Assessment of the Performance of TROPOMI NO 2 and SO 2 Data Products in the North China Plain: Comparison, Correction and Application

: The TROPOspheric Monitoring Instrument (TROPOMI) aboard the Sentinel-5 Precursor satellite has been used to detect the atmospheric environment since 2017, and it is of great signiﬁcance to investigate the accuracy of its products. In this work, we present comparisons between TROPOMI tropospheric NO 2 and total SO 2 products against ground-based MAX-DOAS at a single site (Xianghe) and OMI products over a seriously polluted region (North China Plain, NCP) in China. The results show that both NO 2 and SO 2 data from three datasets exhibit a similar tendency and seasonality. In addition, TROPOMI tropospheric NO 2 columns are generally underestimated compared with collocated MAX-DOAS and OMI data by about 30–60%. In contrast to NO 2 , the monthly average SO 2 retrieved from TROPOMI is larger than MAX-DOAS and OMI, with a mean bias of 2.41 (153.8%) and 2.17 × 10 16 molec cm − 2 (120.7%), respectively. All the results demonstrated that the TROPOMI NO 2 as well as the SO 2 algorithms need to be further improved. Thus, to ensure reliable analysis in NCP area, a correction method has been proposed and applied to TROPOMI Level 3 data. The revised datasets agree reasonably well with OMI observations (R > 0.95 for NO 2 , and R > 0.85 for SO 2 ) over the NCP region and have smaller mean biases with MAX-DOAS. In the application during COVID-19 pandemic, it showed that the NO 2 column in January-April 2020 decreased by almost 25–45% compared to the same period in 2019 due to the lockdown for COVID-19, and there was an apparent rebound of nearly 15–50% during 2021. In contrast, a marginal change of the corresponding SO 2 is revealed in the NCP region. It signiﬁes that short-term control measures are expected to have more effects on NO 2 reduction than SO 2 ; conversely, we need to recognize that although the COVID-19 lockdown measures improved air quality in the short term, the pollution status will rebound to its previous level once industrial and human activities return to normal.


Introduction
Nitrogen oxides (NO x = NO + NO 2 ) and sulphur dioxide (SO 2 ) are essential trace gases both in the tropospheric and stratospheric atmosphere, and they are also conventional pollutants that are harmful to human health and ecosystems. China has achieved an incredible growth of economy and urbanization since the 1980s, and meanwhile, environmental deterioration in China has become increasingly severe [1][2][3]. In the recent decade, the government of China has conducted a series of emission reduction policies and air quality regulations to mitigate air pollution. Since 1995, the Chinese government has paid great attention to harness acid rain and SO 2 pollution and first emphasized the SO 2 emission reduction [4]. After that, the 10th (2001)(2002)(2003)(2004)(2005), 11th (2006)(2007)(2008)(2009)(2010), 12th (2011)(2012)(2013)(2014)(2015) and 13th (2016-2020) five-year plans all set a target of reducing SO 2 and NO x emissions and continue insisting upon the goal of energy conservation [5,6]. NO 2 and SO 2 have been decreasing prominently nationwide since these measures were implemented [7][8][9][10][11][12]. In addition, an enormous reduction of tropospheric NO 2 levels has been found during the COVID-19 outbreak in 2020 [13][14][15]. In order to achieve the target of improving air quality, monitoring of these air pollutants and understanding the local pollutants levels are absolutely necessary [16].
Therefore, several satellite-based instruments have been used for air pollution monitoring. Satellite platforms may obtain continuous observations of gas concentrations and provide spatial-temporal distribution over extensive regions. Until now, satellite sensors such as Global Ozone Monitoring Experiment (GOME), SCanning Imaging Absorption spectroMeter for Atmospheric ChartographY (SCIAMACHY), Ozone Monitoring Instrument (OMI), Global Ozone Monitoring Experiment-2 (GOME-2) and TROPOspheric Monitoring Instrument (TROPOMI) have demonstrated their ability to measure the NO 2 and SO 2 vertical column density (VCD), and they are utilized in a variety of applications such as investigating the trends of pollutants on a regional or global scale [11,[17][18][19], observing pollutants over a particular area or event (e.g., volcanic SO 2 flux, [20]), evaluating the NO 2 and SO 2 emissions from inverse modelling [3,12,21], and analysing pollutant sources [22].
However, satellite observations also have some basic uncertainties from the instruments themselves and the retrieval algorithm, especially in regions with high pollution levels, and as a result, it is possible to relate space-borne remote sensing records with ground-based (GB) observations to assess and determine the degree of atmospheric pollution. Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) is one of GB remote sensing technique and has a wide application on a global scale. Jin et al. [23] compared retrievals of tropospheric NO 2 and SO 2 VCDs from a MAX-DOAS equipment with the corresponding OMI observations at a non-urban site over the North China. They revealed the NO 2 columns of two datasets were highly correlated in summer and recommended that further investigation needs to be conducted for SO 2 as its large discrepancies. Theys et al. [24] established a new algorithm for SO 2 inversion based on OMI and validated against MAX-DOAS over the heavily polluted site of Xianghe (China). The comparative results bear a better agreement. Apart from that, Irie et al. [25], Tian et al. [26] and Chan et al. [27] all evaluated the performance of various versions of OMI NO 2 or SO 2 products with GB observations to prove the reliability of OMI records.
Compared to OMI, the TROPOMI has higher spatial and temporal resolution. Several current studies have reported the performance and verification of TROPOMI NO 2 products, e.g., Griffin et al. [28] and Verhoelst et al. [29] compared TROPOMI NO 2 products with multiple GB observations around the world and found a good agreement between the TROPOMI retrievals and in situ observations. Wang et al. [30] presented the comparisons of NO 2 products retrieved by TROPOMI and OMI over China, together with validation against MAX-DOAS over the Xianghe site. It turned out that TROPOMI and OMI showed high correlations in most cases; however, the TROPOMI values were generally underestimated compared with OMI and GB measurements. This means that the improvement of the TROPOMI NO 2 over China is also needed. In addition, Zhao et al. [31], Ialongo et al. [32] and Judd et al. [33] all assessed TROPOMI NO 2 measurements with different methods focused on various regions. In contrast, it is still rare to investigate the performance and accuracy of TROPOMI SO 2 data.
The goals of this study include: (1) evaluation of the TROPOMI tropospheric NO 2 and total SO 2 products against GB observation and OMI records over the polluted region in China; (2) a correction method proposed and applied on TROPOMI Level 3 (L3) daily data; (3) application of the revised TROPOMI dataset during the COVID-19 period. The data and methodology are presented in Sections 2 and 3, respectively. In Section 4, the TROPOMI data are evaluated with correlative OMI and MAX-DOAS measurements and revised by the correction methodology. Then, the corrected NO 2 and SO 2 results are used to investigate the varieties of NO 2 and SO 2 in times of COVID-19. The last two sections describe the discussion and conclusions, respectively. TROPOMI is a hyperspectral imaging spectrometer mounted on the Sentinel-5 Precursor (S5P) satellite, which was launched on 13 October 2017. The S5P spacecraft has a sun-synchronous low earth orbit with local transit time of nearly 13:30. TROPOMI enables an almost daily global scanning resulting from a swath width of 2600 km. The TROPOMI consists of eight bands covering ultraviolet (UV), visible (VIS), near-infrared and shortwave infrared portions of the radiation energy spectrum [34]. In this study, TROPOMI products are used offline (OFFL) version Level 2 (L2) NO 2 (tropospheric NO 2 VCDs) and SO 2 (SO 2 total VCDs) orbit data [35]. The spatial resolution of the TROPOMI NO 2 and SO 2 observations was 3.5 × 7 km 2 for the footprint at nadir before 6 August 2019 and refined to 3.5 × 5.5 km 2 afterwards. The TROPOMI NO 2 inversion algorithm was developed by the Royal Netherlands Meteorological Institute (KNMI) and built on the heritage of NO 2 DOMINO (Dutch OMI NO 2 ) algorithm and QA4ECV community approach with significant improvements [33]. The full technical details could been seen on the TROPOMI science website [36]. For TROPOMI SO 2 product, the algorithm was completed by the Royal Belgian Institute for Space Aeronomy (BIRA-IASB) on the basis of Differential Optical Absorption Spectroscopy (DOAS) technique [37].
The TROPOMI dataset contains a quality assurance value (qa_value) to indicate the status and quality of the retrieval results, enabling users to conveniently select data for their own purposes. To focus on high quality measurements, the NO 2 and SO 2 records in this work were filtered out with the qa_value less than 0.75, to exclude part of the pixels covered by snow/ice and cloud (cloud radiance fraction > 0.5) as well as questionable records. Apart from that, only solar zenith angle (SZA) below 75 • and 70 • for NO 2 and SO 2 pixels , respectively, are considered.

OMI NO 2 and SO 2 Product
OMI, a push room UV-VIS spectrometer, was launched aboard the NASA's EOS-Aura spacecraft on 15 July 2004. The Aura satellite possesses a near-polar, sun-synchronous orbit, and crosses the equator at 13:45 local time. The spatial resolution of OMI is about 13 × 24 km 2 at nadir. OMI has been operating for nearly 17 years and still continues to offer precious data for atmospheric research and applications. The data quality and uncertainty of OMI product have been confirmed in the current research. For comparison against TROPOMI retrievals, the OMI NO 2 (OMNO2, Version 003) and SO 2 (OMSO2, Version 003) L2 orbit datasets retrieved by the NASA team [38] are taken into account. OMI products use the normalized spectrum in the VIS ranges (402-465 nm) to obtain the NO 2 slant column densities (SCDs) and then combined with stratospheric and tropospheric air mass factors (AMF) to retrieve VCDs. A detailed description of the OMNO2 product is provided in the README guidance document [39]. In OMSO2 product version 1.2 or later, all SO 2 data records are generated with a retrieval algorithm based on principal component analysis (PCA) algorithm applying a fitting window covering 310.5 to 340 nm [40]. SO 2 column amount we used in this study is an estimate of SO 2 VCD produced with SO 2 Jacobians from a more extensive lookup table and monthly a priori profiles based on model simulations. The SO 2 inversion algorithm is presented in detail by Li et al. [41].
The screening criteria to OMI NO 2 and SO 2 are applied following the recommendations by the user guide, and to minimize comparison error with TROPOMI. Regarding OMI NO 2 filtering, we selected the pixels with the SZA < 75 • and effective cloud fraction (CF) < 0.3. For OMI SO 2 filtering, only clear sky scenes, defined as CF less than 0.5, and satellite SZA less than 70 • were collected. Additionally, the pixels affected with row anomalies have also been removed before statistical analysis.

MAX-DOAS Measurements
Here, we present almost 2 years (from July 2019 to April 2021) of continuous MAX-DOAS NO 2 and SO 2 observations at the suburban station of Xianghe, China (39.8  representative site in a highly polluted area over North China Plain (NCP), about 50 km southeast of Beijing (see Figure 1). This MAX-DOAS instrument is designed by BIRA-IASB and operated by the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences. The MAX-DOAS focused on the zenith-sky DOAS technique and includes three main components: an optical head installed on a sun tracker, a thermo-regulated box consisting of two spectrometers, and two computers for equipment control and data storage [42]. This setup can measure both scattered and direct sunlight. One of the spectrometers works in UV band (300-390 nm) and another operates in VIS wavelength (400-720 nm). During the observation, the azimuth direction of the telescope is kept to the north. A complete measurement sequence contains 9 elevation viewing angles (2,4,6,8,10,12,15,30 and 90 • ) and takes approximately 15 min.   In this study, the QDOAS, a spectral fitting software developed at BIRA-IASB, has been used to analyse the spectra observed from MAX-DOAS. The detailed configuration of retrieval is mentioned in Table 1. The fitting spectral ranges of NO 2 and SO 2 are 425-490 nm and 305-317.5 nm, respectively. To facilitate the comparison of different spaceborne data sources, various data need to be resampled to an equal spatial resolution. We use the inverse distance weighted interpolation (IDW) to resample the L2 satellite records into L3 grid data. Details could be seen in Wang et al. [30]. The distance (D i ) from the discrete point (x i , y i ) to the established grid center point (x 0 , y 0 ) can be defined as: and the estimation on grid point Z (x 0 , y 0 ) can be calculated by: where Z i is observed value on each pixel i, N is the total counts of pixels involved in this calculation and P represents the weight coefficient of distance. Thus, the daily TROPOMI and OMI L2 observations were binned to 0.25 • × 0.25 • grids as the L3 datasets which are used in the subsequent verification, correction and related analysis.

Corrections Applied to TROPOMI L3 Data
It is assumed that the OMI and TROPOMI have similar observed results on tropospheric NO 2 and SO 2 columns, since these two instruments have analogous overpass times (13:45 LST for OMI and 13:30 LST for TROPOMI). Thus, to ensure reliable analysis in NCP area, we improve a mathematical correction method proposed by Huang and Sun [15] and revise the TROPOMI L3 data to reconcile the discrepancies with OMI.
For NO 2 correction, we obtained the 2-year average difference between OMI and TROPOMI L3 data in 2019 and 2020 as: where c n (i, j) is the mean difference of OMI minus TROPOMI in a grid. OMI 2year and TROPOMI 2year represent 2-year averages of L3 tropospheric NO 2 VCDs observed by OMI and TROPOMI, respectively, in 2019 and 2020. The correction item c n (i, j) represents the probable sampling and algorithm biases between the different NO 2 products. The discussion of the stability of correction term is detailed in Section 4.1.
On the basis of Huang's [15] method, we add a deviation coefficient a n based on MAX-DOAS NO 2 results observed in Xianghe, which is defined as: Therefore, the corrected TROPOMI NO 2 in month (or year) mi could be expressed as: The correction for TROPOMI SO 2 is the same as NO 2 correction. Thus, the correction factor c s (i, j) for SO 2 is similar to c n (i, j) which is mentioned in Equation (3), and the deviation coefficient a s is also identical to a n expressed in Equation (4). The correction method has been applied to correct the TROPOMI L3 dataset over the NCP region and relevant applications have been exhibited in Section 4.

The Quality of TROPOMI NO 2 Data
The time series of TROPOMI (red dots), OMI (blue dots) tropospheric NO 2 data within a radius of 50 km around Xianghe observatory and the collocated MAX-DOAS measurements are indicated in Figure 2, covering the period July 2019 to April 2021. For MAX-DOAS NO 2 retrievals, we used full-day observed series (light grey dots) as well as the averaged values spanning 12:30 to 14:30 LST based on satellites' overpass time (dark grey dots). The latter is used for quantitative comparison with satellite NO 2 columns. These three observations present the same peaks and mostly abide by the similar day-to-day variability, with maximum values during cold months.

The Quality of TROPOMI NO2 Data
The time series of TROPOMI (red dots), OMI (blue dots) tropospheric NO2 data within a radius of 50 km around Xianghe observatory and the collocated MAX-DOAS measurements are indicated in Figure 2, covering the period July 2019 to April 2021. For MAX-DOAS NO2 retrievals, we used full-day observed series (light grey dots) as well as the averaged values spanning 12:30 to 14:30 LST based on satellites' overpass time (dark grey dots). The latter is used for quantitative comparison with satellite NO2 columns. These three observations present the same peaks and mostly abide by the similar day-today variability, with maximum values during cold months.  Figure 3 employs the comparison of monthly mean NO2 values between satellite and GB measurements as well as the corrected TROPOMI L3 datasets. Notably, the monthly mean data only comprised the coincident observation number of correlative days of three datasets. In general, both satellite and GB data show a similar tendency and a strong seasonality, with lowest NO2 loadings in summer and highest in winter. The seasonality of NO2 fluctuation is mainly related to the removal mechanisms of the OH radical, which has a similar seasonal cycle [26]. Moreover, satellited-based NO2 unfolds negative biases relative to MAX-DOAS, and the OMI deviation is smaller and closer to the ground observation, ranging from 20% to 40%. TROPOMI tropospheric NO2 VCDs are commonly lower than collocated MAX-DOAS by about 30-60%. This finding is consistent with the recent studies of Dimitropoulou et al. [48] and Wang et al. [30]. It is mainly because the representative scales are different between satellite and GB technique [32]. Correlation plots of all related measurements have been shown in Figure 3b. Despite showing negative drifts, the temporal patterns observed from OMI and TROPOMI closely match the GB measurements, since the correlation coefficient (R) values are 0.78 and 0.76 for monthly scales, respectively. The MAX-DOAS and OMI tropospheric NO2 VCDs are highly correlated with the slope of 0.84, while the slope value (0.60) between MAX-DOAS and TRO-POMI indicates that TROPOMI tends to be apparently underestimated.
Regarding the issue that TROPOMI NO2 data are underestimated, previous works have investigated the origin of systematic uncertainties in TROPOMI NO2 retrievals. Boersma et al. [49] presented that primary error sources are mainly attributed to the spectral  Figure 3 employs the comparison of monthly mean NO 2 values between satellite and GB measurements as well as the corrected TROPOMI L3 datasets. Notably, the monthly mean data only comprised the coincident observation number of correlative days of three datasets. In general, both satellite and GB data show a similar tendency and a strong seasonality, with lowest NO 2 loadings in summer and highest in winter. The seasonality of NO 2 fluctuation is mainly related to the removal mechanisms of the OH radical, which has a similar seasonal cycle [26]. Moreover, satellited-based NO 2 unfolds negative biases relative to MAX-DOAS, and the OMI deviation is smaller and closer to the ground observation, ranging from 20% to 40%. TROPOMI tropospheric NO 2 VCDs are commonly lower than collocated MAX-DOAS by about 30-60%. This finding is consistent with the recent studies of Dimitropoulou et al. [48] and Wang et al. [30]. It is mainly because the representative scales are different between satellite and GB technique [32]. Correlation plots of all related measurements have been shown in Figure 3b. Despite showing negative drifts, the temporal patterns observed from OMI and TROPOMI closely match the GB measurements, since the correlation coefficient (R) values are 0.78 and 0.76 for monthly scales, respectively. The MAX-DOAS and OMI tropospheric NO 2 VCDs are highly correlated with the slope of 0.84, while the slope value (0.60) between MAX-DOAS and TROPOMI indicates that TROPOMI tends to be apparently underestimated.
Moreover, they changed the priori vertical profiles measured from MAX-DOAS to recal-culate the satellite NO2 VCDs, leading to a better correlation between the satellite and GB data. Overall, these factors all exert significant impacts on TROPOMI NO2 inversion.
As a result, to reconcile the discrepancies, the approach shown in Section 3.2 are used to correct TROPOMI NO2 L3 data. Compared to original results, the corrected TROPOMI results (TROPOMI_corr for short in Figure 3) are more consistent with MAX-DOS NO2 column concentrations, with the slope being 0.82 (0.62 in original comparison).

Feasibility Analysis of TROPOMI NO2 Correction
In order to prove that the correction coefficient ( , ) is stable within every month and could be used to correct TROPOMI L3 data over the NCP high polluted region, we define the deviation ( , ) as: where ( , ) means the monthly average difference between OMI and TROPOMI of month mi, and ( , ) denotes the deviation value in and on each pixel ( , ). Throughout the two years combined, obvious differences prevail in Eastern China between TROPOMI and OMI as shown in panel (a) of Figure 4. Notably, tropospheric NO2 values derived from the TROPOMI are lower than those from OMI at a nation-wide scale, especially in the NCP (black box highlighted in Figure 4a), where the discrepancies exceed 0.4 (×10 16 molec cm −2 ). It means that the higher the NO2 loadings the greater the underestimation. Considering the regionality of MAX-DOAS observations, we produce a corrected TROPOMI L3 dataset over the NCP region. The probability density distribution plot of ( , ) is reflected in Figure 4b. The ( , ) values denote the deviations derived from the 2-year average difference minus each monthly average difference (OMI- Regarding the issue that TROPOMI NO 2 data are underestimated, previous works have investigated the origin of systematic uncertainties in TROPOMI NO 2 retrievals. Boersma et al. [49] presented that primary error sources are mainly attributed to the spectral fitting, the estimation of the stratospheric NO 2 content and uncertainties of ancillary parameters used in AMF calculation (i.e., cloud information, aerosols, surface albedo, and a priori NO 2 profile). For instance, Dimitropoulou et al. [48] discussed the effects of cloud, aerosol, surface albedo and a priori NO 2 profile on inversion results. Specifically, the cloud parameters are used as inputs in a cloud correction scheme applied to NO 2 retrieval that may lead to biases in the tropospheric NO 2 column. Furthermore, TROPOMI NO 2 inversion is prone to be affected by stricter cloud mask (named FRESCO-S) compared with OMI, which presumably removes some heavy pollution cases in the retrievals and induces an underestimation [30]. In addition, aerosols are considered indirectly in the TROPOMI NO 2 algorithm, which means aerosols are processed through the cloud correction scheme. Moreover, they changed the priori vertical profiles measured from MAX-DOAS to recalculate the satellite NO 2 VCDs, leading to a better correlation between the satellite and GB data. Overall, these factors all exert significant impacts on TROPOMI NO 2 inversion.
As a result, to reconcile the discrepancies, the approach shown in Section 3.2 are used to correct TROPOMI NO 2 L3 data. Compared to original results, the corrected TROPOMI results (TROPOMI_corr for short in Figure 3) are more consistent with MAX-DOS NO 2 column concentrations, with the slope being 0.82 (0.62 in original comparison).

Feasibility Analysis of TROPOMI NO 2 Correction
In order to prove that the correction coefficient c n (i, j) is stable within every month and could be used to correct TROPOMI L3 data over the NCP high polluted region, we define the deviation ∆c mi (i, j) as: where c mi (i, j) means the monthly average difference between OMI and TROPOMI of month mi, and ∆c mi (i, j) denotes the deviation value in c n and c mi on each pixel (i, j). Throughout the two years combined, obvious differences prevail in Eastern China between TROPOMI and OMI as shown in panel (a) of Figure 4. Notably, tropospheric NO 2 values derived from the TROPOMI are lower than those from OMI at a nation-wide scale, especially in the NCP (black box highlighted in Figure 4a), where the discrepancies exceed 0.4 (×10 16 molec cm −2 ). It means that the higher the NO 2 loadings the greater the underestimation. Considering the regionality of MAX-DOAS observations, we produce a corrected TROPOMI L3 dataset over the NCP region. The probability density distribution plot of  Figure 4b. The ∆c mi (i, j) values denote the deviations derived from the 2-year average difference minus each monthly average difference (OMI-TROPOMI) over the NCP region during the study period, collected with all pixels. Evidently, approximately 80% of ∆c mi (i, j) values are lower than regional mean of c n (i, j) values (denoted as c 2year , about 0.34 × 10 16 molec cm −2 ), indicating the feasibility of the correction term to some extent. Furthermore, the monthly change of regional mean of ∆c mi (i, j) is displayed in Figure 4c. The monthly deviation ranges from −0.3 to 0.2 (×10 16 molec cm −2 ), with absolute values less than c 2year . In addition, the positive difference mainly occurs in summer and spring, while the opposite often appears in winter and autumn. These results confirm that the c n (i, j) could be used for TROPOMI NO 2 monthly mean data correction most of the time. TROPOMI) over the NCP region during the study period, collected with all pixels. Evidently, approximately 80% of ( , ) values are lower than regional mean of ( , ) values (denoted as , about 0.34 × 10 16 molec cm −2 ), indicating the feasibility of the correction term to some extent. Furthermore, the monthly change of regional mean of ( , ) is displayed in Figure 4c. The monthly deviation ranges from −0.3 to 0.2 (×10 16 molec cm −2 ), with absolute values less than . In addition, the positive difference mainly occurs in summer and spring, while the opposite often appears in winter and autumn. These results confirm that the ( , ) could be used for TROPOMI NO2 monthly mean data correction most of the time.

Correction for TROPOMI NO2 over the NCP Region
Annual mean geographic distribution of tropospheric NO2 VCDs over the NCP region observed from OMI, TROPOMI as well as the TROPOMI_corr are indicated in Figure  5a-c,e-g. The spatial structure from TROPOMI possesses a great resemblance to that from OMI, while the magnitudes in TROPOMI are lower than in OMI. High NO2 loadings are mainly concentrated around provincial capitals with high emissions. Meanwhile, NO2 declined significantly in most regions in 2020 compared with 2019, from both OMI and TROPOMI. Application of corrected TROPOMI NO2 has improved significantly in magnitudes and shows better agreement with OMI observations. The linear regression ( Figure  5d,h) yields that the slope of TROPOMI versus OMI increased from 0.59 to 0.86 in 2019 and from 0.63 to 0.93 in 2020. Furthermore, the correlation is much strengthened with the R values raised to 0.99 in these two years.  (3)). Black box represents the NCP area. (b) Probability density distribution diagram of the ∆c mi (i, j) for all months and all pixels over the NCP region in 2019-2020. (c) Bar-chart plot representing the temporal evolution of the regional mean ∆c mi (units: 10 16 molec cm −2 ).

Correction for TROPOMI NO 2 over the NCP Region
Annual mean geographic distribution of tropospheric NO 2 VCDs over the NCP region observed from OMI, TROPOMI as well as the TROPOMI_corr are indicated in Figure 5a-c,e-g. The spatial structure from TROPOMI possesses a great resemblance to that from OMI, while the magnitudes in TROPOMI are lower than in OMI. High NO 2 loadings are mainly concentrated around provincial capitals with high emissions. Meanwhile, NO 2 declined significantly in most regions in 2020 compared with 2019, from both OMI and TROPOMI. Application of corrected TROPOMI NO 2 has improved significantly in magnitudes and shows better agreement with OMI observations. The linear regression (Figure 5d,h)  In brief summary, the TROPOMI, OMI and MAX-DOAS NO2 VCDs exhibited similar temporal features during the study period at Xianghe site. Compared with GB measurements, the NO2 VCDs derived from OMI had a regression slope (slope = 0.84) greater than that from TROPOMI (slope = 0.60). Moreover, focusing on the NCP region, the TROPOMI and OMI NO2 VCDs were strongly correlated (R > 0.95) in terms of spatial pattern. However, the magnitudes in the TROPOMI are generally lower than in the OMI by 25% to 35%, particularly over highly contaminated areas in wintertime. Further, the corrected TRO-POMI L3 NO2 datasets have been greatly improved in magnitudes compared with MAX-DOAS and OMI considering either in a single point or over the entire region. Figure 6 shows the time series of SO2 observations at the Xianghe site from July 2019 to April 2021. MAX-DOAS retrieved data are coincidentally averaged in approximately ±2 h (12:30 to 14:30 LST) overpass time of TROPOMI and OMI over the target region. The SO2 VCDs show pronounced seasonal cycle, as evidenced by both remote sensing technique and GB measurement, with a maximum occurring in winter and autumn and a minimum in summer. This marked seasonal fluctuation can be explained by the seasonal feature of emission strengths and lifetimes of the SO2 as well as the atmospheric transport [23,42]. Moreover, it is obvious that SO2 VCDs derived from TROPOMI are apparently higher than that from OMI and MAX-DOAS. In brief summary, the TROPOMI, OMI and MAX-DOAS NO 2 VCDs exhibited similar temporal features during the study period at Xianghe site. Compared with GB measurements, the NO 2 VCDs derived from OMI had a regression slope (slope = 0.84) greater than that from TROPOMI (slope = 0.60). Moreover, focusing on the NCP region, the TROPOMI and OMI NO 2 VCDs were strongly correlated (R > 0.95) in terms of spatial pattern. However, the magnitudes in the TROPOMI are generally lower than in the OMI by 25% to 35%, particularly over highly contaminated areas in wintertime. Further, the corrected TROPOMI L3 NO 2 datasets have been greatly improved in magnitudes compared with MAX-DOAS and OMI considering either in a single point or over the entire region. Figure 6 shows the time series of SO 2 observations at the Xianghe site from July 2019 to April 2021. MAX-DOAS retrieved data are coincidentally averaged in approximately ±2 h (12:30 to 14:30 LST) overpass time of TROPOMI and OMI over the target region. The SO 2 VCDs show pronounced seasonal cycle, as evidenced by both remote sensing technique and GB measurement, with a maximum occurring in winter and autumn and a minimum in summer. This marked seasonal fluctuation can be explained by the seasonal feature of emission strengths and lifetimes of the SO 2 as well as the atmospheric transport [23,42]. Moreover, it is obvious that SO 2 VCDs derived from TROPOMI are apparently higher than that from OMI and MAX-DOAS. Remote Sens. 2022, 14, x FOR PEER REVIEW 10 of 19 Figure 6. Same as Figure 2, but for SO2.

The Quality of TROPOMI SO 2 Data
To better explore SO2 monthly variation and satellite product quality, the monthly SO2 VCDs from space-based and GB measurements are performed. As shown in Figure 7, the monthly mean SO2 columns from MAX-DOAS are well covariates with the OMI data (R = 0.79), and their magnitudes are in great agreement (slope = 0.96), implying well-captured monthly variations. In contrast, differences among TROPOMI-inferred SO2 (marked in yellow line) and those of OMI and MAX-DOAS observations feature a slightly lower agreement (R = 0.71 with MAX-DOAS) and an order of magnitude difference (slope = 2.11 with MAX-DOAS) with TROPOMI typically overvalued. Based on the better consistency between the OMI and MAX-DOAS SO2 VCDs, a method for TROPOMI SO2 correction is developed.
In the following, we present the corrected SO2 results derived from the correction technique introduced above (detailed in Section 3.2). The corresponding plot is also presented in Figure 7. For comparison of corrected TROPOMI and MAX-DOAS, slope is higher than 1 (slope = 1.35), suggesting that corrected TROPOMI observations still provide higher values than MAX-DOAS in several months, especially in wintertime. However, slope values of corrected SO2 VCDs are close to 1 than that of original results (slope = 2.11), also indicating better agreement of corrected TROPOMI SO2 in terms of monthly mean values.

Feasibility Analysis of TROPOMI SO2 Correction
Referring to the previous analysis, a verification for stability of correction coefficient ( , ) was performed. As shown in Figure 8a, the absolute difference in SO2 analysis is defined as TROPOMI minus OMI, which is different with in NO2. The discrepancy is about 1.5 to 3.0 × 10 16 molec cm −2 over NCP area, indicating overestimated SO2 values that To better explore SO 2 monthly variation and satellite product quality, the monthly SO 2 VCDs from space-based and GB measurements are performed. As shown in Figure 7, the monthly mean SO 2 columns from MAX-DOAS are well covariates with the OMI data (R = 0.79), and their magnitudes are in great agreement (slope = 0.96), implying well-captured monthly variations. In contrast, differences among TROPOMI-inferred SO 2 (marked in yellow line) and those of OMI and MAX-DOAS observations feature a slightly lower agreement (R = 0.71 with MAX-DOAS) and an order of magnitude difference (slope = 2.11 with MAX-DOAS) with TROPOMI typically overvalued. Based on the better consistency between the OMI and MAX-DOAS SO 2 VCDs, a method for TROPOMI SO 2 correction is developed. To better explore SO2 monthly variation and satellite product quality, the monthly SO2 VCDs from space-based and GB measurements are performed. As shown in Figure 7, the monthly mean SO2 columns from MAX-DOAS are well covariates with the OMI data (R = 0.79), and their magnitudes are in great agreement (slope = 0.96), implying well-captured monthly variations. In contrast, differences among TROPOMI-inferred SO2 (marked in yellow line) and those of OMI and MAX-DOAS observations feature a slightly lower agreement (R = 0.71 with MAX-DOAS) and an order of magnitude difference (slope = 2.11 with MAX-DOAS) with TROPOMI typically overvalued. Based on the better consistency between the OMI and MAX-DOAS SO2 VCDs, a method for TROPOMI SO2 correction is developed.
In the following, we present the corrected SO2 results derived from the correction technique introduced above (detailed in Section 3.2). The corresponding plot is also presented in Figure 7. For comparison of corrected TROPOMI and MAX-DOAS, slope is higher than 1 (slope = 1.35), suggesting that corrected TROPOMI observations still provide higher values than MAX-DOAS in several months, especially in wintertime. However, slope values of corrected SO2 VCDs are close to 1 than that of original results (slope = 2.11), also indicating better agreement of corrected TROPOMI SO2 in terms of monthly mean values.

Feasibility Analysis of TROPOMI SO2 Correction
Referring to the previous analysis, a verification for stability of correction coefficient ( , ) was performed. As shown in Figure 8a, the absolute difference in SO2 analysis is defined as TROPOMI minus OMI, which is different with in NO2. The discrepancy is about 1.5 to 3.0 × 10 16 molec cm −2 over NCP area, indicating overestimated SO2 values that In the following, we present the corrected SO 2 results derived from the correction technique introduced above (detailed in Section 3.2). The corresponding plot is also presented in Figure 7. For comparison of corrected TROPOMI and MAX-DOAS, slope is higher than 1 (slope = 1.35), suggesting that corrected TROPOMI observations still provide higher values than MAX-DOAS in several months, especially in wintertime. However, slope values of corrected SO 2 VCDs are close to 1 than that of original results (slope = 2.11), also indicating better agreement of corrected TROPOMI SO 2 in terms of monthly mean values.

Feasibility Analysis of TROPOMI SO 2 Correction
Referring to the previous analysis, a verification for stability of correction coefficient c s (i, j) was performed. As shown in Figure 8a, the absolute difference in SO 2 analysis is defined as TROPOMI minus OMI, which is different with in NO 2 . The discrepancy is about 1.5 to 3.0 × 10 16 molec cm −2 over NCP area, indicating overestimated SO 2 values that are apparent in the TROPOMI measurements throughout the entire research area. Moreover, the TROPOMI SO 2 product exhibits severe SO 2 pollution in most areas of China, which is inconsistent with the fact that SO 2 emissions have been reduced significantly in China [50]. approximately 95% of ( , ) values are lower than regional mean of ( , ) v (denoted as , about 1.69 × 10 16 molec cm −2 ), which means that the ( , ) is rea able to be used in each month correction. Considering the monthly change of regi mean of ( , ) in Figure 8c, the monthly deviation values are within ±0.8 (×10 16 m cm −2 ), larger than that of NO2 (within ±0.3 × 10 16 molec cm −2 ). Therefore, the magnitu of the TROPOMI SO2 retrievals need further correction and validation.

Correction for TROPOMI SO2 over the NCP Region
Comparison results of TROPOMI, OMI and TROPOMI_corr SO2 results in 2019 2020 are plotted in Figure 9. Large SO2 columns are standing out over the NCP reg The retrievals by TROPOMI and OMI both reveal similar spatial distribution of the loadings, while the magnitudes in TROPOMI are much higher than in OMI. In term the whole NCP area, the spatial correlations in annual mean SO2 VCDs between the T POMI and OMI remained poor in some regions and the R values in 2019 and 2020 are and 0.41, respectively. When the correction method is applied, TROPOMI SO2 dataset greatly improved, not only in regional distribution but also in magnitudes, with R va increased to above 0.85. As we know, the retrieval accuracy of SO2 columns from T POMI is also limited by several factors, such as uncertainties of SCDs inversion and AMF calculations. For instance, the SO2 is not easy to be extracted as its low content in The probability density distribution plot of ∆c mi (i, j) is also shown in panel (b) of Figure 8. The definition of ∆c mi (i, j) for SO 2 is analogous to that of NO 2 . As we can see, approximately 95% of ∆c mi (i, j) values are lower than regional mean of c s (i, j) value (denoted as c 2year , about 1.69 × 10 16 molec cm −2 ), which means that the c s (i, j) is reasonable to be used in each month correction. Considering the monthly change of regional mean of ∆c mi (i, j) in Figure 8c, the monthly deviation values are within ±0.8 (×10 16 molec cm −2 ), larger than that of NO 2 (within ±0.3 × 10 16 molec cm −2 ). Therefore, the magnitudes of the TROPOMI SO 2 retrievals need further correction and validation.

Correction for TROPOMI SO 2 over the NCP Region
Comparison results of TROPOMI, OMI and TROPOMI_corr SO 2 results in 2019 and 2020 are plotted in Figure 9. Large SO 2 columns are standing out over the NCP region. The retrievals by TROPOMI and OMI both reveal similar spatial distribution of the SO 2 loadings, while the magnitudes in TROPOMI are much higher than in OMI. In terms of the whole NCP area, the spatial correlations in annual mean SO 2 VCDs between the TROPOMI and OMI remained poor in some regions and the R values in 2019 and 2020 are 0.37 and 0.41, respectively. When the correction method is applied, TROPOMI SO 2 datasets are greatly improved, not only in regional distribution but also in magnitudes, with R values increased to above 0.85. As we know, the retrieval accuracy of SO 2 columns from TROPOMI is also limited by several factors, such as uncertainties of SCDs inversion and the AMF calculations. For instance, the SO 2 is not easy to be extracted as its low content in the atmosphere; and the absorption of SO 2 is weaker than that of O 3 in the equal wavelengths, which could be disturbed in the process of spectral fitting [50]. For another example, according to the research of Theys et al. [24], they considered potential factors causing errors in SO 2 retrievals, including the priori profile. They found that the OMI columns, which are corrected by the MAX-DOAS profile shape, agree very well with GB records. Moreover, Xia et al. [50] used a priori profile from GEOS-Chem schema instead of from TM5 simulations in TROPOMI SO 2 inversion, the relative bias between TROPOMI SO 2 results and MAX-DOAS observations descended from 17.9-28.4% to 11.2-12.4%. This illustrates the importance of a priori profiles on the SO 2 inversion. atmosphere; and the absorption of SO2 is weaker than that of O3 in the equal wavelengths, which could be disturbed in the process of spectral fitting [50]. For another example, according to the research of Theys et al. [24], they considered potential factors causing errors in SO2 retrievals, including the priori profile. They found that the OMI columns, which are corrected by the MAX-DOAS profile shape, agree very well with GB records. Moreover, Xia et al. [50] used a priori profile from GEOS-Chem schema instead of from TM5 simulations in TROPOMI SO2 inversion, the relative bias between TROPOMI SO2 results and MAX-DOAS observations descended from 17.9−28.4% to 11.2−12.4%. This illustrates the importance of a priori profiles on the SO2 inversion. In short, the TROPOMI inversions could capture the SO2 temporal manners in general but tended to overstate the magnitudes over Xianghe observatory. For comparison of TROPOMI and OMI SO2 over the NCP region, the apparent overestimation could also be found in TROPOMI, and weak spatial correlations (R < 0.45) were demonstrated. The corrected TROPOMI SO2 L3 data are closer to OMI in magnitude and the correlation over the entire region has also increased. Inter-comparisons of the TROPOMI and MAX-DOAS SO2 columns indicate that the inversion algorithm of TROPOMI SO2 needs further improvement, especially in the heavily polluted areas over China.

Analysis of NO2 and SO2 over NCP during COVID-19 Period
The global lockdown caused by the coronavirus disease (COVID-19) pandemic in 2020 reduced social and economic activities in China. The Chinese government implemented a strict lockdown measure in Wuhan on January 23. By then, a lockdown was enforced in Wuhan and extended to nationwide until 8 April 2020. Based on the corrected NO2 and SO2 TROPOMI L3 datasets, we investigated the responses of the NO2 and SO2 levels resulting from the spread of COVID-19 over the NCP region. Average NO2 columns during January to April in 2019, 2020 (lockdown period) and 2021 are referred to as Phase I, Phase II and Phase III, respectively. Note that the lunar new year holidays in 2019 range from 4 February to 10 February, in 2020 from 24 January to 31 January, and in 2021 from In short, the TROPOMI inversions could capture the SO 2 temporal manners in general but tended to overstate the magnitudes over Xianghe observatory. For comparison of TROPOMI and OMI SO 2 over the NCP region, the apparent overestimation could also be found in TROPOMI, and weak spatial correlations (R < 0.45) were demonstrated. The corrected TROPOMI SO 2 L3 data are closer to OMI in magnitude and the correlation over the entire region has also increased. Inter-comparisons of the TROPOMI and MAX-DOAS SO 2 columns indicate that the inversion algorithm of TROPOMI SO 2 needs further improvement, especially in the heavily polluted areas over China.

Analysis of NO 2 and SO 2 over NCP during COVID-19 Period
The global lockdown caused by the coronavirus disease (COVID-19) pandemic in 2020 reduced social and economic activities in China. The Chinese government implemented a strict lockdown measure in Wuhan on January 23. By then, a lockdown was enforced in Wuhan and extended to nationwide until 8 April 2020. Based on the corrected NO 2 and SO 2 TROPOMI L3 datasets, we investigated the responses of the NO 2 and SO 2 levels resulting from the spread of COVID-19 over the NCP region. Average NO 2 columns during January to April in 2019, 2020 (lockdown period) and 2021 are referred to as Phase I, Phase II and Phase III, respectively. Note that the lunar new year holidays in 2019 range from 4 February to 10 February, in 2020 from 24 January to 31 January, and in 2021 from 11 February to 17 February, which are all included in our research period. Therefore, the impact of "holiday effect" is not considered separately. Figure 10 presents the spatial pattern of time-averaged NO 2 columns over NCP into three phases. Regarding NO 2 , high contents are shown in the provincial capitals and their surrounding areas, and broad-scale reductions by 25% to 45% are prevalent in NCP during Phase II. The reduction pattern shown in Figure 10d implies a substantial reduction in economic activities and human migration during this period. During Phase III, when the epidemic prevention and control gradually alleviated, the NO 2 concentrations exhibit a rapid and sharp increase, with highest amplification in the areas surrounding Tianjin (TJ) and Jinan (JN) by about up to 60%. Overall, the lockdown measure during COVID-19 had a significant effect on NO 2 reductions over the entire NCP area. After that, a prominent rebound trend was noted in the same period in 2021.
11 February to 17 February, which are all included in our research period. Theref impact of "holiday effect" is not considered separately. Figure 10 presents the spatial pattern of time-averaged NO2 columns over N three phases. Regarding NO2, high contents are shown in the provincial capitals a surrounding areas, and broad-scale reductions by 25% to 45% are prevalent in N ing Phase II. The reduction pattern shown in Figure 10d implies a substantial redu economic activities and human migration during this period. During Phase III, w epidemic prevention and control gradually alleviated, the NO2 concentrations e rapid and sharp increase, with highest amplification in the areas surrounding Tia and Jinan (JN) by about up to 60%. Overall, the lockdown measure during COVID a significant effect on NO2 reductions over the entire NCP area. After that, a pro rebound trend was noted in the same period in 2021. According to the NO2 decrease, a SO2 reduction is also be expected during C 19. However, unlike previous conclusions, SO2 columns did not change obviously the blockade period. As shown in Figure 11 In general, high NO2 accumulation was similar to SO2, which may appear o similar hot spots in North China. For quantitative comparison, four major capit over this target region have been given and discussed in Figure 12. The troposphe columns in all spots experienced a dramatic drop during Phase II and then recover gressively. Specifically, the NO2 VCDs decreased by 0.28, 0.22, 0.39 and 0.38 × 10 1 cm −2 in Beijing (BJ), TJ, Shijiazhuang (SJZ) and JN areas, respectively, between Pha Phase II, reflecting overall lower emissions during this period. Then, significant appeared in phase III, indicating that a recovery to previous years after the epide mission is expected. As for SO2, the columns in the lockdown period (Phase I changed little versus during the same period of Phase I. Subsequently, in Phase levels in the four regions increased slightly, with the highest increase in JN by 15.8%. In sum, the NO2 levels during Phase II were overall significantly lower than i I, and the NO2 levels may quickly rebound when public activities in China are re However, SO2 changes were less pronounced during COVID-19. Thus, the res measures that China had implemented to respond to COVID-19 had a more obv fluence on NO2. In addition, although the air quality has been improved in the sho due to the lockdown measures during COVID-19, the pollution status will reboun previous level at once the industrial and human activities return to normal levels. In general, high NO 2 accumulation was similar to SO 2 , which may appear over the similar hot spots in North China. For quantitative comparison, four major capital cities over this target region have been given and discussed in Figure 12. The tropospheric NO 2 columns in all spots experienced a dramatic drop during Phase II and then recovered progressively. Specifically, the NO 2 VCDs decreased by 0.28, 0.22, 0.39 and 0.38 × 10 16 molec cm −2 in Beijing (BJ), TJ, Shijiazhuang (SJZ) and JN areas, respectively, between Phase I and Phase II, reflecting overall lower emissions during this period. Then, significant growth appeared in phase III, indicating that a recovery to previous years after the epidemic remission is expected. As for SO 2 , the columns in the lockdown period (Phase II) have changed little versus during the same period of Phase I. Subsequently, in Phase III, SO 2 levels in the four regions increased slightly, with the highest increase in JN by about 15.8%.

Discussion
The results from the present comparison analysis could improve our understanding of the quality of TROPOMI products in China, especially the validation and investigation of SO2, which is still scarce in current research.
Throughout the analysis above, we found that both the diurnal and monthly NO2 and SO2 variability are revealed well by the TROPOMI, in accordance with OMI and MAX-DOAS measurements in Xianghe site, displaying an evident seasonal characteristic with highest in winter and lowest in summer. However, some uncertainties also exist over highly polluted areas, especially for SO2 data, which cannot well reflect the current pollution status in China. Therefore, combining with other satellite and ground-based dataset, we provided an attempt to correct TROPOMI dataset, hoping to improve its accuracy and make it more consistent with the real pollution situation in China. In other parts of China, this method could also be applied with reliable satellite and ground-based data. In addition, we need to realize that the error source analysis of TROPOMI data products and the improvement of algorithm process over China are still necessary.
When using the modified dataset to study the environmental pollution situation before and after COVID-19 over the NCP area, we found that NO2 experienced a process of rising first and then reducing. In fact, several epidemic-related studies have confirmed the fact that NO2 levels decreased significantly during COVID-19 in 2020, as shown in Bauwens et al. [13], Fan et al. [14], Huang and Sun [15] and Filonchyk et al. [51]. In this study, a comparison of the same period in 2021 also confirms that NO2 has returned to pre-epidemic (in 2019) levels without the strict lockdown policy. In contrast, SO2 concentrations did not fluctuate significantly before and after COVID-19. Although, in the study of Fan et al. [14] and Filonchyk et al. [51], slight declines in SO2 concentrations also appeared in certain areas and cities during COVOD-19 (in 2020). However, compared with the sharp decline of NO2, the change of SO2 seems not obvious. Considering the reasons for this phenomenon, we also made some reasonable guesses. As mentioned in Filonchyk et al. In sum, the NO 2 levels during Phase II were overall significantly lower than in Phase I, and the NO 2 levels may quickly rebound when public activities in China are resumed. However, SO 2 changes were less pronounced during COVID-19. Thus, the restrictive measures that China had implemented to respond to COVID-19 had a more obvious influence on NO 2 . In addition, although the air quality has been improved in the short term due to the lockdown measures during COVID-19, the pollution status will rebound to its previous level at once the industrial and human activities return to normal levels.

Discussion
The results from the present comparison analysis could improve our understanding of the quality of TROPOMI products in China, especially the validation and investigation of SO 2 , which is still scarce in current research.
Throughout the analysis above, we found that both the diurnal and monthly NO 2 and SO 2 variability are revealed well by the TROPOMI, in accordance with OMI and MAX-DOAS measurements in Xianghe site, displaying an evident seasonal characteristic with highest in winter and lowest in summer. However, some uncertainties also exist over highly polluted areas, especially for SO 2 data, which cannot well reflect the current pollution status in China. Therefore, combining with other satellite and ground-based dataset, we provided an attempt to correct TROPOMI dataset, hoping to improve its accuracy and make it more consistent with the real pollution situation in China. In other parts of China, this method could also be applied with reliable satellite and ground-based data. In addition, we need to realize that the error source analysis of TROPOMI data products and the improvement of algorithm process over China are still necessary.
When using the modified dataset to study the environmental pollution situation before and after COVID-19 over the NCP area, we found that NO 2 experienced a process of rising first and then reducing. In fact, several epidemic-related studies have confirmed the fact that NO 2 levels decreased significantly during COVID-19 in 2020, as shown in Bauwens et al. [13], Fan et al. [14], Huang and Sun [15] and Filonchyk et al. [51]. In this study, a comparison of the same period in 2021 also confirms that NO 2 has returned to pre-epidemic (in 2019) levels without the strict lockdown policy. In contrast, SO 2 concentrations did not fluctuate significantly before and after COVID-19. Although, in the study of Fan et al. [14] and Filonchyk et al. [51], slight declines in SO 2 concentrations also appeared in certain areas and cities during COVOD-19 (in 2020). However, compared with the sharp decline of NO 2 , the change of SO 2 seems not obvious. Considering the reasons for this phenomenon, we also made some reasonable guesses. As mentioned in Filonchyk et al. [51], they showed that SO 2 levels decreased slightly in February 2020, compared with February 2019, and coal consumption in power plants and factories recovered to previous levels by the end of March, restoring SO 2 levels to normal. In addition, at the same stage in 2021, SO 2 still remains stable, and similar finding is also mentioned in the study of Wang et al. [52]. They found that SO 2 changes were not statistically significant over the NCP region during the Asian-Pacific Economic Cooperation (APEC) in 2014, showing that the SO 2 reduction was more related to natural or random variability rather than external forcing. Similarly, the specific factors causing such changes in NO 2 and SO 2 during COVID-19 still need further experiments and discussions.

Conclusions
In this study, column NO 2 and SO 2 data derived from TROPOMI/S5P were evaluated against ground-based MAX-DOAS at a single site (Xianghe) from 2019 to 2021. Comparison between TROPOMI retrievals and OMI products over a highly polluted region (NCP) are also conducted. It was found that satellited-based NO 2 data are both negatively biased relative to MAX-DOAS, and the OMI deviation is smaller and closer to the ground observation, ranging from 20% to 40%. Meanwhile, TROPOMI tropospheric NO 2 VCDs are slightly lower than collocated MAX-DOAS observations by about 30-60%. When it comes to SO 2 , the monthly average SO 2 column retrieved from TROPOMI is larger than MAX-DOAS and OMI, with a mean bias of 2.41 (153.8%) and 2.17 × 10 16 molec cm −2 (120.7%) at Xianghe site, respectively. MAX-DOAS comparisons to OMI are more correlated than TROPOMI during the investigated time (R = 0.79 vs. 0.71). SO 2 VCDs derived from TROPOMI seem overestimated and the algorithm needs to be further improved in the future.
After the correction, TROPOMI NO 2 and SO 2 displayed markedly better consistencies with OMI in both magnitudes and distribution over the NCP area. The R values for regional mean concentrations increased greater than 0.95 and 0.85 for NO 2 and SO 2 , respectively.
Finally, we used the corrected TROPOMI NO 2 and SO 2 dataset to investigate the environmental pollution status during COVID-19 period over the NCP region. Evident decreases in NO 2 columns were shown in the lockdown period (Phase II) compared to the same period in 2019 (Phase I), reduced by almost 25-45%, while SO 2 concentration remains fairly stable throughout Phase I and Phase II. Then, NO 2 and SO 2 levels observed from TROPOMI returned to normal in Phase III. This implies that the lockdown measure during COVID-19 had a certain inhibitory effect on environmental pollution and are expected to be more effective on NO 2 reduction than SO 2 . Although the air quality was improved in the short term due to the lockdown measures during COVID-19, the pollution levels may rebound to their previous level once industrial and human activities return to original levels.
Overall, these works will help the assessment and algorithm improvement work for future TROPOMI NO 2 and SO 2 products, and further studies are also needed to investigate the causes of such errors of the NO 2 and SO 2 inversion over China.