Validation of TROPOMI tropospheric NO2 columns using dual-scan MAX-DOAS measurements in Uccle, Brussels

Ground-based Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) measurements of aerosols and tropospheric nitrogen dioxide (NO2) were carried out in Uccle (50.8 N, 4.35 E) Brussels, during one year from March 2018 until March 2019. The instrument was operated in both UV and visible (Vis) wavelength ranges in a dual-scan configuration consisting of two sub-modes: (1) an elevation scan in a fixed viewing azimuthal direction (the so-called main azimuthal 15 direction) pointing to the Northeast and (2) an azimuthal scan in a fixed low elevation angle (2). By applying a vertical profile inversion algorithm in the main azimuthal direction and a parameterization technique in the other azimuthal directions, nearsurface NO2 concentrations (VMRs) and vertical column densities (VCDs) were retrieved in ten different azimuthal directions. The dual-scan MAX-DOAS dataset allows partly resolving the horizontal distribution of NO2 around the measurement site and studying its seasonal variations. Furthermore, we show that measuring the tropospheric NO2 VCDs in different azimuthal 20 directions improves the spatial colocation with measurements from the Sentinel-5 Precursor (S5P), leading to a reduction of the spread in validation results. By using NO2 vertical profile information derived from the MAX-DOAS measurements, we also resolve a systematic underestimation in S5P NO2 data due to the use of inadequate a-priori NO2 profile shape data in the satellite retrieval.

resolution of 0.4 nm. To block the visible light and to reduce the stray-light in the UV wavelength region, a band pass filter (U-340 Hoya) is used. The output of the UV spectrometer is connected to a back-illuminated UV-enhanced Charge Coupled Device (CCD) detector system (Princeton Instrument Pixis 2K). The Vis spectrometer from Horiba (model Micro HR) has a spectral resolution of 0.7 nm and is also mounted on a back-illuminated CCD system (Princeton Instrument Pixis 100). Both CCD detectors are cooled at 235 K (using multi-stage Peltier system). The overall spectrometric unit is thermally stabilized to 5 better than 1 o C.
To control the data acquisition, two computers are used. One records spectra coming from the Vis spectrometer and controls the sun tracker while the second, synchronized with the first one, records the spectra from the UV spectrometer.
In order to measure in dual-scan (elevation + azimuthal) viewing mode, the initial operation mode (elevation scanning in one azimuthal direction) was modified. From March 2018, the instrument was operated in two modes: (1) a vertical scan mode 10 covering nine different elevation angles in one fixed (standard) azimuthal direction (35.5 o with respect to the North in the eastward direction) and (2) a horizontal scan mode covering 9 different azimuthal directions at a fixed elevation angle of 2 o above horizon (Fig. 1). As can be seen in Table 1 and Fig. 9, several configurations were tested in order to select the best combination of horizontal and vertical viewing directions, which is a trade-off between the acquisition time and the horizontal representativeness. Since the NO2 emission sources are located towards the North, more azimuthal directions are selected in 15 this direction. With an integration time of 60 s for each measured spectrum, the total scan duration (azimuthal + elevation viewing modes) ranges between 20 to 30 minutes, depending on the configuration. Each azimuthal direction was qualitychecked by performing horizon scans as during the CINDI-2 campaign (Donner et al., 2019) in order to ensure that obstacles, like trees and buildings, are not present in the different lines of sight.

DOAS analysis 20
The spectra measured in both sub-modes are analyzed using the QDOAS spectral fitting software developed at BIRA-IASB (Fayt et al., 2011) for the retrieval of atmospheric trace gas abundances in the UV, Vis and near infrared spectral ranges. The DOAS technique consists in a separation between narrow absorption features characteristic of molecular species and a spectral background resulting mainly from Mie and Rayleigh scattering and instrumental effects (Platt and Stutz, 2008). Its primary product is the differential slant column density (dSCDs), which represents the light-path integrated trace gas concentration in 25 a measured spectrum relative to the amount of the same absorber in a reference spectrum. In the present case, daily noon zenith spectra are used as reference.
NO2 dSCDs are retrieved in both Vis and UV ranges according to settings defined during the CINDI-2 campaign (see Tables   2 and 3; as well as Kreher et al., 2019). For retrievals in the Vis spectral range, we use the 425 -490 nm fitting interval, while UV retrievals are performed in the 338-370 nm spectral range. 30 https://doi.org /10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License.

Aerosol and OEM-based profile retrievals
Aerosol extinction coefficient and NO2 vertical profiles are retrieved for each MAX-DOAS elevation scan in the main azimuthal direction by applying the Mexican MAX-DOAS Fit (MMF;Friedrich et al., 2019) inversion algorithm to the corresponding measured O4 and NO2 dSCDs. The inversion is performed in two successive steps. First an aerosol extinction 5 profile is retrieved using O4 measurements according to the principles described in Frieß et al. (2006). This aerosol profile is then used as an input for the radiative transfer calculations needed to invert the NO2 vertical profile.
If sufficient aerosols are present in the lower troposphere (boundar y layer), the measured dSCD at two low elevation angles (in the present study, 1 o and 2 o ) are equal. In this case, the concentration of an absorber close to the surface (e.g. NO2) can be considered as box-average near-surface concentration c ̅ and is related to the dSCD as follows (Sinreich et al., 2013): where, dSCD is the differential slant column density of the absorber in molec cm -2 and c ̅ its mean concentration in molec cm -5 3 along the differential effective path lengths (dLeff) in cm.
The unknown variable in Eq. (1) is the differential effective path length of the measurement. The absorption of the oxygen collisional dimer (O4) can be used as a tracer for the light path distribution (Wagner et al., 2004). The concentration of O4 is proportional to the square of the concentration of molecular oxygen O2 which can be accurately determined. Variations in the O4 dSCD are therefore directly related to changes in the state of the atmosphere and changes in the measurement geometry. 10 For each measurement, the differential effective path lengths can be calculated as a ratio of the measured O4 dSCDs to the typical O4 concentration at the altitude of the instrument cO4 (instr): As mentioned above, the profile shape of O4 is an exponentially-decreasing profile with altitude. In contrast, the NO2 profile has a different shape, as this trace gas is emitted close to the surface. Therefore, the dLeff(O4) cannot be used directly in Eq. 15 (1) in order to estimate the NO 2 near-surface VMR. As indicated by Sinreich et al. (2013), Wang et al. (2014), andOrtega et al. (2015), the direct use of the dLeff derived from O4 measurements introduces systematic errors in the near-surface VMRNO2.
In general, dL eff will be overestimated leading to an underestimation of the VMR NO2 by up to a factor of three (Sinreich et al., 2013).
The introduction of a unit less correction factor (fc) accounting for differences between the O4 and NO2 profile shapes is 20 therefore necessary. fc connects the two different dLeff as follows: Taking this relation into account and combining with Eq. (1), (2) and (3), the near-surface concentration of NO2 can be expressed as: Previous studies (Ortega et al., 2015;Sinreich et al., 2013;Wang et al., 2014;Seyler et al., 2019) have highlighted the importance of properly estimating the correction factors, especially in polluted conditions, as those observed in Brussels. The NO2 concentration corresponds to the ratio of dSCDNO2 to the light path length dLeff (NO2). Assuming that the NO2 vertical distribution can be approximated by a box profile of height equal to MLH, one can also express it as the ratio between the VCDNO2 and the Mixing Layer Height (MLH): Combining Eq. (3) and (5) and expressing the dSCD as the product of the VCD and a differential air mass factor (dAMF), it comes for fc: where, MLHNO2 is the mixing layer height of NO2, dAMFNO2, and dAMFO4 are the NO2 and O4 differential air mass factor and 5 VCDO4 is the typical vertical column density of O4 above the instrument. The dAMF of a trace gas expresses the light path enhancement with respect to the vertical path through the atmosphere. The correction factor depends on the aerosol load in the atmosphere, the solar zenith angle (SZA), the relative solar azimuth angle (RSAA), the MLH of the trace gas and the vertical distribution of the aerosols inside the MLH during the measurement.
To estimate MLH, we use the NO2 vertical profile information derived in the main azimuthal direction. Assuming 10 homogeneous mixing in the mixing layer, MLH is derived from the ratio of VCDNO2 to the near-surface concentration of NO2.
Moreover, during one MAX-DOAS scan, the vertical extent of the trace gas profile is considered homogeneous around the measurement site and the MLH values in the main azimuthal direction can also be applied to the other azimuthal directions.
Despite its simplicity, this approach provides robust estimates of the MLH, consistent with local ceilometer observations (for more details see Section 2.3.4). As indicated by Sinreich et al. (2013) and Ortega et al. (2015), the use of a realistic MLH daily 15 variation is a crucial element in the parameterization method. Our approach represents an improvement over the more empirical approach used in previous studies.
The dAMF depends on the geometry (SZA, RSAA and elevation angle) as well as the aerosol and trace gas concentration profiles. For its calculation, we used VLIDORT (Spurr, 2006) version 2.7. The dAMF of O4 and NO2 were estimated for eight different MLH scenarios (250 m -2000 m range) and for the Vis and UV wavelengths, separately. In these scenarios, the 20 aerosol and NO2 a priori profiles are specified as box profiles with a constant concentration from the surface to the MLH. The AOD vary from 0.30 to 0.60, the asymmetry parameter is set to 0.68 and the SSA to 0.92. The resulting correction factors are represented in the upper panels of Fig. 2 as a function of RSAA and for different values of the SZA (for an AOD equal to 0.30). They strongly depend on the RSAA and the MLH. For low RSAA and thick MLH fc reaches a maximum, while a minimum is obtained at high RSAA for a thin MLH. When investigating the dependency of fc on the SZA for different AOD 25 and RSAA values (lower panels in Fig. 2), we observe that it becomes highly dependent on AOD for low RSAA and SZA values close to 50-60°, indicating the limitations of the parameterization technique in those conditions.
The correction factor fc provides information about the state of the atmosphere, such that each measurement can be classified into one of the following three regimes. For fc equal or close to one, the effective light paths of O4 and NO2 are equal (Eq. 3), which means that there is moderate to high aerosol load during the measurement. In contrast, when fc is significantly smaller than one, the measurement is done under aerosol free conditions or thin MLH. Finally, fc can take values larger than one for cases of high SZA and low RSAA (Fig. 2), which are special conditions in which the parameterization method becomes highly dependent on the AOD. Such cases are highly uncertain and we exclude them from further analysis.
To estimate fc (Eq. 6) for every MAX-DOAS measurements in the Vis and UV wavelengths, O4 and NO2 dAMFs were tabulated for eight different values of MLH (AOD set to 0.3) and for a suitable range of RSAA and SZA values. Using this 5 look-up table, O4 and NO2 dAMFs are interpolated at the SZA, RSAA and MLH of each measurement. The near-surface VMR is then obtained by dividing the concentration of the trace gas (Eq. 4) by the air number density (nair). For the calculation of nair, the pressure and temperature profiles were taken from the AFGL 1976 Standard Atmosphere (Anderson et al., 1986) and are the same as used in Section 2.3.1. Furthermore, the VCD is estimated from the product of the near-surface concentration with the MLH. 10 For the analysis, only measurements at SZA smaller than 80 o were selected. As presented in Sinreich et al. (2013), the method is independent of the actual aerosol load, as long as a sufficient amount of aerosols is present in the troposphere (AOD>0.2).
However, it depends slightly on the aerosol layer height. In order to select measurements where the near-surface layer can be parameterized as a box profile (i.e. with homogeneous concentration inside the layer), two conditions should be satisfied. First, the scattering events corresponding to the lowest two elevation angles should occur in a comparable distance and secondly, 15 those scattering events should happen inside the NO2 layer, which can then be considered as homogeneous and therefore, parameterized as a box profile. In order to ensure that those conditions were satisfied, only scans for which the differences between O4 and NO2 dSCDs in the lowest two elevation angles were smaller than 10 44 molec 2 cm -5 and 10 16 molec cm -2 , respectively, were selected. Furthermore, when the O4 dSCD and, consequently the dLeff(O4), is negative or too small because of bad weather conditions, 20 the VMR can become unphysical (negative or close to zero). In consequence, measurements with a value of dLeff (NO2) smaller than 5 km (for both Vis and UV) are excluded from the study. An upper limit of 30 km is also adopted to exclude numerical outliers.
To estimate uncertainties on the retrieved NO2 VMR and VCD using the parameterization method, two main error sources are 25 considered: (1) uncertainties on O4 and NO2 dSCDs, and (2) uncertainties related to the estimation of the correction factors.
Based on Eq. (4) and using a standard error propagation method, the overall uncertainty on the near-surface VMR is given by: Regarding the σdSCD, Bösch et al. (2018) and Kreher et al. (2019) indicated that, in urban or sub-urban polluted conditions, the DOAS fit uncertainty of both O4 and NO2 significantly underestimates the actual dSCD uncertainty, which is mostly driven by atmospheric variability, spatial and temporal fluctuations in the O4 and NO2 fields. In the present study, based on val ues derived during the CINDI-2 campaign, conservative values of 3.5 x 10 15 molec cm -2 (NO 2 ) and 1.5 x 10 42 molec2 cm -5 (O 4 ) 5 were used for the dSCD uncertainties in the UV and Vis ranges. This represents an error of up to 5 -6 % on the O4 dSCD and 4 -5 % on the NO2 dSCD in both the Vis and UV ranges.
The second important error source is related to the correction factors, which depend on air mass factor and MLHNO2 calculations (Eq. 9). The uncertainty related to MLHNO2 can be estimated as a combination of two terms: the total uncertainty of the NO2 near-surface VMR and the NO2 VCD derived by the MMF inversion algorithm. In the Vis range, the error related to MLHNO2 10 is about 4 % and 5 % in the UV range. In order to estimate the uncertainty related to the air mass factor calculation, sensitivity tests about the input parameters in the RTM simulation were performed. In these sensitivity tests, the main inputs in the RTM calculations, such as the height of the assumed trace-gas profile and the aerosol properties, are modified. The corresponding dAMF variability is attributed to the uncertainty of the dAMF calculation. The error related to the dAMFNO2 estimation is about 2 % and 6 % in the UV and Vis ranges, respectively. The error related to dAMFO4 is larger, reaching 18 % and 13 % in 15 the Vis and UV ranges, respectively. Combining all error sources, the total uncertainties on the parameterized NO2 are about 14 % and 20 % for the near-surface VMR and VCD in the visible range, while the corresponding errors in the UV are 7 % and 13 %. A summary of the above-mentioned error sources on the parameterized NO2 is presented in Table 5.

Horizontal distribution of NO2
A qualitative information about the horizontal distribution of NO2 along each azimuthal direction can be obtained by 20 considering how the dSCDs derived in the Vis and UV ranges depend on the retrieved horizontal light path lengths (dLeff (NO2)) (Ortega et al., 2015;Seyler et al., 2019). Indeed, dLeff (NO2) values depend strongly on scattering and atmospheric conditions and, since scattering processes are more pronounced at shorter wavelengths, dLeff (NO2) is shorter in the UV than in the Vis (dLeff(NO2 Vis) > dLeff(NO2 UV)).
During one measurement, four useful pieces of information can be used in order to estimate the distance of the NO2 25 concentration peak with respect to the instrument: the measured NO2 near-surface VMR and the dLeff (NO2) in the Vis and UV ranges. Three different cases can be distinguished: (1) VMRNO2 (Vis) > VMRNO2 (UV). In this case, the NO2 peak (dVMRNO2 = (dSCDVis -dSCDUV)/dLeff(NO2 UV)nair) is located further away from the measurement site and approximately, at the distance dLeff(NO2 UV) < dL < dLeff(NO2 Vis). 30 (2) VMR NO2 (Vis) < VMR NO2 (UV). Here, the NO 2 peak (dVMR NO2 = VMR NO2 (UV)) is located close to the MAX-DOAS instrument in a distance equal to dLeff(NO2 UV).
This information is further exploited in Section 4.1, where the seasonal variation of the dual-scan MAX-DOAS measurements is presented.

Validation of the parameterization method 5
To validate the dual-scan parameterization method used in this study, two different approaches are adopted. First, the MLH, which is used in the calculation of the correction factors, is compared with MLH measurements using a co-located ceilometer.
Second, the NO2 near-surface VMRs and VCDs calculated by the parameterization technique in the main azimuthal angle (35.5 o with respect to the North) is compared to corresponding results obtained with the MMF inversion algorithm.
To validate the MLH estimations, we use a co-located Vaisala CL51 ALC ceilometer operated by RMI. With this instrument, 10 the MLH is retrieved according to an algorithm based on the direct analysis of backscatter gradient and variance (Haij at al., 2007;Haeffelin et al., 2016;Menut et al., 1999). (R=0.84), however the slope value (s=0.89) indicates that MLHMAXDOAS tend to slightly overestimate MLHCEIL, the difference between both MLH values being generally smaller than 500 m. We note that the offset is larger during spring and summer.
Since the ceilometer relies on the aerosol vertical distribution to derive MLH, and the MAX-DOAS uses the NO2 vertical profile, differences in the absolute height values are expected. The NO2 tropospheric columns, near-surface concentrations and atmospheric lifetime show a strong seasonality with maximum values during cold months. During warm months, the solar 20 heating causes warmer air to rise. The typical time for air to rise from the surface to the top of the MLH is about 1 hr or less (Stull, 1988). During spring and summer, the differences between the ceilometer and MAX-DOAS MLH could be explained as follows: since the NO2 lifetime is greater than 1 hr (Ehhalt et al., 1992) and in a combination with air uplifting activity (only present during warm seasons), NO2 could be transported to higher heights than the ones estimated by the ceilometer.
The second approach to validate the parameterization technique consists of comparing the retrieved NO2 near-surface VMR 25 and VCD to the near-surface VMR (0 -200 m) and VCD derived by using the MMF inversion algorithm. The only variable derived from MMF calculations and used in the parameterization technique is the MLH. As we can see in Fig. 5 and Fig. 6, results from both methods are highly correlated. The few cases where the two methods differ more substantially correspond to low dAMFO4 values, which are associated to larger uncertainties. https://doi.org/10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License.

Tropospheric NO2 measure ments from TROPOMI
Flying on board of the S5P satellite platform, the TROPOMI instrument is a passive grating imaging spectrometer covering the UV-Visible (270 -500 nm), near-infrared (710 -770 nm), and shortwave infrared (2314 -2382 nm) spectral ranges (Veefkind et al., 2011). TROPOMI measures the solar back-scattered earthshine radiance in a push-broom configuration. With a full swath width as wide as 2600 km, TROPOMI provides daily global coverage with a true-nadir pixel size of 7 x 3.5 km 2 5 in the UV/ Vis/ Near-Infrared bands. Since 06 August 2019, the TROPOMI spatial resolution is even higher with a pixel size of 5.5 x 3.5 km 2 .
Developed at KNMI ( Van Geffen et al., 2019), the tropospheric NO2 algorithm uses a retrieval-assimilation-modelling system based on the 3-D global TM5 chemistry transport model. This retrieval scheme consists of three main steps. First, the total NO2 slant column density is retrieved from Level-1b radiance and irradiance spectra by applying the DOAS method. In a 10 second step, the total NO2 slant column density is separated into its stratospheric and tropospheric components by using the TM5-based data assimilation system. Finally, the tropospheric and stratospheric NO2 slant column densities are converted to vertical column densities, by applying altitude-dependent AMFs. The AMF look-up tables are calculated on a 1 o x 1 o latitudelongitude grid using NO2 vertical profiles from the TM5-MP model (Williams et al., 2017). They depend on the satellite geometry, terrain height, cloud fraction, cloud height, and surface albedo. 15 The present study is based on RPRO and OFFL datasets of the TROPOMI L2 tropospheric NO2 column product (see Table 6 for the corresponding versions). To focus on high quality measurements, only pixels characterized by a quality assurance value larger than 0.75 are used, so that pixels covered by clouds, snow or ice and erroneous retrievals are excluded from the analysis.
The TROPOMI overpass over Brussels is around 13:30 LT. Figure 7 illustrates a typical comparison case. Superimposed on TROPOMI ground-pixels as measured above Brussels on 06 June 2018, one can distinguish the different azimuthal viewing 20 directions sampled by the Uccle dual-scan MAX-DOAS system. As can be seen, multiple pixels are coincident with one MAX-DOAS azimuthal direction, showing the high spatial resolution of TROPOMI as well as the challenges concerning its validation.

Seasonal variation of dual-scan MAX-DOAS measure ments 25
Box and whisker plots of MAX-DOAS horizontal effective light paths (dLeff (NO2), see Eq. 3) determined in each season for all the viewing azimuthal directions are presented in Fig. 8 for the Vis and UV wavelength ranges. As can be seen, the dLeff (NO2) shows maximum median values during summer, and a minimum during winter, for both wavelength ranges. The seasonality of dLeff (NO2) is related to the seasonal variation of the aerosol content in the troposphere. For high aerosol load conditions, the light path tends to become shorter due to increased scattering. In the Vis range, dLeff (NO2) can reach values of 30 up to 19 km during winter with a mean value of 10 km, while in the UV, the maximum value is around 12 km with a mean https://doi.org/10.5194/amt-2020-33 Preprint.  (NO2)) are generally larger in the Vis than in the UV, because of the more pronounced Rayleigh scattering at UV wavelengths.
In Fig. 9, the seasonal variation of the MAX-DOAS near-surface NO2 VMR is presented for both Vis and UV channels in each azimuthal direction at 11:00 UTC. The length of the lines corresponds to the seasonally-averaged dLeff (NO2). As mentioned 5 above, dLeff (NO2) is longer in the Vis than in the UV range, which leads to a more extended spatial sensitivity in the Vis than in UV. As explained in Section 2.3.3, the relationship between NO2 VMRs and dLeff (NO2)  The near-surface NO2 VMR has a clear seasonal cycle, with a maximum during winter due to higher emissions, lower temperature (and thus longer NO2 lifetime) and shallower MLH, and a minimum in spring and summer. Moreover, the spatial distribution of NO2 concentrations around Uccle shows a seasonal dependence. It should be noted that the main emission sources are located in the North and West part of the city and are associated mainly with the motorway around Brussels (the so-called Ring), the National Airport in Zaventem, and the Drogenbos power plant, the latter being located to the West of 15 Uccle (Tack et al., 2017). In the absence of transport by the wind and given the fact that NO 2 has a shorter lifetime in the MLH (Beirle et al., 2011), the higher NO2 concentrations should appear at the location of main emission sources. As can be seen in Fig. 9, this is not the case during all seasons, due to the influence of seasonal wind patterns. During winter, higher NO2 concentrations are retrieved mainly in the North (N) and Northeast (NE) directions. The fact that the NO2 concentration in the NE direction is higher in the Vis than in the UV, suggests that the NO2 peak is located away from Uccle and closer to the 20 Brussels National Airport. On the other hand, in the N direction, the NO2 concentrations are lower in the Vis than in the UV.
This can be associated with higher anthropogenic activity in the city center of Brussels. During spring and summer, the observed NO2 VMRs are the lowest of the March 2018-March 2019 period. For spring, the maximum concentrations are measured away to the measurement site (Vis) in the South (S) and NW direction. It is worth mentioning that in the East (E) direction, the Vis and UV measurements have almost the same concentrations, indicating that the NO2 field is homogeneous 25 in those areas. During summer, the maximum NO2 VMRs are retrieved in the Vis range and in the NE and NW directions, suggesting that the sources are mainly located away from the measurement site, possibly linked to the airport and city-center activity. One observes that in the S (in the direction of a large forested area), the retrieved concentrations are very low, while they are substantially higher in the NW and NE. Finally, during autumn, higher values are observed away from Uccle in the N direction, corresponding to sources located away from the measurement site, mostly traffic-related. 30 As already noted, the retrieved NO2 VCDs can be influenced by the wind direction. In Fig. 10, MAX-DOAS NO2 VCDs are represented as a function of the wind direction during the MAX-DOAS observations. The wind direction is measured by the BIRA-IASB meteorological station in Uccle. Generally, when the wind is blowing from the NE and SE direction, higher NO 2 columns are retrieved. During winter and autumn, the NO2 VCDs, which are retrieved under different wind directions, differ https://doi.org/10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License. significantly compared to summer and spring. We conclude that emission sources located away from the measurement site influence the measured NO2 concentration levels when wind is blowing in the direction of the site.

Comparison of MAX-DOAS and in-situ measure ments
The in-situ telemetric air quality network (Bruxelles Environne ment/Leefmilieu Brussel) of the Brussels region is used for

Validation of TROPOMI tropospheric NO2 columns
To validate the TROPOMI tropospheric NO2 columns, we adopted three successive approaches: 10 1) A first comparison is performed by selecting only MAX-DOAS data in the main azimuthal direction (35.5° w.r.t N) and the TROPOMI value from the closest pixel located in the same direction as the MAX-DOAS measurement.
2) To improve the spatial coincidence between MAX-DOAS and TROPOMI observations, a second comparison is performed by using the dual-scan MAX-DOAS observations: measurements in every MAX-DOAS azimuthal direction are compared with a weighted average of TROPOMI columns as measured in coincident pixels with the 15 weighting being determined by the MAX-DOAS horizontal segment crossing every pixel.
3) The impact of possible systematic uncertainties in the satellite retrieval (in particular the a-priori profile shape) is investigated.
In order to increase the number of co-location pairs, we compare both UV and Vis MAX-DOAS measurements with TROPOMI. It should be emphasized that UV and Vis MAX-DOAS VCDs correspond to different dLeff (NO2) values (see 20 Fig. 8 and Section 2.3.3) and consequently, different sampling of TROPOMI pixels. In the following sections, the regression analysis parameters (correlation coefficient and slope value) refer to both UV and Vis MAX-DOAS measurements together.

Validation based on one MAX-DOAS azimuthal direction measurements
In this first approach, the MAX-DOAS tropospheric NO2 VCDs, derived in the main azimuthal direction by applying the MMF algorithm, are compared to TROPOMI observations in the same direction as the MAX-DOAS measurement. We select the 25 closest TROPOMI pixel that intercept the MAX-DOAS line-of-sight within a radius of 20 km around Uccle. This approach has generally been used in previous satellite validation studies based on MAX-DOAS observations (e.g., Chen et al., 2009;Irie et al., 2008;Ma et al., 2013). It is adopted for reference against other comparison strategies that make use of more than one azimuthal MAX-DOAS measurement (see section 4.3.2).
We compare TROPOMI daily measurements with MAX-DOAS NO2 VCDs averaged around (± 1 hr) of the TROPOMI 30 overpass time. A first comparison plot is presented in Fig. 12, where the time series of the TROPOMI tropospheric NO2 VCD is displayed together with the Vis MAX-DOAS measurements. All TROPOMI and MAX-DOAS data points presented in Fig. https://doi.org/10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License.
12 satisfy the quality check requirements for both datasets (see Section 2. 3.1 and 3). The MAX-DOAS error bars represent the standard deviation of the mean values (± 1 hr), while the TROPOMI bars are equal to the tropospheric column error of the pixel. Results show that MAX-DOAS measurements have a larger variability than corresponding TROPOMI observations. In addition, TROPOMI tropospheric NO2 columns are systematically lower than co-located MAX-DOAS data. These results indicate that the discrepancy between TROPOMI and MAX-DOAS measurements is significant during all seasons and particularly marked during winter and autumn. A possible explanation could be due to differences in the air masses 15 probed by the two instruments. The use of only one satellite pixel, even if its direction with respect to the MAX-DOAS line of sight is taken into account, is not necessarily the most appropriate comparison method. One azimuthal MAX-DOAS measurement samples air masses along a light path of several kilometers in a fixed direction, which corresponds to more than one TROPOMI pixel, as outlined in Fig. 7. One expects this horizontal sampling effect to be more marked in winter and fall, given the larger NO2 concentration gradients observed during these seasons compared to the other ones (see Section 4.1 and 20 Fig. 9).

Validation based on dual-scan MAX-DOAS measurements
In a second step, we compare TROPOMI tropospheric NO2 columns with the dual-scan parameterized MAX-DOAS NO2 VCDs. Two improvements are introduced: (1) the use of more than one MAX-DOAS azimuthal direction and (2) a better spatial selection of the TROPOMI pixels accounting for the MAX-DOAS horizontal sensitivity (dLeff (NO2)). Only satellite 25 pixels located along the segments of length dLeff (NO2) in the different MAX-DOAS azimuthal directions and timely coincident dual-scan MAX-DOAS observations (TROPOMI overpass time ± 1 hr) are selected. MAX-DOAS NO2 VCDs in every MAX-DOAS azimuthal direction are compared to a weighted average of TROPOMI columns from the different pixels that are crossed by the corresponding MAX-DOAS horizontal line of sight segment. The weight of a given pixel is derived from the length of the segment portion that crosses the pixel. We can use Fig. 7 as a simplified scheme to show two important aspects 30 of this comparison: (1) every MAX-DOAS azimuthal line-of-sight is representative for a segment section that extends from the instrument to a distance equal to dLeff (NO2) and (2), dLeff (NO2) in one azimuthal direction can be separated into different portions that cross each of the selected satellite pixels. https://doi.org/10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License. Fig. 14 show that the agreement between TROPOMI and MAX-DOAS datasets is significantly improved, especially in terms of correlation (R in the 0.65-0.82 range). Owing to the improved spatial coincidence associated to the use of dual-scan MAX-DOAS data and the better spatial coincident criterion between TROPOMI and MAX-DOAS data, the scatter in the data points is also substantially reduced during all seasons and especially in winter. Another interesting feature is the improvement of the slope values, observed in all seasons (slopes in the 0.41-0.71 range). During seasons with a more 5 homogeneous NO2 field, the improvement of the slope values is less pronounced than during seasons, like winter and autumn, where the NO2 field can be highly inhomogeneous. During spring, the slope value is reduced despite the better correlation.

Investigation of systematic uncertainties in TROPOMI NO2 retrievals
To identify the origin of the persisting underestimation of TROPOMI NO2 measurements, we investigated the most relevant 10 sources of uncertainties in the satellite retrievals. Boersma et al. (2004) presented a thorough analysis of satellite tropospheric NO2 column retrieval uncertainties. Main error sources are related to the spectral fitting (dominated by measurement noise), the estimation of the stratospheric NO2 column and knowledge of the main ancillary parameters used for the AMF calculation, i.e. surface albedo, cloud fraction and cloud top height, aerosols, and the a-priori NO2 profile shape. In the following sub-sections, we briefly discuss uncertainties related 15 to cloud, aerosol and surface albedo and afterwards, we investigate in more details the role of the a-priori NO2 profile.

Clouds and aerosols
Clouds can have a major impact on tropospheric NO 2 observations from space, because of their strong influence on the incoming solar radiation (Boersma et al., 2004;Koelemeijer et al., 2001). In the TROPOMI tropospheric NO2 retrieval algorithm, only cloud-free and weakly cloudy scenes are considered as valid measurements satisfying the recommended quality 20 assurance value (QA>= 0.75) (see Section 3). Although this quality flagging effectively minimizes uncertainties due to cl ouds on the NO 2 product, many selected scenes are still partially cloud-covered and affected by cloud-related errors. In the TROPOMI processor, clouds are characterized by using cloud fraction and cloud top height parameters, which are both derived from radiance observations in the O2 A-band. This cloud information is used as an input in a cloud-correction scheme applied to NO2 retrieval (van Geffen et al., 2019). Cloud-induced errors are complex and can lead to positive or negative biases on the 25 tropospheric NO2 column. As a result, cloud-induced errors are generally pseudo-random in nature. So except for specific cases (e.g. persisting contamination by heavy aerosol or cloud layers), cloud-related errors can hardly account for systematic biases in NO2 retrievals.
Like clouds, aerosols can affect the accuracy of tropospheric NO2 retrieval from space (Heckel et al., 2011;Leitão et al., 2010;McLinden et al., 2014). In the TROPOMI NO2 algorithm, aerosols are not explicitly treated which means that all AMF 30 calculations are performed for a Rayleigh atmosphere (clouds being treated as simple Lambertian reflectors). The impact of aerosols is however considered indirectly through the cloud correction algorithm, under the assumption that scattering aerosols https://doi.org /10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License. will tend to increase the cloud fraction. For non-absorbing aerosols of moderate optical thickness, like typically observed in Brussels, this simplified approach was shown to be effective in accounting for the impact of reflecting aerosols on tropospheric NO2 AMFs (Boersma et al., 2011).

Surface Albedo
Surface albedo is another parameter having a significant influence on satellite tropospheric NO2 AMFs. In the study of 5 Boersma et al. (2004), it was shown that the NO2 AMF sensitivity to albedo is large especially for albedos smaller than 0.2.
For albedo values between 0.0 and 0.2, which are common in the blue spectral range over land, a difference of 0.015 in the surface albedo can lead to a 12 % change of the tropospheric NO2 AMF. In order to estimate surface albedo uncertainties in the Uccle conditions, observation from the Airborne Prism Experiment (APEX) performed above Brussels during June 2015 (Tack et al., 2017) were compared with climatological values used in the TROPOMI operational algorithm. The difference 10 between these two independent estimates of the albedo were found to be small in average (smaller than 0.01) suggesting that albedo data used in the TROPOMI algorithm are well representative of the Brussels area in June.
However, we should keep in mind that the surface albedo values used in the TROPOMI retrieval have a spatial resolution of 13 x 24 km 2 (OMI spatial resolution). In reality, inside an area of 13 x 24 km 2 in an urban environment, we expect to have considerable differences between the albedo values at the scale of TROPOMI pixels. So even if the difference between APEX 15 and TROPOMI albedos was found to be small in average for the June 2015 flight, further investigation is needed to fully assess the impact of albedo uncertainties on the TROPOMI NO 2 product (F. Tack, personal communication, 2020).

A-priori NO2 profile shape
The TROPOMI NO2 retrieval algorithm NO2 vertical profiles specified by the TM5-MP model, for 34 vertical layers at the horizontal resolution of 1 o x 1 o in latitude-longitude (Williams et al., 2017). In comparison to the TROPOMI pixel size (3.5 x 20 7 km 2 ), the resolution of TM5-MP (approximately 100 x 100 km 2 ) is thus very coarse and cannot capture spatial gradients at the scale of a city like Brussels.
A way to test how uncertainties on the a-priori profile influence the TROPOMI NO2 VCDs in our observation conditions is to use vertical profiles derived from our MAX-DOAS measurements to recalculate the satellite NO2 VCDs. In order to perform this transformation, we use the Averaging Kernels (AK) information provided in the TROPOMI NO2 product. The AK 25 describes how the sensitivity of the retrieval depends on altitude. For satellite measurements of tropospheric species in the UV-Vis range, the AK generally increases with altitude in the first kilometers above the surface (Fig. 15). Since the NO2 profile has its maximum close to the surface, accurate knowledge of the NO2 vertical distribution in this altitude range is therefore critical for the calculation of the NO2 AMFs.
Using the formula described in Appendix A and daily-averaged MAX-DOAS concentration profiles derived in the main 30 azimuthal direction using the MMF algorithm, a modified version of the TROPOMI tropospheric NO2 column product was generated. Daily-averaged MAX-DOAS profiles were used to minimize the impact of instabilities frequently observed in individual profile retrievals, as illustrated in Fig. 16. https://doi.org/10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License. Figure 17 presents validation results corresponding to the recalculated TROPOMI NO2 columns. Comparing with results from Fig. 14, one can see that the change in NO2 profile shape has a strong impact on validation results, leading to a better agreement between satellite and ground-based data sets. During all seasons, the slopes of the linear regressions are largely improved (slopes in the 0.81-1.16 range), which essentially resolves the previously reported underestimation. In average, the recalculated TROPOMI columns increase by about 55 %. Looking more closely at Figs. 14 and 18, one can see that the application of 5 MAX-DOAS NO2 vertical profiles mostly improves the agreement for tropospheric NO2 columns larger than 1.0 10 16 molec cm -2 (for the cases with NO2 enhancement). One can also note that correlation coefficients are slightly degraded after application of the MAX-DOAS profiles, suggesting that the applied transformation introduces some more scatter in the comparison. Table 7 presents a detailed summary of all the regression analyses conducted.
In conclusion, the change of the a-priori profile in the TROPOMI retrieval has a significant impact on the agreement between

Conclusions
One year of S5P/ TROPOMI tropospheric NO2 columns recorded above Brussels were validated using dual-scan MAX-DOAS measurements. The MAX-DOAS instrument was installed in Uccle, a sub-urban site, located in the south of Brussels-Capital 15 Region. A standard acquisition scheme was implemented combining vertical scans in a fixed azimuthal direction (main azimuthal direction pointing to Brussels Airport) and horizontal scans in ten azimuth angles at a fixed elevation angle (2°).
OEM-based profile retrievals were performed in the main azimuthal direction and a parameterization technique, based on Sinreich et al. (2013) was applied in all the other azimuthal directions to retrieve dual-scan NO2 near-surface VMRs and VCDs.
An appropriate characterization of the MLH was obtained by using the vertical profile inversion results in the main azimuthal 20 direction.
The dual-scan parameterized NO2 VMRs and VCDs were validated using ancillary measurements. Three different comparisons were carried out: (1) the MAX-DOAS-based MLH values used in the parameterization were compared with measurements from a co-located ceilometer instrument, (2) the parameterized NO2 near-surface VMRs and VCDs retrieved in the main azimuthal direction were compared with the same quantities derived from OEM-based profiles, and (3) the dual-scan NO2 25 near-surface VMRs were compared with in-situ NO2 concentrations. A good overall agreement was found for both comparisons (UV and Vis datasets) during the whole year of measurements.
The seasonal variability of the NO2 VMR around the measurement site was investigated. As expected, higher NO2 concentrations are observed during winter due to larger emissions, a shallower MLH, and lower temperatures resulting in longer lifetimes. Wind speed and direction are also found to play a significant role on the distribution of NO2 around the site. 30 As the main emission sources are located to the north of Uccle, concentration peaks are associated with wind blowing mainly from the NE direction. The dual-scan MAX-DOAS retrievals were also compared to NO2 measurements from the in-situ air https://doi.org/10.5194/amt-2020-33 Preprint. Discussion started: 20 March 2020 c Author(s) 2020. CC BY 4.0 License. quality telemetric network of the Brussels region. For this comparison, in-situ stations were selected along the different MAX-DOAS azimuthal directions. Although the in-situ measurements show systematically larger values than those derived from the MAX-DOAS instrument, a good correlation is found between both data sets, especially for urban background sites under moderately polluted conditions.
In a second step, MAX-DOAS data were used to validate TROPOMI tropospheric NO2 measurements. Two different 5 approaches were used. First, the MAX-DOAS NO2 VCDs, derived by applying an OEM-based inversion algorithm in the main azimuthal direction, were compared with the closest TROPOMI pixel, located along the main MAX-DOAS pointing direction.
Results show a clear seasonal behavior and a tendency for satellite data to underestimate the MAX-DOAS tropospheric NO2 columns during all seasons. In the second approach, the dual-scan parameterized MAX-DOAS tropospheric NO2 columns and corresponding effective horizontal distances were used to define a wider sampling area around the measurement site for the 10 selection of the TROPOMI pixels. MAX-DOAS measurements in every azimuthal direction were compared to a weighted average of TROPOMI columns appropriately selected for optimal matching with MAX-DOAS observation directions and effective horizontal distances. Although dual-scan MAX-DOAS measurements lead to improved agreement with satellite data, a systematic underestimation of the TROPOMI tropospheric columns is still observed.
Further, a detailed investigation of the main ancillary parameters used for the AMF calculation in the TROPOMI tropospheric 15 NO 2 columns retrievals revealed that the a-priori NO 2 profile shape uncertainty has a large impact on the satellite measurements. Recalculating the TROPOMI columns using daily median MAX-DOAS profiles as a priori results in a much better agreement between satellite and MAX-DOAS data. This suggests that the use of more appropriate a priori profiles in the TROPOMI retrieval can improve substantially the accuracy of the satellite tropospheric NO2 data, especially in urban areas.
The improvement is however less clear during seasons characterized by highly variable NO2 fields and cloudy conditions. 20 In conclusion, our study shows that dual-scan MAX-DOAS measurements conducted in an urban area offer (1) the possibility to better characterize the spatial variability of short-lived pollutants like NO2, and (2) to improve the validation of satellite measurements in an urban environment. Moreover, the vertical profiling capability of MAX-DOAS measurements allows testing the suitability of the a priori profile shape information used in satellite retrievals. Based on our results, additional work could be done for improving future TROPOMI validation exercises. For instance, the horizontal resolution of the satellite a -25 priori profiles could be further improved by performing vertical MAX-DOAS scans during TROPOMI overpass in more than one azimuthal direction. Additionally, the satellite retrieval uncertainties related to clouds and aerosols could be also investigated into more details based on the azimuthal scan capability of MAX-DOAS instruments.
Where SCDSAT stands for the NO2 slant column density, and AMFSAT for the NO2 air mass factor as used in the operational algorithm, i.e. based on a-priori NO2 vertical profiles specified by the TM5 chemistry-transport model.
For optically thin conditions valid in the blue spectral range where NO2 is retrieved, the satellite AMF (AMFSAT) can be expressed as a linear sum of layer (or box) air mass factors (AMF i SAT ), weighted by the NO2 VCD contribution in each atmospheric layer: 5 where − represents the a-priori NO2 partial column in atmospheric layer i.
In addition, the vertical sensitivity of the NO2 retrieval is given by the averaging kernel (AK) according to: When comparing satellite and ground-based measurements (here from a MAX-DOAS instrument), it is a good practice to 10 smooth the ground-based reference profile using the satellite AK (see e.g. Eskes and Boersma, 2003): An alternative approach is to recalculate the satellite VCD using the MAX-DOAS profile as a-priori in the satellite retrieval.
Only the AMF is concerned and, similarly to equation (A2), we can write: CF developed the QDOAS software and guided ED in the DOAS analysis. QL provided the MLH dataset derived by the ceilometer. FF provided useful information about the in-situ dataset. MVR supervised the present work, provided general guidelines and valuable comments during the whole process of the manuscript preparation, revised and edited the manuscript. 5 All authors reviewed, discussed the results and commented on the manuscript.
Competing interests. The authors declare that they have no conflict of interest.    Total uncertainty on the VCD 20 13