For this study, we use the Weather Research and Forecasting model (WRF) version 3.7.1 , with chemistry and aerosols WRF-Chem,. We use three one-way nested model domains centred around Berlin, at horizontal resolutions of 15 km × 15 km, 3 km × 3 km and 1 km × 1 km (Fig. ). The model top is at 50 hPa, using 35 vertical levels. The first model layer is at approximately 30 m above the surface, with 12 levels in the first 3 km. The setup includes the RADM2 chemical mechanism with the Kinetic PreProcessor (KPP) and the MADE/SORGAM aerosol scheme. RADM2 has been used frequently in air quality applications over Europe e.g.; the effect of this choice of chemical mechanism on modelled concentrations is further discussed in Sect. . We give the priority to using the KPP solver instead of the QSSA (quasi-steady-state approximation) solver, because found that the latter underestimates nighttime ozone titration for areas with high NO emissions. However, this option does not allow us to include the full aqueous-phase chemistry, including aerosol–cloud interactions and wet scavenging, and might thus reduce the model skill in simulating aerosols formed through aqueous-phase reactions as reported in . All settings, including the physics schemes used in this study, are listed in Table , and the namelist can be found in the Supplement. We use the European Centre for Medium-Range Forecast (ECMWF) Interim reanalysis ERA-Interim, with a horizontal resolution of 0.75∘ × 0.75∘, temporal resolution of 6 h, interpolated to 37 pressure levels (with 29 levels below 50 hPa) as meteorological initial and lateral boundary conditions. This also includes the sea surface temperature, which is updated every 6 h. The data are interpolated to the model grid using the standard WRF preprocessing system (WPS). Chemical boundary conditions for trace gases and particulate matter are created from simulations with the global chemistry transport Model for OZone and Related chemical Tracers MOZART-4/GEOS-5,.

An analysis of the USGS land use data commonly used in WRF showed that the land cover of the region around Berlin is not represented well. In addition, the MODIS land use dataset as implemented in the WRF model from v3.6 only includes one category classifying urban areas. Therefore, we implemented the CORINE dataset to replace the USGS dataset. The original CORINE dataset includes 50 land use classes. The land use classes at the spatial resolution of 250 m are remapped to 33 USGS land use classes read by WRF, following suggestions of (see also Table S1). Additionally, we distinguish between inland water bodies (USGS class 28) and other water bodies (USGS class 16). We map the urban land use classes in CORINE to three urban classes used in WRF-Chem, including “commercial/industry/transport” (USGS class 33), high (USGS class 32) and low (USGS class 31) intensity residential , which can be characterised as follows: “low intensity residential” (31) includes areas with a mixture of constructed materials and vegetation. Constructed materials account for 30–80 % of the cover and vegetation may account for 20–70 % of the cover. These areas most commonly include single-family housing units, and population densities are lower than in high intensity residential areas. “High intensity residential” (32) includes highly developed areas with a high population density. Examples include apartment complexes and row houses. Vegetation accounts for less than 20 % of the area and constructed materials account for 80 to 100 %. Commercial/industrial/transportation (33) includes infrastructure (e.g. roads, railroads) and all highly developed areas not classified as high intensity residential.

We implement the new land use categories as described in (Fig. ). In addition, we adjust the initialisation of the dry deposition of gaseous species to account for these new land use categories, as described in . For the base run, we use the bulk approach of the land surface scheme, assigning the most abundant land use class within a model grid cell to the whole grid cell. In a sensitivity simulation, we test the mosaic approach , allowing us to account for a heterogeneous land use classification within one model grid cell. Up to eight different land use types within one model grid cell are considered in our setup.

We use the single-layer urban canopy model to account for the modified dynamics by cities, especially Berlin and Potsdam. The urban model takes into account energy and momentum exchange between urban areas (roofs, walls, streets) and the atmosphere and is coupled to the Noah land surface model. Surface fluxes (heat, moisture) and temperature are calculated as a combination of fluxes from urban and vegetated surfaces, coupled via the urban fraction assigned to the land use type of the grid cell . We choose to not use a more complex parameterisation of the urban canopy, such as the building effect parameterisation (BEP), because the computational cost is already very high at a horizontal resolution of 1 km × 1 km, and a more complex parameterisation of the urban canopy, along with the required increase of vertical model resolution, would increase the computational cost further and require a more detailed input dataset describing the urban structure. Moreover, the BEP is not applicable with the mosaic option in WRF so far and the only applicable planetary boundary layer (PBL) scheme in combination with the BEP and WRF-Chem is the Mellor–Yamada–Janjić scheme. This scheme often led to stronger biases in simulated 2 m air temperature than other parameterisations such as the YSU scheme , the scheme selected for this study. In addition, could show that the BEP did not outperform simpler approaches such as the bulk scheme or the single-layer urban canopy model with respect to simulating 2 m temperature and that the PBL scheme had stronger influence on simulated 2 m air temperature than the urban canopy parameterisation.

In our base simulation, we use the default input parameters as specified in the look-up table included in the standard distribution of the WRF source code available from UCAR. For a sensitivity simulation (Sect. ), we calculate some of the urban input parameters to the model for Berlin (Table ), which in previous studies have been found to be important. Geometric parameters include roof-level building height, standard deviation of the roof height, roof width and road width. The calculations are based on detailed maps of Berlin provided by the Senate Department for Urban Development and the Environment of Berlin. From the original data containing information on the location and number of floors of each house, the mean building height and the standard deviation of the building height is calculated assuming an average height of 3 m per floor, and the mean building length is calculated with the software QGIS, by calculating the surface area of each building geometry in the dataset and assuming its square root as each building's mean length. We combine these data with the CORINE land use data for Berlin mapped to the USGS classes (Sect. ), averaging these parameters over the parts of the city characterised by the same urban class. The maps further provide the location of individual road segments, which we use to calculate the total area covered by roads in Berlin. We combine this with the total length of all roads in Berlin to obtain the average road width, which we assign to all three urban land use categories. We further update the urban fraction using a spatially more detailed classification of the land use types and the fraction of impervious surface of each area, provided by the Senate Department for Urban Development and the Environment of Berlin. Following , we assume the urban fraction of a grid cell to be equal to the fraction of impervious surface. We then define the mean of impervious surface area, weighted by the area of the respective surface within each land use class as the updated urban fraction of the respective class. Following we use the values for thermal conductivity, heat capacity, emissivity and albedo of roofs, walls and streets specified in .

For the base run, anthropogenic emissions of CO, NOx, SO2, non-methane volatile organic compounds (NMVOCs), PM10, PM2.5 and NH3 are taken from the TNO-MACC III inventory, with a horizontal resolution of 0.125∘ × 0.0625∘. The inventory is based on nationally reported emissions for specific sectors, distributed spatially based on proxy data. In comparison to version II of the inventory , version III includes, amongst other updates, an improved distribution of emissions especially around cities. The distribution was improved by no longer using population density as a default for diffuse (non-point-source) industrial emissions but using industrial land use as a distribution proxy. Residential solid fuel use (wood, coal) was allocated more to rural areas than to large city centres on a per capita basis. Seasonal, weekly and diurnal emission profiles for Germany are applied to the aggregated emissions. This, as well as the speciation of the different NMVOCs, is described in and . found that distributing emissions vertically did not strongly impact the model results near the surface. This, along with the low stack height of point sources within Berlin, is why in this study all emissions are released into the first model layer. As much of the NOx emitted within Berlin is emitted from diesel vehicles (off-road and on-road), which studies have shown to be composed of high proportions of NO2 e.g., NOx is emitted as 70 % NO and 30 % NO2 (by mole). The latest available emission dataset is for 2011, which is used in the 2014 simulations. Dust, sea salt and biogenic emissions are calculated online, the latter using the Model of Emissions of Gases and Aerosols from Nature MEGAN v2,.

We perform a sensitivity simulation for testing the model sensitivity to the spatial resolution of the emission input data (Sect. ). As input to this sensitivity simulation, we downscale the anthropogenic emissions within Berlin onto a grid that is one-seventh of the original resolution, based on two proxy datasets, including traffic densities and population . Traffic densities are used to downscale all emissions from road transport, and population data are used to downscale emissions from industry, residential combustion and product use. Point sources are included in the grid cell within which the point source is located. In the TNO-MACC III inventory, all emissions from the energy industry within Berlin are point sources, and of the point-source emissions from other industry sectors ca. 55 % of the total emissions within Berlin for CO, 9–17 % for particulate matter and up to 1 % for other gases are included as point sources. Agricultural emissions within the city boundaries of Berlin are close to zero, which is why these are used at the original resolution.

Simulations are done for summer 2014 (31 May–28 August). We chose to simulate the summer of 2014, as this corresponds to the time period of the BAERLIN measurement campaign e.g.. While mean observed temperatures in June and August showed little deviations from the observed 30-year mean (1961–1990) with mean temperatures of 17.0 ∘C (June) and 17.2 ∘C, the July mean temperature of 21.3 ∘C was 3.4 ∘C higher than the 30-year mean. Precipitation was 12 and 13 % lower than the 30-year mean in June (62.5 mm) and July (60.2 mm), respectively, and it was 48 % lower than the 30-year mean in August, with 33.8 mm .

For the analysis, the first day of all simulations is discarded as spinup. A base run with the settings described above is done in order to evaluate the model performance in simulating observed meteorology and atmospheric composition. In addition, sensitivity simulations done for this study are the following, with the changes applied to all three model domains of horizontal resolutions of 15, 3 and 1 km:

S1_urb: updated representation of the urban characteristics of Berlin (see Sect.  and Table );

The purpose of the sensitivity simulations is to assess which resolution and level of detail in the input data, including land use (S2_mos), emissions (S3_emi) and parameters characterising the urban area (S1_urb), are needed for simulating urban background air pollutant concentrations and their spatial distribution in the Berlin–Brandenburg area, particularly focusing on NOx. We particularly ask whether a horizontal model resolution of 1 km, together with the above-listed specifications of the input data, leads to model results that differ from those obtained with a horizontal resolution of 3 km.

In the following, we list the data and data sources that we use for evaluating the present WRF-Chem setup for Berlin and its surroundings. Table  gives an overview over all observational data and measurement stations in Berlin and its surroundings used in this study.

In order to assess the model's skill in simulating observed meteorology, we compare the modelled (coarse domain) weather types with weather types calculated from the ERA-Interim reanalysis data for Berlin (Sect. ). The weather types are based on indices calculated to classify circulation patterns and are further described in . We then focus on evaluating the modelled meteorology including the following diagnostic variables: 2 m temperature (T2), 10 m wind speed and direction (WS10 and WD10), the atmospheric structure via comparing temperature profiles and mixing layer height (MLH), as well as 2 m specific humidity (Q2) and precipitation. While T2, WS10, WD10 and atmospheric vertical structure are important parameters for simulating atmospheric chemistry and aerosols, Q2 and precipitation will not have an impact on our results, as our setup does not include aqueous-phase chemistry or wet scavenging. However, we include Q2 and precipitation to complete the picture of the evaluation of simulated meteorology as well as to give an indication for future studies based on this setup. Finally, we evaluate the model performance for the main air pollutants including surface O3, NOx and PM, with a main focus on NOx. We evaluate the model results from all three domains with horizontal resolutions of 15, 3 and 1 km, which we also refer to as d01, d02 and d03.

Generally, the modelled weather types (see Sect. ) are consistent with those derived from the reanalysis (Fig. ). Periods in which WRF-Chem weather types disagree with ERA-Interim weather types never exceed two subsequent days and the frequency of WRF-Chem weather types agrees similarly well with ERA-Interim weather types.

The temporal correlation of modelled hourly 2 m temperature with observations is between 0.88 and 0.91 at all stations in and around Berlin and all model domains (Tables  and S3 in the Supplement), which shows that the model represents the observed temperature variability well. This is supported by the analysis of the conditional quantiles (Fig. ), which show that the modelled temperatures match the observations well for a wide range of values. The model is generally biased positively with up to +1.6 ∘C, though the bias at most stations is smaller than +1 ∘C (Tables  and S3). In absolute terms, this is within the same range, but never larger than the biases that and found using COSMO-CLM in combination with different urban canopy models for Berlin. Besides, the absolute mean biases are comparable to those reported by , who mainly found negative biases in near-surface air temperature applying WRF 3.6.1 for Berlin and its surroundings, testing two planetary boundary layer schemes and three urban canopy models.

The histogram in the conditional quantile plot and the extent of the blue line marking the “perfect model” show that WRF-Chem does not reproduce the highest observed temperatures. This suggests that the model might have difficulties in simulating pronounced heat wave periods. However, comparing the modelled daily maximum temperatures to the observed daily maximum temperatures (Tables  and S4) shows that the bias of the daily maximum temperatures is of a similar magnitude as the mean bias, with one difference: while the bias of maximum temperatures modelled with 3 and 1 km resolutions is mainly positive, the bias of the maximum temperatures modelled with a 15 km resolution is negative. In absolute terms, the bias of the daily maximum temperatures is smallest for results obtained with a 1 km resolution, though they only differ very little from the results obtained with a 3 km resolution.

We find two important relationships with respect to model resolution: firstly, the model simulates higher temperatures in the model domain of which the model grid cell land use type is urban (stations Kaniswall, Dahlemer Feld, Marzahn, Schönefeld). Secondly, while the modelled 2 m temperatures generally differ between the 15 and 3 km resolution even if the land use type of both grid cells in which the station is located is the same; the June–July–August (JJA) mean modelled temperature only changes by more than 0.1 ∘C between the 3 and 1 km resolution if the land use type changes (stations Bamberger Straße, Nansenstraße, Schönefeld). This indicates that switching from a horizontal resolution of 15 to 3 km might improve the spatial distribution of modelled temperatures, while switching from a horizontal resolution of 3 to 1 km has only a very little effect on improving the model's skill in simulating the observed temperature, but might be more beneficial if the land use input data are specified with a higher level of accuracy.

The comparison of simulated with observed temperature profiles (Fig. ) shows that the model reproduces the observed temperature profile well at all times, but that the modelled temperature profile at 12:00 UTC is shifted to higher temperatures by ca. 1 ∘C. The result is similar for all model resolutions (the profiles for the 15 km and 3 km resolutions can be found in the Supplement in Figs. S1 and S2). In order to further evaluate how the present WRF-Chem setup simulates the observed vertical structure, we compare the simulated mixing layer height derived from simulated profiles of temperature, wind speed and humidity (in the following also referred to as MLH-calc) to the mixing layer height derived from radiosonde observations at Lindenberg as described in (Fig. ). The results show that the model simulates the observed diurnal cycle of the MLH as well as the magnitude of the observed MLH at Lindenberg reasonably well: the bias of the daily mean MLH ranges between +87 m (13 %) and +113 m (16 %), depending on model resolution, and the biases of the daily maximum and daily minimum are between +268 m (19 %) and +347 m (25 %) and between +26 m (14 %) and +48 m (26 %), respectively (Table ). There is no consistent trend with increasing model resolution. It is important to note that these results refer to the MLH that we calculated from simulated profiles of temperature, wind speed and humidity. However, the MLH diagnosed by the model, in the following also referred to as MLH-YSU, underestimates the observations especially during nighttime (Fig. ), with a bias of the daily minimum MLH between -99 m (-53 %) and -113 m (-60 %), or a MLH lower than the calculated one between -128 and -214 %. Differences between the different ways of deriving the MLH for daily maximum values are less pronounced, ranging between 24 m (1 %) and 73 m (4 %). This leads to the conclusion that the model generally simulates the atmospheric structure well, but that the planetary boundary layer scheme underestimates observed MLH during nighttime. Similarly, this indicates that the mixing might also be underestimated by the boundary layer scheme during nighttime conditions.

Comparing the model results to ceilometer observations from Berlin at the Nansenstraße station also indicates that the diurnal variation is reproduced correctly (Fig. S9 in the Supplement). The comparison of daily minimum MLH with ceilometer observations also shows an underestimation of MLH-YSU in the same range as at Lindenberg. However, we do not know whether the magnitude of the mixing layer height derived from the ceilometer backscatter profile is directly comparable with the mixing layer height calculated from profiles of temperature, wind speed and humidity or with the mixing layer height calculated by the model. This makes it more difficult to evaluate the modelled mixing layer height quantitatively at the urban site Nansenstraße. For this, further studies assessing the comparability of MLH derived from radiosonde and ceilometer observations would be necessary.

Simulated hourly wind speed correlates with observations with a correlation coefficient between 0.5 and 0.6 (Table S5 in the Supplement), which is comparable to simulations for the European domain . Wind speed is overestimated between 0.4 m s-1 (15 %) and 1.4 m s-1 (50 %), depending on the station. The overestimation is especially strong at stations with mean observed wind speeds below 3 m s-1, as well as for a period of easterly winds in mid-July (Fig. ). The most frequently observed wind direction at three stations in Berlin and in Potsdam in June, July and August 2014 is westerly. This is reproduced by the model, with better skill with increasing resolution (Fig. ). Depending on the modelled wind direction, the bias in wind speed differs: while the bias (averaged over all four stations) is lower than 1 m s-1 for modelled wind from north to south-east, the bias is larger for wind simulated from east and north-east. In addition, the conditional quantile plot of wind speed, split by modelled wind direction, also shows that the model's skill in simulating wind speed from west and south-west is higher (see Fig. S3 in the Supplement).

Both the diurnal variability and the magnitude of specific humidity are simulated well by the model, with normalised mean biases between -7 and +7 % and correlation coefficients of 3-hourly values of around 0.8 (not shown). Precipitation is simulated well with the 3 and 1 km horizontal resolution: both the number of days with precipitation rates larger than 0.01 mm h-1 and the total amount of precipitation in the simulated period agree well with the observations (Fig. ). Model results from the 15 km resolution overestimate the number of days with precipitation larger than 0.01 mm h-1 by ca. 30 % and the amount by ca. 50 %. This shows that the higher-resolved domains in the nested setup, using the Grell–Freitas cumulus scheme on all domains, improve the skill in simulating precipitation, which is an important conclusion for future studies with a similar setup aiming at including aqueous-phase chemistry and wet scavenging.

The positive bias in T2 found in the model results at many sites is decreased for urban areas if the input parameters to the urban scheme are specified based on data describing the city of Berlin (simulation S1_urb, Table ), which is mainly due to the fact that T2 is overall simulated lower for urban areas in this sensitivity simulation. Specifically, there is only one site within the urban area (among all urban built-up and urban green stations) for which the model results with the 1 km horizontal resolution (d03) are biased more than ±1 ∘C (S1_urb, d02: 3 stations; base run, d03: 3 stations; base run, d02: 6 stations). Likewise, the simulation of daily maximum temperatures is improved. The results from this sensitivity simulation, similarly to the results from the base run, show that the differences between the results of the 3 and 1 km resolutions are largest if the urban class of the grid cell changes with changing resolution, though overall the results of the 1 km resolution match the observations slightly better than the results obtained with the 3 km resolution (Table ). Even though on average the temperature bias is lower in S1_urb than for the base run, the conditional quantile plots show that the highest observed values are still not captured by the model (Fig. ).

Using the mosaic option of the land surface scheme, and thereby taking into account the sub-grid-scale variability of the land use classes within one model grid cell (simulation S2_mos), has a similar effect on simulated T2 as in S1_urb: overall, simulated T2 is lower than in the base run, which leads to a decrease in T2 bias compared to observations. Furthermore, it leads to the results from the 1 and 3 km resolutions being more similar even at sites with different land use categories, which is referred to as grid convergence by and might indicate that a resolution higher than 3 km is not needed in this case. The conditional quantile plots (Fig. ) underline these results, showing almost identical median values and distributions for the 1 and 3 km resolutions, and furthermore reveal that the temperatures simulated with the 15 km resolution resemble the results with 3 and 1 km resolutions more than in any of the other simulations. At the 15 km model resolution and when applying the mosaic option, gradients at the edges of the city are resolved better than in the other simulations at the 15 km resolution, which is expressed through a lower mean bias at sites at the boundaries of Berlin. An important limitation using this option is the simulated daily maximum T2, which is underestimated at most stations (Table ). This feature was also found by for Berlin and its surroundings when applying the single-layer urban canopy model in combination with the mosaic approach and indicates that T2 might be decreased too much when using this option.

There is no observational data from radiosondes available within the city, which is why we cannot draw conclusions on the importance of updating the urban parameters or using the mosaic option for urban areas from comparisons with observed profiles of temperatures or MLH. However, knowing that the MLH diagnosed from WRF-Chem (MLH-YSU) is biased low in the base run during nighttime, we compare JJA mean nighttime (20:00–02:00 UTC) MLH from the base run and S1_urb as well as S2_mos (Fig. ). The results show that the nighttime MLH-YSU is simulated on average up to ca. 30 m lower in S1_urb than in the base run for most grid cells with the land use type low intensity residential. It is simulated higher than in the base run for grid cells with the land use type high intensity residential and commercial/industry/transport. This shows that the urban parameters can strongly influence the meteorology simulated in urban areas and suggests that they might have to be further refined for simulating the urban atmospheric structure correctly.

The nighttime MLH simulated with S2_mos is up to ca. 70 m lower than in the base run for urban areas, which is an even larger reduction than in S1_urb. As for S1_urb, grid cells with the dominant urban classes being high intensity residential and commercial/industry/transport have a higher MLH-YSU than other urban grid cells, though this effect is smoothed through the use of the mosaic option.

The bias in 10 m wind speed is reduced in S1_urb, ranging from +0.3 m s-1 (10 %) to +1 m s-1 (34 %) depending on the station (Figs. , and Table S5). The bias is especially decreased for two periods in mid-June and mid-August, where observed daily mean wind speeds are between 5 and 6 m s-1, which is relatively high compared to the rest of the simulated period. In the base run, the model overestimates the observations during these periods, which is not the case in S1_urb. Similarly, the wind speeds during the periods in mid-July with easterly wind, where the base run strongly overestimates wind speeds, are biased by ca. 1–2 m s-1 less (Fig. ). The histograms in the conditional quantile plots further shows that the range of modelled wind speeds from S1_urb matches the range of observed wind speed better than in the base run (Fig. S4 in the Supplement).

Similar to S1_urb, the bias in wind speed is decreased in S2_mos, ranging from below +0.1 m s-1 (2 %) to +1.2 m s-1 (40 %) (Figs. , , S4 and Table S5 in the Supplement). However, it should be noted that unlike for S1_urb, where the decrease in wind speed is distributed evenly throughout the day, wind speed in S2_mos is especially lower during nighttime, while maximum diurnal wind speeds are similar to those simulated in the base run (not shown).

Overall, the results show that when using a model setup with highly resolved nests, the simulated meteorology seems to be improved both by specifying land use input data and urban parameters for the simulated region and when using the mosaic option, though the biases in the diurnal cycles of T2 and wind speed are reduced more in S1_urb. Particularly the differences between S1_urb and the base run for grid cells with land use types high intensity residential and industry/commercial/transport reveal that the specification of urban parameters can contribute to improving the model bias also in MLH. The results from S2_mos show that the mosaic option might be a useful alternative if computational resources are too limited to include higher-resolved nested domains.

Mean NOx concentrations simulated with S1_urb are generally higher than those simulated with the base run, with the difference between S1_urb and the base run for grid cells of the measurement stations of up to 9 % (15 km resolution), up to 13 % (3 km resolution) and up to 18 % (1 km resolution). Thus, the positive bias which has been found in the base run is increased in S1_urb. For all three domains, the differences are larger for urban grid cells. An analysis of the diurnal cycles reveals that these differences are mainly due to higher nighttime NOx concentrations in S1_urb (Fig. ). This is consistent with previous results: an underestimation of MLH by the model (MLH-YSU) during nighttime leads to an overestimation of NOx. An even lower MLH in this sensitivity simulation (Sect. ) explains nighttime NOx concentrations being higher than in the base run. The overestimation of nighttime NOx might be further reinforced by lower simulated wind speeds in S1_urb. Daytime NOx, which we define as NOx concentrations between 07:00 and 17:00 UTC, changes only little in S1_urb compared with the base run at urban background stations in Berlin: results with a 3 km horizontal resolution show an increase in daytime NOx in S1_urb between 2 and 5 % and an increase between 5 and 7 % with a 1 km resolution compared to the base run.

Results for simulated NOx from S2_mos are consistent with the results from S1_urb: simulated nighttime NOx is even higher than that simulated in the base run and in S1_urb, which is consistent with the larger difference between MLH-YSU simulated with the base run settings and within S2_mos. Daytime NOx changes even less in S2_mos compared to the base run, with changes between -1 and +2 % (3 km resolution) or +3 to +5 % (1 km resolution).

Overall, the results underline that the underestimation of mixing in the boundary layer is likely to have a strong influence on simulated nighttime NOx concentrations in urban areas, which is not corrected using the mosaic option or specifying the input parameters to the urban scheme. However, since the simulated MLH is sensitive to the change in urban parameters for high intensity residential and commercial/industry/transport urban areas, it shows that this could potentially have an impact on simulated NOx concentrations. The results from both S1_urb and S2_mos show that daytime NOx is influenced little by changes in the modelled meteorology, suggesting that the bias in daytime NOx is due to emissions that are too low or an incorrect distribution of emissions resulting from a resolution of the emission inventory that is too coarse, as mentioned in Sect. . As previously mentioned, a further reason for this bias might be limitations in comparability between grid-cell-averaged simulated concentrations and point observations near the surface.

Evaluating the base run (Sect. ), we found that the improvement in simulating NOx concentrations with a 1 km horizontal resolution, as compared to a horizontal resolution of 3 km, is negligible when using emission input data at 7 km horizontal resolution. This result changes when providing emission input data with a horizontal resolution of ca. 1 km as described in Sect.  (Fig. ): the model is then able to resolve small-scale air pollution patterns and hotspots, which cannot be resolved at a horizontal resolution of 3 km. A comparison of the results for the urban background stations within Berlin (Amrumer Straße, Belziger Straße, Nansenstraße, Johanna und Willi Brauer Platz, Brückenstraße) helps to illustrate this: in order to minimise the bias by too little nighttime mixing, we only compare daytime (07:00–17:00 UTC) NOx simulated with 3 and 1 km horizontal resolution and downscaled emissions. Going from a 3 to a 1 km resolution, daytime NOx changes by +40, +12, -25, +16 and +161 % in S3_emi for the above-mentioned urban background sites, respectively (Fig. ). As a comparison, the respective changes from the base run are +3, +1, -8, -3 and -3 %. This shows that a 1 km horizontal model resolution only leads to different results from a 3 km horizontal resolution when also using highly resolved emission input data.

Furthermore, the results from the above-mentioned urban background stations show that emissions that are too low within the city (either due to emissions that are too low overall or locally because of a coarse resolution of the emission inventory) can be a cause of the bias in daytime NOx concentrations. To illustrate that, we compare the daytime NOx concentrations from the base run and S3_emi. Using the original emissions, the emissions summed up over JJA in the grid cell where the respective station is located are 7.0, 5.4, 6.9, 3.1 and 7.0 t km-2 for the above-mentioned urban background stations, respectively, and 22.4, 8.4, 6.2, 2.5 and 79.9 t km-2 in the downscaled emission data. It should, however, be noted that, though downscaling of the original emissions can lead to a decrease in emission strength in some of the urban grid cells, it generally results in an increase in the city centre and a decrease in the suburban areas. This is due to the population density and the traffic density, which are used as proxies for the emission downscaling, being higher in the city centre. Using the downscaled emission data leads to an increase in simulated daytime NOx of 23, 22, 52, 20 and 51 % (3 km resolution) or 68, 36, 24, 44 and 308 % (1 km resolution) at the above-mentioned urban background stations, as compared to the base run. This shows that, despite small decreases in emissions in some of the grid cells, the generally increased NOx emissions in the city centre led to increases in simulated NOx concentration at all five sites. This result indicates that the downscaled emissions might be more suitable to represent gradients in emissions in the urban area, contributing to correcting the bias in simulated daytime urban NOx in the base run.

A comparison of results from S3_emi with observations at Brückenstraße (Table ) shows that locally the bias in simulated NOx concentrations can increase strongly. While for most urban background stations in Berlin using the downscaled emissions improves both the bias of mean NOx and the bias of daytime NOx, the example of Brückenstraße shows that further modifications to the emission downscaling and processing might be necessary when simulating local NOx patterns: at the Brückenstraße site, the mean bias increases from -4 µgm-3 (1 km resolution, base run) to +26 µgm-3 (1 km resolution, S3_emi). The large overestimation is due to a point source being close to the site and the way point sources have been treated: as mentioned in Sect. , point-source emissions are all released into the first model layer. Furthermore, the point-source emissions are distributed as area sources at the resolution of the emission inventory.This results in much higher emissions over a much smaller area in the downscaled emission inventory, locally increasing the concentrations in the vicinity of point sources. Likewise, the comparison of simulated and observed concentrations at rural and suburban sites just outside of Berlin shows that the model skill suffers from the lack of proxy data specifying the spatial distribution of emissions directly outside of Berlin.

Generally, comparing the results from the base run with the results from S3_emi leads to several conclusions: when simulating NOx concentrations in urban areas, a higher horizontal model resolution can be beneficial if an emission inventory of similarly high resolution is available. However, using a highly resolved emission inventory for a model domain with a similarly high resolution is only beneficial for improving the comparability with observations and the application to local studies if the emission inventory is of sufficient spatial precision. The downscaling approach presented here shows how locally highly resolved emissions can be calculated effectively and consistently by combining a readily available emission inventory with data available for many urban areas, such as population and traffic densities. Our results suggest that a further refinement of the proxy data could be useful, e.g. using proxy datasets covering more than the urban area itself. Further refinements could consist in using the housing type (or high population density as an indication for high-rise buildings) for better distributing residential heating emissions. As for the vertical distribution of emissions, as well as an increased vertical model resolution, state it has little impact on the model results. While this might hold for simulations of rural background air quality with domain resolutions of the order of 45 km, the present results suggest that it is of higher relevance to distribute point-source emissions into several vertical model levels when decreasing the model resolution and the resolution of the emission input data. Similarly, increasing the vertical model resolution at the same time might both help distribute emissions better and improve the modelled mixing.