Spatiotemporal evolution of NO2 diffusion in Beijing in response to COVID-19 lockdown using complex network.

The COVID-19 pandemic and the corresponding lockdown measures have been confirmed to reduce the air pollution in major megacities worldwide. Especially at some monitoring hotspots, NO2 has been verified to show a significant decrease. However, the diffusion pattern of these hotspots in responding to COVID-19 is not clearly understood at present stage. Hence, we selected Beijing, a typical megacity with the strictest lockdown measures during COVID-19 period, as the studied city and attempted to discover the NO2 diffusion process through complex network method. The improved metrics derived from the topological structure of the network were adopted to describe the performance of diffusion. Primarily, we found evidences that COVID-19 had significant effects on the spatial diffusion distribution due to combined effect of changed human activities and meteorological conditions. Besides, to further quantify the impacts of disturbance caused by different lockdown measures, we discussed the evolutionary diffusion patterns from lockdown period to recovery period. The results displayed that the difference between normal operation and pandemic operation firstly increased at the cutoff of lockdown measures but then declined after the implement of recovery measures. The source areas had greater vulnerability and lower resilience than receptors areas. Furthermore, based on the conclusion that the diffusion pattern changed during different periods, we explored the key stations on the path of diffusion process to further gain information. These findings could provide references for comprehending spatiotemporal pattern on city scale, which might be help for high-resolution air pollution mapping and prediction.

Introduction

After the World Health Organization (WHO) declared the coronavirus disease 2019 (COVID-19) outbreak a pandemic on March 11, 2020, the world is still fighting the virus. According to the WHO (https://www.who.int/emergencies/diseases/novel-coronavirus-2019), COVID-19 has cumulatively infected more than 195 million people and claimed 4.18 million lives as of 28 July 2021. To effectively curb further spread and protect general public health, governments around the world have implemented unprecedented measures, of which purpose is to restrict the movement of people, vehicles and industrial activities. The sudden interruption of normal operation leads to severe damage to global economies and societies, while significantly reduced pollution and remarkable environmental improvement have been observed (Zambrano-Monserrate et al., 2020).

In order to evaluate the impacts of COVID-19 on air pollution, large fluctuations in pollutants in various scenarios have been frequently investigated. Based on the evidence from 44 cities, the air quality index in northern China, where the earliest lockdown measure was released, decreased by 7.80%. SO2, PM2.5, PM10, NO2, and CO decreased by 6.76%, 5.93%, 13.66%, 24.67%, and 4.58%, respectively (Bao and Zhang, 2020). Furthermore, the emergence of similar dramatic improvements in Spain (Tobías et al., 2020), Malaysia (Abdullah et al., 2020), India (Mahato et al., 2020) was demonstrated as well. Industrial and traffic operations are primary sources in urban areas that force populated groups to be exposed (He and Gao, 2021). By comparing roadside and non-roadside stations, traffic-related air pollution (TRAP) shows a more significant reduction than other sources (Wu et al., 2021). In Los Angeles, the halted operations of traffic behavior led to decreases in NO2 and PM2.5 by 30.1% and 17.5%, respectively. Heavy-duty trucks are a major contributor to traffic decreases in NO2 (61%) and PM2.5 (70.4%) during the strictest lockdown period (Yang et al., 2021b). It follows that NO2 is one of the most decreased pollutants during COVID-19 in major megacities. It is crucial to evaluate NO2 variation in response to COVID-19 and lockdown measures.

Existing studies have confirmed that the air quality make obvious change during the COVID-19 period. However, the corresponding diffusion pattern on a city scale is seldom mentioned at present stage. Fortunately, complex networks have been frequently mentioned to analyze the dynamic behavior of pollution such as transport, spillover and diffusion in recent years (Fellini et al., 2019, 2020; Li et al., 2019, 2021; Wang et al., 2021; Wu et al., 2022). Li et al. constructed spillover networks at multiple timescales to show the interactions of PM2.5 spillover behavior within Jing-Jin-Ji region (Li et al., 2019). Zhang et al. examined the spatial effects on pollution transport in Cheng-Yu urban agglomeration using complex network in which spatial associations of haze pollution were displayed (Zhang et al., 2020). Rafael et al. converted tropospheric ozone (O3) time series into complex network and applied centrality metrics to differentiate the ozone dynamics between rural and urban regions (Rafael et al., 2019). Zhao et al. abstracted the air quality system into the complex network and detect local similarity and regional interaction in the process of pollution diffusion (Zhao et al., 2019). These models have obtained new inspirations and discoveries through the application of complex network methods which visually express the physical and abstract connections of various complicated behaviors in complex systems.

In summary, complex network has been confirmed to be an effective method to reveal the diffusion patterns. However, the diffusion pattern on city scale in responding to COVID-19 is not clearly understood. The halted operations of human activities make it possible to understand the effect of massively anthropogenic disturbance on air pollution. Hence, we collected the original data in air quality monitoring network in Beijing to reveal spatiotemporal evolution of NO2 diffusion in Beijing in response to COVID-19 lockdown. Firstly, from the perspective of diffusion performance in local areas, we explored evidences that COVID-19 had significant effects on the spatiotemporal distribution, and it was attributed to dramatically reduced human activities after the implement of lockdown measures. Secondly, to further quantify the impacts of disturbance caused by different lockdown measures, we discussed evolutionary diffusion patterns from lockdown period to recovery period. The vulnerability and resilience of diffusion pattern was further analyzed. Finally, based on the conclusion that the diffusion pattern changed during different periods, we explore key stations on the path of diffusion process to further obtain information during different periods.

Study area and data description

Studied area

To deeply comprehend the temporal and spatial dynamics of NO2 diffusion during COVID-19, we selected Beijing, one of the most polluted cities in China, as the study area. On January 24th, Beijing officials held press conference to inform that Beijing activated level Ⅰ public health emergency response mechanism. On the same day, The People's Government of Beijing Municipality (http://www.beijing.gov.cn) declared that Beijing implemented COVID-19 epidemic prevention and control measures in community. Gathering activities in communities were restricted or stopped and public places such as cinemas, shopping malls, and hot springs were closed. When necessary, measures might be taken to block communities designated epidemic areas. Human activities, especially traffic activities closely related to NO2 emission, dramatically reduced. Until February 10, 2020, The People's Government of Beijing Municipality allowed companies in Beijing to gradually return to work and production. According to Beijing Transportation Institute (https://www.bjtrc.org.cn/), the operation of road traffic during pandemic could be roughly divided into two stages, which was consistent with weekly congestion levels in public real-time traffic reports provided by Tomtom (https://www.tomtom.com/en_gb/traffic-index/beijing-traffic/). This division was referenced by this study to define the lockdown period (from February 1 to March 31) and recovery period (from April 1 to May 31). To exclude the impact of Lunar New Year encompassed a 7-day national holiday, during which previous studies have noted the reduction in anthropogenic emissions, we focused the variation of pollution since February in 2020. The new outbreak involving Xinfadi market in June was not considered in this research.

Information about the functional areas will be helpful to explain the observed phenomena in following investigation. Refer to the plan for developing urban functional area (2018–2035) announced by The People's Government of Beijing Municipality, there are four types of urban functional areas. Dongcheng (DC) and Xicheng (XC) districts are core areas of the capital, Chaoyang (CY), Haidian (HD), Fengtai (FT), Shijingshan (SJS) districts are urban functional Expansion areas, Tongzhou (TZ), Shunyi (SY), Changping (CP), Daxing (DX), Fangshan (FS) are new areas for urban development, Mentougou (MTG), Huairou (HR), Pinggu (PG), Yanqing (YQ), Miyun (MY) are ecological conservation and development areas.

Data description

Pollutant data were obtained from the Beijing Municipal Ecological and Environmental Monitoring Center (http://www.bjmemc.com.cn). We primarily used the hourly concentrations of NO2 () to construct a complex network defined by NO2 diffusion system. There were 35 air quality monitoring stations deployed in Beijing for the measurement of pollutants, including 12 urban stations, 11 rural stations, 7 background stations and 5 traffic stations. Due to too much missing data, a botanical garden station was not involved in this paper. Four categories of stations were divided according to their geographical locations. Urban stations and rural stations were used to assess air quality in urban and suburban areas, respectively. Urban stations were located in urban areas while rural stations were located in suburban areas. Background stations were far away from downtown and used to monitor the regional environmental background level to reflect baseline pollution. Traffic stations were used to reflect pollution from traffic sources. The geographical locations of these stations on the map are shown in Fig. 1 (a), where detailed information on the air monitoring stations is illustrated in Table 1 . We classified normal year dataset and pandemic year dataset which span the same period (from February 1 to May 31) in 2019 and 2020, respectively. And concentration data measured in 2020 were further split into 2 groups to characterize the variation in the lockdown period (from February 1 to March 31 in 2020) and recovery period (from April 1 to May 31 in 2020). Overall, 3.85% of the data were missing, which was calculated by the remaining 34 stations discussed in this paper. The missing data were imputed with the average of their previous 24 h.

Fig. 1

Locations of the Beijing air quality monitoring stations and an example of network constructed by the interactions of these stations in normal year.

Table 1

Information for each air monitoring stations in Figure S1.

Station		Labels	District	Urban Function	Stations	Labels	Districts	Urban Function
Urban station					Rural station
	Dongsi	U1	Dongcheng	Core Area	Fangshan	R1	Fangshan	New Area
F	Temple of Heaven	U2	Dongcheng	Core Area	Daxing	R2	Daxing	New Area
	Guanyuan	U3	Xicheng	Core Area	Yizhuang	R3	Daxing	New Area
	Wanshou Temple	U4	Xicheng	Core Area	Tongzhou	R4	Tongzhou	New Area
	Aoti	U5	Chaoyang	Expansion Area	Shunyi	R5	Shunyi	New Area
	Nongzhanguan	U6	Chaoyang	Expansion Area	Changping	R6	Changping	New Area
	Wanliu	U7	Haidian	Expansion Area	Mentougou	R7	Mentougou	Ecological Area
	The North	U8	Haidian	Expansion Area	Pinggu	R8	Pinggu	Ecological Area
	Fengtai Garden	U9	Fengtai	Expansion Area	Huairou	R9	Huairou	Ecological Area
	Yungang	U10	Fengtai	Expansion Area	Miyun	R10	Miyun	Ecological Area
	Gucheng	U11	Shijingshan	Expansion Area	Yanqing	R11	Yanqing	Ecological Area
Background station					Traffic station
	Dingling	B1	Changping	New Area	Qianmen	T1	Dongcheng	Core Area
	Badaling	B2	Yanqing	Ecological Area	Yongding	T2	Dongcheng	Core Area
	Miyunshuiku	B3	Miyun	Ecological Area	Xizhimen	T3	Haidian	Expansion Area
	Donggaocun	B4	pinggu	Ecological Area	Nansanhuan	T4	Fengtai	Expansion Area
	Yongledian	B5	Tongzhou	New Area	Dongsihuan	T5	Chaoyang	Expansion Area
	Yufa	B6	Daxing	New Area
	Liulihe	B7	Fangshan	New Area

The meteorological dataset including air temperature, air pressure, wind direction, wind speed and dew point temperature in Beijing in normal year and pandemic year were obtained from National Climatic Data Center (https://www.ncdc.noaa.gov/), where many monitoring stations all over the world provide meteorological information from over 200 countries. It should be noted that the meteorological data represent the meteorological condition in a city rather than a station. The ecological and environmental information was obtained from Beijing Municipal Ecology and Environment Bureau (http://sthjj.beijing.gov.cn/). Population and corresponding population density data were announced by Beijing Municipal Bureau Statistics (http://tjj.beijing.gov.cn/). The job-housing ratio data was obtained from Aurora Mobile (https://www.jiguang.cn/reports/305).

Meteorology plays an important role in the formation, transportation, and diffusion processes of air pollutants (Hua et al., 2021). To understand following results potentially explained by meteorology conditions in this study, we calculated the T-test for corresponding meteorological parameters by two hourly samples before exploring the impact of COVID-19 on diffusion. The meteorological conditions including air temperature, air pressure, wind direction, wind speed and dew point temperature in normal year (from February 1 to May 31 in 2019) and pandemic year (from February 1 to May 31 in 2020) are presented in Table S1. In terms of the overall period from February 1 to May 31, we observed no significant difference () in air temperature, sea level pressure and wind speed, while dew point temperature () reflecting relative humidity in pandemic year was higher than that in normal year. Wind direction () in pandemic year changed as well compared to normal year.

Methodology

Complex network defined by NO2 diffusion process

In the last few decades, complex network science has generated significant development in various fields. One of the most important reasons why it has been regarded as effective modeling and widely used analytical method is its broad applicability. In other words, the framework of various process has been identified by the topology of networks, in which the nodes represent the agents and the links represent the relationship among agents. The agents in network could be countries, researchers or travelers, while the relationships could be direct relationship such as scientific collaboration, social relationship and commercial intercourse or calculated indirect relationship such as competition, causality and nonlinear correlations. It provides insights into complicated interactions in many evolutionary processes that are difficult to understand clearly. Hence, in order to reveal the mechanism of diffusion that involves plenty of complex scenes such as meteorological, geographical and economic conditions, we modeled the diffusion processes among multiple urban areas using the topology of complex network in which the links were extracted by potential causality that was calculated by time series.

In this section, we illustrate how to transform atmospheric diffusion system in Beijing into a complex network system and explore new insight into it using complex network methods. The network is generally given in the formwhere is a set of nodes that represent agents, and corresponds to edges that represent relationships between nodes.

To visually characterize the NO2 diffusion relationship in complex atmosphere system, the hotspots where air quality monitoring stations located at are defined as nodes, as shown in Fig. 1. Edges are defined by potential correlations of air flow between nodes, which is provided by combined method of Linear Granger causality in terms of temporal scale and Inverse Distance Weighting in terms of spatial scale (Rahman and Kashem, 2017).

Linear Granger causality, which is used to examine temporal correlation among nodes, is calculated by vector autoregression (VAR) model. Time series and are defined as hourly NO2 concentrations measured by station and station , respectively. The VAR models of time series without considering the influence of time series and considering the influence of time series are as follows: where and are parameters that specifies how lags and affect the future evolution of time series . is random disturbance term. The residual sum of squares of and are and . Test statistic F examines the causal correlations between and , as shown in Equation (4).

The directed edge from node y to node x is established if time series Granger-cause time series .

Inverse Distance Weighting is used to examine spatial correlation. Only the node pairs of which spatial correlation is not zero seem possible to establish temporal correlation. Spatial correlation defined by inverse distance weighting for stations and is calculated bywhere is the distance. Here, we set and as described by Yang et al. (2021a).

Fig. 1 (b) exhibits an example of the network constructed by the interactions in the process of NO2 diffusion during normal year (from February 1 to May 31 in 2020). After establishing edges among defined nodes, this network is represented by a binary adjacency matrix. is the number of nodes that is 34 in this paper. The element in matrix if the directed edge from to exists, which represents that is one of the neighbors of . Otherwise, if the directed edge from to does not exist. The general formation is demonstrated as follow:

Metrics of diffusion performance

After developing network model, we proposed improved degree metrics derived from the topological structure of network to check spatiotemporal characteristics. Degree, which was first introduced by researchers in the field of social networks and then introduced into other fields, is the number of neighbors connected with node. It is one of the most important metrics to characterize the properties of network. For directed networks, degree is divided into in-degree and out-degree. The advantage of it is to show how much influence there is between the two connected nodes. Recently, it is commented frequently in the investigation of atmosphere system.

In this network, degree metrics were used to identify the influence of sources areas on receptor areas, which aims to discover the areas where the air pollution caused by upstream airborne pollutants is worth taking seriously. The nodes with high in-degree demonstrate that they are strongly influenced by upstream airborne pollutants, while nodes with high out-degree indicate that they have higher contributions to downstream airborne pollutant concentrations.

The nodes in this paper were defined as hotspots measured by air monitoring stations. However, NO2 is an air pollutant whose concentration field is confirmed by large spatiotemporal variations (van Zoest et al., 2020). To realize the exploration in larger scale, this study proposed improved degree metrics that were used to represent diffusion performance in local area. Additionally, the locations of monitoring stations were mostly not formed by natural evolution but typically anthropogenic selection, which caused the spatial sparsity differences of nodes in different functional area. To prevent such case, the sparsity of surrounding areas was considered in the definition of local degree metrics, namely, local degree index.

Local out-degree

In social network, the out-degree of node is the number of neighbors from to , i.e., . The values of were given to reflect the performance of public opinion transmission. Derived from traditional formation, we proposed normalized out-degree based on local information which is used to demonstrate diffusion in local area. Local out-degree index is calculated bywhere is the sum of neighbors' out-degree, and is the set of neighbors of node .

In order to prevent the error caused by disturbances in regression analysis, we introduced cumulative out-degree distribution to give smoother curve and clearer quantitative analysis. Based on the calculated local in-degree for each node, we could sort nodes by this and then obtain the probability of each degree value , namely, local in-degree distribution. From the perspective of Probability and Statistics, represents the probability that a randomly selected node has an in-degree value . Accordingly, cumulative local in-degree distribution is calculated by

Local in-degree

Similarly, the out-degree of is the number of neighbors form to , i.e., . Local in-degree index is calculated bywhere is the sum of neighbors' in-degree of . And cumulative local out-degree distribution is calculated by

Quantitative variation of diffusion pattern

We introduced the concept of vulnerability and resilience, which was increasingly mentioned in ecosystem management including atmosphere system (Mumby et al., 2014), to describe the variation of diffusion pattern during lockdown period and recovery period respectively. Vulnerability was defined as the measure of damage experienced by a system despite internal or external disruptions, while resilience was defined as the ability of system to return to normal performance, within an acceptable period of time, after being disturbed (Brandon-Jones et al., 2014). They have been proposed to quantize the changes of performance in system in the case of disaster such as earthquakes, hurricane and even traffic jam. The epidemic is a typical scenario where good measurement of vulnerability and resilience assists policymakers in predicting trends and making decisions.

In this study, compared to the same span in normal year, the concept of vulnerability was used to quantitatively examine the variation of diffusion pattern during lockdown period, while resilience was used to quantitatively examine the variation of diffusion pattern during recovery period. Based on unified formation displayed by the magnitude of impact and duration in preceding work, we proposed the measurement of vulnerability and resilience calculated by the changed pattern compared to normal year.

The variation of diffusion pattern during lockdown period is calculated bywhere is the curve fitted by cumulative local degree distribution during lockdown period, and is the curve fitted by the same time span in normal year.

Supposing that vulnerability and are positively related, smaller variation disturbed by lockdown measure implies the smaller vulnerability. We define vulnerability as

The variation of diffusion pattern during recovery period is calculated bywhere is the curve fitted by cumulative degree distribution during recovery period, and is the curve fitted by the same time span in normal year.

Resilience involves the difference between and in definition, where the smaller difference means smaller resilience during recovery period. We define resilience as

The significance of stations in the process diffusion

Centrality indicators, which were commonly mentioned tools to mining key nodes, were applied in this paper to identify the key stations on diffusion path, including out-degree centrality, in-degree centrality, betweenness centrality and closeness centrality.

Out-degree centrality

We used normalized out-degree to define out-degree centrality, which describes the significance of source nodes from the aspect of spillover ability. It is calculated by

In-degree centrality

In-degree centrality, which describes the significance of target nodes from the aspect of receiving ability, is calculated by

betweenness centrality

Betweenness centrality is commonly employed to describe the significance of nodes from the aspect of control ability. The betweenness centrality of a node is the sum of the fraction of all-pairs shortest paths that pass through , i.e.,where is the number of the shortest paths from to , and is the number of those paths passing through node .

The nodes with a larger value of betweenness centrality have a stronger control ability for information transmission along the shortest path. Although in a real network, the diffusion frequency of NO2 between nodes is not always consistent and not all diffusion process is based on the shortest path, the betweenness centrality can also approximate the control ability of nodes in terms of pollutant flows.

closeness centrality

Closeness centrality is utilized to describe the significance of nodes from the aspect of diffusion efficiency. For node on the network, the average distance between node and others is calculated bywhere is the incoming distance from node to node . Closeness centrality is defined by the reciprocal of , i.e.,

A node with a smaller average distance is closer to other nodes, which means that the information can be transferred to other nodes more easily. Therefore, closeness centrality is applied to describe the efficiency of diffusion in this study.

Results and discussion

The impacts of COVID-19 on spatiotemporal distribution in Beijing

In this section, we compared the spatiotemporal distribution of diffusion performance during pandemic year and normal year to evaluate the impacts of COVID-19 on spatiotemporal performance. Local degree index in the same period (from February 1 to May 31 in 2019 and 2020) were analyzed.

The evolution of output distribution from normal year to pandemic year

In Fig. 2 , we compared spatiotemporal distribution of output performances in normal year and pandemic year. Based on the kriging method, local out-degree index in local areas was extended to the investigation in city scale. The reddest parts of map were the areas that have highest contributions to downstream airborne pollutant concentrations, while the bluest part were the areas that have lowest contributions to downstream airborne pollutant concentrations.

Fig. 2

Spatial distribution of local out-degree index in normal year and pandemic year.

From the perspective of spatial distribution, most sources of NO2 in the process of diffusion were located at city center, and the diffusion behavior decreased gradually as the distance from center increased in both normal year (Fig. 2 (a)) and pandemic year (Fig. 2 (b)). Core areas (DC, XC), functional Expansion areas (CY, HD, FT, SJS) and parts of new areas (SY, TZ, DX) were important pollution sources. In fact, it was due to the fact that the sources of NO2 output behavior is closely related to human activities, especially traffic activities. NO2 is one of the most concerned pollutants that are dominantly emitted by transportation (Hua et al., 2021). Beijing Municipal Ecology and Environment Bureau announced that motor vehicles were responsible for up to 86% of all nitrogen oxides emissions in 2019. NO2 output behavior was more prominent in areas where there may be more traffic activities. This pattern can be verified by the references of Beijing Municipal Bureau Statistics, where obtained data in Beijing's 7th census revealed that six urban districts including core areas and functional Expansion areas have the highest population density. Moreover, the job-housing ratio in DC, XC, CY and HD have already over 1, which means that surplus jobs attract commuter and generate extra traffic-related emission. That is to say, population density and commuting behavior were the main reasons for spatial distribution of output performance.

From the perspective of temporal evolution, we observed significant differences between the performance in normal year (Fig. 2 (a)) and pandemic year (Fig. 2 (b)). The red range that was stitched up by core areas, functional Expansion areas and parts of new areas in pandemic year became smaller than in normal year, which leaded to saddle-shaped distribution in pandemic year. Especially, the decrease in CP was more obvious compared to other areas, which was mainly attributable to the distinct change of traffic activities. It has been confirmed that approximately 70–80% reduction in NOx during pandemic was due to reduced traffic emissions, and 20–25% reduction was due to reduced industrial emissions (Huang et al., 2021). Although the population density of CP is average among all the districts in Beijing, there are two of the largest communities including Tiantongyuan and Huilongguan. Besides CY and HD districts, CP has the largest total population. However, the job-housing ratio in CP is lowest among all districts in Beijing. It demonstrates that a large number of travelers are long-term commuters for work, which generates major sources of NO2 emission. After the spread of epidemic and the implement of lockdown measures, commuting activities has been restricted and then output sources were decreased.

Another significant difference between the performance in normal year and pandemic year was deepened color in reduced red range implying upward tendency of output behavior in some areas. This was possibly associated with the strengthened diffusion in local areas, which was caused by combined effect of human activities and diffusion conditions especially unexpected meteorological factors. At the start of pandemic, poor diffusion conditions were dominated by extreme meteorological variation comprising low boundary layer height, stagnant airflow and high relative humidity in February 2020 (Le et al., 2020; Sun et al., 2020). After April, favorable diffusion conditions came and frequent southern winds facilitated NO2 output from the south (Hua et al., 2021), which could explain the few increase of output performance in some areas. But relatively poor diffusion conditions in May were received by Beijing again (Hua et al., 2021). In terms of the overall period from February 1 to May 31 in 2020, the complex meteorological variation promoted output performance in some areas compared to that in normal year.

The evolution of input distribution from normal year to pandemic year

As shown in Fig. 3 , we display the performances of NO2 input in normal year and pandemic year on map. The reddest parts of map were the areas that they are strongly influenced by upstream airborne pollutants, while the bluest part were the areas that they remain almost insusceptible by upstream airborne pollutants.

Fig. 3

Spatiotemporal distribution of local in-degree index in normal year and pandemic year.

From the perspective of spatial distribution, the distribution of input behavior was similar to the scenario of pollution output analyzed above. In normal year (Fig. 3 (a)) and pandemic year (Fig. 3 (b)), Core areas (DC, XC), functional Expansion areas (CY, HD, FT, SJS) and parts of new areas (SY, TZ, DX) were important pollution sources as well. And the performance of NO2 input decreased as the distance from center increased. It demonstrated that diffusion behavior in six urban districts displayed active interactions including input and output.

From the perspective of temporal evolution, the significant differences of input performance were easily observed from normal year (Fig. 3 (a)) to pandemic year (Fig. 3 (b)). Primarily, the red range on the west in pandemic year showed remarkable decrease compared to that in normal year. The most significant decrease occurred in MTG district, with the lowest population density, and its adjacent areas, implying that human activities including vehicle-emitted behavior was a better indicator of input performance. Additionally, some northern areas such as CP and SY displayed more higher input performance, which may be explained by frequent southern winds in April 2020. As analyzed in section 4.1.1, complex meteorological variation from February 1 to May 31 in pandemic year facilitated diffusion behavior in several areas. Compared to the poor diffusion conditions before April and after April, favorable diffusion conditions such as frequent southern winds in April seemed to play more important role to diffusion behavior. That is to say, when frequent southern wind promoted output performance in some area, input performance in northern areas was increased as well.

The impacts of lockdown measures on diffusion pattern in responding to COVID-19

As described above, we found evidences that COVID-19 had significant effects on the spatiotemporal distribution of NO2 output and input behavior. These changes brought by pandemic are mainly caused by lockdown measures that restricted human activities especially transportation activities. To further identify the impacts of different measures, we discussed the evolution of diffusion pattern from lockdown (from February 1 to March 31) period to recovery period (from April 1 to May 31). The same period in normal year and pandemic year were compared. To explore pollution diffusion patterns and quantify the variation disturbed by lockdown measures and recovery measures, we introduced cumulative proportion curve, which was frequently used to understand the basic laws of human society and natural world such as human mobility patterns (Gonzalez et al., 2008). The difference in diffusion patterns between the different periods in pandemic year and the same time span in normal year were further investigate.

The variation of output pattern from lockdown period to recovery period

Fig. 4 displays the variation of diffusion patterns during lockdown period and recovery period compared to the same time span in normal year. In Fig. 4, we divided the values of local degree index of 34 nodes (hotspots of air pollution monitoring stations) in network into 10 intervals (range from 0.2 to 1.2) for statistics. The middle of each interval was the X-coordinate, and the correspondingly calculated cumulative proportion was Y-coordinate. represented the quantitative variation of diffusion pattern during the same period from normal operation to pandemic operation.

Fig. 4

Variation of pollution output pattern during different periods.

Fig. 4(a) and (b) illustrates the variation of output pattern during lockdown period and recovery period compared to the same time span in normal year. Panel (a) demonstrates a similarly exponential curves during lockdown period (from February 1 to March 31) in pandemic year and the same time span in normal year. As the value of local out-degree increased, increasing growth rates of cumulative proportion curve revealed the positive correlation of local out-degree and its corresponding proportion. Consistent with the pattern during lockdown period, the shape of cumulative curves during recovery period (from April 1 to May 31) in Panel (b) of Fig. 4 shows exponential curves as well, but the cumulative proportion curve grew more equally. There was significant decreased variation () during recovery period (panel (b) in Fig. 4) by comparison with variation () during lockdown period (panel (a) in Fig. 4), which revealed decreasing trend with the weakened strength of lockdown policies. During COVID-19, the difference of output pattern between general and pandemic operation firstly increased at the cutoff of lockdown measures but then declined after the implement of recovery measures.

The variation of input pattern from lockdown period to recovery period

Fig. 4 (c) and (d) illustrate the variation of input pattern during lockdown period and recovery period compared to the same time span in normal year. In terms of input pattern, the cumulative curves during lockdown period (from February 1 to March 31) in Panel (c) and recovery period (from April 1 to May 31) in Panel (d) both displayed exponential curves. The variation of input pattern during recovery period () decreased from lockdown period (), which indicated that the difference of input pattern between normal and pandemic operation decreased after the implement of recovery measures.

Furthermore, we noted that the variation of output pattern () in response to lockdown measures was larger than the variation of input pattern () in response to lockdown measures, which manifested that output behavior was more vulnerable than input behavior in the case of anthropogenic cutoff of human activities. This may be contributed to stronger influence of human activities on emission sources of output behavior than input behavior. In response to recovery measures, the slight recovered human activities resulted in 57.4% recovery of output pattern and 61.5% recovery of input pattern. The resilience of input behavior was stronger than output behavior. Hence, the output behavior had greater vulnerability and lower resilience than input behavior.

Identification of the key stations on diffusion path during different periods

Section 4.2 revealed that the effects of measures on diffusion pattern during lockdown period and recovery period are different. To further obtain more information during different periods, the identification of key stations on the path of diffusion is crucial. In this section, we applied centrality indicators to evaluate the significance of nodes from four aspects.

The key categories of stations during different periods

Using two-way ANOVA, Fig. 5 indicates the centrality metrics of four categories (urban stations, rural stations, background stations and traffic stations) during different periods. Out-degree, in-degree, betweenness and closeness centrality reflected the ability of receiving NO2, spillover NO2, control ability and efficiency on the path of diffusion, respectively. As shown in Fig. 5, where the pattern during same period in normal years was used as the control group, a greater value reflected a more significant role in diffusion process. The tendency from lockdown period to recovery period in normal year was attributed to seasonal variation, which was helpful to exclude the changes caused by natural evolution during the different periods in pandemic year and then partially understand the changes caused by different measures. In terms of general comparison of normal and pandemic operation, the most significant categories basically remained the same from normal year to pandemic year, but the most significant categories were different in the four subgraphs. For spillover and efficiency, urban stations were the most significant category. For receiving ability, urban and traffic stations were the most significant categories. For control ability, traffic and background stations were the most significant categories.

Fig. 5

The significance of four categories from four aspects.

The key stations during different periods

To further detailly identify key station, we compared centrality metrics of nodes during different periods in Fig. 6 , where the properties of spillover ability, receiving ability, control ability and efficiency were involved in Panels (a), (b), (c), and (d), respectively. The stations labeled 0–10, 11–21, 22–28 and 29–33 referred to urban, rural, background and traffic monitoring stations, respectively. Normal operation obtained by normal year (from February 1 to May 31 in 2019) was compared to the results during lockdown period and recovery period.

Fig. 6

The significance of each station from four aspects.

Panel (a) of Fig. 6 displays the out-degree centrality representing the spillover ability of 34 stations during different periods. In normal operation, urban stations, traffic stations and some rural stations were key nodes with strong spillover ability. The out-degree centrality decreased after COVID-19. During the lockdown period, traffic stations still played a main role in spillover NO2, while the significance of some urban and rural nodes performed a more obvious decrease. The largest decrease of spillover was R6 (Changping), which was consistent with the changes of output performance analyzed in section 4.1.1. During the recovery period, the spillover ability of most stations further decreased compared to lockdown period. The key stations of spillover during the lockdown period were T3 (Xizhimen) and U9 (Feitai Garden), and that during the recovery period were T3 (Xizhimen) and U8 (The North) from the aspect of spillover ability.

Panel (b) of Fig. 6 shows in-degree centrality representing the receiving ability of nodes. In addition to pollution created by their own traffic emissions and industries, NO2 diffused from other areas became one of the important sources for the nodes with large value of in-degree. In normal year, urban stations, traffic stations and some rural stations were the key stations frequently diffused by other areas. During the lockdown period, the centrality of some stations, including all traffic stations and some urban stations and rural stations, decreased. R7 (Mentougou) was the station with the largest drop of receiving ability, which was consistent with the changes of input performance analyzed in section 4.1.2. The most significant drop occurred at the stations of traffic category. This trend leaded to the result that U2 (Temple of Heaven) and U3 (Guanyuan) became the most significant key stations during the lockdown period. During the recovery period, the values of most urban and rural stations decreased, while traffic station and some background station increased. U2 (Temple of Heaven) and U3 (Guanyuan) still was the most significant nodes on the path of diffusion from the aspect of receiving ability.

Panel (c) of Fig. 6 indicates that control ability of most stations increased after COVID-19. The control ability during the lockdown and recovery periods was stronger than that during normal year, especially urban stations. From lockdown period to recovery period, the control ability of half of stations further increased. It seemed like that the tendency of control ability was contrary to spillover ability and receiving ability. Decreased pollution partly caused an increase in the control ability. The most significant nodes were the R5 (Shunyi) during lockdown period and recovery period from the aspect of control ability. In Panel (d) of Fig. 6, urban and traffic stations were the most significant stations. Except for R7 (Mentougou), there were no significant changes from normal year to pandemic year. The most significant stations for closeness centrality were the same as in-degree centrality during two periods, which implied that efficiency of diffusion was potentially related to spillover ability.

Overall, the significant nodes obtained by Fig. 6 are illustrated in Table S2. It should be noted that most significant nodes form four aspects were urban stations and traffic stations. Meanwhile, R5 (Shunyi) was the critical station in the process of NO2 diffusion from the aspect of control ability.

Conclusions

This paper adopted complex network method to reveal diffusion patterns effected by the different lockdown measures in response to COVID-19. Based on the investigation of air quality changes from normal operation to pandemic operation, we reached following conclusions that might provide references for high-resolution pollution mapping and prediction.

First, the general decrease of influence of sources areas on receptors areas from normal year to pandemic year were confirmed, while few increases emerged in several specific areas. Overall, the spatial ranges of serious sources areas and receptors areas decreased, but the diffusion performance in several areas slightly increased. This mainly resulted from the combined effect of changed human activities and diffusion conditions. It seemed that the declined diffusion behavior from source to receptors was related to job-housing ratio, total population and its corresponding population density, while the increased tendency in several areas was more likely to have caused by unexpected meteorological variations especially frequent southern winds in April.

Second, comparing normal operation with pandemic operation, quantified analysis demonstrated that the difference of diffusion pattern, which displayed by cumulative proportion curve, firstly increased at the cutoff of lockdown measures but then declined after the implement of recovery measures. For output pattern, during recovery period, 57.4% of variations disturbed by the strictest lockdown measures during lockdown period recovered. For input pattern, the variation during lockdown period was smaller than that in the scenario of output pattern. But 61.5%, a more lager proportion than 57.4%, of variations in terms of input pattern recovered during recovery period. That is to say, the source areas had greater vulnerability and lower resilience than receptors areas.

Finally, key stations on the path of NO2 diffusion is identified to provide baseline information that key areas along path should be taken advanced measures to prevent bad air conditions for pollution control. The results revealed that, urban stations were the most significant category from the aspect of spillover and efficiency, urban and traffic stations were the most significant categories from the aspect of receiving ability, traffic and background stations were the most significant categories from the aspect of control ability. In terms of specific stations, most significant nodes form four aspects were urban stations and traffic stations. Meanwhile, Shunyi was the critical station in the process of NO2 diffusion from the aspect of control ability.

The results obtained by this research provide references for comprehending spatiotemporal changes during COVID-19 and the role of lockdown measures on NO2 diffusion pattern. In addition, the identification of key stations is helpful for emergency management of pollution control during pandemic year. Although these results regarding NO2 are based on original data in Beijing, they still propose new insights into the analysis of other pollutants and alternative methods for advisors to make informed decisions in other cities.

Credit author statement

Zhe Zhang: Conceptualization, Methodology, Visualization, Investigation, Writing – review & editing. Hong-di He: Conceptualization, Visualization, Investigation, Writing – review & editing. Jin-Ming Yang: Formal analysis, Writing – review & editing. Hong-Wei Wang: Formal analysis, Writing – review & editing. Yu Xue: Formal analysis, Writing – review & editing. Zhong-Ren Peng: Formal analysis, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.