Inversion of the haze aerosol sky columnar AVSD in central China by combining multiple ground observation equipment

Yingying Ma; Wei Gong; Lunche Wang; Ming Zhang; Zhongyong Chen; Jun Li; Jian Yang

doi:10.1364/OE.24.008170

1. Introduction

Haze is defined as a weather phenomenon wherein the atmospheric visibility is less than 10 km, resulting from dense layers of aerosol particles such as acidic chemicals, organics, black carbon (BC), and fly ash as well as dust accumulated in the air, and with a relative humidity (RH) lower than fog [1]. Since the late 1990s, a widespread layer of haze, named the “atmospheric brown cloud” (ABC), has been observed over south Asia [2]. In recent years, an increasing occurrence of haze events has been reported in China. Wuhan City is a megalopolis in central China, which is faced with many aspects of environmental pressures from demographic explosion and industrial development. Except for Beijing-Tianjin-Hebei, the Yangtze Delta region [2–5 ], and the Pearl River Delta region, the number of haze events has been gradually increasing in central China.

During a haze event, a high concentration of fine particles gathers at low altitudes, which not only pollutes the air and reduce visibility, but also affects human health. In addition, these small particles significantly affect cloud formation, and indirectly impact the Earth's radiation balance and regional climate. To further understand the mechanism of haze formation and diffusion, it is very important to analyze multiple atmospheric parameters. Columnar Aerosol volume size distribution (AVSD) is an important atmospheric parameter and a key indicator of environmental quality; in addition, it is important to understand the physical and chemical properties of aerosols. The inversion of columnar AVSD can be achieved by the retrieval of data from remote sensors like Lidar, sun-photometer, or sky radiometer [6–9 ]. However, because it suffers from some ill-posed problems, it is very difficult to get a reliable solution.

Currently, an increasing number of universities and research institutes are using CIMEL sun-photometers and joining AERONET (Aerosol Robotic Network). As the core detection network of radiometers, AERONET stations have acquired a wide and broad influence. Consequently, columnar AVSD inversion using sun-photometers has been widely used, and Dubovik’s [7] method has become the standard official algorithm. In recent years, the use of sun-photometers for numerous studies on the optical properties of aerosols and the associated radiative forcing has been reported around the world [10–12 ]. There are also several studies regarding the aerosol characteristics in China: Xia et al. [13] reported the seasonal variability of aerosol optical properties over Beijing; Wang et al. [14] analyzed the optical characteristics of aerosols in northeast China; and Che et al. [15] introduce the haze aerosol characteristics in Beijing. However, the ground-based observation stations that have joined AERONET are limited, limited observational data is publicly available, and it is difficult to conduct continuous observations over a long time. In particular, the official method used by AERONET does not use an open source code; it is therefore still difficult to obtain columnar AVSD based on sun-photometer data in some places in China.

It is well known that aerosols emitted from different sources have different physical and chemical properties [6]. Because of a wide variety of sources, the properties of atmospheric aerosol particles, such as their sizes, shapes, chemical compositions, and optical thicknesses, may be heterogeneous, and their temporal and spatial variations can be very large. Therefore, it is critical to study the haze related aerosols in central China. Although in our previous studies, we used the method developed by King 1979 for obtaining the AVSD data [16] and performed data analysis through some joint observational experimentation [17], however, we still lack credible AVSD data for the haze events.

With this background, this study focuses on the following: First, based on a joint observational experimental, the parameters of columnar AVSD over Wuhan were retrieved using the Dubovik’s method [7], and the bimodal logarithmic normal distribution of columnar AVSD was used for training the samples. Second, the AVSD on the earth’s surface was obtained by splicing the observations from the GRIMM 180 PM monitor and the TSI Scanning mobility particle sizers (SMPS). Then, a correlation between the columnar AVSD and the AVSD on the earth’s surface was established. Third, we used GA to find the optimal distribution parameters, and analyzed the characteristics of AVSD on hazy days in Wuhan. Our verification results indicated that the method proposed in this paper can be used for practical applications, and can provide valuable reference data on haze in Wuhan.

2. Observational instruments and methodology

This study was carried out in the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (LIESMARS; 30°32′N, 114°21′E), which is located in Wuhan City in central China. A series of atmospheric and radiation observation apparatuses has been installed in LIESMARS, including a CE-318 sun-photometer, a German GRIMM 180 PM monitor and a TSI SMPS. To fully exploit the advantages offered by these instruments, this study discusses the use of an effective algorithm of for conducting columnar AVSD inversion through simultaneous observations by all the three instruments.

2.1 Observational instruments

The CE-318 sun-photometer is a sun-sky scanning spectral radiometer with nine spectral channels in visible and infrared wavelengths centered at 340 nm, 380 nm, 440 nm, 500 nm, 670 nm, 870 nm, 936 nm, 1020 nm and 1640 nm [18]. Direct solar radiation is measured by this instrument by automatically tracking the position of sun, and the measured solar radiation data can be used to derive aerosol optical properties such as aerosol optical depth (AOD), Angstrom exponent (α) and single scattering albedo (SSA). The CE-318 is annually calibrated using CARSNET (China Meteorological Administration Aerosol Remote Sensing Network) reference instruments to ensure accuracy and reliability of data; detailed calibration procedures have been described in Che et al. [19]. Many researchers use it analysis the global and area AVSD characteristics [10,15 ].

The GRIMM 180 PM monitor can measure real-time aerosol concentrations for 31 particle-size segments and mass concentrations of PM1, PM2.5 and PM10,with a measuring range of 1–1500 μg/m3 and a measuring accuracy of ± 2%. The measurement principle of the GRIMM 180 PM monitor is that environmental air is sucked into the measurement chamber at a constant rate,where a laser source generates a high-frequency laser pulse. If particulate matter (PM) exists in the air, the laser light will be scattered. Then the scattered light is translated into an electrical signal and the concentration of particles is determined according to the signal intensity [20].

The TSI SMPS is an instrument for measuring the particle size of fine aerosol particles, which measures the particle size using a differential mobility analyzer (DMA) and observes the particle concentrations with a condensation particle counter (CPC) [21]. The SMPS adopts the size classification principle, which is based on particle mobility in an applied electric field. It uses a continuous scanning voltage to impart variable mobility to particles and a complex inversion method to derive particle size from the mobility spectrum. In most cases, by combining the TSI SMPS and GRIMM 180 PM monitor, we can obtain a wider range of AVSD on the earth’s surface. Unlike the sun-photometer, the columnar AVSD is acquired only for the total atmospheric column. However, the AVSD observed by TSI SMPS and GRIMM 180 include only the AVSD for the earth’s surface; the units for the AVSD on the earth’s surface and columnar AVSD are um³/um³ and um³/um², respectively.

2.2 Retrieval method

The traditional columnar AVSD retrieval algorithm and improvement algorithm used by the sun-photometer will be introduced in this part. Previously, to obtain the aerosol size distribution, King et al. (1978) proposed an AVSD inversion method that included the inversion of spectral optical depth measurements. The aerosol optical thickness of multiple wavelengths is determined by light extinction of direct sun beam measured by the sun-photometer; the extinction spectrum contains the weight information for the AVSD. The integral equation that relates AOD to AVSD can be written as

τ (λ) = \int_{r_{\min}}^{r_{\max}} Q_{e} (r, λ, m) π r^{2} n (r) d r

where

r

is the radius of the aerosol particles ;

r_{\max}

and

r_{\min}

denote the maximum radius and the minimum radius of the radius range, respectively;

m

represents the complex refractive index;

λ

corresponds to the wavelength of the incident illumination;

Q_{e} (r, λ, m)

is the extinction efficiency factor from Mie theory, which is the function of particle size parameter

x

and the complex refractive index

m

with

x = 2 π r / λ

; and

n (r)

is the unknown columnar aerosol number size distribution (ANSD). Thus, function (1) can be described as

τ (λ) = \frac{3}{4} \int_{r_{\min}}^{r_{\max}} \frac{Q_{e} (r, λ, m)}{r} v (r) d r

where

v (r)

is the columnar AVSD density in the radius range

r

to

r + d r

with

v (r) = (4 π / 3) r^{3} n (r)

. Generally,

Q_{e} (r, λ, m) / r

is expressed as kernel or weighting function in the inversion method. Function (2) can be also written as

τ (λ) = \frac{3}{4} \int_{r_{\min}}^{r_{\max}} \frac{Q_{e} (r, λ, m)}{r^{2}} \frac{d v}{d \ln r} d r

where

\frac{d v}{d \ln r}

is the logarithmic distribution of aerosol volume size.

However, this method needs tremendous artificial intervention and hypothesis, which leads to a greater uncertainty in the results. The inversion method of King et al. is used to invert spectral measurements of optical thickness only, without accounting for multiple-scattering effects in the entire range of the scattering angles [7].

Dubovik and King (2000) [7] proposed a new method by simultaneous fitting of radiances measured in the entire available angular and spectral range. This method has been extensively used in the AERONET, and it can be used to obtain multiple parameters simultaneously. However, this method is complicated and only authorized to the AERONET website. It would take a great deal of manpower to reestablish the model, and there is no guarantee of the computational accuracy. In the next section, we introduce a new method that uses partial least squares (PLS) and genetic algorithm (GA), while combining TSI SPMS, GRIMM 180 PM monitor, and CE-318 and using these three instruments to acquire the columnar AVSD.

3. New method

As mentioned earlier, Wuhan is the biggest city located in central China, with an increasing record of haze days. The remote sensing and surveying of atmosphere is poor in Wuhan as compared to the recording of haze related data in Beijing, the Yangtze Delta region, and the Pearl River Delta region. A limited number of monitoring instruments and stations and lack of an appropriate inversion algorithm aggravate the issue.

In 2014, we combined the observations from one of our experiments with the ones from the National Weather Bureau and other AERONET stations, and fortunately retrieved some columnar AVSD data by using Dubovik’s algorithm. By analyzing the data from this period, we found that most of recorded haze days followed the double lognormal normal distribution. In other words, the bimodal lognormal normal distribution can be described as function (4), but only valid hypothesis parameters of C, R and σ can describe the actual AVSD:

\frac{d V (r)}{d l n (r)} = \frac{C_{f}}{\sqrt{2 π} σ_{f}} \cdot \exp (- \frac{{(l n r - l n R_{f})}^{2}}{2 σ_{f}^{2}}) + \frac{C_{c}}{\sqrt{2 π} σ_{c}} \cdot \exp (- \frac{{(l n r - l n R_{c})}^{2}}{2 σ_{c}^{2}})

In function (4), $\frac{d V (r)}{d l n (r)}$ denotes the particle volume concentration for a range of particle radii, C is the particle volume concentration, R is the median radius, σ is the standard deviation, and f and c represent the fine and coarse particles, respectively.

The columnar ANSD N(r) can be computed by using the following formula:

N (r) \cdot r \cdot (\frac{4}{3} \cdot π \cdot r^{3}) = dV (r) / dln (r)

The real part of the complex refractive index m is usually assumed in the range of 1.33–1.6 [10]. Herein, the real part is assumed as 1.5 and the aerosol extinctive efficiency

Q_{e} (m, r, λ)

is computed by Mie theory. The modeled aerosol optical depth is computed by the following formula:

τ_{λ} = \int_{r_{\min}}^{r_{\max}} π \cdot r^{2} \cdot Q_{e} (m, r, λ) \cdot N (r) \cdot dr

The sum of squared error (SSE) between true AOD and modeled AOD of multi-wavelengths is obtained by the following formula:

\frac{1}{k} {\sum_{i = 1}^{k} (τ_{\mod i} - τ_{o b s i})}^{2}

After determining the minimum value of SSE, the corresponding R_f, R_c, C_f, C_c and σ_f, σ_c values were considered as the optimal solution.

In the method proposed above, bimodal lognormal normal distribution was used to simulate the columnar AVSD. However, many uncertain factors, such as selecting the above mentioned six microphysical parameters and finding the minimum SSE, need to be considered. In order to obtain correct distribution parameters, a method combining partial least squares (PLS) and genetic algorithm (GA) is proposed; the method was utilized to find the minimum SSE. As shown in Fig. 1 , first, we chose some AVSD training samples from the columnar and earth’s surface AVSD, and ensured that all these samples met the bimodal lognormal normal distribution. At the same time, the following functions (8-10) were used to calculate the AVSD parameters: Volume median radius, standard deviation, and volume concentrations for both the fine and coarse modes [10].

Fig. 1 The flowchart of the proposed method.

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lnR = \frac{\int_{r_{\min}}^{r_{\max}} \ln r \frac{d V (r)}{d \ln r} d \ln r}{\int_{r_{\min}}^{r_{\max}} \frac{d V (r)}{d lnr} d \ln r}

σ = \sqrt{\frac{\int_{r_{\min}}^{r_{\max}} {(\ln r - lnR)}^{2} \frac{d V (r)}{d \ln r} d \ln r}{\int_{r_{\min}}^{r_{\max}} \frac{d V (r)}{d lnr} d \ln r}}

C = \int_{r_{\min}}^{r_{\max}} \frac{d V (r)}{d lnr} d \ln r

Second, the PLS method was used because it has proven to be a very versatile method for multivariate data analysis and its application is steadily increasing in various research fields such as bioinformatics, machine learning, and chemometrics [22].

PLS is a linear multivariate method for relating the process variables X with responses variables Y. PLS can analyze data with strongly collinear, noisy, and numerous variables in both X and Y [ 23 ]. PLS reduces the dimension of the predictor variables by extracting factors or latent variables that are correlated with Y while capturing a large amount of variations in X. This means that PLS maximizes the covariance between matrices X and Y. In PLS, the scaled matrices X and Y are decomposed into score vectors (t and u), loading vectors (p and q), and residual error matrices (E and F):

\begin{array}{l} X = \sum_{I = 1}^{a} t_{i} p_{i}^{T} + E \\ Y = \sum_{I = 1}^{a} u_{i} q_{i}^{T} + F \end{array}

where

a

is the number of latent variables. In an inner relation, the score vector t is linearly regressed against the score vector u.

u_{i} = b_{i} t_{i} + h_{i}

where b is a regression coefficient that is determined by minimizing the residual h. It is crucial to determine the optimal number of latent variables and cross-validation is a practical and reliable way to test the predictive significance of each PLS component [24]. The principal disadvantage of PLS is that it gives explanation of structure relationship between process variables and response variables are too abstract, and difficult to understand. Subsequently, it cannot provide quantitative explanation for the relationship between process variables and response variables. Therefore, following this step, we developed a prediction model.

Finally, we used the observed ASD for the earth’s surface to predict the columnar ASD parameters, and these findings were treated as the base values. By converting columnar ASD to columnar aerosol number concentration, and calculating the model AOD, we obtained the sum of squared error (SSE) between the true and modeled AOD. GA is a special search algorithm inspired by natural selection and natural genetics. GA is a highly parallel, stochastic, self-adaptive, and heuristic search technique based on ‘genetic inheritance and Darwinian strife for survival’. The GA approach has been widely used in physical, life and computer sciences and also in engineering [25]. In this work, GA was used to find the optimal solution, that is, the minimum SSE between the true and modeled AOD.

4. Results and discussion

All of the experimental data for this work was obtained from the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, located in Wuhan City in central China. In Wuhan, haze often occurs in fall, winter and spring, but also during the Spring Festival (Chinese New Year) in February when students have a winter break; the quality of the observational data is this difficult to be guaranteed. Considering this, the spring data were deleted and only fall and winter records from 2015 to 2016 were used. Further, the atmospheric environmental quality monitoring data from the Wuhan Environmental Monitoring Center were downloaded and reliable haze records were obtained. For all the sites, East Lake High-tech Development Zone was chosen, because it is the nearest station to Wuhan University. As shown in Table 1 , from October, 2014 to January, 2015, there are 11, 9, 4 and 19 days where the Air Quality Index (AQI) exceeded 150 (150<AQI<200, belong to moderate pollution; 200<AQI<300, belong to heavily polluted; 300<AQI, belong to severely polluted), and several haze events occurred as well. In these haze records, the daily mean of PM2.5 from October 2014 to January 2015 are 146, 188, 175 and 191 um/m³, respectively. It is obvious that PM2.5 mean value is showing an increasing trend in this period, and they are much higher than other months.

Table 1. Haze Records from the East Lake High-tech Development Zone Station

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The observational data form the LIESMARS instruments was combined with the haze records of the East Lake High-tech Development Zone station, while the haze records for the time periods when instruments underwent maintenance or when no data were available were removed. Table 2 gives detailed information on the experimental data. After extracting the limited columnar AVSD records, and deleting some incomplete records from the GRIMM 180 PM monitor and TSI SMPS, usable records for 13 days were obtained (numbers shown in bold). Next, we looked for records which conformed to bimodal logarithmic normal distribution, and which also conformed to triple modal logarithmic or multi-modal normal distribution. For the 13 usable days, 64 such records were obtained; in case quadratic Gaussian fit and R-square>0.97, the data were considered to conform to bimodal logarithmic normal distribution, and when cubic Gaussian fit and R-square>0.95, the records were believed to conform to triple logarithmic normal distribution; the rest of the cases were considered to conform to multi-modal logarithmic normal distribution. Table 3 gives detailed information on the data obtained after the analysis. AOD indicates the aerosol optical depth; CRI is complex refractive index; and SSA is single scattering albedo.

Table 2. Experimental Data Details of the Ground Observation Equipment

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Table 3. Atmosphere Characteristics of Different Columnar AVSD Categories

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From Table 3, it can be observed that 41 records conform to bimodal logarithmic normal distribution. Compared with the other AVSD categories, these have the lowest AOD and PM2.5 values of 0.7926 and 109, respectively. The SSA is defined as the ratio of scattering coefficient and total extinction coefficient. SSA is mostly dependent on the aerosol size, concentration of the absorbing components, and its mixture state with non-absorbing components. The records that conform to triple logarithmic normal distribution have the highest SSAT, SSAF, and SSAC (total, fine and coarse particles) values of 0.8566, 0.8810, and 0.6209, respectively. This is likely because the particle concentrations increase with the AOD, resulting in an enhanced scattering effect due to the hygroscopic properties of the particles. Complex refractive index is an important parameter in determining the scattering and absorption properties of light, and is closely related to the hygroscopic properties and chemical compositions of the aerosol particles and atmospheric humidity. The real part of the refractive index represents the scattering ability and the imaginary part represents the absorption capacity of particles. Clearly, the scattering ability and absorption capacity of the records conforming to multi-modal logarithmic normal distribution are the most striking among all, while there is no obvious difference between other two categories. When the imaginary part of the complex refractive index is equal to 0.0315, the SSAT has the minimum value of 0.8078; this is further proof that Dubovik’s algorithm shows good consistency and the results are reliable. However, a large number of haze records are difficult to be obtained using the Dubovik’s method with an increase in the AOD and PM2.5 values. Therefore, the main objective of this work was to describe the columnar AVSD under conditions of relatively small AOD values during a haze event.

As shown in Fig. 2 ,we plotted gaussian distribution to the fit the bimodal logarithmic normal distribution columnar AVSD, where the grey shaded region indicates the uncertainty value on the AERONET data. In Dubovik’s algorithm, the algorithm returns the columnar AVSD dV (r)/dlnr in 22 equidistant logarithmic radial size bins spanning the range of particle radii of 0.05 ≤ r ≤ 15 µm, normalized to the value of the total volume concentration of aerosols in µm3/µm2. The mean value of the AVSD is shown by the blue line; this columnar AVSD was fitted by using two logarithmic normal distributions shown as the red lines; and R-square is 0.967. The volume concentration of fine particles is greater than those of coarse particles, being 0.1083 and 0.0863, respectively. The proportion of fine particulate is larger on haze days than on common days, obviously. Further, the volume concentration of both the fine and coarse particles vary widely on haze days. All of these characteristics showed distinguished differences with regard to the foreign urban columnar AVSD [26]. For example, in addition to the much higher volume concentration for both the fine and coarse modes, volume median radii of the fine mode is higher, and coarse mode is lower than Goddard Space Flight Center (GSFC)-Washington, US [26], respectively.

Fig. 2 Columnar AVSD on haze days. The blue line indicates the mean value of the AVSD, and the red lines express the bi-lognormal fit. The grey band represents the uncertainty of columnar AVSD. All the data were obtained using the Dubovik’s method.

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Considering the 41 observational records by the sun-photometer, the AVSD on the earth’s surface as estimated by the TSI SMPS and GRIMM 180 PM monitor are shown in Fig. 3 . Figure 3(a) shows the particles number concentration on December 24, 2014 and Fig. 3(b) is the corresponding volume concentration. By splicing the data from the TSI SMPS and GRIMM 180 PM monitor, and comparing Figs. 2 and 3 , the AVSD for the earth’s surface was found to have two distinct modes. Therefore, we used the columnar AVSD parameter calculation formulas, shown in functions (8)-(10), to calculate the AVSD for the earth’s surface. The clear differences between the columnar distribution and the one on the earth’s surface in Fig. 4 prove the AVSD for the earth’s surface to be the guiding parameter. In Figs. 4(a) and 4(b), all the values of the standard deviations of columnar AVSD and volume median radii of fine particles are greater than those for the AVSD on the earth’s surface. Even if some of the points did not comply with this rule, the overall trend is still quite clear. The AVSD for the earth’s surface showed greater values for the ratio of volume concentration of fine to coarse particles, standard deviation of coarse particles, as well as the volume median radii of coarse particles. It can thus be inferred that the parameters of the AVSD for the earth’s surface can be used to assess the columnar AVSD.

Fig. 3 The ASD for the earth’s surface expressed by (a) the particles number concentration on December 24, 2014; and (b) the corresponding volume concentration. The data were obtained by splicing the synchronous observations of the TSI SMPS and GRIMM 180 PM monitor.

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Fig. 4 Comparison of the distribution parameters between the columnar AVSD and AVSD for the earth’s surface. Images on the left: comparison of different samples values; images on the right: boxplots of the AVSD on the earth’s surface and columnar AVSD; (a) Standard deviation of fine particles; (b) Volume median radii of fine particles; (c) The ratio of volume concentration between the fine and coarse particles; (d) Standard deviation of coarse particles; (e) Volume median radii of coarse particles.

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As mentioned above, we introduced PLS and GA, and then combined the parameters for the AVSD on the earth’s surface with the AOD of CE-318 for different wavelengths to deduce the columnar AVSD. First, PLS was utilized to describe the relationships between multiple distribution parameters for the AVSD on the earth’s surface and the columnar AVSD; however, the initial inference results showed certain deviations from the actual values. In order to better approximate the true values, GA was used to find the minimum value of the sum of squared error (SSE) (as shown in function (7)). Figure 5 and Table 4 give the results of fitting and the corresponding data description. Clearly, Figs. 5(a) and 5(c) exhibit better fitting results as compared to Figs. 5(b) and 5(d); the R-square reached up to 0.99, and the lowest R-square was 0.8542. This is because GA can easily fall within the local optimum, and subpar quality for a few data points is unavoidable when dealing with a large quantity of data.

Fig. 5 The experimental results for the 4 cases by using partial least square (PLS) and genetic algorithm (GA). (a) columnar AVSD on December 24, 2014, 10:29, blue diamonds and red stars indicate the original columnar AVSD inversion results using the Dubovik’s algorithm and fitting the result by our proposed method, respectively ; (b) Columnar AVSD on December 30, 2014, 11:32; (c) Columnar AVSD on January 3, 2015, 09:39; (d) Columnar AVSD on January 3, 2015, 14:33.

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Table 4. Data Description and Fitting Evaluations Corresponding to Fig. 5

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Dubovik provided the optical properties of global key aerosol types in 2002, and their paper has been cited more than a thousand times in the literature. Their work described the characteristics of in urban-industrial and mixed area for four different places, and provided the mean and standard deviations of the distribution parameters. Therefore, we introduced mean values in our work, and compared the fitting results with the mean AVSD values in Wuhan. As shown in Fig. 6 , the best results are for Mexico City, i.e., R² = 0.9036, and the second best is Maldives. Aerosol optical properties for Mexico City are σ_f : 0.43 ± 0.03, σ_c: 0.63 ± 0.05, R_f : 0.12 + 0.04τ(440) ± 0.02, R_c: 2.72 + 0.60τ(440) ± 0.23, C_f:0.12τ(440) ± 0.03 and C_c: 0.11τ(440) ± 0.03. We then used these traditional empirical values and GA to obtain optimal solutions; the results are shown in Fig. 7 , the same four cases as used in Fig. 5 are used, and Table 5 gives the corresponding description. The fitting results obtained in this case were not better that the ones obtained by using our proposed method; the best R-square value being 0.8883. These results indicated that the aerosol concentrations in central China were significantly different from the other foreign industrial areas, and even though our method might not be the best, in most cases, it estimated better results for anthropogenic concentrations than the ones obtained using the empirical values.

Fig. 6 Columnar AVSD on January 3, 2015, 09:39. The black line is the original columnar AVSD; the red dashed line indicates the columnar AVSD calculated by the mean values of the distribution parameters in GSFC; the yellow dash-dot line expresses the columnar AVSD calculated by the mean values of the distribution parameters in Crete-Paris; the blue dotted lines and green lines with dots indicate the for Mexico City and Maldives, respectively.

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Fig. 7 The experimental results for the four cases using the traditional empirical values (Mexico City) and genetic algorithm (GA). (a) columnar AVSD on December 24, 2014, 10:29, the blue diamonds and red stars indicate original columnar AVSD inversion result by Dubovik’s algorithm and the fitting result by our new method, respectively ; (b) Columnar AVSD on December 30, 2014, 11:32; (c) Columnar AVSD on January 3, 2015, 09:39; (d) Columnar AVSD on January 3, 2015, 14:33

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Table 5. Data Description and Fitting Evaluations Corresponding to Fig. 7

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In order to further verify the effectiveness of our new method, we considered the triple modal logarithmic normal distribution as well. Two days were selected randomly, and the 36 bi-modal logarithmic normal distribution were used as samples; the results are shown in Fig. 8 , and through a comparison of the original columnar and the new method, the R-Square values for the AVSD were found to be 0.9577 and 0.7641, respectively.

Fig. 8 The new method using triple modal logarithmic normal distribution on two different days.

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After verifying and analyzing the four cases of bi-modal logarithmic normal distribution and two cases of triple modal logarithmic normal distribution, the combination of PLS and GA was considered to be a useful method of haze day columnar AVSD retrieval. However, this does not imply that the current research effort is enough. Figure 9 shows the ANSD observations for the earth’s surface for two consecutive days; unlike the Sun-photometer, TSI SMPS and GRIMM 180 PM monitor can also work in the night time. As can be seen, the ANSD for the earth’s surface is lower in the night time and higher during the day time, and the ANSD peaked from 8:00 a.m. to 11:00 a.m. However, during this time, only 7-8 records per haze day could be retrieval by Dubovik’s algorithm. An increase in the lung cancer incidence indicates heavy aerosol loadings causing serious air pollution in China. Consequently, predicting the diffusion range and influence degree of haze is critical for the country, and in this regard, there is great room for improvement in the columnar AVSD retrieval methods.

Fig. 9 Changes in the ANSD for the earth’s surface on two consecutive days, when heave aerosol loading occurred on January 21 and 22, 2015; the radii were divided as shown in the legend for Fig. 9, r<0.02um, 0.02um<r<0.1um and 0.1um< r<15um

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5. Conclusion

Considering the worsening of weather in terms of haze and an increasing number of sun-photometers installed in China, an efficient utilization of this instrument for obtaining useful atmospheric parameters and predicting the occurrence and development of haze becomes urgent. Columnar AVSD suffers from some ill-posed problems and only a small number of sites have joined the AERONET, making it difficult to obtain reliable solutions.

In this work, based on a joint experimental observation, a small number of sample data was obtained, which included columnar AVSD and scattering characteristics of haze aerosol particles. In combination with these sample data, the optical characteristics of haze aerosols were analyzed and the experimental data were filtered. Finally, from November 2014 to January 2015, 36 haze records which met the requirements of bimodal logarithmic normal distribution, and 3 instruments for conducting synchronous observations were selected. For the experiments, the AVSD for the earth’s surface observed by TSI SMPS and GRIMM 180 PM monitor were used to deduce the initial distribution parameters of the columnar AVSD by using PLS. After this, GA was used to find the minimum SSE and determine an optimal solution. The results indicated the R-Squares for the 4 cases to be 0.9807, 0.9275, 0.9900 and 0.8542, respectively. To demonstrate the superiority and stability of the proposed method, empirical value hypothesis combined with GA and two other cases of triple modal logarithmic normal distribution were discussed. Our research confirmed that the generally accepted empirical hypothesis is not applicable for China. In the absence of an official algorithm for AERONET, the new method proves to be feasible and stable during the haze events.

Our new method can improve the columnar AVSD retrieval accuracy during the haze day; however, several important considerations for improvements are listed below:

• GA may have a tendency to converge towards local optima or even arbitrary points rather than the global optimum of the problem. This means that it does not “know” how to sacrifice short-term fitness to gain longer-term fitness. In our algorithm, the adjustment scale is limited, which can avoid some errors, but can also make it difficult to find the global optimal solution, as shown in Fig. 5(d);
• This approach focuses on bi-modal logarithmic normal distribution, but almost 1/3 of the columnar AVSD samples were found to be close to the tri-modal and multi-modal logarithmic normal distribution. Out of the total records, 61.4% conformed to the bi-modal logarithmic normal distribution; and therefore, the adaptability of this approach needs to be improved;
• During the haze events, Duboviks’ method retrieved only 7-8 or even less records per day, which are not sufficient for long time observations. Further, the size range of the column is fixed form 0.05 um to 15 um, but in fact, as shown in Fig. 9, the fine particles on the earth’s surface vary widely, with radii less than 0.02um to even up to 5 × 10⁴ #/cm³. Development of new methods for regional utility is thus an important subject for future research work.

Acknowledgments

This work was supported by National Natural Science Foundation of China (NSFC) (Grant No.41127901, No. 41401498), Program for Innovative Research Team in University of Ministry of Education of China (Grant No.IRT1278). Specialized Research Fund for the Doctoral Program of Higher Education of China (20120141120010). Cheng Guang Project of Wuhan (2014070404010198). Natural Science Foundation of Hubei Province (Grant No. 2015CFA002).

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Station	October	November	December	January
East Lake High-tech Development Zone	11days AQI>150	9days AQI>150	4days AQI>150	19days AQI>150
East Lake High-tech Development Zone	Two persistent haze events 10.16-10.20 10.26-10.28	Two persistent haze events 11.15-11.17 11.20-11.23	one persistent haze event 12.24-12.25	Four persistent haze events 1.03-1.12 1.16-1.19 1.21-1.22 1.25-1.26

Instruments	October	November	December	January
CE-318 Sun-photometer	10.05,10.12,10.26,10.27;	11.21,11.22;	12.24,12.28,12.30;	01.03,01.04,01.07,01.08, 01.10,01.11,01.16,01.17, 01.18,01.21,01.22;
GRIMM 180 PM monitor ^{a, b}	None;	11.21,11.22;	12.24,12.28,12.30;	01.03,01.04,01.07,01.08, 01.10,01.11,01.16,01.17, 01.18,01.21,01.22;
TSI SMPS ^{a, b}	10.05,10.27;	11.21,11.22;	12.24,12.28,12.30;	01.03,01.04,01.10,01.16, 01.17,01.18,01.21,01.22;

Category of logarithmic normal distribution	Amount	AOD ^a 440nm	CRI^b 440nm	SSA(T,F,C) ^c 440nm	PM2.5
Bimodal logarithmic normal distribution	41	0.7926	Real:1.4321 Image:0.0224	0.8477, 0.8682 0.6138	109
Triple logarithmic normal distribution	21	0.9557	Real:1.4362 Image:0.0206	0.8566, 0.8810 0.6209	127
Multi-modal logarithmic normal distribution	2	0.8407	Real:1.5736 Image:0.0315	0.8078, 0.8635 0.6192	133

Test sample	Dubovik’s method			Fitting results			R-square
	Volume median radius	Standard deviation	Volume concentration	Volume median radius	Standard deviation	Volume concentration
2014/12/24 10:29	f: −1.7927 c: 1.1025	f: 0.6199 c: 0.5936	f: 0.1284 c: 0.0736	f: −1.8258 c: 1.1861	f: 0.6159 c: 0.6362	f: 0.1220 c: 0.0639	0.9807
2014/12/30 11:32	f: −1.6110 c: 1.1626	f: 0.6336 c: 0.6262	f: 0.0675 c: 0.0453	f: −1.7673 c: 1.2016	f: 0.6530 c: 0.5991	f: 0.1003 c: 0.0631	0.9275
2015/01/03 09:39	f: −1.8251 c: 1.0687	f: 0.5926 c: 0.5781	f: 0.1516 c: 0.0720	f: −1.8432 c: 1.0254	f: 0.6053 c: 0.5843	f: 0.1297 c: 0.0524	0.9900
2015/01/03 14:33	f: −1.7693 c: 1.0600	f: 0.6119 c: 0.5756	f: 0.1242 c: 0.0854	f: −1.6065 c: 1.1332	f: 0.6481 c: 0.5766	f: 0.1141 c: 0.1053	0.8542

Test sample	Dubovik’s method			Fitting result			R-square
	Volume median radius	Standard deviation	Volume concentration	Volume median radius	Standard deviation	Volume concentration
2014/12/24 10:29	f: −1.7927 c: 1.1025	f: 0.6199 c: 0.5936	f: 0.1284 c: 0.0736	f: −1.7949 c: 1.0755	f: 0.4552 c: 0.6056	f: 0.0913 c: 0.1046	0.7683
2014/12/30 11:32	f: −1.6110 c: 1.1626	f: 0.6336 c: 0.6262	f: 0.0675 c: 0.0453	f: −1.8079 c: 1.0732	f: 0.4323 c: 0.6131	f: 0.0619 c: 0.0944	0.5903
2015/01/03 09:39	f: −1.8251 c: 1.0687	f: 0.5926 c: 0.5781	f: 0.1516 c: 0.0720	f: −1.7919 c: 1.0822	f: 0.4325 c: 0.6254	f: 0.0922 c: 0.1000	0.7300
2015/01/03 14:33	f: −1.7693 c: 1.0600	f: 0.6119 c: 0.5756	f: 0.1242 c: 0.0854	f: −1.8417 c: 1.1057	f: 0.4201 c: 0.6291	f: 0.1006 c: 0.0907	0.8883

Inversion of the haze aerosol sky columnar AVSD in central China by combining multiple ground observation equipment

Abstract

1. Introduction

2. Observational instruments and methodology

2.1 Observational instruments

2.2 Retrieval method

3. New method

4. Results and discussion

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (9)

Tables (5)

Equations (12)

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