Investigation of the Relationship Between the Air Pollution and Solar Activity

TL;DR

This study explores the weak and indirect relationship between solar activity and air pollution on Earth from 2000 to 2016, using various correlation analyses to identify patterns and potential influences.

Contribution

It provides a comprehensive analysis of the correlation between solar activity indicators and air pollution indices, highlighting the complex and weak nature of their relationship.

Findings

Higher air pollution cities show increased API with rising SSN up to a point

Lower pollution cities exhibit lower correlation between API and SSN

Solar activity influences Earth's atmosphere indirectly affecting air quality

Abstract

How did the Sun affect the air pollution on the Earth? There are few papers about this question. This work investigates the relationship between the air pollution and solar activity by using the geophysical and environmental data during the period of 2000-2016. It is quite certain that the solar activity may impact on the air pollution, but the relationship is very weak and indirect. The Pearson correlation, Spearman rank correlation, Kendalls rank correlation, and conditional probability were adopted to analyze the air pollution index (API), air quality index (AQI), sunspot number (SSN), radio flux at wavelength of 10.7 cm (F10.7), and total solar irradiance (TSI). The analysis implies that the correlation coefficient between API and SSN is weak ($-0.17<r<0.32$) with complex variation. The main results are: (1) For cities with higher air pollution, the probability of high API will be increased along with SSN, then reach to a maximum, and then decreased; (2) For cities with lower air pollution, the API has lower correlation with SSN; (3) The relationship between API and F10.7, or API and TSI are also similar as API and SSN. The solar activities take direct effect on TSI and the energetic particle flux, and indirect and long-term effect on lower atmosphere and weather near the Earth. All of these factors contribute to the air pollution on the Earth.

Tables

Table 1. Table 1  : PCC, SCC, and KCC of various correlation of three cities as example

City	APISSN	APISSN	APISSN	APIF10.7	APIF10.7	APIF10.7	APITSI	APITSI	APITSI
	PCC	SCC	KCC	PCC	SCC	KCC	PCC	SCC	KCC
Beijing	0.084	0.094	0.061	0.10	0.11	0.074	0.079	0.097	0.064
Chengdu	-0.002	0.061	0.042	0.026	0.097	0.065	0.031	0.071	0.048
Kunming	-0.027	-0.009	-0.0057	-0.07	-0.047	-0.031	-0.13	-0.085	-0.056

Full text

††slugcomment: Not to appear in Nonlearned J., 45.00footnotetext: 1CAS Key Laboratory of Solar Activity, National Astronomical Observatories of Chinese Academy of Sciences, Datun Road A20, Chaoyang District, Beijing 100012, China00footnotetext: 2Sate Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing 100190, China00footnotetext: 3School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 100049, China00footnotetext: 4Beidou Intelligence Information and Network Technology Limited Company, Beijing 100041, China

Keywords Air Pollution Index; Sunspot Number; Solar Radio Flux; Total Solar Irradiance; Correlation; Conditional Probability

1 Introduction

The air pollution impact on human health greatly in many ways, such as seeing, breathing, coughing, pulmonary disease, cancer, and so on (Sicard et al., 2011; Cooper et al., 2012). Many people believed that the air pollution should be produced mainly from industry, automobiles and domestic fuels fire, cooking, smoking and so on. (Cooper et al., 2012) provided the worldwide distribution of pollution from local and global sources. The heavy polluted area are spreaded all over the industrial estate and populous zone.

Then, are there some external contributors to the cities air pollution? Because the solar irradiance dominates the total energy acting on the Earth atmosphere, and solar activities vary the total solar irradiance (TSI). Therefore, it is reasonable to suppose that the solar activities may affect on the Earth climate, air ventilation, and even the air pollution (Pudovkin, 2004; Kutiev et al., 2013). Actually, the solar activities affect ionization in the Earth atmosphere, as well as the lower atmosphere state, weather conditions, the distribution of ozone molecules and urban environment, and therefore the air pollution on the earth. However, so far, the relationship between solar activity and air pollution is still not quite certain and have been studied rarely (Sharma et al., 1997; Mavrakis et al., 2008). (Sharma et al., 1997) only deduced and discussed the influence of air pollution theoretically from the Sun, cosmic ray ionization, and lightening activity. (Mavrakis et al., 2008) studied the air quality of Thriassion Plain – Greece covering more than 23 years. But he did not give a certain results or conclusion on the relationship between solar activity and air quality.

This work investigated the relationship between solar activities and the records of air pollution in several typical Chinese big cities. Does the solar activities impact on the cities air pollution? How much is the level of the impact? What is the cause of the relationship? In order to answer these question, we analyze different correlation and mainly conditional probability among the air pollution index and several solar activity index, such as the sunspot number (SSN), solar radio flux at wavelength of 10.7 cm (F10.7), and the total solar irradiance (TSI). In Section 2, we analyze the record data in three typical Chinese big cities, and then analyze globally the data of many cities of three classes. The conclusion and discussion are summarized in Section 3.

2 Data and analysis

2.1 Data Source

The data involving in this research includes the air pollution index (API) of tens of Chinese cities and several solar activity indexes. The later includes sunspot number (SSN), solar radio flux at wavelength of 10.7 cm (F10.7), and the total solar irradiance (TSI). This work focused on investigating the relationship between API and the solar activity indexes.

API data is recorded by the Chinese Ministry of Environmental Protection (MEP) from 2000 to 2013. The API level is based on the level of 6 atmospheric pollutants, namely sulfur dioxide (SO2), nitrogen dioxide (NO2), suspended particulates smaller than 10$\mu$m and 2.5 $\mu$m in aerodynamic diameter (PM10, PM2.5), carbon monoxide (CO), and ozone (O3) measured at the monitoring stations throughout all over the country. Please note that only a few cities included the index of PM2.5, O3, and CO. After 1st January 2014, MEP monitors daily air quality level in hundreds of its major cities and adopt Air Quality Index (AQI). AQI is an index used by government agencies to communicate to the public how polluted the air currently is or how polluted it is forecast to become. An individual score of AQI (IAQI) is assigned to the level of each pollutant and the final AQI is the highest of those 6 scores. The data of API and AQI are obtained from the data center website111http://datacenter.mep.gov.cn/index of the Chinese MEP. The weather data are download from the data center of China meteorological administration222http://data.cma.cn/ and the weather website333http://lishi.tianqi.com/.

The data of SSN and F10.7 are obtained from the website444https://www.ngdc.noaa.gov/ of National Centers for Environmental Information (NCEI). The data of TSI at 1AU is from ACRIMSAT/ACRIM3555ftp://ftp.ngdc.noaa.gov/STP/SOLAR  DATA/ (Willson, 2014) and SORCE/TIM666http://lasp.colorado.edu/home/sorce/data/ (Kopp$\&$Lawrence, 2005; Kopp, et al, 2005). The Active Cavity Radiometer Irradiance Monitor Satellite (ACRIMSAT) is a defunct satellite and instrument that was one of the 21 observational components of NASA’s Earth Observing System program. The ACRIM3 instrument monitored total solar irradiance (TSI). The Solar Radiation and Climate Experiment (SORCE) is a NASA-sponsored satellite mission that is providing state-of-the-art measurements of incoming x-ray, ultraviolet, visible, near-infrared, and total solar radiation. Total Irradiance Monitor (TIM) is one of the four instruments.

2.2 The profile and characteristic of API in single city

At first, we analyze the relationship between API and SSN, F10.7, and TSI, respectively in 3 classes. The 3 classes are classified according to the API distribution in the city. The first class is the city with $\geq 0.55\%$ days (more than two days per year averagely) of large API ($\geq 200$), for example, Beijing. The second class is the city with $0.1\%\leq API<0.55\%$ days of large API ($\geq 200$), for example, Chengdu. The third class is the city with $<0.1\%$ days of large API ($\geq 200$), for example, Kunming. The correlation of API and SSN, API and F10.7, API and TSI are analyzed. In order to make a comparison, we adopted Pearson correlation, Spearman rank correlation, and Kendalls rank correlation. Pearson correlation coefficient (PCC) is a measure of the linear correlation between two variables. Spearman rank correlation coefficient (SCC) is a nonparametric measure of rank correlation between two variables. Kendall rank correlation coefficient (KCC) is statistically used to measure the ordinal association between two measured quantities.

Upper three panels of fig.1 plotted the API in Beijing, Chengdu, and Kunming of 4607 days during 2000-2013, respectively. The red line went through the API curve is the 101 points moving average after excluding the large API. We firstly exclude the point with 2 times of standard deviation larger than the average. Then, each point of the red line is the average value of $\leq 101$ points nearby, ie, $\leq 50$ points before and after. The large API ($\geq 200$) in Beijing, Chengdu, and Kunming are about $3.19\%$ days, $0.48\%$ days, and no day, respectively. The bottom three panels of fig.1 plotted SSN, F10.7, and TSI during 2000-2013, respectively. Table.1 is the PCC, SCC, and KCC of API and SSN, API and F10.7, and API and TSI, for three cities as example. The number of correlation is N=4607 points. Thus the PCC $r\geq 0.038$ could be considered as significant under the significance level of $\alpha=0.01$ (Confidence level is $99\%$). For Beijing city, the PCC are small but higher than 0.038. The SCC and KCC are also small but significant with two-sided significance of its deviation near zero. This indicate the weak but believable correlation between API and SSN, API and F10.7, API and TSI. Beijing city has more than $40.4\%$ windy days (wind scale is $>3$, wind speed is $V>3.4m/s$). It also suffer the sand storm or dust storm sometimes. Thus air particles of Beijing city might have larger percent of dust than other cities with few sand storm or dust storm. These might influence the API moderately. For Chengdu city, the absolute value of PCC are lower than 0.038, and also lower than SCC and KCC. The API of Chengdu city is influenced slightly by the wind and dust with only $7.7\%$ windy days ($V>3.4m/s$) and no dust storm. For Kunming city, all correlation coefficient are negative. The absolute value of PCC are higher than 0.038, and also higher than absolute value of SCC and KCC. The API of Kunming city is also influenced slightly by the wind and dust with only $7.7\%$ windy days ($V>3.4m/s$) and no dust storm. The correlation between API and SSN, API and F10.7, and API and TSI is weak and quite complex in a single city. It might be positive, negative, and varied near zero. We will analyze them systematically in subsection 2.4.

Fig.2 plotted for three cities the scatter diagram of API versus SSN, API versus F10.7, API versus TSI, and percent of large API, respectively. Upper part of panel (a) plotted the scatter diagram of API versus SSN. The red cross is the API average value at given SSN ($\overline{API_{SSN}}$). The $\overline{API_{SSN}}$ is varied and increased along with $SSN\leq 180$, then reach the maximum and is decreased along with $SSN\geq 180$. The $\overline{API_{SSN}}$ around SSN=180 is about two times as large as the $\overline{API_{SSN}}$ of $SSN\leq 50$. Bottom panel of (a) plotted the percent of large API ($>\overline{API}+2\sigma$). It is increased along with $SSN\leq 150$, then reach the maximum around $150\leq SSN\leq 180$, and no large API when $SSN\geq 180$. The highest percent of large API around $SSN=150$ is about four times as large as that of $SSN\leq 90$. The results of $SSN>200$ should be taken care with only $0.56\%$ points. Panel (b) and (c) showed the similar result of API versus F10.7 and API versus TSI. Panel (d), (e), and (f) showed the results of Chengdu city. The $\overline{API_{SSN}}$ and percent of large API have no significant difference along with the SSN, F10.7, and TSI. Panel (g), (h), and (i) showed the similar results of Kunming city.

The AQI of the single city have also been studied. But the result is ambiguous and uncertain since only several hundreds of days of observation. The global result of AQI will be showed in next subsection.

2.3 The global probability distribution of API and AQI in Chinese big cities

There are 120 Chinese cities had measured the API during 2000-2013. The city with insufficient data will be excluded since it will blur the results. The data of two cities of Lanchow and Urumchi were also excluded because the air particle of these two cities have larger percent of sand storm or dust storm than other cities. The sand storm or dust storm will influence the API too much. The solar activity can take almost nothing effect on sand storm or dust storm because it appeared suddenly and intensively. Thus, we only analyze the data of 45 cities with successive data of more than 4000 (Max=4938) days and with few sand storm or dust storm. Among them 14 cities have more than $>0.55\%$ days with large API ($\geq 200$); 16 cities have $0.1\%\sim 0.55\%$ days with large API ($\geq 200$); 15 cities have less than $<0.1\%$ days with large API ($\geq 200$). We will study the global probability distribution and conditional probability of API of 3 classes of Chinese big cities. The conditional probability $P(API|SSN)$, $P(API|F10.7)$, and $P(API|TSI)$ were mainly analyzed. The $P(AQI|SSN)$, $P(AQI|F10.7)$ and $P(AQI|TSI)$ were also analyzed. Globally, during 2000-2013, the probability $P(SSN<100)$, $P(100\leq SSN<200)$, and $P(SSN\geq 200)$ are about $84.3\%$, $15.1\%$, and $0.56\%$, respectively. For all the 45 candidate cities, the probability $P(API<100)$, $P(100\leq API<200)$, and $P(API\geq 200)$ are about $87\%$, $13.1\%$, and $0.87\%$, respectively.

Fig.3 plotted the API probability distribution of the 14 cities with more than $0.55\%$ days of large API ($\geq 200$). Panel (a) plotted the count number distribution of API along SSN. Globally, the probability $P(API<100)$, $P(100\leq API<200)$, and $P(API\geq 200)$ are about $77.4\%$, $22.2\%$, and $1.5\%$, respectively. Given that $SSN<100$, the probability $P(API<100)$, $P(100\leq API<200)$, and $P(API\geq 200)$ are about $77.0\%$, $21.6\%$, and $1.4\%$, respectively. Given that $100\leq SSN<200$, the probability $P(API<100)$, $P(100\leq API<200)$, and $P(API\geq 200)$ are about $61.3\%$, $36.0\%$, and $2.7\%$, respectively. Given that $200\leq SSN<300$, the probability $P(API<100)$, $P(100\leq API<200)$, and $P(API\geq 200)$ are about $73.2\%$, $26.7\%$, and $0.002\%$, respectively. There is no $API\geq 200$ given that $SSN\geq 210$. But it is suspicious to concluded that $P(API\geq 200|SSN\geq 210)$ will be zero with only a very small proportion $0.39\%$ of the sample of one solar cycle. The red circle is the API average at given SSN. It is varied and increased along with $SSN\leq 150$, then reach the maximum and then is decreased along with $SSN\geq 195$. The API average around SSN=150 is about 1.72 times of the API average of $SSN\leq 50$ which showed as green line in panel(a). All these indicated that the API will be more likely higher around certain value of SSN than others. In order to ascertain this, the conditional probability $P(API|SSN)$ should be analyzed in detail. Panel (b) plotted $P(API|SSN)$ given that SSN with bin size of 1. The $P(API|SSN)$ around ($100\leq SSN<150$) is a little more likely to be large $API\geq 200$ than others. The red cross in panel (b) is the boundary of $10\%$ large API and $10\%$ low API. The two green lines are the average value of $10\%$ boundary of large API and low API given $SSN<50$, respectively. The boundary of $10\%$ large API and $10\%$ low API varied similar as API average in panel (a).

Panel (c) plotted $P(API|SSN)$ given that SSN with bin size of 10. For each bin of given SSN, the API was divided into three divisions: $API<100$, $100\leq API<200)$, and $API\geq 200$. When $SSN\geq 210$, the $P(API|SSN)$ of three division varied too much because only $\simeq 0.39\%$ data are in the range of $SSN\geq 210$. When $SSN\leq 210$, the $P(API_{100\sim 200}|SSN)$ and $P(API\geq 200|SSN)$ around $100\leq SSN\leq 150$ are higher than that of other given SSN; while the $P(API<100|SSN)$ around $100\leq SSN\leq 150$) are lower than that of other given SSN. The maximum $P(API_{200\sim 500}|SSN)$ given $120\leq SSN<130$ is about 5.7 times of $P(API_{200\sim 500}|SSN)$ given low SSN. In panel (d) of fig.3, the $P(API\geq 200/F10.7)$ around $200\leq F10.7\leq 210$ are higher than that of others given F10.7. The maximum $P(API\geq 200|F10.7)$ given $200\leq F10.7<210$ is about 5.2 times of $P(API\geq 200|F10.7)$ given low F10.7. In panel (e) of fig.3, the $P(API\geq 200|TSI)$ around $1367.4\leq TSI\leq 1367.5$ are higher than that of others given TSI. The maximum $P(API\geq 200|TSI)$ given $1367.4\leq TSI<1367.5$ is about 7.2 times of $P(API\geq 200|TSI)$ given $1365.2<TSI<1366.5$. The relationship between API and SSN, API and F10.7, and API and TSI are weak but clear. The probability of high API will be increased first, then reach to a maximum, and then decreased along with the increasing of SSN, F10.7 or TSI. We did not plotted the API probability distribution of the 16 cities with $0.1\%\sim 0.55\%$ days of large API ($\geq 200$). The result is similar as fig.3. But when $API=(100\sim 500)$, the $P(API|SSN)$ given $100\leq SSN\leq 150$ are smaller than that of fig.3.

Fig.4 plotted the API probability distribution of the 15 cities with less than $0.1\%$ days of large API ($\geq 200$). Panel (a) plotted the count number distribution of API along SSN. Globally, the probability $P(API<100)$, $P(100\leq API<200)$, and $P(API\geq 200)$ are about $97.6\%$, $2.3\%$, and $0.02\%$, respectively. The API average (red cross) are about the same for all cases of SSN. The Panel (b) plotted $P(API|SSN)$ given that SSN with bin size of 1. The boundary of $10\%$ large API and $10\%$ low API are also about the same for all cases of SSN. Panel (c) plotted $P(API|SSN)$ given that SSN with bin size of 10. For each bin of given SSN, the API was divided into three divisions: $API<100$, $100\leq API<200)$, and $API\geq 200$. When $SSN\geq 210$, the $P(API|SSN)$ of three division also varied too much because only $\simeq 0.39\%$ data. When $SSN\leq 210$, the $P(API_{100\sim 500}|SSN)$ around $90\leq SSN\leq 160$) are a little higher than that of other given SSN; while $P(API<100|SSN)$ are about the same for all cases of given SSN. Panel (d) and (f) showed that $P(API|F10.7)$ and $P(API|TSI)$ are about the same for all cases of given $F10.7\leq 260$ and $TSI\leq 1367.8$. Comparing with fig.3, the SSN (or F10.7, or TSI) take weaker impact on the cities with low API than the cities with high API.

There are 367 Chinese cities had measured the AQI during 2014-2016. The short period of measurement are not sufficient for data analyze of relationship. Only small amount of cities have a small quantity of measured data. Most of the cities with successive data of more than 600 (Max=942) days will be analyzed. Fig.5 plotted the AQI probability distribution of these cities. Globally, the probability $P(AQI<100)$, $P(100\leq AQI<200)$, and $P(AQI\geq 200)$ are about $74.1\%$, $22.5\%$, and $3.4\%$, respectively. The $P(AQI\geq 200)$ about 2.2 times as high as $P(API\geq 200)$ of 15 large API cities. AQI add the index of suspended particulates smaller than 2.5 $\mu$m in aerodynamic diameter (PM2.5). While API of most Chinese cities did not add the index of PM2.5. Thus AQI is lager than API in a city. Panel (a) plotted the count number distribution of AQI along SSN. The AQI average (red cross) at given SSN is also varied and increased along with $SSN\leq 70$, then reach to a maximum and then go on varying along with $SSN\geq 70$. The API average around SSN=150 is about 1.72 times of the API average of $SSN\leq 50$ which showed as green line in panel(a). The Panel (b) plotted $P(AQI|SSN)$ given that SSN with bin size of 1. The boundary of $10\%$ large AQI and $10\%$ low AQI (red cross) is also varied and increased along with $SSN\leq 70$, then reach to a maximum and then go on varying along with $SSN\geq 70$. Panel (c) showed that the $P(AQI|SSN)$ of large $AQI\geq 200$ reach the maximum at given $SSN=60\sim 70$. But the $P(AQI|SSN)$ of large $AQI\geq 200$ are also high at given $SSN=140\sim 150$. This is a little difference comparing fig.3 and fig.4. Please note that only $<5\%$ cases are in the range of $SSN\geq 100$ during 2014-2016.

2.4 The relationship among different correlation,

API level, and wind for most Chinese big cities

For all the 45 candidate cities, we studied the Pearson correlation, Spearman rank correlation, and Kendalls rank correlation of API and SSN. Panel (a) of fig.6 shows the scatter diagram of PCC versus SCC. The difference between PCC and SCC is small and varied symmetrically within a small linear range. Panel (b) of fig.6 shows that the absolute value of PCC is higher than that of KCC globally. Thus we can conclude that the correlation between API and SSN is linearly, that is Pearson correlation. We also studied the PCC, SCC, and KCC of API versus F10.7 and API versus TSI. The correlation of API and F10.7, API and TSI are also linearly (Pearson correlation).

The relationship between API level and correlation are studied. Panel (c) of fig.6 shows the scatter diagram between percent of $API\geq 100$ and PCC of API/SSN. The higher percent of large API $\geq 100$, the higher correlation. Panel (d) of fig.6 also shows higher percent of large API $\geq 200$, the higher correlation coefficient, except that two cities of Lanchow and Urumchi (star symbol). As discussed in subsection 2.3. The air particle of Lanchow and Urumchi are influenced by sand storm or dust storm which appeared suddenly and intensively. The relationship between API level and wind are plotted at panel (e) and (f) of fig.6. The percent of large API will be smaller if the percent of windy days ($\geq 3.4m/s$) is larger. It is easy to understand that the wind blow away the pollution particles.

2.5 The total solar irradiance and sunspot number

The relationship between TSI and SSN is quite certain. The cross correlation between TSI and SSN shows that maximum correlation happened when SSN is 29 days before TSI. The upper panel of fig.7 shows the scatter diagram of TSI versus SSN. The red line is the moving average of the mid value of TSI versus SSN. It shows that the TSI increased globally when $SSN<100$, then reach to a maximum around $100\leq SSN\leq 150$, and then is decreased when $SSN>150$. This is a little difference than the result of (Kondratyeu$\&$Nikolsky, 1970) as showed in bottom panel of fig.7. However, the SSN is not higher than 200 in the result of (Kondratyeu$\&$Nikolsky, 1970).

3 Conclusion and Discussion

The air pollution should be produced mainly from industry, automobiles and domestic fuels fire, cooking, smoking and so on. There is no doubt that weather condition take the major effect on the API (or AQI): Fog, wind, cloud, raining, humidity, temperature, etc. Solar activity can affect the solar irradiance and ionization in the atmosphere, thus impact on the ozone molecule, the lower atmosphere state, weather condition, and urban environment on the earth. With the data analysis between API (or AQI) of hundreds of Chinese cities and SSN (or F10.7, or TSI), we study the relationship among them and find some preliminary results as follows.

For each city, the correlation coefficient (PCC, NCC, KCC) between API and SSN (or F10.7, or TSI) are weak $-0.17<r<0.32$ and complex, considering a sample of one solar cycle ($>4000$ points). It might be positive, negative, and varied near zero. For the Beijing city with high air pollution, both the API average at given SSN and percent of large API at given SSN are varied and increased along with SSN, then reach to a maximum around $150\leq SSN\leq 180$ and then are decreased. The API average around SSN=180 is about two times as large as the API average of $SSN\leq 50$, and the percent of large API around $SSN=150$ is about four times as large as that of $SSN\leq 90$. For the city with moderate or low air pollution, The API average and percent of large API have no significant difference along with the SSN. The relationship between API and F10.7, and API and TSI are similar.

Globally, during 2000-2013, the probability $P(SSN<100)$, $P(100\leq SSN<200)$, and $P(SSN\geq 200)$ are about $84.3\%$, $15.1\%$, and $0.56\%$, respectively. For all the 45 candidate cities, the probability $P(API<100)$, $P(100\leq SSN<200)$, and $P(API\geq 200)$ are about $87\%$, $13.1\%$, and $0.87\%$, respectively. For the 14 high polluted cities: the $P(API\geq 200|SSN)$ around $100\leq SSN\leq 150$ are higher than that of other given SSN, and the maximum $P(API\geq 200|SSN)$ given $120\leq SSN<130$ is about 5.7 times of $P(API\geq 200|SSN)$ given low SSN; the $P(API\geq 200|F10.7)$ around $200\leq F10.7\leq 210$ are higher than that of others given F10.7, and the maximum $P(API\geq 200|F10.7)$ given $200\leq F10.7<210$ is about 5.2 times of $P(API\geq 200|F10.7)$ given low F10.7; the $P(API\geq 200|TSI)$ around $1367.4\leq TSI\leq 1367.5$ are higher than that of others given TSI, and the maximum $P(API\geq 200|TSI)$ given $1367.4\leq TSI<1367.5$ is about 7.2 times of $P(API\geq 200|TSI)$ given low $TSI=1365.2\sim 1366.5$. The relationship between API and SSN, or API and F10.7 or API and TSI are weak but clear. The probability of high API will be increased first, then to a maximum, and then decreased along with SSN, F10.7 or TSI. The result of middle polluted cities are similar but the $P(API\geq 200|SSN)$ around $100\leq SSN\leq 150$ are smaller than that of high polluted cities. The SSN (or F10.7, or TSI) take weaker impact on the cities with lower API than the cities with higher API.

The relationship between AQI and SSN, AQI and F10.7, and AQI and TSI are also weak but a little difference than the relationship between API and SSN, API and F10.7, and API and TSI. It is difficult to give more conclusion now since only a small sample of data during 2014-2016. And the AQI have only $<5\%$ cases in the range of $SSN\geq 100$ and no cases in the range of $SSN\geq 150$.

Comparing the Pearson correlation, Spearman rank correlation, and Kendalls rank correlation, Pearson correlation coefficient is the largest globally. That is, the correlation of API and SSN is linearly. The relationship between API level and PCC indicated that the higher percent of large API, the higher correlation coefficient. The relationship between API level and wind indicated that the percent of large API will be smaller if the percent of windy days ($\geq 3.4m/s$) is larger.

The question brought out in the introduction can be answer now. The solar activity take direct effect on the API and AQI on the earth through solar radiation (Mudakavi, 2012) and high energy particles. The solar activity also take indirect and long term effect on lower atmosphere and weather, thus the API and AQI on the earth. The relationship between API and solar activity is weak and complex. The solar activity does not impact on air pollution monotonously. The probability of high API will be increased first, then to a maximum, and then decreased along with the solar activity. Former works (PAP, 1985) on solar irradiance and sunspot area shows that strong inverse correlation is shown between the irradiance observed by the ACRIM radiometer and the projected areas of the ’active’ sunspots. (Hempelmann, 2012) concluded that the Earth atmosphere acts as an amplifier between space and ground, and that the amplification is probably controlled by solar activity. They suspected the cosmic rays intensity as the link between solar activity and atmospheric transparency. Our preliminary study did not consider the influence of the charged particles on the earth surface. The larger solar activity will result more charged particles thus congregate the polluted particles, thus reduce the number of polluted particles.

The solar activity will influence the air pollution. This influence is weak and complex because man-made environment and weather condition take the dominant influence. We can anticipate that the result will be more clear with a sample of more than one solar cycle.

Acknowledgements The author thanks the referee for helpful and valuable comments on this paper. This work is supported by NSFC grants 11373039, 11433006, 11573039, and 11661161015, the MOST grant 2014FY120300, the Specialized Research Fund for State Key Laboratories of Space Weather. Thanks to NGDC, ACRIMSAT/ACRIM, SORCE/TIM, and China’s MEP for the online data.

4 Citing references

\citep{Cooper12} – (Cooper et al., 2012)

\citep{Hemp12} – (Hempelmann, 2012)

\citep{Kondrat70} – (Kondratyeu$\&$Nikolsky, 1970)

\citep{Kopp05a} – (Kopp$\&$Lawrence, 2005)

\citep{Kopp05b} – (Kopp, et al, 2005)

\citep{Kutiev13} – (Kutiev et al., 2013)

\citep{Mavrakis08} – (Mavrakis et al., 2008)

\citep{Muda12} – (Mudakavi, 2012)

\citep{PAP85} – (PAP, 1985)

\citep{Pudovkin04} – (Pudovkin, 2004)

\citep{Sharma97} – (Sharma et al., 1997)

\citep{Sicard11} – (Sicard et al., 2011)

\citep{Willson14} – (Willson, 2014)