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Abstract
Polarization measurements have been widely used to detect aerosol properties by remote sensing in recent decades. To better understand the polarization characteristics of aerosols by lidar, the numerically exact T-matrix method was used to simulate the depolarization ratio (DR) of dust and smoke aerosols at typical laser wavelengths in this study. The results show that the DRs of dust and smoke aerosols have obviously different spectral dependences. Moreover, the ratio of DRs at two wavelengths has an obvious linear relationship with the microphysical properties of aerosols, including aspect ratio, effective radius and complex refractive index. At short wavelengths, we can use it to invert the absorption characteristics of particles, further improving the detection ability of lidar. Comparing the simulation results of different channels, DR, (color ratio) CR and (lidar ratio) LR have a good logarithmic fitting relationship at 532 nm and 1064 nm, which helps to classify the aerosol types. On this basis, a new inversion algorithm, “1β+1α+2δ”, was presented. By this algorithm, the backscattering coefficient (β), extinction coefficient (α), DR (δ) at 532 nm and 1064 nm can be used to expand the range of inversion and compare lidar data with different configurations to obtain more extensive optical characteristics of aerosols. Our study enhances the application of laser remote sensing in aerosol observations more accurately.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Atmospheric aerosols play a key role in the Earth’s climate system and directly affect the radiation budget by scattering and absorbing solar and terrestrial radiation or indirectly affect it by forming cloud condensation nuclei or ice nuclei [1–5]. In addition, aerosols can also affect the human respiratory system, leading to respiratory diseases and even cancer [6]. Therefore, the detection of aerosol radiation characteristics is crucial to the study of climate change and environmental governance. The radiation characteristics of aerosols depend on their morphological structure and chemical components, while in reality, aerosol particles have irregular morphological structures and complex chemical components [7,8]. For example, the shape of dust aerosols is often cylindrical, ellipsoidal, etc., and sulfate and other substances are often attached, which makes it difficult to accurately observe their radiation characteristics [9,10]. Therefore, confirmation of the aerosol type is very useful for accurate calculation of the aerosol radiative forcing and its related impacts.
Polarization lidar is an important tool for remote sensing that can provide vertically resolved information on aerosol optical properties [11–14]. The backscattering information received by lidar, such as the depolarization ratio (DR), lidar ratio (LR), and color ratio (CR), can be used to classify aerosols and retrieve their microphysical properties [15,16]. DR is defined by the ratio of perpendicular to parallel backscattering intensity with respect to the polarization plane of the emitted laser, and it is an important parameter to measure the particles’ nonsphericity [17]. The microphysical properties of aerosols, including particle size distribution and complex refractive index, also have a great impact on DR [18]. Thus, DR is used to classify aerosol type and to invert the effective radius and mass concentration of particles [19,20]. In particular, Huang et al. [21] found that the spectral dependence of DR has a good fitting relationship with its absorption coefficient.
At present, the T-matrix method is one of the most widely used methods to simulate aerosol optical properties with high accuracy [22]. Mishchenko et al. [23] analyzed measurements of the backscattering linear depolarization ratio (LDR) for a plume of aged smoke at lidar wavelengths ranging from 355 to 1064 nm by using the numerically exact (superposition) T-matrix method. Bi et al. [24] investigated the optical properties of sea salt aerosols using invariant imbedding T-matrix simulations and proved the dependence of the LDR of sea salt aerosols on relative humidity. Information on LDR at laser wavelengths for dust and smoke is important for accurately detecting aerosol properties by lidar. Thus, in this study, the T-matrix method was used to simulate the spectral dependence of aerosols and further investigate the relationship between DR and other aerosol properties, aiming to optimize the polarization channels of aerosol lidar. In addition, the widely used ellipsoidal model was mainly used to simulate the morphological structure of dust and smoke [25,26].
The main purpose of this study is to further improve the detection ability of polarized lidar by providing important information for lidar development and retrieval methods. Simulating the relationship between aerosol optical properties and microphysical properties provides an important theoretical basis. In Section 2, the optical and microphysical properties of aerosols used in this simulation process are briefly introduced. In Section 3, the spectral dependence of DR for dust and smoke is verified. Then, the correlation between optical parameters and microphysical properties was investigated. Finally, a new recognition algorithm is proposed. Section 4 summarizes this study.
2. Method
2.1 Definition of optical parameters
The depolarization ratio (DR or δ) of aerosols is related not only to their shape but also to the wavelength of incident light, spatial orientation, size distribution, complex refractive index and other factors [27,28]. It is assumed in this work that aerosol particles are homogeneous and randomly oriented, the incident light is horizontally polarized, and the size distribution is lognormal. Only the effects of the effective radius (Reff), complex refractive index (M) and aspect ratio (AR) were considered.
The incident and scattered light of particles can be expressed by Stokes parameters as (I0, Q0, U0, V0)T and (I, Q, U, V)T, where T means transpose of given array. When the incident light is horizontally polarized, (I0, Q0, U0, V0)T=(1, 1, 0, 0)T [29]. For the Stokes parameters, $\mathrm{I}=\mathrm{I}_{/ /}+\mathrm{I}_{\perp}$ and $\mathrm{Q}=\mathrm{I}_{/ /}-\mathrm{I}_{\perp}$, where $\mathrm{I}_{/ /}$ and I⊥ denote the intensity of scattered light parallel and vertical to the scattering plane, respectively. I⊥ and $\mathrm{I}_{/ /}$ of the scattered light in the backscattering direction are expressed as I⊥(π) and I∥(π), so δ can be expressed as:
The elements of the normalized 4 × 4 Stokes scattering matrix have the following well-known structure [30]:
Only one parameter of DR has difficulty in accurately classifying aerosol type, so other parameters need to be used. Using the T-matrix method, we can not only obtain the DR of particles but also obtain the CR and LR. CR reflects the size of particles, and LR reflects the direction characteristics of light scattering of particles [31]. There is a certain correlation between different optical parameters, and we can classify aerosol types according to this conclusion [32,33]. For an individual particle, CR and LR can be calculated by the following equation [34]:
2.2 Microphysical parameters
2.2.1 Wavelength (λ)
The four most commonly used channels are selected, which are 266 nm, 355 nm, 532 nm and 1064 nm. At present, the polarization channels are mostly 355 nm and 532 nm, while the polarization channels of 1064 nm are seldom used due to the high excitation energy. However, observations show that DR data at the 1064 nm channel can further identify aerosol types and improve inversion accuracy [35].
2.2.2 Shape
The spectral dependence of simple ellipsoidal particles is modeled to represent that of nonspherical aerosols that is characterized by the aspect ratio (AR). AR is defined as the ratio of the major axis to the minor axis of the ellipsoid. When AR = 1, the particle is a regular sphere. The AR of dust is the range of 1.20-1.60 [36–40], and the step length is 0.04. The shape and structure of smoke are more complex than those of dust. At present, the fractal model was used to simulate smoke in most studies [41]. However, it is convenient to compare the simulation results of smoke and dust by using the ellipsoidal model. The simulation results of Gialitaki et al. [42] show that the near-spherical smoke model is still consistent with the observation results. The AR of smoke is the range of 0.80-1.20 [23,42,43], and the step length is 0.04.
2.2.3 Effective radius (Reff)
Due to the calculation accuracy of the T-matrix method, the size of particles is limited to a certain extent. Dust Reff ranges from 0.2 to 2.4 μm and smoke Reff ranges from 0.1-1.0 μm [23,37,41–43].
2.2.4 Complex refractive index (M)
The complex refractive index, M = MR + MI, reflects the chemical composition of aerosols, where MR is the real part of M and MI is the imaginary part of M. Since MR has slight variations with the wavelength [44], in this study, the impact of MR is not considered, and the MR of dust and smoke are set as constant values of 1.53 and 1.45, respectively. The MI of dust is set as 0.002-0.020, and the MI of smoke is set as 0.005-0.050 [39,40,42] (all parameters are shown in Table 1).
3. Results and discussion
3.1 Spectral dependence of DR
Burdon et al. [45] analyzed DR data from the NASA Langley airborne High Spectral Resolution Lidar-2 (HSRL-2) and noted that there is not a single consistent spectral dependence of DR. Zo et al. [46] found that the spectral variation in DR differed according to the aerosol type. To verify these conclusions, we simulated the effects of AR and Reff on the DR spectra of dust and smoke under different MIs in this section. It is worth mentioning that the simulation range of dust and smoke MI was not consistent. First, the selection of MI refers to the absorption characteristics in actual observations. Second, the impact of aerosol mixing was not considered in this study.
The simulated dust DR in Fig. 1 ranges from 0.064 to 0.391, which is basically consistent with the long-term observations of the Asian dust DR [47,48]. The DR spectrum shows a trend of first increasing and then decreasing, which is also consistent with the observed results of Burdon et al. [45] Fig. 1(a)–1(c) shows the impact of AR on dust. It is not difficult to find that AR and DR do not always show a monotonic increasing relationship. For example, in Fig. 1(c), even DR decreases with increasing AR at 266 nm and 355 nm. In fact, there is a large error in identifying aerosol types only by DR at a single wavelength, which is one of the reasons why this study is devoted to discussing depolarization ratio spectra. Figure 1(d)–1(f) shows the effect of Reff. The influence of Reff varies greatly at different wavelengths. Dust DR is not sensitive to changes in Reff at 355 nm and 1064 nm. Only at 532 nm, dust DR and Reff have obvious positive correlation. The results show that for the detection of different types of aerosols, the longer or shorter wavelength is not the better. Finally, we found that MI mainly affects DR at short wavelengths.
Fig. 1. The effects of microphysical parameters on the depolarization ratio of dust aerosols at 0.266 μm, 0.355 μm, 0.532 μm, and 1.064 μm; (a)-(c) aspect ratio; (d)-(f) effective radius.
Compared with dust, smoke DR shows great differences in range and spectral properties. The range of smoke DR is 0.001-0.773, and the spectrum has a decreasing trend. The reasons for such a huge difference are not only the morphological structure but also the chemical composition, that is, the complex refractive index. It can be seen from Fig. 2(a)–2(c) that the greater the nonsphericity is, the greater the smoke DR. This is also in line with the simulated results from Bi et al. [49], that is, the DR of the near-sphere model basically shows a monotonic increasing trend with nonsphericity. When MI = 0.005 or 0.02, There is no obvious change in smoke DR with the same Reff. At different wavelengths, Reff is positively correlated with smoke DR. But when MI = 0.05, smoke DR of large Reff has changed significantly. Figure 2(f) shows the great impact of MI on the DR spectrum. Smoke DR drops to approximately 0.162-0.268 at the short band, and the spectrum also changes greatly, showing a trend of first increasing and then decreasing, which is consistent with Zo et al. [46]
3.2 Ratio of DRs
The following conclusions can be drawn from the simulated results in Section 3.1: the DRs of aerosols have different spectral dependences and are affected by physical properties such as Reff, AR and MI. This conclusion shows that the spectral properties of DR can help classify aerosol types and retrieve physical properties, which further explores the application potential of DR. [50] We define a parameter, the ratio of depolarization ratios (RDR), to reflect the spectral properties of DR and discuss the impact of aerosol microphysical characteristics on the parameter. RDR=δ1/δ2, where δ1 and δ2 are DRs at wavelengths λ1 and λ2 (λ1>λ2), respectively.
In Fig. 3(a)–3(c), there are not exactly good linear correlation between three microphysical parameters and RDR(Dust), however, it still shows some application prospects of RDR. First, RDR does not cover up the nonsphericity of particles. The relationships among RDR1064/266, RDR1064/355, RDR1064/532 and AR are more linear than those of DR in a single band. Second, in the actual observation of dust, it is rare to see such a large span of absorption characteristics, as shown in Fig. 3(c). Huang et al. [21] found that RDR532/355 has a good fitting relationship with the absorption coefficient. The smoke situation is shown in Fig. 3(d)–3(f). Different from dust, although RDR(Smoke) and microphysical properties have good linear correlations, the values and rates of RDR1064/ 266, RDR1064/355 and RDR1064/532 decrease. Comparing dust with smoke, RDR1064/355 and RDR1064/532 are quite different from aerosol types, but for the same type, there is only little difference between them. This shows that we can choose one of them as a parameter to identify aerosol types. Considering that the polarization channel at 532 nm is more widely used at present, we suggest choosing RDR1064/532. RDR532/355 has a better rate of change, which should be more suitable for inverting microphysical properties in a single aerosol environment.
Fig. 3. The effects of microphysical parameters on RDR of aerosol types; (a-c) Dust aerosols; (d-f) Smoke aerosols.
3.3 Relevant optical parameters
In addition to DR, CR and LR are also important parameters for identifying aerosol types. Bi et al. [51] simulated the sensitivity of CR to ice particle habits at wavelengths of 532 nm and 1064 nm. It is proven that the relationship between CR and Reff is affected by aerosol types. Haarig et al. [52] measured DR and LR of aged smoke particles at 355 nm, 532 nm and 1064 nm and found that spectral dependence of LR is different from that of DR.
3.3.1 Color ratio (CR)
Figures 4,5 show the impact of microphysical properties on CR and LR at 266 nm, 355 nm, 532 nm and 1064 nm, respectively, and the parameters used for simulation are consistent with Fig. 3. It can be seen from Fig. 4 that the dust CR is concentrated at approximately 1.5-4.2, while the value at CR1064/266 is even greater than 6.0. This phenomenon is due to the large difference between the scale parameters of dust at 266 nm and 1064 nm, resulting in a huge difference in the backscattering cross section. For data greater than 6.0, considering the actual observation range of CR, we regard it as the error of the algorithm. Smoke CR is concentrated in the range of 0.3-1.8, which is obviously different from that of dust, which proves the importance of CR in identifying aerosol types.
3.3.2 Lidar ratio (LR)
Figure 5 shows the variation in dust and smoke LRs with microphysical properties. Dust LR is obviously affected by the microphysical properties at 266 nm, which is basically a positive correlation. With increasing wavelength, the rate of change gradually decreases, and LR at 1064 nm is basically kept at 10-30 sr except for the law of sharp decrease when Reff is small. The variation rule of dust LR at 532 nm in Fig. 5(a) also explains why the LR measured by Shen et al. [53] decreases sharply with decreasing height. It is precisely the impact of large size dust transported by dust storms from northwest China. The change rule of smoke LR with wavelength is contrary to that of dust, showing a positive correlation, which is consistent with the observation results of Haarig et al. [52]
3.4 Recognition algorithm
Summarizing the previous simulation results, we find that for different types of aerosols, their optical properties are obviously different, especially in spectral dependence. Using two or more optical parameters at different wavelengths to identify aerosol types and retrieve physical parameters are also mainstream methods at present, such as “3β+2α+1δ” and “2β+1δ” [54,55], where β is the backscattering coefficient and α is the extinction coefficient. We hope to develop a new identification method that can achieve the following purposes: (1) The algorithm can be adapt to different conditions: the long-distance transportation of a single aerosol type or the aerosol identification of a complex environment; and (2) the lidar channels can be reduced as much as possible. The second point is convenient to compare lidar data of different configurations to obtain more extensive physical properties of aerosols.
Figure 6 shows the RDR fitting relationship between CR and the ratio of LRs and their classified effects on dust and smoke, where the red dot represents the observed data from references in Table 2 and 3. We can draw two main conclusions: (1) In general, the classified effect at 1064 nm is more significant, which also conforms to our conclusion in Section 3.2.2; (2) From the simulated results, there is a good fitting relationship with RDR and the other two parameters except 355/266, but the data in references are obviously different from the simulated results except for Fig. 6(l). This is because the aerosol model is different from the actual particles, the error of the algorithm itself, and the sample size is too small. These points prove that the backscatter data at long wavelengths are more conducive to classifying aerosol types. The effect of 1064 nm and 532 nm is better than that of 532 nm and 355 nm, both from the fitting relationship between lidar parameters and the classification effect between different models. Based on the above simulated results and Eq. (4),(5), LR and CR at 532 nm or 1064 nm can be obtained through the remaining Lidar data at these two channels. And we propose a new recognition algorithm: “1β+1α+2δ”. This means that the backscattering coefficient, extinction coefficient, depolarization ratio at 532 nm and depolarization ratio at 1064 nm are used for aerosol identification and physical property inversion. The application of the new recognition algorithm at 355 nm and 266 nm requires the improvement of the aerosol model and the feedback of more observed data.
Fig. 6. The effects of microphysical parameters on RDR of aerosol types; (a-f) Color Ratio; (g-l) The ratio of Lidar ratios.
Table 1. The parameters of the dust and smoke models
Table 2. Depolarization ratio and backscattering coefficient in Ref. [56]
Table 3. Depolarization ratio and lidar ratio in references
4. Conclusion
In this study, the T-matrix method is used to simulate the linear depolarization ratio (LDR) spectra of dust aerosols and smoke aerosols with random orientation and lognormal distribution, and the impact of different microphysical parameters on LDR is discussed. The simulated results show that DR has obvious spectral dependence, and the ratio of DRs can be used to represent the property. In general, researchers use DR to classify aerosol types by the threshold method. In this study, we can also use the same method to exploit RDR. The RDR value of 1.0 could be used as a threshold for distinguishing dust and smoke aerosols at 532 nm and 355 nm. Moreover, we found that RDR has a good fitting relationship with the absorption coefficient, especially at low wavelengths. This conclusion confirms the potential inversion ability of RDR.
Combining the simulation of CR and LR, we finally established suitable detection channels for lidar. High band channels, 1064 nm and 532 nm, are more suitable for identifying aerosol types, and low band channels should be used when retrieving parameters of a single aerosol type. For example, 1064 nm and 355 nm are suitable for retrieving dust aerosols, while 532 nm and 355 nm are more suitable for retrieving smoke aerosols. We further propose a new recognition method: “1β+1α+2δ”. By comparing the data in references, we can verify that the recognition algorithm has a considerable degree of feasibility, but there are still the following shortcomings to be improved: (1) the number of aerosol models used is small, which cannot be adapt to more complex situations, such as the identification and inversion of pollution dust particles and sea salt particles; (2) the inversion of microphysical properties lacks quantitative analysis; and (3) there is still a certain error between the simulated value and the observed value. In fact, the purpose of the algorithm is to expand the retrieval data of lidar and facilitate the comparison of lidar data with different configurations. It is more suitable for a case with fewer lidar channels.
Funding
Gansu Provincial Science and Technology Innovative Talent Program: High-level Talent and Innovative Team Special Project (No.22JR9KA001); the Second Tibetan Plateau Scientific Expedition and Research Program (Grant No. 2019QZKK0602); National Natural Science Foundation of China (41975019); 111 Project (B 13045); Fundamental Research Funds for the Central Universities (lzujbky-2022-kb10, lzujbky-2022-kb11).
Acknowledgments
Thanks for the T-matrix code provided by Prof. M. I. Mishchenko (http://www.giss.nasa.gov/staff/mmishchenko/t_matrix.html).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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