# Ambient Atmospheric Aerosol Extinction Coefficient Reconstruction from PM2.5 Mass Concentrations and Application to Haze Identification in China

Lina Gao1, Peng Yan This email address is being protected from spambots. You need JavaScript enabled to view it.1, Jietai Mao2, Xiaochun Zhang1, Xiaoling Zhang3,6, Yongxue Wu3, Junshan Jing1, Jianming Xu4, Xuejiao Deng5, Wenxue Chi1

1 Meteorological Observation Center, China Meteorological Administration, Beijing 100081, China
2 School of Physics, Peking University, Beijing 100871, China
3 Beijing Meteorological Service, Beijing 100089, China
4 Yangtze River Delta Center for Environmental Meteorology Prediction and Warning, Shanghai 200030, China
5 Institute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou 510080, China
6 School of Atmospheric Sciences Chengdu University of Information Technology, Chengdu 610225 China

Revised: January 21, 2021
Accepted: February 2, 2021

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Gao, L., Yan, P., Mao, J., Zhang, X., Zhang, X., Wu, Y., Jing, J., Xu, J., Deng, X., Chi, W. (2021). Ambient Atmospheric Aerosol Extinction Coefficient Reconstruction from PM2.5 Mass Concentrations and Application to Haze Identification in China. Aerosol Air Qual. Res. 21, 200386. https://doi.org/10.4209/aaqr.200386

## HIGHLIGHTS

• An aerosol extinction coefficient reconstruction method is introduced in this study.
• Linear regression is used to decrease the bias between calculations and observations.
• The threshold of the extinction ratio are selected to identify the haze and fog weather phenomena.

## ABSTRACT

This study developed a method of reconstructing the aerosol extinction coefficient based on hourly observations of the fine-particle (PM2.5) mass concentration, relative humidity (RH), and visibility at 9 stations in China between 2014 and 2015. First, we applied κ-Kӧhler theory to evaluate the number concentration distribution of the fine particles under ambient conditions from the PM2.5 mass and then used Mie theory to calculate the aerosol extinction coefficient. Second, we established the reconstruction model and identified reference values for the relevant parameters. After sensitivity tests confirmed good agreement between the extinction coefficients obtained through combinations of various values and those resulting from the reference values, linear regression was employed to reduce the discrepancy between the reconstructed and the observed coefficients. A closure study enabled us to determine the threshold of the extinction ratio (β/βObs) and identify haze and fog weather phenomena at the stations. Finally, we assessed the bias in the predicted number of hours with haze for 61 stations in China by comparing the estimates derived from different values for the model’s parameters with those derived from the reference values and found a relative bias of less than 15% for approximately 99.8% of the stations, indicating the feasibility of our approach for detecting haze.

Keywords: Aerosol extinction reconstruction, Haze and fog, Identification

## 1 INTRODUCTION

Low-visibility events have frequently occurred in many regions in China due to intense industrial activities and the high population density during recent years, and as a result, high aerosol loadings cause a series of problems affecting human health, economics and climate (Charlson et al., 1987; Tegen et al., 2002; Yu et al., 2002; Chan and Yao, 2008; Zhang et al., 2015). Aerosol particles can directly degrade the visibility through the extinction effect in the visible light spectrum (Yu et al., 2014). However, low-visibility episodes (e.g., with a visibility less than a few hundred meters) can also be caused by water droplets or ice crystal or aerosol hygroscopic growth under high-humidity conditions (Chen et al., 2012; Deng et al., 2016). For example, particles with a high hygroscopicity have been observed in the North China Plain (NCP) (Meier et al., 2009; Liu et al., 2011; Wu et al., 2017; Liu et al., 2020). It has also been revealed that the occurrence of severe haze events is closely related to hydrophilic inorganic water-soluble ions, including sulfate, nitrate and ammonium, in the Yangtze River Delta (YRD) region (Leng et al., 2016). A high ambient humidity can increase the aerosol liquid water content and enlarge the aerosol particle diameter, thereby enhancing the extinction effect and degrading the visibility in the Pearl River Delta (PRD) region (Deng et al., 2016). On the basis of the aerosol hygroscopic observations mentioned above, it is necessary to investigate the statistical relationship between the atmospheric aerosol concentration and visibility under the influence of humidity.

Closure studies can be applied for the estimation of the uncertainty of measurement techniques or numerical models. Many studies exist on the reconstruction of light extinction from aerosol measurements, and a relatively good agreement has been achieved with direct observations. For example, Ma et al. (2011) calculated the dry aerosol scattering coefficient from particle number size distribution (PNSD) observations under different mixing state assumptions with a modified Mie model and reported good correlation coefficients (R > 0.98) between their calculations and direct measurements by nephelometers. Eichler et al. (2008) derived the ambient PNSD from dry PNSD and size-dependent particle hygroscopic growth factors and found that compared to Raman Lidar retrievals, the extinction coefficient under the ambient relative humidity (RH) was suitably estimated with a mean bias less than 3%. Regression equations of the light extinction were also developed on the basis of the aerosol volume concentration and RH with a good agreement between the regression calculations and visibility measurements (Chen et al., 2012).

In addition, there are many other studies on aerosol extinction coefficient reconstruction from the aerosol mass concentration. The Interagency Monitoring of Protected Visual Environments (IMPROVE) method is one basic protocol to reconstruct aerosol light extinction properties from the aerosol chemical composition, although a certain bias exists with direct observations (Lowenthal and Kumar, 2003; Tao et al., 2012; Fu et al., 2016). Focusing on the over- or under-prediction of extinction for different haze periods with the IMPROVE method, many revised algorithms have been developed, and a better agreement has been achieved (Ryan et al., 2005; Wang et al., 2016; Wang et al., 2017; Pitchford et al., 2019). A notable correlation (e.g., R2 = 0.8 for the NCP) between the extinction coefficient and aerosol mass concentration was observed by Luan et al. (2018). Studies have used the mass extinction efficiency to establish quantitative relationships between the ambient extinction coefficient (visibility) and fine-particle (PM2.5) mass concentration (Cheng et al., 2017). Many different models have also been developed to estimate the long-term historical or spatial-temporal PM2.5 concentration from ground visibility monitoring data or satellite retrieval products (Han et al., 2016; Liu et al., 2017; Zeng et al., 2018) since Kastex et al. (1969) introduced the parameter fit equation between the aerosol scattering hygroscopic growth factor f(RH) and RH. In this study, the aerosol extinction coefficient is reconstructed from PM2.5 and RH observations based on statistical methods under assumptions for PNSD and aerosol density and hygroscopic growth, and aerosol extinction closure estimation has been conducted. The results of this study will provide a quantitative relationship between the ambient visibility, PM2.5 mass concentration and RH, and offer a practical method to distinguish haze and fog.

In this paper, a brief introduction of the data and method for aerosol extinction coefficient reconstruction is presented first, followed by the sensitivity analysis and its correction method for reconstructed ambient atmospheric extinction coefficients; and the closure study of the aerosol extinction method and its application for haze identification are given next. Summary and discussions are given in the end.

## 2 DATA

Hourly PM2.5 and PM10 mass concentration data from 2014 to 2016 were obtained from the Air Quality Monitoring Network of the Ministry of Ecology and Environment and the China Atmosphere Watch Network (CAWNET) of the China Meteorological Administration (CMA) (Wang et al., 2015; Gao et al., 2020; Zhang et al., 2020). The data in 2016 are used for method evaluation. High-quality hourly meteorological parameters are acquired from the National Meteorological Information Center of the CMA (http://idata.com). Most meteorological and aerosol monitoring stations are not collocated. Hence, only the aerosol monitoring stations with corresponding meteorological observations within 3 km are considered in this study. Strict data quality control was performed for the analysis. Routine maintenance and calibration procedures for aerosol equipment are referenced according to relevant station logging files, and the nonlinear relationship between the visibility, PM2.5 and RH is also considered for station selection, referring to Chen et al. (2012) (shown in Fig. 1), while data with precipitation are removed. In addition, meteorological and aerosol observations at 61 stations in China are also adopted to evaluate the applicability of the method.

Fig. 1. The site locations of the 9 aerosol monitoring stations in China (blue dot) and scatter plot of the visibility (V) against RH-PM2.5 at each station from 2014–2015. The number (Num) in each panel denotes the validated data (in hours) after precipitation and sand/dust hours were removed. The red triangles denote the site locations of the 61 stations for method evaluation in China. And the lime plus denotes the location of SDZ.

Data were also screened to eliminate the influence of sand weather. It has been reported that the mean mass concentration ratio of fine particles PM2.5 to PM10 (PM2.5/PM10) is above 0.5 at most stations in China except for Lhasa in Tibet (0.41) from 2006–2014 (Wang et al., 2015). The PM2.5/PM10 ratio gradually decreases to approximately 0.2 when sand/dust storms occur (as indicated in Table 1). Thus, observations with PM2.5/PM10 ratios lower than 0.5 are treated as affected by sand/dust storms and removed in this study.

## 3 METHOD FOR AEROSOL EXTINCTION COEFFICIENT RECONSTRUCTION

Observational studies of aerosol optical properties and aerosol size distributions in China suggest that PM2.5 contributes more than 80% of the aerosol extinction coefficient under polluted conditions, and the aerosol extinction coefficient can be suitably estimated from the PM2.5 mass concentration (Ma et al., 2011). In this study, a method based on the Mie model (Wiscombe, 1979, 1980) is applied to reconstruct the extinction coefficient from the PM2.5 mass concentration under assumptions of the aerosol size distribution and hygroscopic growth. The introduction to the related parameters and reconstruction method are as below.

### 3.1 Aerosol Complex Refractive Index

The dry aerosol complex refractive index (dry) is obtained from studies in northern China (Chen et al., 2012; Ma et al., 2015). The “wet” aerosol complex refractive index () under ambient conditions is calculated based on the two-component (dry aerosol and water uptake) aerosol model (Chen et al., 2012; Ma et al., 2015):

where Ddry is the diameter of dry aerosol particles, and Dwet is the diameter of wet aerosol particles (Wex, 2002; Ma et al., 2011).

### 3.2 Aerosol Diameter under Wet Conditions

The calculation of ambient aerosol extinction coefficient required the size of wet aerosol. The size parameter (x) of wet aerosol at wavelength of incident light (λ) is expressed as:

where ambient aerosol particle diameter Dwet can be calculated through the κ-Kӧhler theory (Kӧhler, 1969; Petters and Kreidenweis, 2007) as described in Eq. (3):

where S is the water vapor saturation ratio, which is equivalent to RH under unsaturated conditions (i.e., particles are not activated); κ is the hygroscopicity parameter; σs/a is the surface tension coefficient of water; Mw is the mole weight of water; R is the gas constant; T is the ambient temperature; and ρw is the density of water. Iterative method is adopted to solve the value of Dwet.

The total aerosol volume concentration (V) can be obtained from the aerosol mass concentration (M):

Aerosol density is affected by aerosol chemical compositions and their mixing state. Aerosol density for PM2.5 can be ranged from 1.2–1.8 in China (Hu et al., 2012; Fan et al., 2018).

The diameter of dry aerosol Ddry can be calculated from V when the aerosol size distribution is assumed. Field observations conducted in some regions in China, including the NCP, YRD, and PRD regions, show that the aerosol volume distribution mainly has two modes with one major mode (at about 300–500 nm) and a second mode (> 3 µm) (Chen et al., 2006; Yue et al., 2013; Chen et al., 2014; Peng et al., 2014; Kuang et al., 2016). The major mode mainly contains accumulation-mode particles, which are the most important contributor to aerosol light extinction, while the second mode contains coarse-mode particles whose contribution to light extinction can generally be neglected (D’Andrea et al., 2015; Ma et al., 2015; Qi et al., 2015). Thus, for simplicity, it is feasible to use a one-mode distribution model to represent the aerosol volume size distribution as:

where Dg and σg are the geometric mean and standard deviation, respectively, for dry aerosol particles. From previous studies, Dg ranges from 300 nm to 500 nm, and σg ranges from 1.4 to 2.2 in China (Peng et al., 2014; Ma et al., 2015).

### 3.3 Aerosol Hygroscopicity Parameter (κ)

The value of κ depends on the aerosol chemical composition. It can be calculated according to the simple mixing rule by the volume fraction (ϵi) and hygroscopicity parameter (κi) of the aerosol chemical composition (Petters and Kreidenweis, 2007):

For high hygroscopic aerosol component such as sulfate, κi can be above 0.5. For hydrophobic aerosol component such as black carbon, organic carbon or sand dust, κi can be below 0.1. Previous studies on the value of κ in China are summarized in Table 2. In general, the value of κ is approximately 0.3 in different regions in China. For example, using a κ value of 0.3 with a standard deviation of 20% can suitably describe the observed cloud condensation nuclei (CCN) concentration in Guangzhou (Rose et al., 2010).

## 4 SENSITIVITY ANALYSIS AND EXTINCTION CORRECTION

Based on the analysis above, the values of κρDg and σg are all within a certain range. A set of recommended values of the parameters are given in Table 3, i.e., they are set to be 0.3, 1.5 g cm3, 400 nm and 1.8 in the reconstruction model and are designated as recommended parameters. Hereafter, the reconstruction method with the recommended parameters is referred to as the “reference calculation.” The sensitivity of these parameters will be examined in the following sections.

### 4.1 Test for Hygroscopicity Parameter

When κ is equal to be 0.3, Dwet can be obtained from the κ-Kӧhler theory (Eq. (3)). Then, the size growth factor of aerosols g(RH) at different RHs (e.g., 85–95%) can be calculated with Eq. (7) (Liu et al., 1978):

Comparisons of the calculated curves of g(RH) at different RHs with field observations in different cities, including Beijing (Massling et al., 2009), Tianjin (Liu et al., 2011), Shanghai (Ye et al., 2011), and Guangzhou (Eichler et al., 2008), are shown in Fig. 2. The calculated g(RH) values are consistent with the field observations in most cases. However, the calculations are lower than the observations when RH is high and the aerosol particle size is large.

Fig. 2. Aerosol particle diameter variations of g(RH) under different RH conditions (85–95%). The curves denote the calculated g(RH) when κ is equal to 0.3, and the scatter points denote the field observations obtained in different cities in China.

Furthermore, we adopt the observations at Lanzhou (LZ) station from July to December 2015, to investigate the sensitivity of calculated βMie to parameter κ. The PM2.5 mass concentration ranged from a few µg m3 to more than 500 µg m3 at this station, which can represent the normal PM2.5 situations in China. βMie is calculated with different κ values (0.1–0.5), as shown in Fig. 3. The mean βMie values are 544, 612, and 679 Mm1 for κ values of 0.2, 0.3 and 0.4, respectively, and the correlation coefficients between βMie (κ = 0.3) and βMie (κ = 0.2 or 0.4) are 0.99 at a confidence level of 95%. Even for the nearly hydrophobic (κ = 0.1) or mostly hydrophilic aerosols (κ = 0.5), the correlation coefficients are also larger than 0.90. This means that the value of κ mainly affects the absolute values of βMie.

Fig. 3. Correlations between βMie calculated for κ = 0.3 (reference calculation) and other κ values (0.1–0.5). The asterisk denotes that the correlation coefficient has passed the t-test at a confidence level of 95%.

### 4.2 Test for Aerosol Volume Size Distribution

To investigate the impact of implementing the single-mode aerosol volume size distribution in aerosol extinction calculations, βMie is determined using the bimodal log-normal volume size distribution assumption with a second coarse-mode distribution in addition to the reference fine-mode volume distribution, and parameter values of Dg = 3 µm and σg = 1.6 are assumed for the second (or coarse) mode (Ma et al., 2015). Hence, the PM10 mass concentration is also adopted to calculate the coarse-mode volume concentration. In this test calculation, other parameters, such as κ and ρ for both modes and Dg and σg for the fine mode, are the same as those in the reference calculation. The results and a comparison of βMie calculated with the bimodal distribution to the reference calculation (single fine-particle mode) at the LZ station are shown (in gray dashed line) in Fig. 4.

Fig. 4. Correlations between βMie calculated using the reference” parameters and bimodal lognormal volume size distribution or single fine-mode distribution with different Dg and σg values at Lanzhou (LZ) station from July to December 2015. The asterisk indicates that the correlation coefficient has passed the t-test at a confidence level of 95%.

βMie calculated with the bimodal normal volume size distribution attains a very high correlation coefficient (approximately 1.00) with that calculated using the single fine mode. This implies that the contribution of coarse-mode particles is very small and can be neglected in terms of the aerosol extinction coefficient during periods without dust weather influences. The single fine-mode normal distribution can be reliably applied to describe the volume size distribution of atmospheric aerosol particles under polluted or haze weather conditions.

Another aspect of uncertainty stems from the variation in Dg and σg values, which may vary over a wide range in different regions and seasons. Thus, βMie is also calculated using the single fine-mode log-normal distribution with different Dg (100–600 nm) and σg (1.4–2.2) values, where κ and ρ remain the same as the reference calculation. The results are shown in Fig. 4 and Table 4.

The mean value of βMie calculated with different Dg and σg values ranges widely from 176.73 to 721.95 Mm1 (Table 4). However, the correlation coefficient is greater than 0.99. This is consistent with previous observation studies (Chen et al., 2012).

### 4.3 Test for Aerosol Density (ρ)

The sensitivity of the aerosol density is also evaluated. The mean βMie value calculated at LZ station from July to December 2015 is 540.59 Mm1 with ρ equal to 1.7 g m3 and the other parameters remain the same as the reference parameters. The correlation coefficient between the βMie values for ρ equal to 1.7 g m3 and 1.5 g m3 is approximately 1.00.

### 4.4 Linear Regression

From the discussions above in this section, it is found that the reconstructed extinction coefficients with the reference parameters may differ from the real values due to the site dependence of the parameters. The influence of aerosol size distribution against the reference parameters on βMie ranged from −71.1% to 18.0%. The influence of the maximum and minimum κ value against the reference κ on βMie ranged from −22.2% to 21.9%. When aerosol density increased from 1.5 to 1.7 g m3βMie decreased by −11.7%. However, the correlations of βMie between the reference calculation and the sensitivity test calculation for the different parameters agree quite well. These results suggest that the biases of the reconstructed βMie can be corrected according to the site observations. Accordingly, the linear regression method is adopted to correct the reconstructed aerosol extinction coefficients based on visibility site observations. The regression correction method is described as follows.

Firstly, from Koschmieder’s equation (Koschmieder, 1924), the observed ambient atmospheric extinction coefficient (βObs) can be obtained.

Generally, it is recognized that when RH is below 80%, even considering RH measurement errors and humidity fluctuation, fog droplets are hardly formed in the atmosphere, i.e., the light extinction of the atmosphere is only caused by aerosol particles (including the enhancement via aerosol hygroscopic growth) and air molecules. This is consistent with the guidance for haze observations issued by many organizations and researchers (Wu, 2005; WMO, 2008; CMA, 2010). Thus, the observed atmospheric extinction coefficients with RH < 80% and visibility < 10 km, which are equivalent to the ambient aerosol extinction coefficients, are used to build a correction equation for βMie. The slope (a) and interception (b) of the linear regression equation for βObs with βMie are determined through the least-squares fitting method. Therefore, corrected values of the reconstructed aerosol extinction coefficient β can be obtained by:

With the use of the data at the 9 stations in China from 2014–2015, the slope, intercept, and reconstructed and corrected aerosol extinction coefficients βMie and β, respectively, at each station are obtained, as shown in Fig. 5.

Fig. 5. Mean aerosol extinction coefficients at the 9 stations in China from 2014–2015. βMie and β are the reconstructed and corrected aerosol extinction coefficients, respectively. βObs is the aerosol extinction coefficient calculated from the visibility observations. R is the correlation coefficient between the calculated and observed aerosol extinction coefficients.

It is shown (Fig. 5) that the mean correlation coefficient (R) of the 9 stations is 0.82, with a maximum value of 0.92 at YCG station and a minimum value of 0.59 at PY station. This implies that the extinction coefficient reconstruction method performs quite well at the stations. Low correlation coefficient at PY may be related to the matching problem of PM2.5 and visibility observations. The mean biases between the reconstructed aerosol extinction coefficients and corresponding observations with and without linear regression correction at the 9 stations are −35 Mm1 (a relative bias of approximately 5%) and −87 Mm1 (a relative bias of approximately 18%), respectively. There are differences in the values of linear slope and intercept among different stations, which implies different size distribution or hygroscopicity characteristics at these stations. Considering the measurement errors in PM2.5, RH and visibility, it can be concluded that linear regression correction has effectively improved the reconstructed aerosol extinction calculation.

## 5 AEROSOL EXTINCTION CLOSURE AND APPLICATION FOR HAZE IDENTIFICATION

According to the World Meteorological Organization handbook for weather observations (WMO, 2008), haze is defined as the degradation of visibility by particles, which means that under haze conditions, light extinction of the atmosphere is mainly caused by aerosols and the enhancement of light extinction due to aerosol hygroscopic growth. Fog is another low-visibility weather phenomenon. However, under fog weather conditions, light extinction of the atmosphere is generally dominated by fog droplets, and their contributions to visibility degradation are much greater than those from aerosol particles (Elias et al., 2009). Considering that uncertainties exist in the observations and aerosol light extinction calculations, it is reasonable to assume that when the contribution of light extinction from aerosols to atmospheric extinction exceeds a certain threshold, light extinction of the atmosphere can be regarded as mainly caused by aerosols. Under such an assumption, the threshold of the contribution of light extinction from aerosols can be derived through an aerosol optical extinction closure study.

### 5.1 Optical Extinction Closure under Low-RH Conditions and the Extinction Ratio

The observations from 2016 are used to study the extinction closure under low-RH conditions. The method for light extinction coefficient reconstruction is described in the previous sections (the third section and the fourth part of the fourth section). The relationship between the calculated and observed extinction coefficients at 9 stations under RH < 80% is shown in Fig. 6. The correlation coefficient is 0.84, and the slope is approximately 0.70.

Fig. 6. Relationship between the calculated (β) and observed (βObs) extinction coefficients at RH < 80% at the 9 stations in 2016.

Since low-visibility events (i.e., visibility < 10 km) with RH < 80% are mainly caused by atmospheric aerosol particles, the calculated and corrected light extinction coefficients β should be close to the observations βObs under haze conditions, but much smaller than βObs under fog conditions. Therefore, the ratio of β to βObs (β/βObs) could be used to distinguish haze from fog. The ratio of haze identified by setting different β/βObs thresholds (Haze) against the direct observations (HazeObs), with RH < 80% and visibility < 10 km is shown in Fig. 7(a). The probability distribution function (PDF) of β/βObs for the data is also shown in Fig. 7(b). The Haze/HazeObs ratio decreases with increasing β/βObs ratio threshold (Fig. 7(a)). When β/βObs ratio threshold increases from 0.7 to 1.0, Haze/HazeObs decreased from approximately 0.9 to less than 0.6. When we set β/βObs ratio threshold to be 0.8, about 84% of haze out of the total haze samples can be identified, with the highest value 92% at LZ station and the lowest value 79% at QD.

Fig. 7. (a) Relationship between the Haze/HazeObs and β/βObs ratios and (b) the probability distribution of β/βObs at RH < 80% and visibility < 10 km at the 9 stations in China from 2014–2015.

Ideally, if the contributions of atmospheric extinction were only from fine particles and air molecules, and the aerosol model and parameters were correct, β/βObs should be approximately 1.00 when RH < 80% and visibility < 10 km. However, in actual cases, only 65% and 79% of the total observation samples have β/βObs ratios higher than 0.9 and 0.8, respectively (Fig. 7(b)). This is related to the uncertainties caused by the assumptions on aerosol model and parameters used in the extinction coefficient reconstruction method and observation errors, such as RH observation errors, and so on. This will be discussed in the following sections. Thus, we recommend a β/βObs ratio of 0.8 as the threshold value based on both identification ability and observation facts.

Conclusively, adopting the recommended β/βObs ratio threshold 0.8, about 16% of haze hour in average could not be identified, with the maximum value 20% and the minimum value 7%, implying that the uncertainty of the method can be about 16%.

### 5.2 Application for Haze Identification under High-RH Conditions

Based on the discussions above, we can apply the method and parameters described above to identify the haze weather phenomenon when RH is high, i.e., 80% ≤ RH < 95%, according to the ratio of β/βObs higher than 0.8. The haze and fog hour at the 9 stations are shown in Fig. 8. Different stations have different proportion of haze to fog hour, which may be related to the regional climate conditions and pollutant emission distributions. HZ, XJH, and YCN have higher probabilities of fog/mist than other stations. This is consistent with previous studies that reported more fog/mist days in these locations (Wu et al., 2011b). And this indirectly proves the reliability of the method. Fog mainly concentrated in southeast coastal regions (such as HZ and XJH) and Sichuan Basin but the least in northwest region, the Qinghai-Tibet Plateau and Inner Mongolia (Sun et al., 2008). Besides, mass concentration at HZ and XJH are lower than that at other stations. The reason why YCN had comparable haze and fog hour may be related to its specific terrain-related low-altitude temperature inversion (Deng et al., 2018). YCG, CP, QD, LZ, YJ, and PY have higher probability of haze hours. Firstly, this may be related to higher aerosol loadings at these stations. After all, the essence of haze is the pollution process caused by high aerosol loadings. PY has relatively low PM2.5 concentration, but has relatively high probability of haze. This may be related to its relatively high PM1 loading and its hygroscopicity growth (Yue et al., 2013).

Fig. 8. Haze and fog/mist hours, PM2.5 mass concentration, and RH at the 9 stations at 80% ≤ RH < 95% in China from 2014–2015.

### 5.3 Sensitivity of All Parameters to Haze Identification

To analyze the uncertainties of haze identification using the method presented above, we apply several combinations of parameters with different values, which are likely under real atmospheric conditions, to a series of sensitivity tests in terms of haze identification at the 61 stations. The variations in the parameters are listed in Table 5.

The relative bias of the haze hours identified with the different parameter values against the reference calculation is shown in Fig. 9. The mean value of the bias is −0.87% for the 26 sensitivity tests over 61 stations, with the Dg–σgκ combination 250 nm–2.1–0.2 has the highest negative bias −7.9%, and the combination 550 nm–1.8–0.4 has the lowest positive bias 3.4%.

Fig. 9. Haze hour bias ratio identified for the different parameters (Dg–σgκ) against the reference parameters (400 nm–1.8–0.3) from 2014–2015 at 61 stations in China.

Uncertainties of the method varies from different stations. The maximum relative bias is −16.8% for 61 stations. A total of 63.6% of all stations has a relative bias smaller than 5%, and 94.3% of all stations has a relative bias smaller than 10%, while 99.8% of all stations has a relative bias smaller than 15%. This implies that the method is feasible for haze identification. Over all, mean haze hour bias by all parameters is approximately −0.87%.

### 5.4 Uncertainties by RH and PM2.5 Observation Errors

Monte Carlo method is adopted to estimate uncertainties brought by RH observation errors. RH, visibility and PM2.5 observations at 9 stations during 2015–2016 are used. RH errors between −5% and 5% are randomly added to the RH observations when 90% ≤ RH < 95% (12,025 samples). On the basis of the reference test, 10 groups of tests have been carried out. Therefore, there are 120,250 sets of samples used. Total haze hour at 9 stations are calculated. Compared with the reference test, the mean haze hour bias is −5.2% with a standard deviation 5.5%. Thus, haze hour uncertainty brought by RH observation errors can be estimated at approximately −5.2%.

Ambient aerosol particles may be enlarged under high-RH conditions. And particles with Dwet > 2.5 µm will be cut off by the PM2.5 inlet. The influence of the size cut-off by PM2.5 inlets was estimated adopting the extinction coefficient reconstruction method proposed above. Aerosol extinction coefficients were calculated under different RH conditions with the same dry aerosol size distribution. The influence of the cut-off on aerosol extinction coefficient is estimated at < 0.4% under low-RH conditions (RH < 80%). It is between 0.6–2.5% under high-RH conditions (RH > 80%).

### 5.5 Comparisons of Different Haze Identification Methods

Traditional haze identification methods are mainly based on visibility and relative humidity. Main difference between these methods is in the selection of RH threshold. For example, one haze identification method widely used in observation service in some provinces in China is defined as follows: eliminating the low-visibility phenomena caused by precipitation, sand/dust or blowing snow; RH < 80%; and horizontal visibility < 10 km. We name the method M80. And another haze identification method widely used in scientific research is similar to the M80, except for RH < 90%, which is named M90. The method proposed in this work is named MMie.

Comparison of the haze identification results at the Beijing Shangdianzi station (SDZ; Station ID: 54421; location shown in Fig. 1) during 2015–2016 is shown in Fig. 10. It can be found that M80 identified the least haze hour and M90 identified the most. And the haze hour identified by MMie is in the middle of the two methods.

Fig. 10. Haze hours identified by method used in this study (MMie), M80 and M90 at the Beijing Shangdianzi station during 2015–2016.

## 6 SUMMARY AND DISCUSSION

This study established a model for reconstructing the aerosol extinction coefficient based on hourly observations of the fine-particle (PM2.5) mass concentration, relative humidity (RH), and visibility at 9 stations in China. We obtained the particle number concentration distribution of the dry aerosol from the PM2.5 mass and then calculated it for the wet aerosol using κ-Kӧhler theory. Finally, we evaluated the aerosol extinction coefficient by employing Mie theory.

A closure study conducted under ambient conditions allowed us to derive the threshold of the extinction ratio by comparing the estimated light extinction values to the observed ones (which were determined from the measured visibility). When the RH was low, the method proposed in this study accurately detected more than 80% of the hours during which haze occurred. When the RH was high (80% ≤ RH < 95%), however, this approach more accurately differentiated between haze and fog, which suggests that combining PM2.5 observations with visibility and RH data can enhance haze identification during operational monitoring at meteorological stations.

Although our technique for identifying haze relies on multiple assumptions about the aerosol properties, e.g., the size distribution, hygroscopicity, density, and refractive index, applying linear regression to the model predictions effectively shrank the bias, reducing the overall estimated uncertainty to approximately 16% for the data we analyzed.

## ACKNOWLEDGMENTS

This work was performed under the auspices of the National Key Research and Development Program of China (2017YFC1501702) and the National Natural Science Foundation of China (41705133 and 91644223).

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