Atmospheric aerosols are solid and liquid particles suspended in the atmosphere with diameters that range from ~ 10^-3 µm to 10 µm ( Zhang, 1995) that originate from molecules of nucleated clusters of crustal dust up to tens of microns in cloud droplets D’Almeida et al., 1991). Aerosol particles vary greatly in size, source, chemical composition, optical properties, amount, distribution in space and time, and lifetime in the atmosphere. However, the various factors that influence the characteristics of atmospheric aerosols are not known comprehensively thus far (Intergovernmental Panel on Climate Change (IPCC), 2007).

As a key component of aerosol research, the scattering characteristics of the anterior hemisphere of atmospheric aerosols particles ranged from 0° and 90° along the direction of the incident wave, hereinafter referred to as forward- scattering, has been studied for many years Van de Hulst, 1957; Lü and Wei, 1978; Yang and Liou, 2000). Previous studies Lü et al., 1981; Qiu et al., 1984) have focused mainly on theoretical and experimental analyses of the forward-scattering of atmospheric aerosols within small angles, which were used for the retrievals of size distributions and complex refractive indices of aerosol particles. Qiu and Zhou (1986) discussed the sensitivity of phase function to the scattering parameters of the atmospheric aerosols because of the potential for high accuracy and portability in measuring the atmospheric aerosol optical properties. However, limited studies have been conducted for quantitative analysis of phase function sensitivity to the complex refractive index by size distribution ( Li et al., 1994; Li and Peng, 2012). In the present study, for the selection of optimal forward-scattering angles of aerosols, these sensitivities were studied quantitatively according to observational datasets and numerical simulation.

A prototype of forward-scattering Present Weather Identifiers (PWIs) was developed by the Institute of Atmospheric Physics, Chinese Academy of Science, in December 2008 in which an automatic real-time instrument was proposed that accurately measures visibility and distinguishes weather types such as fog, haze, and mist. This type of instrument is important for near-future automatic weather observations in China China Meteo-rolo-gical Administration, 2006). One of the crucial functions of the instrument is the selection of optimal forward-scattering angles of atmospheric aerosols according to the observed aerosol properties in China. In Section 2 of this paper, we introduce the theoretical basis of forward-scattering detection, and the selection of optimal forward-scattering angles of atmospheric aerosols with typical aerosol models is discussed in Section 3.1. Three types of aerosol conditions including new-particle generation, pollution, and dusty weather are simulated, and the influence of their differences on the selection of optimal forward-scattering angles is discussed in Section 3.2. Finally, we summarize the optimal forward-scattering angles of atmospheric aerosols in North China in Section 3.3.

Briefly, the scattering intensity I(θ) from a fixed forward-scattering angle of atmospheric aerosol particles is defined by the following equation ( Liou, 2004):

(1)

where θ is the forward-scattering angle, I₀ is the incident energy, σ_s is the scattering coefficient, R is the distance from the observation point to the scatters, and P(θ) is the normalized scattering phase function. Equation (1) can be simplified as:

(2)

where k is the measuring constant.

Because the complex refractive index and the number concentration distributions, hereafter referred to as size distributions, of atmospheric aerosol particles change continually, quantitative analysis of the extinction coefficient by a fixed forward-scattering angle of aerosol particles requires the following criteria:

1) The phase function P( θ) is insensitive to the complex refractive index and the particle size distribution; that is, P( θ) can be considered as a constant when the θ angle changes.

2) There is no absorption effect on the aerosol particles or there is a defined linear relationship between the scattering coefficient and extinction coefficient of aerosol particles. That is

σ_s = c × σ_e, (3)

where σ_e is the extinction coefficient, c is a constant, and c ≤ 1.

3) The shape of aerosol particles is spherical.

The first criterion is the theoretical basis of optimal forward-scattering detection, in which the phase function is insensitive to the complex refractive index and the size distribution of aerosols. Because the types of atmospheric aerosol size distribution differ significantly among regions, it is necessary to determine the optimal forward- scattering angles according to the observed aerosol types. The scattering coefficient of aerosol particles can be calculated by Eq. (1).

For some applications related to extinction coefficients, however, such as forward-scattering visibility meters, the second criterion should be considered. Assuming that the incident wavelength is 550 nm ( Han et al., 2012), the complex refractive index is generally less than 0.008 (World Meteorological Organization (WMO), 1983; D’Almeida et al., 1991) excluding some special conditions such as soot-polluted cities. In addition, according to the Mie theory ( Mie, 1908), scattering energy accounts for most of the extinction energy for a high-number concentration and a larger equivalent radius of particles. In such cases, the single scattering albedo (SSA) of particles is close to 1.0.

For the third criterion, it is clear that most of the actual atmospheric aerosol particles are non-spherical. However, the differences in phase functions of spherical and non-spherical particles is negligible for forward-scattering within the forward-scattering angles from 0° to 40° for monodispersed aerosol particles ( Yang and Liou, 2000) and from 0° to 50° for polydispersed particles ( Liou, 2004). Therefore, to facilitate calculation, the assumption of spherical particles was used in this paper.

Considering the aforementioned criteria, it is necessary to determine the aerosol size distributions in the quantitative study of optimal forward-scattering angles. However, the actual aerosol size distributions undergo spatiotemporal changes. For various research purposes, scientists have proposed several aerosol size distribution models such as gamma distribution for environmental aerosol particles ( Deirmendjian, 1969), Junge distribution for urban aerosol particles ( Junge, 1963), and hierarchical representation distribution ( Seinfeld and Pandis, 1998). In these models, lognormal distribution is used most often ( Shi, 2007). For more realistic study ( Jaenicke, 1993), we used the following equation to describe the aerosol size distribution:

(4)

Here N_i (cm^-3) is the number concentration of the ith bin, r(nm) is the diameter of the aerosol particle, r_pi (nm) is the median diameter of the ith bin, and σ_gi is the standard deviation of the ith bin.

In the following sections (3.1-3.3), the sensitivity of phase function to the real part of the complex refractive index for typical aerosol size distributions has been studied by using the Bohren-Huffman Mie model ( BHMIE; Bohren and Huffman, 1983; Wiscombe, 1996; Du, 2004). First, we tested the sensitivity by using typical aerosol models ( Jaenicke, 1993). On the basis of an observed aerosol dataset obtained from Wuqing station in Tianjin, three typical aerosol size distributions were simulated. Therefore, the optimal forward-scattering angles of atmospheric aerosols were studied in North China according to the observation of a regional atmospheric background station.

3.1 Typical aerosol models

On the basis of a large number of observational data obtained from various regions, Jaenicke (1993) categorized seven typical aerosol size distributions including urban, marine, rural, remote continent, free troposphere, polar, and desert. In this section, we selected four of the distribution types that are most affected by human activities (Table 1). To better describe the size distributions, the sensitivity of phase function to the real part of the complex refractive index R(θ, m) is defined by the follow equation:

(5)

where m = m_R - m_I × i is the complex refractive index of aerosol particles, m_R is the real part and m_I is the imaginary part. m₀ = 1.5 - 0.01 × i, m_I = 0.01. The imaginary part refers to the second criterion described in Section 2.

Table 1

Table 1

Table 1 Variables of the Jaenicke aerosol models in four typical regions and their insensitive angles with relative deviation (RD). Type Mode I Mode II Mode III RD ≤ 10% (degree) N1 r p1 (nm) σ g1 N2 r p2 (nm) σ g2 N3 r p3 (nm) σ g3 (a) Urban 9.93e4 6.5 1.76 1.11e3 7.0 4.63 3.64e4 25.0 2.17 28-37 (b) Marine 1.33e2 4.0 4.54 66.6 133.0 1.62 3.1 290.0 2.49 26-33 (c) Rural 6.65e3 7.5 1.68 147 27.0 3.61 1.99e3 42.0 1.85 24-33 (d) Remote continent 3.20e3 10.0 1.45 2.9e3 58.0 1.65 0.3 900.0 2.40 15-37

Table 1 Variables of the Jaenicke aerosol models in four typical regions and their insensitive angles with relative deviation (RD).

Figure 1 shows the sensitivity of the phase function to the real part of the complex refractive index determined by using the Jaenicke aerosol models. The modified phase function R(θ, m) maintained the value of 0.90 to 1.10 with a θ range of 28° to 33°, whereas m_R varied from 1.3 to 1.7 (Table 1). For the urban aerosol model (Fig. 1a), the insensitive angle is in the vicinity of 33° due to the relative deviation of less than 5.0%; the relative deviation is equal to 1- R(θ, m). This conclusion is generally applied to determine forward-scattering angles for visibility meters ( Vaisala, 2002; Zeng et al., 1999). In the following section, three typical aerosol size distributions are simulated and analyzed to determine the various influences on the selection of the optimal forward-scattering angles.

3.2 Numerical simulation

In general, the size distribution and the chemical compositions of atmospheric aerosols change significantly according to various weather conditions or pollution incidents ( Seinfeld and Pandis, 2006). In the present study, three representative events including new particle generation, pollution, and dust intrusion were selected, and the corresponding size distributions were simulated (Table 2). As shown in Table 2, type (a) is the observed average aerosol size distribution from Wuqing station, and types (b)-(d) are the simulation results of aerosol size distribution based on type (a) according to the three events, respectively. To better reflect the simulation results, the new particle generation (type (b)) enhanced the N value of mode I, and the pollution incident (type (c)) enhanced the N value of mode III. The N value of mode I was set to zero, and the N value of mode IV was setting to 100 in the dust intrusion incident (type (d); Seinfeld and Pandis, 2006; Shen, 2009). The rigorously validated raw data (type (a); Ma et al., 2011) was obtained from the research data recorded during the Hachi campaign in Wuqing, Tianjin Province ( Liang, 2012).

Figure 1

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	Figure 1 Sensitivity of the phase function to the real part of the complex refractive index as determined by using Jaenicke aerosol models. The color bar is R(θ,m), and (a)-(d) are urban, marine, rural, and remote continent, respectively.

Table 2

Table 2

Table 2 Variables of the four aerosol models under four weather conditions and their insensitive angles with relative deviation (RD). Type Mode I Mode II Mode III Mode IV RD ≤ 10% (degree) RD ≤ 5% (degree) N1 r p1 (nm) σ g1 N2 r p2 (nm) σ g2 N3 r p3 (nm) σ g3 N4 r p4 (nm) σ g4 (a) 1e4 7.0 2.00 1e4 25.0 2.00 1e3 100.0 1.60 0 0 0 30-51 37-44 (b) 1e5 7.0 2.00 1e4 25.0 2.00 1e3 100.0 1.60 0 0 0 29-52 37-43 (c) 1e4 7.0 2.00 1e4 25.0 2.00 1e4 100.0 1.60 0 0 0 30-52 37-44 (d) 0 0 0 1e4 25.0 2.00 1e3 100.0 1.60 1e2 800.0 2.00 28-40 32-37/0-3

Table 2 Variables of the four aerosol models under four weather conditions and their insensitive angles with relative deviation (RD).

Note: Type (a) is observed average aerosol size distribution obtained from Wuqing station, and types (b)-(d) are the simulation results of aerosol size distribution according to new particle generation, pollution incident and dust intrusion incident, respectively.

The relative deviations of the phase function were less than 10.0% when θ changed from 30° to 52° and were less than 5.0% near 37° (Fig. 2 and Table 2). The phase function of the new particle generation (Fig. 2b) and the pollution incident (Fig. 2c) had a limited effect in the range of the angles, but for the dust intrusion incident, these insensitive angles were in the range of 28° to 40° (Table 2). It was noted that the relative deviation was even less than 5.0% within 0° to 3° in the dust intrusion incident, in which the relative deviation would normally be above 20.0% for other weather conditions. The phenomena of unusually low relative deviation at 0° to 3° has not been reported in other studies and it will supply an additional selection for the optimal forward-scattering angle in desert areas or areas with heavy dust pollution.

It can be concluded from Figs. 1 and 2 that the insensitive angles of the phase function to the real part of the complex refractive index are in the range of 28° to 52° and vary according to the size distributions of the atmospheric aerosols. Thus, it is very important to study typical size distributions of atmospheric aerosols in various regions before determining the optimal forward-scattering angles of aerosols for inversion methods. In Section 3.3, a representative site is selected in North China as an example of such analysis.

3.3 Optimal forward-scattering detection angles in North China

The particle size distributions of atmospheric aerosols in North China were observed by the Chinese Academy of Meteorological Sciences (CAMS) at the Shangdianzi regional atmospheric background station during March 2008 to February 2009 ( Shen, 2009). The observation instruments used were the Twin Differential Mobility Particle Sizer ( TDMPS, IfT, Leipzig, Germany; Birmili et al., 1999) and the Aerodynamic Particle Sizer (APS Model 3320, TSI, Inc., Shoreview, MN USA) that measure magnitudes of aerosols with diameters of 3 nm to 10 µm. Shen (2009) parameterized aerosol distributions to three modal lognormal size distributions according to the seasonal average of the dataset.

Figure 2

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	Figure 2 Sensitivity of the phase function to the real part of the complex refractive index under (a) the average status, (b) new-particle generation, (c) pollution incident, and (d) dusty weather based on the dataset obtained from Wuqing station.

The detailed optimal forward-scattering angles in Shangdianzi determined in the present study are shown in Fig. 3, and the parameterized distributions are shown in Table 3. It is obvious that the relative deviations of the phase function were less than 10.0% when θ was in the range of 30° to 45°. During spring and autumn, θ was slightly smaller than that in winter and summer. However, the changes in all of the aforementioned seasonal angular ranges were significantly smaller than those in the dust intrusion incident (see Fig. 2). Furthermore, the relative deviations of the phase function were less than 5.0% when the forward-scattering angles ranged from 37° to 40° (Table 3). Because the aerosol models in Shangdianzi are typical of those in North China Ke and Yang, 2007; Su et al., 2009), they are considered to be suitable for retrieving forward-scattering parameters, such as extinct coefficient, in this region with the same forward-scattering angles. This conclusion corresponds to the results of observational data recorded in Wuqing ( Fig. 2a; Liang, 2012).

The study introduced a new detection theory based on the forward-scattering of atmospheric aerosols and presented three criteria for forward-scattering retrieval to quantitatively analyze the extinction coefficients of aerosols. The sensitivity of the phase function to the real part of the complex refractive index for typical aerosol size distributions was determined through BHMIE. The results are summarized in the following points:

1) The phase function was insensitive to the changes of the real part of the complex refractive index near 33° in the case of Jaenicke urban aerosol model ( Jaenicke, 1993). The relative deviations of the phase function were less than 5.0% at that angle. This result is the theoretical basis for the selection of forward-scattering angles for the previous instruments of visibility meters and PWIs.

Figure 3

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	Figure 3 Sensitivity of the phase function to the real part of complex refractive index recorded at Shangdianzi station during (a) spring, (b) summer, (c) autumn, and (d) winter.

Table 3

Table 3

Table 3 Seasonal parameterized size distributions and their insensitive angles recorded at Shangdianzi station. Type Mode I Mode II Mode III RD ≤ 10% (degree) RD ≤ 5% (degree) N1 r p1 (nm) σ g1 N2 r p2 (nm) σ g2 N3 r p3 (nm) σ g3 (a) Spring 1.86e4 6.5 2.01 1.02e4 27.5 2.00 6.77e3 95.5 1.69 30-45 37-40 (b) Summer 1.09e3 9.5 1.65 6.06e3 29.0 1.93 3.76e3 102.5 1.64 30-47 37-42 (c) Autumn 1.00e4 6.5 1.79 6.93e3 24.0 2.05 3.85e3 96.5 1.68 30-46 36-40 (d) Winter 1.03e4 5.5 1.59 6.37e3 26.5 2.03 5.34e3 88.5 1.67 30-49 37-42

Table 3 Seasonal parameterized size distributions and their insensitive angles recorded at Shangdianzi station.

2) The numerical simulation showed that the relative deviations of phase function were less than 10.0% in the forward-scattering angles from 30° to 52°, and the relative deviations were less than 5.0% in vicinity of 37°. The types of particle size distribution of new particle generation and pollution incidents had limited influence on the selection of the optimal forward-scattering angles. However, the range of these insensitive angles shifted by ~10 degrees for the dust intrusion incident, and the relative deviations were less than 5.0% within 0° to 3°. This process can be used as an additional selection method for optimal forward-scattering angles in desert areas or areas with heavy dust pollution.

3) The observational data from the Shangdianzi regional atmospheric background station showed that the optimal forward-scattering angles were in the range of 37° to 40° in North China, which had limited influence on seasonal changes of aerosol size distributions.

For accurate retrieval of the extinction coefficients of atmospheric aerosols, the optimal forward-scattering angles are needed. However, due to the variety in actual aerosol size distribution models with time, locations, species, and components, the errors from this method necessitate more discussion.

The above analysis was used as the basis for design of the forward-scattering angles of PWIs. A comparison of the measurements of PWIs with those of various forward-scattering angles by IAP and by other manufacturers should be conducted in the near future. Moreover, the aerosol models and complex refractive index under various weather conditions and regions need further study to determine the optimal forward-scattering angles for reality aerosol conditions in the entire country of China.