4.1 Three approaches to compare model and satellite observations

NO₂ total column retrievals are implicitly dependent on an a priori tracer profile. The retrieval algorithm accounts for the fact that the sensitivity of the instrument is different at different altitudes i.e., the sensitivity is higher in the free troposphere and lower in the boundary layer. This information is encoded in the averaging kernel which is proportional to the measurement sensitivity and depends on the viewing geometry, cloud properties, aerosols, and surface albedo (Eskes and Boersma, 2003).

Based on these considerations, several possible approaches of comparing model output and satellite observations exist, which are presented in Fig. 1. Figure 1a indicates the standard TROPOMI retrieval, as provided in the TROPOMI L2 data files, henceforth denoted as S5P. As explained in the TROPOMI PUM (Eskes et al., 2022), the a priori profiles x^tm5 in the retrieval may be replaced by any other model NO₂ profile information x^model, which is, in our case, CAMS or x^cams, resulting in a new retrieved tropospheric NO₂ column V^trop,cams (Fig. 1c). The method makes use of the tropospheric averaging kernel A^trop and the air mass factors M provided by the TROPOMI L2 data files, as follows (Eskes et al., 2022):

Here, M(x^tm5) is the tropospheric air mass factor provided in the TROPOMI product, depending on the TM5-MP a priori profile x^tm5, and M^′(x^cams) is a new air mass factor computed with the alternative model profile x^cams. The summation over l is over the tropospheric model levels.

The tropospheric averaging kernel vector A^trop of the TROPOMI product is obtained by scaling the total averaging kernel by $M/M^{\mathrm{trop}}$, where M is the total air mass factor, and M^trop is the tropospheric air mass factor (Eskes et al., 2022). All elements of the kernel are set to zero above the tropopause layer $l_{\mathrm{tp}}^{\mathrm{tm}\mathrm{5}}$, or,

All the above quantities are provided in the TROPOMI product.

We therefore also discuss three distinct ways of recomputing the TROPOMI tropospheric column using CAMS NO₂ profiles by using the profile solely from the regional ensemble of CAMS, solely from the global CAMS NO₂ model, or the combined global–regional profile using IFS (compo) above 3 km altitude and CAMS–regional below. These alternative TROPOMI products are indicated by the acronyms S5P-R (R as in regional), S5P-G (G as in global) and S5P-RG (RG as in regional–global), respectively (Fig. 1c). Please note that all references to CAMS–regional in this section or the following sections can refer to either the ENSEMBLE or individual regional models and should be clearly indicated in each case. The same goes for derived columns containing the “-R” suffix, which indicates the use of either the ENSEMBLE or individual models.

The CAMS model simulation of the measured NO₂ column, denoted as C^A in Eq. (3), is obtained by multiplying the CAMS model partial column profile x^cams with the tropospheric averaging kernel A^trop, or

This equation requires a vertical interpolation between the levels for which the model data are available and the TROPOMI data product levels (in which the averaging kernel is defined), which should ideally conserve the total column amount. As above, we distinguish three different CAMS profiles; so CAMS-A can be CAMS-R-A, CAMS-G-A, or CAMS-RG-A ( Fig. 1b).

A direct comparison of the NO₂ tropospheric column as provided in the TROPOMI product (S5P) and a model-generated column would introduce extra uncertainties and biases, as the TROPOMI tropospheric columns depend on the retrieval a priori and therefore on the quality of the TM5-MP profiles used. This comparison approach is depicted in Fig. 1 with an orange arrow. The most common approach for comparing models and satellite retrievals is the comparison of the two upper boxes of Fig. 1 (upper green arrow). As explained in Eskes and Boersma (2003), the relative comparison becomes independent of the a priori profile shape of the TM5-MP model used in the S5P retrieval.

An equally valid comparison approach is the replacement of the a priori profile used in the retrieval by the air quality model a priori and subsequent direct comparison with the modeled tropospheric column (lower green arrow in Fig. 1). In this way, any relative comparison also becomes independent of the a priori profile shape from the TM5-MP model, since this is removed from the retrieval product. The vertical model column can be seen as a multiplication with the identity matrix I. Hence, the notation CAMS-R-I, CAMS-G-I, or CAMS-RG-I is used for this modeled vertical tropospheric column (Fig. 1d).

Figure 2TROPOMI retrieval field of orbit 3704 (one of the orbits on 1 July 2018), plotted on the native grid (a) for the Netherlands area, compared to the regridded field in the CAMS regional grid (0.1^∘ × 0.1^∘ resolution) for the same retrieval (b).

4.2 Implementation of the comparisons

Proper temporal and spatial sampling of the satellite observations and model output fields is essential in order to minimize representativity errors during the comparison. To this end, all available data were regridded to the CAMS regional grid (see Sect. 3). In this process, source grids were either the TROPOMI footprint (i.e., the native grid of TROPOMI, which is different for each orbit), the IFS (compo) grid, or the TM5-MP grid. See Table 2 for the characteristics of each of those grids.

Horizontal regridding is performed by means of an area-weighted average of source cells that correspond to target (i.e., CAMS–regional) cells. For example, a target grid cell o containing retrieval columns ${\widehat{y}}_{\mathrm{i}}^{\mathrm{o}}$ will acquire the value ${\widehat{y}}_{\mathrm{o}}={\sum }_i{w}_i{\widehat{y}}_{\mathrm{i}}^{\mathrm{o}}/{\sum }_i{w}_i$, where weights w_i are given by the retrieval column pixel area. In the case of regridded TROPOMI observations, these may be called superobservations, as typically about three TROPOMI observations are averaged to construct one observation for a CAMS grid cell.

Moreover, to minimize spatial representativeness errors, we imposed an additional constraint regarding the satellite data, i.e., a value for a target grid cell was calculated and assigned only if the coverage of valid source data for this cell were above 50 %. This is on top of the filtering based on the quality assurance parameter qa_value >0.75, following the suggestion of the TROPOMI PUM (Eskes et al., 2022). This area-weighted regridding of a single TROPOMI orbit to the target grid can be seen in Fig. 2. Intensive variables (temperatures, pressures, averaging kernels, tropopause layer index, etc.) are interpolated horizontally using bilinear regridding. Modeled fields were sampled in time at the satellite overpass time over central Europe using the closest available time, based on the temporal resolution of each data source (see Table 2).

Table 2Input data characteristics.

^a There were 60 levels before 10 July 2019. ^b Number of sampling altitudes. Individual models and the ENSEMBLE data have the exact same characteristics. ^c Horizontal resolution at nadir and 3.5×7 km² before 6 August 2019. ^d Levels of the averaging kernels.

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In the vertical, the approach followed was to transform all available data in the TM5-MP vertical levels, i.e., the levels of the TROPOMI product averaging kernel. So, CAMS regional model data were linearly interpolated to the TM5-MP levels from the eight sampling altitudes (Table 2), while, for the global model where data were available in the native model levels, data were interpolated in mass conservative fashion.

All integrations to columns were performed on the TM5-MP vertical levels, and we consider the three possible options mentioned in Sect. 4.1. The first one is taking into account only the CAMS–regional ENSEMBLE (or, for that matter, any individual regional model) for reconstructing the column. In this case, the last TM5-MP level considered was the one which lies just below 5000 m above the surface, which means that a large part of the free troposphere is not accounted for (concentration is assumed to be zero). The second option involves using only IFS (compo) data, where the last TM5-MP level considered is the one assigned to the tropopause, as provided in the form of the tropopause layer index in the TROPOMI product. Finally, we also consider a merger between CAMS–regional and IFS (compo) in the vertical, where we use the regional profile up to about 3000 m above the surface and complement it with IFS (compo) data up to the tropopause. All concentrations are converted to densities (molec. m⁻³) based on temperature profiles provided by TM5-MP (in the case of CAMS–regional data) and pressure profiles from either IFS (compo) or TM5-MP. Comparisons between CAMS and TROPOMI are presented for several regions, indicated in Fig. 3, and for major European cities using boxes of 7×5 (CAMS–regional) grid cells.

Figure 3Definition of the regions of interest for the calculation of column comparison statistics.

5.1 Comparisons for individual days and monthly means

Maps of daily TROPOMI columns and CAMS model mean tropospheric NO₂ columns using CAMS-RG are given in Figs. 4 and 5, for 26 July 2018 and 15 February 2019, respectively. Figure 4 follows the scheme of Fig. 1; thus, columns with S5P, CAMS-RG-A, S5P-RG, and CAMS-RG-I are presented, while in Fig. 5 only S5P-RG and CAMS-RG-I are shown. CAMS–regional data used in this section are the first day forecasts. Based on an inspection of those maps which are based on two largely cloud-free days over central Europe, we can already draw some important conclusions regarding how the two products compare. Most emission hotspots are clearly identifiable in both S5P- and CAMS-RG-based maps. This includes the large- and medium-sized cities and whole areas with increased pollution burden, as in the Po Valley or southwestern Germany. Advection characteristics also agree qualitatively, such as the strong transport of NO₂ from England, the Netherlands, Belgium, and Germany to the North Sea on 15 February 2019 (Fig. 5). Differences, however, are seen in the quantitative details, with the model-based maps leading to longer and more pronounced plumes. This is quite evident in the case of the Liverpool (UK) and English Channel areas (26 July) and in the North Sea (15 February). Some hotspots seem to be absent altogether in the TROPOMI retrieval, for example, the powerplants in the Lusatia region in eastern Germany, possibly related to inaccurate assumptions in the emissions used in the CAMS models (e.g., differences in activity during the examined days or in the emission injection characteristics). Ship tracks can be seen in both TROPOMI and CAMS fields but are generally more prominent in the CAMS fields (e.g., in the Bay of Biscay or the North Sea). TROPOMI also seems to indicate higher background values in summer.

Figure 6Monthly averaged S5P and CAMS-RG-A columns for July 2018 (a, b) and January 2019 (c, d).

Monthly averages of regridded column fields offer wider spatial coverage and a qualitatively different view of the observed and modeled features. The maps in Fig. 6 present the comparison of the mean TROPOMI tropospheric NO₂ columns S5P with CAMS-RG-A for the months of July 2018 and January 2019. Similar to the daily fields, CAMS–regional data in this section are also based on the first day of the 4 d forecasts. CAMS columns appear to be capturing the observed locations of high NO₂ columns well over densely populated regions like the Benelux area, Po Valley, and other large European cities. For July, absolute values at the hotspots seem to be comparable, but background values are higher in the case of S5P. The situation is considerably different in January, where CAMS-RG-A columns are significantly higher over the hotspots. Naturally, these much higher values also seem to affect through advection rural land areas or even areas over the sea.

5.2 Time series

Figure 7 depicts the time series of monthly mean S5P and CAMS-RG-A vertical column densities for nine major European cities, while Fig. 8 shows the corresponding time series for the domains of Fig. 3 from May 2018 to March 2021. For this long time series, the CAMS–regional data utilized were the NRT analyses, as this is the regional product used in the European L2 TROPOMI product, as detailed in Sect. 6.

The spatial averaging required for the time series of the cities (Fig. 7) was performed for 7×5 cell domains (0.7^∘ × 0.5^∘) for all the cities, which corresponds to areas of roughly 70×50 km² centered at the respective city centers. This comparison reveals remarkably similar values between the S5P and CAMS-RG-A columns for some of the cities in southern Europe (Madrid, Rome, and Istanbul), while discrepancies are larger in most of the rest, especially in the wintertime when CAMS-derived column densities almost always acquire higher values. The domain-averaged monthly mean time series of Fig. 8 present a similar picture, where comparison is much more favorable during the summertime, but the two column densities differ substantially during the wintertime in practically all of the examined domains.

Figure 7Time series of monthly mean original TROPOMI columns (S5P; red) and the CAMS combined columns (CAMS-RG-A; blue), with averaging kernels applied for nine major European cities. The retrieval algorithm versions used are as described in Sect. 2. The panels are ordered according to the geographical location. Vertical axes are different for each city. Green vertical bars in July and November 2018 represent the model spread for those 2 months.

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Figure 8Time series of the TROPOMI original columns (S5P; red) and the CAMS combined columns (CAMS-RG-A; blue), with averaging kernels applied for the domains as defined in Fig. 3. The retrieval algorithm versions used are as described in Sect. 2. Vertical axes are different for each domain. Green vertical bars in July and November 2018 represent the model spread for those 2 months.

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5.3 Discussion of the CAMS-TROPOMI differences

The wintertime discrepancies identified in the previous sections may be due to uncertainties in both the satellite retrieval (Lorente et al., 2017) (see also Sect. 2) and chemical transport modeling. Note, however, that the January fields presented above (Sect. 5.1) are unavoidably based on a much fewer observations compared to the July ones due to increased cloud coverage, snow cover, and low solar zenith angles.

As mentioned before, TROPOMI validation indicates a negative bias in tropospheric NO₂ in polluted regions. Part of this may be attributed to the (horizontal resolution of the) global TM5-MP a priori, but in our comparisons, the averaging kernels are accounted for, which removes this source of error. Furthermore, biases in versions 1.2.x and 1.3.x of the retrieval algorithm seem to show a seasonality compared to OMI, from around −20 % in Europe in winter to only small impacts in summer. With version 1.4.0, this difference largely disappears (van Geffen et al., 2022), especially due to increases in TROPOMI columns in wintertime. The large solar zenith angle in winter leads to small sensitivities near the surface, which will enhance potential biases. The presence of snow, on the other hand, will strongly enhance the sensitivity and may reduce retrieval errors. These considerations are broadly in line with the observed TROPOMI-CAMS differences, and it seems likely that part of the systematic seasonal effects is caused by retrieval uncertainties.

Modeling deficiencies can, on the other hand, be related to uncertainties in the input data (primarily, emissions) and also to the modeling of processes such as the injection of emissions into the atmosphere, especially from point sources, chemistry, vertical mixing, or advection. Past studies have indicated that total anthropogenic emissions in the TNO emissions inventory may be overestimated or not properly distributed in time. For example, Petetin et al. (2015) showed that anthropogenic NO_x emissions in the TNO inventory, which is the basis for the MACC-III emissions inventory (used by the CAMS regional models before September 2018) and the CAMS-REG-AP v1.1 emissions inventory (September 2018 to June 2019), were overestimated for the Paris area. Moreover, MACC-III emissions were based on 2011 as a reference year, while CAMS-REG-AP v1.1 was based on 2015, which means that the downward trend in NO_x emissions that prevailed during the preceding decade (e.g., Lorente et al., 2019; Zara et al., 2021) may not have been properly accounted for in the model simulations, leading to overestimations in NO₂ concentrations. Biogenic soil NO_x emissions are also known to be underestimated (Vinken et al., 2014; Visser et al., 2019), which can be one of the reasons behind the lower modeled background columns levels.

In the comparison between regional air quality models and OMI retrievals performed by Huijnen et al. (2010a), the seasonal cycle was found to be overestimated by the model simulations, which is in agreement with results by Blechschmidt et al. (2018) for MAX-DOAS locations in Bremen and Observatoire de Haute-Provence (OHP). However, in Huijnen et al. (2010a), there was a stronger discrepancy between columns from the regional model simulations and satellite retrievals during the summer, while the comparison was more favorable during winter, unlike in Blechschmidt et al. (2018) and the current work.

From a process-based modeling point of view, the discrepancy in question may indicate deficiencies in the treatment of wintertime chemistry. The NO_x lifetime is much longer during winter because of the lower concentrations of OH and RO₂ radicals which act as sinks for NO₂. Thus, a possible underprediction of OH production, via the photolysis of O₃ when less light is available, could lead to higher NO₂ (Shah et al., 2020; Stavrakou et al., 2008). Difficulties in the description of wintertime chemistry may also be related to heterogeneous chemistry, as the conversion of N₂O₅ to aerosol is more sensitive and inherently more uncertain compared to summer conditions. In addition to these, even mild overpredictions of NO_x emissions can, due to the longer NO₂ lifetime, be amplified to produce a larger impact on tropospheric concentrations.

The treatment of vertical mixing can also affect the modeled NO₂ vertical profile shape. Enhanced mixing will tend to lead to lower NO₂ concentrations near the surface and a less steep vertical gradient in the boundary layer. The accurate prediction of the boundary layer development under the often stable wintertime conditions, let alone temperature inversions, is an outstanding challenge for atmospheric models. Under such conditions, turbulent diffusion will often be overestimated, subsequently leading to an overestimation of the boundary layer height (Sandu et al., 2013). This overestimation of vertical mixing has, in turn, been shown to lead to increases in the calculated vertical columns (Huijnen et al., 2010a). NO_x lifetime also generally increases with height. Enhanced transport to higher altitudes will therefore lead to an increase in the column amounts for the same number of emissions. Similarly, the overestimation of injection heights from point sources may lead to higher concentrations aloft, leading to an overestimation of column amounts.

Figure 9Comparison of S5P and CAMS-RG-A columns for seven CAMS regional production models based on the first day forecasts for July 2018.

5.4 Results for the individual regional models

Figure 9 shows the S5P and CAMS-RG-A columns for the ENSEMBLE and for each of CAMS regional production models, based on the available first day forecasts for the month of July 2018. At that time, there were seven operational models providing daily forecasts. As already identified in Sect. 5.1, background values appear higher for S5P columns, but hotspots seem to be comparable. Since the same emissions are, in principle, used by all models, differences between the modeled columns should be attributed to differences in the treatment of transport (both in the horizontal and the vertical), chemistry, or NO₂ removal processes.

Differences between the individual models are further examined in Fig. 10, which depicts maps for the average monthly CAMS-RG-A and S5P-RG column spread, for July and November 2018. These spreads are calculated on the basis of the difference between the minimum and maximum values for these quantities, as calculated by using any of the seven regional models, and can be considered to be a measure of the uncertainty in the CAMS ENSEMBLE-based columns. As expected, the spread is significantly higher (by a factor of almost 5) for the actual modeled columns (CAMS-RG-A) than for the TROPOMI columns when using the CAMS model a priori from the individual models (S5P-RG). Moreover, the spread is considerably larger for November, by a factor of almost 2, compared to the summer month of July. In July, the CAMS-RG-A spread is the largest at urban areas all over Europe but more so in Benelux, the Ruhr area, and England, while for winter CAMS-RG-A is more homogeneous across the domain but prominently high in the Po Valley. A similar behavior arises for S5P-RG, with the largest values of the spread over high activity areas during summer and higher, more homogeneous values during winter.

Some basic statistics for individual cities for July and November 2018 are provided in Table 3, which shows the monthly mean values of S5P and CAMS-RG-A columns, the lowest and highest model values for CAMS-RG-A, ratios between the S5P-RG and S5P columns, the relative difference, and the spatial (Pearson's R) correlation coefficient between S5P and CAMS-RG-A, which is also based on the monthly mean values. We base the calculation of the relative difference on the arithmetic mean of S5P and CAMS-RG-A, using the $|\mathrm{S}\mathrm{5}\mathrm{P}-\text{CAMS-RG-A}|/\left[\right(\mathrm{S}\mathrm{5}\mathrm{P}+\text{CAMS-RG-A})/\mathrm{2}]\cdot \mathrm{100}\mathit{\%}$ formula. The table shows that TROPOMI lies within the model spread for July, but this is not the case for most cities in November. Relative differences are up to 15 % for most cities in July but up to 50 % for most cities in November. Correlations are typically high, except for London in July and Helsinki in November.

For the months of July and November 2018, Figs. 7 and 8 also depict the model spread of the CAMS-RG-A columns in the form of solid green vertical bars. Note that the amount of data involved in the actual regional model output, download time, storage space, and the computational cost required for processing 7 to 11 models has prevented us from calculating the spread for the full length of the time series in these plots. Furthermore, for cities, the spread is also clearly lower in July than in November in the selected domains, but the S5P column values still mostly lie within the range since the comparison is in any case more favorable during the summer. The larger November spread does include the S5P column values for some of the cities/domains, but the wintertime discrepancy discussed above appears to be generally larger than what could be explained by model variability and is thus more systematic in nature. To conclude, both model results and retrievals seem to be more uncertain in winter.

Figure 10Model spread (for a definition, see Sect. 5.4) for tropospheric NO₂ columns. The first row depicts CAMS-RG-A (a, c) and S5P-RG (b, d) for July 2018, while the second row is the same for November 2018. Note the different scales.

Table 3S5P and CAMS-RG-A column statistics at various European cities for July and November 2018, including the S5P-RG $/$ S5P ratio.

^* Relative difference and correlation coefficient between S5P and CAMS-RG-A.

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Figure 11Percentile relative change between TROPOMI tropospheric NO₂ columns derived using a merged CAMS a priori (S5P-RG) based on the regional NRT analysis and regional forecast and averaged over the months of July 2018 (a) and January 2019 (b).

5.5 Results for the regional models – analysis vs. forecast

The assimilation of (primarily surface) observations by the CAMS regional models has been demonstrated to lead to improved assessments of the 3-D concentration fields for NO₂ (Douros et al., 2020). The hypothesis would thus be that, when using analyzed CAMS regional profiles to replace the default TM5-MP a priori, this would lead to improved TROPOMI (S5P-RG) columns. In this section, we aim to investigate the differences introduced by the use of the analyses as compared to the first day forecasts.

Figure 11 depicts the percentage of relative change for July 2018 and January 2019 using the $({\text{S5P-RG}}_{\mathrm{AN}}-{\text{S5P-RG}}_{\mathrm{FC}})/\left|{\text{S5P-RG}}_{\mathrm{FC}}\right|\cdot \mathrm{100}\mathit{\%}$ formula. Positive values indicate higher values for the analyses, while negative values indicate higher values for the forecasts. For July, most areas in mainland Europe show higher values when using analyzed profiles, with the exception of some areas in the North Sea and the English channel, where the columns based on the forecasts seem higher. The situation for January is much more ambiguous, as differences are generally smaller, and there are no distinct patterns on the relative change map. The noisy features in the northern part of the map are probably due to the noise in the TROPOMI retrievals, as the values in this part of the domain are very low.

6.1 Impact of the free tropospheric column on the retrievals and comparisons

A way to evaluate the impact of the free tropospheric column on the retrievals is by comparing TROPOMI retrievals using either CAMS-RG or CAMS-R a priori profiles (S5P-RG and S5P-R, respectively) with the respective CAMS-RG and CAMS-R modeled columns (CAMS-RG-I and CAMS-R-I). Monthly mean maps for July 2018 based on this scheme are shown in Fig. 12.

Modeled columns (CAMS-RG-I and CAMS-R-I; Fig. 12b, d) appear to be quite similar in these maps, while TROPOMI columns (S5P-RG and S5P-R) are considerably different, with background values being fairly higher for S5P-R compared to S5P-RG. Though the free tropospheric column is relatively small, even in summer, the TROPOMI-CAMS comparison nevertheless appears to be very sensitive to it. When the free troposphere is removed, the model columns will be somewhat smaller. The air mass factor in the TROPOMI retrieval, however, will also be significantly lower due to the shape of the averaging kernel, leading to a noticeable increase in the TROPOMI retrieval. These effects are opposite, thus leading to a cumulative increase in the difference between TROPOMI and model-derived columns when the free tropospheric column is too low or missing.

Figure 12Monthly averaged S5P-RG (a), CAMS-RG-I (b), S5P-R (c), and CAMS-R-I (d) columns for July 2018.

An alternative way of investigating the impact of the free troposphere is by calculating the ratios between S5P-CAMS for all available combinations of a priori profiles (S5P-RG, S5P-R, S5P-G) and the native TROPOMI tropospheric column. Figure 13 shows maps of those three ratios averaged over the summer months (June–August, JJA) of 2019. In order to take full advantage of the high resolution of the TROPOMI data, these maps were produced by regridding column fields to a regular lat–long grid of 0.02^∘ × 0.02^∘.

Figure 13The ratio of the retrievals performed with CAMS a priori profiles and the original TROPOMI retrievals. (a) S5P-RG/S5P, (b) S5P-G/S5P, and (c) S5P-R/S5P. Data regridded from the L2 product to a 0.02^∘ × 0.02^∘ grid and averaged over the summer months (JJA) of 2019. Note the different scales.

Figure 14Mean averaging kernel profiles (a, d) and NO₂ profiles for Paris (b, e) and a rural location in France (c, f) during July (a–c) and January (d–f) 2018. Mean NO₂ profiles are plotted based on data from CAMS regional (ENSEMBLE), IFS (compo), and TM5-MP.

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What is quite evident from Fig. 13 is that the S5P-R / S5P ratio is larger than unity almost everywhere in the domain. For S5P-G / S5P, the values are much closer to unity, while for S5P-RG / S5P, the values are larger at most emission hotspots, e.g., at urban areas and across ship tracks in the North Sea but closer to unity for most other areas. A ratio larger than 1 reflects the fact that tropospheric columns are larger when replacing the default TM5-MP a priori with a CAMS modeled profile. But, in order to better understand why this is the case, averaged profiles for both a summer month (July 2018) and a winter one (January 2019) were calculated at two locations, namely the distinctly urban environment of Paris and a fairly remote rural location in the Cantal region of France, away from large emission sources. Those profiles are shown in Fig. 14, together with the respective averaging kernels, and are calculated only for the times of valid TROPOMI observations.

The averaging kernel, which describes the vertical structure of the impact of the a priori information assumed in the retrieval, clearly acquires lower values near the surface for the rural case due to lower albedo values at this location. For July, the averaging kernel is close to unity at about 2 km over the surface, while for January this altitude is much lower, at about 1 km, indicating a shallower boundary layer.

Comparisons between the modeled NO₂ profiles reveal higher mixing ratios as expected near the surface for the regional ENSEMBLE in the urban location, but the ratios are somewhat lower for the rural location. This difference is more prominent during July and is possibly related to a more efficient photochemical conversion of NO_x to NO₂, the shorter lifetime, and higher resolution of the regional models. IFS (compo) mixing ratios near the surface are, in any case, not expected to be representative of most hotspot regions in Europe due to the relatively coarse horizontal resolution of the model. The ENSEMBLE tends to produce very low concentrations at 5 km altitude compared to IFS (compo) and TM5-MP but more similar concentrations around 3 km. IFS (compo) and TM5-MP agree reasonably well in summer, but larger differences are seen in winter.

What is clear from the mean NO₂ profiles for July is that, for urban areas, the CAMS regional ENSEMBLE has a much larger fraction of its column in the boundary layer compared to either TM5-MP or IFS (compo). Moreover, as the averaging kernel provides the contribution of different altitudes to the signal observed by TROPOMI, a large part of this signal is normally interpreted as being representative of the free troposphere, which, in the case of the ENSEMBLE, is largely missing. This skews the S5P-R (and thus the ratio) to higher values. TM5-MP and IFS (compo) have fairly similar profiles, leading to a more balanced ratio when examining the ratio for CAMS-G. The most interesting behavior appears to be when using the CAMS-RG a priori. In urban areas, CAMS-R values are higher close to the surface, mainly due to the higher horizontal resolution of the regional models and the underlying emissions, which is something that leads to higher S5P-RG columns and thus ratios. In rural areas, the averaging kernel has somewhat lower values, and at the same time, the free troposphere now also contributes to the full tropospheric column, leading to lower S5P-RG columns and ratios. The overall impact is therefore a notable increase in the dynamic range of S5P-RG VCDs.

6.2 Validation of the TROPOMI-CAMS regional L2 product against ground-based data

The routine validation of the operational TROPOMI satellite NO₂ tropospheric and total column retrievals largely relies on the global network of MAX-DOAS remote-sensing instruments and the Pandora instruments from the Pandonia Global Network (PGN; Verhoelst et al., 2021; Lambert et al., 2021). Both instrument types are commonly used for the validation of satellite NO₂ data (Celarier et al., 2008; Herman et al., 2009, 2019; Chan et al., 2020; Compernolle et al., 2020; Pinardi et al., 2020) Here we focus on the European S5P-RG product discussed in Sect. 6. We note that earlier validation of S5P NO₂ with regional CAMS profiles was done by Ialongo et al. (2020), using the Pandora instrument at Helsinki. In this study, we have used nine MAX-DOAS and six Pandora stations (see Table 4) that are within the spatial scope of the S5P-RG product. In addition, we compare the operational TROPOMI product and the CAMS-RG-I product with the same reference dataset. This allows for a double-delta validation, i.e., S5P-RG vs. S5P and S5P-RG vs. CAMS-RG-I. Practically, the CAMS-RG-I tropospheric columns can be reconstructed from the fields in the new product by multiplying the smoothed CAMS column (CAMS-RG-A) with the ratio of the operational S5P tropospheric air mass factor (AMF) over the S5P-RG tropospheric AMF, with all the relevant information made available in the new product. This follows that, by rearranging the second line of Eq. (1), we obtain

Figure 15Correlation density plots of S5P, S5P-RG, and CAMS-RG-I (columns 1 to 3) vs. MAX-DOAS (a–c) and vs. PGNtropo (d–f). Quality indicators for bias (mean and median difference and median relative difference), difference dispersion (standard deviation and $\mathrm{1}/\mathrm{2}$ IP68) are provided, in addition to the Pearson's (R) correlation coefficient, the reduced major axis (RMA) regression slope and intercept, and the residual dispersion (standard deviation, SD, and $\mathrm{1}/\mathrm{2}$ IP68) from the RMA regression line.

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Table 4Overview of the stations contributing to the TROPOMI-CAMS tropospheric NO₂ validation in this study.

IUP-B is the Institute of Environmental Physics, University of Bremen. KNMI is the Royal Netherlands Meteorological Institute. MPI-C is the Max-Planck-Institut für Chemie. LMU is the Ludwig-Maximilians-Universität München. AUTH is the Aristotle University of Thessaloniki. BIRA-IASB is the Royal Belgian Institute for Space Aeronomy. PMOD/WRC is the Physical Meteorological Observatory of Davos. FMI is the Finnish Meteorological Institute. INOE is the National Institute for Research and Development in Optoelectronics, Romania. ESA is the European Space Agency. ^* Note that, although the Pandora site of Ny-Ålesund (Svalbard) is within the range of truncated orbits of the S5P-RG product, the product has fill values for the CAMS-specific fields, so this location was not considered.

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In order to focus on the tropospheric VCD, tropospheric columns are estimated from the Pandora total columns by subtracting the S5P stratospheric estimation, as done in Pinardi et al. (2020). This is indicated by PGNtropo. The filter and colocation processing follows Verhoelst et al. (2021). Only satellite pixels with qa_value >0.75 and covering the ground-based instrument location are kept. Regarding PGN data, only the highest-quality label (0 and 10) is used. MAX-DOAS data are retained if the data within ±1 h of overpass time are available; the interpolated value at overpass time is then used. PGN data are retained if the data within ±0.5 h of overpass time are available; the average value is then used. Figure 15 presents the results of the validation as density scatterplots of the three datasets (the operational S5P, the S5P-RG, and the CAMS-RG-I shown as columns in the figure) versus the MAX-DOAS data (upper row) and the PGN data (lower row), where the co-located data are merged over all stations. Quality indicators for the bias (mean and median difference and median relative difference) and difference dispersion (standard deviation, SD, and one-half of the 68 inter-percentile, $\mathrm{1}/\mathrm{2}$ IP68) are provided, in addition to the Pearson's (R) correlation coefficient, the reduced major axis (RMA) regression slope and intercept, and the residual dispersion (SD and $\mathrm{1}/\mathrm{2}$ IP68) from the RMA regression line. For both the comparisons with MAX-DOAS and with PGN, one can conclude the following:

• The overall bias (both absolute scale and relative) of S5P is more negative than that of S5P-RG, which in turn is more negative than that of CAMS-RG-I.

• The bias of S5P clearly has a multiplicative component, as indicated by the low RMA regression slope. This component is reduced for S5P-RG.

• Data are more scattered, with higher difference dispersion parameters, in the case of CAMS-RG-I, while the dispersion parameters are comparable for S5P and S5P-RG. The correlation is slightly better for S5P than for S5P-RG, while it is decidedly lower for CAMS-RG-I.

• The dispersion from the regression line is lower for S5P than for S5P-RG, which in turn is lower than for CAMS-RG-I.

Figure 16Median biases and relative bias changes for the different comparisons at all the MAX-DOAS (a, b) and Pandora (c, d) stations. The left column (a, c) presents the comparison between SP5 (gray) and SP5-RG (black), while the right column (b, d) presents the comparison between CAMS-RG-I (gray) and S5P-RG (black).

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Figure 16 is based on the same data, separated per station, that shows both the relative bias (median relative difference) for each dataset and the bias change with respect to S5P or CAMS-RG-I. Blue bars indicate a reduction in the bias, while red bars indicate an increase in the bias. At all stations, except the PGN sites of INOE, S5P-RG presents a reduction in the bias from 5 % to 18 % compared to S5P, showing the impact of the a priori profile shapes used in the satellite retrievals. Bias changes in S5P-RG compared to CAMS-RG-I can be positive or negative, are highly station dependent, and can be much larger in absolute value. The largest discrepancies (over 40 %) are found at the MAX-DOAS sites of De Bilt, Cabauw, Bremen, and Uccle. Difference dispersions per station (not shown) are mostly comparable between S5P and S5P-RG, while they are higher for CAMS-RG-I.

One should be aware that, even when a better a priori profile is used, it will still be different from the true profile. In combination with the different vertical sensitivity between the satellite and the reference data, a discrepancy will remain. Therefore, when profiles retrieved by MAX-DOAS are available, an alternative approach is the application of the satellite averaging kernels to the NO₂ lower tropospheric profiles derived from the MAX-DOAS observations. This latter approach removes the TROPOMI a priori dependence from the relative comparison, and it has been shown in the recent quarterly validation report for the TROPOMI products (Lambert et al., 2021) that the (negative) bias estimate is reduced by up to 20 % when the MAX-DOAS profile data are smoothed vertically using S5P averaging kernels, indicating a significant impact of the profile shape due to the different vertical sensitivity profiles of MAX-DOAS versus the satellite retrievals. It was also shown in Liu et al. (2021) that using the S5P averaging kernel reduced the bias of about 16 % in Munich for their regional TROPOMI product. It is therefore likely that application of the satellite averaging kernel would remove part of the residual bias of S5P-RG. However, as there are profile measurements available for only one MAX-DOAS of the stations in Table 4, this topic is not pursued in this study.

In summary, one can conclude that the bias of the tropospheric NO₂ of S5P-RG is improved compared to that of the operational S5P product for almost all stations by 5 %–18 %, while the overall dispersion of both products is similar, but the dispersion from the RMA regression line is better for the standard S5P. The difference dispersion and correlation parameters are superior for S5P and S5P-RG compared to CAMS-RG-I.

Figure 17Time series from May 2018 to March 2021 of the ratio of TROPOMI NO₂ retrievals at sites with a MAX-DOAS instrument. The ratio is defined as the retrieval using the CAMS a priori profiles divided by the operational retrieval. The seven sites are Athens in Greece, Bremen in Germany, De Bilt in the Netherlands, Uccle in Belgium (urban), Cabauw in the Netherlands (close to urban areas), Observatoire de Haute-Provence (OHP) in France, and Jungfraujoch in Switzerland (remote).

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In Fig. 17, we present the ratio of the CAMS a-priori-based retrieval by the original retrieval at the MAX-DOAS locations. Most locations show values of around 1.1, indicating that the coarse resolution of the TROPOMI a priori may lead to a 10 % underestimation of the tropospheric column in urban regions. For Athens, this is about 30 %, showing that the exact ratio will depend strongly on the location of the MAX-DOAS instrument. The remote locations show values smaller than unity, as discussed above. Interestingly, the ratio is relatively constant over the whole time period, with no obvious seasonality.