A priori NO2 profile shapes used in the TROPOMI retrieval algorithms are specified using the TM5-MP CTM, which is an improved version of the TM4 CTM operated for the OMI DOMINO v2.0 product. TM5-MP has a finer spatial resolution (1∘ × 1∘), updated information on NOx emissions, and an improved description of relevant physical (photolysis rate constants) and chemical (reaction rate constants) processes (van Geffen et al., 2018). However, highly polluted areas typically exhibit strong NO2 vertical and horizontal gradients (see, e.g. Dieudonné et al., 2013; Ialongo et al., 2020; Zhao et al., 2020; Dimitropoulou et al., 2020; Pinardi et al., 2020). The sharp gradients between pollution plumes and background areas cannot be resolved properly at the horizontal scale of the model (∼ 100 km × 100 km). In Dimitropoulou et al. (2020), TROPOMI tropospheric NO2 VCDs were recalculated based on high-resolution MAX-DOAS profiles, while in Ialongo et al. (2020) a priori NO2 profiles were extracted from the Copernicus Atmospheric Monitoring Service (CAMS) regional CTM (Marécal et al., 2015; https://www.regional.atmosphere.copernicus.eu, last access: 18 January 2021). These transformations generally led to increased NO2 VCDs, resulting in a better agreement with reference ground-based measurements. In this study, a custom TROPOMI tropospheric NO2 product was also prescribed, based on NO2 profile shapes from the CAMS regional CTM ensemble. CAMS NO2 profiles, being a merge of CAMS regional (0.1∘ × 0.1∘; surface to 3 km altitude in seven layers; hourly data) and CAMS global (0.4∘ × 0.4∘; 3 km to TOA; 3-hourly data), analysed at the 0.1∘ grid of CAMS regional, were used to recompute the tropospheric AMFs and corresponding TROPOMI NO2 VCDs, referred to as VCDTROPO-CRE in the continuation of this work. In general, we find that the VCDs are increased by about 5 % to 40 % over the Brussels–Antwerp regions, depending on the day and location (see Fig. 2). In the absence of NO2 hotspots and plumes, the impact of changing the a priori profile is small. Both the standard and the custom TROPOMI NO2 products are compared with airborne APEX mapping data in Sect. 5.2.

For the APEX retrievals, AEPs and a priori NO2 profiles were constructed from the AOT and PBL height observations, as discussed in Sect. 4.2. In order to yield retrievals independent from the satellite, box profiles were used instead of the TROPOMI TM5-MP profiles, as displayed in Fig. 3a. When TM5-MP or CAMS profiles would be applied as a priori for the APEX retrievals, the AMF would increase with, respectively, 9 % and 10 % on average, which is largely consistent with a similar sensitivity study reported in Tack et al. (2017). For the APEX retrievals, we assumed a well-mixed NO2 and aerosol box profile scenario and urban aerosols with a high single-scattering albedo (SSA) of 0.93. This causes a multiple scattering scenario and an enhancement of the optical path length in the NO2 layer and results in an increase in the AMF. When instead considering a no-aerosol scenario for the APEX retrievals, the AMF drops by 10 % on average. We assume that the opposing effects of using (1) a priori profile shape assumptions different from the TROPOMI retrievals and (2) different aerosol assumptions tend to cancel each other out in the APEX retrievals.

Box AMFs were computed and plotted in Fig. 3b for APEX, operating at 6.5 kma.g.l., and TROPOMI, for both a low and high surface reflectance scenario and with fixed values for the other RTM parameters. The box AMFs describe the sensitivity of the observations as a function of altitude (Wagner et al., 2007). The shapes of both TROPOMI and APEX box AMFs are similar below the aircraft altitude (6.5 kma.g.l.), but APEX has a higher sensitivity. As can be seen, the nadir-looking airborne instrument has a peak in sensitivity in the layer directly under the sensor. Above the airborne platform, the sensitivity to NO2 converges rapidly with increasing altitude to a constant box AMF of 1.6, a value which corresponds to the geometrical AMF at the SZA of 50∘ assumed for this simulation. Due to scattering and absorption, the sensitivity decreases towards the ground surface where the bulk of the tropospheric NO2 is residing. The decrease in sensitivity is stronger for TROPOMI, due to the larger probability of scattering above the NO2 layer. For a low albedo case, i.e. 0.02, the box AMF of the layer closest to the ground surface (50 m thickness) is ∼ 50 % larger for APEX when compared to TROPOMI, while this is ∼ 15 % for a very high albedo case, i.e. 0.2. For the ensemble of the four data sets, the total tropospheric AMF is 1.1 ± 0.1 on average for TROPOMI retrievals and 1.7 ± 0.1 for APEX retrievals or approximately 50 % higher. This can be partly explained by a stronger decrease in sensitivity with increasing platform altitude due to the larger scattering probability above the absorbing layer.

The surface albedo used in the TROPOMI retrievals is currently based on a climatology made from 5 years of OMI data, aggregated to a grid of 0.5∘ × 0.5∘, as discussed in Sect. 4.1. In this section, we first compare the TROPOMI albedo at 440 nm with the surface reflectance product retrieved from the APEX at-sensor radiance at 490 nm (see Sect. 4.2). Similar to the assessment of coincident NO2 VCDs in Sect. 5.2.2, the spatiotemporal coinciding TROPOMI and APEX albedo grids are quantitatively compared by spatial averaging of all APEX albedo values within each TROPOMI pixel footprint for the ensemble of the APEX data sets. The latter is defined by the pixel corner coordinates provided in the L2 product, while the APEX albedo locations are defined by their respective pixel centre coordinates. TROPOMI pixels currently take the albedo values from the coarse OMI LER (∼ 50 km × 50 km), implying that groups of neighbouring TROPOMI pixels are assigned the same value. As a result, usually one APEX data set over a particular city covers only one to two different OMI LER albedo values. As APEX measures the albedo at high resolution (75 m × 120 m), we consider it as a good approximation of the effective albedo. By comparing the APEX albedo to the TROPOMI albedo, we can have an indication of the effective albedo variability over an urban area and how this is smoothed out in the TROPOMI/OMI LER due to its coarser resolution.

Analysing the ensemble of the four acquired APEX data sets provided in Table 1 at the native APEX spatial resolution of 75 m × 120 m, the APEX albedo is 0.040 on average and the variability within one TROPOMI pixel, expressed as the SD (standard deviation), is 0.022 on average or ∼ 55 % but can be up to 100 % for certain pixels. When resampled at the resolution of TROPOMI, the variability of the APEX-derived albedo is 0.012 on average or ∼ 30 %, with values ranging between 0.015 and 0.065 (see Fig. 4). The OMI-based TROPOMI albedo variability is low, i.e. 0.001, as only four different 0.5∘ OMI LER pixels are sampled over the APEX scenes. The strong effective albedo variability over urban areas, as illustrated by the APEX albedo, is not captured by the OMI LER. This is likely to introduce a noise in the NO2 VCD retrieval since this variability is not accounted for in the computed AMFs. In Sect. 5.2.2, it is shown that the comparison of APEX with coincident TROPOMI tropospheric NO2 SCDs exhibits a slightly smaller spread than when comparing APEX and TROPOMI VCDs.

The albedo for coincident TROPOMI pixels over the APEX scenes is 0.051, on average, or 0.011 (∼ 27 %) higher than APEX. This is somewhat surprising at first glance as one would expect that high albedo values, typically observed over urban areas (Heiden et al., 2007), would be smoothed out in the OMI LER low-resolution albedo product and that this would result in a lower overall albedo when compared to the high-resolution APEX product. However, Kleipool et al. (2008) discusses that a statistical analysis approach is used to yield a climatologically averaged reflectance in the OMI LER, instead of using an absolute minimum reflectance method or so-called minimum Lambertian equivalent reflectance (MLER). The statistical analysis approach results in a higher reflectance value than provided by the MLER. This is to take into account the presence of boundary layer haze and persistent cloud features. It seems that for clear-sky conditions, the OMI LER overestimates the surface reflectance and that for these conditions the MLER would be a better approximation. Over Belgium, OMI MLER (not provided in the TROPOMI L2 NO2 product) is approximately 0.005 lower than the OMI LER reflectance value, which would reduce the overestimation of TROPOMI reflectance to 0.006 when compared to APEX for the clear-sky flights. According to Boersma et al. (2004), for albedo values smaller than 0.200, an overestimation of the albedo by 0.005–0.010 can result in a 5 %–10 % increase of the tropospheric AMF and thus in a potential underestimation of the retrieved TROPOMI NO2 VCD.

The APEX and TROPOMI albedos have been both compared with Moderate Resolution Imaging Spectroradiometer (MODIS) albedo data and more specifically with the MODIS MCD43A3 black-sky albedo daily L3 500 m v006 product at 470 nm. Coincident APEX and MODIS albedo pixels are compared for the data set acquired over Antwerp on 27 June 2019, and the scatter plot is shown in Fig. 5a. The regression analysis shows a high correlation (R = 0.96) and a slope close to unity on a total of 2800 compared pixels, while the absolute difference is smaller than 0.005, on average. When comparing TROPOMI and MODIS albedo, both data sets are regridded to 0.5∘, which is the grid size of the OMI LER. Albedo pixels are compared for all of Belgium on 27 June 2019, and the scatter plot is shown in Fig. 5b. The dynamic range is much lower than for the comparison between APEX and MODIS albedo, and high albedo values (> 0.06), typically observed over urban areas, are smoothed out. The regression analysis shows a lower correlation (R=0.84), and the TROPOMI albedo is approximately 0.012 higher than MODIS. Similar statistics were found when comparing the data sets acquired on the other campaign days. The albedo is wavelength dependent and albedo products at different wavelengths have been compared: OMI LER at 440 nm, MODIS MCD43A3 at 470 nm, and APEX albedo at 490 nm. The wavelength dependency has been assessed by analysing the relative difference of the OMI LER albedo over Brussels and Antwerp between 440 and 470–490 nm for both the yearly and monthly OMI LER product (June). Overall, the OMI LER albedo increases slightly with wavelength but the increase is smaller than 4 % between 440 and 490 nm.

The observed overestimation of the OMI LER seems to be consistent with comparison studies reported in Kleipool et al. (2008). In the study, the OMI LER has been assessed for the entire globe by comparison with a similar LER map, based on data from the Total Ozone Mapping Spectrometer (TOMS) at 331, 340, 360, and 380 nm. The TOMS LER was approximately 0.015 lower than the OMI LER on average. GOME albedo at 335, 380, 440, and 494 nm was ∼ 0.005 lower on average. The OMI LER was approximately 0.020 higher than the black-sky albedo, derived from MODIS at 470 nm. According to Kleipool et al. (2008), this is partly related to viewing geometry effects of the bidirectional reflectance distribution function (BRDF) of the surface. The TROPOMI and MODIS reflectance products are also not provided at the same wavelength, and a statistical analysis approach is used to determine the reflectance value, instead of the OMI MLER. Even if a direct comparison of different albedo products is not trivial due to BRDF effects and albedo wavelength dependencies, among others, there is an indication that the OMI LER is overestimating the effective albedo in certain conditions, requiring a revision of the product and algorithm. Retrievals over strongly polluted areas also require an albedo product at higher resolution in order to resolve the typically strong albedo variability. A global gapless geometry-dependent LER (G3_LER) daily map product at 0.1∘, retrieved from the TROPOMI L1B radiances, is currently under development and discussed in Loyola et al. (2020). Also KNMI is working on a new TROPOMI LER product, extended compared to the OMI LER by including a viewing angle dependency, and will become available after the L1B product has been reprocessed to v2. As soon as a TROPOMI LER product becomes available, and its impact has been tested, this will be implemented to replace the OMI albedo climatology. New APEX validation flights over the Antwerp and Brussels region are foreseen for summer 2021 and will be valuable to assess (1) the retrieval impact of replacing the OMI LER by the TROPOMI LER and (2) the v2 reprocessing of the TROPOMI NO2 product.

Furthermore, for the NO2 retrieval, a surface albedo adjustment scheme has already been implemented and will become operational from v2.0 onwards (upgrade planned for the second half of 2020; Eskes et al., 2020). In this approach, the reflectivity measured in the NO2 fitting window will be compared with a computed reflectivity based on the LER climatology. In the event that the observed reflectivity is lower, the albedo value will be reduced to match the observation, and the AMF will be computed with the adjusted albedo. This approach should remedy part of the shortcomings of the current albedo climatology.

Due to the cloud-free conditions for Flight nos. 2 to 4, cloud parameters do not contribute to the uncertainties here. Nevertheless, the effective cloud fraction for the NO2 retrieval window at 440 nm, computed by FRESCO (Wang et al., 2008) and provided in the L2 product, was checked. For Flight nos. 2–4, a cloud cover of less than 1 % on average was computed over Belgium. During Flight no. 1, scattered clouds were present and a cloud fraction of on average 12 % was computed over Belgium.

A small cloud fraction of 12 % indicates that there is more scattering in the atmosphere than computed based on the LER value. In the TROPOMI NO2 retrieval, such small “cloud fractions” are used to implicitly compensate for aspects like too-small LER values (e.g. often the case over cities which have a higher reflectivity than the surroundings not resolved in the OMI map) or the presence of scattering aerosols, haze, or residual clouds. Ideally, the cloud pressure will indicate the altitude at which the scattering takes place. In practice, this is a challenge because cloud pressure uncertainties are large for small cloud fractions.

The TROPOMI L2 tropospheric NO2 product (OFFL v1.03.01) has been assessed based on independent high-resolution airborne APEX data, acquired over the target areas within 1 h of the S-5P overpass time. The mission accuracy and precision requirements for the TROPOMI L2 products have been formulated by the L2 Quality Working Group (QWG) and agreed on with the S-5P Mission Advisory Group (MAG). The accuracy of the tropospheric NO2 VCD product is targeted to be around 25 %–50 %, with a precision of 0.7 × 1015 moleccm-2 (Fehr, 2016).

The TROPOMI NO2 processing chain provides a realistic error budget. The total TROPOMI tropospheric NO2 VCD error, σVCDTROPO, is driven by (1) error propagation of the slant column errors, (2) errors associated with the separation of the stratospheric and tropospheric contributions, and (3) tropospheric AMF errors (van Geffen et al., 2018). The overall error in the TROPOMI tropospheric NO2 columns can be quantified based on Boersma et al. (2004): 1σVCDTROPOi=σSCDTROPOiAMFTROPOi2+σSCDTROPOistratoAMFTROPOi2+(SCDTROPOi-SCDTROPOistratoAMFTROPOi2⋅σAMFTROPOi)2.

The overall error variance is provided for each retrieval in the L2 product and is fully described in van Geffen et al. (2018). Analysis of the TROPOMI L2 NO2 VCDs, coinciding with the APEX data sets, reveals a mean VCD and absolute error of 6.8 (VCDTROPO) and 7.9 (VCDTROPO-CRE) ± 2.1 × 1015 moleccm-2 or a relative error of approximately 31 % and 27 %, respectively. The maximum relative error observed was 42 %. In general, larger relative errors are seen mostly over semi-background areas, reflecting mainly uncertainties in the slant and stratospheric column retrieval. Over polluted regions, the absolute errors increase, while the relative errors drop. Here, the retrievals are largely dominated by systematic errors in the computation of the AMFs. These are related to uncertainties in the assumptions made for the RTM parameters with respect to the true atmospheric state and are dominated by the NO2 profile shape, surface albedo, and cloud parameters (cloud fraction and height). Uncertainties propagated due to the NO2 profile assumptions and surface albedo have been discussed in Sect. 4.3. The effect of clouds, however, was not considered in this study, as data acquisition took place in mostly clear-sky conditions.

The TROPOMI precision is targeted to be better than 7.0 × 1014 moleccm-2 (Fehr, 2016). We looked into the fitting error, σSCDTROPOi, as a proxy to assess compliance with the mission precision requirement, as instrument noise is the dominant source of errors in the spectral fitting of TROPOMI level-1b spectra. Averaged over the four campaign days over Belgium, the precision is estimated to be 5.6 ± 0.4 × 1014 moleccm-2 and thus well within the requirement. This is consistent with an assessment performed over the Pacific Ocean and discussed in van Geffen et al. (2018), reporting precision levels between 5.0 and 6.0 × 1014 moleccm-2. Note that the TROPOMI noise level is approximately 30 % lower than the initial OMI noise level (as measured in 2005). This is due to the higher radiometric SNR of TROPOMI, which is around 1400–1500 (∼ 900–1000 for OMI) for an individual level-1b spectrum in the 400–500 nm range (van Geffen et al., 2018).

A full error budget for APEX NO2 VCD retrievals has been discussed in Sect. 4.6 in Tack et al. (2017). Like for TROPOMI, the overall error on the retrieved APEX NO2 VCDs, σVCDAPEX, is dominated by uncertainties related to the DOAS fit and AMF computation. The error on the retrieved differential slant column density (DSCD) or the slant error, σDSCDAPEX, estimated from the fit residuals in the DOAS analysis, is 3.1 × 1015 moleccm-2, on average. The error on the AMF computation, σAMFAPEX, depends on uncertainties in the assumption of the RTM inputs with respect to the true atmospheric state and is dominated by systematic errors in the surface albedo, NO2 profile, and aerosol parameters. An estimate of approximately 15 % is obtained for σAMFAPEX, following the detailed error budget described in Sect. 4.6 in Tack et al. (2017). Due to the negligible spatiotemporal variability of the stratospheric NO2 field in the time between the acquisition of the reference spectrum and the measurements, i.e. less than 1 h, the stratospheric NO2 contribution to the signal is expected to cancel out in the case of APEX retrievals and is consequently not treated as a key error source. On the other hand, the error originating from the estimation of the NO2 residual amount in the reference spectrum, σSCDref, can be considerable as discussed in Tack et al. (2017). SCDref is derived from co-located mobile-DOAS measurements and the error can be up to 1.8 × 1015 moleccm-2. The overall error in the APEX tropospheric NO2 columns can be quantified based on the following error propagation method: 2σVCDAPEXi=σDSCDAPEXiAMFAPEXi2+σSCDrefAMFAPEXi2+SCDAPEXiAMFAPEXi2⋅σAMFAPEXi2.

Analysis of all coincident APEX NO2 VCD reference measurements for the ensemble of the four flights reveals a mean VCD and absolute error of 8.0 ± 2.3 × 1015 moleccm-2 or a relative error of approximately 29 %. This is consistent with the retrieval errors found during previous APEX campaigns, e.g. BUMBA (Tack et al., 2017) and AROMAPEX (Tack et al., 2019), and is also in line with the typical error found for similar airborne hyperspectral imaging instruments (Tack et al., 2019). Spatiotemporal coinciding TROPOMI and APEX NO2 VCD grids are quantitatively compared in Sect. 5.2.2 by spatial averaging of all APEX NO2 VCDs within each TROPOMI pixel footprint, resulting in a decrease of the overall random uncertainty on APEX retrievals. As discussed in Sect. 3.2, the average APEX noise level is expected to decrease from ∼ 2.6 × 1015 to ∼ 5.0 × 1013 moleccm-2 after spatial aggregation. Propagating this into the mean APEX VCD error, σVCDAPEX is expected to be reduced from 2.3 to 1.6 × 1015 moleccm-2 or a reduction of the relative error from ∼ 29 % to ∼ 21 % on the retrieved APEX NO2 VCDs. The noise reduction has the biggest impact on retrievals over (urban) background areas, as the errors here are dominated by uncertainties in the slant column retrieval.

Satellite products can be optimally assessed based on airborne observations as a large amount of satellite pixels can be fully mapped at high resolution in a relatively short time interval, reducing the impact of spatiotemporal mismatches. The spatiotemporal coinciding TROPOMI and APEX NO2 VCD grids are quantitatively compared by spatial averaging of all APEX NO2 VCDs within each TROPOMI pixel footprint. The latter is defined by the pixel corner coordinates provided in the L2 product, while the APEX VCD locations are defined by their respective pixel centre coordinates. Note that TROPOMI pixels are only considered in the further analysis when they are covered for more than 50 % by APEX pixels in order to reduce undersampling. Prior to the comparison, TROPOMI retrievals were checked based on their quality assurance (QA) value. Only pixels with a QA value equal to or larger than 0.75 were selected, removing cloudy pixels (cloud radiance fraction > 0.5) and erroneous retrievals (van Geffen et al., 2018). Note that all TROPOMI retrievals over the target scenes were compliant with the QA threshold.

In Appendix A, tropospheric NO2 VCD statistics for coincident TROPOMI and APEX pixels are provided for Flight nos. 1 to 4 in Tables A1 to A4, respectively. In total, 58 TROPOMI pixels were assessed. For each TROPOMI pixel acquired over the target area, the tropospheric NO2 VCD is provided for both the TM5-MP-based (NO2 VCDTROPO) and CAMS-based (NO2 VCDTROPO-CRE) product. On average, NO2 VCDTROPO is 6.8 × 1015 moleccm-2 and NO2 VCDTROPO-CRE is 7.9 × 1015 moleccm-2. For the APEX NO2 retrievals, the mean and median NO2 VCD are provided for each TROPOMI pixel, as well as the SD, relative SD or coefficient of variation (RSD), and minimum and maximum NO2 VCD. On average, over all flights, NO2 VCDAPEX is 8.0 × 1015 moleccm-2, which is in good agreement with the average CAMS-based TROPOMI NO2 VCDs. The SD and RSD are on average 2.3 × 1015 moleccm-2 or 29 %, respectively. They provide a measure for the subpixel variability or spatial heterogeneity of the NO2 field within a TROPOMI pixel, which is studied in more detail in Sect. 6. Highest concentrations are observed in the plume over the Antwerp harbour with maxima of up to 40 × 1015 moleccm-2.

Corresponding scatter plots and linear regression analyses of co-located TROPOMI and averaged APEX NO2 VCD retrievals are provided in Fig. 8 for the ensemble of all four data sets. In Fig. 8a, TROPOMI pixels are only included in the comparison when they are covered for more than 50 % by APEX pixels, in order to reduce undersampling. However, for reference, linear regression analysis is also applied to all TROPOMI pixels having coincident APEX pixels and is provided in Fig. 8b. The data points are colour coded based on the number of APEX pixels averaged within a particular TROPOMI pixel. Vertical error bars indicate the overall error in NO2 VCDTROPO (Eq. 1), while the horizontal whiskers represent the error in NO2 VCDAPEX retrievals (Eq. 2), averaged over all APEX pixels coinciding with a particular TROPOMI pixel. Regression lines are colour coded grey and black for the comparison of NO2 VCDAPEX with NO2 VCDTROPO, and NO2 VCDTROPO-CRE, respectively. Note that data points are shown for the comparison of NO2 VCDAPEX with VCDTROPO-CRE only. Corresponding correlation statistics are provided in Table 4 for each individual data set, as well as for the ensemble of the four data sets.

Overall, for the ensemble of the four flights, good agreement can be observed for both low and high retrievals. The standard TROPOMI NO2 VCD product is well correlated (R = 0.92) and has a slope and intercept of 0.82 and 0.3 × 1015 moleccm-2 with respect to APEX NO2 reference observations. The observed negative bias is expected to be due to a combination of the limited spatial resolution of a priori input for the AMF computation, i.e. NO2 profiles at 1∘ from the TM5-MP CTM and surface albedo at 0.5∘ from the OMI LER. When replacing the TM5-MP a priori NO2 profiles by CAMS-based profiles, the correlation coefficient increases to 0.94 and the slope increases by 11 % to 0.93. Correcting for the estimated systematic bias of 0.005 to 0.010 in the TROPOMI/OMI LER in the case of clear-sky days, as discussed in Sect. 4.3.2, would scale up the TROPOMI VCD retrievals by 5 % to 10 %. In Fig. 8b, a less favourable slope (0.77) and a reduced correlation (R = 0.86) can be observed due to the effect of undersampling when considering all covered TROPOMI pixels. When considering only TROPOMI pixels which are fully covered by APEX observations (only 31 instead of 58 pixels), the statistics are of the same order as when applying the condition that TROPOMI pixels should be covered at least half by APEX observations. This assures us that the data set based on the latter condition is representative while increasing the amount of TROPOMI pixels that can be assessed.

Note that Table 4 also shows correlation statistics for the comparison of the tropospheric NO2 slant column product, which has been compared in the same way as the VCDs. The slope is around 0.5 as the APEX airborne retrievals have a higher sensitivity to the NO2 layer than the TROPOMI retrievals, resulting in larger SCDs. This is properly accounted for by the AMFs when converting to the vertical columns. When looking at the scatter, the SCDs exhibit a slightly larger correlation coefficient and lower root mean square error (RMSE), i.e. 7.8 and 8.1 × 1014 moleccm-2, for the comparison of SCDs and VCDs, respectively. As discussed in Sect. 4.3.2, this could be related to noise introduced in the VCD retrieval by the difference between the effective albedo variability and the albedo from the coarse OMI LER climatology used in the computation of the AMFs.

The NO2 VCD bias, defined by VCDTROPO(-CRE) - VCDAPEX, and NO2 VCD relative bias, defined by (VCDTROPO(-CRE) - VCDAPEX) / VCDAPEX ⋅ 100, have been calculated as well for the ensemble of the four data sets and are provided in Fig. 9 and Table 4. Data points and statistics are colour coded grey and black for the comparison of TM5-MP-based and CAMS-based TROPOMI NO2 VCDs with APEX NO2 VCDs, respectively. On average, the bias is -1.2 ± 1.2 × 1015 moleccm-2 or -14 ± 12 % for the difference between the standard TROPOMI NO2 VCD product and APEX. The bias is substantially reduced when replacing the coarse TM5-MP a priori NO2 profiles by CAMS-based profiles, which is -0.1 ± 1.0 × 1015 moleccm-2 or -1 ± 12 %. When the absolute value of the difference is taken, the bias is 1.3 × 1015 moleccm-2 or 16 %, and 0.7 × 1015 moleccm-2 or 9 % on average, when comparing VCDAPEX with VCDTROPO and VCDTROPO-CRE, respectively. In general, a stronger bias can be observed for high VCDs, related to the larger uncertainties on both the APEX and TROPOMI retrievals. Both sets of retrievals are well within the mission accuracy requirement of a maximum bias of 25 %–50 % for the TROPOMI tropospheric NO2 product for all individual compared pixels. These thresholds are indicated by the dashed red (25 %) and full (50 %) horizontal lines in Fig. 9b. Nevertheless, the standard tropospheric NO2 product is clearly biased low over polluted areas when compared to reference observations at higher resolution and this is consistent with the findings in other studies (Griffin et al., 2019; Ialongo et al., 2020; Zhao et al., 2020; Dimitropoulou et al., 2020; Judd et al., 2020; Verhoelst et al., 2021).

In addition to the limitations of a priori assumptions in the AMF computation, studied in Sect. 4.3, the remaining disagreement between the data sets can be potentially attributed to the following:

There is disagreement due to different sensitivities to the NO2 layer due to instrumental and algorithmic differences.

Both on 26 and 29 June 2019, there were two early afternoon S-5P overpasses over Belgium with a time difference between the two orbits of approximately 100 min. To assess the impact of the temporal NO2 variability, the changes in the NO2 field have been studied in the subsequent overpasses for the Belgian domain. Prior to the comparison, the data sets have been regridded to a common grid of size 0.1∘. On 26 June, the absolute value of the differences observed over the full Belgian domain was 3.8 ± 5.3 × 1014 moleccm-2 or 12 ± 10 %, on average. A maximum difference of 5.8 × 1015 moleccm-2 or 57 % was observed for a pixel over the harbour of Antwerp, most likely due to a combination of moving air masses in the key plumes and slight changes in the wind pattern. Additionally, the TROPOMI pixel footprints have different sizes and orientations which also has an effect when sampling the effective NO2 patterns and when regridding to the common grid size of 0.1∘. On 29 June, the absolute value of the differences observed was 3.6 ± 3.2 × 1014 moleccm-2 or 11 ± 8 %, on average, with a maximum of 2.0 × 1015 moleccm-2, again seen over the harbour of Antwerp.

When analysing the tropospheric NO2 VCD diurnal variation, retrieved from the Uccle MAX-DOAS station (50.8∘ N, 4.4∘ E; 100 ma.s.l.) for the four campaign days, we see a low variability during the merged APEX flight time (11:00–13:44 UTC) for Flight nos. 2 to 4 (see Fig. 11). The relative SD is lower than 10 %. However, during Flight no. 1, we observe a strong increase of the VCD from 1.5 to 2.9 × 1016 moleccm-2 and a RSD of 32 %. The instrument location is indicated by a white triangle in Fig. 7 and is pointed towards the Brussels city centre (35∘ N).

For the flights over the Brussels region, we have also compared the TROPOMI and APEX NO2 VCD with the MAX-DOAS NO2 VCD at the time of overpass and results are provided in Table 5. The TROPOMI NO2 VCD is provided for the pixel in which the station resides for both the TM5-MP-based and CAMS-based products. The APEX NO2 VCD is provided for the average within the TROPOMI pixel footprint over the MAX-DOAS station and for the specific APEX pixel over the station. As the MAX-DOAS is performing elevation scans in a fixed azimuth direction (35∘ N), APEX observations are also averaged along this line of sight (LOS) in order to take into account the instrument directivity and in order to reduce potential mismatches due to differences in spatial representativity. In this case, however, temporal mismatches can occur as APEX pixels, acquired in different flight lines, are averaged. Based on the study of Dimitropoulou et al. (2020), the horizontal sensitivity of the MAX-DOAS is estimated to be on the order of 10 km for measurements in Brussels during summertime and in the visible wavelength range. Subsequently, APEX pixels are integrated along the LOS up to a distance of 10 km. MAX-DOAS observations are filtered based on the degrees of freedom which should be larger than 2. Secondly, the relative RMSE of the difference between measured and calculated differential slant column densities with respect to the zenith spectrum of each scan should be smaller than 15 % (Dimitropoulou et al., 2020). On 26 June, there was clearly a pollution event not seen over the station but further northeast along the MAX-DOAS LOS, as can be observed in the APEX NO2 VCD grid (see Figs. 7a and 11). When averaging the APEX pixels along the MAX-DOAS LOS up to a distance of 10 km, the difference in MAX-DOAS and APEX NO2 VCD is reduced from 4.8 to 0.1 × 1015 moleccm-2. On 28 June, the diurnal variation in the NO2 field was much smaller. We see a slight underestimation of 0.3 × 1015 moleccm-2 for the APEX observation above the station when compared to MAX-DOAS, while the latter is overestimated by 1.2 × 1015 moleccm-2 when averaging along the LOS.