MAX-DOAS measurements of tropospheric NO2 and HCHO in Munich and the comparison to OMI and TROPOMI satellite observations

We present two dimensionally scanning Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) observations of nitrogen dioxide (NO2) and formaldehyde (HCHO) in Munich. Vertical columns and vertical distribution profiles of aerosol extinction coefficient, NO2 and HCHO are retrieved from the 2D MAX-DOAS observations. The measured surface aerosol extinction coefficients and NO2 mixing ratios derived from the retrieved profiles are compared to in-situ monitor data, 5 and the surface NO2 mixing ratios show good agreement with in-situ monitor data with a Pearson correlation coefficient (R) of 0.91. The aerosols optical depths (AODs) show good agreement as well (R = 0.80) when compared to sun-photometer measurements. Tropospheric vertical column densities (VCDs) of NO2 and HCHO derived from the MAX-DOAS measurements are also used to validate OMI and TROPOMI satellite observations. Monthly averaged data show good correlation, however, satellite observations are on average 30 % lower than the MAX-DOAS measurements. Furthermore, the MAX-DOAS observa10 tions are used to investigate the spatio-temporal characteristic of NO2 and HCHO in Munich. Analysis of the relations among aerosol, NO2 and HCHO shows higher aerosol to HCHO ratios in winter indicating a longer atmospheric lifetime of aerosol and HCHO. The analysis also suggests that secondary aerosol formation is the major source of aerosols in Munich.

All measurement spectra were corrected for the spectrometer CCD non-linearity, as well as for offset and dark current. The DOAS technique (Platt and Stutz, 2008) is then applied to the measurement spectra to derive slant column densities (SCDs) of the trace gases. In this study, the measurement spectra are evaluated using the spectral analyzing software QDOAS version 3.2.
The spectral fit is performed at two different wavelength bands of 338 -370 nm and 324.5 -359 nm. O 4 DSCDs used for aerosol extinction profile retrieval and NO 2 DSCDs used for NO 2 profile retrieval are taken from the former fitting band (338 -370 nm). Due to the stronger absorption structure of HCHO in the shorter wavelengths, HCHO DSCDs used for the retrieval of HCHO profiles are taken from the latter fitting window (324.5 -359 nm). Detailed procedure of the combined retrieval of aerosol and trace gas profiles is presented in Section 2.1.3. The zenith spectrum (α = 90 • ) of the corresponding measurement cycle is used as reference spectrum to retrieve the differential slant column densities (DSCDs), which are defined as the difference between the SCDs of an off-zenith spectra and the corresponding zenith reference spectrum. A 5 th order polynomial in the DOAS fit is 5 responsible for removing broadband spectral structures caused by Rayleigh and Mie scattering. The absorption cross section of several trace gases used in the retrieval are listed in Table 1 for both wavelength ranges. These settings are based on the results from previous studies (Pinardi et al., 2013;Peters et al., 2017;Kreher et al., 2019). In order to compensate for possible instabilities due to small thermal variations of the spectrograph, shift and squeeze parameters of the spectra are included in the fitting process as well. An example of the DOAS retrieval of NO 2 and HCHO DSCDs from a MAX-DOAS spectrum taken on 10 4 November 2016 at 10:02 (local time) with α = 2 • is shown in Fig. 2.  (2000) NO2 (a) 298 K Vandaele et al. (1998) NO2 (a,b) 220 K × Vandaele et al. (1998) O3 ( (b) Orthogonalized to NO2 cross-section at 298 K (Vandaele et al., 1998).
Several previous studies have shown that there is a systematic discrepancy between observation and model simulation of O 4 DSCDs (Wagner et al., 2009;Clémer et al., 2010;Wagner et al., 2011;Chan et al., 2015;Wang et al., 2016;Chan et al., 2018;Zhang et al., 2018). The discrepancies can be related to the systematic error of the O 4 absorption cross section, model error, optical properties of aerosols and aerosols above the retrieval height (Ortega et al., 2016;Wagner et al., 2019 absorption cross section are known to be small (Wagner et al., 2019;Wang et al., 2019). In order to avoid over-correction due to outliers, we take the 10 th percentile instead of the minimum value of the simulated and measured O 4 DSCD ratio as the

Aerosols and trace gases retrieval
In this study, aerosol extinction coefficient profiles are retrieved from the observations of O 4 DSCD at the 338 -370 nm band using the Munich Multiple wavelength MAX-DOAS retrieval algorithm (M 3 ). As the O 4 DSCDs are retrieved within a relatively 15 narrow spectral band, we can assume the wavelength dependency of the optical path within the fitting window is negligible.
Thus, the forward radiative transfer simulation can be calculated at a representative wavelength of 360 nm, where the strongest O 4 absorption is located. A brief description of the aerosols and trace gases retrieval is presented below, a more detailed description can be found in Chan et al. (2018Chan et al. ( , 2019. The conversion of MAX-DOAS observations to aerosol extinction and trace gases profiles requires an inversion of the underlying radiative transfer equation (Wagner et al., 2004;Hönninger et al., 2004;20 Sinreich et al., 2005;Frieß et al., 2006;Hartl and Wenig, 2013). The oxygen collision complex, O 4 , has several absorption bands in the UV and VIS spectral range. Due to its known vertical distribution, the absorption signal of O 4 , which is a combination of the concentration profile and the photon paths, which in turn are influenced by the aerosol distribution, can be used for the aerosol retrieval.
The vertical profile of the aerosol extinction coefficient is retrieved from a set of MAX-DOAS observations with different 25 viewing directions y(α, φ). A set of MAX-DOAS observations y(α, φ) is defined as the O 4 DSCD observations at the same scanning azimuth angle φ with different elevation angles α within a single measurement cycle. These observations of O 4 DSCD are grouped together for the aerosol vertical profile retrieval. We assume that the set of measurement (y) can be reproduced by forward radiative transfer simulations and the forward simulations of O 4 DSCD are dependent on the aerosol extinction profile (x) and aerosol optical properties. Assuming aerosols are horizontally homogeneously distributed within the MAX-DOAS 30 measurement range, so that the observation vector (y) can be described by Eq. 1.
where and δ are the observation and simulation uncertainties, respectively. The aerosol extinction profile can be retrieved by fitting the forward simulations to the O 4 DSCD observations. In this study, all forward radiative transfer simulations were carried out using the library for Radiative transfer (libRadtran) radiative transfer model (Mayer and Kylling, 2005;Emde et al., 2016). The U.S. Standard Atmosphere (Anderson et al., 1986) mid-latitude profiles for winter (January) and summer (July) are temporally interpolated to each month of the year for the radiative transfer calculations.

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As the information contained in the observation vector y is not sufficient to retrieve an unique aerosol extinction profile, the optimal estimation method is employed for the aerosol inversion. The optimal estimation approach supplemented the necessary information to the inversion in a form of an a-priori aerosol profile (x a ). The cost function χ 2 of the retrieval can be defined by Eq. 2. 10 where S represents the observation uncertainty matrix, while S a is the a-priori uncertainty covariance matrix. We assume the observations at different elevation angles are independent so that S is a diagonal matrix. The aerosol extinction is assumed to be correlated with the neighboring layers, so that S a is defined by Eq. 3.
where z is the altitude of the center of the layer. Since in urban areas, aerosols are typically emitted and formed close to the 15 surface, we assume an a-priori aerosol extinction profile following an exponentially decreasing function with a scale height of 0.5 km. The aerosol optical depth of the a-priori aerosol profile is set to 0.2, which is the average AOD measured by the co-located sun-photometer at 340 nm. The uncertainty of the a-priori aerosol profile is set to 50 % and the correlation length η corr of the aerosol inversion is assumed to be 0.5 km. As MAX-DOAS measurements are more sensitive to the aerosol and trace gases close to the instrument, we divide the lowest 3.0 km of the troposphere unevenly into 20 layers. The lowest 1 km from the co-located sun-photometer. As the radiative transfer in the atmosphere is non-linear, therefore, the inversion of the aerosol extinction is solved iteratively by using the Gauss-Newton method.
The M 3 profile retrieval algorithm is featured with a dynamic a-priori module to avoid over-regularizing the retrieval under extreme conditions and reduce the dependency on a-priori information (Chan et al., 2019). The algorithm first use a fixed initial a-priori (as mentioned above) to retrieve an initial aerosol profile. The fixed a-priori profile is then scaled to have the 30 same aerosol optical depth retrieved from the initial run. The scaled a-priori is then used in the next retrieval to derive a new aerosol extinction profile. This procedure repeats until the difference of aerosol optical depth between the new and previous result is less than 10 % or the number of iterations reaches the limit, which is set to 5 in this study.
The aerosol information obtained from the procedure described above is used for the calculation of the differential box air mass factors ∆DAMFs, required for the trace gas profile inversion. The ∆DAMFs are calculated at a single wavelength for the retrieval of trace gas profiles using libRadtran with the Monte Carlo simulation module MYSTIC (Emde et al., 2016), assuming 5 them to be constant within the rather narrow DOAS spectral fitting window. The relationship between ∆DAMF and DSCD can be described by the following equations.
where c j is the concentration of the corresponding trace gas at the vertical layer j. As NO 2 DSCDs are retrieved at the 10 same spectral band as O 4 , thus, the forward simulation of ∆DAMFs for NO 2 profile retrieval are also calculation at the O 4 absorption bands of 360 nm. HCHO DSCDs are retrieved at a slightly shorter wavelength band than O 4 . Therefore, aerosol extinction profiles obtained at 360 nm are converted to 340 nm assuming a fixed Ångström exponent (Ångström, 1929) of 1.05 for the HCHO vertical profile retrieval. This value is the annual averaged Ångström exponent calculated from the co-located sun-photometer. The single scattering albedo (0.95), asymmetry parameter (0.70) and ground albedo (0.04) at 340 nm used for 15 the radiative transfer calculations are assumed to be same as at 360 nm. The ∆DAMFs for the HCHO profile retrieval are then calculated using the converted aerosol profile at 340 nm. The layer settings of the trace gas profile retrieval are the same as the one used in the aerosol profile retrieval.
Following Eq. 4 and 5, a set of linear equations can be formulated by considering the measurements at different elevation angles α i . Similar to the aerosol profile retrieval, the information contained in the MAX-DOAS observation is not sufficient 20 to derive an unique solution. Therefore, the M 3 algorithm use the optimal estimation method (Rodgers, 2000) with a dynamic a-priori approach for the trace gas profile inversion (Chan et al., 2019). The algorithm first use a fixed initial a-priori to retrieve an initial trace gas profile. The fixed a-priori profile is then scaled to the vertical column derived in the first retrieval. The scaled a-priori is subsequently used in the next retrieval. The process iterates until the difference between retrieved and previous trace gas column is less than 10 % or the number of iterations reaches the limit, which is set to 5 in this study.

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The atmospheric layer settings of the trace gas profile retrieval are identical to the ones used in the aerosol profile retrieval.
In this study, the a-priori NO 2 and HCHO profiles are assumed to be also exponential decreasing with a scale height of 0.5 km.
The NO 2 vertical column density (VCD) of the a-priori is set to 1 × 10 16 molec/cm 2 whereas the a-priori HCHO VCD is set to 8 × 10 15 molec/cm 2 . The vertical distribution of NO 2 and HCHO above the retrieval height (3 km Fig. 1). Ambient NO 2 mixing ratios are measured by an in-situ chemiluminescence NO 2 analyzer, 5 while PM 10 concentrations are measured with a beta attenuation and light scattering based in-situ particle analyzer. Details of the air quality monitoring network as well as air quality monitoring data can be found on the website of the European Environment Agency (https://www.eea.europa.eu/).

Sun-photometer measurements
A sun-photometer (CIMEL Electronique, CE-318) is installed next to the 2D MAX-DOAS instrument, providing multi-10 wavelength measurements of aerosol optical properties (Holben et al., 2001). As part of the AERosol RObotic NETwork (AERONET) (Holben et al., 1998), instrument #198, data include measurements at 7 different wavelengths, which are 340, The OMI NO 2 products derived within the framework of the quality assurance for the essential climate variables (QA4ECV) project are used in this study (Boersma et al., 2018). NO 2 SCDs are derived from earthshine radiance spectra in the visible 25 band from 405 -465 nm using a DOAS retrieval. The SCDs are then converted to vertical column densities (VCDs) using the concept of air mass factors (AMFs) (Solomon et al., 1987). The AMFs used in the QA4ECV OMI NO 2 product are calculated at

TROPOMI satellite observations
The TROPOspheric Monitoring Instrument (TROPOMI) is a passive nadir viewing satellite borne push-broom imaging spectrometer on board the Copernicus Sentinel 5 Precursor (S5P) satellite. The satellite was launched on 13 October 2017 on a sun-synchronous orbit at an altitude of ∼824 km with a local equator overpass time of 13:30 on ascending node. The instrument has 8 spectral bands covering UV, VIS, near infrared (NIR) and short-wavelength infrared (SWIR). The instrument takes 5 measurements at 450 positions across the orbital track which cover a swath of ∼2600 km, providing daily global coverage observations. The spatial resolution of the instrument is 3.6 km (across-track) × 7.2 km (along-track) for measurements taken before 6 August 2019. Thereafter the instrument was switched to a better spatial resolution of 3.6 km (across-track) × 5.6 km (along-track). A more detailed description of the TROPOMI instrument can be found in Veefkind et al. (2012).
The operational TROPOMI NO 2 and HCHO products are used in this study (van Geffen et al., 2019;De Smedt et al., 2018). 10 The operational TROPOMI NO 2 retrieval algorithm is very similar to the OMI product as demonstrated in the QA4ECV project. The operational TROPOMI HCHO product retrieves HCHO SCDs with a large fitting window of 328.5 -359 nm. The retrieved SCDs are then converted to VCDs using the AMF approach. The AMFs are calculated at 340 nm using HCHO vertical profiles from the global chemistry transport model TM5-MP. Similar to the operational NO 2 product, albedo data are taken from the OMI climatology and will be updated to TROPOMI albedo product when it is available. A more detailed description 15 of the TROPOMI HCHO retrieval algorithm can be found in (De Smedt et al., 2018).
We have regridded and calculated the annual average of TROPOMI tropospheric NO 2 and HCHO VCDs over Germany and its surrounding regions. The annual averaged TROPOMI tropospheric NO 2 and HCHO maps are shown in Fig. 3. The location of Munich is indicated by the circle marker in Fig. 3. Significant NO 2 hot spots can be observed over major cities indicating the significant contribution of anthropogenic emissions. On the other hand, the spatial distribution of HCHO is rather 20 homogeneous due to strong natural emissions.
3 NO 2 and HCHO retrievals for Munich

Spatial variability
In order to investigate the spatial variability of NO 2 and HCHO, we utilize the azimuthal scans of the MAX-DOAS. Tropospheric NO 2 VCD measured by the MAX-DOAS with different viewing azimuth angles are plotted in Fig. 4. Fig. 4a shows 25 the measurements in winter (December, January and February), while measurements in summer (June, July and August) are shown in Fig. 4b  lifetime of NO 2 is longer in winter due to lower photolysis rate which also leads to more homogeneous NO 2 distribution. In the south of the measurement site where the city center is located, higher NO 2 levels are observed during summer. There are several local emission hot spots in the city, such as a number of busy crossroads and a minor natural gas power plant. In addition, lower wind speed and shorter lifetime of NO 2 reduced the dispersion in summer, thus resulting in rather inhomogeneous NO 2 distribution.  Compared to NO 2 , the weekend reduction effect of HCHO is less pronounced. HCHO vertical columns and surface mixing 5 ratios are reduced by 13 % and 9 % for Saturday and Sunday, respectively. As natural emission, such as biogenic emission from plants, do not show a weekly pattern, the reduction during the weekend suggests that anthropogenic emissions of HCHO and its precursors have a substantial (>10 %) contribution to the ambient VOCs.

Relations among aerosol, NO 2 and HCHO
The correlations among aerosol extinction coefficients, NO 2 and HCHO mixing ratios can be used to investigate the composi-10 tion and sources of aerosols (Veefkind et al., 2011). Fossil fuel combustion is the most significant primary source of NO 2 and aerosols, while HCHO correlates strongly with secondary organic aerosol formation. Fig. 6a shows the correlation between surface aerosol extinction coefficients (ε surf ) and NO 2 mixing ratios, while the correlation between ε surf and HCHO mixing ratios is shown in Fig. 6b. the same sources, a rather constant aerosol to NO 2 ratio indicates the sources of primary emission are similar in summer and winter. On the other hand, a higher aerosol extinction to HCHO ratio is observed during winter compared to summer ratio.
Higher aerosol extinction to HCHO ratio reflects a longer atmospheric lifetime of secondary aerosol and HCHO in winter, whereas higher photolysis rates in summer result in a lower aerosol to HCHO ratio.
Assuming that NO 2 mixing ratios are related to primary emissions of aerosols and HCHO mixing ratios are related to 5 secondary aerosol formation, we used a multiple linear regression model to estimate the contribution of primary and secondary aerosols. The comparison of modeled and MAX-DOAS measurements of aerosol extinction coefficients is shown in Fig. 6c.
The Pearson correlation coefficients (R) between modeled and measured aerosol extinction coefficient for summer and winter Aerosol extinction coefficients are related to the particle concentrations in the atmosphere, depending on the aerosol composition and size distribution. Thus, as a first approximation assuming constant composition, we compare the aerosol extinction coefficients at the lowest layer (ε surf ) of the MAX-DOAS profile retrieval to PM 10 concentrations reported from the nearby air quality monitoring station. Time series of ε surf at 360 nm and PM 10 concentrations are shown in Fig. 7a. As the in-situ air quality monitoring station only provides hourly data, MAX-DOAS measurements for all azimuth directions are averaged to hourly and monthly data for comparison. Both, ε surf and PM 10 , show similar variation pattern with slightly higher values in winter, however, ε surf varies in a wide range with hourly value ranging from 0.005 km −1 up to 1.859 km −1 . The correlation 5 between MAX-DOAS measurements of ε surf and PM 10 concentrations from in-situ measurement is shown in Fig. 7b. Monthly averaged MAX-DOAS data show a reasonable agreement with the in-situ PM 10 measurements with R of 0.66. This moderate correlation can be explained by the differences in physical quantities of the two measurements. The aerosol extinction coefficient is not only related to the aerosol mass concentration, but also strongly related to the micro-physical properties of aerosol, such as the size distribution and particle composition. Meteorological factors, such as, humidity and temperature, could have 10 big impacts on the aerosol size distribution and optical properties. Therefore, the relation between ε surf and PM 10 concentrations can be very different in different seasons (Schäfer et al., 2008). In addition, the spatial coverage of the two measurements is quite different. MAX-DOAS observations typically cover a few kilometers around the measurement site, whereas the in-situ measurements are only representative for the small area surrounding the station and governed by local conditions (see e.g. Geiß et al., 2017). 15 We have also compared the surface NO 2 mixing ratios retrieved from the MAX-DOAS observations to the in-situ monitor, altitudes. In addition, the MAX-DOAS reports NO 2 mixing ratios averaged along a long optical path, which covers residential areas and city parks, where the NO 2 mixing ratios are expected to be lower. As a consequence, the MAX-DOAS is in general 30 measuring lower surface NO 2 mixing ratios than the in-situ monitoring station. In-situ NO 2 mixing ratio (ppbv)    The scatter plot of OMI and TROPOMI observations of tropospheric NO 2 VCDs against MAX-DOAS measurements is shown in Fig. 9b. Both OMI and TROPOMI NO 2 observations show good correlation with MAX-DOAS measurements with R = 0.85 and R = 0.93, respectively. However, both space borne observations report lower NO 2 columns than the MAX-DOAS.

Comparison of aerosol optical depth
Averaged difference between OMI and TROPOMI satellite observations and MAX-DOAS measurements of NO 2 VCDs are 10 -2.32 × 10 15 molec/cm 2 and -2.25 × 10 15 molec/cm 2 , respectively. The underestimation of NO 2 VCDs is partly related to the a-priori vertical distribution profile of NO 2 used in the air mass factor calculation of the satellite retrieval. These satellite apriori profiles are taken from the TM5 chemistry transport model simulation. The horizontal resolution of TM5 is rather coarse (1 • × 1 • ) which is not able to fully resolve emission hot spots over cites. In order to quantify the influence of the a-priori NO 2 profile in the satellite retrieval, we have recomputed the OMI and TROPOMI NO 2 VCDs by using MAX-DOAS NO 2 profiles 15 as a-priori information (labeled as OMI corr. and S5P corr. in Fig. 9). Monthly averages of the a-priori NO 2 profiles used in the satellite retrieval are shown in Fig. 10a, while the corresponding MAX-DOAS retrievals are shown in Fig. 10b. MAX-DOAS NO 2 profiles show about 4 times higher NO 2 levels at the surface compared to the original a-priori profiles used in the satellite retrieval. Using the MAX-DOAS NO 2 profiles as a-priori information generally increased the OMI and TROPOMI NO 2 VCDs by ∼45 % and ∼17 %, respectively. Due to difference in temporal coverage, OMI provides longer term measurement while TROPOMI measurements are only available after November 2017, the percentage increase of OMI and TROPOMI NO 2 VCDs are quite different. If we only consider the same period of November 2017 to July 2019, the percentage of increase is similar for OMI and TROPOMI. As can be seen in Fig. 9 the absolute values of OMI and TROPOMI NO 2 VCDs retrieved with MAX-DOAS NO 2 profiles as a-priori agree better with the MAX-DOAS measurements with correlation nearly unchanged. Previous satellite observations often underestimated the tropospheric NO 2 columns over cities or pollution hot spots. The underestimation is partially related to the large satellite footprint which is not able to capture the spatial gradient of NO 2 due to the averaging over large satellite pixels (Wenig et al., 2008;Chan et al., 2012). This averaging effect over hot spots can be estimated by using high resolution TROPOMI observations. Tropospheric NO 2 VCDs measured by TROPOMI are spatially averaged with different radii are shown in Fig. 11. Satellite data with their pixels center coordinate within certain radius of the 5 MAX-DOAS measurement site are used in the spatial averaging. The MAX-DOAS measurement in the UV typically covers a range of 5 -8 km depending on the visibility, while the measurement in the VIS has a better coverage of 8 -12 km. Therefore, the percentage of underestimation relative to the 5 km average is shown in Fig. 11 as reference. The result shows that the averaged NO 2 VCDs decreases with increasing averaging radius. NO 2 columns are underestimated by ∼8 % with an averaging radius of 10 km which is approximately the size of OMI footprint at nadir (13 km × 24 km). The underestimation increases to ∼13 % 10 and ∼34 % for averaging radius of 15 km (average OMI pixel size) and 50 km. These numbers are characteristic for pollution hot spots of the size of Munich (approximately 5 km in radius), but they could be different for hot spots of different size and spatial distribution. Although the spatial resolution of TROPOMI observations have been significantly improved compared to its predecessors, satellite observations are still critical to resolve spatial features of pollutant within a city. Therefore, ground based measurements are essential for the investigation of small scale pollution within a city.    Fig. 13b) instead of the TM5-10 profiles (see Fig. 13a) as a-priori information to estimate the influence of the a-priori profile. The MAX-DOAS profiles show larger amounts of HCHO in the lower troposphere. Using the MAX-DOAS profile as a-priori in the satellite retrieval in general enhanced the HCHO columns by ∼50 %. The averaged TROPOMI HCHO VCD increased to 6.37 × 10 15 moles/cm 2 . The slope of the regression line of the new data-set also increased to 1.04 (see Fig. 12b). Similar to the discussion on NO 2 retrievals we have analyzed the spatial averaging effect of satellite observations over a 15 HCHO emission hot spot. TROPOMI HCHO VCDs are spatially averaged with different radii surrounding the MAX-DOAS measurement site and the result is shown in Fig. 14. The underestimation relative to the 5 km average is also shown on the right axis. As expected the averaged HCHO VCDs decrease with increasing averaging radius. HCHO column for an averaging radius of 10 km is ∼7 % lower than the 5 km average. The underestimation increases to ∼8 % and ∼15 % with an averaging radius of 15 km and 50 km, respectively. The decrease pattern indicated that there are significant anthropogenic HCHO or HCHO precursor emission in Munich. However, compared to the decreasing pattern of NO 2 , HCHO shows a more homogeneous distribution as it is mainly originated from regional sources. Percentage (%) Figure 14. Tropospheric HCHO VCDs measured by TROPOMI spatially averaged with different radii surrounding the MAX-DOAS measurement site.

Summary and conclusion
In this paper, we present the first 2D Multi-AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) observations 5 of nitrogen dioxide (NO 2 ) and formaldehyde (HCHO) vertical profile in Munich, Germany. The measurement covers the time period from October 2016 to July 2019. We have determined vertical columns and vertical profiles of the aerosol extinction coefficient, NO 2 and HCHO for Munich. The measured data are used to analyze the spatio-temporal variation of NO 2 and HCHO. The spatial distribution of NO 2 was in general quite homogeneous in winter, however, with higher values at the city center during summer. Spatial pattern of HCHO shows higher values in the south in winter and a rather homogeneous 10 distribution in summer. Analysis of the relations between aerosols, NO 2 and HCHO shows higher aerosol to HCHO ratios in winter indicating a longer atmospheric lifetime of aerosol and HCHO and suggests that secondary aerosol formation is the major source of aerosol in Munich.
Our MAX-DOAS retrievals were also compared to independent data-sets: we used in-situ data from an ambient monitoring station for the intercomparison of surface aerosol extinction coefficients and MAX-DOAS derived NO 2 mixing ratios. A

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Pearson correlation coefficient of R = 0.91 was found between MAX-DOAS and in-situ measurements of surface level NO 2 , however, the MAX-DOAS reports ∼50 % lower NO 2 mixing ratios. Lower NO 2 values measured by the MAX-DOAS are due to the differences in spatial averaging. MAX-DOAS measurement of AOD was compared to AERONET data. The annual cycle was coherent with the MAX-DOAS measurements, and shows higher values in summer and lower values in winter.
Finally, we use tropospheric vertical column densities (VCDs) of NO 2 and HCHO derived from MAX-DOAS measurements to validate OMI and TROPOMI satellite observations. Monthly averaged data show good correlation with each other. However, satellite observations are on average 30 % lower than the MAX-DOAS measurements. Underestimation of NO 2 and HCHO 5 columns are largely related to the coarse spatial resolution of a-priori profiles of the satellite retrieval. Using MAX-DOAS observations as a-priori in satellite retrievals greatly reduce the underestimation.
In summary, our results demonstrate a wide range of applications of MAX-DOAS measurements in a global frame work, but also for investigations of the air quality in metropolitan areas. An obvious advantage is that different atmospheric components can be retrieved simultaneously. Thus, for the understanding of details of and reasons for the interactions between trace gases, 10 aerosols and meteorological variables, MAX-DOAS measurements can provide a substantial contribution, however, only the combination of different observation techniques (e.g. Schäfer et al., 2012;Geiß et al., 2017) and city scale resolving models (Vlemmix et al., 2015;Maronga et al., 2019a, b) can ultimately resolve the open questions and lead to (political) regulations for the future design of urban environments to meet high air quality standards.