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Scientific Reports
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10.1038/s41598-024-71532-x
Article
Comparison study between nitrate and sulfate aerosols and their coating effect on the scattering properties of mineral aerosol
Dai Congming 14
Zhang Xuehai zhangxuehai2012@163.com

2
Lian Wentao 13
Wei Heli 14
Liu Jia 5
Zou Shuguang 2
1 grid.9227.e 0000000119573309 Key Laboratory of Atmospheric Optics, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, 230031 China
2 https://ror.org/05sbgwt55 grid.412099.7 0000 0001 0703 7066 School of Information Science and Engineering, Henan University of Technology, Zhengzhou, 450001 China
3 https://ror.org/04c4dkn09 grid.59053.3a 0000 0001 2167 9639 School of Environmental Science and Optoelectronic Technology, University of Science and Technology of China, Hefei, 230026 China
4 Advanced Laser Technology Laboratory of Anhui Province, Hefei, 230037 China
5 https://ror.org/01p884a79 grid.256885.4 0000 0004 1791 4722 College of Quality and Technical Supervision, Hebei University, Baoding, 071002 China
18 9 2024
18 9 2024
2024
14 2175628 5 2024
28 8 2024
© The Author(s) 2024
2024
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The existing numerical models generally employ sulfate instead of nitrate to simulate the scattering properties of aerosol, the corresponding radiative deviation needs to be evaluated urgently. Moreover, the sophisticated mixture of nitrate, sulfate, and mineral particles is formed through a series of chemical reactions, which makes it extremely challenging to understand the scattering properties of atmospheric aerosols. In this study, the core–shell ellipsoid model is used to flexibly characterize the morphology and mixed structures of nitrate, sulfate, and mineral in the fine mode radius range. The T-matrix method is used to compare the scattering properties of nitrate, sulfate, and mineral within different morphologies and mixing states at four selected wavelengths (0.44, 0.675, 0.87, and 1.02 μm). The results show that the difference of mean extinction efficiency factor (< Qe >) and mean single scattering albedo (< ω >) between nitrate and sulfate-containing particles is very small, mainly within 2%. However, their mean scattering phase function P11(θ) is quite different. The difference of forward scattering phase function P11(0) is up to 7%, while the difference of backward scattering phase function P11(π) can reach more than 25%. Overall, particle morphology and incident wavelength regulate the value of the optical parameters, whereas the coatings on the mineral play a more important role in drifting, but the differences between nitrate- and sulfate-containing particles are still very pronounced.

Subject terms

Optics and photonics
Applied optics
Optical physics
http://dx.doi.org/10.13039/501100012166 National Key Research and Development Program of China 2019YFA0706004 Dai Congming Scientific and Technological Program of Henan Province212102310020 222102320087 Zhang Xuehai Zou Shuguang the S&T Program of HebeiD2021201002 Liu Jia http://dx.doi.org/10.13039/501100013066 Key Scientific Research Project of Colleges and Universities in Henan Province 21A416002 Zou Shuguang issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Over the recent decades, the emission of fine particles, NO2, SO2, and other pollutants in the atmosphere have increased rapidly, and the frequent haze episodes as well as the normal high concentration of fine particulate matter in China have attracted considerable research attention1. During the haze episodes, physical and chemical reactions including absorption, migration, and transformation of gases such as SO2 and NO2 occur on the surface of mineral particles, which form visible shells on the surface of mineral particles. Further, the mixing ratio of mineral, nitrate, and sulfate changes during the haze aging process2, which in turn affects their scattering properties and global radiation significantly3,4. Hence, more emphasis should be concentrated on the effect of nitrate, sulfate, and their heterogeneous reactions with mineral dust on the optical and radiation properties during haze episodes.

Mineral and sulfate are the two typical major components of atmospheric aerosols, and various optical and radiation models have been widely used to simulate their optical and radiative properties5,6. Furthermore, in recent years, rapid industrialization and urbanization have resulted in an increased in nitrate precursor emissions and a decrease in sulfate7–9. As a result, Nitrate has become one of the main causes of haze formation in China10,11,the concentration of nitrate even exceeds those of sulfate in some regions10,12–14. However, the treatment of nitrate aerosols is still substantially rudimentary as compared to that of sulfate aerosols. The existing numerical models generally use sulfate instead of nitrate to simulate the scattering properties of aerosols, and only a few studies have focused on the differences in the scattering properties between nitrate and sulfate aerosols, which lead to significant errors in the analysis. For example, Zhang et al.15 reported that the local forcings can be underestimated by up to 6.2%. The results of Wang et al.16 also suggest that, compared to sulfate, nitrate aerosol has un-ignorable effect on regional climate. Bauer et al.17 reported that when coating layers exceed 20%, the scattering and radiative properties differ significantly from uncoated dust, and the impact of nitrate on future projections is becoming even more significant. Hence, the scattering property difference and radiation deviation between nitrate and sulfate need to be rigorously evaluated15,17,18.

Although various non-spherical particle models have been developed to simulate the scattering properties of aerosol19–21, traditional studies commonly adopt spherical or core–shell spherical models to analyze the scattering properties of nitrate, sulfate, and mineral. However, the results usually significantly deviate from the observations due to the oversimplification of particle morphology and mixed state22–24. For example, Kahnert et al.25,26 systematically investigated the influence of particle morphology on radiance and flux simulations, the results show that using non-spherical model can substantially improve the accuracy of radiance and flux simulations. Therefore, it is imperative to establish a more accurate model for simulating the influence of sulfate and nitrate coatings on the scattering properties of aerosols. In this study, we focus on the relative differences between the scattering properties of aerosol caused by nitrate and sulfate. First, the scattering properties of sulfate and nitrate aerosols and their quantitative differences are simulated by spheroid models. Furthermore, the scattering properties and quantitative differences of poly-disperse dust-nitrate (DN) and dust-sulfate (DS) particles within different morphologies and mixing states are theoretically simulated by using core–shell spheroid models. Section "Methodology" introduces the basic particle model and the numerical methods for scattering simulations. The results are discussed in Section "Results and discussion", and Section “Conclusion” concludes the study.

Methodology

Several analytical instruments such as Transmission Electron Microscopy (TEM), Scanning Transmission X-ray Microscopy (STXM), Atomic Force Microscopy (AFM) have been widely employed to study the composition, mixing state, and morphology structures of single particles27. These instruments are of great significance for studying the microphysical and optical properties, and the potential radiative and climate impacts of mineral dust during aging process. Figure 1 shows some selected TEM and STXM images of the coated mineral dust particles. It shows that the nitrate and sulfate shells are wrapped on the surface of mineral particles, which exhibit highly complex morphology and mixed structures2,28. Kojima et al.29 also reported that mineral particles could acquire nitrate and sulfate shells during transported process in the atmosphere by absorbing acid gas. The process will change the morphology and mixed characteristics between mineral and sulfate/nitrate in the atmosphere, thereby changing their scattering properties in the atmosphere. In this study, we propose a core–shell spheroid model that simultaneously depicts the variation in the morphological and coating state between mineral and nitrate/sulfate particles. In Fig. 2, the black part represents the mineral core, while the gray part represents the sulfate and nitrate shell. The coating ratio (fcoating) and the aspect ratio (α) are expressed as follows:1 fcoating=Rout-RinRout=b-cb

2 α=ba

where a is the revolution axis, and b is the vertical axis of the outer spheroid particle, respectively, and c is the vertical axis of the inner spheroid particle. In the actual atmosphere, particle morphology and mixed state are very complex and change dynamically. It may not be suitable to reproduce its scattering properties with fixed morphology and mixed state, but to quantitatively analyze the influence of each factor and simplify the model requirements, it is still necessary to select fixed parameters to simulate the influence of particle morphology (mixed state) on the scattering properties simulation. In recent researches, many mode or mean aspect ratios of various mineral dust particles have been reported, such as 1.331, 1.3732, 1.3833,1.4, 1.631, 1.6433,34, 1.735, and 1.8434, respectively. In addition, the fine mode and coated particles tend to be shifted toward small aspect ratios as compared to those of pure dust particles2,3,36. Hence, in this study, α=1.37 is selected to obtain the results closest to the natural state when comparing the effects of sulfate and nitrate coatings on the scattering properties of mineral particles. For investigating the effect of particle morphology, the coating ratio is assumed to be 0.5, and the aspect ratio is between 1.0 and 2.0, as shown in Fig. 2b.Fig. 1 TEM and STXM images of the coated mineral dust particles27,28,30.

Fig. 2 The core–shell spheroid models for nitrate/sulfate coated mineral aerosol. (a) models with different coating ratio and fixed aspect ratio of 1.37, (b) models with different aspect ratio and fixed coating ratio of 0.5

To match the wavelength of AERONET and enhance the application of the proposed model, four wavelengths of 0.44, 0.675, 0.87, and 1.02μm are used to examine the scattering properties of aerosols. The complex refractive indices(RI) of mineral, nitrate, and sulfate used are shown in Table 137.Table 1 Complex refractive indices of mineral, nitrate, and sulfate at the four selected wavelengths.

Wavelength (μm)	Mineral	Nitrate	Sulfate	
Real	Imaginary	Real	Imaginary	Real	Imaginary	
0.44	1.53	0.008	1.56	1.19 × 10–9	1.54	1 × 10–7	
0.675	1.53	0.008	1.55328	1.2 × 10–9	1.52458	1 × 10–7	
0.870	1.52	0.008	1.55	3.6 × 10–8	1.51714	1.14 × 10–7	
1.020	1.52	0.008	1.54797	1.55 × 10–6	1.51154	9.5 × 10–7	

We consider randomly oriented core–shell spheroids38. The scattering matrix is given by39,403 p11(θ)p12(θ)00p21(θ)p22(θ)0000p33(θ)p34(θ)00-p34(θ)p44(θ)

where θ is the scattering angle, p11(θ) satisfies the following normalization condition:4 12∫0πp11(θ)sin(θ)dθ=1

The log-normal size distribution is usually used to describe aerosol’s size distribution41:5 N(r)=12πδrexp-ln2(rrr0r0)2δ2

where r is the volume equivalent radius, δ is the mean geometric standard deviation, r0 is the mean geometric radius. In this study, we set r0=0.25μm, and δ=0.9 to fit the actual haze atmosphere32,42–44.

For the given particle size distribution, The mean scattering matrix Pij(θ), the mean extinction efficiency factor (< Qe >), and the mean single scattering albedo (< ω >) are shown in Eqs. (6), (7), and (8):6 Pij(θ)=∑r=rminrmaxPij(θ,r)Qs(r)N(r)d(r)∑r=rminrmaxQs(r)N(r)d(r)

7 <Qe>=∑r=rminrmaxQe(r)A(r)N(r)d(r)∑r=rminrmaxA(r)N(r)d(r)

8 <ω>=∑r=rminrmaxω(r)A(r)N(r)d(r)∑r=rminrmaxA(r)N(r)d(r)

where Qe, Qs, and ω is the single extinction, scattering efficiency factor, and single scattering albedo, respectively. A is the projected area.

Results and discussion

Comparison between the scattering properties of nitrate and sulfate aerosols

Figure 3 shows the variation in the extinction efficiency factor (Qe) of nitrate and sulfate aerosols and their ratio under an aspect ratio of 1.37 at the four selected wavelengths. As shown in Fig. 3a, at the wavelength of 0.44 μm, Qe increases rapidly when the effective particle radius is less than 0.25 μm, and when the particle radius is greater than 0.25 μm, Qe exhibits an oscillatory decreasing trend with the increase in the effective particle radius. As the wavelength increase, the Qe peak moves towards larger particle radius, and the oscillation period of Qe increases, which is due to the decrease in particle size parameter 2πr2πrλλ. Figure 3b shows that the Qe of nitrate is larger than that of sulfate in a small particle size region, indicating that nitrate has a stronger extinction ability. With the increase in the particle size, the nitrate-to-sulfate ratio of Qe decreases and begins to fluctuate, and the ratio can reach more than 1.15. When the nitrate-to-sulfate ratio of Qe is equal to 1, the particle radius corresponding to the four wavelengths is approximately 0.27, 0.45, 0.55, and 0.65 μm. Figure 3b also demonstrates that the difference of Qe between nitrate and sulfate is mainly reflected in the fine-mode particle region, while in the coarse mode, the difference between nitrate and sulfate is not obvious. During the haze episodes, fine particles are predominant with a peak radius of nearly 0.25 μm, which means that for visible and infrared bands, the extinction ability of nitrate is stronger than that of sulfate. Further, the radiative forcing of nitrate aerosol can be underestimated if the sulfate equivalent hypothesis is used for single-particle simulation.Fig. 3 Extinction efficiency factor (Qe) of nitrate and sulfate (a), and the nitrate-to-sulfate ratio of Qe (b) at the four selected wavelengths.

Figure 4 shows the mean extinction efficiency factor (< Qe >) of nitrate and sulfate and their ratio as a function of aspect ratio at the four selected wavelengths. It is clear that the non-spherical particles tend to have higher < Qe > than spherical particles, which is in agreement with other previous works45,46.As shown in Fig. 4a, < Qe > increases with the increase in wavelength and aspect ratio in general. In the short waveband, < Qe > is closely related to the aspect ratio, and the relative difference of < Qe > can reach more than about 10%. Furthermore, as the wavelength increases, the influence of aspect ratio on < Qe > decreases. When λ = 1.02 μm, < Qe > is basically independent of the aspect ratio. These results indicate the necessity to consider the non-spherical characteristics of particles while studying the scattering properties of aerosol. Figure 4b shows that the difference of nitrate-to-sulfate ratio of < Qe > is no more than 2% for all the selected wavelengths and aspect ratios. This implies that the sulfate scheme substitution is feasible under certain conditions. Zhang et al.15 compared the nitrate-to-sulfate ratio of < Qe > in multiple wavelength regions by spherical model, and the results indicate that the nitrate-to-sulfate ratio of < Qe > was basically equal to 1, which is consistent with our study.Fig. 4 <Qe > of nitrate and sulfate (a) and the nitrate-to-sulfate ratio of < Qe > (b) at the four selected wavelengths.

Figure 5 illustrates the mean scattering phase function (P11(θ)) of nitrate and sulfate and their ratio under the aspect ratio of 1.37 at the four selected wavelengths. For all the wavelengths, the P11(θ) of nitrate and sulfate exhibit the same variation trend with the scattering angle, and as the wavelengths increases, the forward scattering phase function(P11(0)) and the backward scattering phase functionP11(π) decrease gradually, but the change in the side-scattering phase function is not obvious. As shown in Fig. 5b, the influence of chemical composition of particles on the value of P11(θ) is undeniable. As the scattering angle increases, the nitrate-to-sulfate ratio of P11(θ) increases. In the forward scattering direction, the scattering ability of nitrate is weaker than that of sulfate, while in the backward scattering direction, the result is opposite. Meanwhile, Fig. 5b also shows that the nitrate-to-sulfate ratio of P11(θ) initially increases and then decreases monotonically with the increase in the wavelength. When λ = 0.87 μm, the nitrate-to-sulfate ratio of P11(θ) has a low value of 0.93 in the forward scattering direction, and the maximum value is of 1.16 in the backward scattering direction, which is due to the enhancement of Rayleigh scattering with the increase in wavelength, thus the dependence of P11(θ) on the particle composition reduces. Therefore, in the study of aerosol properties using forward or backward scattering information from sun-photometer, LIDAR, etc., the use of the scattering properties of sulfate instead of nitrate properties may lead to large uncertainties.Fig. 5 Scattering phase function P11(θ) of nitrate and sulfate (a) and the nitrate-to-sulfate ratio of P11(θ) (b) at the four selected wavelengths.

The P11(0) and P11(π) have special significance and wide application in the atmospheric aerosol detection and remote sensing47–49. This study analyzed the variation of P11(0) andP11(π)with aspect ratio at the four selected wavelengths separately.

Figure 6 shows the variation in the P11(0) of nitrate and sulfate and their ratio as a function of aspect ratio at the four selected wavelengths. It is clear that P11(0) of nitrate is lower than that of sulfate, and P11(0) is strongly sensitive to both aspect ratio and wavelength. Further, the sensitivity of P11(0) to the wavelength is higher than to the aspect ratio. According to Fig. 6b, the variation in the nitrate-to-sulfate ratio of P11(0) with wavelength is obvious, with the relative differences of more than 5%, but the variation with aspect ratio is relatively small, with the relative differences under ± 1%, demonstrating that the relative difference of P11(0) is independent of particle morphology, and it is only related to particle composition at a given wavelength, which means that there may be little need to consider particle morphology selection in aerosol composition inversion, thus providing a reference for simplifying the physical model of aerosol composition inversion.Fig. 6 P11(0) of nitrate and sulfate (a) and the nitrate-to-sulfate ratio of P11(0) (b) at the four selected wavelengths.

Figure 7 shows the same results as Fig. 6, but for the backward scattering phase function P11(π). It is evident from Fig. 7a that the P11(π) is strongly dependent on the aspect ratio and wavelength. The P11(π) of nitrate is reduced from 1.0 to 0.31 at 0.44 μm, which corresponds to an attenuation factor of 3.23, while the attenuation factor is 1.79 at 1.02 μm, illustrating that the equivalent sphere method may seriously overestimate the backscattering phase function P11(π), and the influence of particle non-spherical characteristics must be considered. It is also clear that P11(π) of nitrate is higher than that of sulfate, and the difference between nitrate and sulfate decreases with the increase in aspect ratio. Contrary to the variation trend of the nitrate-to-sulfate ratio of P11(0) with the aspect ratio, the nitrate-sulfate ratio of P11(π) decreases monotonically with the aspect ratio (Fig. 7b). The nitrate-to-sulfate ratio of P11(π) is reduced from 1.16 to 1.08 at 0.44 μm. As the wavelength increases, the nitrate-to-sulfate ratio of P11(π) initially increases and then decreases with the maximum relative difference of nearly 10%. The results also show that the equivalent sphere method may be overestimating their differences, and the influence of non-spherical properties should be considered when comparing the scattering properties of nitrate and sulfate.Fig. 7 P11(π) of nitrate and sulfate (a) and the nitrate-to-sulfate ratio of P11(π) at the four selected wavelengths.

Comparison between the coating effect of nitrate and sulfate on the scattering properties of mineral

Comparison of < Qe > and < ω > 

Figure 8 shows the mean extinction efficiency factor < Qe > and mean single scattering albedo < ω > of DN and DS and their ratio as a function of aspect ratio under a coating ratio of 0.5 at the four selected wavelengths. As shown in Fig. 8a, c, < Qe > and < ω > increases with the increase in wavelength and aspect ratio in general. In the short waveband, < Qe > is closely related to the aspect ratio, and as the wavelength increases, the influence of aspect ratio on < Qe > decreases. When λ=1.02μm, < Qe > is basically independent on the aspect ratio. However, < ω > is basically independent on the aspect ratio for all selected wavelengths, except for a slight decrease in extreme non-spherical states(α = 2). Figure 8b illustrates that the DN-to-DS ratio of < Qe > exhibits a complicated variation trend with the aspect ratio. In the short waveband, the DN-to-DS ratio of < Qe > is independent of the aspect ratio with a value of about approximately 1. In the long waveband, the DN-to-DS ratio of < Qe > increases with the increase in aspect ratio, which may be due to the change in the particle cross section with the increase in aspect ratio. Overall, the relative difference of DN-to-DS ratio of < Qe > and < ω > is less than 2%, and 0.5% for different aspect ratios, respectively. Which suggests that there is no need to consider the impact of particle morphology in the retrieval of particle composition and mixed states.Fig. 8 <Qe > and < ω > of DN and DS (a, c), and the DN-to-DS ratio of < Qe > and < ω > (b, d) at the four selected wavelengths.

Figure 9 illustrates the mean extinction efficiency factor < Qe > and mean single scattering albedo < ω > of DN and DS and their ratio as a function of coating ratio under an aspect ratio of 1.37 at the four selected wavelengths. It is evident from Fig. 9a that the coating ratio has a slight impact on the < Qe > of DN and DS. The < Qe > of DS remains constant because the real parts of the refractive index of sulfate and mineral particles are similar. The < Qe > of DN first increases and then decreases with the increase in the coating ratio. Figure 9b shows that as the coating ratio increases, the DN-to-DS ratio of < Qe > fluctuates with a value of 2%, and the DN-to-DS ratio of < Qe > is basically unchanged when the coating ratio is greater than 0.8. This illustrates that the variation in < Qe > with the coating ratio is quite weak in the case when the fine-mode particles dominate during the haze episodes. Unga et al.32 showed that the thickness of the shell has a minor effect on the optical parameters of particles under fine mode conditions, which is consistent with our study. Figure 9c shows that coating ratio has a significant impact on the < ω > of DN and DS. The < ω > of DN and DS increases with the increase in the coating ratio and wavelength. But the DN-to-DS ratio of < ω > remains unity basically, which mainly due to the fact that both sulfate and nitrate are non-absorbent aerosols, and the change in < ω > is mainly caused by the content of mineral dust aerosol. However, the results also indicate that the mixing of sulfate/nitrate and mineral dust aerosols can lead to an increase in < ω > , and the influence of sulfate/nitrate on the < ω > during haze processes cannot be ignored.Fig. 9 <Qe > and < ω > of DN and DS (a, c), and the DN-to-DS ratio of < Qe > and < ω > (b, d) at the four selected wavelengths.

For further clarify the optical properties of mineral dust, nitrate, sulfate, and their mixture, we summarized some previous researches on the key optical parameters (< Qe > and < ω >), as shown in Table 2. Table 2 also shows that the < Qe > and < ω > are dependent on the wavelength, composition. However, to our knowledge, there is little researches on the studies of the optical parameters (< Qe > and < ω >) of DN and DS, which also means that the study maybe enrich this content to a certain extent.Table 2 the key optical parameters of mineral dust, nitrate, sulfate, and their mixture.

Composition	λ	 < Qe > 	 < ω > 	References	
Mineral dust	0.3		0.81	Hans et al.50	
0.405		0.953.1ce	Hans et al.50	
0.4416		0.91–0.98	Kahnert et al.26	
0.6328		0.999–0.9	Kahnert et al.26	
0.87		0.996–0.9	Hans et al.50	
0.3–1.1	2.4–3.1	0.8–0.99	Bauer et al.17	
Nitrate	0.2–1.0	1.5–3.0	1	Zhang et al.15	
0.2–1.9		1	Shen51	
0.44–1.02	2.6–3.2	1	This study	
Sulfate	0.2–1.0	1.5–3.0	1	Zhang et al.15	
0.3–1.1	2.4–3.0	1	Bauer et al.17	
0.2–1.9		1	Shen51	
0.44–1.02	2.6–3.2	1	This study	
DS	0.3–1.1	2.4–3.0	0.82–0.99	Bauer et al.17	
0.44–1.02	2.6–3.2	0.88–1	This study	
DN	0.44–1.02	2.6–3.2	0.88–1	This study	

Overall, it can be seen that < Qe > is weakly correlated with both aspect ratio and coating ratio, and the < ω > is weakly dependent on aspect ratio, but strongly dependent on coating ratio. The error of sulfate substitution scheme is need not to be considered when using < Qe > and < ω > for simulation calculation, but the impact of coating process cannot be ignored when using < ω > for simulation calculation. However, we suggest that < Qe > and < ω > should also be strongly dependent on the particle size distribution, incident wavelength, and the complex refractive index of core and shell layers. Different conditions may lead to completely opposite results, which warrants further investigations.

Comparison of P11(0) and P11(π)

Figure 10 shows the variation in the P11(0) of DN and DS and their ratio as a function of coating ratio under an aspect ratio of 1.37 at the four selected wavelengths. It is evident that the P11(0) of DN is lower than that of DS, and P11(0) is strongly sensitive to the wavelength, but it slightly decreases with coating ratio. Especially for DS, the P11(0) is essentially independent of the coating ratio because the real parts of complex refractive index of sulfate and mineral are similar, as shown in Table 1. Further, Fig. 10b shows that the DN-to-DS ratio of P11(0) decreases with the increase in the coating ratio. Moreover, the variation in this ratio is mainly concentrated in the range of 0.2–0.8, while when the coating ratio is less than 0.2 and greater than 0.8, the DN-to-DS ratio of P11(0) essentially remains unchanged. This is because when the coating ratio is greater than 0.8, the nitrate and sulfate shells play a dominant role in the particle scattering characteristics, and when the coating ratio is less than 0.2, the particle scattering characteristics are mainly affected by the mineral core. This conclusion is consistent with the results of Bauer et al.17. Notably, Fig. 10b shows that the change in the DN-to-DS ratio of P11(0) with coating ratio is negligible at 0.44μm with the relative difference of nearly 1%. However, for longer wavelength, the change in the DN-to-DS ratio of P11(0) with the coating ratio is obvious, where the relative difference is nearly 7%. This indicates that the scheme of nitrate substitution by sulfate can underestimate the scattering properties. Moreover, the results also suggest that particle composition information can be distinguished by using the multi-band forward scattering phase function.Fig. 10 P11(0) of DN and DS (a), and the DN-to-DS ratio of P11(0) (b) at the four selected wavelengths.

Figure 11 shows the same results as Fig. 10, but for P11(π). It is clear from Fig. 11a that the P11(π) is regularly dependent on the coating ratio and wavelength. The P11(π) of DN is increased from 0.42 to 0.6 at 0.44 μm, which corresponds to an enhancement factor of 1.43, while the enhancement factor is 1.12 at 1.02 μm, indicating that the scheme of replacing nitrate by sulfate underestimates the backscattering ability. It is also evident that P11(π) of DN is higher than that of DS, and the difference between P11(π) of DN and DS increases with the increase in coating ratio due to the impact of the mineral core. Figure 11b shows that the DN-to-DS ratio of P11(π) increases monotonically as the coating ratio increases. With the increase in the wavelength, the DN-to-DS ratio of P11(π) first increases and then decreases under the same coating ratio, and the DN-to-DS ratio of P11(π) at 0.44 μm are significantly lower than the other three wavebands, illustrating that the DN-to-DS ratio of P11(π) are more sensitive to the changes in size parameter when the value of size parameter is relatively small. The results of Halder and Ganesh52 also show that the P11(0) and P11(π) are more sensitive to the changes in particle effective radius when the value of particle effective radius is relatively small, which also confirmed our view.Fig. 11 P11(π) of DN and DS (a), and the DN-to-DS ratio of their P11(π) (b) at the four selected wavelength.

Figure 12 shows the variation in the P11(0) of DN and DS and their ratio with the aspect ratio at the four selected wavelengths. Compared to the weak impact of coating ratio on the value of P11(0) shown in Fig. 10, the particle morphology obviously has a greater influence on the value of P11(0) with an enhancement factor of approximately 1.19. However, with the increase in the aspect ratio, the relative difference of P11(0) between DN and DS is less than 2% at 0.44μm, which indicates that for large particle size parameter, the influence of particle morphology on the DN-to-DS ratio of P11(0) can be ignored. Moreover, the variation in the DN-to-DS ratio of P11(0) with wavelength also illustrates that the impact of coating material on P11(0) is mainly size-dependent. Specifically, the impact is observed in the intermediate particle size parameter of 1 to 4. However, the haze episodes are dominated by the fine-mode particles with the median radius between 0.2 and 0.3 μm, which is just within the main influence range of the coating layer on the particles. Therefore, using the scattering properties of sulfate instead of nitrate may overestimate the optical and radiation characteristics when the forward scattering phase function is utilized for the aerosol radiation calculation and other applications.Fig. 12 P11(0) of DN and DS (a), and the DN-to-DS ratio of P11(0) (b) at the four selected wavelengths.

Figure 13 shows the same results as Fig. 12, but for P11(π). It is clear from Fig. 13a that the variation in P11(π) with the aspect ratio and wavelength is essentially the same as that of pure sulfate and nitrate (see Fig. 7), except that the value decreases slightly, which is due to the influence of mineral core. As the aspect ratio increases, the value of P11(π) remains essentially the same as that of pure nitrate and sulfate when the aspect ratio is 2, which is mainly due to the increase in the fraction of sulfate and nitrate in the whole particles. The comparison between Figs. 7b and 13b also supports this view. Overall, the aspect ratio mainly affects the value of P11(π) but has a slight effect on the DN-to-DS ratio of P11(π) for the given coating ratio.Fig. 13 P11(π) of DN and DS (a), and the DN-to-DS ratio of their P11(π) (b) at the four selected wavelength.

Conclusion

In this study, the properties of nitrate and sulfate aerosols and their coating effect on the scattering properties of mineral aerosol under multi-wavelength conditions were rigorously examined by core–shell spheroid model. We mainly emphasized on the sensitivities of the scattering parameters to the particle composition, incident wavelength, aspect ratio, coating ratio, and wavelength. By comparing the sensitivities of the scattering parameters, it was clear that different scattering parameters had different responses to the changes in the particle composition, incident wavelength, coating ratio, and aspect ratio. The coating ratio serves as a factor when tuning the scattering parameter response, while the wavelength and aspect ratio performs this function. For example, the incident wavelength could be used to determine the value of scattering parameters due to the change in the particle size parameter. The value of mean extinction efficiency factor < Qe > and mean single scattering albedo < ω > were independent of the particle composition with the relative difference of nitrate and sulfate under ± 2%, while the P11(π) strongly depended on the particle composition with a relative difference higher than 25%, which may be useful to distinguish between sulfur and nitrogen aerosols in LIDAR observation. The aspect ratio determined the absolute value of the scattering parameters of aerosols, but it had a minor effect on the value of the DN-to-DS ratio of scattering parameters, due to the impact of the fraction in the whole particles. However, the coating ratio significantly affected the value of the DN-to-DS ratio with a relative difference of more than 25%, but the effect on the value of scattering parameters was relatively small, which was dependent on the difference between the complex refractive index of core and shell materials. Therefore, using sulfate instead of nitrate to simulate the scattering properties of aerosol can bring some errors, and it is necessary to consider nitrate as one of the main components in the study of climate forcing and radiation transfer.

Here, we mainly focused on the quantitative effects of sulfate and nitrate coatings on the scattering properties of fine mode mineral aerosols, rather than establishing one or a group of non-spherical geometry at the fixed particle shape or mixed state to reproduce the scattering properties. By simply changing the aspect ratio and coating ratio during the numerical calculation, and combined with the aspect ratio distribution function and coating ratio function, such as the discussions in Mishchenko53, it is possible to characterize the scattering properties of mineral aerosols during different haze aging processes while ensuring the removal of quality errors due to the sulfate substitution scheme, even if the ellipsoid geometry used in this study is fixed. Moreover, it also exhibits immense potential in simplifying the model development for complex haze aerosols.

Acknowledgements

This work was supported by the National Key Research and Development Program of China[2019YFA0706004], the Scientific and Technological Program of Henan Province[212102310020, 222102320087], the S&T Program of Hebei[D2021201002], the Key Scientific Research Project of Colleges and Universities in Henan Province[21A416002].

Author contributions

C.D.: Conceptualization Ideas, Writing-Original Draft, Review &Editing. X.Z.: Data Curation, Supervision, Project administration, Funding acquisition. W.L.: Formal analysis, Visualization Preparation, Investigation. H.W.: Writing-Review and Editing, Supervision, Project administration. J.L.: Validation, Visualization. S.Z.: Formal analysis, Visualization Preparation. All authors reviewed the manuscript.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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