## Introduction

Due to rapid urbanization and industrialization and mounting energy consumption, fine particulates have become a major air pollutant in China’s urban atmosphere1. As one of the most important fine particles, PM2.5 (particulate matter with aerodynamic diameter less than 2.5 μm) consists of heavy metals, volatile organic compounds, and carbonaceous substances2, which could produce detrimental effects on human respiratory system3. The World Health Organization (WHO) considers a concentration of PM2.5 over 10 μg/m3 as hazardous to human health4, while this measurement in large cities of China can range from 50 to 125 μg/m35. It is estimated that long-term exposure to high level of particulate pollution caused 1.36 million premature deaths per year in China6.

To better inform air quality control and build sustainable cities, tremendous efforts have been devoted to understanding potential contributing factors of PM2.5 concentration. It is widely recognized that PM2.5 are mainly influenced by human activities, natural environment, and atmospheric chemical reactions. Among these three factors, human activities, such as vehicle exhaust emission and industrial production7,8, are the dominant factors of PM2.5 pollution9. Natural environment, such as meteorological conditions (e.g., precipitation and wind speed)10, facilitate the transportation and diffusion of PM2.5, while atmospheric chemical reactions stimulate the secondary formation of PM2.511. All of these factors interact with PM2.5 at different spatial and temporal scales, and thus can have varying effects on PM2.5 distribution. Tremendous efforts have been paid to understanding such varying effects at multiple spatial scales, such as the national, provincial, and urban cluster scales. In existing literature, the effects of these factors on PM2.5 have been primarily investigated at the seasonal scale, while those at the hourly, daily and monthly scales have been understudied. Lack of such knowledge makes it imperative to identify temporally dependent strategies for PM2.5 control.

Ensemble Empirical Mode Decomposition (EEMD), a new time-series signal processing method, was recently proposed with the support of signal detection technology12. EEMD was designed for non-stationary and nonlinear signal detection and can gradually separate different oscillation or trend components from the original signal12. In recent years, EEMD has been adopted by a number of scholars to analyze time series data of PM2.513,14,15,16,17,18, but few of them used it to investigate PM2.5 over multiple temporal scales. This article attempts to fill this gap by taking the city of Nanjing, China as the study area. Specifically, the objectives of this study are to: (1) explore the variation of PM2.5 at multiple temporal scales, and (2) investigate how PM2.5 responds to air pollutants and meteorological factors over different temporal scales. Findings from our research can offer better understanding on the temporal variability of PM2.5, and improve regional air quality assessment and air pollution source apportionment.

## Data and methods

### Study area

Nanjing is the capital city of Jiangsu Province in eastern China (Fig. 1). It is situated in the subtropical monsoon climate zone and has four distinct seasons. On the one hand, Nanjing is one of the four garden cities in China, with park green area of 16.01 m2 per capita. On the other hand, it is a heavily air-polluted area by PM2.5, attributed to the combined effects of large amount of population and on-road vehicles, valley basin landform, numerous polluting enterprises in the suburbs (e.g., petrochemical factories), and the prevailing wind direction of east-south-east (Fig. 1).

### Data

This study acquired three datasets regarding PM2.5 concentrations, other air pollutants, and meteorological factors as described below.

### PM2.5 and air pollution factors

Besides PM2.5, five other major air pollutants monitored in China were included in the analysis, namely, PM10, SO2, NO2, CO and O3. We retrieved the hourly concentrations of PM2.5 and five other air pollutants of Nanjing between January 1, 2014 and December 31, 2018 from the Jiangsu environmental data public service station (https://218.94.78.75:20001/sjzx/).

There are nine national monitoring stations in Nanjing (Fig. 1). The hourly concentrations of PM2.5 and other five pollutants were derived from the nine stations, and were averaged to indicate daily concentrations of the entire city.

### Meteorological factors

Based on previous studies, wind speed, precipitation, atmospheric pressure, temperature and humidity have shown a strong correlation with PM2.510,19, and thus were considered as meteorological factors in this research. For the same time period (January 1, 2014–December 31, 2018), the daily average wind speed (WS), 24-h cumulative precipitation (PR), daily average atmospheric pressure (AP), daily maximum temperature (MaxT), daily minimum temperature (MinT) and daily surface air relative humidity (RH) for the Nanjing city were retrieved from the National Meteorological Information Center website (https://data.cma.cn/) which were reported from the Nanjing weather station, shown in Fig. 1.

### EEMD

EEMD was developed from the Empirical Mode Decomposition (EMD). EMD is a signal analysis method suitable for non-stationary, nonlinear data that can decompose any type of signal in an adaptive manner20. The aim of EMD is to decompose raw signals into a set of intrinsic mode functions (IMFs) to better reveal the signal characteristics. The IMFs need to meet the following requirements: (1) the number of extreme and the number of zero crossings must be equal to each other or at most differ by one; (2) at any point, the mean value of the envelope defined by the local maximum and local minimum must be zero.

Although EMD has better adaptability, there is a defect of mode mixing due to the influence of the original signal frequency. Therefore, on the basis of EMD, Wu and Huang proposed a noise-assisted data analysis method-Ensemble Empirical Mode Decomposition (EEMD)12. EEMD effectively processes the ‘mode mixing’ issue in EMD by adding white noise to filter IMF components. Meanwhile, EEMD can also complete the significance test that EMD cannot complete by means of perturbation of white noise sets, to obtain the reliability of each IMF21. The EEMD algorithm is shortly described as follows:

Denote an original signal as x(t), where t represents time. Then, add a white noise series w(t) to x(t) with a certain signal-to-noise ratio and obtain a new signal X(t):

$$X\left( t \right) = x\left( t \right) + w\left( t \right)$$

Use EMD to decompose the new signal X(t) into a number of IMFs:

$$X\left( t \right) = \sum\limits_{i = 1}^{n} {c_{i} + r_{n} }$$

where ci represents the ith IMF component and rn denotes the residual.

The above steps are repeated. That is, adding a new white noise series wj(t) of the same amplitude to the new signal each time, where Xj(t) represents the total signal of the jth addition of the new white noise, and cji represents the ith IMF component of the total signal of the jth addition of the new white noise, and rjn represents the residual of the total signal of the jth added new white noise:

$$X_{j} \left( t \right) = \sum\limits_{i = 1}^{n} {c_{ji} } + r_{jn}$$

It is assumed that after adding m-times new white noise series, the decomposed signals satisfy the two requirements of the IMF, and the IMF component ci(t) corresponding to the original signal is expressed as:

$$c_{i} \left( t \right) = \frac{1}{m}\sum\limits_{j = 1}^{m} {c_{ji} \left( t \right)}$$

Similarly, the residual rn(t) corresponding to the original signal is expressed as:

$$r_{n} \left( t \right) = \frac{1}{m}\sum\limits_{j = 1}^{m} {r_{jn} \left( t \right)}$$

The final decomposition result is expressed as:

$$x\left( t \right) = \sum\limits_{i = 1}^{n} {c_{i} \left( t \right)} + r_{n} \left( t \right)$$

The reliability of each IMF component obtained by EEMD decomposition can be verified by the perturbation of the white noise set. If the IMF energy obtained by the decomposition is above the 95% confidence line compared to the periodic distribution, then the periodic oscillation represented by the IMF component is passed the 5% significance level test, which is the main period of the signal change, also called the strong period; on the contrary, it indicates that the periodic oscillation represented by the IMF component is not very significant, called the weak period.

Relevant to this study, the EEMD method was applied to decompose original time series data of PM2.5, other air pollutants (PM10, SO2, NO2, CO and O3), and meteorological factors (WS, PR, AP, MaxT, MinT and RH), respectively. Their potential primary components were extracted in order to reveal multi-scale temporal changes. The resulting IMF components showed the cycles, frequencies, and trend that characterize the temporal variation of PM2.5, other air pollutant, and meteorological factors. The inherent oscillations of different temporal scales in the original signal (quasi-periodic changes) were also revealed by the IMF components, which reflect the nonlinear relationship between natural driving processes within the atmospheric system and the external human activities, and accurately and succinctly reflect the relationships between PM2.5 and both other air pollutants and meteorological data.

## Results

### Descriptive statistics of time series data

Descriptive statistics of PM2.5 data with other air pollutants and meteorological factors data of Nanjing from January 1, 2014 to December 31, 2018 are calculated (Table 1). The average PM2.5 concentration is 52 μg/m3, but the standard deviation is large, indicating the sample data is fluctuant greatly, which has certain research significance.

### Temporal variation of PM2.5

#### Undecomposed temporal variation of PM2.5

Results from the anomaly processing of the average daily PM2.5 data suggest that the original daily average PM2.5 concentration in Nanjing presented a significant volatility reduction trend during 2014–2018 (Fig. 2). Before December 2017, the PM2.5 concentration was relatively higher and presented a weak downward trend, while after that the PM2.5 was lower and exhibited the seasonality of “decrease–increase”, i.e., high concentration in spring and winter and low concentration in summer and autumn.

The PM2.5 concentration varied dramatically from day to day. The difference between the highest pollution and the lowest was up to 297 μg/m3. Meanwhile, the 30-day moving averages curve of PM2.5 concentration implied non-linear and non-stationary volatility characteristics of PM2.5. Therefore, the EEMD method was needed to further reveal the complex process of PM2.5 in Nanjing.

#### Decomposed temporal variation of PM2.5

The daily average time series of original PM2.5 concentration was decomposed by EEMD. For decomposition, the ensemble number was set to 100 and the amplitude of added noise was set to 20% of the standard deviation of the original data. The EEMD analysis produced nine IMF components (IMF1-9) and one trend component (RES), as shown in Fig. 3. Each IMF component a range of frequencies from high (HF, less than a 30-day period) to low (LF, greater than or equal to a 30-day period) at different temporal scales, and the final trend component represents the trend of the original PM2.5 data over time.

The significance of each IMF component was tested (Table 2). Except for IMF4, all other components passed the 5% significance level test, indicating that these IMF components contain information with actual physical meaning and the corresponding oscillation periods are the main oscillation period of the PM2.5 time series.

The average daily concentration change of PM2.5 has a relatively stable quasi-periodicity (Fig. 3 and Table 2), following the daily circle and the monthly circle. At the daily scale, it exhibits periodic changes of quasi-3 days (IMF1), quasi-7 days (IMF2), quasi-14 days (IMF3) and quasi-27 days (IMF4); At the monthly scale, it exhibits periodic changes of quasi-60 days (IMF5), quasi-140 days (IMF6), quasi-406 days (IMF7), quasi-913 days (IMF8) and quasi-1826 days (IMF9).

According to Table 2, the variance contribution rates of IMF1, IMF2, IMF3, IMF4, IMF5, IMF6, IMF7, IMF8, IMF9 and RES of the daily average concentration of PM2.5 in Nanjing are 19.98%, 16.33%, 8.59%, 4.72%, 3.96%, 4.86%, 11.55%, 1.96%, 1.53% and 26.55%, respectively, showing the fact that the contribution rate of high-frequency signal to low-frequency signal of PM2.5 concentration gradually decreases. Although the IMF4 component obtained by EEMD decomposition does not pass the significance test, it still contributes to the fluctuation of the original data series.

The influence of PM2.5 daily oscillation (IMF1 ~ 4) on the overall variation of PM2.5 is 49.61%, while the monthly oscillation (IMF5 ~ 9, RES) is 50.39%, and the contribution of monthly oscillation is slightly higher than that of daily oscillation. Therefore, the daily and monthly scales are two important temporal scales in the PM2.5 time series in Nanjing, which is consistent with the temporal of PM2.5 that found in other studies as daily, monthly, and annual22.

The results of PM2.5 decomposition in Nanjing were reconstructed at both the daily scale and monthly scale and compared with the original PM2.5 concentration and trend (Fig. 4). The inter-day variation was obtained by adding the IMF1, IMF2, IMF3, and IMF4, which can be considered as filtering out large-scale oscillations, while the inter-month variation was obtained by adding the IMF5, IMF6, IMF7, IMF8, IMF9 and RES (including larger time scale fluctuation over the study period).

The reconstructed inter-day variation of PM2.5 is basically consistent with the original sequence change trend, which can well show the slight change of PM2.5 concentration during the study period, while the reconstructed inter-month variation of PM2.5 shows a fluctuation of high concentration in spring and winter and low concentration in summer and autumn throughout the study period, which can effectively reveal the high-low state of PM2.5 in Nanjing in different seasons. The inter-day and inter-month fluctuations of PM2.5 can reflect the fluctuations of the original PM2.5 series from different temporal and have obvious inter-modulation effects as well.

### Response of PM2.5 to air pollutants and meteorological fluctuations

#### Undecomposed temporal variation of air pollutants and meteorological factors

During the study period, the trends of air pollutants PM10, SO2, NO2, CO, O3_8h were “decrease–increase”, “progressively decrease”, “decrease–increase”, “increase–decrease” and “increase–decrease”, respectively (Fig. 5a). The trends of meteorological fluctuation—Wind Speed, Precipitation, Air Pressure, MaxT, MinT, and Relative Humidity were “progressively decrease”, “increase–decrease”, “decrease–increase”, “increase–decrease”, “increase–decrease” and “progressively decrease”, respectively (Fig. 5b). The temporal patterns of PM10, SO2 and NO2 are similar to PM2.5.

The turning points of CO, O3_8h, Precipitation, Air Pressure, MaxT, and MinT were December 2014, September 2016, January 2017, September 2015, April 2016 and March 2017, respectively, while that of PM2.5 was December 2017, indicating that the change of PM2.5 had time lags. As important indicators of air quality, CO and O3 were inextricably linked to the formation of PM2.5. Therefore, PM2.5 was found to be responsive to CO, O3, PR, AP, MaxT, and MinT.

#### Decomposed temporal variation of air pollutants and meteorological factors

Absolute anomalies in the air pollutants concentration and meteorological factors data were decomposed by EEMD, and the periods were counted (Table 3). The inter-day variation period of air pollutants in Nanjing was highly consistent with PM2.5, while at the inter-month scale, the variation period of air pollutants was different from PM2.5. Similarly, the inter-day variation period of meteorological factors in Nanjing was generally consistent with PM2.5. However, on the inter-month scale, the meteorological factors show larger inter-year variation, which was consistent with the large time scale characteristics of meteorological fluctuation.

#### Correlation between PM2.5 and atmospheric pollutions and meteorological factors

Correlation analysis was conducted between PM2.5 and the six metrics at the both reconstructed scale (at the inter-day and the inter-month scale) and original data. As shown in Fig. 6, PM2.5 was differently correlated with CO, O3_8h, PR, AP, MaxT, and MinT at different temporal scales.

The correlation between PM2.5 and CO was positively on the daily scale, and the correlation coefficient was slightly higher than that on the monthly scale. The correlation coefficient of the original data was between the two scales. The correlation between PM2.5 and O3_8h was slightly negative when using the original data, but it was positive at the daily scale. At the monthly scale, the correlation was negative and the correlation coefficient was greater than that at the daily scale.

The correlation between PM2.5 and PR was negative at both scales and more intense at a broader time scale (inter-month scale). PM2.5 and AP were negatively correlated at the inter-day scale, while at the inter-month scale; it was a stronger positive correlation. The original PM2.5 showed a significantly negative correlation with MaxT and MinT, and the correlation was positive on the smaller time scale (inter-day scale) but strongly negative at the larger time scale (inter-month scale).

In summary, the responses of PM2.5 to O3_8h, AP, MaxT and MinT were in opposite directions at the daily and monthly scales. The responses were in the same direction for PR and CO at both temporal scales, while the response to PR is more intense at the monthly scale but the response to CO is more obvious at the daily scale. PM2.5 has different degrees of significant correlation with other different pollutants and meteorological factors at different temporal, so it has a multi-scale response.

## Discussion

This study contributes to answering the broader question on the anthropogenic and environmental factors that affect the formation of PM2.5 pollution. The sources of pollution caused by human activities mainly include fixed sources with fossil fuel combustion and mobile sources with vehicle exhaust emissions. The sulfur and nitrogen oxides produced by them can be directly converted into PM2.5. Natural environment mainly involves meteorological factors such as wind speed, precipitation, air pressure, temperature, and humidity, etc. The favorable meteorological conditions conduce to the diffusion and dilution of PM2.5 and reduce the risk of pollution.

Human activities are the main cause of PM2.5 pollution, and natural environment plays an important role in the aggregation and diffusion of particulate matter. On a short time scale, human activities and environmental actors (especially meteorological conditions) can change dramatically, and thus the contribution of human activities to PM2.5 is fluctuant; On a long time scale, human activities have undergone major changes due to the regulation of macroeconomic policies, while overall changes in environmental conditions are small, so the contribution of human activities to PM2.5 is stable.

Our findings advance the understanding of how PM2.5 responds to the other air pollutants at different temporal scales. PM10 is a particle with the size less than 10 μm, which contains PM2.5, and its variability is often synchronous with PM2.5. SO2 and NO2 are important precursors in the formation of PM2.5, and their trends are similar to PM2.5. CO is an intermediate product formed during the combustion of carbon-containing fuels, and it is not directly related to PM2.5. However, studies have shown that the spatial distribution of CO and particulate matter concentration tends to be the same in most parts of the day23, which supports the conclusion in this study that PM2.5 has a strong positive correlation with CO. Under the macro-control of low-carbon emissions, the development of a low-carbon economy in Nanjing controls carbon emissions from adjusting industrial structure, improving energy efficiency and increasing ecological land24. Carbon management was carried out from both “source” and “sink”, which also effectively reduced the production of CO. Meanwhile, the vigorous development of new energy vehicles in recent years has alleviated carbon emissions from mobile sources. The production of PM2.5, which is based on carbon fuel combustion and vehicle exhaust emissions, is effectively controlled. Therefore, low-carbon policies of energy saving, new energy development is conducive to the regulation of PM2.5.

O3 is a pollutant formed by the conversion of nitrogen oxides under light radiation and suitable meteorological conditions, and it is also not directly related to PM2.5. However, studies have shown that the correlation between O3 and PM2.5 in different seasons is reversed25,26, which is similar to the findings in this study. PM2.5 and O3 showed significant inverse correlations on the temporal of inter-day and inter-month and the correlation coefficient on the inter-month scale is larger. The source of PM2.5 and O3 is consistent. The high concentration of O3 can promote the formation of secondary particles under strong atmospheric oxidation conditions and increase the concentration of PM2.5, and high concentration of PM2.5 can weaken solar radiation and inhibit the production of O3. On the small time scale, source consistency is an important reason for the significant positive correlation between PM2.5 and O3, while on the large time scale, the rapid advancement of urbanization, industrialization, and motorization, and massive emission of atmospheric active substances are the main reasons for the increase in surface O3 concentration27. Since the implementation of the “Air Pollution Prevention Action Plan”, the cooperation mechanism for air pollution prevention and control in the three provinces and one city of the Yangtze River Delta has effectively curbed the growth of PM2.5, but O3 pollution has become increasingly severe, which indicates that the issue of O3 pollution should be further addressed in the continued implementation of the ten policies of the atmosphere.

How does PM2.5 respond to the meteorological factors at different temporal scales? The dilution effect of wind speed on PM2.5 rises at first and then tends to be gentle28, and high humidity environment has the effect of agglomerating PM2.529. Studies have shown that precipitation contributes to the dilution of PM2.5, and PM2.5 concentration before and after precipitation has an important effect on its dilution effect30. This study shows that the dilution effect of PM2.5 is more significant with the increase of time scale, which provides a new idea for the impact of precipitation on the macroscopic time scale of PM2.5.

Few studies have investigated the effect of air pressure on PM2.5, and this study found that the response of PM2.5 to air pressure is inversely correlated at different temporal scales and is more strongly correlated on the large time scale. Under the low-pressure circulation situation, there are more rainy days and the wind direction changes more frequently, which helps the diffusion and dilution of particulate matter; while the high-pressure circulation situation brings more sunny days and the weather system is relatively stable, forcing the particulate matter to be stagnate in the near-surface layer. Hence, the response of PM2.5 to air pressure appears to be positive on a large time scale.

This study found that PM2.5 and temperature have a significant correlation at the daily scale, meanwhile, the results show that PM2.5 and temperature are significantly negative on the monthly scale, in line with the distribution characteristics of PM2.5 “winter-high, summer-low” in Nanjing31,32.

This study has shown that there exist seasonal variations of the correlation between PM2.5 concentration and meteorological factors33,34,35. Therefore, the multi-temporal scales cannot be ignored when studying the influence of the natural environment (especially meteorological factors) on PM2.5; meanwhile, the multi-temporal scale provides a new perspective for PM2.5 research.

## Conclusion

By investigating PM2.5 responses to other air pollutants and meteorological factors at across multiple temporal scales, this research generated three major findings. First, the original daily average concentration of PM2.5 exhibited a significant downward trend and the periodic law of “decrease–increase”, which had time lags compared with other air pollutants (CO, O3,) and meteorological fluctuation (PR, AP, MaxT, and MinT). Second, the decomposed temporal variation of PM2.5 by EEMD has a relatively stable quasi-periodicity in the inter-day and the inter-month temporal scale, and followed daily circle and monthly circle. Third, the responses of PM2.5 to other air pollutants and meteorological factors varied at different temporal scales. The temporal pattern of PM10, SO2 and NO2 is synchronous with that of PM2.5. At the daily and monthly scales, PM2.5 was positively correlated with CO and negatively correlated with 24-h cumulative precipitation. At the daily scale, PM2.5 was positively correlated with O3, daily maximum and minimum temperature, and negatively correlated with atmospheric pressure, while the correlation pattern was opposite at the monthly scale.

Such findings help improve our understanding on how PM2.5 responds to the changes of other air pollutants and meteorological fluctuation at different temporal scales, which contribute to future regional air quality assessment and source apportionment studies. They also suggest that in order to mitigate PM2.5 and other air pollution problems, different measures should be devised to target different time scales (especially at inter-day scale and inter-month scale). Especially, the issue of O3 increase should be further addressed when we have effectively curbed the growth of PM2.5 at a longer temporal scale.

It is important to point out that China has begun to publicize the PM2.5 concentration data since December 2013, thus the PM2.5 time series of Nanjing selected in this study started on January 1, 2014. With the continuous accumulation of data, longer temporal scales can be considered in future research, especially the inter-annual and inter-decadal variations of PM2.5. In addition, the source analysis of the multi-temporal response of PM2.5 from two perspectives of human activities (air pollutants) and natural environment (mainly meteorological factors) is mainly realized by qualitative methods so far, and can be further explored by quantitative methods in the future research.