Mineral dust, as one of the most important aerosols, plays a crucial role in the atmosphere by directly interacting with radiation, while there are
significant uncertainties in determining dust optical properties to quantify radiative effects and to retrieve their properties. Laboratory and in
situ measurements of the refractive indices (RIs) of dust differ, and different RIs have been applied in numerical studies used
for model developments, aerosol retrievals, and radiative forcing simulations. This study reveals the importance of the dust RI for the
development of a model of dust optical properties. The Koch-fractal polyhedron is used as the modeled geometry, and the pseudospectral time domain
method and improved geometric-optics method are combined for optical property simulations over the complete size range. We find that the scattering
matrix elements of different kinds of dust particles are reasonably reproduced by choosing appropriate RIs, even when using a fixed
particle geometry. The uncertainty of the RI would greatly affect the determination of the geometric model, as a change in the RI,
even in the widely accepted RI range, strongly affects the shape parameters used to reproduce the measured dust scattering matrix
elements. A further comparison shows that the RI influences the scattering matrix elements in a different way than geometric factors, and,
more specifically, the

Atmospheric aerosols play an important role in the global radiation balance directly by scattering and absorbing incident solar radiation and indirectly by influencing cloud formation as cloud condensation nuclei (CCN) or ice nuclei (IN) (Chýlek et al., 1978; Sokolik et al., 2001; Yi et al., 2011). According to the IPCC Fifth Assessment Report (IPCC, 2014), aerosols are still one of the largest sources of uncertainty in the total estimate of radiative forcing. As a major type of aerosol, mineral dust is widely distributed around the world, especially in arid regions. Mineral dust single-scattering properties are fundamental for quantifying radiative effects, and for developing satellite retrieval algorithms from optical observations (Kahn et al., 2005; Huang et al., 2014; Xu et al., 2017a).

Several aerosol optical property databases, e.g., the Global Aerosol Data Set (GADS; Koepke et al., 1997) and the Optical Properties of Aerosols and Clouds (OPAC; Hess et al., 1998), have been built to meet the needs of aerosol remote sensing and radiation studies for all aerosols as well as for particular kinds of aerosols (Meng et al., 2010; Bi et al., 2018b; Liu et al., 2019). However, for simplification, the optical properties of atmospheric aerosols are often investigated by assuming a relatively simple model, e.g., using spheres and spheroids, which has resulted in obvious errors (Mishchenko et al., 1997; Feng et al., 2009). For example, the measured phase functions of dust particles are clearly different from the phase functions of spherical particles at sideward and backward scattering angles (Koepke and Hess, 1988; Dubovik et al., 2002; Nousiainen, 2009). Databases with more accurate dust optical properties can contribute to applications such as radiative forcing calculation and remote sensing.

Several efforts have been devoted to studying the optical properties of dust aerosols (Bi et al., 2010; Meng et al., 2010; Ishimoto et al., 2010; Liu et al., 2013; Jin et al., 2016; Xu et al., 2017b). Although it is difficult but possible to mathematically define the exact shape of an actual dust particle in numerical studies (Kahnert et al., 2014; Lindqvist et al., 2014), the use of a simplified but optically equivalent model is more convenient and easier to process (Nousiainen and Kandler, 2015; Liu et al., 2013). By using the measured particle size information and the assumed refractive index (RI), most studies treat the geometry as an unknown variable and look for geometric parameters that result in simulated optical properties that are consistent with measurements (Bi et al., 2010; Dubovik et al., 2006; Liu et al., 2013; Lin et al., 2018; Mishchenko et al., 1997; Osborne et al., 2011). Different nonspherical shapes have been developed and applied, such as spheroids (Mishchenko et al., 1997; Dubovik et al., 2002; Ge et al., 2011; Merikallio et al., 2011), ellipsoids (Bi et al., 2009; Meng et al., 2010; Kemppinen et al., 2015), and superellipsoids (Bi et al., 2018a). Additionally, more complex and irregular particles have also been considered, e.g., spatial Poisson–Voronoi tessellation (Ishimoto et al., 2010), Gaussian random field (GRF) particles (Grynko et al., 2013), Koch-fractal particles (Liu et al., 2013; Jin et al., 2016), and nonsymmetric hexahedra (Bi et al., 2010; Liu et al., 2014). These “irregular” geometries as well as spheroids can achieve close agreement with measurements by using appropriate shape parameters or combining the results from multiple shapes, which indicates that certain geometries may be optically similar or equivalent with respect to scattering light. Nousiainen and Kandler (2015) found that the scattering properties of a cube-like dust particle can be mimicked by those of spheroids with a suitable shape distribution. Liu et al. (2014) found that the surface roughness and irregularity also share an optical equivalence. Lin et al. (2018) revealed that the scattering matrix elements of different types of dust particles can be achieved by changing only two parameters to specify the geometry of the superspheroids. Such “optical equivalences” are important for practical applications using dust optical properties because we can use those from a relatively simple numerical model, instead those based on the exact and actual dust particles, for downstream remote sensing and radiative transfer applications.

Refractive index from different sources. The color bar indicates the wavelengths at which the corresponding refractive indices are given (for the two lines and dots).

In addition to the particle geometry, there are also significant uncertainties related to the dust RI, which is often considered an inherent characteristic (Kahnert and Nousiainen, 2006; Stegmann and Yang, 2017), to which much less attention has been devoted during the model development. Previous studies often assumed a fixed RI during simulations of the corresponding optical properties at the incident wavelength of interest. The real part (Re) of dust RI is normally set to approximately 1.5, and, excluding hematite and magnetite, the imaginary part (Im) is normally set between 0.001 and 0.01 at visible wavelengths (Sokolik and Toon, 1999; Volten et al., 2001; Kandler et al., 2007; Meng et al., 2010). Previous studies using both measurements and numerical investigations reveal that a relatively large variation in the RI of dust materials in different regions or with different components does exist (Meng et al., 2010; Bi et al., 2011; Stegmann and Yang, 2017). Kemppinen et al. (2015) revealed that the retrieved dust RIs based on the comparisons of scattering matrices between simulations and laboratory measurements deviate from the true dust RIs.

Figure 1 shows some examples of the RIs around the visual wavelengths, and we illustrate values from various studies, including those from
two well-accepted optical properties databases, i.e., the Global Aerosol Data Set (GADS; Koepke et al., 1997) and the Optical Properties of Aerosols
and Clouds (OPAC; Hess et al., 1998), and the RI spectra of silicates and calcites (important components of mineral dust) based on
measurement studies (Stegmann and Yang, 2017) with the incident wavelengths from 200 to 1000

This study uses the measured dust scattering properties from the AGLSD as the reference to “evaluate” the modeled results. However, we will not pay too much attention to the effect or performance of different geometric factors, as this topic has been covered in several previous studies. Considering the obvious uncertainties and less attention related to the particle RI, this study introduces the important roles of the dust RI in developing corresponding models for the numerical simulation of their optical properties. Section 2 introduces the models considered and the computational methods applied in this study. Section 3 investigates the impacts of the RI on the reproduction of the optical properties of several types of mineral dust particles. The effects of the RI on model development are revealed in Sect. 4, and the impacts of RI and geometry on the optical properties of dust are compared. Section 5 concludes the work.

This study focuses on the effects of the RI on modeling the dust scattering matrix elements. The Koch-fractal particle is used as the presumed geometry (Macke et al., 1996; Falconer, 2004; Liu et al., 2013; Jin et al., 2016). The Koch-fractal particle geometry has been used to produce concave polyhedra based on tetrahedron elements of different generations and is flexible in representing both the particle overall geometries and their detailed surface structures. Macke et al. (1996) used second-generation Koch-fractal particles with different irregularities to explore the scattering properties of complex ice crystals using a geometric-optics method. Liu et al. (2013) extended the applications of Koch-fractal particle geometries to mineral dust particles and found that the corresponding optical properties represent those from measurements.

Figure 2 shows three examples of third-generation Koch-fractal particle geometries. The sequential number of the Koch-fractal generation indicates the complexity of the surface structure, and an irregular ratio (IR), which specifies particle irregularity, is a real number within the range [0, 0.5] used to constrain the random movement of the positions of successor-generation tetrahedra apexes to generate irregular particles. A larger IR makes the Koch-fractal geometry surfaces more irregular and asymmetrical. Liu et al. (2013) introduced the aspect ratio (AR, the ratio of height to width) to generate prolate or oblate particles. Macke et al. (1996) and Liu et al. (2013) include more details on the definition of Koch-fractal particles. In Fig. 2, the Koch-fractal particle on the left is a regular particle with an AR of 1.0 and an IR of 0. The middle particle has an IR of 0 but an AR of 2.5, and the particle on the right, which is the most irregular particle, has an AR of 2.5 and an IR of 0.3. Previous studies indicate that geometries with proper irregularity have better potential to characterize the geometric features of several types of actual dust particles. To constrain the geometric variations considered, all particles considered in this study will be third-generation Koch-fractal particles with an IR of 0.3, and we will only consider different ARs. If not particularly mentioned, the two values (for IR and AR) will be used as our default particle geometry.

Third-generation Koch-fractal particles with different geometric parameters. The aspect ratios of the particles from left to right are 1.0, 2.5, and 2.5, and the irregular ratios are 0, 0, and 0.3, respectively.

Simulated scattering matrix elements for Koch-fractal particles with different refractive indices. Here, the imaginary part is fixed at
0.001

To account for irregular geometries, multiple numerical models are available for calculating the single-scattering properties of nonspherical
particles (Yang and Liou, 1996a; Mishchenko et al., 1997; Yurkin and Hoekstra, 2011; Bi et al., 2013). Following Liu et al. (2013), this study uses
a combination of the pseudospectral time domain (PSTD) method (Liu, 1997; Liu et al., 2012) and the improved geometric-optics method (IGOM; Yang and Liou, 1996b;
Yang and Liou, 1998; Bi et al., 2014) to cover the required range of dust size parameters at visible incident wavelengths. For the irregular fractal
particles, we use

The squared values of the relative differences between the simulated and measured

The scattering matrices of feldspar, quartz, loess, Lokon volcanic ash, and red clay from the AGLSD are considered references, and again this
study emphasizes the role of the RI of dust. These actual dust particles have different compositions, shapes, and size distributions, which
cause their unique optical properties. Therefore, by considering multiple kinds of dust particles, we attempt to demonstrate that the effects of the
RI generally hold. Furthermore, the influences of particle geometries can hardly be isolated or avoided during the study, so the roles of the
RI and geometry will be compared. Note that the phase functions will be presented by normalizing

Similar to Fig. 3, except that the real part is fixed at 1.6, the imaginary part is changed from 10

As discussed in Sect. 1, large variations in the RIs at visible wavelengths do exist for dust particles in different regions due to the
differences in their components. To take advantage of the numerical investigation, we consider relatively larger ranges of RIs. The
Re ranges from 1.4 to 2.2 in steps of 0.1 (nine values), and values from 10

Comparison of the scattering matrix elements of feldspar, quartz, loess, red clay, and Lokon volcanic ash particles with different refractive indices
between laboratory measurements (hallow dots) and computed results (shaded areas) at a wavelength of 633

Figure 3 illustrates the bulk scattering matrices of simulated Koch-fractal particles with different Re values. Third-generation Koch-fractal
particles with the AR of 2.5 and the IR of 0.3 are applied. Figure 3 clearly shows that different scattering matrix elements have
distinct sensitivities to the changes in the Re. The effects of Re on the normalized phase function

Figure 4 is similar to Fig. 3 but for results with different Im values. Im directly affects particle absorption, but its impact on
particle scattering properties cannot be ignored. We consider a dust sample with relatively larger sizes to better demonstrate the effect of the
Im. The bulk scattering matrix elements are obtained based on the size distribution of Lokon volcanic ash samples, which have an effective radius of
7.1

Figures 3 and 4 clearly show the impacts of the RIs on the modeling particle scattering matrix elements. With the size distribution measured simultaneously, the RI and geometry both remain variables for the numerical studies. In contrast to previous studies with a fixed RI and variable particle shapes (Merikallio et al., 2011, 2013; Ishimoto et al., 2010; Tang and Lin, 2013; Bi et al., 2010; Nousiainen and Kandler, 2015), this study tests whether the scattering matrix elements of different dust aerosols can be reproduced by models with a fixed particle shape but different RIs.

The estimated refractive index (RI) values given by the Amsterdam–Granada Light Scattering Database (AGLSD) and the RIs corresponding to our optimal numerical results.

Comparisons of the scattering matrix elements between the measured and computed results for feldspar at wavelengths of 442 and
633

Similar to Fig. 6, but for the loess sample. The optimal RI is

Figure 5 compares the simulated scattering matrices of five dust species (i.e., feldspar, quartz, loess, red clay, and Lokon volcanic ash, from left to right),
with measured values. For the modeling results, the default geometry, i.e., the third-generation Koch-fractal particle with the AR of 2.5 and the IR of 0.3, is used for all simulations. Most previous numerical and observational studies suggest that the Re values lie between 1.5
and 1.6, and the scattering matrix elements are more sensitive to the Re change when the Re values are relatively small. Therefore,
we include an additional Re of 1.55 in this study, which results in a total of 50 complex RIs (10 Re and 5 Im
values). The blue shaded regions in Fig. 5 indicate the variations in the simulated scattering matrix elements with the 50 RIs, and the red
curves correspond to the optimal cases that give the minimum

Comparison of the scattering matrix elements between the simulations and measurements for quartz samples with three different particle
ARs at two different RIs:

Figure 6 compares the computed and measured scattering matrices of feldspar at two different incident wavelengths, where blue and red represent the
results at incident wavelengths of 633 and 442

However, the results for loess and Lokon volcanic ash are slightly different. Figure 7 illustrates the results for the loess sample as an example. The optimal
results at wavelengths of 442 and 633

The importance of particle geometry in modeling dust optical properties has been well studied (Bi et al., 2010; Osborne et al., 2011; Lin et al., 2018), and Sect. 3 indicates the clear role of the RI. Thus, with particle size relatively well constrained, it becomes interesting to investigate whether the geometry or RI plays the same or different roles in modeling the dust optical properties for remote sensing and radiative forcing studies.

We first test whether different presumed RIs influence the determination of particle geometries for developing dust optical models. Figure 8
gives the measured and simulated scattering matrix elements of quartz, and the simulated results of Koch-fractal particles with three different
geometries (different ARs only) and two different RIs are illustrated. The particles with ARs of 0.25, 1.0, and 3.0 and the
RIs of

Furthermore, we directly compare the roles of the RI and geometry in reproducing dust scattering matrices. To assess the effects of the
geometry, third-generation Koch-fractal geometries with different ARs and the fixed IR of 0.3 are tested. Because the AR
shows the most significant influences on the scattering properties for our Koch-fractal particles, 10 different ARs (0.25, 0.5, 0.75, 1.0,
1.5, 2.0, 2.5, 3.0, 3.5, and 4.0) are considered in the tests. The RI is fixed at

Comparison between the simulated results of the scattering matrix elements of the Lokon volcanic ash samples with different variable parameters, including coverage with the AR as the variable (shaded blue area), coverage with the RI as the variable (shaded red area), optimal case for the two variable parameters (blue and red lines), and the measurement given by the AGLSD (black hallow dots).

Figure 9 illustrates the scattering matrices of Lokon volcanic ash and the simulated results for particles with different ARs and RIs. The blue
curves indicate the optimal case (AR

Similar to Fig. 9 but for the red clay sample.

Figure 10 is similar to Fig. 9, except for the red clay particles. The blue curves correspond to results with the AR of 0.25, and the red
curves correspond to those with the RI of

Similar to Figs. 9 and 10 but for the feldspar sample.

For the results of the feldspar particles in Fig. 11, the most notable feature is that the two optimal cases with different variables are highly
consistent; the reproductions of the matrix elements (excluding

Obviously, both RI and geometry significantly affect mineral dust optical properties; however, they do so quite differently. Furthermore, even without consideration of the influence of particle size, an accurate RI has to be determined to develop an appropriate dust geometric model, and vice versa. However, if only an optically equivalent model at a single wavelength or a limited number of wavelengths is required, our results indicate that either RI or geometry can be treated as a variable while fixing the other. Thus, instead of constructing a dust model by building different geometries (e.g., Mishchenko et al., 1997; Bi et al., 2010; Liu et al., 2012; Lin et al., 2018), it is potentially possible to consider only the results from a fixed particle geometry but with various RIs. Fixing a geometry and changing only RI may be more convenient, because the RI can be defined more quantitatively.

This study investigates the role of the RI in modeling dust scattering matrix elements. Instead of reproducing the dust scattering properties by building one or a group of nonspherical geometries at a fixed RI, which may or may not be accurate, we emphasize the sensitivities of the scattering matrix on the particle RI. By simply changing the RI during numerical modeling, it is possible to characterize the optical properties of different dust particles, even if the model geometry is fixed. As a result, it becomes possible to simplify the model developments for different mineral dust particles. To be more specific, instead of constructing and testing various geometric models, using results from particles with different RIs but a fixed geometry can also be a solution for calculating the scattering properties of dust particles at different wavelengths, which would be more flexible and computationally efficient.

As expected, if different RIs are considered for dust optical property simulations, the appropriate geometry that leads to the best agreement to the observation will change accordingly. By comparing the sensitivities of the dust scattering matrix elements, it is noticed that the reproductions of the scattering matrix elements of different dust particles respond differently to changes in the RI and geometry. With a known particle size distribution, the scattering matrix of some kinds of dust (e.g., feldspar, quartz, and loess) can be well reproduced by adjusting either the RI or the geometry with the other parameters fixed, but those of other dust particles (e.g., red clay and Lokon volcanic ash) can only be reproduced by applying an extreme and fixed geometry or RI. As a result, more efforts should also be devoted to better constraining the particle RI during the development of aerosol optical properties for remote sensing and radiative transfer applications. Finally, to better constrain either particle RI or geometry for dust optical property studies, more observations on dust microphysical and optical properties should be considered.

The measured data are provided by the Amsterdam-Granada Light Scattering Database (AGLSD) at

YH and CL designed the study, carried out the research, and performed the numerical simulation. YH, CL, BY, YY, and LB discussed the results and wrote the paper. All authors gave approval for the final version of the paper.

The authors declare that they have no conflict of interest.

We thank the Amsterdam–Granada Light Scattering Database for providing the measured data on the geometric and scattering properties of dust.

This research has been supported by the National Natural Science Foundation of China (grant no. 41571348) and the Natural Science Foundation of Jiangsu Province (grant no. BK20190093).

This paper was edited by Jianzhong Ma and reviewed by two anonymous referees.