An improved tropospheric NO 2 column retrieval algorithm for TROPOMI over EuropeAn improved TROPOMI tropospheric NO 2 research product over Europe

. Launched in October 2017, the TROPOspheric Monitoring Instrument (TROPOMI) aboard Sentinel-5 Precursor provides the potential to monitor air quality over point sources across the globe with a spatial resolution as high as 5.5 km × 3.5 km (7 km × 3.5 km before 6 August 2019). The DLR nitrogen dioxide (NO 2 ) retrieval algorithm for the TROPOMI instrument consists of three steps: the spectral ﬁtting of the slant column, the separation of stratospheric and tropospheric contributions, 5 and the conversion of the slant column to a vertical column using an air mass factor (AMF) calculation. In this work, an improved DLR tropospheric NO 2 retrieval algorithm from TROPOMI measurements over Europe is presented. The stratospheric estimation is implemented using the STRatospheric Estimation Algorithm from Mainz (STREAM), which was developed as a veriﬁcation algorithm for TROPOMI and does not require chemistry transport model data as input. A directionally dependent STREAM (DSTREAM) is developed to correct for the dependency of the stratospheric NO 2 on the viewing 10 geometry by up to 2 × 10 14 molec/cm 2 . Applied to synthetic TROPOMI data, the uncertainty in the stratospheric column is 3 . 5 × 10 14 molec/cm 2 for polluted conditionsin case of signiﬁcant tropospheric sources. Applied to actual measurements, the


Introduction
Tropospheric nitrogen dioxide (NO 2 ) is an important atmospheric trace gas because of its contribution to the formation of tropospheric ozone, urban haze, and acid deposition (Charlson and Ahlquist, 1969;Crutzen, 1970;McCormick, 2013). NO 2 is a prominent air pollutant affecting the human respiratory system (World Health Organization, 2006). Substantial amounts of NO 2 are produced in the boundary layer from combustion processes. In Europe, cities regularly exceed the air quality standards 30 for NO 2 (European Commission, 2017), with road transport as the largest contributor, ahead of the energy and the industry sectors (Crippa et al., 2018).
To monitor and quantify the NO 2 column, NO 2 measurements have been provided for more than a decade on a global scale and daily basis by European satellite instruments, such as Global Ozone Monitoring Experiment (GOME) (Burrows et al., (MODIS) dataset (e.g. Vasilkov et al., 2017;Qin et al., 2019). In this study we use a new algorithm developed at DLR to retrieve geometry-dependent effective LER (GE_LER) in the VIS based on the full-physics inverse learning machine (FP_ILM) technique (Loyola et al., 2020b). Compared to the typical climatological LER or the directionally dependent (DLER) data 85 (Tilstra et al., 2021), the GE_LER data represents better the actual surface conditions such as snow/ice scenarios based on each single TROPOMI measurements with a high spatial resolution. GE_LER has been successfully applied in the retrievals of TROPOMI total ozone columns in the UV (Loyola et al., 2020b) and cloud parameters in the NIR (Loyola et al., 2020a) and is being used in the corresponding operational version 2.1 cloud products (see introduction below).
The varying sensitivity of the satellite to NO 2 at different altitudes is considered in the tropospheric AMF calculation using 90 vertically resolved box-AMFs and a priori NO 2 profiles. Typically prescribed by a chemistry transport model, the importance of applying a priori NO 2 profiles with sufficiently detailed resolution has been addressed (e.g. Russell et al., 2011;McLinden et al., 2014;Kuhlmann et al., 2015;Boersma et al., 2016;Laughner et al., 2016), particularly for TROPOMI with a small pixel size (Griffin et al., 2019;Liu et al., 2020b;Ialongo et al., 2020;Tack et al., 2020). Routine simulations of tropospheric trace gases and aerosols have been provided by POLYPHEMUS/DLR since 2014 with a spatial resolution of 0.2 • ×0.3 • (latitude, 95 longitude) covering Europe and parts of North Africa. POLYPHEMUS/DLR is an air quality modelling platform operated at DLR based on the POLYPHEMUS chemistry transport model (Mallet et al., 2007)

coupled to the Weather Research and
Forecasting (WRF) model (Skamarock et al., 2008). It has been further developed within the PASODOBLE project for sensitivity studies of the mountainous Black Forest region (Bergemann et al., 2012) and to cover urban areas in southern Bavaria (Khorsandi et al., 2018). It uses the TNO-MACC emission inventory (Kuenen et al., 2014). Daily model forecasts are freely 100 available via DLR Geospatial Web Services (http://wdc.dlr.de/cgi-bin/produkt_4d_w?).
The NO 2 retrieval is affected by the presence of clouds, because high clouds shield underlying parts of the atmosphere, and low clouds can enhance the NO 2 absorption due to cloud albedo and multiple scattering if they are below or at the same height as the NO 2 layer (Martin et al., 2002;Kokhanovsky and Rozanov, 2008). The operational cloud retrieval for TROPOMI is implemented using Optical Cloud Recognition Algorithm (OCRA) and Retrieval Of Cloud Information using to the surface is obtained for the smallest elevation angles, whereas measurements at higher elevations provide information on the rest of the column.
In this paper, a number of improvements to the tropospheric NO 2 retrieval over Europe are introduced. To estimate and 120 remove the stratospheric contribution, an improved STREAM algorithm is developed and evaluated by applying it to synthetic TROPOMI data and actual satellite observations. To calculate the tropospheric AMFs, the surface albedo is described by the GE_LER data consistently in both NO 2 and cloud retrievals; a priori NO 2 profiles are obtained from the regional POLYPHE-MUS/DLR chemistry transport model; the CAL cloud model from the new version 2.1 OCRA/ROCINN processor is used for cloud correction. 125 In Sect. 2, we introduce the reference algorithm at DLR for the TROPOMI NO 2 retrieval, which is based on an improved algorithm originally designed for GOME-2  and adapted for TROPOMI measurements with optimization related to the specific instrumental aspects. In Sect. 3 and 4, we improve the stratosphere-troposphere separation and the tropospheric AMF calculation, respectively. In Sect. 5, examples of applying the retrieval algorithm to TROPOMI measurements are shown, and the error estimates are discussed. In Sect. 6, we show a comprehensive validation of the TROPOMI NO 2 data 130 using ground-based MAX-DOAS observations in Europe.
2 Reference retrieval for TROPOMI NO 2 measurement 2.1 DOAS slant column retrieval Applied to the backscattered spectra measured by TROPOMI, the DOAS fit (Platt and Stutz, 2008) is a least-squares inversion to isolate the trace gas absorption from the background processes, which are approximated by a fifth-order polynomial P (λ) 135 at wavelength λ: The measurement-based term is defined as the natural logarithm of the measured earthshine radiance spectrum I(λ) divided by the daily solar irradiance spectrum I 0 (λ liquid water (H 2 O liq ) absorption at 297K from Pope and Fry (1997), smoothed as in Peters et al. (2014).
The contribution of the rotational Raman scattering to the measured spectrum, namely the Ring effect (Grainger and Ring, 1962;Solomon et al., 1987), is treated as a pseudo absorber, by means of an additive Ring reference spectrum R(λ) and a 150 scaling coefficient α R as fitting parameter. A linear intensity offset correction of f set(λ) is fitted as an additional effective cross-section to correct for the stray light in the spectrometer, the inelastic scattering in the ocean, and remaining calibration issues in the level 1 data . The TROPOMI level 1b version 1 spectra are analysed using the QDOAS software developed at BIRA-IASB (Fayt et al., 2011;Danckaert et al., 2017). Figure 1 shows examples of the TROPOMI NO 2 slant columns over Europe in February and August 2019, where large NO 2 hotspots can be identified. Note that the slant columns 155 are scaled by geometric AMFs to correct for the angular dependencies of TROPOMI measurements.
The NO 2 slant columns from single orbits show an across-track striping pattern, a well-known feature of observations of push-broom spectrometers such as OMI TROPOMI (van Geffen et al., 2020a), which is likely caused by the viewing zenith angle (VZA) dependency of the spectral calibration and detector sensitivity . To reduce the systematic stripes, a de-striping correction amplitude is calculated empirically  tribution of total columns to the stratospheric estimation: potentially polluted pixels are weighted low, cloudy observations with medium cloud heights are weighted high, and the weights are further adjusted in case of large biases in the tropospheric residues. Depending on these weighting factors, stratospheric NO 2 fields are derived by a weighted convolution of the total 170 columns using convolution kernels, which are wider at lower latitudes to account for the low longitudinal variability assumption of stratospheric NO 2 and narrower at higher latitudes to reflect the stronger natural variations.
STREAM was developed as a verification algorithm for the TROPOMI instrument, as a complement to the operational stratospheric correction based on data assimilation (van Geffen et al., 2020b). STREAM has been successfully applied to the NO 2 measurements from GOME, SCIAMACHY, OMI, and GOME-2 (Beirle et al., 2016;Liu et al., 2019) with the advantage 175 of requiring no model input. In contrast to previous modified reference sector methods which normally apply a conservative masking approach (flagging pixels as either clean or polluted and skipping the latter for stratospheric estimation) and hardly use information over continents, STREAM introduces an improved treatment of polluted and cloudy pixels by defining weighting factors for each satellite pixel. Stratospheric NO 2 columns from STREAM differ by up to 3 × 10 14 molec/cm 2 as compared to results from data assimilation and other modified reference sector methods, within the general uncertainties of stratosphere-180 troposphere separation (Beirle et al., 2016;. The STREAM stratospheric NO 2 columns show an average bias of 1 × 10 13 molec/cm 2 with respect to the ground-based zenith-scattered light differential optical absorption spectroscopy (ZSL-DOAS) measurements (Compernolle et al., 2020b).

AMF calculation
The conversion between the slant column S and the vertical column V is implemented by division with an AMF M : Given the small optical depth of NO 2 , M can be derived as: where m l is the box-AMFs in layer l, x l is the partial column from the a priori NO 2 profile, and c l is a correction coefficient to correct for the temperature dependency of the NO 2 cross section (Boersma et al., 2004;Nüß et al., 2006;Bucsela et al., 190 2013). m l is a function of model inputs b, which include TROPOMI measurement geometries, surface albedo, and surface pressure. The box-AMFs m l values are calculated at 437.5 nm (near the mid-point wavelength of fitting window 405-465 nm), as recommended by , using the linearised vector code VLIDORT (Spurr, 2006). The light path in the troposphere is affected by scattering on air molecules as well as cloud and aerosol particles, and therefore the tropospheric AMF calculation depends on surface albedo, a priori NO 2 profiles, and cloud properties. Table 1 summarises the parameters 195 used in the AMF calculation. Figure 2 shows the tropospheric NO 2 columns retrieved from the reference algorithm over Europe in February and August 2019. A large amount of NO 2 is located in the troposphere for industrialised and urbanised areas (see   In the reference algorithm, the surface albedo is described by a monthly climatology based on four years (2004)(2005)(2006)(2007) of OMI LER measurements at 440 nm (Kleipool et al., 2008) with a similar overpass time and viewing conditions as TROPOMI.

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The surface albedo for each TROPOMI pixel is calculated by an area-weighted tessellation of the OMI monthly averaged surface albedo maps (0.5 • ×0.5 • ) and a linear interpolation in time to the measurement day.
Daily TM5-MP vertical NO 2 profiles (Williams et al., 2017) simulated at a global 1 • ×1 • resolution are used as a priori NO 2 vertical profiles due to the operational advantage, as summarized in Table 2. The a priori profiles are determined for the satellite overpass time and interpolated to the center of the TROPOMI pixel based on four nearest neighbour TM5-MP cell centers.

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In the presence of clouds, the AMF calculation adopts the independent pixel approximation (Cahalan et al., 1994): where M cl represents the AMF for completely cloudy sky and M cr for completely clear sky. M cl and M cr are derived with Eq.
(3) with M cl mainly relying on the cloud pressure (height) and the cloud albedo (optical depth). The cloud radiance fraction Table 2. Summary of the chemistry transport model specifications.

Sweby flux limiter
Convection ECMWF WRF (Skamarock et al., 2008) Diffusion Holtslag and Boville (1993) second-order Rosenbrock method (Verwer et al., 2002) ω is derived from the TROPOMI cloud fraction c f : with I cl and I cr representing the radiances for cloudy and clear scenes, respectively. I cl and I cr are calculated using the LIDORT model (Spurr et al., 2001), depending mostly on TROPOMI viewing geometries, surface albedo, and cloud albedo.
The operational TROPOMI cloud parameters from the OCRA/ROCINN algorithms (Lutz et al., 2016;Loyola et al., 2018) with clouds treated as opaque Lambertian surfaces (CRB model) are applied for the cloud correction. OCRA derives the cloud (Koelemeijer et al., 2001;Wang et al., 2008). FRESCO for Sentinel (FRESCO-S) (Wang and Sneep, 2019) is implemented as a support product for the TROPOMI operational NO 2 processing (van Geffen et al., 2020b). FRESCO-S retrieves the cloud fraction and cloud pressure from the reflectance in and around the O 2 A-band. The cloud albedo is assumed to be 0.8, as opposed to OCRA/ROCINN, where cloud albedo is retrieved.

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3 New Stratosphere-troposphere separation STREAM was originally designed for TROPOMI and optimized for OMI within TROPOMI verification activities (Beirle et al., 2016). STREAM consists basically of two steps: the definition of weighting factors for each satellite pixel and the application of weighted convolution. To identify potentially polluted areas, a climatology of tropospheric NO 2 columns is derived in this study using TROPOMI NO 2 measurements from 2018-2019, instead of using SCIAMACHY NO 2 measurements from 2003-235 2011 as in the original STREAM. Based on the pollution weight, as well as the cloud weight and tropospheric residue weight, STREAM estimates stratospheric fields for individual orbits using a weighted convolution on 0.5 • ×0.5 • grid pixels.
As a result of wide swath (∼2600 km), local time differences across a TROPOMI swath are considerable at high latitudes, and the NO 2 measurements show dependency on VZA (directly related to local time) due to the diurnal variation of stratospheric NO 2 Belmonte Rivas et al., 2014). Figure 3 shows the total NO 2 columns measured by TROPOMI 240 in January 2019 for different latitudes as a function of VZA. The impact of local time changes across the orbit is up to 2 × 10 14 molec/cm 2 at the swath edge for latitudes higher than 50 • , in agreement with estimations for OMI measurements (Beirle et al., 2016).
In the following, the concept of a directionally dependent STREAM (DSTREAM) is introduced to estimate the stratospheric NO 2 column (Sect. 3.1). The performance of STREAM and DSTREAM is analyzed using synthetic TROPOMI NO 2 data 245 (Sect. 3.2), and both algorithms are applied to TROPOMI measurements (Sect. 3.3).

DSTREAM
To correct for the VZA dependency of stratospheric NO 2 , the DSTREAM is developed, which divides the orbit swath into Note that the VZA is defined negative for observations on the west side of the orbit swath throughout the study. For each of the 250 orbit swath containers, the original STREAM is applied based on data from the respective orbit swath segment.
For each individual satellite pixel with a VZA, a directionally dependent stratospheric NO 2 column V dir s is parameterized using a linear interpolation on the DSTREAM grid results estimated using the eastern, central, and western segments of the orbit swath. As the VZA dependency is negligible for low latitudes (from Fig. 3), and the interpolation error may increase for V dir s due to less orbital overlap, the final stratospheric NO 2 column V s is calculated as the weighted mean in dependence on 255 latitude θ: By this method, the stratospheric NO 2 from the original STREAM V ori s is applied for equator, and the VZA dependency is captured for polar regions with significant orbital overlap.

Application to synthetic data 260
The performance of the original STREAM and the improved DSTREAM for TROPOMI is evaluated with simulated NO 2 fields from the IFS(CB05BASCOE) experiment (Huijnen et al., 2016).   between the estimated and a priori results is 4 × 10 14 molec/cm 2 for STREAM and 3.5 × 10 14 molec/cm 2 for DSTREAM with improvements mainly for latitudes higher than 50 • .    Surface albedo is an important parameter for an accurate retrieval of trace gas columns and cloud properties. The sensitivity of backscattered radiance to the boundary layer NO 2 is strongly related to the surface albedo, especially over polluted areas.
In this study, the surface albedo is described using GE_LER retrieved by the FP_ILM algorithm (Loyola et al., 2020b). Unlike 290 conventional approaches (Rodgers, 2000;Doicu et al., 2010), FP_ILM is a machine learning based approach consisting of a training phase wherein an inverse function is derived from synthetic data generated with a radiative transfer model and an operational phase wherein the inverse function is applied to measured spectra. The FP_ILM algorithm has been employed to retrieve ozone profile shapes and sulfur dioxide layer heights from GOME-2 and TROPOMI (Xu et al., 2017;Efremenko et al., 2017;Hedelt et al., 2019).

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Combining the DOAS equation Eq. (1) and the conventional forward model, our forward problem can be formulated as an approximation of the DOAS-fitted slant column density (SCD) and the DOAS polynomial (P ) using the forward model (F ) with the solar/satellite viewing geometry (Θ), effective surface pressure (p e ), and surface albedo (A s ): During the training phase, synthetic TROPOMI spectra in the 405 -465 nm range are simulated by LIDORT (Spurr et al., 2001) 300 in conjunction with the smart sampling technique . The cloud impact is considered in the simulations with the use of the effective surface pressure p e , which depends on OCRA cloud fraction, ROCINN_CRB cloud pressure, and surface pressure (Loyola et al., 2020b). The aerosol influence is not considered. The DOAS fitting is applied to the simulated spectra using the consistent DOAS settings as introduced in Sect. 2.1. The simulation results from Eq. (7) are grouped as inputs to a multi-layer neural network, and the neural network is trained to learn the inverse function. In the operational phase, GE_LER is 305 generated using the trained neural network and the DOAS results from the measured spectra. An additional polynomial fitting is subsequently included to account for the bidirectional reflectance distribution function (BRDF) effect.
For consistency with the NO 2 retrieval, the GE_LER retrieval is performed for every single ground pixel using the same TROPOMI spectrum and DOAS configurations. Global maps are generated from the GE_LER retrievals under clear-sky conditions (OCRA cloud fraction small than 0.05) and updated on a daily basis on a time window between one and four weeks 310 depending on cloudiness. In contrast to the OMI LER climatology, the GE_LER data relies on the measurements from the TROPOMI instrument itself with an improved spatial resolution (0.1 • ×0.1 • ) and better characterizes the actual surface conditions, particularly for snow/ice scenarios. GE_LER enables a better representation of surface features. Larger differences by more than 0.2 are found in winter over snow/ice regions such as Russia and the Alps, because GE_LER captures the actual snow/ice conditions. The GE_LER values are higher by up to 0.05 over the North Sea, due to the use of only one month of TROPOMI data compared to the multiple years for OMI climatology, which makes GE_LER more likely affected by aerosol contamination. In the near future, an improved aerosol screening based on TROPOMI aerosol index data will be implemented in the GE_LER algorithm. 320 Figure 8 shows the monthly average differences in the tropospheric NO 2 columns retrieved using the climatological OMI LER and the TROPOMI GE_LER in February and August 2019. An effect is noticed mainly in winter under polluted conditions. Consistent with the LER changes in Fig. 7, the general reduced surface LER from GE_LER results in a decrease in the tropospheric AMF and thus an increase in the calculated tropospheric NO 2 column by up to 3 × 10 15 molec/cm 2 . A reduction by up to 1 × 10 15 molec/cm 2 is found for snow/ice coverages and aerosol scenes.

A priori NO 2 profiles
To account for the varying sensitivity of the satellite to NO 2 at different altitudes, the POLYPHEMUS/DLR simulations (Mallet et al., 2007) with a spatial resolution of 0.2 • ×0.3 • (latitude, longitude) and a temporal resolution of 1 h are applied for Europe in this study. Compared to the reference algorithm using TM5-MP a priori NO 2 profiles, it can be expected that the improved   resolution of POLYPHEMUS/DLR is better able to capture accurately the local NO 2 distribution, particularly for regions with 330 large heterogeneity and variability.
As summarized in Table 2, the meteorological parameters are provided by Weather Research and Forecasting (WRF) Version 3.5 daily forecasts with a 30 km×30 km spatial resolution, initialized by daily Global Forecast System (GSF) global forecast from National Oceanic and Atmospheric Administration (NOAA). The original POLYPHEMUS model is an assembly of several Eulerian and Gaussian models for handling passive tracers, photochemistry, and aerosol dynamics (Mallet et al., 2007) 335 and is developed based on the chemistry transport model Polair3D (Boutahar et al., 2004). In this study, the Regional Atmospheric Chemistry Modeling (RACM) chemical mechanism (Stockwell et al., 1997)   surface layer NO 2 concentration and yields a tropospheric AMF that is reduced by 0.36 (36.7%). Figure 9 additionally shows 345 the low-tropospheric NO 2 profile derived from the ground-based MAX-DOAS data (Chan et al., 2020) and the tropospheric AMF calculated using the MAX-DOAS NO 2 profile as a priori information (assuming a constant profile shape for the high  representation of the tropospheric boundary layer have the largest influence (not shown). The generally steeper profile shape from POLYPHEMUS/DLR (see Fig. 9) increases the retrieved tropospheric NO 2 columns by more than 2 × 10 15 molec/cm 2 for pollution hot spots, e.g. regions with large population or heavy industry in the Benelux, northern Italy, and western Turkey, as well as highways with intense road traffic in northern Spain, southern France, and western Germany.  The update of cloud-free background maps increases the cloud fractions by more than 0.1 for large cloud fraction values and 375 reduces the values by more than 0.1 for snow/ice covers, e.g. over the Alps and the Ore Mountains. Figure 12 shows the OCRA cloud fractions as a function of VZA. Mainly due to the improved VZA correction, the overestimation of cloud fractions, particularly at the east side of the orbit swath, are corrected by more than 0.3 for the new version 2.1 processor.   tion larger than 0.15 and cloud pressure larger than 700 hPa), e.g. northern Germany and the Benelux, the tropospheric NO 2 columns increase by more than 1 × 10 15 molec/cm 2 , because the increase in cloud fraction (and thus cloud radiance fraction) makes the retrieval less sensitive to the NO 2 below the cloud.

CAL cloud model
The cloud correction in our TROPOMI NO 2 retrieval is improved using the CAL model from the ROCINN cloud algorithm ). The CAL model, which regards the clouds as optically uniform layers of light-scattering water droplets, is more representative of the real situation than the CRB model, which treats the clouds as idealized Lambertian reflectors with zero transmittance. The CAL model considers the multiple scattering of light inside the cloud and the contribution of the 395 atmospheric layer between the cloud bottom and the ground. Compared to the CRB-based cloud correction, the use of CAL model considers the sensitivities inside and below the cloud layers and increases the tropospheric AMFs by 0.09 (13.2%) for Munich. Figure 16 presents the monthly average differences in the tropospheric NO 2 columns retrieved using the ROCINN_CRB and 405 ROCINN_CAL cloud models in February and August 2019. The use of CAL cloud correction decreases the tropospheric NO 2 columns by more than 1 × 10 15 molec/cm 2 for polluted regions in winter, when most of the NO 2 concentrations are located at the surface (as shown in Fig. 9) and the cloud fractions are generally larger due to the seasonal variation of clouds. The effect is less than 5 × 10 14 molec/cm 2 for summer.

Uncertainty estimates
Derived by uncertainty propagation (Boersma et al., 2004), the overall uncertainty on the tropospheric NO 2 column is directly related to the main retrieval steps, which are performed independently and assumed to be uncorrelated. The slant column 425 uncertainty, estimated following a statistical method (Boersma et al., 2007)  columns is 3.5×10 14 molec/cm 2 for polluted conditions based on the daily synthetic data (see Sect. 3.2) and 1×10 14 molec/cm 2 for monthly averages.
The tropospheric AMF calculation, which is the largest source of NO 2 uncertainty for polluted scenarios (Lorente et al.,430 2017), is mainly dependent on surface albedo, a priori NO 2 profile, cloud fraction, and cloud pressure, as introduced in Sect.
2.3 and 4. The tropospheric AMF uncertainties are calculated based on uncertainty propagation (Boersma et al., 2004) and typical uncertainties of each parameter (De Smedt et al., 2018, Table 8 therein). Figure 19 shows the estimated tropospheric AMF uncertainties due to the errors in the surface albedo, cloud pressure, and a prior NO 2 profile. The uncertainty contribution from the a prior NO 2 profile is practically described by a parameter referred 435 to as profile height, defined as the altitude (pressure) below which resides 75% of the integrated NO 2 profile . As the satellite measurements are normally filtered for cloud radiance fraction smaller than 0.5 or cloud fraction smaller than ∼0.2, the uncertainties related to the cloud fraction are generally smaller than 15% (not shown). From Fig. 19, larger uncertainties are found for small albedo values and for scenarios with large albedo biases such as new snow/ice coverage. The uncertainties due to the cloud pressure and a priori NO 2 profile can be up to 70% when the cloud is located below or within the 440 NO 2 layer, particularly for thick clouds at low altitudes and for polluted situations (large profile heights).
The presence of aerosols can affect the sensitivity to tropospheric NO 2 , depending on the particle properties and the NO 2 and aerosol vertical distribution (Martin et al., 2003;Leitão et al., 2010). The aerosol effect is not explicitly corrected in this study assuming that the effective cloud parameters from OCRA/ROCINN have partly accounted for the effect of aerosols on the light paths (Boersma et al., 2004. In comparison to the simple CRB-based cloud correction, which can not fully describe the 445 effects inherent to aerosol particles (Chimot et al., 2019), the use of CAL cloud correction considers the sensitivities inside and below the cloud/aerosol layers and reduces the AMF errors by more than 10% (Liu et al., 2020c). Figure 19. Tropospheric AMF uncertainties related to the surface albedo, cloud pressure, and a priori NO2 profile errors. By default, the surface pressure is 1050 hPa, the surface albedo is 0.05, the profile height is 840 hPa, the cloud pressure is 840 hPa, the cloud fraction is 0.2.
The definition of profile height is given in the text.
Note that the use of averaging kernel, which describes the vertical sensitivity of measurements of NO 2 concentrations, can remove the uncertainty contributed by the a priori NO 2 profile for applications such as data assimilation and validation study (Eskes and Boersma, 2003). Therefore, for a typical polluted scene, the tropospheric AMF uncertainty is estimated to be 20% 450 for mostly clear sky and 50% in the presence of clouds, leading to a total uncertainty in the tropospheric NO 2 columns in the 30-60% range.

TROPOMI tropospheric NO 2 validation
The validation of the improved TROPOMI tropospheric NO 2 columns is based on ground-based MAX-DOAS measurements from nine stations in Europe. Table 3 provides the information about the stations, most of which are characterised by urban or   20 includes the statistical information on the Pearson correlation coefficient as well as the slope and intercept obtained with the robust Theil-Sen estimator (Sen, 1968;Vigouroux et al., 2020). A correlation coefficient of 0.85, a slope of 0.70, and an intercept of −0.52 × 10 15 molec/cm 2 are derived when comparing the monthly mean values.  Figure 21 presents the daily and monthly mean absolute and relative differences of TROPOMI and MAX-DOAS measurements in Uccle. The differences are generally within 1 × 10 16 molec/cm 2 with a mean difference of −2.6 × 10 15 molec/cm 2 .
The NO 2 levels are underestimated by 34% by TROPOMI with a standard deviation of 16%, which is mostly explained by the relatively low sensitivity of spaceborne measurements near the surface, the aerosol shielding effect, and the gradient smoothing effect. These effects are often inherent to the remaining impact of structural uncertainties (Boersma et al., 2016), such as the 470 impact of the choice of the a priori NO 2 profiles and/or the albedo database assumed for the satellite AMF calculations, and to the different measurement types or the specific conditions of the validation sites.
To analyse the gradient smoothing effect for Uccle, TROPOMI measurements for 2018-2020 are aggregated based on an area-weighted tessellation to a resolution of 0.01 • ×0.01 • , and the systematic variation in tropospheric NO 2 columns between the satellite pixel location and the ground-based station position is shown in Fig. 22, following the method from Chen et al.

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(2009); Ma et al. (2013); Pinardi et al. (2020). From Fig. 22, the smoothing effect is largest for summer (up to 19%), as the NO 2 gradients are large due to the shorter lifetime, in agreement with Ma et al. (2013). For the Uccle site, which is located south of Brussels at a distance of ∼6 km from the city center, the tropospheric NO 2 columns increase by up to 4% outwards until 6 km due to the influence of the surrounding emission sources during summer and autumn. This effect is additionally influenced by the seasonal wind pattern, particularly for winter, when the wind is blowing in the direction of the site from north 480 (Dimitropoulou et al., 2020).   Figure 23 shows an overview of the daily differences between satellite and ground-based data for the improved and reference algorithms. impact of the algorithm improvements leads to a decrease of the mean absolute difference in urban/suburban conditions from −4.13 × 10 15 molec/cm 2 to −2.71 × 10 15 molec/cm 2 and relative difference from -55.3% to -34.7%. The largest absolute bias (−5.6 × 10 15 molec/cm 2 in Mainz) is reduced to −4.4 × 10 15 molec/cm 2 (relative bias from -60% to -40%), while the smaller absolute bias (−3.4 × 10 15 molec/cm 2 in Thessaloniki_ciri) is reduced to −2.2 × 10 15 molec/cm 2 (relative bias from -54% to -34%). The largest reduction is found for Athens (-27% reduction from the reference to improved algorithm).

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Smaller biases are found for the improved algorithm, not only in comparison with the reference algorithm but also compared to the operational product in Fig. 23, particularly for Athens, Thessaloniki_ciri, Thessaloniki_lap, Uccle, and Mainz. The relative biases ranging from -26 to -45% in Table 4 are lower than those reported by validation exercises for the operational TROPOMI product, where the NO 2 levels are normally found to be underestimated by the TROPOMI instrument by 30% to 50% for polluted conditions (Dimitropoulou et al., 2020;Verhoelst et al., 2020;Wang et al., 2020). These results are not 495 directly comparable to results e.g. obtained by Dimitropoulou et al. (2020), as they use a more elaborated ground-based dataset with several pointing directions and specific area-weighted pixel selections in the MAX-DOAS line-of-sight. Note that the operational tropospheric NO 2 columns have been increased with an upgrade of the NO 2 processor (version 01.04.00) since 29 November 2020 due to the improved handling of cloud pressures .
To investigate the impact of satellite a priori NO 2 profiles on the comparison, the satellite averaging kernel (see Sect. 5.2) 500 is used to relate the MAX-DOAS retrieved NO 2 profiles to satellite column measurements by calculating the smoothed MAX-DOAS columns as: The smoothed MAX-DOAS NO 2 columns V GB,smoothed are derived by convolving the layer (l)-dependent daily profile x GB,l (expressed in partial columns and interpolated to the satellite overpass time) with the satellite averaging kernel AK SAT,l . 505 Figure 24 shows the original and smoothed comparisons of satellite and MAX-DOAS data for the Munich station. The use of the averaging kernel smoothing reduces the MAX-DOAS columns and thus improves the agreement between the satellite and MAX-DOAS columns. When the satellite averaging kernels are used to remove the contribution of the a priori NO 2 profile shape, the mean absolute difference reduces from −3.4×10 15 molec/cm 2 to −1.9×10 15 molec/cm 2 , and the relative difference reduces from -39% to -23%. stratospheric NO 2 which amounts up to 2 × 10 14 molec/cm 2 at high latitudes is captured by DSTREAM.
In the tropospheric AMF calculation, the surface albedo from the monthly OMI LER climatology is replaced by the TROPOMI GE_LER data, which is consistently applied in both NO 2 and cloud retrievals. GE_LER in the NO 2 fitting window is retrieved using the machine learning based approach FP_ILM with inputs from the DOAS fitting. In comparison with the climatological LER values from previous satellite missions, the GE_LER data relies on the real-time measurements from 530 the TROPOMI instrument itself with an improved spatial resolution of 0.1 • ×0.1 • . Therefore, GE_LER better characterizes the actual surface conditions with an impact on the tropospheric NO 2 columns by up to 3 × 10 15 molec/cm 2 under polluted conditions.
Mesoscale-resolution a priori profiles (0.2 • ×0.3 • ), obtained from the regional POLYPHEMUS/DLR chemistry transport model based on the European TNO-MACC_II emission inventory, provide a better description of the spatial variability in the 535 NO 2 fields for Europe. Compared to the currently used TM5-MP profiles, the POLYPHEMUS/DLR profiles generally show higher surface NO 2 concentrations, which reduce the tropospheric AMFs and thus enhance the tropospheric NO 2 columns by more than 2 × 10 15 molec/cm 2 for polluted regions.
The presence of clouds is considered using the TROPOMI operational cloud retrieval algorithms OCRA/ROCINN. In a new version 2.1 processor, OCRA separates a spectral scene (in the UV-VIS wavelength range) into cloudy contribution and cloud-540 free background using TROPOMI-based background maps (0.1 • ×0.1 • ) instead of OMI-based ones, and ROCINN applies the surface albedo from the GE_LER data in the TROPOMI NIR instead of a static climatology. The overestimation of cloud fractions at the swath edge is corrected. Larger differences in cloud fractions and cloud pressures are found for relatively thick clouds, which affect the tropospheric NO 2 columns by more than 1 × 10 15 molec/cm 2 . In the tropospheric AMF calculation, the CRB model from ROCINN, in which clouds are idealized Lambertian reflectors, is replaced with the CAL model, in which clouds are represented by uniform layers of water droplets. CAL is more representative of the real situation and preferred for small TROPOMI ground pixels and for low clouds. The application of CAL cloud parameters considers the sensitivities inside and below the cloud layers and reduces the tropospheric NO 2 columns by more than 1 × 10 15 molec/cm 2 for polluted regions.
The uncertainty in the NO 2 slant columns is 4.5×10 14 molec/cm 2 , derived from the spatial variability over the Paficic Ocean.
The uncertainty in the stratospheric columns is 3.5 × 10 14 molec/cm 2 for polluted regions based on daily synthetic TROPOMI 550 data. The tropospheric AMF uncertainty is estimated to be 20% for mostly clear sky and 50% in the presence of clouds, leading to a total uncertainty in the tropospheric NO 2 column in the 30-60% range.
Validation of the improved TROPOMI tropospheric NO 2 columns is performed by comparisons with ground-based MAX-DOAS measurements. The validation is illustrated for nine European stations with urban/suburban conditions. The improved data shows a similar seasonal variation in the tropospheric NO 2 columns as the MAX-DOAS measurements with an average 555 correlation coefficient of 0.78. Compared to the reference data, the improved algorithm shows a significant improvement with absolute differences decreasing from −4.13 × 10 15 molec/cm 2 to −2.71 × 10 15 molec/cm 2 on average and relative differences from -55.3% to -34.7%. When the satellite averaging kernels are used to remove the contribution of a priori NO 2 profile shape, the absolute difference at the Munich station reduces from −3.4 × 10 15 molec/cm 2 to −1.9 × 10 15 molec/cm 2 , and the relative difference reduces from -39% to -23%.

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In the future, the spectral effect of extending the fitting window to 490 nm will be analysed, when the pixel blooming is better treated in a future update of the TROPOMI level 0-1b processor. The operational OCRA/ROCINN cloud parameters will be compared with other cloud products such as FRESCO-S and MICRU. The interpretation of the cloud product for aerosol-dominated scenes and the impact on the NO 2 retrieval algorithm will be further investigated. Aerosol contamination will be removed in the GE_LER retrieval using TROPOMI aerosol index data. The NO 2 data quality will be further analysed 565 using data from additional ground-stations covering different pollution conditions and data from validation campaigns with independent instruments.
The NO 2 retrieval algorithm can be adapted for new instruments and missions, such as the polar-orbiting Sentinel-5 and geostationary Sentinel-4 missions, which offer new perspectives for monitoring NO 2 with a fast revisiting time and a high spatial resolution and provide information on atmospheric variables in support of European policies.

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Data availability. The TROPOMI NO2 datasets used in the study are available upon request.
Author contributions. SL and PV developed the retrieval framework. SL processed the data, analysed the results, and contributed to the level 1 products. We thank DLR colleagues for developing the Universal Processor for UV/Vis Atmospheric Spectrometers (UPAS) system used for generating level 2 products from TROPOMI. This paper contains modified Copernicus Sentinel data processed by DLR. Eskes, H. J. and Boersma, K. F.: Averaging kernels for DOAS total-column satellite retrievals, Atmos. Chem. Phys., 3, 1285Phys., 3, -1291Phys., 3, , 2003