, our model is helpful for the parameterization of the optical properties of dust with different shapes (but not for faceted dust particles). To evaluate the capability of spheroids to reproduce the single dust particle scattering properties, we used single spheroidal particles that fit well with the phase function of single dust particles with irregular shapes, and then we investigated their capability to reproduce all the elements of the scattering matrix.

The single-scattering properties of single dust particles with irregular shapes were investigated. We found that both the erosion of external force and binding force from the mass center can have a significant impact on the dust shapes, so they significantly affect the single-scattering properties of dust. Besides, the applicability of the best-fitted spheroids in estimating the scattering matrix was evaluated. With a small particle size, the differences in the scattering matrix between best-fitted spheroids are not substantial. With a diameter of 0.2

To see how the dust shapes affect the polarimetric remote sensing, we have calculated the normalized radiance, PBRF and DoLP of dust using the SOS model. Our findings show that dust shapes have a relatively unobvious impact on the normalized radiance, PBRF or DoLP when the particle size is small, while the effects become rather obvious as the particle size increases. Our findings show that both the erosion degree and the binding force can significantly affect the angular distribution of normalized radiance, PBRF and DoLP. The differences between irregular dust particles and best-fitted spheroids were also investigated. When the particle size is small, the spheroid model can provide good estimations. With a

The DDSCAT code can be available from

he data used in this work can be obtained from

The supplement related to this article is available online at:

JL and ZL conceptualized the idea. JL developed the models, performed the computations and wrote the paper. ZL, CF, HX, YZ, WH, LQ, HG, MZ, YL and KL verified results. ZL revised the paper and supervised the findings of this work. All authors discussed the results and contributed to the final paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was financially supported by the National Outstanding Youth Foundation of China (grant no. 41925019) and the National Natural Science Foundation of China (grant nos. 41871269 and 42175146). We particularly thank Michael Mischenko for making the T-matrix code publicly available and Bruce Draine and Pjotr Flatau for making the DDSCAT program publicly available. We also thank the two anonymous reviewers for their thoughtful reviews and valuable comments on the article.

This research has been supported by the National Natural Science Foundation of China (grant nos. 41925019, 41871269, and 42175146).

This paper was edited by Vassilis Amiridis and reviewed by two anonymous referees.