Backscattering ratios of soot-contaminated dusts at triple LiDAR wavelengths: T-matrix results

Xiaoyun Tang; Lei Bi; Wushao Lin; Dong Liu; Kejun Zhang; Weijun Li

doi:10.1364/OE.27.000A92

1. Introduction

Dust and soot are two major components of atmospheric aerosols [1]. As one of the largest natural aerosol sources, dust aerosols originate mainly from desert and semiarid land surfaces. The mobilized dust can then be transported over short- or long-range distances, and even spread globally [2,3]. Soot particles are anthropogenic aerosols, which are produced by an incomplete combustion of fossil and biomass fuels [4,5]. Dust and soot both have quite complex morphologies that can profoundly affect their optical properties. Moreover, during the process of aerosol transport, dust particles are often found to be mixed with soot [6–8]. Previous studies have shown that mixing dust with soot aerosols can significantly change dust scattering and absorption properties [9–11], which justifies the consideration of contaminated states in both remote sensing and radiative transfer studies. However, there is a growing need to improve optical modeling of soot-contaminated dust aerosols for reducing uncertainties involved in various applications [12,13].

This study focused on modeling relevant optical properties of soot-contaminated dusts for light detection and ranging (LiDAR) applications. As the most widely applied technique, LiDAR exploits the correlation between backscattering signals and aerosol microphysical properties (particle size, shape, and composition) for aerosol typing and property retrieval. Since 2006, the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) on the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) space-based platform has been monitoring atmospheric aerosols at two LiDAR wavelengths (0.532 and 1.064 μm) [14]. Of the two channels, the 0.532 μm channel has a polarization detection capability. As a future satellite mission, the Earth Cloud Aerosol and Radiation Explorer (EarthCARE) will be equipped with a 0.355 μm high spectral resolution polarization LiDAR instrument [14], which is expected to decrease LiDAR ratio uncertainties in the retrieval algorithm. Various ground-based measurements [15–18] have shown that multi-wavelength polarization LiDARs, which collect backscattering and polarization signals at multiple wavelengths (such as 0.355, 0.532, and 1.064 μm), appear to be promising in retrieving more accurate microphysical properties of aerosols [15–21]. Therefore, in this study, theoretical simulations were performed at the three wavelengths (0.355, 0.532, and 1.064 μm), which can be used as references for either single- or multi-wavelength LiDAR studies.

Specifically, this study investigated the way in which backscattering ratios (LiDAR, depolarization, and color ratios) change from bare dust to soot-contaminated dust at the three above-mentioned wavelengths. For dust aerosols, we used a super-spheroid model for modeling non-spherical geometries. Following protocols from previous studies [5], we used the fractal model for soot aerosols. Soot-contaminated dust aerosols were then represented as a super-spheroid with adhesion of fractal clusters. The single-scattering properties of these model particles were computed by using an invariant imbedding T-matrix method [22–24]. With the accurate T-matrix results, we can then understand the way in which backscattering changes with respect to size and soot-contamination. In addition, the refractive index of soot can be artificially modified in order to investigate the main factors that cause the changes in depolarization, color, and LiDAR ratios. Furthermore, the aforementioned models allow us to examine the spherical assumption of dust in soot-contaminated dust and also examine the uncertainties involved in treating the mutual interactions between dust and soot. Finally, by discussing the modeling results and LiDAR observations, suitable soot-contaminated dust models are proposed.

The paper is divided into five sections. In Section 2, we outline quantities and basic definitions related to the modeling study. Section 3 contains the approaches to construct dust, soot, and soot-contaminated dust particle models. The calculation results and comparison with observational data are presented in Section 4. The conclusions are given in Section 5.

2. Quantities and definitions

For an ensemble of randomly oriented particles with mirror symmetry, the scattering phase matrix has the following well-known structure [25]:

[\begin{matrix} P_{11} (θ) & P_{12} (θ) & 0 & 0 \\ P_{12} (θ) & P_{22} (θ) & 0 & 0 \\ 0 & 0 & P_{33} (θ) & P_{34} (θ) \\ 0 & 0 & - P_{34} (θ) & P_{44} (θ) \end{matrix}],

in which

θ

is the scattering angle ranging from 0 to 180°, and

P_{11}

satisfies the following normalization condition:

\frac{1}{2} \int_{0}^{π} P_{11} (θ) \sin (θ) d θ = 1 .

Realistic atmospheric particles may have no mirror symmetry; however, the off-diagonal elements are found to be small (see Fig. 3 in Ref [22] as an example).

To calculate the bulk scattering properties of an ensemble of particles with different sizes, we need to consider the size distribution of these particles. The elements of the scattering phase matrix were calculated by the following equation:

P_{i j} = \frac{\int_{r_{\min}}^{r_{\max}} P_{i j} (r) C_{sca} (r) \frac{d N}{d r} d r}{\int_{r_{\min}}^{r_{\max}} C_{sca} (r) \frac{d N}{d r} d r},

in which

i, j

are subscripts of the elements,

C_{sca}

is the scattering cross section, and

d N

is the number of particles within the radius interval

(r - d r / 2, r + d r / 2)

of a small volume element. The depolarization, color, and LiDAR ratios were calculated by using the following equations:

δ = \frac{1 - \int_{r_{\min}}^{r_{\max}} P_{22, 180 °} (r) C_{sca} (r) \frac{d N}{d r} d r / \int_{r_{\min}}^{r_{\max}} P_{11, 180 °} (r) C_{sca} (r) \frac{d N}{d r} d r}{1 + \int_{r_{\min}}^{r_{\max}} P_{22, 180 °} (r) C_{sca} (r) \frac{d N}{d r} d r / \int_{r_{\min}}^{r_{\max}} P_{11, 180 °} (r) C_{sca} (r) \frac{d N}{d r} d r},

χ_{λ_{1}, λ_{2}} = \frac{\int_{r_{\min}}^{r_{\max}} P_{11, λ_{1}, 180 °} (r) C_{sca, λ_{1}} (r) \frac{d N}{d r} d r}{\int_{r_{\min}}^{r_{\max}} P_{11, λ_{2}, 180 °} (r) C_{sca, λ_{2}} (r) \frac{d N}{d r} d r},

S = \frac{\int_{r_{\min}}^{r_{\max}} C_{ext} (r) \frac{d N}{d r} d r 4 π}{\int_{r_{\min}}^{r_{\max}} P_{11, 180 °} (r) \frac{d N}{d r} d r \int_{r_{\min}}^{r_{\max}} C_{sca} (r) \frac{d N}{d r} d r},

in which

λ_{1}

and

λ_{2}

are the wavelength subscripts. The subscript 180° indicates that the scattering matrix element is at direct backscattering, and

C_{ext}

is the extinction cross section. Physically, depolarization ratio is defined as the ratio of cross-polarized and co-polarized scattered intensities at direct backscattering direction. Color ratio refers to the backscattering cross sections at two wavelengths. LiDAR ratio is extinction-to-backscatter ratio, which is sensitive to the absorptivity of aerosols. When considering the distribution of aerosol shapes (such as two shapes), by setting the elements of scattering phase matrix to

P_{i j}^{1}

and

P_{i j}^{2}

, and the scattering cross section to

C_{sca}^{1}

and

C_{sca}^{2}

, the shape-averaged bulk scattering properties can be calculated by the weighted summation of their respective scattering properties, given by:

P_{i j} = \frac{\int_{r_{\min}}^{r_{\max}} C_{sca}^{1} (r) P_{i j}^{1} (r) \frac{d N}{d r} d r + \int_{r_{\min}}^{r_{\max}} C_{sca}^{2} (r) P_{i j}^{2} (r) \frac{d N}{d r} d r}{\int_{r_{\min}}^{r_{\max}} C_{sca}^{1} (r) \frac{d N}{d r} d r + \int_{r_{\min}}^{r_{\max}} C_{sca}^{2} (r) \frac{d N}{d r} d r} .

For theoretical studies, we use the log-normal size distribution [26]:

\frac{d N}{d r} = \frac{N_{0}}{\sqrt{2 π} r \log (σ) \ln (10)} \exp {- \frac{1}{2} {[\frac{\log (r) - \log (r_{m})}{\log (σ)}]}^{2}},

in which

N_{0}

is the total number of particles per volume, r is the maximum semi-major axis of particles,

σ

is the geometric standard deviation, and

r_{m}

is the mean geometric radius. Different particle modes (fine or coarse) have different values for these parameters. By considering that the mixing of dust and soot usually occurs when dust transports over a long distance, we use the transported mode to describe dust aerosol particles. According to Hess et al. [26], the transported mode has a reduced number of large particles with a mean geometric radius 0.5 μm, and the geometric standard deviation is 2.2. Considering that

N_{0}

has no effect on the depolarization, color, and LiDAR ratios, we set the value to 1

c m^{- 3}

. Figure 1 shows the size distribution of dust under the transported mode. In numerical simulations, the maximum size parameter of dust aerosols is 50, which corresponds to the radii of 2.825, 4.234, and 8.467 μm at the wavelengths of 0.355, 0.532, and 1.064 μm, respectively.

Fig. 1 Size distribution of the transported-mode dust (the parameters shown in the figure are from Ref [26].).

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3. Particle models

3.1 Dust model

Dust aerosol particles are exclusively non-spherical and irregular [27]. It is well known that spherical assumptions lead to wrong results or significant errors in remote sensing applications [28]. Research progress on optical modeling of mineral dust can be found in Refs [29–37]. However, there has not been a widely-accepted or consistent approach based on non-spherical particles for dust optical modeling. In addition, the applicability of the dust model depends on the application perspectives, which further complicates the modeling choice. The present study follows the recent progress on using super-spheroids for computing the optical properties of non-spherical particles [38,39]. The equation of super-spheroid is given as follows [40]:

{(\frac{x}{a})}^{2 / n} + {(\frac{y}{a})}^{2 / n} + {(\frac{z}{c})}^{2 / n} = 1,

in which

a

and

c

are horizontal and vertical semi-axes, respectively, and which determine the size of super-spheroid.

n

is a roundness parameter that determines the shape of super-spheroid. Note that super-spheroid is a special case of super-ellipsoid, which is widely used in computer graphics due to its elegance in modelling a variety shapes including spheres, cylinders, cubes, octahedrons, and concave or convex geometries. The first use of super-spheroids in light scattering computation can be found in [41]. Recently, Bi et al. [38] systematically assessed the depolarization capabilities of non-spherical particles in a super-spheroidal space with a wide range of shape parameters and refractive indices. Furthermore, the super-spheroid was employed to model the optical properties of sea salt aerosols [39]. By comparing the theoretical simulations of scattering matrices and laboratory measurements in the Amsterdam-Granada Light Scattering Database [42], it was found that super-spheroids with constrained roundness parameters can reasonably reproduce the scattering matrices for a majority of dust samples by using equi-probability aspect ratios [43]. As an example, Fig. 2 compares measured scattering matrix elements and simulated results of Feldspar aerosols; the roundness parameter of super-spheroid is 2.6. In order to reduce the computational burden, we set

n = 2.6

, 2.4, 2.2, 2.0 and

a / c

to be 0.5, 0.8, 1.0, 1.5, and 2.0 for the dust models used in this paper. The shapes of super-spheroids are given in Fig. 3.

Fig. 2 Comparison between the simulated and laboratory-measured scattering matrix of Feldspar aerosols [42].

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Fig. 3 Shapes of dust model with different aspect ratios (a/c) and roundness parameters (n).

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3.2 Soot model

Soot aerosols primarily arise from an incomplete combustion of carbonaceous material. The morphologies of soot particles are most commonly in fractal clusters formed by spherical monomers. The structure of soot particles can be described by the following statistical scaling law [5]:

N_{s} = k_{0} {(\frac{R_{g}}{a})}^{D_{f}},

in which

a

and

N_{s}

are the radii of the spheres and the total number of spheres in the cluster, respectively;

k_{0}

and

D_{f}

are referred to as a fractal prefactor and fractal dimension, respectively; the radius of gyration

R_{g}

satisfies the following equation:

R_{g}^{2} = \frac{1}{N_{s}} \sum_{i = 1}^{N_{s}} r_{i}^{2},

in which

r_{i}

is the distance of the i^th sphere to the center of mass of the cluster. Following the previous studies [5,9], we used the MATLAB software to generate the soot model. The procedure starts with a sphere at the origin of coordinate system followed by attaching another sphere to the surface of the first sphere with a random contact point. Similarly, the i^th sphere can be attached to available spheres through a random procedure. Note that the sphere should be discarded if it overlaps with the other spheres. In addition, each newly formed cluster should satisfy Eq. (10). Otherwise, the sphere should be discarded and a new sphere will be generated. Due to numerical errors, Eq. (10) cannot be strictly satisfied. In practical computations, we used the following relationship:

| N_{s} - k_{0} {(\frac{R_{g}}{a})}^{D_{f}} | < ε,

in which

ε

is a predefined small number in order to control the numerical procedure. The computational time for generating a soot cluster depends on the value of

ε

. The smaller the parameter

ε

is, the more computing time is required. For simplicity, we set

ε

equal to 0.01 in this paper. Figure 4 shows examples of soot clusters formed by a hundred spheres with different values of

k_{0}

and

D_{f}

. Obviously, the cluster becomes more compact as

D_{f}

increases. If

D_{f}

is a constant value, soot clusters become more compact as

k_{0}

increases. Studies [5,44,45] have shown that the fresh soot particles usually have chain-like structures such as Figs. 4(a)–4(d), and the aged soot particles usually have compact structures such as Figs. 4(e)–4(h). The scattering properties of fractal fresh soot and compact aged soot were extensively discussed by Liu and Mishchenko [46]. In this study, we choose representative soot parameters to study the optical properties of soot-contaminated dust.

Fig. 4 Soot clusters formed by 100 spheres with different values of $k_{0}$ and $D_{f}$ . For (a) –(f), $k_{0}$ = 1.7 and $D_{f}$ = 1.3, 1.5, 1.7, 1.9, 2.1, 2.3, respectively; for (g) and (h), $k_{0}$ = 0.7 and 1.2, respectively, and $D_{f}$ = 3.

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3.3 Mixed model of dust and soot

A model for mixing dust and soot is required in order to investigate the effect of soot contamination on the optical backscattering properties of dust. For a volume element of soot-contaminated dusts, both external mixtures (independent scattering of dust and soot) and soot-adhesion aggregates could exist. For soot-adhesion scenarios, we used the MATLAB software to build a dust-soot adhesion model based on dust and soot models described in Sections 3.1 and 3.2. The only required step is to translate the position of soot particle so that the soot particle is attached to the dust surface. If more than one soot cluster is considered to attach to the dust, the above procedure will be repeated, provided that these soot clusters do not overlap with each other. Another condition to generate the model is to guarantee that the soot particle is entirely outside of the super-spheroid.

For numerical computations, consider the ageing process of soot particles [44,45], we set values of $k_{0}$ and $D_{f}$ to 0.7 and 3.0. The number of spherical monomers of soot clusters $N_{s}$ is assumed to be 16. Soot models with different parameters were widely discussed by other researchers [47–49]. We choose one specific set of parameters for the soot model to investigate the changes of backscattering properties of dust after mixing with soot. We divided fractal soot-contaminated dust (FSD) into three groups, consisting of FSD1–3. The number of soot clusters $N$ is assumed to be (5, 9, 12, 10, 10), (10, 18, 25, 21, 20) and (20, 36, 50, 42, 40) corresponding to the five aspect ratios for FSD1–3, respectively. The ratio of the sphere’s and the maximum dust’s radii was set to be 40 according to the software package OPAC (Optical Properties of Aerosol and Clouds) [26]. In addition, we compared the scattering properties of fractal soot-contaminated and spherical soot-contaminated dust (SSD). Corresponding to FSD1–3, three groups of SSD (namely SSD1–3) are defined. For comparison, the mass and number of spherical soot particles are identical to those of fractal soot clusters. The examples of dust particle contaminated by soot particles are given in Fig. 5. Note that if the roundness parameter is not mentioned in this study, all of the roundness parameters of PD, FSD, and SSD are 2.6.

Fig. 5 Models of pure dust (PD), fractal-soot-contaminated dust (FSD) and spherical- soot-contaminated dust (SSD) with different aspect ratios. The roundness parameter is 2.6 for all the aspect ratios. Models with the roundness parameter n = 2.0, 2.2, and 2.4 are not shown.

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The complex refractive indices of dust and soot at three wavelengths (0.355, 0.532, and 1.064 μm) are (1.53 + 0.008i, 1.53 + 0.008i, 1.523 + 0.008i) and (1.752 + 0.4671i, 1.751 + 0.4405i, 1.752 + 0.4402i), respectively [50–52]. Considering that the refractive indices are similar at the three wavelengths for both dust and soot, we only chose the refractive indices 1.53 + 0.008i (dust) and 1.752 + 0.4671i (soot) for calculations in this study. Thus, the results of one size parameter can be used to obtain the optical properties of different sizes at the three wavelengths.

4. Results and discussion

4.1 Soot contamination effect

We first investigated how the depolarization, color, and LiDAR ratios change from pure dust to soot-contaminated dust. The dust models we used are illustrated in Fig. 3. The scattering properties of pure dust (PD) were averaged by the five dust models with different aspect ratios. Similarly, the scattering properties of fractal soot-contaminated dust (FSD1–3) were averaged by considering five soot-adhesion models shown in Fig. 5.

Figure 6 shows the depolarization ratios of PD and FSD as functions of the mean geometric radius. We can see that the depolarization ratios of PD and FSD both increase with increasing mean geometric radius (<1μm). This feature also explains the fact that the depolarization ratio generally decreases as the wavelength increases because the size parameter for larger wavelength becomes smaller. Of more practical interest in dust-transport studies, the effect of soot contamination results in the decrease of the depolarization ratio of dust over a wide range of radii. Meanwhile, with the increase in soot cluster numbers, the depolarization ratio was obviously reduced.

Fig. 6 Depolarization ratios of PD (black lines), FSD1 (green lines), FSD2 (blue lines), and FSD3 (red lines).

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Figure 7 shows the color ratios of PD and FSD as functions of the mean geometric radius. The color ratios of both PD and FSD increase with increasing mean geometric radius. The soot contamination results in the decrease of the color ratio of dust as the mean geometric radius is larger than a critical value. However, the adhesion of soot results in the increase of the color ratio of dust when the mean geometric radius is quite small. The lager the number of soot clusters is, the more obviously the color ratio changes.

Fig. 7 Color ratios of PD (black lines), FSD1 (green lines), FSD2 (blue lines), and FSD3 (red lines).

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Figure 8 shows the LiDAR ratios of PD and FSD as functions of the mean geometric radius. We can see that the LiDAR ratios of PD and FSD both decrease as the mean geometric radius increases from 0.1 to 1.0μm at 0.355μm wavelength while increase first and then decrease at 0.532μm and 1.064μm wavelengths. The soot-contamination results in the increase of the LiDAR ratio of dust. Meanwhile, the LiDAR ratio apparently increases with increasing soot cluster numbers.

Fig. 8 LiDAR ratios of PD (black lines), FSD1 (green lines), FSD2 (blue lines), and FSD3 (red lines).

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From Figs. 6–8, it can be seen that the depolarization and LiDAR ratios are more sensitive to soot contamination than color ratios.

4.2 “Causes” of the change–a sensitivity study

With the adhesion of soot clusters, there are two possible reasons causing the differences found in Figs. 6–8, namely, the morphology change and the absorptivity of soot. Both factors are essentially bundled together to affect the optical properties. However, to empirically understand which factor is critical to the change of backscattering ratios, we set the imaginary component of soot to zero for comparison studies. Figure 9 shows the depolarization ratios of pure dust and different type fractal soot-contaminated dust as functions of the mean geometric radius. Solid lines represent pure dust, and dashed and dotted lines represent fractal soot-contaminated dust mixed with absorptive soot and “non-absorptive” soot, respectively. As can be seen from Fig. 9, the differences of depolarization ratios between the two types of fractal soot-contaminated dust are relatively small, indicating that the change of dust morphology after mixing with soot is “the main reason” for the decrease in depolarization ratio. Meanwhile, the soot-contaminated dust absorptivity slightly enlarged the values of depolarization ratios. However, as can be seen from Fig. 10, the color ratios of soot-contaminated dust mixed with soot are much larger than those mixed with “non-absorptive” soot. Thus the change of dust morphology after mixing with soot is the main reason for the decrease in color ratio, but the soot absorptivity has the opposite impact on the values of the color ratio. As can be seen from Fig. 11, the LiDAR ratios of soot-contaminated dust mixed with soot are much larger than those mixed with “non-absorptive” soot. Therefore, the change in dust absorptivity after mixing with soot could be the main reason for the increase in the LiDAR ratio. We have also assumed the refractive index of soot to be the same as that of dust for comparison studies. The results are not shown here, because they are similar to those in Figs. 9–11.

Fig. 9 Depolarization ratios of dust (solid line) and soot-contaminated dust by using realistic soot refractive index (dashed lines) and “non-absorptive” soot refractive index (dotted lines).

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Fig. 10 Color ratios of dust (solid line) and soot-contaminated dust using a realistic soot refractive index (dashed lines) and “non-absorptive” soot refractive index (dotted lines).

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Fig. 11 LiDAR ratios of dust (solid line) and soot-contaminated dust by using realistic soot refractive index (dashed lines) and “non-absorptive” soot refractive index (dotted lines).

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4.3 Different soot models

Considering that spherical soot model is sometimes used to calculate the scattering properties of soot-contaminated dust aerosols [11,53], we compared the results of dust with fractal soot and spherical soot adhesion. Figures 12–14 show the results from the comparison of depolarization, color, and LiDAR ratios between FSD and SSD. Figure 12 shows that the depolarization ratios of FSD and SSD have no obvious differences. However, as can be seen from Fig. 13, the color ratios of SSD are much larger than those of FSD. As the soot number increases, the differences among FSD and SSD became more obvious. Figure 14 shows that the LiDAR ratios of FSD and SSD also have no obvious differences, except for the case with a large soot number.

Fig. 12 Depolarization ratios of fractal soot-contaminated dust (solid line) and spherical soot-contaminated dust (dashed lines) at 0.532 μm.

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Fig. 13 Color ratios of fractal soot-contaminated dust (solid line) and spherical soot-contaminated dust (dashed lines) at 0.532 and 1.064 μm.

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Fig. 14 LiDAR ratios of fractal soot-contaminated dust (solid line) and spherical soot-contaminated dust (dashed lines) at 0.532 μm.

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4.4 Different roundness parameters

We further investigated the depolarization, color, and LiDAR ratio changes of dust and soot-contaminated dust with different roundness parameters. In order to show the changes clearly, we only chose the values of PD and FSD2 with a mean geometric radius of 0.5 μm under the roundness parameters n = 2.0, 2.2, 2.4, and 2.6. The upper panel of Fig. 15 shows that soot contamination results in a decrease in the dust depolarization ratio for all roundness parameters. In addition, the depolarization ratios of PD and FSD2 decrease as the roundness parameter increases. The color ratios are shown in the middle panel of Fig. 15, which shows that the soot contamination results in a color ratio decrease when n = 2.4 and 2.6, but the color ratios increase when n = 2.0 and 2.2. In general, the color ratio is relatively insensitive to the roundness parameter. As shown in the bottom panel of Fig. 15, soot contamination is found to increase the LiDAR ratios at all roundness parameters. Contrary to the depolarization ratios, the LiDAR ratios of PD and FSD2 both increase with respect to the roundness parameter. Therefore, the color ratio does not seem to be a clear indicator of soot-contamination compared to the LiDAR and depolarization ratios.

Fig. 15 Depolarization, color, and LiDAR ratios of PD (solid line) and FSD2 (dashed lines) with a mean geometric radius of 0.5 μm under the roundness parameters n = 2.0, 2.2, 2.4, and 2.6.

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4.5 Different mixing approaches

Finally, we examined the differences in scattering properties of polluted dust with different mixing approaches. For simplicity, the non-contact mixing approach (the mutual interactions between dust and soot are neglected) is often used to calculate the scattering properties of soot-contaminated dust aerosols. Specifically, the optical properties of dust and soot are computed separately and then averaged by neglecting the interaction between dust and soot. However, the uncertainties of such treatment remain unclear.

Figures 16–18 show the depolarization, color, and LiDAR ratios of PD and mixtures of PD with different numbers of soot clusters by using the non-contact mixing approach. Computational parameters of soot are the same as those of the soot clusters in FSD. The calculation of soot optical properties was performed with the multiple sphere T-matrix (MSTM) program [54]. The changes in trends of all backscattering ratios with soot contamination are similar to those in the soot-adhesion models. However, the effectiveness of the two mixing approaches in causing the change of backscattering ratios is different. Figure 19 shows comparison of the depolarization ratios of soot-contaminated dust by adopting the two mixing approaches. It was found that the difference is negligible only when the mean geometric radius is below a critical value. Once the mean geometric radius is larger than the critical value, the non-contact mixing approach will result in lower depolarization ratio values. Figure 20 shows the color ratios of soot-contaminated dust with the two mixing approaches. Differences between the results are generally small and more obvious at small sizes. Figure 21 shows the LiDAR ratios of soot-contaminated dust with the two mixing approaches. It was found that the results of the non-contact mixing approach appear to be much smaller than those of the soot-adhesion mixing approach.

Fig. 16 Depolarization ratios of PD (black lines) and mixtures of PD with 50 (green lines), 100 (blue lines) and 150 (red lines) soot clusters.

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Fig. 17 Color ratios of PD (black lines) and mixtures of PD with 50 (green lines), 100 (blue lines) and 150 (red lines) soot clusters.

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Fig. 18 LiDAR ratios of PD (black lines) and mixtures of PD with 50 (green lines), 100 (blue lines) and 150 (red lines) soot clusters.

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Fig. 19 Depolarization ratios of soot-contaminated dust with different mixing approaches. Solid lines indicate that dust mixed with soot using the non-contact mixing approach. Dashed lines indicate that dust mixed with soot using the contact mixing approach.

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Fig. 20 Color ratios of soot-contaminated dust with different mixing approaches. Solid lines indicate that dust mixed with soot using the non-contact mixing approach. Dashed lines indicate that dust mixed with soot using the contact mixing approach.

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Fig. 21 LiDAR ratios of soot-contaminated dust with different mixing approaches. Solid lines indicate that dust mixed with soot using the non-contact mixing approach. Dashed lines indicate that dust mixed with soot using the contact mixing approach.

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4.6 Comparison with observations

LiDAR observations of dust depolarization at dual or triple wavelengths have been reported in Refs [55,56]. Burton et al. [55] presented two observational cases of transported dust aerosols at different wavelengths (0.355, 0.532, and 1.064 μm) by using the NASA Langley airborne high-spectral-resolution lidar (HSRL) instruments. Haarig et al. [56] reported triple-wavelength polarization LiDAR measurements of Saharan dust layers at Barbados. These results are shown in Table 1.

Table 1. The Particle Depolarization Ratios of Dust from Literature

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In addition to LiDAR observational studies, laboratory measurements concerning the 9depolarization ratios for dust aerosol particles from different regions were conducted by Järvinen et al. [57]. Although the laboratory measurements are performed at the near-backscattering angle (178°), the values should be close to direct backscattering if the particle sizes are not large. They found the depolarization ratios of fine-mode particles increased almost linearly with particle median diameter, while the coarse-mode particle depolarization ratios always remained constant. Based on these laboratory measurements, Mamouri and Ansmann [58] estimated the particle linear depolarization ratios for fine dust to be around 0.21 ± 0.02, 0.16 ± 0.02, and 0.09 ± 0.03 at the wavelengths of 0.355, 0.532, and 1.064 μm, respectively. The values also agree with the laboratory measurements of Sakai et al. [59], who found fine-mode dust particle depolarization ratios of 0.14–0.17 ± 0.03 at 0.532 μm.

A controlled laboratory experiment was performed by Miffre et al. [60] to accurately evaluate depolarization ratio from mineral dust particles in the exact backward scattering direction (180 ± 0.2°). They carried out the experiments of Arizona Test Dust particles at the wavelengths of 0.355 and 0.532 μm. Two aerosol samples with different size distributions were studied. The measured depolarization ratios at the two wavelengths are 0.375 ± 0.015 (0.350 ± 0.015) and 0.355 ± 0.015 (0.305 ± 0.015), respectively (the data in parenthesis are for different size distributions).

Concurrent measurements of the LiDAR ratio of dust at the three wavelengths of 0.355, 0.532, and 1.064 μm were reported by Tesche et al. [61]. Specifically, three ground-based Raman LiDARs and an airborne HSRL were operated during SAMUM 2006 in southern Morocco. It was found that the spectral dependence of the LiDAR ratio was weak [61]. The LiDAR ratios of dust at the two wavelengths of 0.355 and 0.532 μm were measured by many other researchers, and the values are shown in Table 2 [62–65].

Table 2. The LiDAR Ratios of Dust from Literature

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Here we choose simulation results of dust particles with mean geometric radii of 0.8 and 0.2 μm to compare with LiDAR and laboratory measurement results. The roundness parameter of super-spheroids is 2.6. Figure 22 shows that the simulation results of depolarization ratios agree well with the LiDAR observations at 0.532 and 1.064 μm. The depolarization ratio was found to have a slight decrease as the wavelength increased from 0.532 to 1.064 μm. However, large difference between simulation and LiDAR observation results was found at 0.355 μm, which is difficult to be explained based on current modeling studies. Different from LiDAR observations, the laboratory measurement results agree very well with simulation results. Figure 22 also shows the agreement between simulations and observations of the LiDAR ratio. The LiDAR ratio shows minimal changes as the wavelength increases.

Fig. 22 Comparison between observation and simulation results on the depolarization and LiDAR ratios of dust. Note that the horizontal coordinates of observations at 0.355 and 0.532 μm are slightly shifted.

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In order to examine possible factors causing the difference between the simulations and LiDAR observations at 0.355 μm, we also calculated the depolarization and LiDAR ratios of dust under the refractive indices of 1.53 + 0.012i and 1.53 + 0.016i at 0.355 μm. The values $(δ, S)$ of dust depolarization and LiDAR ratios with a mean geometric radius 0.8 μm are (0.32, 0.29) and (68.45, 89.2) at the two refractive indices. We can see that the depolarization ratio decreases slowly with an increase in the imaginary part of the refractive index, but the LiDAR ratio increases significantly. This phenomenon is inconsistent with observations. Similar findings were reported by Gasteiger et al. [66]. It was found that using the mixed model of absorbing and non-absorbing dust particles can yield good results that match observation results, and they think that no agreement with LiDAR observations is possible for models that only consider the wavelength dependence of the imaginary part of refractive index but not the inhomogeneity of the absorption properties [66]. Lindqvist et al. [67] simulated light scattering by single, inhomogeneous mineral dust particles that were simulated based on shapes and compositions derived directly from measurements of real dust particles and found the depolarization ratio is sensitive to inhomogeneity. Because super-spheroids are assumed to be homogeneous, the impacts of inhomogeneity cannot be straightforwardly examined.

Now we turn to LiDAR observations of soot-contaminated dust. The particle depolarization and LiDAR ratios of Saharan dust and mixtures of biomass-burning aerosols from southern West Africa and Saharan dust was observed by Groß et al. [62] during the SAMUM2 at Cape Verde between January 22 and February 9, 2008. Figure 23 shows theoretical simulations and the observations of depolarization and LiDAR ratios of Saharan dust in addition to the mixture of Saharan dust and biomass-burning smoke. We chose the simulation results of the depolarization and LiDAR ratios with the mean geometric radii ranging from 0.2 to 0.8 μm. The roundness parameter of super-spheroids is 2.6. Simulation results of the non-contact mixing scenario are also shown as dashed lines. It can be seen that both mixing approaches show a decrease in the depolarization ratio and increase in the LiDAR ratio of dust. Although the change in trends were the same as the observations, the values of the depolarization and LiDAR ratios of soot-contaminated dust under a non-contact mixing assumption were much closer to the observations than the soot-adhesion mixing scenario.

Fig. 23 Depolarization and LiDAR ratios of Saharan dust (yellow spots with error bar) and mixtures of Saharan dust and biomass-burning smoke (brown spots with error bar) at 0.355 μm (the upper panel) and 0.532 μm (the bottom panel). The solid lines and dash lines show the simulation results.

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As reported in Bohlmann et al. [68], the optical properties of Saharan dust partly mixed with biomass-burning smoke were measured near the Cabo Verde islands. Five layers of dust soot mixtures were examined. For one layer, they found that the mean LiDAR ratio is 63 ± 8 at 0.355 μm and 57 ± 7 sr at 0.532 μm, and the particle depolarization ratio is 24 ± 1% at 0.355 μm and 19 ± 1% at 0.532 μm. The LiDAR ratio can increase to 68 sr at 0.532 μm and 88 sr at 0.355 μm, and the depolarization ratio decreases to a lower range of 8-16% at 0.532 μm and 5-13% at 0.355 μm for different layers [68]. The change of the backscattering ratios of soot-contaminated dust is closely related to the relative fraction of dust and soot, which is similar to our simulation results.

Note that the exact comparison between simulations and observations might have no scientific meaning because we have no precision information regarding the aerosol shape, composition, and size distribution. For more relevant meaning, a reasonable dust and soot-contaminated dust model should explain the optical property changes and predict a reasonable range of relevant backscattering quantities. For remote sensing applications, the model should have the capability to represent the underlying physical parameters associated with nonsphericity and mixing state, and such physical parameters can be flexibly constrained through observations. From this regard, the proposed model in this study is highly promising.

5. Conclusions

We studied the effect of soot contamination on the optical backscattering properties of dust at three LiDAR wavelengths (0.355, 0.532, and 1.064 μm). We focused on transported dust, which has a much smaller mean radius (<1.0μm). Dust and soot particles were represented as super-spheroids and fractal clusters, respectively. The effectiveness of the super-spheroidal dust model with constrained roundness parameters has been tested by comparing theoretical simulations with laboratory measurements. The particle depolarization, color, and LiDAR ratios of the models were computed at the triple wavelengths by using the invariant imbedding T-matrix method. For the roundness parameter n = 2.6, the results show that the depolarization and color ratios of dust decrease after mixing with soot over a wide range of particle mean radii, and the LiDAR ratio increases after mixing with soot. We also found that the change in dust morphology after mixing with soot is the main reason for the decrease in the depolarization and color ratio. The change in dust absorptivity after mixing with soot is the main reason for the increase in the LiDAR ratio. We also investigated the influence of dust’s roundness parameter on the depolarization, color, and LiDAR ratios. These findings provide a reasonable explanation for the dust optical scattering property changes in the process of transporting. Additionally, we studied the influence of different dust and soot models and different mixing approaches on the optical scattering properties of polluted dust mixed with soot. It is found that two soot-contaminated models (fractal soot and spherical soot attachments) show relatively small differences. Large differences occur only when the soot number is particularly large. Note that the present study employs what we believe to be reasonable model parameters to investigate the changing rules of the backscattering ratios. The parameters are not exhaustive. In particular, the maximum size parameter is limited. Furthermore, it might be improper to directly compare the absolute values of depolarization, color, and LiDAR ratios with the LiDAR observations. However, the order of magnitude and the change in rules of these dust ratios with the wavelength, size, and soot contamination appear to be highly suggestive in LiDAR aerosol applications.

Funding

National Key Research and Development Program of China (2016YFC0200700); National Natural Science Foundation of China (41675025); Zhejiang University K. P. Chao’s High Technology Development Foundation; and the Fundamental Research Funds for the Central Universities.

Acknowledgments

We acknowledge Mackowski and Mishchenko for using the MSTM program in Figs. 19-21, and Ms. Rui Liu from the Training Center of Atmospheric Sciences of Zhejiang University for her effort related to managing computing resources. A portion of the computations was performed on the National Supercomputer Center in Guangzhou (NSCC-GZ) and the cluster at State Key Lab of CAD&CG at Zhejiang University.

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Location	0.355 μm	0.532 μm	1.064 μm	Reference
Midwest USA	0.246 ± 0.018	0.304 ± 0.005	0.270 ± 0.005	Burton et al. (2015) [55]
Caribbean	-	0.327 ± 0.018	0.278 ± 0.012	Burton et al. (2015) [55]
Barbados	0.252 ± 0.03	0.28 ± 0.02	0.225 ± 0.02	Haarig et al. (2017) [56]

Location	0.355 μm	0.532 μm	1.064 μm	Reference
Ouarzazate	52.9 ± 7	54.8 ± 6.7	54.9 ± 12.7	Tesche et al. (2009) [61]
Cape Verde	58 ± 7	62 ± 5	-	Groß et al. (2011) [62]
Munich	58 ± 13	56 ± 10	-	Wiegner et al. (2011) [63]
Gwangju	56 ± 10	51 ± 6	-	Noh et al. (2008) [64]
Mbour	54 ± 8	53 ± 8	-	Veselovskii et al. (2016) [65]

Location	0.355 μm	0.532 μm	1.064 μm	Reference
Midwest USA	0.246 ± 0.018	0.304 ± 0.005	0.270 ± 0.005	Burton et al. (2015) [55]
Caribbean	-	0.327 ± 0.018	0.278 ± 0.012	Burton et al. (2015) [55]
Barbados	0.252 ± 0.03	0.28 ± 0.02	0.225 ± 0.02	Haarig et al. (2017) [56]

Location	0.355 μm	0.532 μm	1.064 μm	Reference
Ouarzazate	52.9 ± 7	54.8 ± 6.7	54.9 ± 12.7	Tesche et al. (2009) [61]
Cape Verde	58 ± 7	62 ± 5	-	Groß et al. (2011) [62]
Munich	58 ± 13	56 ± 10	-	Wiegner et al. (2011) [63]
Gwangju	56 ± 10	51 ± 6	-	Noh et al. (2008) [64]
Mbour	54 ± 8	53 ± 8	-	Veselovskii et al. (2016) [65]

Backscattering ratios of soot-contaminated dusts at triple LiDAR wavelengths: T-matrix results

Abstract

1. Introduction

2. Quantities and definitions

3. Particle models

3.1 Dust model

3.2 Soot model

3.3 Mixed model of dust and soot

4. Results and discussion

4.1 Soot contamination effect

4.2 “Causes” of the change–a sensitivity study

4.3 Different soot models

4.4 Different roundness parameters

4.5 Different mixing approaches

4.6 Comparison with observations

5. Conclusions

Funding

Acknowledgments

References

Cited By

Figures (23)

Tables (2)

Equations (12)

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