MAX-DOAS Measurements of Tropospheric NO2 and HCHO Vertical Profiles at the Longfengshan Regional Background Station in Northeastern China

The vertical profiles of nitrogen dioxide (NO2) and formaldehyde (HCHO) in the troposphere at the Longfengshan (LFS) regional atmospheric background station (127°36′ E, 44°44′ N, 330.5 m above sea level) from 24 October 2020 to 13 October 2021 were retrieved from solar scattering spectra by multi-axis differential optical absorption spectroscopy (MAX-DOAS). We analyzed the temporal variations of NO2 and HCHO as well as the sensitivity of ozone (O3) production to the concentration ratio of HCHO to NO2. The largest NO2 volume mixing ratios (VMRs) occur in the near-surface layer for each month, with high values concentrated in the morning and evening. HCHO has an elevated layer around the altitude of 1.4 km consistently. The means ± standard deviations of vertical column densities (VCDs) and near-surface VMRs were 4.69 ± 3.72 ×1015 molecule·cm−2 and 1.22 ± 1.09 ppb for NO2, and they were 1.19 ± 8.35 × 1016 molecule·cm−2 and 2.41 ± 3.26 ppb for HCHO. The VCDs and near-surface VMRs for NO2 were high in the cold months and low in the warm months, while HCHO presented the opposite. The larger near-surface NO2 VMRs appeared in the condition associated with lower temperature and higher humidity, but this relationship was not found between HCHO and temperature. We also found the O3 production at the Longfengshan station was mainly in the NOx-limited regime. This is the first study presenting the vertical distributions of NO2 and HCHO in the regional background atmosphere of northeastern China, which are significant to enhancing the understanding of background atmospheric chemistry and regional ozone pollution processes.


Introduction
Tropospheric nitrogen dioxide (NO 2 ) and formaldehyde (HCHO) are two important trace gases [1]. NO 2 is not only an important air pollutant of photochemical smog and nitric acid rain [1,2], but also one of the precursors of ozone (O 3 ), secondary aerosols, and peroxyacetyl nitrate (PAN) [1]. NO 2 is produced by natural processes (such as lighting and ammonia oxidation [3]) and anthropogenic emission (such as transportation [4], heating/power generation [5] and coal mining [6]). Moreover, nitrogen oxides (NO x ) production are closely related to the conditions of internal combustion [7]. NO 2 is chemically removed by photolysis and reactions with various types of free radicals or O 3 [2]. As the most abundant carbonyl compound in the troposphere, HCHO comes from the combustion of fossil fuels and biomass and the chemical oxidation of volatile organic compounds (VOCs) in the atmosphere [8]. Atmospheric HCHO can be removed by various photochemical reactions [9][10][11]. NO 2 and HCHO are usually treated as proxies for nitrogen oxides (NO x ) and VOCs, respectively, to investigate the sensitivity of O 3 production [12,13].
Tropospheric columns of NO 2 and HCHO can be measured by satellite remote sensing, such as by the Tropospheric Monitoring Instrument (TROPOMI) [14]. Although TROPOMI has high spatial resolution (5.5 × 3.5 km 2 at nadir), there are still large uncertainties of retrieved tropospheric NO 2 and HCHO in the background regions over mountain terrains [15]. For surface NO 2 and HCHO, there are a few methods to achieve their measurements, such as Fourier transform infrared spectroscopy (FTIR) [16] and long-range active differential optical absorption spectroscopy for NO 2 [17]. However, the column or surface measurements without the information of NO 2 and HCHO vertical distributions have limitations in understanding the spatio-temporal variations of NO 2 and HCHO, which are significant to the investigation of the mechanisms of atmospheric chemistry in regional pollution.
Multi-axis differential optical absorption spectroscopy (MAX-DOAS), a passive groundbased remote sensing observation technique, can be used to measure the vertical column densities (VCDs) and profiles of trace gases in the troposphere [18,19]. It is characterized by high sensitivity, fast response, simple operation, and low operating cost [20]. As early as 2001, MAX-DOAS was used to measure the NO 2 emissions on highways [21]. Since then, a large number of studies on MAX-DOAS have been conducted in many countries [22]. In recent years, tropospheric vertical profiles of trace gases were successfully achieved by using MAX-DOAS [23]. In the past decade, many studies on NO 2 and HCHO observed by ground-based MAX-DOAS have been reported in China [24][25][26][27][28][29]. These studies were mainly concentrated in urban and severely polluted areas with large populations and developed economies, such as Beijing-Tianjin-Hebei, Yangtze River Delta, Pearl River Delta, and Sichuan-Chongqing [30][31][32][33][34]. Under the framework of World Meteorological Organization Global Atmosphere Watch (WMO/GAW) in China, MAX-DOAS observations were performed at the background stations of Shangdianzi in the North China Plain and Waliguan in the Tibetan Plateau, revealing the levels and temporal variations of NO 2 and HCHO in the background atmosphere of the regions [35,36]. However, to our knowledge, no investigation on levels and temporal variations of NO 2 and HCHO vertical distributions has been made at a background site in the northeastern China, which limits our understanding of the photochemistry and regional pollution formation mechanisms of ozone in this area.
In this study, we performed MAX-DOAS observations at the Longfengshan regional atmospheric background station from October 2020 to October 2021 in order to enhance our understanding of the characteristics of temporal evolutions of NO 2 and HCHO vertical distribution in the background atmosphere. Section 2 introduces the site and instrument as well as the methods of spectral analysis and profile retrieval of NO 2 and HCHO. Section 3 presents the temporal variations of NO 2 and HCHO vertical profiles as well as the sensitivities of O 3 production to the ratio of HCHO to NO 2 . Finally, the discussion and conclusions are given in Sections 4 and 5, respectively.

Site and Instrument
Ground-based MAX-DOAS measurements were performed at the Longfengshan (LFS) regional atmospheric background station (127 • 36 E, 44 • 44 N, 330.5 m a.s.l.) from 24 October 2020 to 13 October 2021 (with a break from 10 December 2020 to 3 March 2021 due to instrument malfunction). At present, the LFS station is the only background station under the framework of the WMO/GAW in the Northeast China [37]. The atmospheric observations started in 1991 at LFS [38], which represents the background atmospheric condition in the Northeast Plain region. The LFS station is located on the west side of Longfengshan reservoir, 60 km to the southeast of Wuchang City and 185 km to the southeast of Harbin City (Figure 1). It is located at the intersection of the Songnen plain condition in the Northeast Plain region. The LFS station is located on the west side of Longfengshan reservoir, 60 km to the southeast of Wuchang City and 185 km to the southeast of Harbin City (Figure 1). It is located at the intersection of the Songnen plain and the Zhangguangcai ridge of the Changbai mountains. On the western side of the LFS station is the plain area, and on the eastern side is the mountainous forest area [39,40]. There are no villages in the range of 2 km away from the site, no high-density population, and no significant industrial emission sources in the range of 30 km away from the site [41]. We used a mini MAX-DOAS instrument from the Hoffmann Messtechnik GmbH, Germany, which was also used in our previous studies [24,36]. During the Second Cabauw Intercomparison Campaign for Nitrogen Dioxide Measuring Instruments (CINDI-2), the mean relative differences in the slant column from the reference value for the Mini MAX-DOAS were −2.10% for NO2 and −20.70% for HCHO [42]. The observation system consisted of an indoor section and an outdoor section. The outdoor section contains the entrance optics, fiber-coupled spectrograph, and controlling electronics inside a metal box. A stepper motor was installed outside the metal box to drive the instrument to rotate in the vertical direction for observation at different elevation angles [19]. In this study, each sequence contained 9 elevation angles (0°, 1°, 2°, 3°, 6°, 10°, 20°, 30°, and 90°), and it took about 4 min for a complete sequence. The spectrograph covered the wavelength range of 290-447 nm. A temperature control module was used to ensure that the spectrograph was operating at stable temperature lower than the ambient temperature. Solar scattering spectra were collected during the daytime period. The spectra of dark current and electron offset were also measured at specific operating temperatures, which were used to correct the measured spectra in the daytime and then reduce the influence of the spectrograph's photoelectric noise [32]. More information about the instrumentation parameters can be found in the previous studies [31,43,44]. We used a mini MAX-DOAS instrument from the Hoffmann Messtechnik GmbH, Germany, which was also used in our previous studies [24,36]. During the Second Cabauw Intercomparison Campaign for Nitrogen Dioxide Measuring Instruments (CINDI-2), the mean relative differences in the slant column from the reference value for the Mini MAX-DOAS were −2.10% for NO 2 and −20.70% for HCHO [42]. The observation system consisted of an indoor section and an outdoor section. The outdoor section contains the entrance optics, fiber-coupled spectrograph, and controlling electronics inside a metal box. A stepper motor was installed outside the metal box to drive the instrument to rotate in the vertical direction for observation at different elevation angles [19]. In this study, each sequence contained 9 elevation angles (0 • , 1 • , 2 • , 3 • , 6 • , 10 • , 20 • , 30 • , and 90 • ), and it took about 4 min for a complete sequence. The spectrograph covered the wavelength range of 290-447 nm. A temperature control module was used to ensure that the spectrograph was operating at stable temperature lower than the ambient temperature. Solar scattering spectra were collected during the daytime period. The spectra of dark current and electron offset were also measured at specific operating temperatures, which were used to correct the measured spectra in the daytime and then reduce the influence of the spectrograph's photoelectric noise [32]. More information about the instrumentation parameters can be found in the previous studies [31,43,44].

Spectral Analysis
According to the Beer-Lambert law, the differential slant column density (dSCD) can be retrieved from the measured scattering spectra by the DOAS method [19]. The dSCDs are the differences in slant column densities between the measured and reference spectra. The spectral analysis procedure was implemented by QDOAS software [45]. Before the spectral analysis, the spectra during the observation period were divided into 9 segments based on the operating temperature of the spectrograph. The observed spectra within each segment are corrected by using their corresponding spectra of dark current and electron offset. The high-resolution solar spectral were used for the wavelength calibration. NO 2 and HCHO dSCDs were retrieved in wavelength ranges of 351~390 nm and 324~359 nm, respectively. The fitting parameters for NO 2 and HCHO spectral analyses were similar as in previous studies [36,45,46], see Table 1. In this study, in order to improve the credibility of the data, only the spectra with root mean square (RMS) of the spectral fitting residuals < 0.003 and solar zenith angle (SZA) < 75 • were retained [46,47]. Under the control of these two thresholds, we retained 70.67% of the NO 2 profiles and 68.77% of the HCHO profiles. Figure 2 shows an example of spectral fitting for NO 2 and HCHO dSCDs from the spectrum measured at 10:00 Beijing time (BJ, UTC + 8 h) on 5 July 2021 at an elevation angle of 10 • .

Spectral Analysis
According to the Beer-Lambert law, the differential slant column density (dSCD) can be retrieved from the measured scattering spectra by the DOAS method [19]. The dSCDs are the differences in slant column densities between the measured and reference spectra. The spectral analysis procedure was implemented by QDOAS software [45]. Before the spectral analysis, the spectra during the observation period were divided into 9 segments based on the operating temperature of the spectrograph. The observed spectra within each segment are corrected by using their corresponding spectra of dark current and electron offset. The high-resolution solar spectral were used for the wavelength calibration. NO2 and HCHO dSCDs were retrieved in wavelength ranges of 351~390 nm and 324~359 nm, respectively. The fitting parameters for NO2 and HCHO spectral analyses were similar as in previous studies [36,45,46], see Table 1. In this study, in order to improve the credibility of the data, only the spectra with root mean square (RMS) of the spectral fitting residuals < 0.003 and solar zenith angle (SZA) < 75° were retained [46,47]. Under the control of these two thresholds, we retained 70.67% of the NO2 profiles and 68.77% of the HCHO profiles. Figure 2 shows an example of spectral fitting for NO2 and HCHO dSCDs from the spectrum measured at 10:00 Beijing time (BJ, UTC + 8 h) on 5 July 2021 at an elevation angle of 10°. Black and red curves are the measured and fitted differential optical depths, respectively. The NO2 and HCHO dSCDs are 1.10 × 10 16 molecule·cm −2 and 2.30 × 10 16 molecule·cm −2 , respectively. The RMS between measured and fitted spectra are 7.63 × 10 −4 for NO2 and 8.98 × 10 −4 for HCHO, respectively.

Retrieval of NO 2 and HCHO Vertical Profiles
The vertical profiles of NO 2 and HCHO VMRs in the lower troposphere (0~4 km) were retrieved from the dSCDs by using the Profile inversion algorithm of aerosol extinction and the trace gas concentration algorithm (PriAM) [47]. The inversion consists of two procedures. In the first step, the vertical profiles of aerosol extinction (AE) were retrieved from the measured O 4 dSCDs. Then the retrieved AE profiles were used for the inversion of the trace gas profiles [45,47]. For HCHO, the AE profiles at 360 nm were transformed into profiles at 343 nm by using the Ångström exponent. In this study, we set the Ångström exponent as 0.7, which was estimated based on the ERA5 reanalysis data. The entire observation period was divided into six segments according to the working temperature of the spectrograph. The inversion parameters of surface albedo, single scattering albedo, and asymmetry factor were listed in Table 2. Table 2. Surface albedo, single scattering albedo, and asymmetry factor for each segment of profile inversion. The PriAM algorithm was based on the optimal estimation method to obtain the vertical profiles via loop iteration, which minimized the parameter of cost function [47,52].

NO. Start and End Time
The smaller values of the cost function correspond to the more reliable retrieval results. The relative deviations of dSCDs reflect the differences between the PriAM and MAX-DOAS measurements. In order to balance the data quality and quantity, we retained the profiles with cost function < 30 and dSCDs relative deviations < 45% during the post-processing. With respect to the selected thresholds, 61.72% of NO 2 profiles and 51.71% of HCHO profiles were left.

Ancillary Datasets
The in situ NO 2 concentration and meteorological data such as surface temperature, relative humidity, and wind speed used in this study were derived from synchronous operational observations at the LFS station. Surface temperature, relative humidity, and wind speed were measured using an automatic meteorological station (DZZ5, Huayun Sonding, China), with precisions of ± 0.1 • C, ± 1%, and ± 0.1 m/s, respectively. The meteorological measurements follow the standard (QX/T 61−2007). The Ångström exponent, surface albedo, planetary boundary layer height (PBLH), and temperature-pressure a priori profiles were obtained from ERA5 reanalysis data (https://www.ecmwf.int/en/ forecasts/dataset/ecmwf-reanalysis-v5, accessed on 25 May 2021). The asymmetry factor, single scattering albedo, and Ångström exponent were also referred to the data from the Aerosol Robotic Network (AERONET, https://aeronet.gsfc.nasa.gov/, accessed on 26 May 2021). The instrument used in the AERONET network was the CE318 multi−wavelength solar photometer (CIMEL, Paris, France).

Overview
The averaged NO 2 and HCHO vertical profiles below 4 km for the whole observation period are shown by the lines with dots in Figure 3. The NO 2 VMR has the largest value at the surface and decreases with increasing altitude. There is an elevated HCHO pollution layer with VMRs larger than 2 ppb around the altitudes of 1.4 km. The means ± standard deviations of NO 2 and HCHO VCDs are 4.69 ± 3.72 × 10 15 and 1.19 ± 0.84 × 10 16 molecule·cm −2 , respectively. Correspondingly, the near-surface VMRs are 1.22 ± 1.09 ppb for NO 2 and 2.41 ± 3.26 ppb for HCHO. The near-surface VMRs of NO 2 and HCHO in this study are higher than those of NO 2 (7~100 ppt) and HCHO (0.9 ppb) at the Waliguan regional atmospheric background station from 2012 to 2015 [36]. molecule·cm −2 , respectively. Correspondingly, the near-surface VMRs are 1.22 ± 1.09 ppb for NO2 and 2.41 ± 3.26 ppb for HCHO. The near-surface VMRs of NO2 and HCHO in this study are higher than those of NO2 (7~100 ppt) and HCHO (0.9 ppb) at the Waliguan regional atmospheric background station from 2012 to 2015 [36].

Monthly Variations
The monthly variations of the vertical profiles were different between NO2 and HCHO ( Figure 4). The larger NO2 VMRs occur at the near-surface and decrease with increasing altitudes each month. The NO2 VMRs were lower in the lower troposphere in summer than in other seasons. For HCHO, larger VMRs appear not only near the surface but also at upper levels (~1.4 km altitude) in most observational months.
The maxima (minimum) of monthly averaged NO2 near-surface VMRs ( Figure 4a) and VCDs (Figure 5a) were 2.51 ppb (0.47 ppb) and 8.6 × 10 15 molecule·cm −2 (2.00 × 10 15 molecule·cm −2 ) in November 2020 (August 2021). Tropospheric NO2 VCD shows a monthly variation trend of being higher in colder months and lower in warmer months ( Figure 5a). The open burning of straw in autumn and the burning of fuel for heating in winter probably lead to an increase in NO2 emissions compared to summer. The cold and dry atmospheric conditions in autumn and winter are not conducive to gas spreading, resulting in the highest NO2 concentrations in autumn and winter [53].
The monthly HCHO VCDs maintained a high level from March to July 2021, with a maximum of 1.45 × 10 16 molecule·cm −2 in June (Figure 5b). The HCHO minimum for both near-surface VMRs (1.12 ppb, Figure 4b) and VCDs (6.83 × 10 15 molecule·cm −2 , Figure 5b) appeared in October 2021. The near-surface HCHO VMRs were enhanced from late October to early December 2020, probably due to increased primary HCHO emissions from fossil fuel combustion in North China during the heating period [54]. The HCHO vertical distribution and column were influenced by complex factors, such as primary source from fossil fuel combustion [8] and secondary sources from chemical oxidation reactions [9]. The causes of HCHO temporal variation should be further investigated by comprehensive observation in future.    The cold and dry atmospheric conditions in autumn and winter are not conducive to gas spreading, resulting in the highest NO 2 concentrations in autumn and winter [53].

Diurnal Variations
In this study, we use April, July, and October 2021 as representatives of spring, summer, and autumn, respectively. The sample number in winter was too small to be discussed here. Figure 6 shows the diurnal variations of the vertical profile of NO2 and HCHO VMRs in April, July, and October 2021. High near-surface NO2 VMRs occurred in the early morning (5:00-9:00 BJ) and late evening (15:00-17:00 BJ) during April and July, but were stable throughout the daytime in October. In all three months, a polluted layer of NO2 was present in the residual layer. The planetary boundary layer developed to a maximum at 13:00 BJ. The elevated layer of NO2 disappeared gradually as the planetary boundary layer developed. The elevated layer existed throughout the day. Active photochemical reactions in the upper planetary boundary layer can contribute to the persistence of the HCHO elevation layer in the afternoon [55]. This characteristic is consistent with our observations at Raoyang meteorological station [46].  Figure 5b) appeared in October 2021. The near-surface HCHO VMRs were enhanced from late October to early December 2020, probably due to increased primary HCHO emissions from fossil fuel combustion in North China during the heating period [54]. The HCHO vertical distribution and column were influenced by complex factors, such as primary source from fossil fuel combustion [8] and secondary sources from chemical oxidation reactions [9]. The causes of HCHO temporal variation should be further investigated by comprehensive observation in future.

Diurnal Variations
In this study, we use April, July, and October 2021 as representatives of spring, summer, and autumn, respectively. The sample number in winter was too small to be discussed here. Figure 6 shows the diurnal variations of the vertical profile of NO 2 and HCHO VMRs in April, July, and October 2021. High near-surface NO 2 VMRs occurred in the early morning (5:00-9:00 BJ) and late evening (15:00-17:00 BJ) during April and July, but were stable throughout the daytime in October. In all three months, a polluted layer of NO 2 was present in the residual layer. The planetary boundary layer developed to a maximum at 13:00 BJ. The elevated layer of NO 2 disappeared gradually as the planetary boundary layer developed. The elevated layer existed throughout the day. Active photochemical reactions in the upper planetary boundary layer can contribute to the persistence of the HCHO elevation layer in the afternoon [55]. This characteristic is consistent with our observations at Raoyang meteorological station [46]. Sensors 2023, 23, x FOR PEER REVIEW The daily variations of NO2 and HCHO VCDs are shown in Figure 7. NO2 remained at almost the same level throughout the day in April, with a slight increa 14:00 BJ. In July, NO2 VCDs slightly decreased from 5:00 to 9:00 BJ, stayed almost th from 10:00 to 15:00 BJ, and then increased slightly after 16:00 BJ. In October, NO2 were nearly constant throughout the day. The NO2 diurnal patterns were differen those in urban areas, where there are two peaks in the morning and evening due to emissions [56]. For all three months, the NO2 diurnal variations ranges were small, ing that the local anthropogenic emission and photochemical reactions were weak LFS background station.
In April, HCHO VCDs varied gently during the period from 06:00 to 12:00 started to increase at 12:00 BJ until they reached the highest value at 16:00 BJ. I HCHO concentrations were high in the morning and evening but low at noon, w maximum value appearing at 05:00 BJ. HCHO VCDs decreased to a minimum at 1 The daily variations of NO 2 and HCHO VCDs are shown in Figure 7. NO 2 VCDs remained at almost the same level throughout the day in April, with a slight increase after 14:00 BJ. In July, NO 2 VCDs slightly decreased from 5:00 to 9:00 BJ, stayed almost the same from 10:00 to 15:00 BJ, and then increased slightly after 16:00 BJ. In October, NO 2 VCDs were nearly constant throughout the day. The NO 2 diurnal patterns were different from those in urban areas, where there are two peaks in the morning and evening due to traffic emissions [56]. For all three months, the NO 2 diurnal variations ranges were small, implying that the local anthropogenic emission and photochemical reactions were weak at the LFS background station. and remained stable until 15:00 BJ. By comparing with the corresponding temperature and relative humidity qualitatively (Figure 8), we found that high NO2 VCDs tended to occur at low temperatures and high humidity, but this relationship was not found between HCHO and temperature. Because of the low wind speeds, the LFS station was mainly influenced by emissions from local sources.  In April, HCHO VCDs varied gently during the period from 06:00 to 12:00 BJ and started to increase at 12:00 BJ until they reached the highest value at 16:00 BJ. In July, HCHO concentrations were high in the morning and evening but low at noon, with the maximum value appearing at 05:00 BJ. HCHO VCDs decreased to a minimum at 12:00 BJ and remained stable until 15:00 BJ. By comparing with the corresponding temperature and relative humidity qualitatively (Figure 8), we found that high NO 2 VCDs tended to occur at low temperatures and high humidity, but this relationship was not found between HCHO and temperature. Because of the low wind speeds, the LFS station was mainly influenced by emissions from local sources. and remained stable until 15:00 BJ. By comparing with the corresponding temperature and relative humidity qualitatively (Figure 8), we found that high NO2 VCDs tended to occur at low temperatures and high humidity, but this relationship was not found between HCHO and temperature. Because of the low wind speeds, the LFS station was mainly influenced by emissions from local sources.

Temporal Variation
The production of tropospheric ozone (O 3 ) in most regions is associated with VOCs and NO x [57]. The ratio of HCHO to NO 2 is an effective indicator for investigating the sensitivity of chemical ozone production to nitrogen oxides (NO x ) and VOCs [46,58,59]. "RA" is used to refer to the ratio of HCHO to NO 2 , either in VMRs (RA VMR ) or tropospheric VCD (RA VCD ). According to previous studies, O 3 production can be divided into VOCslimited (RA < 1), transition zone (1 < RA < 2) and NO x -limited (RA > 2) [60,61]. In this study, in order to balance the quality and quantity of the data, only HCHO VMRs between 1 and 10 ppb and NO 2 larger than 0.1 ppb were considered for the calculation of RA [46].
RA with respect to VMR has an elevated layer at the altitude of around 1.5 km (Figure 9a). The vertical distribution of the monthly means of RA (Figure 9b) shows that the height of the lower boundary of the elevated RA fell from October 2020 (1.2 km) to May 2021 (0.8 km). The larger RA filled the entire lower troposphere (below 2 km) from June until September 2021. In October 2021, RA in the lower troposphere decreased, and the lower boundary of the elevated layer rose again to 1.2 km. The majority of RA were less than 2 above the altitude of 2 km and less than 1 above the altitude of 2.5 km. The RAs of near-surface VMR and tropospheric VCD had the same seasonal variation patterns, with annual averages of 2.97 ± 3.04 for near-surface VMR and 4.03 ± 3.63 for tropospheric VCD (Figure 9c). The largest values of both RA VMR and RA VCD appeared in July, being 6.25 ± 4.00 and 8.22 ± 3.62, respectively. Correspondingly, the lowest RA appeared in December with the values of 0.96 ± 0.36 for RA VMR and 1.53 ± 0.67 for RA VCD .

Temporal Variation
The production of tropospheric ozone (O3) in most regions is associated with VOCs and NOx [57]. The ratio of HCHO to NO2 is an effective indicator for investigating the sensitivity of chemical ozone production to nitrogen oxides (NOx) and VOCs [46,58,59]. "RA" is used to refer to the ratio of HCHO to NO2, either in VMRs (RAVMR) or tropospheric VCD (RAVCD). According to previous studies, O3 production can be divided into VOCs-limited (RA < 1), transition zone (1 < RA < 2) and NOx-limited (RA > 2) [60,61]. In this study, in order to balance the quality and quantity of the data, only HCHO VMRs between 1 and 10 ppb and NO2 larger than 0.1 ppb were considered for the calculation of RA [46].
RA with respect to VMR has an elevated layer at the altitude of around 1.5 km ( Figure  9a). The vertical distribution of the monthly means of RA (Figure 9b) shows that the height of the lower boundary of the elevated RA fell from October 2020 (1.2 km) to May 2021 (0.8 km). The larger RA filled the entire lower troposphere (below 2 km) from June until September 2021. In October 2021, RA in the lower troposphere decreased, and the lower boundary of the elevated layer rose again to 1.2 km. The majority of RA were less than 2 above the altitude of 2 km and less than 1 above the altitude of 2.5 km. The RAs of near-surface VMR and tropospheric VCD had the same seasonal variation patterns, with annual averages of 2.97 ± 3.04 for near-surface VMR and 4.03 ± 3.63 for tropospheric VCD (Figure 9c). The largest values of both RAVMR and RAVCD appeared in July, being 6.25 ± 4.00 and 8.22 ± 3.62, respectively. Correspondingly, the lowest RA appeared in December with the values of 0.96 ± 0.36 for RAVMR and 1.53 ± 0.67 for RAVCD.  The diurnal variation patterns of RA vertical distribution varied with seasons ( Figure 10). In each month, the elevated layer of RA appeared around the altitudes of 1.5 km. In April, the RA was mainly between 1 and 2 in the lower boundary layer (0-0.4 km), with RA < 1 above 2.5 km. In July, RA > 2 filled the entire boundary layer (up to 2 km), with RA < 2 only appearing above 2 km. In October, RA was almost between one and two near the surface. The RA VCD was larger than two in all the three months. On average, the RA in July was~3.2 and 2.8 times higher than that in April and October, respectively.
Sensors 2023, 23, x FOR PEER REVIEW 11 of 18 the data grouped for each month. HCHO/NO2 = 1 and 2 are also marked with dashed lines. The white grid cells in panel (b) indicate the missing data owing to lacking observation and data quality control.
The diurnal variation patterns of RA vertical distribution varied with seasons ( Figure  10). In each month, the elevated layer of RA appeared around the altitudes of 1.5 km. In April, the RA was mainly between 1 and 2 in the lower boundary layer (0-0.4 km), with RA < 1 above 2.5 km. In July, RA > 2 filled the entire boundary layer (up to 2 km), with RA < 2 only appearing above 2 km. In October, RA was almost between one and two near the surface. The RAVCD was larger than two in all the three months. On average, the RA in July was ~3.2 and ~2.8 times higher than that in April and October, respectively.

Implication for O3 Production
To analyze the sensitivities of O3 production to the ratio of HCHO to NO2, we assume that daily O3 production at the LFS is approximately equal to the range of daytime O3 concentration variations at the surface, considering that the photochemical O3 production was a strong driver of the diurnal surface O3 variation [46,59]. Figure 11 shows the daily

Implication for O 3 Production
To analyze the sensitivities of O 3 production to the ratio of HCHO to NO 2 , we assume that daily O 3 production at the LFS is approximately equal to the range of daytime O 3 concentration variations at the surface, considering that the photochemical O 3 production was a strong driver of the diurnal surface O 3 variation [46,59]. Figure 11 shows the daily O 3 production as a function of the daily average values of HCHO and NO 2 for nearsurface VMR (Figure 9a) and VCD (Figure 9b) during the daytime (05:00 to 17:00 BJ). The distribution patterns of O 3 production, as classified by RA VMR and RA VCD , are similar. For most of the days, O 3 production was concentrated in the NO x -limited regions or transition regions. On only a few days was the weaker O 3 production (<20 ppb d −1 ) located in the VOCs-limited regions. Differently, the strongest near-surface O 3 production occurred in the transition region for RA VMR , but in the NO x -limited region for RA VCD . From October 2020 to March 2021, the RA VMR varied between 1 and 2, implying that O 3 production was in the transition regime. As a whole, O 3 production was in the NO x -limited regime.
O3 production as a function of the daily average values of HCHO and NO2 for near-surface VMR ( Figure 9a) and VCD (Figure 9b) during the daytime (05:00 to 17:00 BJ). The distribution patterns of O3 production, as classified by RAVMR and RAVCD, are similar. For most of the days, O3 production was concentrated in the NOx-limited regions or transition regions. On only a few days was the weaker O3 production (<20 ppb d −1 ) located in the VOCs-limited regions. Differently, the strongest near-surface O3 production occurred in the transition region for RAVMR, but in the NOx-limited region for RAVCD. From October 2020 to March 2021, the RAVMR varied between 1 and 2, implying that O3 production was in the transition regime. As a whole, O3 production was in the NOx-limited regime.

Relationship to Meteorological Conditions
The correlation coefficient between RAVMR and temperature (relative humidity) is 0.62 (0.53), implying that O3 production at LFS tended to be in the NOx−limited region when the temperature and relative humidity were higher (Figure 12a, b). In July, the temperature and relative humidity were high, and the RA was basically larger than two. There is no correlation relationship between RAVMR and wind speed (Figure 12c), with the correlation coefficient of 0.01 (not shown in figure). However, the RAVMR is dependent on the wind directions (Figure 12d-f). In April, maximum frequencies for RAVMR ≥ 2 and 1 < RAVMR < 2 were 14.81% in the SSW sector and 11.11% in the NNW sectors. Almost all the RAVMR values in July were larger than two and distributed in the SE-WSW sectors, with the largest frequency occurring in the S direction. In October, the largest frequency for RAVMR > 2 was 33.33% in the SSW direction and the frequencies for 1 < RAVMR < 2 were smaller and in the N and ESE directions. As a whole, the sensitivity of O3 production to NO2 and HCHO is closely related to temperature and relative humidity. Air masses from different directions can lead to different sensitivities of O3 production to NOx and VOCs at LFS Station.

Relationship to Meteorological Conditions
The correlation coefficient between RA VMR and temperature (relative humidity) is 0.62 (0.53), implying that O 3 production at LFS tended to be in the NOx−limited region when the temperature and relative humidity were higher (Figure 12a, b). In July, the temperature and relative humidity were high, and the RA was basically larger than two. There is no correlation relationship between RA VMR and wind speed (Figure 12c), with the correlation coefficient of 0.01 (not shown in figure). However, the RA VMR is dependent on the wind directions (Figure 12d-f). In April, maximum frequencies for RA VMR ≥ 2 and 1 < RA VMR < 2 were 14.81% in the SSW sector and 11.11% in the NNW sectors. Almost all the RA VMR values in July were larger than two and distributed in the SE-WSW sectors, with the largest frequency occurring in the S direction. In October, the largest frequency for RA VMR > 2 was 33.33% in the SSW direction and the frequencies for 1 < RA VMR < 2 were smaller and in the N and ESE directions. As a whole, the sensitivity of O 3 production to NO 2 and HCHO is closely related to temperature and relative humidity. Air masses from different directions can lead to different sensitivities of O 3 production to NO x and VOCs at LFS Station.
The background levels of NO 2 and HCHO at LFS are useful to investigate as long-term trends in future studies.
The ranges of diurnal variation of NO 2 VCDs are smaller at the LFS station than at another WMO/GAW background region in the North China Plain [35]. The vertical profile structures of both NO 2 and HCHO at LFS in summer are similar to those observed at Raoyang, a rural site in the North China Plain [46]. The MAX−DOAS measurements at Raoyang were performed only for a summer period, and the elevated HCHO layer can be attributed to the air pollution and oxidization process in the lower atmosphere in the North China Plain [55]. The causes of larger VMRs at upper levels (~1.4 km altitude) at the LFS background station need to be fully understood in future studies.
Meteorological conditions affected the concentration levels, vertical distribution, and temporal variations of NO 2 and HCHO, as well as the sensitivity of O 3 production at the LFS station. There are at least three reasons: (1) The boundary layer evolution led to the vertical mixing of air masses; (2) The temperature and relative humidity affected the efficiency of O 3 photochemical processes and the natural source emission; (3) Different wind speeds and directions were accompanied by air masses with different pollution levels.

Conclusions
We carried out MAX−DOAS observations at the Longfengshan regional atmospheric background station in Heilongjiang Province of China from October 2020 to October 2021, performed the spectral analysis with QDOAS software, and retrieved vertical profiles of NO 2 and HCHO by using the PriAM algorithm. We explored the concentration, temporal, and spatial variation of NO 2 and HCHO, and the sensitivity of O 3 production to the ratio of HCHO to NO 2 . The conclusions are as follows: The average levels of near-surface VMRs for NO 2 and HCHO were 1.22 ± 1.09 ppb and 2.41 ± 3.26 ppb throughout the observation period, respectively. The NO 2 vertical structure shows a declining pattern with increasing altitude, while HCHO has an elevated layer around the altitude of 1.4 km.
The NO 2 VMRs in the lower troposphere tend to be higher in colder months and lower in warmer months at the LFS station. HCHO has an opposite monthly trend, especially at upper levels (~1.4 km altitude). There was a polluted layer of NO 2 in the residual layer, which disappeared gradually with the development of planetary boundary layer. However, the HCHO elevated layer maintained throughout the daytime. Different from the gentle diurnal variations of NO 2 VCDs, the HCHO VCDs are high in the morning and evening but low at noon in July. The qualitative comparisons show that high NO 2 VCDs tended to occur at low temperatures and high humidity, but this relationship is not found for HCHO.
Although there were monthly and diurnal variations in the vertical profiles of the VMR ratio of HCHO to NO 2 , on most of the days, O 3 production was in the NO x -limited regions or transition regions at the LFS station. There were only a few days of the experiment time when the weaker O 3 production (<20 ppb) was located in the VOCs-limited regions. Besides the dependencies of wind direction, the O 3 production at the LFS tended to be in the NOx-limited region when the temperature and relative humidity were higher.
The results of this study will be helpful for better understanding the spatiotemporal distribution characteristics of NO 2 and HCHO in the background region, in addition, more comprehensive observations, such as concurrent measurements of O 3 and VOCs together with MAX-DOAS, are recommended, which are significant for evaluating and designing the strategies for controlling O 3 pollution.