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, NO2, and SO2 (Zhang et al., 2019). 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 (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 NO2 product OMNO2.003 Version 4 is adopted for tropospheric NO2 VCD in this study (10.5067/Aura/OMI/DATA2017, Krotkov et al., 2019).

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 NO2 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).

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) (Li et al., 2017; Zheng et al., 2018). Surface HCHO and NO2 concentrations were measured by long-path differential optical absorption spectroscopy (LP-DOAS) at the Jiangwan campus of Fudan University in Shanghai (31.34∘ N, 121.52∘ E). The O3 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).

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 12.78×1015 molec.cm-2 in 2010 to the lowest value of 10.37×1015 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 (Zhang et al., 2019). Before 2018, the high VCD was concentrated in June to August with about 15×1015 to 20×1015 molec.cm-2, the low VCD appeared in January to February and November to December with about 3×1015 to 9×1015 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 6×1015 to 15×1015 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 10×1015 molec.cm-2, while those in western regions adjacent to other provinces were relatively higher, about 13×1015 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 (An et al., 2021). 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 (Su et al., 2019; Zhang et al., 2020, 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 different seasons. HCHO VCD in summer was basically above 12×1015 molec.cm-2. In winter, the value was around 7×1015 molec.cm-2 for most regions except for Qingpu district, while in spring and autumn, it was at the moderate level of about 10×1015 molec.cm-2. The spatial distribution of HCHO VCDs in different seasons was similar to the 10-year-averaged characteristics of high values in the west and low values in the east.

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 (R2=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. Li et al., 2019). 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. Li et al., 2014, 2019). 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-NOx conditions (Table S1 in the Supplement) (Shen et al., 2019).

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 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 9.07×109 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 (Shen et al., 2019; 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 NOx conditions (Palmer et al., 2006; Marais et al., 2012; Miller et al., 2017). Within the context of the continuous NOx decreases in Shanghai, the estimation using a fixed HCHO yield may overestimate secondary HCHO production in later years (Xue et al., 2020). However, the NOx concentration in Shanghai (about 30–60 ppbv in urban areas) is still much higher than the high-NOx conditions (1 ppbv) defined in previous studies (Gao et al., 2017). Therefore, in such a high-NOx conditions, the effect of NOx decreases on HCHO yield needs to be further studied.

As the important precursors of O3, HCHO, and NO2 can be served as indicators for VOCs and NOx. On this basis, the HCHO / NO2 ratio from satellite observation (FNRSAT) can be employed to identify the O3 formation regime. The variations of monthly averaged VCDs of HCHO, NO2, and FNRSAT in Shanghai over the past 10 years are given in Fig. 5. NO2 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 NO2, resulting in the dip (Wang et al., 2018; Xue et al., 2020). FNRSAT 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 O3 formation regime in Shanghai was usually NOx-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 NOx-limited regime, and FNRSAT reached the highest value over the past 10 years. In 2019, the value of monthly FNRSAT fluctuated gently, which showed the trend moving towards the transitional regime threshold of 1–2.

The spatial distribution of FNRSAT in Shanghai is presented in Fig. 6. Comparing FNRSAT in 2019 with that in 2010, the NOx-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 NOx-limited and VOC-limited regimes with the increase in the transitional regime. Referring to previous study on the variation of NO2 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 NOx-limited areas. Meanwhile, the transitional regime area increased from 40.0 % to 63.8 %. Xu et al. (2019) suggested that the O3 formation regime in Shanghai trends to transform from a VOC-limited regime to a NOx-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 NOx-limited regime.

Figure 6c to f show the spatial distribution of FNRSAT 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 NOx-limited at the same time, which was mainly caused by the increase in HCHO and the decrease in NO2. 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 O3 formation regime inferred by FNRSAT, the emission reduction measures for the O3 precursors would be more rational.

As well as this, there are differences in the O3 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 NOx-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 O3 pollution is relatively serious from April to September, this period was chosen as a research case. The maximum 8 h average concentrations of O3 at the Hongkou and the Qingpu Dianshan Lake Site were used to characterize O3 concentrations in urban and suburban areas. NO2 VCDs in the urban area were higher than those in the suburban area, while HCHO VCDs presented the opposite character (Fig. 7a). The lower NO2 in the suburban area was associated with less NOx emission than that in the urban area, corresponding to the larger FNRSAT. From Fig. 7b, the O3 production was under a transitional regime in the urban area, while a NOx-limited regime occupied for most years in the suburban area. The O3 concentration in the suburban area was always higher than that in the urban (Fig. 7c). In this study, high concentrations of NOx in the urban area may lead to titration of O3 by NO, which would cause the lower O3 concentration in the urban area (Geng et al., 2008; Duncan et al., 2010).

FNR was originally proposed as an indicator to characterize the sensitivity of the instantaneous O3 production rate (Duncan et al., 2010). Satellite observation only reflects the averaged column of the trace gases around overpass time, so the FNRSAT may not accurately infer the surface O3 formation regime during the day (Duncan et al., 2010; Jin and Holloway, 2015; Jin et al., 2017). FNRSAT was compared with FNRLP at the satellite overpass time on the monthly and daily scales. Results show that FNRSAT and FNRLP were consistent well on a monthly scale (R2=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 FNRLP with a high temporal resolution throughout the day, and FNRLP was in good agreement with hourly O3 concentrations. It means that FNRLP should be a good indicator to distinguish the formation regime of surface O3 on a detailed timescale. In addition, the highest value of FNRLP at noon means that FNRSAT at overpass time is approximately close to the highest level in a day. Thus, it would be valuable to introduce the time series of FNRLP to make FNRSAT better reflect the characteristics of O3 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 O3 exceeding 200 µgm-3 (secondary concentration limit stipulated in ambient air quality standards of China, GB 3095-2012). In Fig. 9a and c, the upward trend in FNRLP as the O3 concentration increases means that the formation of O3 was under a VOC-limited regime in Case 1 and 3. VOC-limited and transitional regimes caught in Case 1 through FNRSAT were different from that identified by FNRLP. In Case 3, the O3 formation regime remained in a VOC-limited regime, which was the same as FNRLP. As shown in Fig. 9b, FNRLP indicated that the O3 formation regime switched between three regimes in Case 2. As O3 concentration increased, the growth of FNRLP at the beginning indicated a VOC-limited regime, while the subsequent slow variation suggested a transitional regime. When O3 concentration reached maximum, FNRLP got smaller, which implied a NOx-limited regime. But FNRSAT only captured the VOC-limited and transitional regime in Case 2. According to the results above, it is feasible and necessary to correct FNRSAT to better represent the sensitivity of surface O3 formation. Due to less O3 pollution in winter, FNRSAT was only corrected for the remaining three seasons.

The correction of FNRSAT was achieved through the following process. Firstly, the ratio of FNR at satellite overpass time to averaged FNR during the O3 pollution period (ΔO3 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: 1FNRSATFNR‾SAT=FNRLP,overpass timeFNR‾LP, where FNR‾LP is the weighted average of FNR during the O3 pollution period observed by ground surface LP-DOAS measurements, and FNRLP,overpass time is ground surface FNR observed at satellite overpass time. FNRLP,overpass time/FNR‾LP reflects the numerical relationship of FNR between satellite overpass time and the O3 polluted period during a day and can serve as the correction coefficient to realize the correction for FNRSAT on a timescale to obtain the FNR‾SAT. Considering the relationship between time series of FNR and O3 formation, ΔO3 was involved to calculate the weighted average of FNRLP (FNR‾LP) during 07:00 to 13:00 LT via Eq. (), which can better indicate the ozone formation in a day. 2FNR‾LP=∑T=713FNRLP,T×ΔΩO3,T∑T=713ΔΩO3,T,3ΔΩO3,T=ΩO3,T-ΩO3,T-1, where ΔΩO3,T is the increase in O3 concentration at time T, and FNRLP,T is the FNRLP at time T. Moreover, variation characteristics of FNRLP in different seasons (as shown in Fig. 8a to c) suggest that the correction of FNRSAT 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 FNRLP value for OMI overpass time being relatively larger than other times. It would inevitably make the O3 formation regime inferred by corrected FNRSAT trend VOC-limited. There were 87 months with effective FNRSAT 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 NOx-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 NOx-limited regime. Jin et al. (2020) used O3 exceedance probability as the indicator to analyze non-linear dependence of long-term surface O3 concentrations on precursor emissions and determined the OMI HCHO / NO2 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 O3 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 NOx-limited regime area transformed into having a transitional regime, and the area of the transitional regime increased by about 16.2 %. In autumn, the NOx-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 O3 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 O3 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, O3 formation regimes determined by satellite FNR before and after the correction were compared with those of surface observations. The variations of O3 with surface HCHO and NO2 have been plotted to determine the O3 formation regimes from the surface observation (Fig. 11). The daytime surface HCHO and NO2 are from LP-DOAS measurements, and the O3 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. O3 formation regimes inferred from satellite FNR before and after the correction have also each been marked in Fig. 11.

For Case I, O3 decreases with the increase in NO2, which can be attributed to the titration of O3 by NO (Duncan et al., 2010). O3 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 O3 appeared with high HCHO and low NO2, 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 VOC-limited regime, which is consistent with the results of surface observation. It indicates that the correction of FNRSAT in this study can be considered to be effective and sensible.