We simulate the geometry of the S5P and MTG-S (for S4) orbits and field of view using the System Tool Kit (STK, developed by AGI, http://www.agi.com/products/, last access: 16 September 2019). For S5p, using the orbit characteristics, the STK provides the time-dependent geolocation of the edges of the swath. Based on the location of the edges, we compute the coordinates of the individual observations assuming a spatial resolution of 7 × 7 km2 at nadir. We first compute the geometry of one S5P orbit and then apply appropriate time and longitude shifts to obtain all the orbits needed for both study periods. Subsequently, we compute the geometry for each individual observation (the solar, viewing and azimuth angles). Note that normally the size of the footprints away from nadir increases roughly by 1∘ per viewing angle. For S5P the size of the real footprints at the edges of the swath are reduced by a factor of 2 by changing the binning, leading to a more uniform footprint size across track. The footprints of the generated synthetic observations are 7 km at nadir up to ∼8.5 km at the edges. This is not fully realistic but approximates the real footprints when using the binning. For S4 the viewing angle decreases with latitude, and pixels become stretched from roughly 7 km in a north–south direction at 40∘ N up to 25 km at 70∘ N.

As a final step, we store only the part of the orbit that has an overlap with the model domain. The data are stored in formatted files that mimic the format of current NO2 column products from satellite retrievals.

The satellite measurements of S4 and S5P, once available, will be used to retrieve cloud properties like cloud fraction and cloud pressure, using either the O2-A band (Wang et al., 2008) or the O2-O2 absorption feature around 477 nm (Veefkind et al., 2016). However, for an OSSE those need to be estimated differently. For this purpose we take cloud information and other relevant model fields from the ECMWF weather forecast archive for the two 3-month study periods at a resolution of 0.25∘. The retrieved fields are temperature, pressure, liquid and ice water content, specific humidity, and cloud fraction. To simulate the cloud parameter observations, we convert the ECMWF cloud quantities to cloud optical properties, which determine the reflectance at the top of the atmosphere. Based on these reflectances, we simulate the effective cloud fraction and effective cloud top height similar to the procedure in the O2-O2 cloud retrieval. The distribution of effective cloud fractions obtained in this way was compared with OMI O2-O2 cloud observations for the year 2006, and a reasonable qualitative agreement of the histograms was found for summer and winter months, with somewhat fewer cloud free days and more intermediate cloud fractions in the OMI dataset, which could in part be due to the above-average number of sunny days in 2003 (Williams et al., 2013). We use the simulated effective cloud fraction and cloud pressure in the synthetic retrievals.

We convert the cloud fraction into a cloud radiance fraction (the fraction of the top-of-atmosphere radiance coming from the cloud-covered part of the scene) by computing radiances using the surface albedo map and assuming a cloud albedo of 0.8. The surface albedo is taken from the 5-year OMI Lambertian reflectivity dataset, extended from the 3-year dataset published by Kleipool et al. (2008). Figure 2 shows an example of the cloud radiance fraction simulated in this way for the 13:30 LT (local time) afternoon overpass of S5P on a day with mainly cloud-free conditions over continental Europe.

The ideal approach for the generation of synthetic observations would involve the following steps: (1) use the NR profile and radiative transfer model to simulate radiances at the top of the atmosphere, (2) add noise to the simulated radiances based on the satellite specifications, (3) apply the retrieval approach to the simulated radiances, and (4) add extra noise related to uncertainties in retrieval parameters such as cloud fraction and surface albedo. Due to the large number of observations provided by the Sentinels, this approach is not feasible.

Following Rodgers (2000), we note that applying the forward radiative transfer model, followed by the retrieval is equivalent (after linearisation) to applying the kernel matrix A, and the synthetic observations xr can be generated with the equation xr=xa+A(x-xa)+ϵ, where xa is the a priori column or profile, and ϵ is the error due to the instrument and retrieval errors. As shown by Eskes and Boersma (2003), for differential optical absorption spectroscopy (DOAS) column retrievals (A-I)xa=0, and the equation simplifies to xr=Ax+ϵ. Here x is the true vertical profile of NO2 and the averaging kernel is a 1-D vector. For the DOAS column retrievals considered here, we compute the elements of the averaging kernel from the height-dependent air-mass factors (AMFs) or box AMFs (Eskes and Boersma, 2003).

Using the radiative transfer toolbox DISAMAR (Determining Instrument Specifications and Analysing Methods for Atmospheric Retrieval; de Haan, 2012), we generate lookup tables for the box AMFs for the range of geometries of the S4 and S5P. Results are stored for 21 pressure levels between 1050 and 0.1 hPa, 9 surface albedos, 10 cloud surface pressures, 10 solar zenith angles, 15 viewing zenith angles, and 3 relative azimuth angles. We use linear interpolation to find the AMF values for the satellite geometries.

The Sentinel-4–5 Mission Requirements Traceability Document (ESA, 2017) specifies signal-to-noise ratios for Sentinel-4 and Sentinel-5(P). With the DISAMAR tool, we can translate these irradiance and radiance requirements to NO2 retrieval uncertainties using either DOAS or optimal estimation. We experimented with this but found that the uncertainty estimates are very sensitive to assumptions on spectral correlations in the noise. For the final set of simulations, we adopted the DOAS approach following an early version of the TROPOMI NO2 Algorithm Theoretical Baseline Document (ATBD) (van Geffen et al., 2014). We base this approach on our experience with the OMI instrument. We extrapolate the uncertainty estimate for TROPOMI from the OMI DOAS slant column retrievals and obtain an absolute estimate of 0.7×1015 molecules cm-2 for NO2 (of the order of 10 % for moderately polluted conditions) for the slant column, nearly independent of geometry or latitude. We use this estimate in the retrievals.

Other uncertainties due to retrieval input parameters, affecting the AMFs, are propagated through the DOAS equations following the approach described in Boersma et al. (2004). We assume fixed uncertainties for the cloud pressure (50 hPa), the cloud fraction (0.02) and the surface albedo (0.015). We do not explicitly model the stratospheric NO2 distribution but implicitly assume that a method will be adopted to estimate the stratospheric column, so that for the synthetic observations only the uncertainty of the stratospheric estimate needs to be accounted for. Again, based on our experience with OMI, SCIAMACHY and GOME-2 (van Geffen et al., 2014), the stratospheric vertical column uncertainty resulting from this procedure is set to 0.15×1015 molecules cm-2 or about 6 % of an average mid-latitude stratospheric column.

We compute the synthetic observations by applying the averaging kernels to the values from the NR linearly interpolated to the locations from the orbit simulator. We add Gaussian noise to the retrievals making use of the estimated retrieval uncertainty (Sect. 2.2.4). Figure 3 gives an example of one 13:30 LT overpass of S5P, based on the NR of 1 June 2003. Figure 3c shows the MOCAGE NR tropospheric column amount. Due to the wind from the south, there is transport of pollution from the Benelux over the North Sea. We show the uncertainty modelled in the synthetic retrieval in the Fig. 3b. We determine the detection limit noise level by combining the slant column noise with the stratospheric column uncertainty. The AMF retrieval errors related to cloud and albedo scale linearly with the retrieved column and are of the order of 25 %–50 %.

S4 will fly on a geostationary platform; this will provide additional diurnal information about NO2. We simulate the S4 observations each hour during daytime. Figure 4 provides an example of the S4 observations as simulated, one in the early morning 04:00 UTC and one during midday at 12:00 UTC. The images demonstrate the large diurnal cycle present in the MOCAGE NR of NO2.

The LOTOS-EUROS set-up features an active data assimilation system based on the ensemble Kalman filter (EnKf) technique (Evensen, 2003). A Kalman filter computes probability density functions (pdf's) of the true state, given (1) a transition model to propagate the state in time with associated uncertainties and (2) observations with associated representation error. Starting from the initial pdf, the filter first performs a forecast step propagating the pdf in time until the first moment that observations become available. Then, during the analysis step, we replace the forecast pdf with an analysed version that takes into account the new information available. The Kalman filter is an example of sequential assimilation, since forecast and analysis steps follow each other sequentially in time and use only information from the past. To be able to apply this technique to a large-scale air quality model, the pdf is described by an ensemble of model states in a so-called EnKF (Evensen, 2003). The spread between the ensemble members should describe the uncertainty in the state quantities as the mean and covariance of the state is computed from the ensemble statistics. The number of required ensemble members depends on the complexity of the pdf, commonly determined by the non-linearity of the transition model and the complexity of the associated model uncertainty. In practice, an ensemble with 10–100 members is acceptable to keep computations feasible. The data assimilation system in LOTOS-EUROS has been successfully applied for assimilation of O3, NO2, SO2, and aerosol observations from either ground-based or satellite instruments (Barbu et al., 2009; Curier et al., 2012; Eskes et al., 2014; Fu et al., 2017; Schaap et al., 2017; Segers et al., 2010; Timmermans et al., 2009).

The ensemble specification has a number of settings that need to be set prior to the assimilation experiments. These include the selection of uncertain model parameters (e.g. emissions), the amplitude of the assumed uncertainties and their temporal correlation. Additionally, the assimilation system requires a number of other parameters to be set that influence the results: ensemble size, localisation length scale for different types of observations and representation error covariance. The latter quantifies the differences caused by the different resolutions of the model and the observations.

In this study, we use the selection of model parameters as used in the operational national and European CAMS forecasts, which are the emissions of the ozone precursors (NOx and non-methane volatile organic carbons, NMVOCs), deposition velocity of ozone and the boundary conditions for ozone, all with an assumed uncertainty of 50 % and assumed temporal error correlation of 1 d.

The localisation length scale for the ground-based ozone observations is set to 50 km following Curier et al. (2012). The length scale for assimilation of the synthetic NO2 observations has been set to 0 km.

We base the representation error covariance for the satellite observations on observation minus simulation statistics and spatial correlations present in the observations. We obtain the representation error for the surface ozone observations by analysing the impact of spatial averaging. This depends on the spatial variance in the ozone fields, i.e. higher at coastlines and in mountain areas where we find the highest ozone gradients.

An important parameter in the filter is the ensemble size. In general, the ensemble size should be large enough to represent the covariance structure imposed by model uncertainties and the model physics. In this application, the covariance structure is rather simple, since we describe all uncertainty by the local sources, and observations are available regularly over the domain. With the chosen configuration, we show that an ensemble size of 12 members is sufficient to obtain stable results.

Within the data assimilation system, the synthetic observations are ingested using their estimated uncertainties. The available averaging kernels from the synthetic observations are applied to the model profiles from the surface to the tropopause to make them comparable to the column observations from satellites.

In case the assimilation system is unable to represent an observation correctly, the assimilation may lead to instability of the system. Such an instability can occur if the model lacks certain physical parameterisations or if the model is unable to represent a measurement resulting in a mismatch of the model and measurement spatial or temporal resolution. To avoid this, we apply a screening procedure to reject those measurements that cannot be represented correctly by the assimilation system. The screening procedure is taken from Järvinen and Undén (1997). If the square of the difference between observation and filter mean is more than a factor of 3 larger than the expected variance of this difference, we reject the observation.

In addition, we filter out all synthetic observations with cloud radiance fraction higher than 50 % (to exclude cloudy pixels) and those with surface albedo higher than 0.3 (the high reflectance complicates the NO2 retrieval and for OMI data users are advised to discard scenes with surface albedo values >0.3; Boersma et al., 2011). All observations within the model grid cells are averaged before assimilation using weights according to overlap between pixel footprint and grid cell.

Table 1 provides an overview of the different configurations of the assimilation runs. The runs with assimilation of synthetic surface ozone observations only serve as reference runs to represent current operational system capabilities. The runs with assimilation of GEO, LEO, or GEO and LEO observations combined serve to evaluate the added value of the new satellite instruments under study. We perform these runs for a European, zoom and fire domain, as presented in Fig. 6. The fire domain covers part of the Iberian Peninsula and is only included in a run for a short episode (first 2 weeks of August 2003) with large fires in Portugal.

Figure 10 shows the bias around time of overpass of S5P (over central Europe at 14:00 UTC) between modelled NO2 columns and the synthetic NO2 observations from the CR without any assimilation and the ARs with assimilation of either S4 or S5P data averaged over the summer period June–July–August (JJA) in 2003. The CR overestimates the NO2 columns, especially over the Benelux, the Ruhr area in Germany and the south-eastern part of the UK. These regions are characterised by high NO2 concentrations due to high density of sources such as traffic, shipping and industry. A strong decrease in the bias is visible after assimilation of the synthetic Sentinel data in combination with ground-based ozone observations. On average, the impact of the S4 and S5P observations in combination with the ground-based observations is very similar at the overpass time. Note that in the eastern part of the domain, the bias is not zero for the S5P case, but observations do not cover this region around 14:00 UTC. Figure 11 shows that the temporal correlation improves by the assimilation of the Sentinel observations. Over large parts of the domain and especially the areas with high NO2 concentrations, the temporal correlation increases significantly. Considering the overpass time, the temporal correlation in this case is a measure of the representation of the day-to-day variability. This result shows that the system is working as expected and the data assimilation pulls the modelled values towards the observations.

For the winter period, the conclusion is the same as for the summer period: bias and RMSE decrease while the temporal correlation increases (not shown).

To evaluate the added value on top of the ground-based observations, we compare the results with the reference run (RR), where we assimilate only ground-based observations. Figure 12a and b shows the statistical evaluation for the high-resolution zoom domain as function of the time of the day, for the modelled NO2 column. We see that for the modelled NO2 columns, the assimilation of ground-based ozone observations in the RR during the summer study period leads, on average, to a negative impact on RMSE (an increase) during the night and on correlations throughout the entire day. Further investigation demonstrates that the assimilation of the ozone observations improves the surface ozone concentrations. The reason for this negative impact on NO2 column may lie in the fact that the errors in modelled surface ozone concentrations and in modelled NO2 columns are not dominated by the same error source. Another reason could be that the assimilation system is not adapting the dominant parameter responsible for both the ozone and NO2 column errors. Remember there are four uncertain model parameters in the set-up used in this study that can be adapted through the assimilation. Assimilation of observations should, therefore, always be evaluated with care and one should analyse individual impacts of observation sets or impacts on different components.

The additional assimilation of satellite NO2 column observations improves the RMSE and correlations in NO2 columns in comparison to the RR. This impact is clearer in the results focusing on the fire episode over the Iberian Peninsula (Fig. 12c and d). The impact of the GEO S4 observations is visible throughout the entire day, while the impact of the LEO observations at the overpass time is smaller than the impact of the S4, which continuously feeds the model and lasts for several hours. The combined assimilation of S4 and S5P observations for the zoom domain only, minimally increases the correlation around the overpass time of S5P in comparison to the assimilation of S4 data only and does not show a benefit on the RMSE.

While the results above demonstrate that the system is working as expected and is able to decrease the difference between the model and synthetic NO2 observations, the goal of our study is to investigate the added value of the Sentinel observations for air quality analyses at the surface where the impact of air pollution is the most significant for human health and the ecosystem.

Figure 13 illustrates the impact of the assimilation on modelled surface NO2 concentrations. Here we also see a positive impact of assimilating S4 and/or S5P observations. The RMSE decreases by about 30 % during daytime hours (or from the overpass time onwards for S5P), and the correlation increases by about the same amount. On average, the impact here is slightly smaller than on the modelled NO2 column. Whereas concentrations of NO2 show very distinct high-resolution features in a small surface layer, mixing towards larger upper layers leads to less pronounced features in the column values. The observed NO2 columns, therefore, do not contain the level of detail that the surface NO2 does. The comparison with modelled NO2 columns is more direct, covers the same altitude region and therefore, as expected, shows a larger impact than the comparison with surface NO2. As the Sentinel tropospheric NO2 columns do not contain any information about the vertical distribution within the troposphere, the assimilation of NO2 columns may in some cases also lead to a deterioration of modelled surface concentrations when the vertical NO2 profiles in the model are incorrect.

Figure 14 shows the positive impact on modelled surface NO2 concentrations in a geographical form. This figure shows the bias of the different runs, averaged over the summer period at 10:00 UTC (shortly after the morning rush hour), for a region centred over France where traffic highways are highly pronounced. The CR overestimates the surface NO2 concentrations over traffic highways and large urban areas (e.g. Paris and London). While the ground-based ozone observations in the RR are able to decrease this positive bias, (averaged over the zoom domain from 0.8 to 0.4 ppb), the S4 observations (available throughout the day) are able to decrease this bias further over the traffic highways (average bias over zoom domain is eliminated). Furthermore, over the shipping lane through the English Channel, between the UK and France, the bias significantly decreases from values around 5 to nearly 0 ppb. The S5P, with its afternoon overpass time, has an expected negligible impact at 10:00 UTC. As could be seen in Fig. 13, at 14:00 UTC the impact of the S5P for surface NO2 concentrations is similar to the impact of S4.

For the winter period, the impact of the assimilation of Sentinel data on surface NO2 concentrations shows a mixed picture, which hints to the importance of the model profile shape for improvements at the surface when assimilating column observations. A mismatch between the bias in column NO2 and surface NO2 can lead to a negative impact of the satellite observations. Figure 15 shows the bias compared to the NR surface NO2 concentrations for the CR without any assimilation and the AR including the assimilation of surface ozone observations and S4 synthetic observations. The CR shows an overestimation of the NR concentrations over central Europe, large cities in southern Europe and the shipping lanes in the Mediterranean. Differently, the CR shows an underestimation of surface NO2 concentrations over the north-eastern part of the domain. The assimilation of the synthetic observations clearly decreases the modelled concentrations over the central European area and leads to a reduced bias over, for example, Germany. Over some of the eastern European countries, the concentrations increase and the negative bias decreases, for example in Romania, Ukraine and Belarus. However, these positive impacts are not present over the entire domain. Over some areas, the positive bias increases (e.g. over Austria, Slovenia and Northern Italy) or changes to a negative bias (e.g. over Barcelona, Belgium and the Netherlands). We have found that, in many of these situations, the bias in surface NO2 concentration does not match the bias in tropospheric NO2 column. For example, in the area covering Austria and Slovenia, the CR underestimates the NO2 column from the NR. Assimilation of synthetic S4 observations derived from the NR then increases the NO2 values and can only do so by increasing the sources at the surface. Even if we would only be able to increase the concentrations at higher altitudes, the satellite measurements do not provide information about the vertical profile or at which altitude the model is biased. The increased emissions at the surface then lead to even higher concentrations and an increased positive bias in this specific situation. These results demonstrate the importance of a correct representation of the vertical distribution in the model and of an evaluation of model profiles with independent profile information, for example from MAX-DOAS or aircraft measurements. In our experiment, the vertical distribution of the NR and CR in some cases differs in this way, leading to occasional negative impacts from the assimilation of the synthetic observations.

We perform the OSSE in this study with an ensemble Kalman filter approach, which optimises the NO2 concentrations by specification of uncertainties in model parameters, as described in Sect. 2.5.2. The parameter that most directly influences the NO2 concentrations is NOx emissions; other parameters such as NMVOC emissions and ozone deposition velocities are more related to ozone. As an example of the change in model parameters, Fig. 16 shows average NOx emission adjustments for the summer period for the RR and AR with S4 data. The distribution of emission adjustments is quite similar between both runs, which gives confidence to the choice of uncertain parameters. The assimilation of high-resolution S4 NO2 observations has a relatively large additional impact over some areas of the domain. For example, the NOx emissions over the centre of the Netherlands increase, while the NOx emissions over the shipping route in the English Channel decrease. Due to the high resolution of the S4 data and the smaller length scale set in the assimilation, the S4 observations bring more detailed emission updates than ground-based ozone observations only. Note that this assimilation set-up, with uncertainties in the emissions, is less flexible at remote locations with small emission fluxes.