The instrument setup is schematically shown in Fig. 1a. Firstly, the dried sample aerosols are guided to a X-ray soft diffusion charger and then lead to a DMA (Model 3081, TSI, USA). The quasi-monodisperse aerosols that pass though the DMA at a given diameter are then drawn into an SP2 to measure the aerosol-scattering properties with a flow ratio of 0.12 L min-1 and a condensation particle counter (CPC; Model 3776, TSI, USA) to count the aerosol number concentration with a flow ratio of 0.28 L min-1. Thus, the sample flow (Qa) of the DMA is 0.4 L min-1. Accordingly, the sheath flow (Qsh) of the DMA is 4 L min-1. The DMA is set to scan the aerosol diameter from 12.3 to 697 nm over a period of 285 s and repeats after a pause of 15 s. The combination of the DMA, CPC and SP2 can provide information on aerosol PNSD and size-resolved RRI.

On 8 June 2018, the measurement system was employed at the field measurement of the AERONET station of BEIJING_PKU (39∘59′ N, 116∘18′ E) to test the reliability of retrieving the ambient size-resolved RRI. This measurement site is located in the northwest of the city of Beijing, China, and is about 1.8 km north of the Zhongguancun, Haidian district, which is one of the busiest areas in Beijing. It is surrounded by two main streets: Zhongguancun North Street to the west and Chengfu Road to the south. This site can provide representative information on the urban roadside aerosols (Zhao et al., 2018).

When a voltage (V) is applied to the DMA, only a narrow size range of aerosol particles, with the same electrical mobility (Zp), can pass through the DMA (Knutson and Whitby, 1975). The Zp is expressed as 2Zp=Qsh2πVLln⁡r1r2, where Qsh is the sheath flow rate, L is the length of the DMA, r1 is the outer radius of annular space and r2 is the inner radius of the annular space. The transfer function refers to the probability that a particle with a certain electrical mobility can pass through the DMA. For a given V, the transfer function is shaped like a triangle, with the peaking value of 100 % and a half width (HW) of 3ΔZp=ZpQaQsh. The aerosol Zp, which is highly related to the aerosol diameter (Dp) and the number of elementary charges on the particle (n), is defined as 4Zp=neCDp3πμDp, where e is the elementary charge, μ is the gas viscosity coefficient, and C(Dp) is the Cunningham slip correction that is defined by 5C=1+2τDp1.142+0.558e-0.999Dp2τ, where τ is the gas mean-free path.

Based on the discussion above, the aerosols that pass through the DMA with the same Zp can have different Dp values and different elementary charges.

The SP2 is a widely used instrument that can measure the optical properties of every single particle. The measurement principle and instrumental setup of the SP2 have been discussed in detail previously (Stephens et al., 2003; Schwarz et al., 2006) and will be briefly described here. When the sample aerosol particles pass through the continuous Nd:YAG laser beam at 1064 nm with the circulating power of about 1 mW cm-2 in the cavity, eight sensors distributed at four directions synchronously detect the emitted or scattered light by using an avalanche photodetector (APD) at different angles (45 and 135∘). For each direction, the two APDs sample the same signal with different sensitivities to get a wider measurement range. The low-gain channels are less sensitive to the measured signal and can be used to measure the stronger signal of larger particles. Accordingly, the high-gain channels are more sensitive to the measured signal and can be used to measure the weaker signal of smaller particles. The optical head of the SP2 is shown schematically in Fig. 1b.

In this study, we utilize signals from four channels of the SP2: two of them measure the scattering signals, and another two measure the incandescent light between 350 and 800 nm. The peak height (H) of the incandescence signals is used to infer whether the sampled aerosol contains black carbon (BC). If the H of the incandescence signal is larger than 500, the sample aerosol contains BC and the scattering signals should deviate from the signals of pure scattering aerosols. Those sample aerosols are not considered when dealing with the aerosol-scattering signals. This is achieved by just studying the signals when the particles are recognized as pure scattering particles.

Despite some aerosol particles being internally mixed with a small BC core, whose incandescence signal is below the detection threshold of SP2, we demonstrate that these particles have little influence on the retrieved aerosol RRI. At the same time, there are some weakly absorbing organic components that absorb light intensity in the near-infrared range, which were termed as brown carbon (BrC). These BrC components have insignificant influence on the retrieving of the aerosol RRI, which will be discussed in detail in Sect. 4.2. Thus, the imaginary part of complex refractive index is set to zero in the following discussion.

From Fig. 1b, the APDs of the SP2 receive signals that were scattered by the sampled aerosols in a certain small range at 45 and 135∘. Thus, the scattering intensity (S) measured by the APD can be expressed as 6S=C0⋅I0⋅σ⋅(PF45∘+PF135∘), where I0 is the laser's intensity, σ is the scattering coefficient of the sampled aerosols, PF45 and PF135∘ are scattering phase function at 45 and 135∘ respectively of the sampled aerosols, and C0 is a constant that is determined by the distance from the aerosol to the APD and the area of the APD. The scattering intensity of the aerosol is recorded as the H of the scattering signals in SP2. The following calibration studies show that the scattering intensity S is highly related to the H measured by SP2. Therefore, the SP2 can be used as a powerful tool to measure the scattering signals of the sampled aerosols, thus determining the corresponding scattering intensity.

Based on the Mie scattering theory, the scattering coefficient σ can be calculated by integrating the square of scattering intensity function Q(θ,x,RRI) from 0 to 180∘. Angle θ is defined as the angle between the light incident direction and scattering-light direction. The size parameter x is defined as x=πDpλ, where λ is the light incident wavelength. The scattering phase function can be directly derived from Sθ,x,m, too. Therefore, the σ, PF45∘ and PF 135∘ in Eq. (6) are determined by the Dp and RRI of the aerosol. The amount of scattering signals from the sample aerosol varies with the aerosol Dp and RRI (Bohren and Huffman, 2007). The scattering intensity at different aerosol diameters and RRI is calculated based on Eq. (6) and shown in Fig. 2. The C0 is assumed to be 1 here. From Fig. 2, we can see that the aerosol-scattering intensity increases monotonously with the increasing aerosol RRI at a given Dp, which makes it possible to retrieve the aerosol RRI with given Dp and the scattering intensity.

Bridging the scattering H values measured by the SP2 scattering channel and the scattering intensity S defined by Eq. (6) is achieved by calibrating the SP2 with ammonium sulfate. The instrument setup of the calibration procedure is the same as that described in Sect. 2.1. The diameters of the aerosols passing through the DMA are manually changed from 100 to 450 nm with a step of 10 nm. For each diameter, the scattering H value and incandescence signal of every particle are analyzed. When calibrating, there is no aerosol that has an incandescence signal exceeding 1000 (this value depends on the stability of the instrument and working conditions; this can be different for different instruments), which means that the SP2 works stably and the incandescence signal channel can distinguish the BC-containing aerosols well. With the calibration, the relationship between the measured H and theoretically calculated S can be determined.

The procedure of retrieving the RRI is summarized as follows: (1) measuring the scattering H values at a given Dp, (2) transferring the H into to S by the established relationship from calibration, and (3) calculating the refractive index with the given Dp and S by using Eq. (6).

Figure S1 in the Supplement gives the aerosol-scattering H probability distribution under different aerosol diameters. For each diameter, the distributions of the scattering H may have more than one mode for both the high-gain and low-gain channels. The following discussions would give an explanation about the multiple mode distributions of H.

For each mode, the number of recorded aerosol particles at a given H is fit by the log-normal distribution function 7NH=N02πlog⁡(σg)⋅exp⁡-log⁡H-log⁡(H0)2log⁡2σg, where σg is the geometric standard deviation, H0 is the geometric mean value of H and N0 is the number concentrations for a peak mode. The geometric standard deviation is highly related to the half width of the transfer function (Eq. 3). The H0 is further used for discussion in the following part.

The H0 values corresponding to different elementary charges are labeled with different markers in Fig. 3. The σg is fitted to be a small range at 1.182±0.02 for different modes and different aerosol diameters. In the following discussion, we conclude that the different H0 values in Fig. 3 represent the aerosols being charged with a different number of elementary charges. Based on the Mie scattering theory (Bohren and Huffman, 2007), the scattering intensity increases with increasing Dp, which implies that the H0 of the singly charged aerosol should increase with the increment of Dp. Thus, the black square markers in Fig. 3 represent the aerosols that are singly charged. At the same time, the relationships between the H0 and Dp can be interpolated.

Other colored markers represent the aerosols having more than one charge. We calculated the corresponding diameter (D̃p) of the aerosols that share the same Zp but different charges with those particles that have a diameter of Dp with one charge. Next the corresponding H0̃ at D̃p ia calculated. Then the relationship between H0̃ and Dp is shown in the dashed line in Fig. 3a. From Fig. 3a, the calculated H0 shows good consistency with the measured H0.

From the discussion above, we conclude that the SP2 can only detect those ammonium sulfate aerosols with the diameter larger than 160 nm. However, the ambient aerosol RRI is always lower than that of ammonium sulfate (Liu and Daum, 2008); thus the lower detecting limit of the ambient scattering aerosols should be larger than 160 nm. The measured H0 values of the SP2 scattering low-gain channel signals are shown in Fig. 3b. From Fig. 3b, the same results can be deduced as those of the high-gain channel signals.

Figure 4a gives the relationships between the calculated scattering intensity and the SP2 aerosol-scattering H0 at different diameters. When calculating the scattering intensity, the RRI value of ammonium sulfate is set to 1.521 (Flores et al., 2009), and the C0 in Eq. (6) is set to unity. The aerosol-scattering intensity shows good consistency with the peak height (R2=0.9992), which to some extent reflects the high accuracy of our proposed method. When regressing the scattering intensity on the measured peak height, the value 0.36 was obtained for the slope, which means that the scattering intensity can be calculated by multiplying the peak height by a factor of 0.36.

Ammonium chloride is used to validate the method of deriving the RRI from SP2. The RRI value of ammonium chloride is 1.642 (Lide, 2006). The scattering H of the ammonium chloride under different diameters is measured and analyzed. Figure 4b shows the comparison between the measured scattering high-gain peak heights and the theoretical peak heights at different aerosol diameters. Results show that the measured peak heights and the calculated ones are well correlated with R2=0.9994, which means that the DMA and SP2 can be used to derived the aerosol RRI with high accuracy.

Figure S2 gives the corresponding results of the scattering low-gain channel. In Fig. S2, the relationship between the aerosol-scattering peak height of the low-gain channel and the scattering intensity is determined. At the same time, the comparison between the measured peak height and the calculated peak height shows good consistency, too.

Figure 5 shows the measured average probability distribution of the ambient size-resolved RRI and the measured mean PNSD over 2 h during the measurement. From Fig. 5, we can see that the derived RRI is 1.46±0.02 and does not vary significantly with a diameter between 199 nm and 436 nm. The aerosol chemical component may not vary significantly for different diameters during the measurement. Another field measurement shows that the measured RRI varies significantly from 1.47 at 198 nm to 1.54 at 450 nm, as shown in Fig. S4.

The measured aerosol PNSD during the measurement has a maximum of 26 400 # cm-3 at 107 nm. The mass concentration of the BC measured by the SP2 is 6.31 µg m-3. Based on the measured PNSD and the measured RRI, the size distribution of the scattering coefficient is calculated based on the Mie scattering theory. The results in Fig. 5 show that the measured RRI diameter range covers most of the aerosols that contribute a fraction of 0.63 to the aerosol-scattering properties, with an integrated scattering coefficient at 385 Mm-1. Thus, the derived size-resolved RRI of this range is representative of the ambient aerosol-scattering properties.