Untangling the contributions of meteorological conditions and human mobility to tropospheric NO2 in Chinese mainland during the COVID-19 pandemic in early 2020

Abstract In early 2020, unprecedented lockdowns and travel bans were implemented in Chinese mainland to fight COVID-19, which led to a large reduction in anthropogenic emissions. This provided a unique opportunity to isolate the effects from emission and meteorology on tropospheric nitrogen dioxide (NO2). Comparing the atmospheric NO2 in 2020 with that in 2017, we found the changes of emission have led to a 49.3 ± 23.5% reduction, which was ∼12% more than satellite-observed reduction of 37.8 ± 16.3%. The discrepancy was mainly a result of changes of meteorology, which have contributed to an 8.1 ± 14.2% increase of NO2. We also revealed that the emission-induced reduction of NO2 has significantly negative correlations to human mobility, particularly that inside the city. The intra-city migration index derived from Baidu Location-Based-Service can explain 40.4% ± 17.7% variance of the emission-induced reduction of NO2 in 29 megacities, each of which has a population of over 8 million in Chinese mainland.


INTRODUCTION
To curb the spread of COVID-19, the Chinese government implemented nationwide strict control measures from late January to March 2020 [1,2]. Lockdowns were imposed in cities and provinces, leading to a gradual cessation in inter-city and inter-province traffic [1]. Inside cities and villages, strict self-quarantine was also implemented. People had to stay at home, except for shopping for necessities or seeking medical treatment. Businesses and industries suspended operations or largely reduced production. The intensive lockdown measures led to a dramatic decrease in human mobility [3,4].
Nitrogen dioxide (NO 2 ), as one of the most important air pollutants, is harmful to the human respiratory system [5][6][7] and plays essential roles in the formation of acid rains, second order aerosols [8] and ozone [9][10][11]. The dominant sources of tropospheric NO 2 over east China are anthropogenic combustions in winter, of which the contributions from power generation, industry and transportations are about 19%, 42% and 35%, respectively [12]. The decrease in human mobility resulting from the lockdown measures is expected to have produced impacts on tropospheric NO 2 via effects on industry and transportation activities [13,14]. Recent studies have reported a satellite-observed large drop in column NO 2 density during this period because of the COVID-19 quarantine [1,13,15].
Besides anthropogenic emissions, tropospheric NO 2 concentrations are also strongly modulated by changes in meteorological conditions [16][17][18][19]. Changes in wind speed, atmosphere stability (related to temperature and pressure etc.), solar radiation and humidity from day to day can quickly change the atmospheric NO 2 densities [16,20]. Temperature and humidity are crucial to the photochemical processes related to NO 2 [21]. Higher temperature and higher humidity can reduce the lifetime of NO 2 and accelerate the conversion of NO 2 to secondary nitrate aerosols [17,19], thus resulting in a negative correlation with atmospheric NO 2 concentration in most places [16,19]. Solar radiation is the key factor controlling the photodissociation rate of NO 2 (NO 2 →NO + O), and can greatly affect the lifetime of NO 2 [21,22]. This is strongly supported by observation of increased NO 2 concentration during the solar eclipse [22]. In general, surface NO 2 concentration is found to decrease with increasing solar radiation [16,21]. In addition, high wind speed and high planetary boundary layer height (PBLH) both favor dispersion and dilution of air pollutants in the boundary layer of the atmosphere [16,17] and can reduce NO 2 concentration [21,23,24].
Anthropogenic emissions and meteorological conditions can both affect atmospheric NO 2 concentration, but their effects are often tangled. Although the reported literature demonstrates the important influences of lockdowns on tropospheric NO 2 [13,25], the respective contributions from anthropogenic and meteorological processes are not clear.
Chemical transport models can be used to analyze the sources of atmospheric composition changes. However, the modelled results can be affected by potential uncertainties in the emission and chemistry processes. For example, Liu et al. showed that the modelled surface NO 2 over North China Plain is about 34% lower than surface measurement with the GEOS-Chem model, but is 26% higher using the CMAQ model [26]. Recent studies suggest the possibility of constraining the observation-based anthropogenic and meteorological influences with statistical models to avoid the effects of potential uncertainties in model simulations [27][28][29]. During the early stages of the COVID-19 pandemic, anthropogenic emissions in China were much lower than before [13,15], while changes in meteorology conditions in 2020 were expected to be smaller than changes in emissions. This provides an ideal test-bed to study the separate impacts of emission and meteorological changes on atmospheric NO 2 with statistical models.
In this study, we investigated the effects of meteorology conditions and human mobility associated with COVID-19 quarantine on atmospheric NO 2 in China using a statistical model to represent the NO 2 [27]. The human mobility strengths, including migration and intra-city flow were quantified using Baidu Migration data [3,30]. We focused on the month before (hereafter Month-01) and the month after (hereafter Month-02) the Chinese Spring Festival in 2017, 2018, 2019 and 2020 to take the holiday effect on human mobility into account.

Statistical model of troposphere NO 2
According to the annual Report on the State of the Environment in China from 2015 to 2019 (http:// english.mee.gov.cn/Resources/Reports/soe/), the mean NO 2 concentrations of the cities in China were relatively stable from 2017 to 2019. Before that, anthropogenic NOx emissions (normalized in 2010) were reduced by about 21% in 2012-2015 (7%/year) and about 6% in 2015-2017 (3%/year) [12]. The dramatic declines of anthropogenic NOx emissions in 2012-2015, as well as the subsequent slowdown of emission reductions, were mainly driven by installation of selective catalytic reduction (SCR) systems in utilities for coal-fired power plants [12].
Recent studies have revealed that the satelliteobserved column NO 2 density in China in 2020 Month-02 was much lower than that in 2019 [15], and concluded that this drop was attributed to the COVID-19 related city lockdowns and travel bans [1]. However, it must be recognized that the atmospheric NO 2 concentration is also greatly affected by meteorology conditions [15].
Assuming the real measurements of atmospheric NO 2 (in logarithm) can be separated into two parts, NO 2 contributed by emission F E mi s (x, t) and by meteorology conditions G Me te (x, t), we have the following function associated with geolocation (x) and time (t) [27]:  [12], F E mi s (x, t) based on 2018 and 2019 should provide a good approximation for the anthropogenic influences for 2017 and 2020. Thus, we assumed the temporal variations of F E mi s (x, t) were negligible at each grid of 0.5 × 0.5 degree. (ii) The temporal and spatial variations of G Me te (x, t) can be modelled using a simplified linear function of five key meteorology parameters as described in Data and methods. We found these two assumptions resulted in good agreement between the observed and modelled tropospheric NO 2 , based on self-consistency check (using training data) and independent check (using independent data). Therefore, we have: It should be noted that the modelled emission term F E mi s (x) M O D in Eq. (2) is only a function of geolocation. In other words, its value stays constant at given 0.5 × 0.5 degree box based on statistical regression. The detailed regression procedures and sensitivity tests are described in Data and methods. The difference between satellite observations and modelling results can be expressed as: where the first term at the right hand of Eq. (3) represents the error introduced by ignoring the temporal variations of emission. The second term represents the modelling error of G Me te (x, t).
The performance of the model was analyzed using independent (from establishing the model) observations in 2017. The model successfully predicted the monthly mean atmospheric NO 2 in 2017 Month-02 ( Fig. 1), with negligible bias in most areas in China. Even in the heaviest polluted areas in central and eastern China with NO 2 over 10 × 10 15 molec/cm 2 , the mean bias is only 4.3% com-pared with satellite observations. On the other hand, the spatial correlation coefficients between model prediction and satellite NO 2 are as high as 0.97 (P < 0.001). Similar results for 2018 and 2019 can be seen in Fig. S4.
The model also works well at predicting daily NO 2 . At the scales of provinces ( The above results demonstrate that the contribution of emission to the atmospheric NO 2 , in the same month of the adjacent years, can be estimated as a time-independent geolocation-based function. The spatial and temporal variations of meteorology effects can be modelled using the linear function of five selected key parameters. The modelling error is generally <5% based on validations in 2017. The reason for the emission situation in 2017 was similar to that in 2018/2019, and the regression model captured the quantitative dependence of atmospheric NO 2 on meteorology conditions. Consequently, if the anthropogenic emissions in 2020 were similar to those in 2018/2019 (i.e. without the effects from COVID-19 quarantine), the model was expected to provide good prediction for tropospheric NO 2 in 2020.
It should be noted that changes in column atmospheric NO 2 are not linearly associated with emissions because of nonlinear effects from atmospheric chemistry. Based on results from the GEOS-Chem chemical transport model study ( Fig. S17), we found a broadly linear response of modelled tropospheric NO 2 columns to changes in anthropogenic NOx and VOCs emissions, that is 50% reduction of anthropogenic emissions results in about 45% reduction of tropospheric NO 2 columns. The model simulations suggest that the influence from nonlinear processes is small (about 5%).

Quarantine-induced reduction in troposphere NO 2
In 2020, although NO 2 variations related to meteorology conditions could still be modelled with good accuracy, the emissions of NO 2 were significantly reduced because of the city lockdowns and travel bans. Therefore, the foundation of the statistical model describing the contribution from emissions collapsed.
(3) in 2020 became much larger than that in 2017. The model overestimated monthly mean NO 2 by 6-9 × 10 15 molec/cm 2 in the heavily polluted areas in China (Fig. 1d). Similar overestimation also could be seen from the time series of daily mean NO 2 in most polluted cities and provinces (Figs S7-S10), such as Tianjin, Shanghai, Shandong, Jiangsu and Beijing.
If we compare the satellite observation of atmospheric NO 2 in 2020 with that in 2017, we could decompose the difference into three isolated terms [31]: where the first term represents the emission-induced reductions in 2020; the second represents the meteorology induced variations; and the third represents the modelling error. Using real satellite observations and modelling results in 2020 and 2017, the map of the contributions (unit: %) from emission and meteorology (i.e. the above three terms) to the reduction of NO 2 is shown in Fig. 2. In most of China's cities with monthly mean NO 2 over 3 × 10 15 molec/cm 2 , we found that emission-induced reductions in 2020 ( Fig. 2b) were larger than the satellite-observed reductions ( Fig. 2a), because the meteorology in 2020 led to a net increase of NO 2 compared to 2017 (Fig. 2c).
Overall, the Ozone Monitoring Instrument (OMI) observed troposphere NO 2 decreased by 37.8 ± 16.3% in 2020 from that in 2017. Using the model mentioned above, we estimated that if the weather conditions in 2020 were the same as that in 2017, the NO 2 columns should have decreased by 49.3 ± 23.5% because of the reduced anthropogenic emission, which means the emission-induced reduction of NO 2 resulting from the COVID-19 quarantine was actually higher than OMI actual observations. The meteorological conditions in 2020 did not favor the dilution and ventilation of air pollutants, and thus led to an increase of NO 2 of 8.1 ± 14.2%. Meanwhile, the modelling error of the above estimation is only 3.32 ± 17.8%, which is significantly smaller than the other two terms.
The statistic model results are consistent with GEOS-Chem model simulations. As shown in Fig. 2e The results are also consistent with other studies in the literature [14,[32][33][34]. Zhang et al. estimated the daily NOx emission in 2020 by combining TROPOMI NO 2 observation with WRF-GEOSChem simulations, and reported a 50% decrease of emission after the COVID-19 lockdown [14]. Marlier et al. observed a 49% decline of NO 2 after the Lunar New Year, and found the weather conditions weakened the emission reduction [33]. Zhao et al. applied the emission inventory of 2017 to WRF-CMAQ, and concluded that the meteorological condition in 2020 elevated the NO 2 concentration in over half of the cities in China [34]. Wang et al. found the reduction of PM2.5 simulated by WRF-CMAQ is smaller than the reduction of precursor emissions, also indicating the unfavorable meteorology (lower PBLH, WS and higher RH) for the dilution of the pollutants [35].
Therefore, the COVID-19 quarantine actually has caused a reduction of NO 2 larger than that seen from the satellite observation (i.e. a direct comparison of 2020 with 2017), but the weather effect has cancelled out some of the emission effect. The modelling error is significantly smaller than each of the two effects, particularly the mean value. This is the first time contributions of emission and weather to the satellite-observed reduction of NO 2 in early 2020 have been isolated. Similar analyses using  situations in 2018 and 2019 are given in the Supplementary data (Figs S11 and S12). Overall, when comparing 2020 with 2018 and 2019, the emissioninduced reduction of NO 2 was also significantly larger than the satellite-observed reduction from the meteorology contribution. This confirmed the conclusion derived from the 2020-2017 comparison.

Human mobility and NO 2
Based on Eq. (3), the difference between satellite observations and model prediction in 2020, i.e. logrNO 2 (2020) = logNO 2 (x, 2020) M O D − logNO 2 (x, 2020) O B S , mainly represents the emission-related reduction of NO 2 (hereafter logrNO 2 ), which can be attributed to multiple factors including the prohibition of human mobility implemented by the government, closure of businesses consuming fossil fuels, such as restaurants, hotels etc., reduction of industrial production because of weakened domestic and international trades etc. It is hard to make a thorough survey to measure all of those factors in the current situation when COVID-19 remains a serious threat to human health. Fortunately, satellite location-based services (LBS) describing human mobility [36] are useful proxies of anthropogenic emissions. To what extent can the emission-related reduction of NO 2 in 2020 be explained using LBS data? To quantitatively understand the roles of city lockdowns and travel bans played in reducing the air pollutants in China, we investigated the correlations between the emission-related reduction of NO 2 and Baidu migration data (Data and methods) of three indices representing the relative population flow moving in (I-index), moving out (E-index) and moving inside the city (C-index). The spatial patterns of Natl Sci Rev, 2021, Vol. 8, nwab061  As shown in Fig. 3, as people started to go home for family reunions in Month-01 2020, the immigration index (I-index, red curves) and emigration index (E-index, dash red line) in megacities with a population over 8 million rapidly increased and peaked around 23 January 2020 when Wuhan, Hubei, was locked down because of a COVID-19 outbreak. After that, both I-index and E-index decreased sharply and remained at very low values during Month-02 2020 [4]. In Month-01, shopping and visiting inside cities also increased in preparation for the coming Spring Festival, and the intra-city C-index (blue curves) was also high before 23 January 2020. For the same reason, the C-index dropped after the lockdowns. The 'Spring Festival Effect' was also shown in 2019, except that the C-index picked up quickly several days after the Spring Festival.
Meanwhile, the emission-related change of logrNO 2 (vertical bars in Fig. 3) in 2020 just oscillated around zero each day before 23 January. After that, it stayed at positive values and was significantly larger than the standard variations. In contrast, in 2019, the difference between satellite observation and model prediction of NO 2 (ie, logrNO 2 ), remained at small values during the whole period of Month-01 and Month-02, and the temporal variations were always within the range of standard deviation. The difference between 2020 and 2019 confirmed that the emission changes in 2020 induced a large reduction in NO 2 .
To investigate the quantitative relationship between logrNO 2 and the human mobility indices, we constructed scatter plots of daily logrNO 2 to daily indices in 2019 and 2020 in cities populated over 8 million (lower panel in Fig. 3). In 2019, the correlations between logrNO2 and all migration indices are weak because the emission-induced variations in NO 2 were very small. While in 2020, daily logrNO 2 in individual cities or that averaged in all cities both negatively correlated with those migration indices, with P < 0.001. The intra-city migration C-index showed the strongest correlation and could explain 22.1% (i.e. the R 2 at individual city level) to 60.8% (the R 2 averaged in all megacities) variance of the logrNO 2 . The immigration I-index could explain 13.0% to 36.0%; the emigration E-index could explain 12.3% to 27.0%.
A list of the explained variance of logrNO 2 by migration indices (from high to low) of all 29 megacities is given in Table 1. In some of the cities in southern China such as Guangzhou and Dongguan, the C-index could explain as much as ∼70% variance. In mid-and eastern China, cities like Suzhou, Heze and Xuzhou also showed explained variance of over 60% by the C-index. This indicates that human mobility inside the city is more important in terms of effects on NO 2 emissions than the population flow toward (I-index) or out (E-index) of the city.
Not only in those megacities, but negative correlations between logrNO 2 and migration indices were also seen nationwide in the mainland of China in 2020. In Fig. 4, among cities with mean NO 2 over Table 1. The explained variance of emission-based reduction of NO 2 by the migration indices of C-index R 2 (C), the I-index R 2 (I) and the E-index R 2 (E) in 29 megacities with a population of over 8 million. The cities are sorted by the R 2 (C) from large to small. NaN: insignificant correlation coefficient. 3 × 10 15 molec/cm 2 , the logrNO 2 showed significantly negative correlations with I-index in 116 cities and with E-index in 110 cities, with explained variance of 0.203 ± 0.120 and 0.208 ± 0.124, respectively. For the C-index, 156 cities showed significantly negative correlations with explained variance of 0.279 ± 0.159. No city showed positive correlation with logrNO 2 for the C-index. The results indicate that these LBS migration indices, particularly the intra-city index (C-index), to a large extent, provided reasonable explanation for the temporal variations of emission-induced reduction of NO 2 in large areas of China in early 2020.

DISCUSSION AND CONCLUSION
The unprecedented lockdowns and travel bans during the COVID-19 lockdown have led to a large reduction in anthropogenic emissions of air pollution [13]. We took the opportunity of this unintentionally conducted circumstance to investigate the isolated effects of emission and meteorology condition on atmospheric NO 2 , and the quantitative relationship between the reductions of NO 2 and human mobility using state-of-the-art satellite remote sensing products and location-service-based big data. We established a statistical model representing the column density of NO 2 as a function of only five key meteorology parameters, with the assumption that emission was constant. Compared with satellite observations in early 2017, the modelpredicted monthly mean NO 2 was only biased by 4.3% in the heaviest polluted areas in central and eastern China and showed spatial correlation coefficient of 0.97 (P < 0.001). Using the statistical model, it was found that the travel bans and lockdowns of China in 2020 have resulted in a decrease of observed NO 2 . Meanwhile, changes in meteorological conditions, such as lower PBLH, lower solar radiation etc., have led to an increase of atmospheric NO 2 (Fig. 5). As shown in Fig. 5, compared with 2017, the anthropogenic emission changes in early 2020 led to a 49.3 ± 23.5% reduction of atmospheric NO 2 , and the changes in meteorological conditions led to an 8.1 ± 14.2% increase. Consequently, the net reduction of NO 2 was brought down to 37.8 ± 16.3%. The modelling error was 3.3 ± 17.8%. We revealed, for the first time, that the COVID-19 quarantine caused a reduction of atmospheric NO 2 which was actually larger than what we saw from the satellite observations. In addition, the emission-induced reduction of NO 2 shows statistically significant correlations to human mobility. Quantitatively, the migration index representing the movement inside the city has the highest explained variance among all indices: it can explain 40.4% ± 17.7% variance on average in 29 megacities with a population of over 8 million in the mainland of China. This study established a method to untangle the contributions of emissions and meteorology conditions to the reduction of atmospheric NO 2 , and quantitatively assessed the effect of the city lockdowns and travel bans on the tropospheric NO 2 reduction during the COVID-19 outbreak in early 2020. This analysis may shed light on the parameterization of NO 2 emission related to human mobility, as well as the understanding of the effect of transportation on atmospheric NO 2 . The indices based on the Baidu Big Data are able to provide daily information on human activities, and thus can predict the change of NO 2 . In future, the data could be used to modify the emission model and make the emission estimation more accurate [37,38].
In this study, we employed a simplified model from Ref. [27] to describe the dependence of atmospheric NO 2 on emissions and meteorology. Compared with physical and chemical transfer models, which require a large source of computing time [26] and are affected by uncertainties in modelled physical or chemical processes, the approach shown in this work is fast and accurate with relative error <5% even in the heaviest polluted area in China, provided the emission does not change significantly. Our findings demonstrate the reliability of statistic approaches to predict tropospheric NO 2 changes.
We suggest further efforts to develop novel statistic-based approaches as important supplements to the chemical transport models, particularly to understand the sensitivity of NO 2 to various meteorological variables to provide more accurate predictions. The uncertainty in the statistic model deserves further studies, in particular its dependence on the background NO 2 concentration, as well as the sensitivity of NO 2 to each selected meteorological parameter. More meteorological parameters or more complicated functions to describe the dependence of atmospheric NO 2 on meteorology conditions, also deserve further study.

Data
The standard product of tropospheric NO 2 column density retrieved from the Ozone Monitoring Instrument (OMI) onboard Aura satellite (OMNO2, Level 2, version 003, available at https://disc.gsfc.nasa.gov/datasets/OMNO2 003/ summary) was used in this study. Original orbit data were gridded into 0.25 * 0.25 degree to collocate with reanalysis data. To exclude the potential impacts from cloud contamination, only samples with cloud fraction <30% and NO 2 column concentration <50 × 10 15 molec/cm 2 were used in our study. Row anomaly issues were carefully treated using the official quality flag of OMNO2 (see OMNO2 README file) based on the abnormal proportion of negative value in the data (if the ratio of negative value in an x-track was >2%, all the data in the track were not used).
The ECMWF atmospheric reanalysis data (ERA5, Single Level and Pressure Level) were used to provide meteorological parameters in this study. Original ERA5 data have a spatial resolution of 0.25 * 0.25 degree and a temporal resolution of 1 hour. I-index, E-index and C-index data are maintained by Baidu, Inc. and are available at https://qianxi.baidu.com/. The information is derived from billions of location requests per day using the Baidu Map app, with permission to share from users. All of the proxies are not absolute numbers of travelers but proportional values.

Statistical model of atmospheric NO 2
A multiple variable linear regression model was developed to quantify tropospheric nitrogen dioxide (NO 2 ) as a function of meteorological factors, which was inspired by the model described by de Foy and Schauer [27] and Seo et al. [31], using combined satellite observations and atmosphere reanalysis data. Based on our statistics on the satellite retrievals (refer to Fig. S17) and the studies [28,39], the values of atmospheric column NO 2 are log-normally distributed. Therefore, we used log(NO 2 ) for the multiple regression analysis so that we could scale to a normal distribution with zero mean and unit standard deviation. Contributions from emission source are assumed unchanged with time in this model. The tropospheric NO 2 is considered to be a linear function of five key meteorological factors [25]: planetary boundary layer height (PBLH), solar radiation (SR), surface temperature (T), relative humidity (RH) and wind speed (WS). To ensure all variables have similar order of magnitude, a logarithm transformation was conducted on NO 2 column density, PBLH and SR. As a result, the regression model can be expressed as follows.
log(NO 2 ) = b 0 + b 1 · log(P B L H) The coefficients of b 0 to b 5 are regression coefficients determined with the Iterative Reweighted Least Squares (IRLS) fitting method [27]. We used 2018 and 2019 data from 45 days before to 65 days after the Chinese Spring Festival (Chinese New Year based on Lunar Calendar) as training data to build up the regression model, and used 2017 data to test the model and assess the modelling error. Then we extended the model with estimated error to predict the column NO 2 density in 2020, assuming there were no changes of anthropogenic emission. For more details on development of the model, see the Supplementary data.

CODE AVAILABILITY
The computer codes used to analyze the data are available from the corresponding author on reasonable request.