Horizontal distribution of tropospheric NO 2 and aerosols derived by dual-scan multi-wavelength MAX-DOAS measurements in Uccle, Belgium

Dual-scan ground-based Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) measurements of 10 tropospheric nitrogen dioxide (NO 2 ) and aerosols were carried out in Uccle (50.8 o N, 4.35 o E; Brussels region, Belgium) for two years, from March 2018 to February 2020. The MAX-DOAS instrument was operating in both UV and Visible wavelength ranges in a dual-scan configuration consisting of two sub-modes: (1) an elevation scan in a fixed viewing azimuthal direction and (2) an azimuthal scan in a fixed low elevation angle (2 o ). By analyzing the O 4 and NO 2 dSCDs at six different wavelength intervals along every azimuthal direction and by applying a new Optimal-Estimation-based inversion approach, the horizontal 15 distribution of the NO 2 near-surface concentrations and vertical column densities (VCDs) and the aerosols near-surface extinction coefficient are retrieved along ten azimuthal directions. The retrieved horizontal NO 2 concentration profiles allow the identification of the main NO 2 hotspots in the Brussels area. Correlative comparisons of the retrieved horizontal NO 2 distribution were conducted with airborne, mobile, and satellite datasets, and overall a good agreement is found. The comparison with TROPOMI observations reveals that the characterization of the horizontal distribution of tropospheric NO 2 20 VCDs by ground-based measurements, the appropriate sampling of TROPOMI pixels, and an adequate a priori NO 2 profile shape in TROPOMI retrievals lead to a better consistency between satellite and ground-based datasets. fit quality and the reduction of the uncertainties for the UV retrievals. Sensitivity tests and comparisons with radiative transport simulations also show that the resulting O 4 and NO 2 dSCDs are consistent throughout the whole wavelength range covered by the six intervals. For NO 2 and O 3 , which are the strongest absorbers in all the fitting windows, a correction for the solar I 0 effect (Aliwell et al., 2002) is applied. A high-resolution solar atlas (Kurucz et al., 1984) is used for the wavelength calibration of the measured spectra. comparison MLH parameterization show 2 measurements priori profile

Aerosols with small diameter are estimated to cause millions of premature deaths per year globally because of their ability to penetrate deeply into the lungs (Khomenko et al., 2021). Aerosols influence the Earth's climate system by changing its 30 radiation budget by scattering and absorbing sunlight (Quaas et al., 2008). In the boundary layer of urban regions, the horizontal distribution of NO2 is highly heterogeneous given the fact that it is a short-lived species (Beirle et al., 2003). For those reasons, the regional and global monitoring of NO2 and aerosols at high spatial resolution is crucial.
Since 1995, with the ERS-2 GOME (Global Ozone Monitoring Experiment) instrument (Burrows et al., 1999), satellite nadir air-quality measurements of atmospheric backscattered sunlight in the UV-visible range have provided daily global 35 tropospheric column measurements of numerous trace gases, such as NO2. Many satellite missions dedicated to air-quality monitoring followed over the next years with increasing spatial resolution. More recently, the TROPOspheric Monitoring Instrument (TROPOMI) sensor launched onboard the Sentinel-5P Precursor (S5P) platform in October 2017 reached an initial spatial resolution of 7x3.5 km 2 , and augmented on 6 August 2019 to 5.5x3.5 km 2 . Due to TROPOMI's fine spatial resolution, monitoring the horizontal distribution of NO2 in urban regions and identifying specific emission sources is made easier than 40 with previous satellite missions but still, TROPOMI cannot fully capture the fine-scale (sub-kilometer) structures in the effective NO2 field. Consequently, TROPOMI requires further attention concerning its measurements validation.
Tropospheric vertical columns of many trace gases like NO2, formaldehyde (HCHO), sulphur dioxide (SO2), nitrous acid (HONO) and O 3 can be retrieved by the Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) technique (Hönninger et al., 2004;Wittrock et al., 2004;Pinardi et al., 2008Pinardi et al., , 2013Clémer et al., 2010;Hendrick et al., 2014;Irie et al., 45 2011Irie et al., 45 , 2012Sinreich et al., 2007;Wagner et al., 2011;Wang et al., 2018). In recent years, MAX-DOAS measurements have been widely used as reference datasets for the validation of nadir airborne and space-borne air-quality measurements. MAX-DOAS instruments measure the scattered sunlight in the UV and Visible spectral ranges at multiple elevation angles above the horizon. For absorbers located close to the surface, such as tropospheric NO2, the higher sensitivity is achieved for low MAX-DOAS elevation angles. During the last years, MAX-DOAS measurements in more than one azimuthal direction are emerging 50 (Ortega et al., 2016;Wang et al., 2014;Chan et al., 2020;Schreier et al., 2021). Multi-azimuthal MAX-DOAS measurements offer many possibilities on air-quality monitoring, such as a better characterization of the effective NO2 field around the station.
These ground-based datasets can be valuable for validating satellite missions with fine spatial resolution in regions where the NO2 horizontal distribution is heterogeneous, such as urban and sub-urban areas.
In this study, a new aerosol and NO2 horizontal distribution inversion approach based on two years (March 2018-February 55 2020) of dual-scan multi-wavelength MAX-DOAS measurements in Uccle (Brussels-Capital region, Belgium) is presented.
In every azimuthal viewing direction, parameterized NO2 near-surface concentrations, NO2 tropospheric columns and aerosol extinctions measured at six different wavelengths are used as input in a new horizontal distribution inversion approach. On this basis, the near-surface aerosol extinction and NO2 horizontal distributions are retrieved at a spatial resolution of about 3km in a range of about 20 km around the measurement site. These horizontal profiles are used to validate collocated 60 TROPOMI tropospheric NO 2 columns. One complete year of data (March 2018-March 2019) and two wavelength intervals (one in the UV and one in the Visible) have already been used in Dimitropoulou et al. (2020). It is proven that multi-azimuthal

Multi-wavelength DOAS analysis
The measured radiance spectra of a full measurement scan are analyzed using the QDOAS spectral fitting software developed 105 by BIRA-IASB (Fayt et al., 2011). The DOAS technique separates the narrow absorption features of trace gases in the UV-Visible spectral range from a spectral background caused mainly by Mie and Rayleigh scattering and instrumental effects. The https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License.
trace gas concentration integrated along the light-path in a measured spectrum relative to the amount of the same absorber in a reference spectrum is the primary product of the DOAS analysis and is called differential slant column density (dSCD). Here, average zenith spectra before and after each measurement scan are used as a reference. 110 The O4 and NO2 dSCDs are retrieved in six different wavelength intervals: Three intervals in the UV spectral range (330-361 nm, 350-370 nm, and 360-383.5 nm) and three in the Visible range (420-460 nm, 450-490 nm, and 510-540.1 nm). These fitting windows were selected to optimize the determination of the O4 and NO2 dSCDs at the maximum number of different O4 absorption bands available in the wavelength domain of the instrument. Figure 2 shows an example of the O4 and NO2 fits in all the intervals used in the present work. In each chosen fitting window, we select a reference wavelength, which 115 corresponds to the maximum of an O4 absorption peak (or close to it) in the respective wavelength intervals (see Fig. 2), and it is subsequently used for radiative transport calculations and further analysis. The different reference wavelengths are 343 nm, 360 nm, 380 nm, 447 nm, 477 nm and 530 nm (see Fig. 2). To optimize the derivation of the dSCDs at the six selected wavelengths, the fit of a slope parameter, which accounts for the variation of the dSCD wit hin the fitting interval (Puķīte et al., 2010), is necessary. This is especially important when the reference wavelength is not located in the center of the fitting 120 window (i.e., 330-361 nm, 350-370 nm, 420-460 nm, and 450-490 nm). The DOAS settings used for each fitting interval are presented in Table S1. As shown in this table, two different O4 cross-sections are used in this study: (1) Finkenzeller (private communication) in the UV fitting intervals and (2) Thalman and Volkamer, (2013) in the Vis fitting intervals. The main motivation for using the O4 cross-section from Finkenzeller (measured at 25 o C) in the UV fitting intervals is the significant improvement of the fit quality and the reduction of the uncertainties for the UV retrievals. Sensitivity tests and comparisons 125 with radiative transport simulations also show that the resulting O4 and NO2 dSCDs are consistent throughout the whole wavelength range covered by the six intervals. For NO2 and O3, which are the strongest absorbers in all the fitting windows, a correction for the solar I0 effect (Aliwell et al., 2002) is applied. A high-resolution solar atlas (Kurucz et al., 1984) is used for the wavelength calibration of the measured spectra.
TROPOMI measures in a push-broom configuration with a full swath width as wide as 2600 km, and it provides daily global coverage at a spatial resolution (true-nadir pixel size) of 7x3.5 km 2 , further improved to 5.5x3.5 km 2 on 6 August 2019. The TROPOMI tropospheric NO2 algorithm has been developed at KNMI and uses a retrieval-assimilation-modeling system that is based on the 3-D global TM5 chemistry transport model (van Geffen et al., 2019;Williams et al., 2017). 145 We use the reprocessed (RPRO) and offline (OFFL) datasets of the TROPOMI L2 tropospheric NO2 column product (see Table 1 for the corresponding versions). According to the guidelines provided by van Geffen et al. (2019), RPRO dataset are available only for the first period of the present study (see Table 1). For the remaining periods, OFFL datasets are used, which are the main data products being available within two weeks from the TROPOMI measurement. To ensure best measurements' quality, only pixels with a quality assurance value larger than 0.75 are used. This quality flagging eliminates pixels with a 150 cloud radiance fraction larger than 0.5, snow or ice, and erroneous retrievals. https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License.
Next to operational products, two additional TROPOMI data sets are also used (see Section 5). In the first one, the TROPOMI retrieval is performed with different a priori profiles (Douros et al., in preparation). The coarse TM5-MP a priori NO2 profiles, using a spatial resolution of 1 o x 1 o , is replaced by NO2 profile shapes from the CAMS (Copernicus Atmospheric Monitoring Service) regional Chemistry Transport Model (CTM) ensemble at a spatial resolution of 0.1 o x 0.1 o . The replacement of a 155 coarse a priori information by a finer one can lead to significant changes in the TROPOMI retrieved NO2 tropospheric columns.
In the second additional product, the TROPOMI retrieval is performed with an improved cloud product (Eskes et al., 2021;van Geffen et al., 2021). According to van Geffen et al. (2021), the improvement in the FRESCO-S cloud pressure retrieval scheme to the FRESCO-wide product, has an impact on the NO2 AMFs and consequently, on the NO2 tropospheric columns 160 over polluted areas. More precisely, the existing FRESCO-S product had a negative bias in the cloud top pressure values, which resulted in a low NO2 tropospheric column (Compernolle et al., 2020). The TROPOMI tropospheric NO2 columns are retrieved using an improved FRESCO-S cloud retrieval scheme, called FRESCO-wide, in v1.4 since 29 November 2020. In the present study, the diagnostic data sets (DDS) are used, which are an ensemble of reprocessed data for past periods analyzed with new versions (van Geffen et al., in preparation Table 2 and Section 4.2) to obtain information about the horizontal sensitivity (LNO2) and AOD as a function of O4 dSCDs, wavelength, and MLHNO2.
Then, in the next step, a new dual-scan parameterization technique is applied to the O4 and NO2 dSCDs at the six different 180 wavelengths and in all the azimuthal directions with MLHNO2, measured O4 dSCDs, and measurement geometry being the main input parameters to retrieve the horizontal sensitivity of NO2 and, consequently, the NO2 near-surface concentrations and VCDs, and near-surface aerosol extinction (see Section 4.2).
In the final step, a new OEM-based horizontal distribution inversion approach is developed using the six near-surface NO2 concentrations and aerosol extinction values per azimuthal direction to retrieve horizontal NO2 and aerosol extinction 185 horizontal profiles in an output horizontal grid of 500m thickness (see Section 4.3).
A flow chart describing the dual-scan multi-wavelength MAX-DOAS inversion approach is shown in Fig. 3.   However, there is no consensus on the fundamental reason for applying this scaling (see e.g. Ortega et al., 2016). As found by Tirpitz et al. (2021), the choice of the scaling factor has only a small effect on the performance of the trace gas retrieval, so we decided not to apply it in the present study. The aerosol extinction profile retrieved from each scan is used as an input to the 200 radiative transfer calculations used to retrieve the NO2 retrieval profile. Further details about the MMF inversion algorithm, the input a priori parameters, the quality check of each scan, and the estimated uncertainties of the aerosol and NO2 vertical profile can be found in Dimitropoulou et al. (2020).

Dual-scan MAX-DOAS retrieval method
A complete MAX-DOAS measurement scan is composed of two different sub-scans, as described in Sect. 2.1. The aerosol and NO2 vertical profiles are retrieved from the elevation scan in the main azimuthal direction. In the other azimuthal directions, measurements are performed only in a single low elevation angle (2°), and therefore, the retrieval of aerosol and NO2 vertical profiles is not possible. Using the fact that the lowest elevation angles have the highest sensitivity to trace gases 220 located nearby the surface due to the long light path in this layer, a new dual-scan MAX-DOAS retrieval strategy was https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License. developed here. This new retrieval strategy is an extension of the work presented in Dimitropoulou et al. (2020) and aims to retrieve the near-surface NO2 box-averaged volume mixing ratios (VMRs) and the NO2 VCDs at six different wavelengths. In Dimitropoulou et al. (2020), the applied dual-scan NO2 MAX-DOAS retrieval was itself an adaptation of the parameterization technique proposed by Sinreich et al. (2013). More precisely, in the presence of sufficient aerosols in the atmosphere (i.e., 225 sufficient aerosols to constrain the light path in a near-surface layer and ensure that the near-surface NO2 concentration can be approximated by a near-surface box profile), the measured NO2 dSCDs at one low elevation angle (2 o ) can be related to the near-surface NO2 box-averaged concentration as follows: where dSCDNO2 is the differential slant column density of NO2 and cNO2 its mean concentration along the differential effective light path, LNO2.
Consequently, the knowledge of the differential effective light-path's length (i.e., LNO2) is crucial to derive the near-surface NO2 concentrations. The oxygen collisional complex (O4) can be used as a tracer for the effective light-path in the atmosphere: 235 as its concentration is well-known (it is the square of O2 concentration). As a result, observed changes of the O4 dSCDs can be directly attributed to changes in the light-path due to the presence of particles like aerosols and clouds. LO4 is calculated as follows: where cO4 is the typical O4 concentration at the altitude of the instrument.
However, the direct use of the O4 light-path length in the NO2 retrieval is not possible under moderate to high pollution conditions, such as those in Brussels, because the profile shapes of O4 and NO2 are not the same. In Dimitropoulou et al. (2020), we used radiative transfer model (RTM) simulations to estimate a unitless correction factor, which accounts for these profile 245 shape differences. This unitless correction factor indicates that under moderate to high pollution conditions, LNO2 is equal to or smaller than LO4. For a correction factor equal or close to one, LO4 is equal to LNO2, which means that there is a moderate to high aerosol load in the atmosphere during the measurement. On the other hand, correction factors smaller than unity are obtained for measurements performed under aerosol-free conditions or a thin MLH. Assuming a homogeneous NO2 distribution inside the MLH, the MLH is derived from the NO2 vertical profiles in the main azimuthal direction and is defined 250 as the ratio of the NO2 VCD to the near-surface concentration of NO2. For more information, we refer the reader to Dimitropoulou et al. (2020). In the present study, a new dual-scan NO2 MAX-DOAS retrieval method, which is more suitable for interpreting multiwavelength measurements than the previous approach (Dimitropoulou et al., 2020), is developed. It is presented in detail in the following subsection.

Developed dual-scan MAX-DOAS retrieval method
The main advantages of the new dual-scan NO2 MAX-DOAS retrieval method (which are also the main differences with 260 respect to Dimitropoulou et al., 2020) are the following: (1) the direct use of the measured O4 dSCDs to estimate LNO2 for every measurement, (2) retrieval of near-surface aerosol extinction close to the ground, and (3) the exploitation of the wavelength dependency of the horizontal path representative of MAX-DOAS measurements for the retrieval of the horizontal distribution of aerosols (and therefore NO2) around the measurement site. The latter is done using O4 and NO2 dSCDs measured at six different wavelengths. This new method is described below. 265 Assuming that the NO2 vertical distribution can be approximated by a box profile of height equal to mixing layer height (MLHNO2), the following equation can be used: This means that the NO2 near-surface concentration can be expressed as a ratio of the dSCDNO2 to the LNO2 (see Eq. 1) or as a ratio of the VCDNO2 to the MLHNO2. Using this equation, L NO 2 can be estimated as follows: Here, O4 dSCDs and LNO2 are simulated using the radiative transfer model VLIDORT version 2.7 (Spurr, 2006). Seasonal median MAX-DOAS NO2 vertical profiles, as retrieved by applying the MMF inversion algorithm in the main azimuthal direction (see Sect. 4.1), show that the bulk (70 %) of the NO2 concentration is located inside the MLHNO2, which is expected since MLHNO2 is estimated as the ratio of VCDNO2 to the near-surface NO2 concentration. On the other hand, this is not the case for aerosols (only 30 % of the aerosol content is seen to be located inside the MLHNO2). Considering this feature, for the 280 VLIDORT simulations, the NO2 a priori profiles are modeled as box profiles with a constant concentration equal to 1.5x10 11 molec/cm 3 from the surface to the MLHNO2. Two layers compose the aerosol a priori profiles: (1) the MLHNO2 and (2) the free troposphere. The equation, which is applied to estimate the aerosol extinction profile a(z), is the following (see Wang et al., 2014): https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License. and, where AOD is the aerosol optical depth, p is the fraction of AOD inside the MLHNO2, b is a normalizing constant for the exponential component (see Eq. 5 from Wang et al., 2014), z is the simulation altitude grid, and is the scaling height for the aerosols located outside the MLHNO2, which is set to 5 km (Wang et al., 2014). In the present study, the fraction of AOD 290 located within the MLHNO2 is set to p=0.3 (see above). The effect of the p value and the NO2 profile shape on the retrieved NO2 near-surface VMRs and VCDs were investigated and considered in the error budget (see Sect. 4.2.2).
The MLHNO2 is estimated per measurement scan, as the ratio of VCDNO2 to the NO2 near-surface concentration as retrieved in the main azimuthal direction by the MMF inversion algorithm.
The RTM simulations have in total nine input parameters, which are the elevation angle, SZA, RAA, AOD, MLHNO2, cNO2, 295 AOD (p and ξ), and wavelength. It should be noted that the elevation angle is kept constant (i.e., 2 o ). For the six different wavelengths (343 nm, 360 nm, 380 nm, 447 nm, 477 nm, and 530 nm), we separately perform RTM simulations and LNO2 (see Eq. 4) are calculated for the assumed SZA, RAA, MLHNO2, cNO2, and AOD input scenarios presented in Table 2. The O4 dSCDs are a function of the input parameter AOD. The relation between the simulated O4 dSCDs and the input AOD values is shown in Fig. 4. A Piecewise cubic hermite interpolating polynomial fitting through the AOD as a function of the simulated O4 dSCDs for each SZA, RAA, and MLHNO2 combination can be used in order to perform an inverse method (i.e. 305 to estimate the near-surface aerosol extinction from the measured O4 dSCDs).
For every combination of all eight parameters (i.e., all the parameters of Table 2, except the AOD values), a polynomial fit of LNO2 as a function of simulated O4 dSCDs is applied. Fig. 5 shows simulated LNO2 as a function of simulated O4 dSCDs, and a second-order polynomial is fitted through the data points. Since NO2 is an optically thin absorber, LNO2 is not a function of cNO2 and consequently, a LNO2 value can be estimated for each measurement. Based on the corresponding SZA, RAA, measured 310 O4 dSCD, and MLHNO2, a LNO2 is attributed to each low elevation MAX-DOAS measurement through this polynomial fit. To express LNO2 as a function of four different parameters (i.e., O4 dSCD, SZA, RAA, and MLHNO2), LNO2 is interpolated linearly at the O4 dSCD, SZA, RAA, and MLHNO2 of each measurement. For example, a MAX-DOAS measurement with SZA=30 o , RAA=60 o , MLHNO2=1km, and measured O4 dSCD=6.10 43 molec 2 .cm -5 will have a LNO2 equal to 15 km at 477 nm (see Fig. 6).
Based on this approach, the near-surface NO2 concentration can be calculated at the six different wavelengths by using Eq. (1) 315 and the derived LNO2 values. The corresponding near-surface NO2 VMR are obtained by dividing the NO2 concentrations by the air number density. To derive the air number density, we use monthly averaged pressure and temperature profiles over a 20-year period. These profiles are extracted from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis. In the last step, the tropospheric NO2 VCD is calculated from the product of the near-surface NO2 concentration with the MLHNO2. 320 Regarding the aerosols, the AOD is estimated for every off-axis measurement (see Fig. 4). The near-surface aerosol extinction is then calculated as the ratio between the aerosols inside the MLHNO2 (i.e., AOD times p) and MLHNO2. The near-surface aerosol extinction refers to the layer that extends from the surface to the MLHNO2. As discussed above, around 30% of the total aerosols is expected to be found inside this layer. 325 The effect of SZA, RAA, and MLHNO2 on the simulated LNO2 is investigated in the supplement. First, the simulated LNO2 are presented in Fig. S1 as a function of RAA for different MLHNO2 and wavelengths and a single AOD and SZA value. LNO2 strongly depends on MLHNO2. The lower the MLHNO2, the shorter the LNO2 is. The same NO2 concentration and aerosol load are used for the three different MLHNO2 scenarios. So, when aerosols are concentrated in a thin layer (i.e., MLHNO2=0.5 km), 330 LNO2 becomes shorter. Secondly, we observe that LNO2 depends on RAA. The larger the RAA, the longer the LNO2. In Fig. S2, simulated LNO2 are plotted for each wavelength and each considered MLHNO2 as a function of SZA (at a constant AOD and RAA). LNO2 depends strongly on SZA. The highest dependency is observed for large SZA values, where LNO2 becomes maximum. Finally, in both Fig. S1 and S2, we observe that LNO2 becomes longer with wavelength, which is expected because of the less pronounced Rayleigh scattering at longer wavelengths. derived for the wavelengths of interest, and ultimately, near-surface NO2 concentrations and tropospheric NO2 VCDs are estimated. In the last step, the near-surface aerosol extinction values are assigned to the six different wavelengths.

Uncertainty budget
To estimate uncertainties on the dual-scan parameterized NO2 near-surface concentration and VCD, the standard error propagation method is used as: According to Kreher et al. (2019) and Bösch et al. (2018), in urban or suburban polluted conditions, the use of the DOAS fit uncertainty of NO2 for the dSCDNO2 uncertainty is not appropriate, because the dSCDNO2 uncertainty is mostly driven by 375 atmospheric variability as well as spatial and temporal fluctuations in the O4 and NO2 fields. In this study, a conservative value of 3.5x10 15 molec.cm -2 is attributed to 2 (Kreher et al., 2019). This represents an error of up to 5% on the NO2 dSCDs in the visible range (477 nm).
The second error source is related to the estimation of LNO2 from the RTM simulations. To estimate this error, sensitivity tests on the input aerosol and NO2 vertical profiles were performed. The fraction of aerosols located inside the MLHNO2 (40% and 380 60% instead of 30%) and the NO2 profile shape (linearly decreasing instead of box) were modified. The error related to the RTM simulations is about 11% in the Visible range (477 nm).
The NO2 VCD is the product of the NO2 near-surface concentration and MLHNO2. According to Dimitropoulou et al. (2020), 385 the uncertainty related to MLHNO2 is about 4%. It is found that the relative difference between MLHNO2 values derived in the main azimuthal directions and in other three additional directions depends strongly from the direction (see Section 4.2.3). In a refined version, this direction dependent error source on the NO2 near-surface concentration will be included in the uncertainty budget.

Validation of the dual-scan MAX-DOAS retrieval method
The sanity check and validation of the dual-scan MAX-DOAS retrieval method in Uccle is based on two different correlative comparisons. 395 The sanity check compares the NO2 near-surface VMRs and tropospheric VCDs retrieved by the dual-scan parameterization in the main azimuthal direction to the same quantities retrieved with the MMF inversion algorithm at the two main wavelengths (360 nm and 477 nm). As can be seen in Figures 7 and 8, both data sets are in good agreement, with correlation coefficient values in the range of 0.86 to 0.95 and slope values close to unity for all the four comparisons.
The validation step is based on the same type of comparison as the first one but for three additional azimuthal directions, where 400 elevation scans, and hence profile retrievals, are available for some periods. Onward July 3, 2019, elevation scans were performed in these three additional azimuthal directions to complement the already existing measurement set-up. These elevation scans were performed once per day, around noon, in the 11 o , 105 o , and 262.5 o azimuthal directions. Figure 9 shows https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License.
the comparison between near-surface NO2 VMRs and tropospheric VCDs retrieved by the dual-scan parameterization method and the corresponding results obtained with the MMF inversion algorithm. Overall good agreement is obtained (R=0.79 and 405 0.84 for near-surface VMR and VCD, respectively). We observe that the comparison concerning the near-surface NO2 VMR seems to be noisier than in the main azimuth direction. This is mainly due to the use of the MLHNO2 calculated in the main azimuthal direction for all the different azimuth angles in the dual-scan method. Additionally, the parameterization technique slightly underestimated the near-surface NO2 VMR (s=0.84) while a slope value of 1.00 is obtained for tropospheric VCDs.

Horizontal distribution inversion approach
The parameterized NO2 near-surface concentrations at the six different wavelengths are used as input in a new horizontal distribution inversion approach. As parameterized NO 2 near-surface concentrations, we refer to the conversion of the measured 440 NO2 dSCDs (i.e. at the elevation angle of 2 o ) to near-surface NO2 concentrations by applying the dual-scan MAX-DOAS retrieval method as described in Sect. 4.2. Figure 10  The parameterized NO2 near-surface concentrations at the different wavelengths are the mean concentrations along the horizontal effective light paths (see Section 4.2), which are also called differential effective light paths because they are linked to the dSCDNO2. When having information coming from one wavelength only, it is not possible to know how the NO2 is distributed along this light path. In the present work, the knowledge of mean NO2 concentrations at six different wavelengths is used to retrieve a horizontal NO2 profile, assuming the horizontal box model described in Fig. 10. This new retrieval method 455 is described below.
The measurement vector y consists of the six retrieved surface concentrations (called as c ̅ NO2 ; see method presented in Sect.
Fcalcul, which represents the forward model, can be expressed as follows: where x is the horizontal distance and the NO2 near-surface concentration as a function of x, the distance from the MAX-DOAS instrument.
Our retrieval of the horizontal distribution of is based on the inversion theory (Rodgers, 2000), in which a horizontal 470 profile cNO2 (state vector) is retrieved given an a-priori horizontal profile xα, the measurement vector y, the matrix of the weighting function K, the uncertainty covariance matrix of the a priori S α and the uncertainty covariance matrix of the measurement Se:

480
where A is the coverage percentage of the differential effective light path length at the last horizontal grid.
An example of weighting functions is presented in Fig. 11. As can be seen, each measurement is sensitive from t he MAX-DOAS instrument location to the horizontal distance equal to the differential effective light path length of each measurement.
As each last horizontal grid is not fully covered by each measurement, the coverage percentage is considered for these gri d cells. It should be noted that since NO2 is an optically thin absorber, the measurements depend linearly on each horizontal 485 box's concentration. For this reason, OEM for the linear case is considered here, and only one inversion step is needed (see Eq. 10).
The selected output horizontal grid for the retrieval extends from the MAX-DOAS instrument to the maximum differential effective light path (LNO2 at 530 nm) per azimuthal direction and consists of successive boxes of 0.5 km thickness on the horizontal axis. 490 Since this inversion problem is ill-conditioned, more than one horizontal NO2 profile can be consistent with the measurement vector. To reject unrealistic solutions, the a priori profile xa and its uncertainty covariance matrix must be included in the retrieval. In the OEM, the a priori information usually comes from an independent source, like a model or other correlative measurements. In the present study, RIO model data were chosen as a priori. RIO is a land-use regression model based on the interpolation of the hourly NO2 near-surface concentrations measured by the in-situ telemetric air quality network in Belgium 495 (Hooyberghs et al., 2006;Janssen et al., 2008). RIO provides hourly NO2 concentration maps on a 4x4 km 2 spatial resolution.
Seasonal average maps of RIO NO2 near-surface concentration are constructed (see Fig. S3) and after, seasonal averages of RIO NO2 near-surface concentration horizontal profiles were calculated in each azimuthal direction and interpolated on the retrieval's horizontal grid by regridding the initial 4x4 km 2 spatial resolution to a finer one (see Fig. 12). The shape of the RIO a priori NO2 profiles per azimuthal direction stays the same during different seasons of the year, indicating that the wind effect 500 on NO2 transportation disappears by the seasonal averaging and that the same sources contribute to the NO2 horizontal field.
A mean scaling factor equal to the mean ratio between the measured and RIO NO2 near-surface concentrations is applied because of the systematic underestimation of NO2 near-surface concentrations by MAX-DOAS when compared to in-situ measurements (Dimitropoulou et al., 2020).
For the aerosols horizontal distribution retrieval, there are not sufficient independent measurements that provide information 505 about the horizontal distribution of AOD and can serve as an a priori AOD profile. Therefore, a horizontally constant a priori AOD profile is used in the AOD retrieval based on CIMEL observations. An AOD equal to 0.18, which is the yearly-averaged AOD value from CIMEL at 477 nm, is used. To construct the near-surface aerosol extinction a priori profiles, it is considered https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License. that 30% of the total amount of AOD is located inside the MLH (i.e., known for each MAX-DOAS vertical scan from the MMF inversion algorithm; see Section 4.1). 510 The diagonal elements of the Sa matrix are set equal to the square of a scaling factor times the NO2 concentration a priori profile. The non-diagonal elements, which account for correlation between the different horizontal grid cells, are set as follows (Barret et al., 2002): where xi and xj are the horizontal distances at the i th , and j th horizontal boxes and γ is half of the correlation length. γ is set equal to 3.5 km. To eliminate inversion instabilities, Sa elements which are smaller than 0.1% of the maximum Sa element are set equal to zero.
To estimate the correlation length, a covariance matrix was constructed by exploiting the airborne observations above Brussels 520 (28 June 2019). The airborne observations have a spatial resolution of approximately 100 x 100 m 2 . NO2 horizontal profiles were constructed in different azimuthal directions in a spatial resolution of 500 x 500 m 2 , expanding from the MAX-DOAS's position to a maximum distance of 20 km, and were used to calculate a covariance matrix. A correlation length equal to 7 km, and consequently, a gamma value equal to 3.5 km, is found to be representative for the NO2 horizontal profiles in Brussels.
Using this correlation length, a variance of 45% is used. This choice was conducted based on the seasonal variance of the RIO 525 a priori profiles compared to their seasonal mean value. It is found that the seasonal variance of RIO observations has a mea n value of 45%. Additionally, it is found to be a good compromise for obtaining reasonable retrieval results e.g. in terms of information content, and while avoiding unrealistic oscillations in the retrieved aerosol and NO2 profiles.
The measurement covariance matrix Se is chosen to be diagonal, with elements corresponding to the uncertainties of the dualscan parameterized NO2 near-surface concentration (see Section 4.2.2). 530 An example of the retrieved NO2 horizontal profile is presented in Fig. 13, together with corresponding measured and simulated c ̅ NO2 at the six different wavelengths for July 2, 2018 (25 o azimuthal direction). RMS is calculated between measured and simulated NO2 near-surface concentrations of the horizontal retrieval normalized by the mean of the measured NO2 nearsurface concentrations (upper panel in Fig. 13). For distances smaller than the minimum LNO2 (around 8 km), the measurements do not give information about the horizontal distribution of NO2. Consequently, the retrieved NO2 horizontal profile at these 535 ranges is coming from the a priori profile. Similarly, the measured and retrieved near-surface aerosol extinction coefficient and the retrieved aerosol horizontal profile are shown in Fig. 14, for one sample case on 11 September 2018 (167.5 o azimuthal direction).
An essential condition of the dual-scan MAX-DOAS retrieval and the new horizontal inversion approach at six different wavelengths is the increasing trend of the horizontal sensitivity as a function of wavelength. Consequently, every wavelength 540 is sensitive to a different horizontal region and the six different wavelengths can be used to retrieve the horizontal distribution https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License. of aerosols and trace gases. Sensitivity tests were conducted in which simulated LO4 are expressed as a function of the six different wavelengths for different aerosol conditions. As can be seen in Fig. S4, the linear relationship between LO4 (and LNO2) and wavelength exists for AOD values ranging from 0 to 1. An AOD equal to unity is chosen as the maximum AOD of the simulations because in Uccle, AOD values rarely exceed one (see in https://aeronet.gsfc.nasa.gov/ for the Brussels 545 measurement site). Therefore, the relation stays linear as the aerosol load changes for the conditions observed in Uccle. The only condition leading to non-linearity is when clouds are present. However, as explained in Sect. 4.1, a cloud filtering approach is applied, rejecting the broken cloud scenes, which are the more problematic ones.

Characterization of the retrieval 590
To characterize the retrieval, the averaging kernels, AK, play a crucial role. The AK matrix is calculated as follows (Rodgers, 2000): The AKs are the rows of the AK matrix. They present the sensitivity of the retrieved (cNO2 ) on the true (cNO2_true) atmospheric profile. Ideally, the AK matrix should be an identity matrix. In Fig. 15, an example of selected AKs is shown. As can be seen, for distances smaller than the first measurement (e.g., near-surface NO2 concentration retrieved at 343 nm), the AKs are constantly zero (or have small values) from the MAX-DOAS instrument until these distances. This indicates a low sensitivity on these short distances, and therefore information about the horizontal distribution of NO2 is coming essentially from the a 600 priori profile. The AKs create a maximum flat plateau close their nominal horizontal distance for larger distances (d=7.25 km, d=8.75 km, and d=15.75 km). For this particular example, the AKs do not exceed the values of 0.25.
Another important information about the retrieval is the trace of the AK matrix, which refers to the number of degrees of freedom for signal (DOFS). The DOFS are an indication of the number of independent pieces of information that one can retrieve from the measurements. Ideally, the DOFS would be equal to the number of horizontal boxes for the horizontal 605 distribution. In reality, the DOFS are lower, because of the limited horizontal resolution of the measurements. In Fig. 15, the DOFS are close to three, which means that three independent pieces of information are contained in the measurements for this particular example.
In the present work, the total retrieval error is equal to the error related to the measurement noise. According to Rodgers (2000), 610 the retrieval noise error is estimated as: with, G being the gain matrix: The horizontal profiles of the measurement error in percentage are shown in Fig. 16. As can be seen, the measurement error becomes maximum for the longest distance.
To eliminate the unsuccessful retrievals, the percentage of accepted retrievals with respect to the total number of retrievals 620 during the four seasons is investigated when a specific filtering on RMS and DOFS is applied (see Table 3). From these tests, it is found that most of the retrievals have DOFS larger than 1.5. RMS is defined as the root-mean-square deviation between measured and simulated cNO2 normalized by the mean of the measured cNO2 (e.g., same RMS as in Fig.13). Table 3 indicates that most of the retrievals have an RMS smaller than 6% with a median RMS value of around 4.5% during all seasons. Based on these investigations, DOFS>1.5 and RMS<6% are used as retrieval quality control criteria. Table 3. Seasonally averaged root-mean-square (RMS) and DOFS values. RMS is calculated between measured and retrieved NO2 near-surface concentrations of the horizontal retrieval (Fig. 13a). DOFS represent the degrees of freedom of the horizontal retrieval (Fig. 15). The percentage of the accepted retrievals is presented for the different selection  For the S5P validation campaign over Belgium (S5PVAL-BE, https://s5pcampaigns.aeronomie.be/), airborne measurements of the two largest urban regions over Belgium, i.e., Antwerp and Brussels, took place from 26 to 29 June 2019 (Tack et al., 2021). The Airborne Prism EXperiment (APEX) imaging spectrometer was used to measure the horizontal distribution of 690 tropospheric NO2 columns with a spatial resolution of approximately 75 m x 120 m (Tack et al., 2017;Tack et al., 2019).
The APEX tropospheric NO2 columns are compared to the tropospheric NO2 horizontal distribution as retrieved by applying our new MAX-DOAS inversion approach to the 28 June 2019 measurements. During the same day, TROPOMI pixels (OFFL 010302 product; see Table 1) selected over the Brussels region are compared to MAX-DOAS observations. MAX-DOAS horizontal profiles of tropospheric NO2 VCDs are selected around TROPOMI overpass time (±1 hour). The horizontal profile 695 of MAX-DOAS NO2 VCDs on each horizontal line-of-sight has a horizontal sampling of 0.5 km (see Fig. 13b). The MAX-DOAS NO2 VCDs on the horizontal segment crossing a TROPOMI pixel and located inside the pixel are averaged and compared to the corresponding TROPOMI NO2 VCD. It should be noted that the MAX-DOAS segments are not weighted by their relative length inside each pixel. APEX observations located inside each TROPOMI pixel were used to assign one APEX NO2 VCD value per pixel. Maps of co-located TROPOMI, averaged MAX-DOAS, and averaged APEX NO2 VCDs for the 700 28 June 2019 are shown in Fig. 19. Two maps of APEX observations are presented: one with APEX in its initial resolution and one with spatially averaged APEX observations in the area covered by a TROPOMI pixel. The NO2 plume as detected by APEX is covering the NW, N, and NE parts of the Brussels region. MAX-DOAS successfully detected the same NO2 plume in the NW and N but not in the NE direction. The correlation and agreement between APEX and MAX-DOAS observations is very good (R=0.83 and s=1.10). As we can observe in Fig. 20, the APEX tropospheric NO2 VCDs tend to be larger than the 705 MAX-DOAS ones, with an intercept equal to -2.10x10 15 molec.cm -2 .
During the S5PVAL-BE flight over Brussels, car mobile-DOAS observations were performed by the BIRA-IASB mobile-DOAS, the so-called AEROMOBIL (Merlaud, 2013). The AEROMOBIL consists of a compact double Avantes spectrometer recording simultaneously scattered light in two channels (i.e., one at 30 o elevation angle and one at zenith). The AEROMOBIL was used to measure the spatial distribution of tropospheric NO2 columns mainly over the Ring road of Brussels. Similarly as 710 with APEX, the AEROMOBIL NO2 VCDs, which are located inside a TROPOMI pixel are averaged and compared to the corresponding MAX-DOAS VCDs (see Fig. 19e and 19f). AEROMOBIL and MAX-DOAS agree perfectly on the location of maximum (i.e. NW direction) and minimum (i.e. SE direction) NO2 tropospheric VCDs (Fig. 19d, 19e, and 19f). We can observe in Fig. 20b, that the correlation coefficient is moderate (R equal to 0.61) and the slope value is equal to 2.62. The correlation plot between both datasets reveals that AEROMOBIL gives higher NO2 tropospheric VCDs compared to MAX-715 DOAS ones. This finding could be partly explained by the fact that AEROMOBIL follows busy routes, where the NO 2 https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License.
tropospheric VCDs reach maximum values because of the contribution of NO2 production resulted by vehicles' engines via fossil fuel combustion.
The correlation between TROPOMI and MAX-DOAS tropospheric NO2 columns during the day of the airborne measurements above Brussels is presented in Fig. 20c. Excellent agreement is obtained, with a correlation coefficient value equal to 0.81. 720 The slope value is equal to 0.72. During that day, MAX-DOAS and TROPOMI are in good agreement but TROPOMI tends to underestimate the tropospheric NO2 columns. It should be noted that during that day, the range of observed NO2 VCDs is from 3.4x10 15 to 8.7x10 15 molec.cm -2 , as retrieved by the MAX-DOAS observations.

MAX-DOAS observations, (b) the tropospheric NO2 columns derived by car mobile-DOAS measurements (AEROMOBIL), and the MAX-DOAS observations and (c) the tropospheric NO2 columns derived by MAX-DOAS
observations and the TROPOMI tropospheric NO2 columns over Brussels on 28 th of June 2019.

Comparison results of the March 2018-February 2020 period
To compare the TROPOMI and MAX-DOAS tropospheric NO2 columns, the following 5-step approach is used, similarly as in Section 5.2: 1. Only MAX-DOAS horizontal profiles of tropospheric NO2 VCDs retrieved around (±1 hour) TROPOMI overpass 755 time are selected.
2. The time-coincident MAX-DOAS tropospheric NO2 VCD horizontal grids from all the azimuthal directions are spatially averaged (i.e. one MAX-DOAS mean NO2 VCD value per pixel) within the overlapping TROPOMI pixels.
3. To take into account the distance between each azimuthal direction crossing a TROPOMI pixel and the TROPOMI pixel center, the MAX-DOAS average is a weighted mean with the weighting depending on their relative direction 760 with respect to the direction of the TROPOMI pixel center. Consequently, the weights are equal to the difference between 360 o and the azimuthal difference between MAX-DOAS grid and TROPOMI pixel central coordinates. 5. TROPOMI and MAX-DOAS tropospheric NO2 columns are compared, and the seasonally-averaged maps of those VCDs on the area covered by the TROPOMI pixels are created. To generate these maps, the ensemble of TROPOMI pixels recorded on 28 June 2019 is chosen as reference and TROPOMI pixels that coincide with this reference grid 770 are averaged. The daily horizontal profiles of MAX-DOAS NO2 columns are averaged on the daily TROPOMI grids and then, the reference grid is used to create the seasonally-averaged MAX-DOAS maps.
The seasonally and annually-averaged maps of TROPOMI and MAX-DOAS NO2 VCDs are presented in Fig. 21 and Fig. 22.
Only pixels including at least 20 comparison days are taken into account in the analysis. It is found that the locations of the 775 NO2 peaks and dips show a reasonably high degree of similarity between TROPOMI and MAX-DOAS during all seasons. The NO2 peaks appear mainly above Brussels city center, the Drogenbos power plant (W direction) and the NW part of the Ring road, which are the main known emission sources, as mentioned earlier. These maps also indicate that the tropospheric NO2 column over the Brussels area has a clear seasonal cycle, with a maximum during winter. studies (Verhoelst et al., 2021;Tack et al., 2021;Judd et al., 2020;Dimitropoulou et al., 2020;Ialongo et al., 2019). When seasonally-averaged TROPOMI and MAX-DOAS pixels (the pixels shown in Fig. 21) are compared one-by-one (see SEAS In a second step, the impact of the spatial sampling is investigated. Generally, a varying number of MAX-DOAS NO2 columns 795 cover each TROPOMI pixel. The coverage percentage is estimated as the ratio of the covered area by MAX-DOAS (i.e., number of coincident MAX-DOAS NO2 VCDs) inside each TROPOMI pixel to the total number of MAX-DOAS NO2 VCDs that could fill-in the TROPOMI pixel. When selecting only TROPOMI pixels covered by at least a given percentage of MAX-DOAS grids (10% and 20%), it is found that the correlation between both datasets improves for all seasons, except summer for a coverage equal and greater than 20%. The most significant improvement is observed during spring. The correlation 800 coefficient value is equal to 0.83 (instead of 0.66) when taking into account TROPOMI pixels covered more than 20% by The seasonal regression analysis parameters between TROPOMI and dual-scan MAX-DOAS measurements derived in the 805 present study are compared to the same parameters presented in Dimitropoulou et al. (2020). Both studies make use of the dual-scan MAX-DOAS instrument in Uccle. In addition to the different approach (i.e., the retrieval of NO2 horizontal profiles), in the present study, almost two years of measurements are used, while in Dimitropoulou et al. (2020), only one year is exploited for the TROPOMI validation. In Table 4, for the present study, only one year of measurements are used to have a comparable time coverage for both studies. As presented in Table 4, here, the largest slope value is found in spring, while in 810 Dimitropoulou et al. (2020), in winter. The season in which the highest correlation coefficient is obtained differs between both studies (here, in spring, in autumn in Dimitropoulou et al. (2020)). The main advantage of the new approach is the larger number of comparison points between TROPOMI and MAX-DOAS leading to significantly more reliable statistics. In the present study, the deviation of the comparison points from the fitted regression line is increased mainly because of the uncertainties in the horizontal inversion approach. The scatter increase is reflected in the correlation coefficient values, which 815 are smaller for all seasons, except winter. Regarding the slope value, it is larger in spring and summer, and is smaller in autumn and winter.
Overall, our investigation about the spatial sampling lead to the following three important findings: 1. The dual-scan multi-wavelength approach allows a better identification of the main emissions sources in urban 820 regions, in agreement with the spatial allocation of the main emission sources observed by APEX and TROPOMI.
2. The characterization of the NO2 concentration horizontal field using the dual scan multi-wavelength approach results in obtaining larger slope values between TROPOMI and MAX-DOAS observations. The high spatial resolution of TROPOMI requires ground-based measurement that can provide information about the horizontal distribution of tropospheric NO2 columns in urban regions. 825 3. Even for a better spatial sampling between TROPOMI and ground-based observations, TROPOMI still underestimates the ground-based measurements (see Fig. 22). Therefore, this is an additional indication that this underestimation is caused by other factors.

Investigation of the a priori NO2 profile shape and clouds in TROPOMI NO2 retrievals
Three additional comparisons were conducted in this study. First, a TROPOMI tropospheric NO2 column product with an improved FRESCO-S cloud retrieval was tested. As discussed in Dimitropoulou et al. (2020), clouds can significantly affect 885 tropospheric NO 2 VCD retrievals from satellite observations. The dataset is available for four different periods in 2018 -2019 (see Sect. 3). Fig. 24 shows that the slope value increases by about 56% (equal to 0.53 instead of 0.34 for the baseline product), as well as the correlation coefficient between both datasets (R equal to 0.68 instead of 0.45). This is in agreement with the TROPOMI Routine Operations Consolidated Validation Report (ROCVR; https://mpc-vdaf.tropomi.eu/), where the use of the improved FRESCO-wide resulted in a bias reduction with respect to ground-based NO2 data. 890 Secondly, a new TROPOMI data product covering the November 2018 to February 2020 period is used. In this product, the coarse TM5-MP a priori NO2 profiles are replaced by NO2 profile shapes from the CAMS regional CTM ensemble at a spatial resolution of 0.1 o x 0.1 o (Douros et al., in preparation;Ialongo et al., 2019;Tack et al., 2021). As can be seen in Fig. 24, using a spatially finer a priori NO2 vertical profile improves slightly the slope value, which is equal to 0.77 (instead of 0.75 for the baseline TROPOMI product). This represents an increase of the slope by about 3%. This finding indicates that part of the 895 TROPOMI underestimation of tropospheric NO2 columns is caused by inadequate a priori profiles in the TROPOMI retrievals https://doi.org/10.5194/amt-2021-308 Preprint. Discussion started: 18 October 2021 c Author(s) 2021. CC BY 4.0 License.
for urban conditions. On the other hand, the fact that the slope value is still lower than unity, even when CAMS regional a priori profiles are used, indicate that other factors contribute to the TROPOMI underestimation or that CAMS profiles are still sub-optimal, as suggested by results obtained when applying MAX-DOAS profiles to TROPOMI (see below).
Finally, the impact of the a priori profile in the TROPOMI NO2 retrieval is investigated using MAX-DOAS profile data. For 900 this test, TROPOMI NO2 columns are recalculated, similarly as in Dimitropoulou et al. (2020), using daily median MAX-DOAS vertical profiles derived in the main azimuthal direction by applying the MMF inversion algorithm. Those TROPOMI NO2 columns are then compared to the horizontally-resolved MAX-DOAS data, as in Sect. 5.3.1. Figure 25 presents the comparison results per season. When comparing it with Fig. 23, we find that the change in the NO2 vertical profile shape improves the slope value in the comparison with ground-based observations. Except for winter, the slopes are largely improved 905 (slopes in the 0.56 -1.11 range) due to an increase of the recalculated TROPOMI columns. This result confirms once again that the a priori profile in the TROPOMI retrieval is a key player in the TROPOMI underestimation of tropospheric NO2 columns in urban conditions, as already stated in previous studies (see e.g. Dimitropoulou et al., 2020;Ialongo et al., 2019;Tack et al., 2021). The present study suggests that in urban conditions, daily median MAX-DOAS vertical profiles are more suitable than NO2 profile shapes from the CAMS regional CTM ensemble in order to be applied as a priori information in the 910 TROPOMI retrieval.

Figure 25. Seasonal scatter plots between the horizontally-averaged MAX-DOAS NO 2 VCDs and TROPOMI NO 2 940
columns recalculated using me dian daily MAX-DOAS vertical profiles as a priori information.

Conclusions
Two years (March 2018 to February 2020) of dual-scan MAX-DOAS measurements in Uccle (urban background site located in the south of the Brussels-Capital Region) were used to develop a new strategy for the retrieval of near-surface NO2 concentrations and aerosol extinction horizontal profiles. A full dual-scan measurement is composed of one vertical scan at a 945 fixed azimuthal direction pointing towards the city center and horizontal scans in ten azimuthal directions at a fixed low elevation angle (2 o ).
The first step of this new retrieval strategy is to analyze measured radiance spectra in six different fitting windows. This provides O4 and NO2 dSCDs at the following six wavelengths: 343 nm, 360 nm, 380 nm, 447 nm, 477 nm and 530 nm. Then, information about the vertical extent of NO2 in the troposphere (MLHNO2) is derived from profile retrievals in the main 950 azimuthal direction performed using the OEM-based MMF algorithm. In the third step, a new parameterization technique is applied, with MLHNO2, measured O4 dSCDs, and measurement geometry being used as input parameters to retrieve the horizontal sensitivity of NO2 and, consequently, the NO2 near-surface concentrations and VCDs, and near-surface aerosol extinction in all the azimuthal directions for the six different wavelengths. Compared to the method presented in Dimitropoulou et al., (2020), the new retrieval method offers the possibility of the direct determination of LNO2, and near-surface aerosol 955 extinction based on the measured O4 dSCDs.
The retrieved dual-scan NO2 near-surface concentrations and VCDs are verified via comparisons to the MMF NO2 vertical profiles in the main azimuthal directions and in three additional azimuthal directions. A good overall agreement is found for the two comparisons during the two years of measurements.
The dependence of the horizontal sensitivity on the wavelength is then used to develop a new OEM-based horizontal 960 distribution inversion approach. Considering a horizontal box model, horizontal NO2 and aerosol extinction profiles are retrieved in an output horizontal grid of 500m thickness starting from the instrument to each of the measurement maximum horizontal representative distance.
The daily variability of NO2 horizontal profiles in all the azimuthal directions provides information about the location of the NO2 hotspots in the Brussels-Capital Region and how the plumes are transported. Similarly, the NO2 horizontal profiles' 965 seasonal variability over March 2018-February 2020 reveals that the NO2 hotspots are mainly found above the Brussels citycenter, the Drogenbos power plant and the NW part of the Ring road during all seasons.
On 28 June 2019, airborne measurements (APEX) of NO2 were performed over Brussels. The MAX-DOAS NO2 VCD horizontal profiles are compared to APEX, mobile car-DOAS (i.e., AEROMOBIL), and TROPOMI measurements, and a good overall agreement is found between the different data sets for this day. 970 In the second part of the study, MAX-DOAS retrievals are compared to TROPOMI tropospheric NO2 observations over the March 2018-February 2020 period. The comparison of seasonal maps shows a good overall agreement between both datasets as to the NO2 horizontal distribution over the Brussels area. This agreement improves systematically when only TROPOMI pixels covered by a minimum of 20% of MAX-DOAS grid cells are compared, showing the benefit of ground-based measurements at high horizontal resolution for the validation of high-resolution space-borne air-quality measurements. Results 975 also show that during all seasons, TROPOMI underestimates the MAX-DOAS tropospheric NO2 columns. The role of the a priori NO2 profile shape in the TROPOMI retrievals was investigated and TROPOMI tropospheric NO2 columns are recalculated with the MAX-DOAS vertical profiles. We show that the knowledge of the NO2 horizontal distribution derived by the MAX-DOAS measurements combined with a more adequate a priori profile in TROPOMI retrievals leads to a much better agreement between satellite and ground-based data.
To conclude, our study presents a new horizontal distribution inversion approach for NO2 and aerosols developed by using dual-scan multi-wavelength MAX-DOAS measurements over an urban area. This approach provides a better characterization of the horizontal distribution of an important urban pollutant, NO2, which leads to an improved agreement between satellite and MAX-DOAS measurements in moderate to highly polluted conditions. Based on our study, further modifications of the measurement mode aiming at a better sampling of the vertical and horizontal NO2 distribution could be implemented and 985 investigated. For instance, performing vertical scans in several azimuthal directions throughout the day and/or horizontal scans in more than ten azimuthal directions could further improve our knowledge about the tropospheric NO2 spatial variability in urban regions, and therefore the satellite validation results in those conditions. Data availability. The datasets generated and analyzed in the present work are available from the corresponding author on 990 request.
Author contributions. ED undertook the development and validation of the dual-scan multi-wavelength MAX-DOAS retrieval strategy in Uccle, exploited the MAX-DOAS retrievals during two year, performed the validation of the TROPOMI tropospheric NO2 columns, and wrote the paper. FH supported and guided ED in the development of the dual-scan multi-995 wavelength MAX-DOAS retrieval strategy, provided general guidelines, and revised and edited the paper. MMF provided the MMF inversion algorithm and the RTM as well as supporting and guiding ED in the new OEM-based horizontal profile retrieval. FT provided the airborne APEX dataset and contributed to scientific discussions. GP provided the dataset of the TROPOMI tropospheric NO2 columns and supported ED in the TROPOMI validation approaches. AM provided the AEROMOBIL dataset and contributed to scientific discussions. CF and CH provided technical and software support for the 1000 MAX-DOAS instrument in Uccle. CF developed the QDOAS software and guided ED in the DOAS analysis. FF provided the RIO model dataset. MVR supervised the present work, provided general guidelines and valuable comments during the whole process of the paper preparation, and revised and edited the paper. All authors reviewed, discussed and commented on the paper.