The Impacts of the COVID-19 Lockdown on Air Quality in the Guanzhong Basin, China

: The Corona Virus Disease 2019 (COVID-19) appeared in Wuhan, China, at the end of 2019, spreading from there across China and within weeks across the whole world. In order to control the rapid spread of the virus, the Chinese government implemented a national lockdown policy. It restricted human mobility and non-essential economic activities, which, as a side e ﬀ ect, resulted in the reduction of the emission of pollutants and thus the improvement of the air quality in many cities in China. In this paper, we report on a study on the changes in air quality in the Guanzhong Basin during the COVID-19 lockdown period. We compared the concentrations of PM 2.5 , PM 10 , SO 2 , NO 2 , CO and O 3 obtained from ground-based monitoring stations before and after the COVID-19 outbreak. The analysis conﬁrmed that the air quality in the Guanzhong Basin was signiﬁcantly improved after the COVID-19 outbreak. During the emergency response period with the strictest restrictions (Level-1), the concentrations of PM 2.5 , PM 10 , SO 2 , NO 2 and CO were lower by 37%, 30%, 29%, 52% and 33%, respectively, compared with those before the COVID-19 outbreak. In contrast, O 3 concentrations increased substantially. The changes in the pollutant concentrations varied between cities during the period of the COVID-19 pandemic. The highest O 3 concentration changes were observed in Xi’an, Weinan and Xianyang city; the SO 2 concentration decreased substantially in Tongchuan city; the air quality had improved the most in Baoji City. Next, to complement the sparsely distributed air quality ground-based monitoring stations, the geographic and temporally weighted regression (GTWR) model, combined with satellite observations of the aerosol optical depth (AOD) and meteorological factors was used to estimate the spatial and temporal distributions of PM 2.5 and PM 10 concentrations with a resolution of 6 km × 6 km before and after the COVID-19 outbreak. The model was validated by a comparison with ground-based observations from the air quality monitoring network in ﬁve cities in the Guanzhong Basin with excellent statistical metrics. For PM 2.5 and PM 10 the correlation coe ﬃ cients R 2 were 0.86 and 0.80, the root mean squared errors (RMSE) were 11.03 µ g / m 3 and 14.87 µ g / m 3 and the biases were 0.19 µ g / m 3 and − 0.27 µ g / m 3 , which led to the conclusion that the GTWR model could be used to estimate the PM concentrations in locations where monitoring data were not available. Overall, the PM concentrations in the Guanzhong Basin decreased substantially during the lockdown period, with a strong initial decrease and a slower one thereafter, although the spatial distributions remained similar.

March were presented by [25]. Furthermore, [17] researched the impact of the control measures during the COVID-19 outbreak on air pollution in China for the period of 30 days before and after the Spring Festival, based on a comparison with the three preceding years, using both satellite and ground-based data. The Guanzhong Basin (GZB), located in Shaanxi Province (see Figure 1), is the most economically developed area in northwest China and its serious long-term air pollution has become a focus issue in China [26]. As an enclosed region, the geographical condition of the basin surrounded by high mountains leads to stagnant air and a low wind speed in the valley, which results in the accumulation of pollutants. These meteorological conditions play a key role in the formation, transformation, diffusion, migration and removal of air pollutants [27]. Since the outbreak of COVID-19, Shaanxi Province, which is adjacent to Hubei Province, has also actively responded to the lockdown policy and achieved good results in the prevention and control of the epidemic. The effects of these measures on the air quality in this special enclosed region are reported in this study. Pollutants measured at ground-based monitoring stations in the GZB area (PM2.5, PM10, SO2, NO2, CO and O3) during the periods before and after the COVID-19 outbreak are compared and analyzed in detail. In addition, different than other studies, our study covered the period from 1 January to 31 August 2020, i.e., including the period before the COVID-19 outbreak, the lockdown stage, the pandemic stage and the control stage in China to comprehensively and systematically explore the impact of COVID-19 on air quality. Another difference from previous studies is that we not only compared and analyzed concentrations of pollutants that are routinely measured at the ground-based monitoring stations, but also used a model together with satellite observations to estimate the near-surface PM2.5 and PM10 concentrations with a resolution of 6 km × 6 km over the entire Guanzhong Basin area. This model estimates the complement sparsely distributed air quality ground-based monitoring stations and is used to explore spatial and temporal changes of PM concentrations with high spatial resolution during the period of COVID-19 pandemic. The model uses aerosol optical depth (AOD) from the Visible Infrared Imaging Radiometer Suite (VIIRS) satellite. AOD is the column-integrated aerosol extinction coefficient, which can be used as a proxy for the particulate matter concentration in the atmospheric column and the degree of air pollution [28]. However, the PM-AOD relationship depends on meteorological factors (such as planetary boundary layer height, relative humidity, wind speed and temperature) that need to be accounted for when PM concentrations are derived from satellite AOD measurements [29]. The normalized difference vegetation index (NDVI) could be used as another independent variable to predict the PM concentration [30]. AOD measured from satellites has been widely used together with statistical models, such as a linear mixed effects model [31], a Another difference from previous studies is that we not only compared and analyzed concentrations of pollutants that are routinely measured at the ground-based monitoring stations, but also used a model together with satellite observations to estimate the near-surface PM 2.5 and PM 10 concentrations with a resolution of 6 km × 6 km over the entire Guanzhong Basin area. This model estimates the complement sparsely distributed air quality ground-based monitoring stations and is used to explore spatial and temporal changes of PM concentrations with high spatial resolution during the period of COVID-19 pandemic. The model uses aerosol optical depth (AOD) from the Visible Infrared Imaging Radiometer Suite (VIIRS) satellite. AOD is the column-integrated aerosol extinction coefficient, which can be used as a proxy for the particulate matter concentration in the atmospheric column and the degree of air pollution [28]. However, the PM-AOD relationship depends on meteorological factors (such as planetary boundary layer height, relative humidity, wind speed and temperature) that need to be accounted for when PM concentrations are derived from satellite AOD measurements [29]. The normalized difference vegetation index (NDVI) could be used as another independent variable to predict the PM concentration [30]. AOD measured from satellites has been widely used together with statistical models, such as a linear mixed effects model [31], a geographically weighted regression model [30] or a random forests machine learning model [32] to estimate particulate matter (PM) Remote Sens. 2020, 12, 3042 4 of 23 concentrations. In this study, the geographic and temporally weighted regression (GTWR) model [33] was used to evaluate both the spatial and temporal variability of PM based on satellite observations of AOD with meteorological factors and NDVI data.
The National Emergency Response Plan for Public Emergencies issued by the State Council of China (http://www.scio.gov.cn/xwfbh/zdjs/Document/1078861/1078861.htm, last access 11 September 2020) classifies public emergencies into four levels: 1st level (especially serious), 2nd level (serious), 3rd level (heavy) and 4th level (general). Following this classification, we divided the whole research period into six stages to get insight into the effects of the various measures on the air quality in the study area: the stage before the COVID-19 lockdown is the Pre-lockdown stage (1-24 January 2020). The first-level emergency response phase for public health incidents launched by the Shaanxi Province is the Level-1 stage (25 January-27 February 2020). The transition between the 1st level and the 3rd level emergency response phase is the Level-2 stage (27 February-26 March 2020). The COVID-19 measures in Shaanxi Province were relaxed from 27 March 2020, and the period until April 30 is the Level-3 stage (27 March-30 April 2020). The Level-4 and Level-5 stages cover the period from 1 May until 31 August 2020. It is split into two stages because the VIIRS AOD data were only available until 24 June 2020, which determines the Level-4 stage (1 May-24 June 2020). The Level-5 stage is from 24 June until the end of the study period, i.e., 24 June-31 August 2020.

Study Area
The Guanzhong Basin (GZB) is located in the central part of Shaanxi Province (Figure 1). There are 54 cities and districts in the Guanzhong Basin, including five prefecture-level cities (second level administrative divisions of China, Xi'an, Xianyang, Tongchuan, Baoji and Weinan). It is a region distributed in the urban cluster of Shaanxi, with a total area of 55,623 km 2 . GZB is the Weihe River alluvial plain with an average altitude of about 500 m. The basin is surrounded by the Qinling Mountains to the south and the Loess Plateau to the north. The mountains form a natural barrier around the Guanzhong Basin which prevents the transport of air pollutants out of the basin resulting in their accumulation. The air pollution in this area is serious due to dense population, the concentration of urban agglomerations and a large number of boilers and coal burning used in the winter heating period [27,34,35]. According to the Environmental Status Bulletin of Shaanxi Province in 2019, the air pollutants in the Guanzhong Basin area are mainly PM 2.5 and PM 10 and the air quality is lightly polluted or above on nearly 40% of the days throughout the whole year (http://sthjt.shaanxi.gov.cn/newstype/hbyw/hjzl/hjzkgb/20200604/55508.html, last access 11 September 2020).

Ground-Based Air Quality Data
The hourly concentrations of air pollutants were collected from the ground-based observations freely available from China's National Environmental Monitoring Center (CNEMC, http://www. cnemc.cn, last access 11 September 2020). Previous studies have shown the statistical reliability of the CNEMC data [36,37]. The data include PM 2.5 , PM 10 , SO 2 , NO 2 , CO and O 3 . For the current study, hourly concentrations of these species were collected from 33 air quality stations (shown in Figure 1) in five cities during the same period (1 January to 31 August) in each year from 2017 to 2020. Invalid data due to equipment failure (recorded with the value NA) were deleted. The daily mean concentration in each city was calculated by averaging hourly concentrations at all stations in that city (13 in Xi'an, 4 in Xianyang, 4 in Weinan, 4 in Tongchuan and 8 in Baoji) to represent the citywide pollution exposure condition.

Satellite Data
Suomi National Polar-orbiting Partnership (S-NPP) is the first of a new generation of earth observation satellites launched by the USA to replace the previous generation whose service life was about to expire. S-NPP is a polar orbiting satellite with a daytime overpass time at about 13:30 local solar time (LST). S-NPP is equipped with five optical sensors, including the Visible Infrared Imaging Radiometer Suite (VIIRS) [38]. VIIRS is an environmental remote sensing sensor which provides, among others, cloud cover and aerosol characteristics [39] with daily global coverage. Environmental data record (EDR) is the official VIIRS level 2 product with AOD at 11 wavelengths (0.412, 0.445, 0.488, 0.55, 0.555, 0.672, 0.746, 0.865, 1.24, 1.61 and 2.25 µm) with a spatial resolution of 6 km [39]. VIIRS_EDR provides four different pixel-level quality assurance (QA) flags: not produced (QA = 0), low quality (QA = 1), medium quality (QA = 2) and high quality (QA = 3) (https://www.star.nesdis.noaa.gov/smcd/ emb/viirs_aerosol/documents/Aerosol_Product_Users_Guide_V2.0.1.pdf, last access 11 September 2020). [35] evaluated the VIIRS EDR AOD product with QA = 2 and QA = 3 over the Guanzhong Basin by comparing with ground-based AOD measurements in Xi'an, part of the Sun-sky radiometer Observation NETwork (SONET) [40]. The results showed that the use of VIIRS AOD with QA = 3 provides much better accuracy than using AOD with QA = 2. Therefore, VIIRS EDR AOD data at 550 nm wavelength with QA = 3 (https://www.bou.class.noaa.gov/saa/products/welcome, last access 11 September 2020) over the GZB were collected for the study period from 1 January to 24 June 2020 (data after 24 June 2002 were not available at the time of this study). It is noted that VIIRS retrieval fails in some conditions, such as in the presence of clouds, ephemeral water bodies, high reflectance of surfaces covered with snow or ice, or a combination of multiple factors [41], which is a serious problem. Figure 2 illustrates the spatial coverage of VIIRS AOD with QA = 3 during the study period (1 January-24 June 2020). The AOD coverage is mainly between 10-30%.

Satellite Data
Suomi National Polar-orbiting Partnership (S-NPP) is the first of a new generation of earth observation satellites launched by the USA to replace the previous generation whose service life was about to expire. S-NPP is a polar orbiting satellite with a daytime overpass time at about 13:30 local solar time (LST). S-NPP is equipped with five optical sensors, including the Visible Infrared Imaging Radiometer Suite (VIIRS) [38]. VIIRS is an environmental remote sensing sensor which provides, among others, cloud cover and aerosol characteristics [39] with daily global coverage. Environmental data record (EDR) is the official VIIRS level 2 product with AOD at 11 wavelengths (0.412, 0.445, 0.488, 0.55, 0.555, 0.672, 0.746, 0.865, 1.24, 1.61 and 2.25 µm) with a spatial resolution of 6 km [39]. VIIRS_EDR provides four different pixel-level quality assurance (QA) flags: not produced (QA = 0), low quality (QA = 1), medium quality (QA = 2) and high quality (QA = 3) (https://www.star.nesdis.noaa.gov/smcd/emb/viirs_aerosol/documents/Aerosol_Product_Users_Gu ide_V2.0.1.pdf, last access 11 September 2020). [35] evaluated the VIIRS EDR AOD product with QA = 2 and QA = 3 over the Guanzhong Basin by comparing with ground-based AOD measurements in Xi'an, part of the Sun-sky radiometer Observation NETwork (SONET) [40]. The results showed that the use of VIIRS AOD with QA = 3 provides much better accuracy than using AOD with QA = 2. Therefore, VIIRS EDR AOD data at 550 nm wavelength with QA = 3 (https://www.bou.class.noaa.gov/saa/products/welcome, last access 11 September 2020) over the GZB were collected for the study period from 1 January to 24 June 2020 (data after 24 June 2002 were not available at the time of this study). It is noted that VIIRS retrieval fails in some conditions, such as in the presence of clouds, ephemeral water bodies, high reflectance of surfaces covered with snow or ice, or a combination of multiple factors [41], which is a serious problem. Figure 2 illustrates the spatial coverage of VIIRS AOD with QA = 3 during the study period (1 January-24 June 2020). The AOD coverage is mainly between 10-30%. The other satellite product that was used in this study was the NDVI (Normalized Difference Vegetation Index, unitless). NDVI data are available from the Moderate Resolution Imaging Spectroradiometer (MODIS). It is a Level 3 product with a spatial resolution of 250 m × 250 m and a time resolution of 16 days (product code MOD13Q1) which can be downloaded from https://modis.gsfc.nasa.gov/data/dataprod/mod13.php (last access 11 September 2020).

Meteorological Data
The meteorological data over the study area for the period from 1 January to 24 June 2020 were derived from the latest version ERA5 data from the European Centre for Medium-Range Weather Forecasts (ECMWF) (https://cds.climate.copernicus.eu, last access 11 September 2020). The ERA5 The other satellite product that was used in this study was the NDVI (Normalized Difference Vegetation Index, unitless). NDVI data are available from the Moderate Resolution Imaging Spectroradiometer (MODIS). It is a Level 3 product with a spatial resolution of 250 m × 250 m and a time resolution of 16 days (product code MOD13Q1) which can be downloaded from https://modis.gsfc.nasa.gov/data/dataprod/mod13.php (last access 11 September 2020).

Meteorological Data
The meteorological data over the study area for the period from 1 January to 24 June 2020 were derived from the latest version ERA5 data from the European Centre for Medium-Range Weather Forecasts (ECMWF) (https://cds.climate.copernicus.eu, last access 11 September 2020). The ERA5 replaced the ERA-Interim re-analysis data which stopped on 31 August 2019. The ERA5 dataset contains Remote Sens. 2020, 12, 3042 6 of 23 hourly atmospheric, terrestrial and oceanic climate variables since 1950 with a spatial resolution of 0.25 • . Air temperature (TP, • C), relative humidity (RH, %), planetary boundary layer height (PBLH, m) and wind speed vector into meridional component wind speed U (WSU, m/s) at 13:00 and 14:00 local time (i.e., within half an hour of the VIIRS satellite overpass time) were extracted.

Data Integration
The above multi-source data are point data (ground-based monitoring data) and raster data (AOD, NDVI and meteorological data) that have different temporal and spatial resolutions. These data were used for establishing a model to estimate the PM concentration. In order to reduce the influence of temporal and spatial differences of multi-source data, they were integrated over a 6 km × 6 km grid, established in the GZB according to the resolution of VIIRS AOD. First, the PM 2.5 , PM 10 , AOD, NDVI and meteorological data were projected to the Albers equal-area conic coordination system [30,35]. When there was only one ground-based station in the 6 km × 6 km grid, the PM value of this station was assigned to the grid cell. If there was more than one air quality monitoring station in the same grid cell, the PM values of all stations were averaged and then assigned to the corresponding grid cell. Next, the NDVI, PBLH, TP, RH and WSU data were resampled into the 6 km × 6 km grid by the nearest neighbour interpolation method. Finally, in view of the actual VIIRS overpass time over the GZB at about 13:30 LST, the average values of PM 2.5 , PM 10 and meteorological data were extracted at 13:00 and 14:00 every day. Since the time resolution of NDVI was 16 days, the NDVI data closest to each day were used. Thus, for each 6 km x 6 km grid cell a dataset was constructed including PM 2.5 /PM 10 , AOD, NDVI, TP, RH, PBLH and WSU data within half an hour of the satellite overpass time. At least four datasets per day were needed for geographically weighted regression model fitting and validation [30], so only days with 4 or more datasets were selected. This resulted in a total of 2116 datasets for the study period from 31 January to 24 June 2020. For the analysis of the variations of the PM 2.5 , PM 10 , SO 2 , NO 2 , CO and O 3 concentrations at the ground-based monitoring stations, mean daily values or mean city daily concentration data of these pollutants were obtained for the period from 1 January to 31 August in each year from 2017 to 2020.

Statistical Analysis
The surface concentrations of PM 2.5 , PM 10 , SO 2 , NO 2 , CO and O 3 in the GZB were analyzed to assess the influence of the COVID-19 outbreak control measures. To this end, the temporal variations of the daily and mean weekly concentrations during the study period in 2020 were compared with those during the previous years (2017 to 2019). The statistics of the mean daily concentrations in each of the 5 largest cities were used to analyze different effects of the virus containment measures on the air pollution level in each city.

GTWR Model
To determine the spatial and temporal relationships between PM 2.5 /PM 10 and AOD in the study area, two models were considered: the geographically and temporally weighted regression (GTWR) model and a two-stage model based on linear mixed effects and geographically weighted regression (LME-GWR) model. The LME model with random intercepts and slopes obtains daily slope estimates but uses data from all days to stabilize the estimates [31]. The GTWR model maintains the spatial similarity and heterogeneity of geographical parameters [33]. The observations close to the regression points have a larger influence on the estimation of the parameters than those located further away [42,43]. In fact, the GTWR model generates continuous parameters by local model fitting. It can be used to deal with both spatial and temporal non-stationarity. Previous studies have shown that meteorological conditions (such as RH, PBLH, TP) and NDVI have a large impact on the estimation of near surface PM 2.5 or PM 10 concentrations [30,32]. Furthermore, [35] has shown that WSU has a significant effect on the PM 2.5 concentrations in the GZB. In this paper, the GTWR model for the PM-AOD relationship is formulated as: where PM 2.5,i and PM 10,i represent the near-surface PM 2.5 and PM 10 concentrations (µg/m 3 ) in grid are the slopes of the corresponding independent variables; AOD i , TP i , RH i , PBLH i , WSU i and NDVI i represent the VIIRS AOD value (dimensionless), surface temperature ( • C), relative humidity (%), planetary boundary layer height (m), meridional component of the wind speed U (positive value indicates that the wind direction is from west to east, negative value indicates that the wind direction is from east to west, m/s) and NDVI (dimensionless) in grid cell i; ε i is the random error term of grid cell i. Previous research [35] showed that there was no significant correlation between the zonal component wind speed V (north-south wind speed, WSV) and the PM2.5 concentration. Additionally, the prediction accuracy of model decreased after adding WSV or wind speed (WS) factors in the model. Therefore, we only used the meridional wind component U (WSU) in the model to improve the prediction accuracy of ground based PM2.5 concentrations. The variables' coefficients in Equation (1) are functions of the spatiotemporal position.
We introduced a weighting matrix to measure the spatiotemporal weight between two points to obtain these coefficients [44]. It is a monotonically decreasing function of the spatiotemporal distance between two points, which is formulated as follows: where ω ij is a weight matrix; d S ij and d T ij represent the spatial and temporal distances between points i and j; q is a scale factor for the time distance; h ST represents the non-negative parameter of the spatio-temporal bandwidth, which will have an attenuation effect with distance. Considering the uneven distribution of the ground-based PM observations in the study area, we used the minimum Akaike information criterion (AICc) to obtain an adaptive optimal bandwidth to better describe the impact of spatial variations. The AICc provides a measure of the information distance between the model which has actually been fitted and the unknown model using the maximum likelihood principle. It could determine the optimal value for the bandwidth, and the bandwidth with the lowest AICc value is used in the estimation of the model parameters (such as weight) [45].

LME-GWR Model
The LME and GWR models can capture the effects of temporal changes and geographic variations [30]. We used a combined LME-GWR model to compare with the GTWR model. In this paper, the LME model was adopted as the first-stage model to reflect the variation of the PM-AOD relationship with time. The meteorological factors and NDVI were also used as auxiliary independent variables. The fixed effect item of the LME model could explain the average effect of the relationship between the independent variable and the PM 2.5 /PM 10 concentration during the whole study period, and the random effect item could explain the daily change of this relationship. The model is formulated as follows: values at grid cell s on day t; β 0 and β 0,t are the fixed effect slope and random effect intercept; β 1 -β 6 are the fixed effect slope terms of their variables; β 1,t -β 5,t represent the slopes of the random effect of the corresponding values; ε 1,st is the random error of grid s on day t. β 0,t -β 5,t are the multivariate normal distributions, and Σ is the variance-covariance matrix of the random effect. The first stage model could reflect the temporal variation of PM. The GWR model was used in the second stage to build the model for the residual of the first stage LME model. The AOD data in each grid cell are considered to reflect the continuity variation on a spatial scale. Similar to the principle of the GTWR model, the GWR model can obtain the regression coefficients of different weights for each grid point by calculating the spatial position relationship between observation points and regression points. Generally, a continuous monotone decreasing function "Gaussian spatial weight function" was used to express the relationship between weight and distance [35]. This leads to the following formulation: where PM 2.5 _resi st and PM 10 _resi st represent the PM 2.5 and PM 10 concentration residuals in grid cell s on day t obtained by the LME model; AOD st is the VIIRS AOD value for grid s on day t; γ 0,s is the intercept term of grid cell s; γ 1,s is the slope of grid cell s; ε 2,st represents the error term of grid s on day t.

Model Validation
The 10-fold cross validation (CV) method was used to assess the degree of model over-fitting in this paper [46]. We randomly divided the datasets used in the modeling into 10 groups. The data of 9 groups were used for model fitting, and the 10th group was used to assess the model performance. This process was repeated 10 times until all groups were predicted. The coefficient of determination (R 2 ), the bias, and the root mean squared prediction error (RMSE) between predicted values and ground-based observations were calculated to compare the model fitting and cross validation results and assess the model performance and overfitting.

Change in Surface Concentrations of Pollutants
The hourly concentrations of PM 2.5 , PM 10 , SO 2 , NO 2 , O 3 and CO measured by each ground-based monitoring station in the Guanzhong Basin were daily averaged over the same periods in 2017-2019 as those associated with the Pre-lockdown, Level-1, Level-2, Level-3, Level-4 and Level-5 periods in 2020. The results are presented in Figure 3 as boxplots showing the mean and median concentrations together with some other statistics for each pollutant. Time series of the weekly averaged PM 2.5 , PM 10 , SO 2 , NO 2, CO and O 3 concentrations are plotted in Figure 4 for the first 35 weeks in each of the years from 2017 to 2020. The data in Figure 3 show that the concentrations during the Pre-lockdown period in 2020 were similar to or slightly lower than those in previous years, for all pollutants except O 3 , with a decreasing tendency over the last three (PM, NO 2 ) or four (SO 2 and CO) years, although the differences are statistically not significant. The time series in Figure 4 show the differences in the concentrations between each of the four years, the strong week-to-week variations in each year and the overall decrease from the Pre-lockdown stage to the Level-4 stage for all species except O 3 , which increases. The week-to-week variations are due to meteorological conditions and changes in emissions. Overall, the concentrations were lower in 2020 than in the three years before.
Remote Sens. 2020, 12, 3042 9 of 24  The overall decrease of the concentrations during each year follows the common seasonal variations which are related to overall changes in emissions and boundary layer effects during the annual cycle. Differences between the concentrations in the four years may be due to emission reductions in response to policy measures to improve the air quality in China. For the trace gases NO 2 , SO 2 and CO the concentrations in 2019 are smaller than in 2017 and 2018, and in 2020 the concentrations in the Pre-lockdown period are substantially smaller than in 2019. For aerosols the situation is different and there is no tendency in the year-to-year variations of the PM 2.5 concentrations during the four years considered here, whereas for PM 10 the concentrations during the Pre-lockdown period were substantially lower than in other years. Previous research showed that in China the AOD, used as a measure of the aerosol amount, was less affected by the COVID-19 containment measures, likely due to the different formation mechanisms and the influence of meteorological factors [17]. [47] analyzed several periods of heavy haze pollution in Eastern China during the COVID-19 lockdown period and concluded that the formation of haze was driven by the enhancement of secondary pollution due to increased oxidizing capacity of the atmosphere driven by the reduced NO 2 concentrations. [48] concluded that differential impacts of the economic lockdown resulted in less reduction of AOD than NO 2 whereas meteorological conditions and chemical interactions likely enhanced aerosol formation. Moreover, pollution transport is another likely reason for the different behaviour of aerosol in the GZB. Due to blocking by the Loess Plateau (the northern part of the GZB), the GZB area is rarely affected by transport of pollutants from the North China Plain. However, dust from the Taklimakan and Gobi deserts could be transported to the GZB from over the Loess Plateau [35,49]. The aerosol pollution in GZB may be aggravated by the transport of pollutants from the eastern polluted plain area. These differences are reflected by the contributions of coarse particles to the total aerosol content in the GZB. This is the starting condition for the assessment of the effect of the COVID-19 lockdown measures on the concentrations.  For PM, NO 2 , SO 2 and CO, the concentrations in all four years were lower after the Pre-lockdown stage than before. In 2020, the PM 2.5 , PM 10 , SO 2 , NO 2 and CO concentrations decreased substantially from Pre-lockdown to Level-1, more than in previous years. In 2020 this reduction was in part due to the COVID-19 containment measures which however were preceded by reduced emissions connected with the Spring Festival (also called the Lunar New Year), which varies from year to year in the solar calendar. The Lunar New Year dates are indicated in Figure 4, which shows that it occurred during the Level-1 period in all four years between 2017-2020. Lunar New Year is the most important holiday in China during which many factories and businesses are closed to allow people to celebrate with their families at home, resulting in the strong reduction of emissions during the 1-2 weeks [17], as observed from the concentrations in Figures 3 and 4.
In 2020 the reduction was enhanced and extended over a longer period in response to the lockdown. Figures 3 and 4 show that the decrease in the measured concentrations of PM 2.5 and PM 10 and the trace gases was largest during the first stage of the lockdown. The concentrations of PM 2.5 , PM 10 , SO 2 , NO 2 and CO decreased by 37%, 30%, 29%, 52% and 33% with respect to those before the COVID-19 outbreak, while the O 3 concentration increased by 82%. Figure 4 shows that the mean weekly SO 2 and CO concentrations decreased steadily during the whole period, while PM 2.5 , PM 10 and NO 2 decreased rapidly from the Pre-lockdown stage to the lockdown Level-1 period. After the Level-1 stage the concentrations continued to decrease slowly, although in particular the NO 2 concentrations increased substantially during Level-2 to close to those during the Pre-lockdown period, before decreasing during Level-3. A similar but much less pronounced behaviour was also observed for SO 2 . The rebound of these trace gas concentrations may be explained by the less restricting measures when the number of infections decreased and people's lives started to return to normal, leading to a gradual increase of the emissions. During the Level-4 period, PM 2.5 , PM 10 and NO 2 concentration decreased slowly. The PM 10 and NO 2 concentrations also decreased slightly during the Level-5 period, while the concentrations of PM 2.5 and SO 2 did not change much from Level-4 to Level-5. Especially, CO rebounded slightly in the Level-4 and 5 stages. After the continuous increase of the O 3 concentrations from the Pre-lockdown stage to the Level-4 stage, it began to decline during the Level-5 stage. We also found that the concentrations of the pollutants contributing to the air quality during the Level-4 and 5 stages in 2020 were very similar to those in 2019. The small changes during the Level-4 and 5 stages could be due to the epidemic being under control and peoples' activities resuming to normal. The O 3 and NO 2 concentrations are anti-correlated, which reflects that the increase of O 3 is related to the reduction of NO 2 concentration: the catalytic effect of NOx is weakened, which leads to the decrease of ozone titration [18,19].

Changes of Pollutant Concentrations between Cities
The mean concentrations of the six air pollutants monitored by ground based stations in five cities in the GBZ Region (Xi'an, Xianyang, Tongchuan, Baoji and Weinan) are presented as box plots in Figure 5, for two periods in 2017-2020 corresponding to the Pre-lockdown and Level-1 period after the COVID-19 outbreak in 2020. Figure 5 clearly shows that the concentrations of all species except ozone were substantially lower during the Level-1 lockdown period than Pre-lockdown. As explained in Section 3.1., this is due to the Spring Festival effect, in 2020 augmented by the lockdown effect. Figure 5 also shows that the reduction in the concentrations varies between cities, which may be related to the geographical location, weather factors, as well as the policy measures and implementation by each city during the COVID-19 lockdown period. In 2020, the concentrations of PM 2.5 , PM 10 , NO 2 and CO in the five cities during the Level-1 stage were lower by more than 20% than during the Pre-lockdown stage. The PM 2.5 and NO 2 concentrations in Baoji City decreased most significantly and the reductions of these species in 2020 were 31% and 21% larger than in the same period of 2019. In Baoji, some pollution is due to transport from the central cities in the GZB area. Hence the reduction of the concentrations in Xi'an, Weinan and Xianyang contributes to that in Baoji. The concentration of SO 2 is highest in Tongchuan and Weinan where multiple large coal mines are located, and SO 2 is emitted by burning of sulfur-containing minerals. During the lockdown period, the SO 2 concentration in Tongchuan City declined fastest (31%). Figure 5 shows that NO 2 concentrations generally decrease faster than those of CO. The reason may be that the main emission source of NO 2 is from diesel-fuelled vehicles, while the main source of CO is small cars [1]. During the COVID-19 outbreak, the use of heavy vehicles such as trucks and freight were reduced more than small cars. Furthermore, NO 2 has a much shorter atmospheric life time than CO and thus the reduction of NO 2 emissions leads to a faster reduction of the concentrations than for CO. The increase in O 3 concentrations is most prominent in Xi'an, Xianyang and Weinan. In addition to the reduction in NOx, the increase in O 3 concentration may also be due to the decrease in aerosol concentrations (PM) resulting in increased transmission of sunlight through the atmosphere and thus higher intensity of solar radiation available for photochemical reactions and the production of O 3 [50,51]. Among the five cities, the air quality improvement of Baoji is the most obvious. The data in Figures 3-5 show that, from 2017 to 2020, the concentrations of air pollutants in the five cities decreased year by year, which indicates the benefits of the air pollution control policies in the Guanzhong Basin in recent years.  Figure 6 shows histograms of PM2.5, PM10, VIIRS AOD, NDVI and the auxiliary meteorological variables used for building the models, including some statistical information: maximum (Max), minimum (Min), mean, median and standard deviation (Std.Dev.). As shown in Figure 6, all variables are approximately normally distributed, with a single peak. The frequency distributions of PM2.5 and  Figure 6 shows histograms of PM 2.5 , PM 10 , VIIRS AOD, NDVI and the auxiliary meteorological variables used for building the models, including some statistical information: maximum (Max), minimum (Min), mean, median and standard deviation (Std.Dev.). As shown in Figure 6, all variables are approximately normally distributed, with a single peak. The frequency distributions of PM 2.5 and PM 10 are similar to those of the AOD data. The mean PM 2.5 and PM 10  PM10 are similar to those of the AOD data. The mean PM2.5 and PM10 concentrations are 42.81 µg/m 3 and 89.27 µg/m 3 , respectively. PM2.5 values are much higher than the first and second level concentration limits specified in China's ambient air quality standard of 15 µg/m 3 and 35 µg/m 3 , respectively, and the mean PM10 value is also higher than the first and second level limits of 40 µg/m 3 and 70 µg/m 3 , respectively (http://www.mee.gov.cn/ywgz/fgbz/bz/bzwb/dqhjbh/dqhjzlbz/201203/W020120410330232398521.pd f, last access 11 September 2020). The mean AOD is 0.43. These high mean PM and AOD values show that the aerosol load and the near surface particulate matter are seriously high in the Guanzhong Basin. The meridional component of the wind speed WSU ranges from −5.47 to +4.80 m/s and the WSU absolute values (0-5.47 m/s) are smoothly distributed. This shows that the meridional wind speed is rather low, which together with the basin topography, leads to an unfavourable condition for pollutant diffusion in the GZB.

Statistical Analysis of Modeling Data
The correlations between each of the independent variables used for model building were calculated, and the R 2 results are shown in Table 1. We could judge whether there is multicollinearity of every independent variable from the Variance Inflation Factor (VIF, 1/1-R 2 ). For a VIF value smaller than 2.5, it is considered that there is no multicollinearity between the variables, and the closer the value is to 1, the lower the multicollinearity [52]. Considering the correlation coefficients in Table  1, the VIF values vary between 1.00 and 1.16, i.e., there is no multicollinearity problem between the variables.  The correlations between each of the independent variables used for model building were calculated, and the R 2 results are shown in Table 1. We could judge whether there is multicollinearity of every independent variable from the Variance Inflation Factor (VIF, 1/1-R 2 ). For a VIF value smaller than 2.5, it is considered that there is no multicollinearity between the variables, and the closer the value is to 1, the lower the multicollinearity [52]. Considering the correlation coefficients in Table 1, the VIF values vary between 1.00 and 1.16, i.e., there is no multicollinearity problem between the variables.

Model Fitting and Validation
The PM 2.5 and PM 10 concentrations calculated with the GTWR and LME-GWR models are compared with observations in the density scatter plots in Figures 7 and 8. For a direct comparison, the correlation between the calculated and measured PM 2.5 concentrations is better for the GTWR model ( Figure 7a); R 2 = 0.86) than for the LME-GWR model (Figure 7b, R 2 = 0.82). The RMSEs of the GTWR and LME-GWR models are 11.03 µg/m 3 and 14.33 µg/m 3 , respectively, and the biases are 0.19 µg/m 3 and −0.26 µg/m 3 . For PM 10 (Figure 8a,b) the R 2 for the GTWR model is 0.80 and for the LME-GWR model 0.76. The RMSE for the GTWR model is 2.19 µg/m 3 lower than the RMSE (17.06 µg/m 3 ) of LME-GWR model. There is no significant difference between the biases for the two models for PM 10 , which were −0.27 µg/m 3 and −0.52 µg/m 3 , respectively. These metrics show the better performance of the GTWR model than that of the LME-GWR model, and that the model results are better for estimating PM 2.5 than for PM 10 . The latter can be explained by the difference between PM 10 and PM 2.5 , which are the aerosol coarse mode fractions with particles with aerodynamic diameters between 2.5 µm and 10 µm, respectively. The AOD at 550 nm is the column-integrated aerosol extinction at a wavelength of 550 nm, which is more sensitive to sub-micron particles than to coarse particles, resulting in higher fitting accuracy of PM 2.5 than PM 10 [53]. The reason that the GTWR model performance is statistically better than that of the LME-GWR model may be that the GTWR model accounts for both the spatial and temporal variabilities together, while the LME-GWR model considers the influence of spatiotemporal variations separately by using two stages.
The performances of the two models was further evaluated by using the cross validation method described in Section 2.4.3. The results are presented as density scatter plots in Figure 7c,d for PM 2.5 and in Figure 8c,d for PM 10 . The statistical metrics for the comparison of the CV results with the ground-based observations shows the reduced performance with respect to the model fitting results, for both models. The correlation coefficients R 2 for the CV results for predicting PM 2.5 decreased by 10% and 9%, compared with the R 2 of the fitting results for the GTWR and LME-GWR models, respectively. The respective RMSE values were 5.42 µg/m 3 (49%) and 3.61 µg/m 3 (25%) higher than those of the model fitting results. Similar to the CV results of PM 2.5 , the CV results for estimating the PM 10 concentrations based on the GTWR and LME-GWR models was less good than those from the model fitting results, with lower R 2 values of 9% and 8%, respectively, and higher RMSE values 4.59 µg/m 3 (31%) and 5.7 µg/m 3 (33%). As expected, for the GTWR model and the LME-GWR model the R 2 values of the model fitting results were slightly higher, while the RMSE values were slightly lower, which indicates that there is always over-fitted in the model fitting process. and PM2.5, which are the aerosol coarse mode fractions with particles with aerodynamic diameters between 2.5 µm and 10 µm, respectively. The AOD at 550 nm is the column-integrated aerosol extinction at a wavelength of 550 nm, which is more sensitive to sub-micron particles than to coarse particles, resulting in higher fitting accuracy of PM2.5 than PM10 [53]. The reason that the GTWR model performance is statistically better than that of the LME-GWR model may be that the GTWR model accounts for both the spatial and temporal variabilities together, while the LME-GWR model considers the influence of spatiotemporal variations separately by using two stages.   The performances of the two models was further evaluated by using the cross validation method described in Section 2.4.3. The results are presented as density scatter plots in Figure 7c,d for PM2.5 and in Figures 8c,d for PM10. The statistical metrics for the comparison of the CV results with the ground-based observations shows the reduced performance with respect to the model fitting results, for both models. The correlation coefficients R 2 for the CV results for predicting PM2.5 decreased by Figures 7 and 8 also show that for PM 2.5 concentrations larger than 100 µg/m 3 and for PM 10 concentrations larger than 150 µg/m 3 , the data pairs are more scattered and often the predicted values are below the identity line, i.e., the models underestimate the PM concentrations, especially for the CV results. The underestimation of the PM 2.5 and PM 10 concentrations in strongly polluted conditions is because mainly PM 2.5 values smaller than 100 µg/m 3 and PM 10 values smaller than 150 µg/m 3 were used for model development and thus high concentrations have less weight [35]. Another possible reason is the local occurrence of high PM concentrations which are not well represented by the models in a lager grid cell with coarse spatial resolution [54]. Overall, both model fitting and CV validation results show that the performance of the GTWR model is better than that of the LME-GWR model in capturing the spatial and temporal variability of the PM 2.5 and PM 10 concentrations.

Estimation of the PM Distribution Using the GTWR Model
The PM concentrations in the Guanzhong Basin during the five stages of the COVID-19 lockdown period, for areas where no air quality monitoring stations are available, were estimated using the GTWR model because statically it has better prediction ability than the LME-GWR model. The spatial variations of the PM 2.5 and PM 10 concentrations during the Pre-lockdown, Level-1, Level-2, Level-3 and Level-4 periods and during the whole period used for building model were calculated with a resolution of 6 km × 6 km and the results are presented in Figure 9 for PM 2.5 and in Figure 10 for PM 10 . For some days, no VIIRS EDR AOD data were available for all pixels as described in Section 2.  The spatial distributions of the PM2.5 and PM10 concentrations in the four stages are similar, as shown in Figures 9 and 10. The highest PM concentrations occur around the three cities of Xi'an, Xianyang and Weinan in the heart of the study area. PM values are slightly lower in Baoji city and Tongchuang city which are located in the west and north of the GZB. These results confirmed the analysis and comparison results of ground-based monitoring data for PM2.5 and PM10 in Section 3.2, and supplement the details of PM concentration variation with high spatial resolution in the study  The spatial distributions of the PM2.5 and PM10 concentrations in the four stages are similar, as shown in Figures 9 and 10. The highest PM concentrations occur around the three cities of Xi'an, Xianyang and Weinan in the heart of the study area. PM values are slightly lower in Baoji city and Tongchuang city which are located in the west and north of the GZB. These results confirmed the analysis and comparison results of ground-based monitoring data for PM2.5 and PM10 in Section 3.2, and supplement the details of PM concentration variation with high spatial resolution in the study   10 were 82 µg/m 3 and 118 µg/m 3 , respectively. During the Level-1 period, the mean values of PM 2.5 and PM 10 were reduced to 60 µg/m 3 and 95 µg/m 3 , i.e., 27% and 20% lower than during the Pre-lockdown stage. During the Level-2 period the concentrations had declined further, to 22% and 15% lower than those during the Level-1 period and the reduction continued from the Level-2 to the Level-3 period with another 13% and 9% to reach mean PM 2.5 and PM 10 concentrations of 41 µg/m 3 and 74 µg/m 3 . During the Level-4 period, the PM2.5 and PM10 concentrations were slowly reduced further with 39 µg/m 3 and 70 µg/m 3 to 5% and 6% lower than during the Level-3 stage. The overall reductions of PM 2.5 and PM 10 from before the lockdown to the Level-4 period were 52% and 41%. These values are still substantially higher than China's ambient air quality standard (Section 3.3) which indicates the significant health risks caused by PM 2.5 and PM 10 in the GZB even during the COVID-19 lockdown. Hence, even the strong emission reductions due to the strict lockdown measures were not sufficient to reach China's ambient air quality standard for PM.
The Pre-lockdown period was in the middle of the winter when the PM concentrations are at their maximum [32,55]. During the winter, an important reason for the aggravation of PM in the GZB is the use of coal for heating. During the COVID-19 situation in 2020, five cities in the Guanzhong Basin region headed by Xi'an extended the collective heating (or elastic heating) to 25 March (15 March in previous years) (https://china.huanqiu.com/article/3xQ6GNd7S9K, last access 11 September 2020) to reduce the effects of the cold spell and temperature changes on citizens' health. Therefore, during three stages, the Pre-lockdown, Level-1 and Level-2 (from 1 January to 25 March), the measures of extended collective heating (or elastic heating) reduced the effect of coal fired heating on PM 2.5 and PM 10 pollution. The PM 2.5 and PM 10 concentrations during the five stages estimated by the GTWR model are similar to those from measured at the air quality ground-based monitoring stations presented in Section 3.1. The PM concentration continued downward from the lockdown period, with the largest decrease from the Pre-lockdown stage to Level-1.
The spatial distributions of the PM 2.5 and PM 10 concentrations in the four stages are similar, as shown in Figures 9 and 10. The highest PM concentrations occur around the three cities of Xi'an, Xianyang and Weinan in the heart of the study area. PM values are slightly lower in Baoji city and Tongchuang city which are located in the west and north of the GZB. These results confirmed the analysis and comparison results of ground-based monitoring data for PM 2.5 and PM 10 in Section 3.2, and supplement the details of PM concentration variation with high spatial resolution in the study area. The population, industry and transportation in the GZB are mostly concentrated in the central area [27], and the geography of the basin together with the low wind speed all year round, is conducive for the accumulation of PM resulting in high concentrations. Furthermore, recent research showed that the strong reduction of trace gas concentrations during the COVID-19 lockdown period resulted in enhanced concentrations of aerosol due to complex atmospheric chemistry reactions [47,48].

Discussion
The Guanzhong Basin is known as one of the areas with serious air pollution in China [35,56]. The complex basin terrain structure is not conducive for the diffusion of air pollutants. The mass concentrations of PM 2.5 and PM 10 are usually exceeding China's ambient air quality standard. As in other regions in China and most other countries all over the world, the concentrations of PM 2.5 , PM 10 , SO 2 , NO 2 and CO in the Guanzhong Basin decreased significantly in response to policy measures to constrain the further spreading of COVID-19. Automobile exhaust is one of the main sources of NO 2 and CO [57,58]. During the lockdown period, people were restricted to their homes resulting in the substantial reduction of road and off road transportation, which led to a significant reduction of NO 2 and CO emissions. Moreover, fossil fuel burning from power plants and other factories is also a major source of NO 2 [57], and biomass burning (such as straw burning) is a major source of CO [59]. The shutdown of some factories had an obvious effect on the decline of NO 2 emissions.
The problem of dust particles in the GZB is very serious, and dust pollution leads to an increase of PM concentrations [56,60]. During the lockdown period, some construction sites and mining plants were shut down, resulting in reduced concentrations of dust and fine particles. The decrease of PM concentrations may also be due to the reduction of NO 2 and SO 2 concentrations, which plays an important role in the formation of secondary particulate matter [61]. However, [47] reported the increase of aerosol concentrations due to complicated atmospheric chemistry while [48] indicated the additional effects of differentiating economic effects. Generation of thermal power accounts for 20% of the total SO 2 emissions and 33% of the total NOx emissions in China [62]. The decrease of SO 2 and NO 2 concentrations is closely related to the shutdown of these plants. A study by [25] showed that the NOx emissions from powerplants decreased by 61% during the closure period of COVID-19 in Shaanxi Province, and the emission levels rebounded afterwards. The temperature in the GZB increased after the COVID-19 outbreak, with the increase of sunlight and the decrease of NO 2 and aerosol concentrations which led to the increased intensity of solar radiation available for photochemical reactions and ozone formation [23]. Previous research has shown that also the reduction of emissions of volatile organic compounds (VOCs) will inhibit the formation of O 3 in the Guanzhong Basin [26]. The O3 formation depends on the VOC-NOx ratio [63], i.e., with "VOC-limited" conditions, a reduction in VOCs emission reduces the O 3 formation, but a reduction in NOx emission increases the O 3 formation [19]. In addition to photochemical reactions, heterogeneous chemical processes at the surface of aerosol particles is also an important pathway for the interaction between ozone and PM [64].
The pandemic leading to enormous damage to the global economy has as a side effect improved air quality providing us with ideas and directions on how to reduce air pollution and improve air quality in the future, with additional challenges. We could get better insights into the effects of different sources contributing to air pollution and this knowledge can be used to effectively formulate emission control strategies. In a relatively short period of time, the major sources of air pollution from industry and transportation were closed down, resulting in a significant improvement of air quality. The air pollution due to emission of exhaust will be greatly reduced if we gradually reduce the use of cars and replace them with electrically powered vehicles or public transportation. Air quality can also be improved by replacing fossil fuels with renewable energy and other low-carbon sources. However, the increase of ozone concentrations and the effects on aerosols [47] pose other challenges. The increasingly serious ozone issue in the study region urgently needs to be solved by reduction of the atmospheric oxidation capacity.
There is a guiding significance for the improvement of air quality and human health in the Guanzhong Basin from our research, but there are also some limitations. Firstly, the lack of satellite AOD data at some pixels on some days is a serious problem, which makes it impossible to obtain full spatial coverage and capture the spatial variation of particulate matter in detail. Secondly, the research did not consider effects of meteorological conditions and the overall seasonal variations on the pollutants, which may vary between different years. The lower concentrations in the pre-lockdown period indicate that 2020 may have been an extraordinary year. In addition, night time light data were not considered in this study. [65,66] showed that during the period of COVID-19, night lighting dimmed as a result of the pandemic in China. In future research, night time light could be the proxy to explore the variation of the concentrations of air pollutants during night time. Finally, our research only focused on the Guanzhong Basin region of China, which is not representative for other regions, future studies are needed to extend to other areas.

Conclusions
The aim of this study was to analyze and discuss the variations of the concentrations of aerosols and trace gases affecting air quality (PM 2.5 , PM 10 , SO 2 , NO 2 , CO and O 3 ) in the Guanzhong Basin. In this study, six periods were considered from 1 January to 31 August 2020 (Pre-lockdown, Level-1, Level-2, Level-3, Level-4 and Level-5) and for comparison the same periods in the years 2017-2019 were used in the analysis of data from ground-based monitoring stations. The monitoring stations provided local information. To extend the study to cover areas where no ground-based measurement are available, satellite observations of AOD and NDVI and meteorological data were used with the GWTR model to predict PM concentrations with a spatial resolution of 6 km × 6 km over the whole Guanzhong Basin. The model was only applied to the period from 1 January to 24 June 2020, because thereafter VIIRS AOD were not available at the time of this study. The main conclusions are as follows: (1) During the lockdown period, human activities were largely reduced, resulting in a significant reduction in emissions from transportation, industry, construction and road dust. There is a statistically significant relationship between social lockdown and air pollution. During the strictest Level-1 emergency response period, the concentrations of PM 2.5 , PM 10 , SO 2 , NO 2 and CO decreased by 37%, 30%, 29%, 52% and 33%, while ozone increased by 82%, with respect the concentrations in the Pre-lockdown period. Basin, the GTWR model was selected because of its better performance than the LME-GWR model. Comparison with ground-based measurements showed the good performance of the GTWR model for PM 2.5 (R 2 = 0.86) up to 100 µg/m 3 and for PM 10 (R 2 = 0.80) up to 150 µg/m 3 ; for higher concentrations both PM 2.5 and PM 10 were underestimated. (5) Even during the Level-1 and Level-2 lockdown stages after the COVID-19 outbreak, the mean concentrations of the PM 2.5 and PM 10 concentrations in the Guanzhong Basin highly exceeded China's ambient air quality standards; these high concentrations have adverse effects on human health.