The QA4ECV NO2 OMI version 1.1 data product is retrieved from Level 1 UV–Vis spectral measurements (OMI-Aura_L1-OML1BRVG radiance files) from the Dutch–Finnish UV–Vis nadir-viewing OMI (Ozone Monitoring Instrument) spectrometer on NASA's Earth Observing System Aura (EOS-Aura) polar satellite. The nominal footprint of the OMI ground pixels is 24×13 km2 (across × along track) at nadir to 165×13 km2 at the edges of the 2600 km swath, and the ascending node local time is 13:42 LT. For more details on the instrument, see . The data product provides a Level 2 (L2) tropospheric, stratospheric and total NO2 VCD.

The QA4ECV algorithm includes the following steps: (i) retrieving the total slant column density (SCD) Ns using differential optical absorption spectroscopy (DOAS), (ii) estimating the stratospheric SCD Ns,strat from data assimilation using the TM5 (Tracer Model, version 5) chemistry transport model (CTM), (iii) obtaining the tropospheric contribution by subtraction and (iv) calculating the tropospheric air mass factors (AMFs) Mtrop by converting the SCD to a VCD Nv,trop (see Table ). The retrieval equation is as follows: 1Nv,trop=Ns-Ns,stratMtrop More information can be found in the “Product Specification Document for the QA4ECV NO2 ECV precursor product” and in and . A preliminary evaluation of the data indicated that QA4ECV NO2 values are 5 %–20 % lower than the earlier version of the OMI NO2 data product, DOMINO v2, over polluted regions, and that they agree slightly better with MAX-DOAS NO2 VCD measurements in Tai'an (China) and De Bilt (the Netherlands) than the DOMINO v2 VCDs .

The data product files contain a comprehensive amount of metadata. For each pixel, the satellite data product provides a total ex ante uncertainty on the retrieved tropospheric VCD as well as a breakdown of the uncertainty uSAT into an ex ante uncertainty budget with the following uncertainty source components: uncertainty in total SCD uSAT,Ns; stratospheric SCD uSAT,Ns,strat; and tropospheric AMF uSAT,Mtrop, which contains contributions from uncertainties in surface albedo uSAT,As, cloud fraction (CF) uSAT,fcl, cloud pressure uSAT,pcl and a priori profile shape uSAT,Sa; and an albedo-CF cross-term, with cAs,fcl representing the error correlation coefficient between both properties Sect. 6. 2uSAT2=uSAT,Ns2+uSAT,Ns,strat2+uSAT,Mtrop2uSAT,Mtrop2=uSAT,As2+uSAT,fcl2+uSAT,pcl2+uSAT,Sa2+2cAs,fcluSAT,AsuSAT,fcl Furthermore, the satellite data files provide several relevant instrument parameters, influence quantities (e.g. cloud fraction, surface albedo and terrain height), intermediate quantities (e.g. SCD, AMF and stratospheric SCD) and the column averaging kernel aSAT, which relates the retrieved VCD to the true profile. The a priori NO2 profiles (simulated with TM5) are not stored in the data files. If users have to adapt a (measured or modelled) profile xh at a high vertical resolution to the vertical sensitivity of the satellite, they can apply Eq. (11) from : 3aSAT⋅xh=xh,sm, where the a priori profile xSAT,a is not explicit. The dependence of the retrieval on xSAT,a is already implicit via the averaging kernel aSAT.

However, the reference data in the current work are column retrievals or profile retrievals with a limited vertical resolution and are based on an a priori profile that is different from the satellite retrieval. Before smoothing, satellite and reference retrievals should be adjusted such that they use the same a priori profile ; therefore, knowledge of the satellite a priori profile is relevant. These can be derived from the TM5-MP data files , which are available upon request seefor contact details, by spatially interpolating the profiles to the location of the satellite ground pixel.

In this work, we considered data from 2004 up to and including 2016 for the tropospheric VCD and up to and including 2017 for the stratospheric VCD.

The Stratospheric Estimation Algorithm From Mainz (STREAM; ) was included as an alternative stratospheric estimation scheme in the QA4ECV NO2 data files. In STREAM, the estimate of stratospheric columns is based on satellite observations with a negligible tropospheric contribution, i.e. generally over regions with low tropospheric NO2 levels, and for satellite pixels with high clouds, where the tropospheric column is shielded. The stratospheric field is then smoothed and interpolated globally, assuming that the spatial pattern of stratospheric NO2 does not feature strong gradients.

Although not the main focus of this work, we do include NASA's OMI NO2 data – OMNO2 version 3.1 – as a benchmark comparison of an alternative retrieval product with QA4ECV MAX-DOAS. Like QA4ECV OMI NO2, OMNO2 is also based on the DOAS approach, although nearly all retrieval steps are different between the QA4ECV and NASA OMI NO2 algorithms (Table ). A detailed comparison of the QA4ECV and NASA fitting approaches showed small differences between NO2 SCDs ; thus, differences between the spectral fitting approaches only explain a small part of the differences in the tropospheric VCDs. The stratospheric correction approach differs between the two algorithms. Although the QA4ECV and NASA stratospheric SCDs have not been compared directly, previous evaluations suggest that differences between the approaches typically lead to small but spatially widespread differences of up to 0.5–1.0×1015 molec.cm-2 in tropospheric VCDs. This leaves differences between the tropospheric AMF calculations (and especially the prior information used in their calculations) as the most likely explanation for the lower NASA values compared with QA4ECV NO2 VCDs e.g..

The ZSL-DOAS data are part of the Network for the Detection of Atmospheric Composition Change (NDACC; see also http://www.ndaccdemo.org/, last access: 22 April 2020), which is a major contributor to the WMO's Global Atmospheric Watch. A significant part of the multi-decadal ZSL-DOAS data is provided by the Système d'Analyse par Observation Zénithale SAOZ; see subnetwork from the IPSL Atmospheres Laboratory (LATMOS), using SAOZ instrumentation in automated data acquisition mode and with fast data delivery.

Zenith-sky measurements are performed during twilight at sunrise and sunset. Due to this measurement geometry with a long optical path in the stratosphere, the measured column is about 14 times more sensitive to stratospheric NO2 than to tropospheric NO2 . Moreover, it allows for usable measurements to also be made during cloudy conditions. Processing followed the NDACC standard operation procedure (http://ndacc-uvvis-wg.aeronomie.be/tools/NDACC_UVVIS-WG_NO2settings_v4.pdf, last access: 22 April 2020), as implemented, for instance, in the LATMOS_v3 SAOZ processing. From slant column intercomparisons, deduce an uncertainty of about 4 %–7 %, but this excludes the uncertainty on the AMF required to convert the slant to vertical columns. estimate a total uncertainty on the vertical columns of 21 %, but this is probably an overestimation for the most recent processing, as now suggest a 13 % total uncertainty. A visualization of the geographical distribution of the instruments is provided in Fig. . More details about the particular co-location scheme, considering the large horizontal smoothing of these measurements and the photochemical adjustment required to convert twilight measurements to satellite overpass times, are provided in Sect. .

The tropospheric NO2 VCD data used as a reference are a long-term record of MAX-DOAS (multi-axis DOAS) measurements from 10 instruments, reprocessed by different teams for the QA4ECV project (see Table ). MAX-DOAS instruments measure scattered sunlight under different viewing elevations from the horizon to the zenith . The observed light travels a long path (the length is dependent on the elevation angle) in the lower troposphere, while the stratospheric contribution is removed by a reference zenith measurement. Two different MAX-DOAS data processing methods were used for the current validation study, QA4ECV MAX-DOAS and bePRO (Belgian Profiling) MAX-DOAS , with the latter being part of NDACC.

Thanks to an extensive harmonization effort within the QA4ECV project, reference QA4ECV MAX-DOAS data sets were produced by the different teams for all 10 instruments. These data sets are available at http://uv-vis.aeronomie.be/groundbased/QA4ECV_MAXDOAS/index.php (last access: 22 April 2020). This effort was based on a four-step approach see http://uv-vis.aeronomie.be/groundbased/QA4ECV_MAXDOAS/QA4ECV_MAXDOAS_readme_website.pdf, last access: 22 April 2020;, including (i) the establishment of recommendations for DOAS analysis settings from an intercomparison of NO2 slant column densities retrieved from common spectra, (ii) the development of NO2 AMF look-up tables (LUTs) to harmonize the conversion of SCDs into VCDs, (iii) the establishment of a first harmonized error budget and (iv) the generation of MAX-DOAS data files in the Generic Earth Observation Metadata Standard (GEOMS) as a common format. It is worth noting that as only SCDs measured at a relatively high elevation angle (typically 30∘) are used to minimize the impact of aerosols and a priori profile shape on the retrieval in this QA4ECV approach, the horizontal location of the centre of the effectively probed air mass is close to the instrument location (typically within 1 km). The NO2 AMF LUTs are produced using the bePRO/LIDORT radiative transfer suite . This tool uses the following input (among others): a set of NO2 vertical profile shapes, vertical averaging kernel LUTs, geometry parameters (e.g. solar angles and viewing angles) and aerosol optical density (AOD) vertical profile shapes. Column averaging kernel LUTs were calculated based on the approach, using the bePRO/LIDORT radiative transfer model initialized with similar parameter values to those used for the calculation of the AMF LUTs. Interpolated AMFs as well as the corresponding vertical profile shapes and column averaging kernels are generated by the tool. More detail is provided in .

The second processing method, bePRO MAX-DOAS , is available for three BIRA-IASB instruments (at Bujumbura, Uccle and Xianghe). This approach, which is based on the optimal estimation method OEM; see, provides profile measurements, albeit with a limited degree of freedom for signal in the vertical dimension, which is typically ∼2 (Bujumbura and Uccle) or ∼3 (Xianghe). The horizontal extension of the air masses probed by profile retrieval MAX-DOAS is about 5–15 km from the instrument in the viewing direction . The extension depends on the atmospheric visibility (lower extension for lower visibility) and the altitude of the NO2 layer (lower extension with decreasing profile height). This is in line with the typical distances estimated by studies such as their Fig. 17. The horizontally projected area of the air mass probed by the MAX-DOAS is estimated to be of the order of 0.01 to 0.2 km2 for QA4ECV MAX-DOAS and ∼1 km2 for bePRO MAX-DOAS, assuming a 1∘ field of view and a simple geometrical approximation.

There is a clear distinction between the QA4ECV MAX-DOAS and bePRO retrieval algorithms. In the QA4ECV MAX-DOAS algorithm, the VCD is obtained by dividing a differential SCD by a differential AMF at a single elevation angle (see Sect. 1.3 of ). In the bePRO approach , a VCD is obtained by integrating a vertical NO2 profile retrieved by an optimal estimation method using measurements at several elevation angles.

MAX-DOAS instruments probe the lower troposphere, with the highest sensitivity (described by the column averaging kernel) close to the surface, typically in the lowest 1.5 km of the atmosphere. Nevertheless, the vertical grid extends to ∼10 km for QA4ECV MAX-DOAS and ∼3 km for bePRO MAX-DOAS.

The MAX-DOAS sites span a wide range of NO2 levels, from relatively low at Observatoire de Haute-Provence (OHP) and Bujumbura, with a mean tropospheric MAX-DOAS VCD around the OMI overpass time of ∼3 Pmolec.cm-2, to strongly polluted at Xianghe, with a mean MAX-DOAS value of ∼24 Pmolec.cm-2 (see Fig. c, black boxplots), whereas the other sites are moderately polluted (mean value of between 5.6 and 11 Pmolec.cm-2).

The MAX-DOAS tropospheric VCD is provided with an ex ante uncertainty in the GEOMS data files. Unfortunately the uncertainty estimation approach employed is not harmonized among all data providers. Therefore, we set the total uncertainty at 22.2 % of the retrieved VCD for QA4ECV MAX-DOAS instead, following the QA4ECV deliverable D3.9 recommendation . Using sensitivity tests, aerosol effects (20 %) and the NO2 a priori profile shape (8 %) were identified as the main contributors to the MAX-DOAS uncertainty, whereas the uncorrelated instrument noise was only 2 %. However, we did not follow D3.9 in its recommended division of the uncertainty into the random error and systematic error contributions

In D3.9, the systematic error uncertainty is set at 3 %, arising from absorption cross-section-related systematic error uncertainty on the SCD, whereas the random error uncertainty is set at 22 %, arising from uncertainty on the AMF. However, the assumption that an error in a priori profile shape, for example, would translate to a random error on the retrieved column is not evident in our opinion. In a later analysis , a comparison of QA4ECV MAX-DOAS with more advanced MAX-DOAS profiling methods was performed. This highlighted systematic differences between -12 % and +7 %, which are considerably larger than the systematic error uncertainty of 3 % recommended by the D3.9. This suggests that a larger part of the total uncertainty is due to systematic error. Therefore, in this work, we only consider a total uncertainty of 22.2 %, which is derived from the sum of the recommended systematic and random components in quadrature.

We note that the bePRO profile retrieval algorithm has recently been compared to several other retrieval algorithms . In future validation work, the consideration of other retrieval algorithms that performed well in the intercomparison exercises of and would be of high interest.

As the accuracy of satellite or ground-based remote sensing can be affected by the presence of aerosol, tracking aerosol optical depth (AOD) is useful. The bePRO MAX-DOAS provides AOD measurements at the same temporal sampling resolution as the NO2 measurements. The QA4ECV MAX-DOAS provides an AOD climatology based on AERONET (Aerosol Robotic Network) data ; however, we found that the precision of this climatological data set was inadequate for the current work, especially for urban sites. Instead, we considered AOD directly from AERONET (; http://aeronet.gsfc.nasa.gov, last access: 22 September 2019), whose measurements are based on Cimel Electronique Sun–sky radiometers. Level 2.0 AOD at a wavelength of 440 nm was chosen, which is within the QA4ECV MAX-DOAS retrieval window of 425–490 nm. Note that the AERONET data are already cloud filtered.

A limitation when investigating AOD dependencies in satellite MAX-DOAS comparisons using AERONET AOD with QA4ECV MAX-DOAS tropospheric NO2 VCD data (compared with using bePRO AOD with bePRO NO2 data) is that it implies subsetting: for part of the QA4ECV MAX-DOAS NO2 data, no co-located AERONET AOD data are available. Moreover, as opposed to the bePRO NO2/bePRO AOD combination, co-located QA4ECV MAX-DOAS NO2 / AERONET AOD data pairs have a temporal co-location mismatch and (where instruments are at different locations) a spatial co-location mismatch. A test was performed (results not shown) using the bePRO NO2 / AERONET AOD combination, and it was generally found that the results are less clear than for the bePRO NO2/bePRO AOD combination.

Filters are applied to the satellite data product following the recommendations in the QA4ECV NO2 product specification document (PSD; ) as well as to minimize comparison error with MAX-DOAS.

Following the QA4ECV NO2 PSD , satellite data are kept for tropospheric NO2 validation if the following conditions are met: (1)

no raised error flag;

Regarding the OMNO2 data product, we followed the recommendation of by only including ground pixels for which the least significant bit of the VcdQualityFlags variable is zero (indicating good data). Furthermore, the effective cloud fraction must be less than 0.2 and the pixel area must be less than 950 km2.

No screening was applied to the ground-based reference data sets. In particular, filtering is not applied on the MAX-DOAS cloud flag as a baseline, as it is not available for all data sets. It should be noted that clouds can impact the quality of MAX-DOAS retrievals (see e.g. radiative transfer simulations of , and ).

The air mass to which a ZSL-DOAS measurement is sensitive spans over many hundreds of kilometres towards the rising or setting Sun e.g.. The co-location scheme employed here takes this into account by averaging all OMI ground pixels of a temporally co-located orbit (with a maximum allowed time difference of 12 h) that have their centre within the ZSL-DOAS observation operator. This observation operator is a 2-D polygon that results from the parametrization of the actual extent of the air mass to which the ZSL-DOAS measurement is sensitive. Its horizontal dimensions were derived using the UVSPEC/DISORT ray tracing code , mapping the 90 % interpercentile range of the stratospheric vertical column to a projection on the ground, and then parameterizing it as a function of the solar zenith and azimuth angles during the twilight measurement, where the SZA during a nominal single measurement sequence is assumed to range from 87 to 91∘ (at the location of the station). Note that the station location is not part of the area of actual measurement sensitivity. The average OMI stratospheric column over this observation operator can then be compared to the column measured by the ZSL-DOAS instrument. An illustration of a single such co-location is presented in Fig. . Note that the above-mentioned SZA range may not be covered entirely at polar sites. For more details, we refer the reader to and .

To account for effects of the photochemical diurnal cycle of stratospheric NO2, the ZSL-DOAS measurements, obtained twice daily at twilight at each station, are adjusted to the OMI overpass time using a model-based factor. The latter is extracted from LUTs that are calculated with the PSCBOX 1-D stacked-box photochemical model initiated by daily atmospheric composition and meteorological fields from the SLIMCAT chemistry transport model . The amplitude of the adjustment depends strongly on the effective SZA assigned to the ZSL-DOAS measurements; it is taken here to be 89.5∘. The uncertainty related to this adjustment is of the order of 10 % or 1 to 2 1014molec.cm-2.

Regarding the tropospheric column validation, satellite data are kept if the satellite ground pixel covers the MAX-DOAS instrument location and if a MAX-DOAS measurement is within a 1 h interval centred on the satellite measurement time. The average of all MAX-DOAS measurements within this 1 h interval is taken. The typical number of MAX-DOAS measurements taken within this time interval was between two and four for most sites. This procedure was applied to both QA4ECV OMI NO2 and the OMNO2 comparisons.

Part of the discrepancies between the OMI and the MAX-DOAS data sets are due to comparison errors. Starting from the general comparison equation , the difference between satellite and reference measurements can be approximated in this specific case as 4Nv,trop,SAT-Nv,trop,REF=etotal=-eREF+eSAT+eSr+eΔr+eΔt+eΔz, where Nv,trop,SAT and Nv,trop,REF are the tropospheric VCD values measured by satellite and reference ground-based sensors respectively, eSAT and eREF are the errors in both measurements, eSr is the horizontal smoothing difference error (as the horizontal projection of the probed air mass of satellite and ground-based measurements is different), and eΔr,eΔt and eΔz are the horizontal, temporal and vertical sampling difference error respectively (as satellite and ground-based measurement are not taken at exactly the same space and time).

The temporal sampling difference error and the MAX-DOAS uncorrelated random error are already mitigated by averaging the MAX-DOAS measurements within a 1.0 h interval. We found that using larger time intervals can lead to an increase in the bias, which is likely due to the photochemical evolution and transport of the NO2 molecule, but at this small time window the temporal sampling difference error has a random character

This is checked by comparing MAX-DOAS measurements before and after the satellite overpass time for the different overpasses.

Tropospheric NO2 has a large spatial variability, especially at polluted sites; therefore, random and systematic features in the true NO2 field at the scale of the distance between the MAX-DOAS location and the co-located satellite ground pixel (typically a few kilometres to a few tens of kilometres, ∼10–14 km on average) can be expected. However, one must realize that (i) there is no directional preference in the co-locations, meaning that directional features are averaged out in the comparison, and (ii) the satellite measurements are strongly spatially smoothed.

To estimate the impact of the horizontal sampling difference error, we compare two sets of QA4ECV OMI NO2 tropospheric VCDs. Regarding the first set (Nv,trop,SAT1), it is required that its ground pixel covers the MAX-DOAS site and its pixel centre is within 5 km of the site. The second set (Nv,trop,SAT2) has its ground pixel second-nearest to the site, within the same overpass. SAT1 pixels are within 3–4 km of the site on average, SAT2 pixels are within 11–12 km of the site, and the distance between SAT1 and SAT2 pixels is typically 13.6 km, i.e. comparable to the mean distances encountered in the OMI vs. MAX-DOAS comparisons. Note that the discrepancy between Nv,trop,SAT1 and Nv,trop,SAT2 is due to both the horizontal sampling difference error and the random noise error.

Details on the analysis are given in Sect. S3 in the Supplement. The main conclusions are as follows:

The bias caused by the horizontal sampling difference error reaches ∼-0.6 Pmolec.cm-2 at most (at Athens, Bremen and Mainz) and is therefore only a very minor contributor to the observed bias between OMI and MAX-DOAS (discussed later in Sect. ).

Two sources of vertical sampling difference error can be identified. First, the surface altitude of the ground-based MAX-DOAS sensor and the mean surface altitude of the OMI ground pixel are not exactly the same. To estimate a correction, we applied a VMR-conserving vertical shift of the satellite a priori profile, described by . The ground levels are shifted by 0.03 km on average (Cabauw and De Bilt) to 0.4 km (Athens and Bujumbura). This hardly changed Nv,trop,SAT-Nv,trop,REF (bias changes of 0.3 Pmolec.cm-2 or less). This VMR-conserving approach probably underestimates the discrepancy at the Athens and Bujumbura sites which have a complicated orography. The MAX-DOAS instrument at Athens is located on one of the hills surrounding the city at an altitude of 527 m, while the mean surface altitude of the co-located satellite pixels is ∼200 m. Therefore, the MAX-DOAS measurement misses the lowest part of the tropospheric column, and correcting for this would increase the already negative bias. The MAX-DOAS instrument at Bujumbura is at an altitude of 860 m at the edge of the city, which is located in a valley surrounded by 2000–3000 m high mountains ; this causes the mean surface altitude of the co-located satellite pixels (∼1.2 km) to be higher than the MAX-DOAS instrument.

A second source of vertical sampling difference error is the fact that the MAX-DOAS only measures the lower tropospheric NO2 VCD, whereas the satellite measures the full tropospheric VCD. This is, in principle, a source of positive bias in Nv,trop,SAT-Nv,trop,REF and, therefore, cannot explain the observed negative bias in the comparison. A proper quantification of this bias source depends critically on the assumed vertical profile shape and is outside the scope of the current work.

Ideally, subpixel variation in the tropospheric VCD would be estimated using a high-resolution model with grid cell area comparable to the MAX-DOAS horizontally projected area of the probed air mass. Instead, we employ two semi-quantitative approaches here to estimate the bias from horizontal smoothing difference error.

In the first approach, the horizontal smoothing effect is estimated from the QA4ECV OMI NO2 data. The “superpixel” OMI tropospheric VCDs are constructed by averaging OMI VCDs of individual pixels of a relatively small size (≤500 km2) within a 20 km radius centred on the MAX-DOAS site. For each overpass, a superpixel VCD is compared with the individual ground pixel VCD covering the MAX-DOAS site. Using this procedure, a superpixel consists of three individual ground pixels on average. The mean difference per season, from 2004 to 2016, is presented in Fig. . The second approach is similar, but uses S5P TROPOMI NO2 data, from May 2018 to May 2019, RPRO (reprocessed) + OFFL (offline) data with processor version 01.02.00–01.02.02, and the superpixel tropospheric VCD is constructed by averaging VCDs of individual pixels that are within a latitude, longitude box of Δlat=0.14∘, Δlong=0.7∘ centred on the MAX-DOAS site for each overpass. TROPOMI has a similar overpass time to OMI (early afternoon) and a considerably finer resolution (3.5×7 km2 at nadir). The area of this superpixel corresponds to ∼700–900 km2, i.e. about the size of a bigger OMI pixel, and typically contains 20 TROPOMI ground pixels.

The OMI-based approach has as the advantage that the time range is appropriate, but it is limited by the large ground pixel size. Regarding the finer resolution TROPOMI data, one should keep in mind that its ground pixel size is still large compared with the horizontally projected area of the probed air mass of the MAX-DOAS

The horizontal distance of the QA4ECV MAX-DOAS measurements is small compared with a TROPOMI pixel in both the viewing and the perpendicular direction. Regarding bePRO MAX-DOAS, although it has a small field of view, its probed distance in the viewing direction (∼10 km) is of similar or slightly larger magnitude compared with the cross section of a TROPOMI ground pixel.

Figure  (black boxplots) presents boxplots of the difference of QA4ECV OMI with co-located QA4ECV MAX-DOAS for each MAX-DOAS site. At all sites, the bias of QA4ECV OMI with respect to QA4ECV MAX-DOAS is negative. On an absolute scale, it is the lowest at the less polluted OHP and Bujumbura sites (mean difference of -0.9 and -1.7 Pmolec.cm-2 respectively), and highest at the Thessaloniki and Mainz sites (mean difference of ∼-4 Pmolec.cm-2). On a relative scale, the bias is lowest (median relative difference between -15 % and -20 %) at the Uccle, Cabauw, De Bilt and Xianghe sites and highest (median relative difference of ∼-70 %) at Bujumbura and Nairobi. The difference dispersion, expressed as the interquartile range (IQR), is lowest at the Bujumbura, OHP and Nairobi sites (∼1–2 Pmolec.cm-2) and largest at the Mainz and Xianghe sites (∼5–6 Pmolec.cm-2).

As discussed in Sect. –, among the different comparison error components, only the horizontal smoothing difference error is expected to induce an important negative bias, and this is only true for some sites (e.g. Thessaloniki and Mainz), whereas for other sites (e.g. OHP and Xianghe) this is not expected. This means that the bias is (at least in some cases) due to error in the satellite and/or MAX-DOAS measurement, not due to comparison error.

We present in the same figure boxplots of the tropospheric NO2 VCD difference between OMNO2 data and QA4ECV MAX-DOAS measurements (blue boxplots). The bias of OMNO2 vs. QA4ECV MAX-DOAS is comparable to that of QA4ECV OMI NO2 vs. QA4ECV MAX-DOAS, although slightly more negative at all sites except Cabauw. If one only considers the subset of the OMNO2 pixels where QA4ECV OMI has an accepted pixel, the OMNO2 bias becomes closer to that of QA4ECV OMI for most sites. Although bePRO MAX-DOAS has a better correction for aerosols and vertical profile effects compared to QA4ECV MAX-DOAS in principle, the bias of QA4ECV OMI with respect to bePRO MAX-DOAS (Fig. , green boxes, only for the Bujumbura, Uccle and Xianghe sites) is comparable to that of QA4ECV OMI vs. QA4ECV MAX-DOAS.

In most cases, we conclude that mutual differences between the tropospheric NO2 VCD of the two OMI satellite data products and between both MAX-DOAS processing methods are small compared with the differences between the satellite OMI data products and the MAX-DOAS measurements. The main exception is at OHP, where the median difference and relative difference of OMNO2 vs. QA4ECV MAX-DOAS (-1.4 Pmolec.cm-2, -60 %) is considerably more negative than that of QA4ECV OMI vs. QA4ECV MAX-DOAS (-0.8 Pmolec.cm-2, -30 %). The observation of higher MAX-DOAS tropospheric VCD compared with satellite measurements is a common finding in the literature e.g.. Therefore, the negative bias is not specific to a particular satellite or MAX-DOAS data product.

Figures  and present a seasonal plot (i.e. all data mapped to 1 year) of QA4ECV OMI tropospheric NO2 VCD, of QA4ECV MAX-DOAS, and of the difference for each site. Also indicated are the rolling monthly mean and median as well as outliers identified by iterative 4σ clipping.

A seasonal cycle in the bias, with a larger underestimation in seasons with high NO2, is a recurring feature (Fig. ). This is the case at the more polluted sites such as Xianghe, Mainz and Thessaloniki in winter months and is in agreement with several literature results . Note, however, that we also find a seasonal cycle in the bias at the relatively clean OHP site. A very strong seasonal cycle in bias (tenfold increase) is present at Nairobi, where the MAX-DOAS sensor measures a strongly elevated NO2, peaking in July and August, which is either not detected or hardly detected by the satellite. This is likely a (spatially) local phenomenon, which would be consistent with the locally enhanced NO2 in Fig. S5. This site is characterized by local traffic. The enhanced NO2 concentrations in July and August (as measured by MAX-DOAS) are possibly related to meteorology. This season is characterized by low precipitation, low wind speeds (see https://weather-and-climate.com/average-monthly-Rainfall-Temperature-Sunshine,Nairobi,Kenya, last access: 22 September 2019) and high cloud cover (as indicated by the QA4ECV OMI cloud fraction measurements) that limits NO2 photolysis; therefore, a build-up of locally emitted NO2 is a possible explanation. The fact that OMI hardly measures this elevated NO2 could be due to the local character of the emissions.

The discrepancy, as measured by the root-mean-squared difference (RMSD) between satellite measurements and MAX-DOAS data, exceeds the combined ex ante uncertainty for all sites

Although the root-mean-squared error (RMSE) and uncertainty are not exactly equivalent, they should be roughly comparable if all error sources are well characterized. If all error is purely random, the RMSE equals the standard deviation of errors, of which the uncertainty is an ex ante estimate. If the error is fully systematic and constant, the RMSE equals the absolute value of the bias, which is expected to be smaller than twice the uncertainty with a 95 % probability.

Applying a more strict screening protocol can, at least in principle, mitigate discrepancies in bias and dispersion, at the expense of data loss. In the case at hand, results are mixed for the different sites (see Figs. S9–S13); stricter criteria do not resolve bias or dispersion for all sites. For the Uccle, Mainz, Cabauw and Xianghe sites strong reductions in bias and/or dispersion (∼0.5–2 Pmolec.cm-2) can be achieved by filtering more strictly on the effective cloud properties cloud fraction, cloud pressure, the uncertainty component due to cloud pressure uSAT,pcl, the MAX-DOAS cloud flag (removing scenes with thick or broken clouds) or the AOD. This suggests that part of the discrepancy is caused by clouds and/or aerosol. More minor reductions in the bias and/or dispersion are achieved for the Bujumbura, Nairobi, Athens, Bremen and De Bilt sites.

Screening more strictly on the ground pixel area leads to improvements in the bias for Mainz and Thessaloniki, confirming (see Sect. ) that the horizontal smoothing difference error is a component of the bias. Improvements in dispersion are found for Mainz, Thessaloniki, Uccle and Xianghe.

Using a stricter filter on effective cloud properties, the RMSD can be made consistent with the ex ante uncertainty for the Uccle and Cabauw-De Bilt sites (results not shown). For Mainz, this can be achieved if ground pixels larger than 400 km2 are also excluded (keeping only 25 % of the data). Finally, we note that the RMSD and uncertainty are consistent in the months from May to (and including) August (when NO2 values are low) at the OHP site without the need for stricter filtering.

For most sites, additional screening (within reasonable limits) cannot lower the RMSD enough that it matches the uncertainty. Some uncertainty components in either OMI or MAX-DOAS data are likely underestimated or not included.

While we found that stricter screening using the uncertainty component due to cloud pressure, uSAT,pcl, often leads to better results, the threshold values obtained are quite low. This indicates that uSAT,pcl is underestimated in the satellite data product. As expected, relaxing the cloud fraction filter beyond the baseline can lead to an increase in bias and/or dispersion (see e.g. Bujumbura, Nairobi and Uccle in Figs. S9–S13), motivating the CF ≤0.2 (or almost equivalently CRF ≤0.5) recommendation. On the other hand, relaxing the AMF ratio filter beyond the baseline has no large impact on the comparison, whereas further restricting it sometimes has a negative impact (e.g. an increase in the bias and/or dispersion at Uccle, Xianghe and Cabauw). Therefore, the current recommended baseline lower bound (AMFtropAMFgeo≥0.2) can be replaced by a lower value (e.g. 0.1 or 0.05).

The nonuniform vertical sensitivity of the satellite measurement, combined with an approximate a priori profile shape, is a source of error in the satellite measurement. The bePRO MAX-DOAS provides not only column but also profile shape information (albeit with a limited vertical resolution) and, therefore, allows for this error source to be assessed separately. Figure  shows the impact of directly applying Eq. () on the bePRO MAX-DOAS profile (after vertical alignment using the method from ) on the mean-squared deviation (MSD) as well as its bias, seasonal cycle and residual components for the Uccle and Xianghe sites. While direct smoothing of the MAX-DOAS profile improves the MSD for Uccle, it increases it for Xianghe because the seasonal cycle component increases. The increase in seasonal variance is caused by the interplay of the seasonal variation in the MAX-DOAS vertical profile and of the satellite vertical averaging kernel. Specifically, for the Xianghe case, it is found that averaging kernels have higher values close to the surface in wintertime, while MAX-DOAS NO2 profiles can also be peaked at the surface. This combination causes increased MAX-DOAS columns upon vertical smoothing. This is also seen in cases such as the comparison of the GOME-2 AC SAF GDP 4.8 NO2 product with MAX-DOAS at Xianghe (see Fig. 7.14 and 7.15 of , and Figs. S3 and S5 of ). While the a priori harmonization seems to mitigate this effect, it does not resolve it. Thus, whether the situation could be improved by improved MAX-DOAS a priori profiles and/or improved satellite averaging kernels should be a focus of future research.

However, one should consider that the retrieved bePRO profiles have a low vertical resolution and depend on their own a priori profile shape. As is well known (Eq. 10 of , see also the general profile harmonization overview of ), a priori profiles of satellite and reference data should be harmonized before comparison and smoothing. Here, we aligned the surface levels of the profiles following and changed the a priori shape profile of the bePRO data to that of the satellite while keeping the bePRO a priori VCD size (which is actually obtained from measurement, see ) intact. More detail on the operations applied is provided in Sect. S6. The harmonization operation reduces all components of the MSD (bias, seasonal cycle and residual component) for the Xianghe site. When smoothing is also applied after the a priori harmonization, the bias component (blue bar in Fig. ) is almost completely removed, but the other two components increase. Therefore, application of the averaging kernel does not necessarily lead to an improvement in all aspects of a comparison; this should be the focus of further research. As the bias component is almost completely removed after harmonization and smoothing at Uccle and Xianghe, one can conclude that – at least at these two sites – the bias is largely due to errors in the a priori profile shape. Therefore, using better quality a priori profiles in both satellite and MAX-DOAS data (e.g. from regional-scale models) is recommended.

When the averaging kernel is applied, it is recommended that the satellite a priori shape component is removed from the uncertainty budget . This component was tentatively assigned 10 % of the VCD value. This only leads to a modest reduction in the combined uncertainty in Fig.  (compare the non-hatched and hatched pink bars), as the dominant contribution to the OMI AMF uncertainty component is related to surface albedo rather than profile shape. For example, the combined uncertainty at Uccle decreases from 2.8 to 2.7 Pmolec.cm-2. However, the smoothing operation decreases the RMSD at Uccle by about 2 Pmolec.cm-2, which strongly suggests that the current 10 % uncertainty assignment is an underestimate.