Measuring the Vertical Profiles of Aerosol Extinction in the Lower Troposphere by MAX-DOAS at a Rural Site in the North China Plain

Ground-based multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurements were performed during the summer (13 June–20 August) of 2014 at a rural site in North China Plain. The vertical profiles of aerosol extinction (AE) in the lower troposphere were retrieved to analyze the temporal variations of AE profiles, near-surface AE, and aerosol optical depth (AOD). The average AOD and near-surface AE over the period of study were 0.51 ± 0.26 and 0.33 ± 0.18 km−1 during the effective observation period, respectively. High AE events and elevated AE layers were identified based on the time series of hourly AE profiles, near-surface AEs and AODs. It is found that in addition to the planetary boundary layer height (PBLH) and relative humidity (RH), the variations in the wind field have large impacts on the near-surface AE, AOD, and AE profile. Among 16 wind sectors, higher AOD or AE occur mostly in the directions of the cities upstream. The diurnal variations of the AE profiles, AODs and near-surface AEs are significant and influenced mainly by the source emissions, PBLH, and RH. The AE profile shape from MAX-DOAS measurement is generally in agreement with that from light detection and ranging (lidar) observations, although the AE absolute levels are different. Overall, ground-based MAX-DOAS can serve as a supplement to measure the AE vertical profiles in the lower troposphere.


Introduction
Along with the rapid development of economy and society, aerosol loading levels across China sharply increased over the past several decades [1]. Although the concentrations of particulate matter in aerodynamic diameter less than or equal to 2.5 µm (PM 2.5 ) have continued to decrease in most cities since 2013, events of haze associated with high aerosol extinction (AE) still occur frequently, especially in the North China Plain (NCP) during the winter [2]. Aerosol particles not only greatly affect the air quality, but also have direct effects on radiative forcing and indirect effects on clouds [3,4]. Therefore, 300 m altitude [49]. Recent MAX-DOAS observations in the central western NCP showed that high AEs are mainly located below 1.4 km altitude with frequent lifted layers, and induced by complex factors, such as regional transport [50]. However, the knowledge of AE profile in the NCP is still incomplete, and the comparisons of AE profile between MAX-DOAS inversion and other measurement are also sparse.
We made MAX-DOAS measurements during the field campaign of the Vertical Observations of trace Gases and Aerosols (VOGA) at Raoyang, a rural site of NCP, in summer 2014. The primary objective of this study is to retrieve the AE profiles from the MAX-DOAS measurement data, investigate the characteristics and temporal evolution of the AE vertical distribution over this polluted rural area, and compare MAX-DOAS results with lidar AE profiles. Section 2 describes the observational site, MAX-DOAS, and lidar instruments, process of spectral analysis, and the retrieval of AE vertical profiles. The time series and diurnal variation of AE vertical profiles as well as a comparison with lidar are shown in Section 3. The summary and conclusions are given in Section 4.

Site and Instrument
The MAX-DOAS system was set up at the Raoyang meteorological station (115 • 44 E, 38 • 14 N; 20 m above sea level), a rural site in the NCP (Figure 1a). This station is located in an agriculture county in the middle of Heibei Province, China. There are no large local industrial sources. However, it is surrounded by a cluster of industrial and populated cites, such as Hengshui, Shijiazhuang, Baoding, Cangzhou, Tianjin and Beijing at distances from 50 to 200 km [18,22,51,52]. MODIS satellite observations (here we use the MYD04_3K product) show that the AODs are higher in major neighborhood cities than at the observatory ( Figure 1b).
We made MAX-DOAS measurements during the field campaign of the Vertical Observations of trace Gases and Aerosols (VOGA) at Raoyang, a rural site of NCP, in summer 2014. The primary objective of this study is to retrieve the AE profiles from the MAX-DOAS measurement data, investigate the characteristics and temporal evolution of the AE vertical distribution over this polluted rural area, and compare MAX-DOAS results with lidar AE profiles. Section 2 describes the observational site, MAX-DOAS, and lidar instruments, process of spectral analysis, and the retrieval of AE vertical profiles. The time series and diurnal variation of AE vertical profiles as well as a comparison with lidar are shown in Section 3. The summary and conclusions are given in Section 4.

Site and Instrument
The MAX-DOAS system was set up at the Raoyang meteorological station (115°44′ E, 38°14′ N; 20 m above sea level), a rural site in the NCP (Figure 1a). This station is located in an agriculture county in the middle of Heibei Province, China. There are no large local industrial sources. However, it is surrounded by a cluster of industrial and populated cites, such as Hengshui, Shijiazhuang, Baoding, Cangzhou, Tianjin and Beijing at distances from 50 to 200 km [18,22,51,52]. MODIS satellite observations (here we use the MYD04_3K product) show that the AODs are higher in major neighborhood cities than at the observatory (Figure 1b).
Ground-based MAX-DOAS observations were conducted from 13 June to 20 August 2014 at Raoyang. The Mini MAX-DOAS instrument is a compact and relatively small instrument made by the Hoffmann Messtechnik GmbH in Germany and it contains the entrance optics, stepper motor, temperature controller, spectrograph, operational controller and data collector. The instrument was automatically run, recording the spectra of scattered sunlight at 11 elevation angles (1-6°, 8°, 10°, 15°, 30° and 90°). The telescope pointed approximately towards the southeast. The exposure time of each individual spectrum was ∼0.5 min. The spectrograph covered the wavelength range of 292-447 nm, operating at a stable temperature of 5 °C. The spectra of dark current and electronic offset were also collected for correcting the measured spectra. A laptop with professional software was used to control the observation procedure. More descriptions about the same type of instrument are available in previous works [53][54][55][56][57][58]. operating at a stable temperature of 5 • C. The spectra of dark current and electronic offset were also collected for correcting the measured spectra. A laptop with professional software was used to control the observation procedure. More descriptions about the same type of instrument are available in previous works [53][54][55][56][57][58].

Spectral Analysis
Based on the Beer-Lambert law, the O 4 differential slant column densities (dSCDs) were retrieved from the measured spectra through the DOAS method [59]. The O 4 dSCDs represent the differences of O 4 absorption between measurement spectra and the reference spectra. Two zenith spectra, measured before and after an off-zenith sequence of elevation angles, were interpolated and used as the reference spectrum. In this case, the O 4 dSCDs from spectral fitting can be approximately regarded as tropospheric O 4 dSCDs, usually referred to as O 4 delta slant column densities (delta SCDs) [29]. The spectral analysis was implemented using the QDOAS software (http://uv-vis.aeronomie.be/software/QDOAS/), based on the non-linear least squares fitting algorithm. For each measured spectrum a wavelength calibration is performed before spectral fitting. The setting of DOAS retrieval parameters can be referred to previous studies [50]. The O 4 dSCDs were retrieved by the configured parameters, involving the fitting window (338-370 nm), the cross sections of nitrogen dioxide (NO 2 , 294K, 220K), ozone (O 3 , 223K, 243K), O 4 (293K), formaldehyde (HCHO, 298K), bromine oxide (BrO, 228K), water (H 2 O, 293K), nitrous acid (HONO, 296K) and two Ring spectra, as well as polynomial degree (5 order) and intensity offset (polynomial of order 1). In the process of data quality control, we rejected the O 4 dSCDs when the root mean square (RMS) of spectral fitting residual was bigger than 0.003, based on previous studies [50]. Figure 2 shows an example of DOAS fitting of O 4 , indicating that the O 4 absorption structure can be extracted from measured spectra and fitted well.

Spectral Analysis
Based on the Beer-Lambert law, the O4 differential slant column densities (dSCDs) were retrieved from the measured spectra through the DOAS method [59]. The O4 dSCDs represent the differences of O4 absorption between measurement spectra and the reference spectra. Two zenith spectra, measured before and after an off-zenith sequence of elevation angles, were interpolated and used as the reference spectrum. In this case, the O4 dSCDs from spectral fitting can be approximately regarded as tropospheric O4 dSCDs, usually referred to as O4 delta slant column densities (delta SCDs) [29]. The spectral analysis was implemented using the QDOAS software (http://uv-vis.aeronomie.be/software/QDOAS/), based on the non-linear least squares fitting algorithm. For each measured spectrum a wavelength calibration is performed before spectral fitting. The setting of DOAS retrieval parameters can be referred to previous studies [50]. The O4 dSCDs were retrieved by the configured parameters, involving the fitting window (338-370 nm), the cross sections of nitrogen dioxide (NO2, 294K, 220K), ozone (O3, 223K, 243K), O4 (293K), formaldehyde (HCHO, 298K), bromine oxide (BrO, 228K), water (H2O, 293K), nitrous acid (HONO, 296K) and two Ring spectra, as well as polynomial degree (5 order) and intensity offset (polynomial of order 1). In the process of data quality control, we rejected the O4 dSCDs when the root mean square (RMS) of spectral fitting residual was bigger than 0.003, based on previous studies [50]. Figure 2 shows an example of DOAS fitting of O4, indicating that the O4 absorption structure can be extracted from measured spectra and fitted well. The black and red symbol-lines indicate the derived absorption structures from the measured spectra and the fitted absorption cross section, respectively. The fitted O4 differential slant column density (dSCD) is 1.65 × 10 43 molec 2 ·cm −5 , and the root mean square (RMS) of fitting residual between measured and fitted spectrum is 7.63 × 10 −4 .

Retrieval of the Vertical Profiles of Aerosol Extinction
For each elevation sequence (~12 min), a vertical profile of aerosol extinction at 360 nm in the troposphere is retrieved from O4 delta SCDs by the optimal estimation (OE) algorithm of the "Profile inversion algorithm of aerosol extinction and trace gas concentration developed by the Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences (AIOFM, CAS), in cooperation with the Max Planck Institute for Chemistry (MPIC)" (PriAM) [60]. Then the aerosol extinction in the 0-50 m layer adjacent to the surface, hereafter called near-surface AE, can be extracted from the vertical profiles, and the AODs can be obtained by vertical integration. The parameters of surface albedo, single scattering albedo of aerosol particles, and asymmetry factor of scattering on aerosol particles were set as

Retrieval of the Vertical Profiles of Aerosol Extinction
For each elevation sequence (~12 min), a vertical profile of aerosol extinction at 360 nm in the troposphere is retrieved from O 4 delta SCDs by the optimal estimation (OE) algorithm of the "Profile inversion algorithm of aerosol extinction and trace gas concentration developed by the Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences (AIOFM, CAS), in cooperation with the Max Planck Institute for Chemistry (MPIC)" (PriAM) [60]. Then the aerosol extinction in the 0-50 m layer adjacent to the surface, hereafter called near-surface AE, can be extracted from the vertical profiles, and the AODs can be obtained by vertical integration. The parameters of surface albedo, single scattering Atmosphere 2020, 11, 1037 5 of 17 albedo of aerosol particles, and asymmetry factor of scattering on aerosol particles were set as 0.06, 0.95, and 0.60, respectively, referring to previous measurements at the same or nearby stations [18,22,50,52]. Temperature and pressure profiles were averaged from the ECMWF Reanalysis-Interim (ERA-Interim) product (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim) at 0:00, 6:00, and 12:00 UTC for the summer (June, July, and August) of 2014. A smoothed box-shaped a priori AE profile was used in this study, the same as that used in a previous study [50]. The diagonal elements of the a-priori covariance matrix were set as 0.25 and didn't decrease with the altitudes in order to balance the flexibility and stability of the profile inversion. For the post-processing, we retained the data with the cost function of profile inversion smaller than 30 and the relative deviations of PriAM modelled and MAX-DOAS measured O 4 dSCDs less than 30%. The selected thresholds are based on the balance of data quality and amount. Under the condition of the selected thresholds, 71.41% AE profiles are retained and the average of OE cost function is 8.83. In addition, we have tried to identify and classify the sky condition through MAX-DOAS observation [61,62]. However, the amount of MAX-DOAS data under clear sky condition is very limited (14.14% among the qualified profile data) and the uncertainties of sky condition classification are hard to evaluate. Therefore, we use all the qualified MAX-DOAS data below without the classification of sky condition. Meanwhile, the aforementioned data quality process may partly reduce the influence of different sky conditions. Finally, 342 hourly AE profiles can be used for this research.

Light Detection and Ranging (Lidar) Observation
As part of the field campaign, the vertical profiles of aerosol extinction were also observed by the Leosphere lidar [22]. Based on the interaction of light with matter, a laser pulse at 355 nm was sent into the atmosphere, scattered back to the optical collection system, converted into an electronic signal and recorded by a computer. The full overlap between the outgoing beam and the field of view of the telescope was around 200 m. The optical parameters of atmospheric particles at 355 nm, such as extinction coefficients profiles, were retrieved from the lidar measurement using a default lidar ratio of 35 sr. The assumed constant lidar ratio may cause 20% uncertainties of the retrieved aerosol extinction [39,40,63]. The vertical and temporal resolutions of aerosol particle extinction profile were set as 15 m and 1 min, respectively. We calculated the signal-to-noise ratio for each vertical profile of original signal (SNR), and discarded the outliers in the aerosol extinction profile once SNR was less than 20. The selected SNR threshold can discard the outliers at the high altitude and retain the data in the planetary boundary layer as many as possible. The qualified profiles were compared with MAX-DOAS results in the following section. More details of software and hardware about lidar can be found in the user manual of aerosol lidar ALS300 and ALS450 [22,63].

Time Series of the Vertical Distribution of Aerosol Extinction
Based on the aforementioned methods of spectral analysis and profile inversion, the AE profiles up to 4 km altitude with a vertical grid of 200 m were derived from MAX-DOAS observations. Due to no substantial information for the AE above 2 km altitude [6], we only show the time series of hourly AE profiles below 2 km in Figure 3a Figures 3e and 4b), implying an influence of the aerosol hygroscopicity on the AE. Linear regression analysis shows that the correlation coefficient between near-surface AEs and RHs (R = 0.42) is larger than that between AOD and RHs (R = 0.32) (Figure 4b). Surface in-situ measurements confirm that hygroscopic growth noticeably enhances the aerosol scattering coefficient at Raoyang, especially for conditions of high content of water-soluble secondary inorganic aerosols and fine particles [19,64]. The wind direction and speed have an important impact on the AE by transport of pollutants from different emission sources. For example, from the period of high AOD and near-surface AE (8 July) to the clean period (9 July), the RH stayed constantly around 60%, but the wind direction changed from the southeast (more pollution) to the WNW section (less pollution), with the average wind speed increasing from 1.56 m/s to 3.80 m/s (Figure 3f).
Atmosphere 2020, 11, x FOR PEER REVIEW 6 of 17 that between AOD and RHs (R = 0.32) (Figure 4b). Surface in-situ measurements confirm that hygroscopic growth noticeably enhances the aerosol scattering coefficient at Raoyang, especially for conditions of high content of water-soluble secondary inorganic aerosols and fine particles [19,64]. The wind direction and speed have an important impact on the AE by transport of pollutants from different emission sources. For example, from the period of high AOD and near-surface AE (8 July) to the clean period (9 July), the RH stayed constantly around 60%, but the wind direction changed from the southeast (more pollution) to the WNW section (less pollution), with the average wind speed increasing from 1.56 m/s to 3.80 m/s (Figure 3f).   To further investigate the influence of the wind direction and speed, we present the corresponding roses ( Figure 5) using the hourly data shown above (Figure 3). During the observation period, the frequent wind directions (WD) were in the sectors of S, SSE, NE, and SSW (Figure 5a). Hourly wind speeds (WS) larger than 5 m/s appeared in the WNW sector, and the average WS in all 16 WD sectors were between 1.6 m/s and 3.0 m/s. Among the 16 wind directions (Figure 5b,c), the highest frequencies of the largest (AOD > 1, AE > 0.75 km −1 ) and smallest (AOD < 0.2, AE < 0.15 km −1 ) values occurred in the sectors of NE and WNW, respectively. Both AODs and near-surface AEs varied strongly with wind direction (Figure 5d). In the NE to SSW sectors, the AOD (near-surface AE) means are high and close to each other, possibly connected with the cities distributed in these directions. Similarly, high AOD (near-surface AE) is also found in the NW sector, where Baoding city is located upstream (Figure 1b). Furthermore, to analyze the influences of pollutant transport, we calculated the weighted AOD and near-surface AE by the occurrence frequency of WD (Figure 5e). The highest weighted AOD and near-surface AE are concentrated on the directions of NE, SSE, S, and SSW, indicating that pollutants from the northeast and south, where cities with high source emissions are distributed [52], contribute significantly to the AE level at the Raoyang station. Figure 5f also shows the change of correlation coefficient between AOD and near-surface AE with the wind direction. Most of correlation coefficients are near to or higher than 0.8. Excluding the NW, WSW, and ENE cases for the reason of few samples, weaker correlation in the NE may be caused by the heterogeneous distribution of AE in the vertical profiles. Therefore, the wind field, coupled with inhomogeneous spatio-temporal emission sources, could significantly impact the vertical distribution of the AE.  To further investigate the influence of the wind direction and speed, we present the corresponding roses ( Figure 5) using the hourly data shown above ( Figure 3). During the observation period, the frequent wind directions (WD) were in the sectors of S, SSE, NE, and SSW (Figure 5a). Hourly wind speeds (WS) larger than 5 m/s appeared in the WNW sector, and the average WS in all 16 WD sectors were between 1.6 m/s and 3.0 m/s. Among the 16 wind directions (Figure 5b,c), the highest frequencies of the largest (AOD > 1, AE > 0.75 km −1 ) and smallest (AOD < 0.2, AE < 0.15 km −1 ) values occurred in the sectors of NE and WNW, respectively. Both AODs and near-surface AEs varied strongly with wind direction (Figure 5d). In the NE to SSW sectors, the AOD (near-surface AE) means are high and close to each other, possibly connected with the cities distributed in these directions. Similarly, high AOD (near-surface AE) is also found in the NW sector, where Baoding city is located upstream (Figure 1b). Furthermore, to analyze the influences of pollutant transport, we calculated the weighted AOD and near-surface AE by the occurrence frequency of WD (Figure 5e). The highest weighted AOD and near-surface AE are concentrated on the directions of NE, SSE, S, and SSW, indicating that pollutants from the northeast and south, where cities with high source emissions are distributed [52], contribute significantly to the AE level at the Raoyang station. Figure 5f also shows the change of correlation coefficient between AOD and near-surface AE with the wind direction. Most of correlation coefficients are near to or higher than 0.8. Excluding the NW, WSW, and ENE cases for the reason of few samples, weaker correlation in the NE may be caused by the heterogeneous distribution of AE in the vertical profiles. Therefore, the wind field, coupled with inhomogeneous spatio-temporal emission sources, could significantly impact the vertical distribution of the AE. cities with high source emissions are distributed [52], contribute significantly to the AE level at the Raoyang station. Figure 5f also shows the change of correlation coefficient between AOD and near-surface AE with the wind direction. Most of correlation coefficients are near to or higher than 0.8. Excluding the NW, WSW, and ENE cases for the reason of few samples, weaker correlation in the NE may be caused by the heterogeneous distribution of AE in the vertical profiles. Therefore, the wind field, coupled with inhomogeneous spatio-temporal emission sources, could significantly impact the vertical distribution of the AE.

Diurnal Variations
Diurnal pattern of AE profiles, as well as associated AODs and near-surface AEs, are shown in Figure 6a-c. Averaged over the observational period, the hourly mean AOD varies from 0.3 to 0.6, reaching the minimum around 9:00 LT and sustaining at a high level of ~0.5 at 11:00-18:00 LT (Figure 6a). The hourly mean AE also reaches a low value at 8:00-9:00 LT, but it gradually decreases after reaching a peak at 11:00 LT (Figure 6b). The correlation coefficient of hourly mean values between AOD and near-surface AE diurnal variation is 0.32. During the period of 6:00-19:00 LT (Figure 6c), the lifted AE layers occurred for 10 h (7:00, 10:00-18:00 LT). Therefore, the difference in the diurnal pattern between the AOD and near-surface AE is significant, which can be attributed to the non-uniform distribution of AE in the vertical direction. In addition, high AOD and near-surface AE occurred in early morning (6:00-7:00 LT). Previous studies indicated that the loading of black carbon aerosols within the mixing layer was highest in the early morning, leading to strong absorption below 200 m and possibly high AOD and near-surface AE at that time [52]. The high AEs below 200 m at 6:00-7:00 ( Figure 6c) were also possibly connected with the favorable conditions for aerosol hygroscopic growth in the early morning at high RH (Figure 6d) [22]. Similarly, the low AE value at 9:00 LT can also be attributed to low RH (Figure 6b,d). The wind direction changes within the sectors of SSW-E (~202-90°), with a maximum wind speed of 2.5 m/s at 14:00LT (Figure 6e). There is no distinct relationship for the diurnal variations between aerosol extinction and wind, which is probably related to the relatively small wind speed. The planetary boundary layer begins to develop from 8:00 LT until its peak height of 1.65 km at 14:00 LT (Figure 6f

Diurnal Variations
Diurnal pattern of AE profiles, as well as associated AODs and near-surface AEs, are shown in Figure 6a-c. Averaged over the observational period, the hourly mean AOD varies from 0.3 to 0.6, reaching the minimum around 9:00 LT and sustaining at a high level of~0.5 at 11:00-18:00 LT (Figure 6a). The hourly mean AE also reaches a low value at 8:00-9:00 LT, but it gradually decreases after reaching a peak at 11:00 LT (Figure 6b). The correlation coefficient of hourly mean values between AOD and near-surface AE diurnal variation is 0.32. During the period of 6:00-19:00 LT (Figure 6c), the lifted AE layers occurred for 10 h (7:00, 10:00-18:00 LT). Therefore, the difference in the diurnal pattern between the AOD and near-surface AE is significant, which can be attributed to the non-uniform distribution of AE in the vertical direction. In addition, high AOD and near-surface AE occurred in early morning (6:00-7:00 LT). Previous studies indicated that the loading of black carbon aerosols within the mixing layer was highest in the early morning, leading to strong absorption below 200 m and possibly high AOD and near-surface AE at that time [52]. The high AEs below 200 m at 6:00-7:00 ( Figure 6c) were also possibly connected with the favorable conditions for aerosol hygroscopic growth in the early morning at high RH (Figure 6d) [22]. Similarly, the low AE value at 9:00 LT can also be attributed to low RH (Figure 6b,d). The wind direction changes within the sectors of SSW-E (~202-90 • ), with a maximum wind speed of 2.5 m/s at 14:00LT (Figure 6e). There is no distinct relationship for the diurnal variations between aerosol extinction and wind, which is probably related to the relatively small wind speed. The planetary boundary layer begins to develop from 8:00 LT until its peak height of 1.65 km at 14:00 LT (Figure 6f). It is clear that the AODs do not change with the planetary boundary layer height (PBLH) during the period 11:00-18:00 LT, but the AE profiles are basically within a fully developed convective boundary layer. The correlation coefficients (R, Figure 6f) indicate the consistency of AE variation between the surface and vertical column upward. The R minimum at 10:00 LT may be caused by the vertical structure of AE profile, such as the elevated AE layer. Overall, the obvious diurnal variations in the AOD, near-surface AE, and the AE profile at the Raoyang station are associated with both the source emission and meteorological conditions (RH and PBLH).
Atmosphere 2020, 11, x FOR PEER REVIEW 10 of 17 period 11:00-18:00 LT, but the AE profiles are basically within a fully developed convective boundary layer. The correlation coefficients (R, Figure 6f) indicate the consistency of AE variation between the surface and vertical column upward. The R minimum at 10:00 LT may be caused by the vertical structure of AE profile, such as the elevated AE layer. Overall, the obvious diurnal variations in the AOD, near-surface AE, and the AE profile at the Raoyang station are associated with both the source emission and meteorological conditions (RH and PBLH).  Figure 6a,b are the 10th (90th), 25th (75th) percentiles, minima (maxima) of the data grouped in each h, respectively. Hyphens inside the boxes and curves with circles in Figure 6a,b separately denote the medians and the mean values. The numbers of integrated sampling days for specific h are labeled at the top axis in Figure 6a,b. The error bars in Figure 6d-f denote standard deviations of RH, WD, WS, and PBLH for each h, respectively. Note that the PBLH is from linearly interpolated reanalysis data with time interval of 3 h (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5).  Figure 6a,b are the 10th (90th), 25th (75th) percentiles, minima (maxima) of the data grouped in each h, respectively. Hyphens inside the boxes and curves with circles in Figure 6a,b separately denote the medians and the mean values.
The numbers of integrated sampling days for specific h are labeled at the top axis in Figure 6a,b. The error bars in Figure 6d-f denote standard deviations of RH, WD, WS, and PBLH for each h, respectively. Note that the PBLH is from linearly interpolated reanalysis data with time interval of 3 h (https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5). Figure 7a shows the average vertical profile of AE obtained by MAX-DOAS for the whole observational period and the comparison with lidar extinction profiles. It should be noted that the MAX-DOAS AE profiles, retrieved by the optimal estimation method (OEM), are the true extinction profiles weighted by so-called averaging kernel (AK) matrix [65]. The AK matrix quantifies the sensitivity of the retrieved profile to the true atmospheric profile. For comparison, we also show the lidar AE profile with AK weighting in Figure 7a. It is clear that the AK weighting smooths the lidar measurement. As a whole, the weighted lidar extinction profile presents a relatively good agreement with MAX-DOAS. Both of them found the lifted AE layers, indicating aerosol accumulation, secondary formation or long-range transport at higher altitudes [50]. The qualitative comparisons at a suburban background site over Athens, Greece, also showed an encouraging agreement in aerosol layer shape between MAX-DOAS and lidar [39]. However, there are still some differences with respect to the vertical distribution structure derived by the two measurement methods, such as the height of the lifted layer, the absolute AE level, and the AE vertical gradient. The differences of the average AE profiles are at least partly impacted by three aspects. Firstly, for the extraction of the AE profiles from the commercial EZ aerosol lidar a default lidar ratio is used, which can be substantially different from the truth due to the variation of aerosol type. In consequence, the uncertainties of the absolute values of the AE profile might reach 20% [39,63,66]. Secondly, it should be noted that in this study no scaling factor for the O 4 dSCDs was applied during the MAX-DOAS inversion. There is still no consensus on the need of such a scaling factor (e.g., [67]), and in our study we did not find it necessary to apply such a scaling factor. Nevertheless, it might be worth mentioning that the application of a scaling factor (e.g., 0.8 like in Beijing; [35]) would be applied, the derived AE values would be systematically increased, leading to a better agreement between the two observation methods. Finally, since clouds were not explicitly filtered, remaining cloud contamination might also have an impact on the MAX-DOAS results.

Average Vertical Profile of Aerosol Extinction and Comparison with Lidar
For hourly AE profiles, there is still a consistency between MAX-DOAS and lidar with a correlation coefficient of R = 0.63, although they are different at the high level of AE > 2 km −1 (Figure 7b). Based on the correlation of hourly AE profiles between MAX-DOAS and lidar, we found that higher correlation appears when the AOD from MAX-DOAS and RH are higher (Figure 7c,d). At present, we cannot explain why there are such differences in the correlation between the two methods under such different environmental conditions. Anyhow, in contrast to the limitations of lidar, blind region in particular, MAX-DOAS can serve as a supplement to observe the AE profiles in the lower troposphere [40].
Based on the correlation of hourly AE profiles between MAX-DOAS and lidar, we found that higher correlation appears when the AOD from MAX-DOAS and RH are higher (Figure 7c,d). At present, we cannot explain why there are such differences in the correlation between the two methods under such different environmental conditions. Anyhow, in contrast to the limitations of lidar, blind region in particular, MAX-DOAS can serve as a supplement to observe the AE profiles in the lower troposphere [40].

Conclusions
Ground-based MAX-DOAS and lidar measurements were performed during the VOGA field campaign in summer (13 June-20 August) 2014 at Raoyang (115°44′ E, 38°14′ N), a rural site in the North China Plain. The aerosol extinction (AE) vertical profiles in the lower troposphere were retrieved through QDOAS software (http://uv-vis.aeronomie.be/software/QDOAS/) spectral analysis and PriAM profile inversion. We analyzed the time series and diurnal variation of AE profiles, near-surface AE, and AODs during the field campaign. We also compared the AE profile retrieved by MAX-DOAS with that measured by lidar. The main findings are summarized below.
1. The average AOD and near-surface AE were 0.51 ± 0.26 and 0.33 ± 0.18 km −1 during the effective observation period, respectively. The time series of AODs and near-surface AEs presented similar variation trends, with several high value events occurring simultaneously. From the time series of AE profile, elevated AE layers were found to occur frequently. Both AODs and near-surface AEs were positively correlated with the relative humidity (correlation coefficient R = 0.32, 0.42, respectively). 2. The AOD and near-surface AE roses show that there are significant differences for averages of AODs and near-surface AEs in 16 wind sectors, with higher AOD or AE means often occurring in the upstream directions of cities. The weighted AOD and AE indicated that pollutant transport from the northeast and south contributes significantly to the AE level at the Raoyang station. The correlation coefficient between AODs and near-surface AEs depends on the wind direction. The low correlation in NE sector implies heterogeneous distribution of AE in the vertical direction. Therefore, the wind field and spatio-temporal distribution of emission sources significantly impact the near-surface AE, AOD, and AE profile. 3. The average diurnal variations of AE profile, AODs and near-surface AE were significantly correlated, due to synchronized effects of the source emission and meteorological condition.

Conclusions
Ground-based MAX-DOAS and lidar measurements were performed during the VOGA field campaign in summer (13 June-20 August) 2014 at Raoyang (115 • 44 E, 38 • 14 N), a rural site in the North China Plain. The aerosol extinction (AE) vertical profiles in the lower troposphere were retrieved through QDOAS software (http://uv-vis.aeronomie.be/software/QDOAS/) spectral analysis and PriAM profile inversion. We analyzed the time series and diurnal variation of AE profiles, near-surface AE, and AODs during the field campaign. We also compared the AE profile retrieved by MAX-DOAS with that measured by lidar. The main findings are summarized below.

1.
The average AOD and near-surface AE were 0.51 ± 0.26 and 0.33 ± 0.18 km −1 during the effective observation period, respectively. The time series of AODs and near-surface AEs presented similar variation trends, with several high value events occurring simultaneously. From the time series of AE profile, elevated AE layers were found to occur frequently. Both AODs and near-surface AEs were positively correlated with the relative humidity (correlation coefficient R = 0.32, 0.42, respectively).

2.
The AOD and near-surface AE roses show that there are significant differences for averages of AODs and near-surface AEs in 16 wind sectors, with higher AOD or AE means often occurring in