OMI-observed HCHO in Shanghai, China, during 2010–2019 and ozone sensitivity inferred by an improved HCHO / NO 2 ratio

. In recent years, satellite remote sensing has been increasingly used in the long-term observation of ozone (O 3 ) precursors and its formation regime. In this work, formaldehyde (HCHO) data from Ozone Monitoring Instrument (OMI) were used to analyze the temporal and spatial distribution of HCHO vertical column densities (VCDs) in Shanghai from 2010 to 2019. HCHO VCDs exhibited the highest value in summer and the lowest in winter, the high VCD being concentrated in western Shanghai. Temperature largely inﬂuences HCHO by affecting the biogenic emissions and photochemical reactions, and industry was the major anthropogenic source. The satellite-observed formaldehyde-to-nitrogen dioxide ratio (FNR SAT ) reﬂects that the O 3 formation regime had signiﬁcant seasonal characteristics and grad-ually manifested as a transitional ozone formation regime dominating in Shanghai. The uneven distribution in space was mainly reﬂected in the higher FNR SAT and surface O 3 concentration in suburban areas. To compensate for the short-coming of FNR SAT that it can only characterize O 3 formation around satellite overpass time, correction of FNR SAT was implemented with hourly surface FNR and O 3 data. After correction, the O 3 formation regime showed the trend moving towards being VOC-limited in both time and space, and the regime indicated by FNR SAT can better reﬂect O 3 formation for a day. This study can help us better understand HCHO characteristics and O 3 formation regimes in Shanghai and also provide a method to improve FNR SAT for characterizing O 3 formation in a day, which will be signiﬁcant for develop-ing O 3 prevention and control strategies.

Abstract. In recent years, satellite remote sensing has been increasingly used in the long-term observation of ozone (O 3 ) precursors and its formation regime. In this work, formaldehyde (HCHO) data from Ozone Monitoring Instrument (OMI) were used to analyze the temporal and spatial distribution of HCHO vertical column densities (VCDs) in Shanghai from 2010 to 2019. HCHO VCDs exhibited the highest value in summer and the lowest in winter, the high VCD being concentrated in western Shanghai. Temperature largely influences HCHO by affecting the biogenic emissions and photochemical reactions, and industry was the major anthropogenic source. The satellite-observed formaldehyde-tonitrogen dioxide ratio (FNR SAT ) reflects that the O 3 formation regime had significant seasonal characteristics and gradually manifested as a transitional ozone formation regime dominating in Shanghai. The uneven distribution in space was mainly reflected in the higher FNR SAT and surface O 3 concentration in suburban areas. To compensate for the shortcoming of FNR SAT that it can only characterize O 3 formation around satellite overpass time, correction of FNR SAT was implemented with hourly surface FNR and O 3 data. After correction, the O 3 formation regime showed the trend moving towards being VOC-limited in both time and space, and the regime indicated by FNR SAT can better reflect O 3 formation for a day. This study can help us better understand HCHO characteristics and O 3 formation regimes in Shanghai and also provide a method to improve FNR SAT for characterizing O 3 formation in a day, which will be significant for developing O 3 prevention and control strategies.

Introduction
Formaldehyde (HCHO) is an important trace gas in the atmosphere. It has an irritating effect on human eyes, skin, and respiratory mucosa and can also cause cancer in high concentration (Zhu et al., 2017a;R. Liu et al., 2018). Atmospheric HCHO is an intermediate product of almost all volatile organic compound (VOC) oxidation, it can be therefore indicative of the overall VOC level (Chan et al., 2019). HCHO can also be emitted through anthropogenic sources, biogenic sources, and biomass combustion. Anthropogenic sources like transportation, power, industry, and residential emissions increase the amount of HCHO by emitting VOCs into the atmosphere (Wang et al., 2017). In addition, biogenic volatile organic compounds (BVOCs) are also important sources of HCHO. Isoprene emitted by plants can be oxidized to generate HCHO, which causes the concentration of HCHO in some lush vegetation areas to be largely affected by emission of BVOCs (Millet et al., 2008). The removal of HCHO is mainly through photolysis, reaction with OH radicals, and the deposition (Ling et al., 2016;Xing et al., 2020).
Satellite remote sensing can achieve large-scale observation of atmospheric pollutant gases including HCHO, which has been widely used in recent years. Sensors currently available for HCHO observation include the Global Ozone Monitoring Experiment (GOME) on ERS-2 Martin et al., 2004b); Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) on ENVISAT (Bovensmann et al., 1999;Stavrakou et al., 2009); Ozone Monitoring Instrument (OMI) on Aura (Levelt et al., 15448 D. Li et al.: OMI-observed HCHO and ozone sensitivity in Shanghai, China 2006;Zhu et al., 2017b); GOME-2 A, B, and C on METOP as the successor of GOME (Callies et al., 2000;De Smedt et al., 2012); Ozone Mapping and Profiler Suite (OMPS) on Suomi-NPP ; and Tropospheric Monitoring Instrument (TROPOMI) on Sentinel-5P Vigouroux et al., 2020). OMI can provide daily data of HCHO with higher spatial resolution (13 km × 24 km). As part of a new generation of sensors, TROPOMI was launched in 2017, and it has better spatial resolution (7 km × 7 km) but lacks long-term observations so far. It would be an advantageous tool of satellite remote sensing to achieve more detailed analysis in the future .
Previous studies reported satellite-observed long-term and large-scale distribution and variation of HCHO in China and all over the world (Millet et al., 2008;Zhu et al., 2017a;Liu et al., 2020). The 12-year multi-satellite observations (OMI, GOME-2, SCIAMACHY) showed that the trend of HCHO vertical column densities (VCDs) over eastern China is consistent with that of anthropogenic VOCs . Based on 10-year observations of OMI HCHO, R. Liu et al. (2018) indicated that high HCHO VCDs in tropical forest regions are greatly affected by biomass burning and meteorological factors including temperature and precipitation. In addition, the ground-based remote sensing can also be available for HCHO observation, such as multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurement. The vertical distribution of HCHO derived from MAX-DOAS measurement was characterized by the higher HCHO concentrated near the surface (Lee et al., 2015;Chan et al., 2019). By employing the box model, X.  found that isoprene oxidation initiated by OH radicals has a great contribution to the HCHO formation in semi-rural regions of the Pearl River Delta (PRD) in China.
HCHO participates in the complex photochemical reaction of NO x (NO x = NO + NO 2 ) and directly affects the production of O 3 in troposphere. Due to the short lifetime of HCHO and NO 2 , their spatial distributions were greatly affected by local emission of VOCs and NO x , which received widespread attention as precursors of tropospheric O 3 (Zaveri et al., 2003;Chan et al., 2019). Consequently, HCHO and NO 2 can be assumed to be indicators of VOCs and NO x , and the ratio of formaldehyde to nitrogen dioxide (HCHO / NO 2 , FNR) can be an indicator to analyze the O 3 formation regime (Sillman, 1995;Martin et al., 2004a;Schroeder et al., 2017). For instance, by using FNR from long-term OMI HCHO and NO 2 data, O 3 sensitivity of the United States was evaluated. A O 3 formation regime can be designated as VOC-limited for FNR < 1, NO x -limited for FNR > 2, and transitional for 1 < FNR < 2, which serves as the transitional regime between VOC-limited and NO xlimited regimes, indicating the production of O 3 can be changed by both VOC and NO x (Duncan et al., 2010). In view of China, OMI products over three representative regions (North China Plain (NCP), the Yangtze River Delta (YRD), and the PRD) were investigated, revealing that the O 3 formation regime varied in both time and space, and the contribution of emission sectors to precursors changed with the type of regimes (Jin and Holloway, 2015). During special events such as the Asia-Pacific Economic Cooperation in 2014 and Grand Military Parade in 2015, FNR in Beijing had become higher compared with previous periods, and the O 3 formation regime shifted toward a NO x -limited regime with control strategies (Liu et al., 2016).
In this study, OMI satellite data were used to investigate the temporal and spatial distribution characteristics of atmospheric HCHO in Shanghai from 2010 to 2019, combined with meteorological data and emission inventories to analyze the influencing factors. FNR calculated by satellite HCHO and NO 2 were applied to capture variations of the O 3 formation regime in Shanghai over the past decade. Considering that satellite data only reflect the column density of trace gases around overpass time, hourly surface FNR and O 3 concentration increments were proposed to correct the satellite FNR, so that it can better indicate O 3 formation in the daytime.
2 Data and methods

Satellite data
OMI on Aura orbits the earth in about 98 min, which can achieve full coverage of the earth in one day. It overpasses at 13:45 LT each day. The scanning width is 2600 km and is divided into 60 rows. The sensor contains three channels, including UV-1, UV-2, and VIS, with a wavelength coverage of 264-504 nm. This band allows a variety of trace gases to be observed, e.g., HCHO, NO 2 , and SO 2 . The retrieval algorithm of this product is based on nonlinear least-squares fitting which get slant column density (SCD) as the result. Then SCD can be converted to VCD through air mass factors (AMFs). The Level-2 OMI HCHO product OMHCHO Version 3 is used in this study (https://doi.org/10.5067/Aura/OMI/DATA2015, Chance, 2007). Since atmospheric HCHO is mainly distributed in the troposphere, the total VCD can be regarded as the tropospheric VCD of HCHO (Duncan et al., 2010). The Level-2 OMI NO 2 product OMNO2.003 Version 4 is adopted for tropospheric NO 2 VCD in this study (https://doi.org/10.5067/Aura/OMI/DATA2017, Krotkov et al., 2019).

Methodology
In this study, Shanghai and surrounding areas were gridded into to a spatial resolution of 0.01 • × 0.01 • . Then pixels falling within a 24 km radius of the grid center were averaged and were further assigned to that grid (Fioletov et al., 2011;McLinden et al., 2012;Zhu et al., 2014). In order to remove data with poor quality as much as possible, HCHO data with cloud fraction ≤ 30 %, solar zenith angle ≤ 70 • , and main data quality flag = 0 were selected in this study. In addition, the quality of pixel data with large size is poor, so 5 marginal pixels on each side were abandoned, and only pixel data within 6-55 were selected (Zhu et al., 2017a;Xue et al., 2020). Because OMI has experienced a row anomaly since 2007, Xtrack quality flags = 0 was required to eliminate the influence of poor-quality data affected by the row anomaly (http://projects.knmi.nl/omi/research/ product/rowanomaly-background, last access: 24 December 2019). As HCHO satellite data have large errors, fitting root mean square (RMS) ≤ 0.003 was limited to remove most outliers (Souri et al., 2017). The selection of NO 2 satellite data was basically the same as that of HCHO, but without fitting RMS parameter filtering, and cloud radiance fraction ≤ 30 % was required (Krotkov et al., 2016;Xue et al., 2020). Moreover, the linear regressions of monthly deseasonalized zonal mean HCHO VCDs with 0.5 • latitude steps over remote pacific region (29-33 • N, 160-140 • W) indicated that the OMI HCHO product used in this study does not show obvious drift (Zhu et al., 2017b).

Auxiliary data
The meteorological data, including monthly temperature, sunshine hours, precipitation, and relative humidity, are acquired from the National Bureau of Statistics of China (http://www.stats.gov.cn/, last access: 3 October 2021). The anthropogenic sources of HCHO in Shanghai are calculated based on the Multi-resolution Emission Inventory for China (MEIC, http://www.meicmodel.org/, last access: 3 October 2021) Zheng et al., 2018). Surface HCHO and NO 2 concentrations were measured by longpath differential optical absorption spectroscopy (LP-DOAS) at the Jiangwan campus of Fudan University in Shanghai (31.34 • N, 121.52 • E). The O 3 data of Qingpu Dianshan Lake Site (31.09 • N, 120.98 • E) and Hongkou Site (31.30 • N, 121.47 • E) in Shanghai are obtained from the Shanghai Environmental Monitoring Center (http://www.semc.com.cn/aqi/ Home/Index, last access: 3 October 2021).

The temporal and spatial variation of HCHO
HCHO VCDs for annual, monthly, and seasonal variations in Shanghai from 2010 to 2019 are shown in Fig. 1. HCHO VCDs decreased from the highest value of 12.78 × 10 15 molec. cm −2 in 2010 to the lowest value of 10.37 × 10 15 molec. cm −2 in 2012, then rebounded from 2012 to 2014, and fluctuated slightly in the following years (Fig. 1a). The column value and variation are similar to previous study in the YRD, China . Before 2018, the high VCD was concentrated in June to August with about 15×10 15 to 20×10 15 molec. cm −2 , the low VCD appeared in January to February and November to December with about 3 × 10 15 to 9 × 10 15 molec. cm −2 , and VCDs were comparable in the remaining months (Fig. 1b). In addition, the amplitude of monthly HCHO VCDs was relatively smaller in 2018 and 2019 and mainly concentrated from 6 × 10 15 to 15 × 10 15 molec. cm −2 . The HCHO VCDs varied with the season, with the maxima and minima corresponding to the respective summer (June, July, and August) and winter (December, January, and February) and moderate levels in spring (March, April, and May) and autumn (September, October, and November) (Fig. 1c). Previous MAX-DOAS and OMI observations also exhibited the same seasonal patterns of HCHO in the YRD, China (Jin and Holloway, 2015;Chan et al., 2019). High temperature and abundant radiation are conducive to the plant growth to produce BVOCs and the photochemical reaction of VOCs, which boost the HCHO formation in summer (Sharkey and Loreto, 1993;Duncan et al., 2009;Narumi et al., 2009). Thus, HCHO VCDs would be relatively low in winter under the opposite weather conditions.
The HCHO VCDs within 10 km of the LP-DOAS measurement site were averaged to compare with the surface HCHO between 13:00 and 14:00 LT (Fig. S1 in the Supplement). This shows that HCHO VCDs and surface HCHO concentrations are not very consistent, as HCHO is not completely concentrated near the ground but has a high concentration at higher altitudes (Chan et al., 2019;Wang et al., 2019). Spatial heterogeneity of surface HCHO in the horizontal can also impact the consistency of the comparison. However, the surface HCHO observed by LP-DOAS shows the same seasonal characteristics as HCHO VCDs (Fig. 1d).
The spatial distribution of 10-year-averaged HCHO VCD was given in Fig. 2a. In general, HCHO VCDs in the eastern coastal area were relatively low, with the level of about 10 × 10 15 molec. cm −2 , while those in western regions adjacent to other provinces were relatively higher, about 13 × 10 15 molec. cm −2 . Note that areas with the highest HCHO VCD in Shanghai did not appear in the city center (marked by the red box) but in the relatively remote Qingpu (QP) district, followed by Songjiang (SJ) and Jinshan (JS) district. Compared to the anthropogenic non-methane volatile organic compound (NMVOC) emissions, the distribution of HCHO VCDs does not show the same spatial pattern . The high HCHO in western Shanghai was frequently observed and may be explained by the transport of air masses containing high concentrations of reactive VOCs, sometimes from Zhejiang and Jiangsu provinces, and the significant contribution of local biogenic isoprene to HCHO Zhang et al., 2020Zhang et al., , 2021. Figure 2b shows the difference of HCHO VCDs between 2019 and 2010. It suggests that except for the eastern and southern coastal areas, as well as the eastern area of Chongming Island, HCHO VCDs in Shanghai showed an overall downward trend during the past 10 years, with western regions experiencing the largest decline. Figure 2c to f display the spatial distribution of HCHO VCDs in differ- ent seasons. HCHO VCD in summer was basically above 12 × 10 15 molec. cm −2 . In winter, the value was around 7 × 10 15 molec. cm −2 for most regions except for Qingpu district, while in spring and autumn, it was at the moderate level of about 10 × 10 15 molec. cm −2 . The spatial distribution of HCHO VCDs in different seasons was similar to the 10-yearaveraged characteristics of high values in the west and low values in the east.

Influencing factors
The relationship between monthly HCHO VCDs and meteorological variables including temperature, sunshine hours, precipitation, and relative humidity were analyzed via the linear regression. The stepwise regression results show that only temperature correlated with HCHO VCDs significantly among these four meteorological factors. The linear regression of temperature contribution and HCHO VCD was shown in Fig. 3. The temperature contribution has a good correlation with the observed HCHO VCD (R 2 = 0.73), which means that temperature can explain about 73 % of the variation of HCHO VCD. The remaining part that cannot be explained by temperature appears in the form of a residual, which is considered as the influence of other changing factors such as anthropogenic emissions (K. . The residual in summer in some years would be particularly large, which indicates that, in addition to temperature, there are other factors affecting HCHO VCD significantly. The precipitation and relative humidity reached a peak in June, when the sunshine hours were significantly low, and HCHO VCD declined as the temperature rose (Fig. S2 in the Supplement). Shanghai has a subtropical monsoon climate with rain and heat in the same period. Abundant precipitation largely favored the wet deposition of HCHO and offset the impact of rising temperature, resulting in a small decrease in HCHO VCDs in June (Pang et al., 2009). The result of Fisher's exact test also illustrates that when the relative humidity changes remarkably, the variation of HCHO VCDs in summer would be significantly affected (P < 0.05).
To explore the impacts of anthropogenic sources on HCHO abundance, primary emissions and secondary productions of HCHO from anthropogenic sources were estimated. NMVOC emissions from MEIC v.1.3 grid inventories for the year 2010, 2012, 2014, and 2016 were mapped to SAPRC07 mechanism species (M. . Primary HCHO was directly obtained from the inventory, and secondary HCHO production was calculated based on 1 d HCHO yields of several NMVOCs under high-NO x conditions (Table S1 in the Supplement) .
In Fig. 4a and b, for the total of primary emissions and secondary productions, the contribution of the industrial sector was much higher than other sectors, accounting for about 79.3 % of the total, followed by transportation sector, accounting for about 15.7 %. Residential and power sectors were far lower; the proportions over these years were less In (a) the city center is marked with a red box; Chongming Island is displayed with a red boundary. QP, SJ, and JS refer to Qingpu, Songjiang, and Jinshan districts. than 5 %. In the major sectors, the contribution of industry increased by 17.2 %, while the contribution of transportation decreased by about 35.2 %. The primary emission of HCHO keeps decreasing (about 34.2 % compared to 2010), while secondary produced HCHO did not change significantly. Furthermore, the changes and proportional relationships between primary emission and secondary production of HCHO for these sectors are different, which means the VOC source profile of different emission sectors would affect the amount of secondary HCHO production. It should be noted that the estimation here is the potential of secondary HCHO production from anthropogenic NMVOCs and does not represent those actually produced in the atmosphere.
In addition, HCHO produced by biogenic sources in 2014 was also calculated, and the BVOC emissions were referred from Liu et al. (2018a, b). HCHO yield from BVOC emission was about 9.07 × 10 9 g, which is much smaller compared with the anthropogenic contribution, indicating that anthropogenic activity is the main contributor of secondary production of HCHO in Shanghai Fan et al., 2021). The spatial distribution of surface land types in Shanghai (Fig. S3 in the Supplement) also suggest less emission and contribution of biogenic sources in urbanized and densely populated area compared to forested regions. Figure 4c shows that the annual trend of HCHO VCDs is not synchronized with that of primary or secondary HCHO. It means that, besides the combined effect of the primary and secondary source, the changes of HCHO VCDs should also be affected complexly by various factors. In addition, it should be noted that HCHO yield from VOCs is proportional to NO x conditions (Palmer et al., 2006;Marais et al., 2012;Miller et al., 2017). Within the context of the continuous NO x decreases in Shanghai, the estimation using a fixed HCHO yield may overestimate secondary HCHO production in later years (Xue et al., 2020). However, the NO x concentration in Shanghai (about 30-60 ppbv in urban areas) is still much higher than the high-NO x conditions (1 ppbv) defined in previous studies (Gao et al., 2017). Therefore, in such a high-NO x conditions, the effect of NO x decreases on HCHO yield needs to be further studied.

FNR and O 3 formation regime
As the important precursors of O 3 , HCHO, and NO 2 can be served as indicators for VOCs and NO x . On this basis, the HCHO / NO 2 ratio from satellite observation (FNR SAT ) can be employed to identify the O 3 formation regime. The variations of monthly averaged VCDs of HCHO, NO 2 , and FNR SAT in Shanghai over the past 10 years are given in Fig. 5. NO 2 VCDs were featured by the highest in winter and the lowest in summer, which was opposite to HCHO and fluctuated more fiercely. The peaks were mainly on account of its longer lifetime in winter (Zhang et al., 2007), while in summer, the adequate sunlight and precipitation accelerated the photochemical removal and wet deposition of NO 2 , resulting in the dip Xue et al., 2020). FNR SAT also exhibited the obvious annual cycle of high in summer and low in winter. According to the criteria proposed by Duncan et al. (2010), the O 3 formation regime in Shanghai was usually NO x -limited from June to August and controlled by a VOC-limited and transitional regime for the rest of the months. From May to September in 2014, Shanghai was under a NO x -limited regime, and FNR SAT reached the highest value over the past 10 years. In 2019, the value of monthly FNR SAT fluctuated gently, which showed the trend moving towards the transitional regime threshold of 1-2.
The spatial distribution of FNR SAT in Shanghai is presented in Fig. 6. Comparing FNR SAT in 2019 with that in 2010, the NO x -limited regime in the western Shanghai transformed into a transitional regime, and a VOC-limited regime on the northern Chongming Island almost completely became a transitional regime. It manifests itself in the reduction in the NO x -limited and VOC-limited regimes with the in-  crease in the transitional regime. Referring to previous study on the variation of NO 2 VCDs spatial distribution in Shanghai observed by satellite, this phenomenon may be related to the spatial characteristics of concentration variations of two precursors (Xue et al., 2020). This result is also reflected in Fig. 5b. In the past 10 years, the proportion decreased from 33.4 % to 24.9 % for VOC-limited areas, and from 26.7 % to 11.3 % for NO x -limited areas. Meanwhile, the transitional regime area increased from 40.0 % to 63.8 %. Xu et al. (2019) suggested that the O 3 formation regime in Shanghai trends to transform from a VOC-limited regime to a NO x -limited regime after 2020 through WRF-Chem model simulation. In this study, the increase in the transitional regime may be the transition state from a VOC-limited to a NO x -limited regime. Figure 6c to f show the spatial distribution of FNR SAT for different seasons during the decade. In spring, the northern area of Shanghai was VOC-limited regime while the southern area had a transitional regime. From spring to summer, the VOC-limited area almost transformed into having a transitional regime, and the transitional regime nearly turned NO xlimited at the same time, which was mainly caused by the increase in HCHO and the decrease in NO 2 . The distribution in autumn was similar to that in spring. In winter, Shanghai was basically under a VOC-limited regime. In the light of the temporal and spatial distribution of O 3 formation regime inferred by FNR SAT , the emission reduction measures for the O 3 precursors would be more rational.
As well as this, there are differences in the O 3 formation regime in urban and suburban areas of Shanghai, with the main manifestation being that the central urban area was inclined to be in a VOC-limited regime and the suburban area was more likely to be in a NO x -limited regime. In order to analyze the differences in more detail, an area within 10 km around the Jiangwan campus of Fudan University was selected to represent the urban area (about 12 km to the city center), and an equally sized area around Dianshan Lake (31.09 • N, 120.98 • E) of Qingpu district was regarded as the suburban area (about 50 km to the city center). Since O 3 pollution is relatively serious from April to September, this period was chosen as a research case. The maximum 8 h average concentrations of O 3 at the Hongkou and the Qingpu Dianshan Lake Site were used to characterize O 3 concentrations in urban and suburban areas. NO 2 VCDs in the urban area were higher than those in the suburban area, while HCHO VCDs presented the opposite character (Fig. 7a). The lower NO 2 in the suburban area was associated with less NO x emission than that in the urban area, corresponding to the larger FNR SAT . From Fig. 7b, the O 3 production was  under a transitional regime in the urban area, while a NO xlimited regime occupied for most years in the suburban area. The O 3 concentration in the suburban area was always higher than that in the urban (Fig. 7c). In this study, high concentrations of NO x in the urban area may lead to titration of O 3 by NO, which would cause the lower O 3 concentration in the urban area (Geng et al., 2008;Duncan et al., 2010).

Correction of FNR SAT
FNR was originally proposed as an indicator to characterize the sensitivity of the instantaneous O 3 production rate (Duncan et al., 2010). Satellite observation only reflects the averaged column of the trace gases around overpass time, so the FNR SAT may not accurately infer the surface O 3 formation regime during the day (Duncan et al., 2010;Jin and Holloway, 2015;Jin et al., 2017). FNR SAT was compared with FNR LP at the satellite overpass time on the monthly and daily scales. Results show that FNR SAT and FNR LP were consistent well on a monthly scale (R 2 = 0.95, between April and August), but they were quite different on the daily scale, and the relationship was easily affected by the boundary layer height (BLH) and other factors (Schroeder et al., 2017).
As shown in Fig. 8a to c, LP-DOAS observation provided FNR LP with a high temporal resolution throughout the day, and FNR LP was in good agreement with hourly O 3 concen- trations. It means that FNR LP should be a good indicator to distinguish the formation regime of surface O 3 on a detailed timescale. In addition, the highest value of FNR LP at noon means that FNR SAT at overpass time is approximately close to the highest level in a day. Thus, it would be valuable to introduce the time series of FNR LP to make FNR SAT better reflect the characteristics of O 3 formation during the daytime.
Three cases during the LP-DOAS observation at the Jiangwan campus of Fudan University were selected for further discussion under the criteria of the hourly concentration of O 3 exceeding 200 µg m −3 (secondary concentration limit stipulated in ambient air quality standards of China, GB 3095-2012). In Fig. 9a and c, the upward trend in FNR LP as the O 3 concentration increases means that the formation of O 3 was under a VOC-limited regime in Case 1 and 3. VOClimited and transitional regimes caught in Case 1 through FNR SAT were different from that identified by FNR LP . In Case 3, the O 3 formation regime remained in a VOC-limited regime, which was the same as FNR LP . As shown in Fig. 9b, FNR LP indicated that the O 3 formation regime switched between three regimes in Case 2. As O 3 concentration increased, the growth of FNR LP at the beginning indicated a VOC-limited regime, while the subsequent slow variation suggested a transitional regime. When O 3 concentration reached maximum, FNR LP got smaller, which implied a NO x -limited regime. But FNR SAT only captured the VOClimited and transitional regime in Case 2. According to the results above, it is feasible and necessary to correct FNR SAT to better represent the sensitivity of surface O 3 formation. Due to less O 3 pollution in winter, FNR SAT was only corrected for the remaining three seasons.
The correction of FNR SAT was achieved through the following process. Firstly, the ratio of FNR at satellite overpass time to averaged FNR during the O 3 pollution period ( O 3 greater than 0, i.e. , 07:00 to 13:00 LT; see Fig. 8d) obtained from ground surface measurement was assumed to be same as that of satellite observation, which is expressed as follows: where FNR LP is the weighted average of FNR during the O 3 pollution period observed by ground surface LP-DOAS measurements, and FNR LP,overpass time is ground surface FNR observed at satellite overpass time. FNR LP,overpass time /FNR LP reflects the numerical relationship of FNR between satellite overpass time and the O 3 polluted period during a day and can serve as the correction coefficient to realize the correction for FNR SAT on a timescale to obtain the FNR SAT . Considering the relationship between time series of FNR and O 3 formation, O 3 was involved to calculate the weighted aver- Figure 9. Comparison of FNR SAT and FNR LP in three O 3 pollution cases. The curves are polynomial fit of FNR LP , and the points are FNR SAT in corresponding cases; the gray area indicates the transitional regime for FNR SAT . Only LP-DOAS-measured data between 08:00-18:00 LT were used.
(2), which can better indicate the ozone formation in a day.
where O 3 ,T is the increase in O 3 concentration at time T , and FNR LP,T is the FNR LP at time T . Moreover, variation characteristics of FNR LP in different seasons (as shown in Fig. 8a to c) suggest that the correction of FNR SAT should be discussed seasonally.
Afterwards, the seasonal correction coefficients of 0.85, 0.84, and 0.77 were obtained for spring, summer, and autumn, respectively. It is noted that all the correct coefficients were less than 1 due to the FNR LP value for OMI overpass time being relatively larger than other times. It would inevitably make the O 3 formation regime inferred by corrected FNR SAT trend VOC-limited. There were 87 months with effective FNR SAT in three seasons during 2010-2019, and the proportion of months for different regimes was listed in Table 1. Before the correction, the VOC-limited and NO x - limited regimes, as well as the transitional regime, almost accounted for about one-third of the total months. After the correction, months that had VOC-limited and transitional regimes increased. The months under the VOC-limited regime increased by 21.4 %, while there was a decrease of about 25.9 % for NO x -limited regime. Jin et al. (2020) used O 3 exceedance probability as the indicator to analyze nonlinear dependence of long-term surface O 3 concentrations on precursor emissions and determined the OMI HCHO / NO 2 under a transitional regime ranging from 3.2 to 4.1. These thresholds are significantly larger than the value proposed by Duncan et al. (2010), which has the equivalent effect as the use of correction factors less than 1 in this study.
In terms of spatial distribution, the O 3 formation regime after correction in different seasons is shown in Fig. 10. Compared with Fig. 6, part of the transitional regime area in spring transformed into a VOC-limited regime after the correction, and this VOC-limited regime obviously expanded and increased by about 18.2 %. Most areas on Chongming Island transformed into having a VOC-limited regime. In summer, part of the NO x -limited regime area transformed into having a transitional regime, and the area of the transitional regime increased by about 16.2 %. In autumn, the NO x -limited regime almost disappeared, and the proportion of the transitional regime area also decreased significantly, by about 10.4 %, while the proportion of the VOC-limited regime area increased by about 21.5 %. The O 3 formation regime on Chongming Island was basically under a transitional regime. Researchers also pointed out that thresholds of criteria would be regionally dependent, so the local surface FNR and O 3 concentration should be introduced in satellite correction (Duncan et al., 2010;Jin et al., 2020).
In order to verify whether the correction of the satellite FNR improved the regime classification, O 3 formation regimes determined by satellite FNR before and after the cor- rection were compared with those of surface observations. The variations of O 3 with surface HCHO and NO 2 have been plotted to determine the O 3 formation regimes from the surface observation (Fig. 11). The daytime surface HCHO and NO 2 are from LP-DOAS measurements, and the O 3 was observed by SP-DOAS (short-path DOAS), which is also located at the Jiangwan campus of Fudan University and has a high temporal resolution. O 3 formation regimes inferred from satellite FNR before and after the correction have also each been marked in Fig. 11. For Case I, O 3 decreases with the increase in NO 2 , which can be attributed to the titration of O 3 by NO (Duncan et al., 2010). O 3 increased from top to bottom indicating it was under a VOC-limited regime in Case I (Luo et al., 2020). For Case II, it can be seen that the high O 3 appeared with high HCHO and low NO 2 , indicating it was under a VOC-limited regime. The uncorrected satellite FNR indicated that these two cases were both under a transitional regime, while the corrected satellite FNR indicated they transferred to a VOClimited regime, which is consistent with the results of surface observation. It indicates that the correction of FNR SAT in this study can be considered to be effective and sensible.

Summary and conclusions
Satellite data of OMI were used to study the temporal and spatial variation of HCHO in Shanghai from 2010 to 2019. HCHO VCDs fluctuated during the 10 years with obvious seasonal characteristics of highest value in summer, the lowest value in winter, and a moderate level in spring and autumn. In terms of spatial distribution, HCHO VCDs in western areas were much higher than that in eastern coastal area. Compared with 2010, HCHO VCDs of Shanghai in 2019 showed an overall downward trend. As for the influencing factors, temperature give the significant positive effect on HCHO VCDs while the abundant precipitation reduces HCHO in summer. Industry was an important contributor of HCHO, and anthropogenic secondary production of HCHO constituted the majority of the HCHO source.
In the past 10 years, the O 3 formation regime changed toward a transitional regime gradually. The O 3 formation regime in urban areas was more likely to be a VOC-limited regime, while a regime in suburban areas was more likely to be NO x -limited. FNR SAT was corrected based on the hourly surface FNR and O 3 data to make it better to reflect O 3 formation in a day. After correcting FNR SAT with seasonal correction coefficients of 0.85, 0.84, and 0.77 for spring, summer, and autumn respectively, the O 3 formation regime in Shanghai was more inclined to be VOC-limited in both time and spatial distribution, and the effectiveness of the FNR SAT correction was confirmed by the surface observation. Thus, this correction is significant for using satellite data to improve the accuracy in indicating surface O 3 formation.
Data availability. Data are available for scientific purposes upon request to the corresponding author.
Author contributions. DL and SW designed and implemented the research and prepared the paper. RX contributed to the analysis of OMI products and MEIC inventory. JZ provided the HCHO and NO 2 data observed by LP-DOAS. SZ and ZS revised the paper. BZ provided constructive comments and supported the DOAS measurements.
Competing interests. The authors declare that they have no conflict of interest.
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