We use the Weather Research and Forecasting model (WRF) version 3.8.1 , with chemistry and aerosols WRF-Chem,. The set-up includes two model domains centred over Berlin, at horizontal resolutions of 15 km × 15 km and 3 km × 3 km, using one-way nesting. The model top is at 50 hPa, using 35 vertical levels with the first model layer top at approximately 30 m above the surface. There are 12 levels in the lowest 3 km. Urban processes (meteorology) are parameterized with the single-layer urban canopy model, with input parameters specified for Berlin as described in and three urban land use categories. The set-up further includes the RADM2 chemical mechanism with the Kinetic Pre-Processor (KPP) and the MADE/SORGAM aerosol scheme. The MOZART chemical mechanism is used in a sensitivity test. All physics and chemistry schemes used in this study are listed in Table .

Small changes in the code have been made. The initialization of the dry deposition (module_dep_simple.F) has been adapted in order to account for three urban land use categories as described in , and references therein. Nighttime mixing over urban areas is not accounted for sufficiently by the urban parameterization and the PBL scheme and is thus adjusted (dry_dep_driver.F) as described in the Supplement. There, we also show illustrative results (Figs. S1–S3 in the Supplement) of two test simulations comparing the impact of changes in this model set-up with respect to , including the modification of nighttime mixing and the modification of the diurnal distribution of traffic emissions (see Sect. ).

We use the European Centre for Medium-Range Weather Forecasting (ECMWF) Interim reanalysis ERA-Interim, with a horizontal resolution of 0.75∘ × 0.75∘ and a temporal resolution of 6 h, interpolated to 37 pressure levels (with 29 levels below 50 hPa) as meteorological initial and lateral boundary conditions. The sea surface temperature is updated every 6 h. The data are interpolated to the model grid using the standard WRF pre-processing system (WPS). Chemical boundary conditions for trace gases and particulate matter are created from simulations with global chemistry transport Model for Ozone and Related chemical Tracers MOZART-4/GEOS-5,. Instead of the standard USGS land use data we use CORINE data , remapped to the USGS classes, using three categories characterizing the urban area. This provides a more realistic characterization of the land use in the Berlin–Brandenburg area . The emission input data and their pre-processing are described in Sect. .

Following the workflow used in AQMEII phase 2 , we re-initialize the simulation every 2 days, with a 1-day spin-up of the model meteorology. To ensure consistency in the chemical fields, we start each new 2-day simulation from the chemistry fields of the previous simulation. For the base run using the RADM2 chemistry scheme, we do a full-year (2014) simulation. The results of this simulation are used to derive a correction factor for road traffic emissions, as explained in Sect. 6.1. For computational reasons, the simulation is divided into two parts covering the first 6 and last 6 months of the year. Both simulations are initialized using data from ERA-Interim (meteorology) and MOZART4/GEOS5 (chemistry) and are preceded by a spin-up period of 4 days. We do a 1-month sensitivity simulation with the MOZART chemistry scheme (July 2014), and two sensitivity simulations with increased traffic emissions for January and July 2014, all with the same simulation procedure. All model simulations are listed in Table .

NO2, NOx and O3 measurements are taken from AirBase , a database compiling air quality observations from the EU Member States and associated countries, performed as required by EU clean air legislation. The files can directly be downloaded from the AirBase website. In the case of Germany the measurements are performed by the federal states. For the comparison with model results, observations from stations within Berlin and in the adjacent surroundings in the Federal State of Brandenburg representing “urban background”, “suburban background” and “rural near-city” conditions are used (Fig. ; also see Supplement Fig. S4 and Table S1). For our analysis, we re-classify AirBase station DEBE066 in Berlin–Karlshorst from “urban background” to “suburban background”, as the station is not located in the core area of the city and pollutant concentrations measured there are similar to concentrations measured at other suburban background stations. As a result, four stations for each classification type are used in this study: Amrumer Straße (DEBE010), Brückenstraße (DEBE068), Belziger Straße (DEBE018) and Nansenstraße (DEBE034) in the urban background, Blankenfelde-Mahlow (DEBB086), Buch (DEBE051), Groß Glienicke (DEBB075) and Johanna und Willy Brauer Platz (DEBE066) in the suburban background, and Frohnau (DEBE062), Grunewald (DEBE032), Müggelseedamm (DEBE056) and Schichauweg (DEBE027) in the rural near-city background.

In addition, five measurement stations representing “traffic” conditions within Berlin, which are located next to major roads within the core area of the city, and assumed to be primarily influenced by traffic emissions, are used for the observation-based analysis (Sect. ).

NO2 concentrations used for this study were measured using chemiluminescence. With this method, NO2 is converted to NO with a molybdenum converter before being detected using chemiluminescence, as NO reacts with O3 to form NO2 and O2 while emitting light see e.g.. A limitation of this method is that other nitrogen-containing species (PAN, HNO3) are also converted to NO in this process. In a comparison study, found that only 73–82 % of the NO2 measured with this method is “real” NO2, at a rural background site in Switzerland. However, they state that reasonable results are obtained with this type of converter at urban background sites. compared NO2 concentrations in urban smog conditions in Santiago de Chile using chemiluminescence detection with a molybdenum converter and differential optical absorption spectroscopy and found large differences between measured concentrations during daytime. Further sources of uncertainty are introduced in the detection itself, for which NO reacts with O3, producing the luminescence signal to be detected. assess the uncertainty of NO2 measurements, and derive a simplified procedure in order to calculate the NO2 measurement uncertainty, which we apply in order to obtain a rough estimate of the uncertainty range of NO2. Accordingly, the uncertainty (u) of the observed NO2 concentrations x at time i is quantified as follows: u(xi)=urRV⋅(1-α)xi2+α⋅RV2.

Here, urRV is an estimate of the relative uncertainty around a reference value RV, and α is the fraction of uncertainty not proportional to the reference value. We use the coefficients corresponding to the mean uncertainties of the individual parameters, i.e. urRV=0.09, α=0.06 and the reference value RV = 200 µgm-3 .

In order to complement the analysis and to investigate potential influences of the modelled meteorology on modelled NO2 concentrations, we include a comparison of modelled meteorology with observations. This includes observations of 2 m temperature, and 10 m wind speed and direction, all provided by the German Weather Service and available online . In addition, mixing layer height derived from ceilometer measurements at Nansentraße during the BAERLIN2014 campaign are used for a qualitative comparison with the modelled mixing layer height seefor a discussion of this type of comparison. The data are generally available between 20 June and 27 August 2014, but include a number of gaps.

Modelled NO2 concentrations are evaluated with the aim of using the model set-up for policy-relevant analyses of urban NO2 concentrations and NO2 reduction measures with high temporal and spatial resolution, and in order to identify the main sources of the errors in modelled NO2 concentrations. For this, we use both operational and diagnostic evaluation metrics, which are explained in the following.

Operational evaluation metrics applied here are based on and . They include an analysis of the mean bias (MB) and normalized mean bias (NMB), the correlation coefficient (R), and the root mean square error (RMSE, as defined in the Supplement). The model error is compared with the model quality objective (MQO) and performance criteria calculated from NO2 observations and their uncertainty. The MQO is defined as follows: MQO=12RMSERMSU, with RMSU being the root mean square of the measurement uncertainty. Following and , a MQO lower than 0.5 indicates that the model results are on average within the range of the measurement uncertainty, and further efforts to improve model performance are not meaningful. A MQO between 0.5 and 1 indicates that the uncertainties of model and observations overlap, and that the model might still be a better predictor of the true value than the observations. A MQO greater than 1, on the other hand, indicates significant differences between the model and the observations.

The performance criteria for mean bias, normalized mean bias and correlation coefficient as defined in are listed in the Supplement. As the uncertainty of NO2 measurements is partly concentration-dependent, the MQO and the other performance criteria differ between station classes and seasons.

The operational evaluation and model quality objectives are intended to support an assessment of the extent to which a model can be used for policy-relevant analyses, but do not point to the underlying processes that might lead to a disagreement between model results and observations. Furthermore, the calculation of the NO2 measurement uncertainty underlying the calculation of the MQO and performance criteria is also based on a number of uncertain parameters.

We thus complement the analysis with a diagnostic evaluation, comparing the individual spectral components of the modelled and observed time series. This is done following and : we use a Kolmogorov–Zurbenko filter , a widely used filter in the analysis of air quality data based on calculating the iterative moving average of a time series, in order to decompose the modelled and observed time series into contributions from different timescales. The Kolmogorov–Zurbenko filter is a low pass filter, with the length of the moving average window and the number of iterations determining the spectral component to be filtered. Taking the difference between two filtered time series (band-pass filter) makes it possible to decompose the observed and measured time series into an intra-diurnal component (ID, < 0.5 days), a diurnal component (DU, 0.5–2.5 days), a synoptic component (SY, 2.5–21 days) and a long-term component (LT, > 21 days) with the property TS(x)=LT(x)+SY(x)+DU(x)+ID(x). Here, TS describes the full time series of species x. This is described in detail in and , and references therein. Further details are also given in the Supplement.

By assessing the error of each component individually it is then easier to relate the error to the model process(es) characteristic at the respective timescale. The error analysis of the different spectral components is done by “error apportionment” , breaking down the mean square error (MSE) into bias, variance (σ) error and minimum achievable mean square error (mMSE) as follows: MSE=(mod-obs)2+(σmod-rσobs)2+mMSE.

As described by , the minimum achievable mean square error is determined by the observed variability that is not reproduced by the model. While this approach helps in investigating the sources of model errors, it does not allow for clear identification or quantification of them as several processes take place on similar timescales, and because this filtering method does not allow for a complete separation of the different spectral components seefor a discussion of this issue.

In addition to this operational and diagnostic analysis of simulated NO2 concentrations, we include a brief evaluation of selected key meteorological parameters (temperature, wind speed and direction) as well as further chemical species (O3, NOx), the former because WRF-Chem is an online-coupled model, and the latter because NO2 is tightly linked to NO and O3.

As traffic emissions are the focus of this study, the analysis of the model results is complemented with an analysis based on observations of roadside and urban background NO2 concentrations and traffic counts. Like in many chemistry transport modelling studies, we assume a linear scaling of traffic emissions with traffic counts, which are used as a proxy for calculating time profiles of traffic emissions for each month, day of the week and hour of the day. While it has been shown that model results can be improved by taking into account country-specific driving patterns as well as by applying separate diurnal cycles for heavy and light duty vehicles , local traffic conditions (e.g. congestion) are currently not taken into account in the calculation of the diurnal cycles.

Using observations of traffic counts and roadside NOx concentrations in Berlin obtained at the same locations and times (data described in Sects.  and ), we assess how much of the observed variance in NOx concentrations can be explained with traffic counts in a linear model. In addition to a linear fit, other types of relationships (e.g. quadratic, exponential) are also explored. We neglect other influences on observed NOx concentrations such as other emission sources and large-scale and local meteorological conditions. In order to account for different conditions at different hours of the day, we fit the data separately for each hour of the day. The intention of this analysis is not to build a statistical model for roadside NOx concentrations, but rather to give insight into the type of relationship between roadside NOx concentrations and traffic counts, complementing the model simulations done in this study.

An in-depth evaluation of modelled meteorology obtained with a similar model set-up is presented in for the summer (JJA) of 2014. Here, model results for the whole year of 2014 are presented and discussed. Changes in the model set-up compared with the set-up presented in are the planetary boundary layer scheme (MYNN, instead of YSU, ) and re-initialization of the model meteorology every 2 days as described in Sect. . Tests showed that though the change in the planetary boundary layer scheme did not introduce considerable improvements, it did seem to lead to a slightly better match of model results with observations in the timing of the decrease in the boundary layer in the evening. Here an additional brief model evaluation is done in order to ensure that the modelled meteorology still reproduces observations reasonably well.

Modelled and observed 2 m temperature and 10 m wind speed are compared at five stations run by the German Weather Service, including Schönefeld, Tegel and Tempelhof in Berlin and Lindenberg and Potsdam outside of Berlin (Table ). Across the stations, annual mean temperature is simulated well, with mean biases smaller than -1 ∘C outside of Berlin and just above -1 ∘C within Berlin. Modelled and observed hourly temperatures correlate well with R=0.96 at all five stations. Small seasonal differences exist, with somewhat higher biases in winter (as large as -1.7 ∘C in Tegel) and somewhat lower biases in spring (e.g. -0.1 ∘C in Schönefeld). Annual mean wind speed is somewhat overestimated within Berlin (between 0.02 and 0.45 m s-1, or up to 13 %), with correlations of the hourly values between 0.74 and 0.78 within Berlin. In winter, wind speed is slightly underestimated at two out of the three stations within Berlin (-2 and -7 % at Tegel and Schönefeld, respectively), while it is overestimated somewhat more in spring and summer (up to 0.58 m s-1, or ca. 20 % in Tegel). In spring and summer, the main wind directions are captured relatively well by the model (see Figs. S6 and S7 in the Supplement). In autumn, wind from the east, the main wind direction, is modelled less frequently than observed, but wind from the south-east is modelled too frequently compared with observations. In winter, modelled wind comes from south and south-west too frequently compared with observations, at the expense of south-easterly wind directions, as depicted in Figs. S6 and S7. Compared with , an improvement in summer mean bias in wind speed is seen; with the JJA mean bias between 0.3 and 0.4 m s-1 smaller than that of the comparable simulation in at all Berlin stations, and JJA correlation coefficients improved by ca. 0.1. This can probably be attributed to the continuous re-initialization of modelled meteorology in this simulation.

In addition, modelled and ceilometer-derived mixing layer heights (MLHs) are compared (Fig. S8 in the Supplement). Even though a quantitative comparison between the modelled MLH and the MLH height derived from optical measurements is difficult to interpret see, a qualitative comparison of mean diurnal cycles gives insight into the timing of the deepening of the MLH. The comparison shows that the modelled increase in the summer MLH in the morning is too early, already starting at ca. 04:00 in the model. Though the precise time of the observed MLH increase cannot be determined from the available data, it takes place between 05:00 and 07:00 (Fig. S8 in the Supplement). An early modelled deepening of the mixing layer might lead to overly early and thus overly strong mixing of chemical species in the model.

Seasonally and station-class averaged performance metrics are listed in Table  for NO2, NOx and O3. NO2 and total NOx are biased low throughout the seasons and station classes, with the highest (absolute and relative) mean biases for urban background stations both annually and seasonally. The model bias is relatively low at rural and suburban background stations, with annual mean biases of only up to -2.8 µgm-3 (-19 %). Correlation coefficients of modelled with observed hourly concentrations are R=0.50 and R=0.55 in the rural and suburban backgrounds, respectively.

NO2 at urban background sites is biased by -7.8 µgm-3 (-29 %) on average, with a higher negative bias in spring (-10.2 µgm-3, -38 %) and summer (-9.3 µgm-3, -41 %) and smaller negative biases in autumn (-4.9 µgm-3, -17 %) and winter (-6.8 µgm-3, -22 %). Modelled hourly concentrations correlate reasonably well with observations in autumn, spring and winter (R between 0.51 and 0.55), but worse in summer (0.36).

Modelled hourly ozone concentrations correlate reasonably well with observations at all station classes throughout the whole year (R between 0.70 and 0.73), but with lower correlations for individual seasons. This shows that intra-seasonal differences are represented well by WRF-Chem, with slightly worse representations of inter-seasonal variations. Modelled ozone concentrations are biased high at most stations and in most seasons, with the exception of a low bias in summer in the urban background.

For NO2, the MQO (Eq. ) is greater than 0.5, but smaller than 1, both annually averaged and in all seasons at rural near-city background and suburban background stations. For urban background sites the MQO is larger than 1 both on annual average and in spring and summer, and just below 1 in autumn and winter, emphasizing that the model performs reasonably well in the rural and suburban background, but the disagreement between model results and observations is larger in the urban background. This suggests that processes or emissions typical for urban areas are an important source of model error.

In order to test the sensitivity of the results to the selected chemical mechanism, we compare modelled NO2 and total NOx concentrations for July with two different chemical mechanisms: RADM2 (the base configuration in this study) and MOZART. For all station classes in and around Berlin, the modelled NOx and NO2 concentrations only show very small mean differences of -0.04 to -0.4 µgm-3 (NOx) and -0.4 to -0.5 µgm-3 (NO2, RADM2 – MOZART). This suggests that the model bias in NO2 and total NOx concentrations of the base configuration is not strongly influenced by the choice of chemical mechanism, but rather results from other sources of error.

In order to further assess the model performance and identify the main sources of the model bias, a diagnostic evaluation is done, by spectrally decomposing the modelled and observed time series of NO2 and analysing the type of error of each component.

Averaging the decomposed time series over each station class, the modelled long-term (LT) and synoptic (SY) components as defined in Sect.  correlate well with the observations: the correlation coefficient for the LT component is 0.83, 0.81 and 0.72 for rural near-city, suburban and urban backgrounds, respectively, and 0.60, 0.63 and 0.65 for the SY component (Fig. ). This suggests that changes on timescales of ca. 2.5 days to a few weeks are captured relatively well by WRF-Chem, which includes for example the modelled synoptic (meteorological) situation and is consistent with the good model performance in simulating observed meteorology. The correlation coefficients for the diurnal (DU) component are smaller, with 0.45, 0.52 and 0.48 for rural near-city, suburban and urban backgrounds, respectively. This suggests that the model has more difficulties in capturing variations on timescales of a few hours to 2.5 days than on longer timescales. This might be related to the diurnal variations in modelled mixing, but also to the diurnal cycle of emissions. Particularly the latter is strongly influenced by traffic emissions in the urban area and might also point to deviations of the model-prescribed diurnal cycle in emissions from the real-world diurnal cycle.

With the procedure used for spectrally decomposing the NO2 time series, the LT component is the only systematically biased component, with the other components fluctuating around zero. Decomposing the model error shows that the bias of the LT component has the largest contribution to the error for urban background stations (ca. 30 %, Fig. ). NO2 has a short lifetime and is mainly influenced by local and regional sources. This means that the boundary conditions are not likely to be a strong source of error. The negative bias in the LT component is consistent with both problems in daytime vertical mixing and an underestimation of emissions. As discussed in Sect. , NO2 concentrations detected with chemiluminescence using a molybdenum converter might be biased high due to interferences with other nitrogen-containing species (e.g. PAN, HNO3) and could further contribute to discrepancies between modelled and observed NO2 concentrations.

The second largest error at urban background stations and the largest error at rural near-city and suburban background stations is the mMSE of the diurnal component. This means that part of the observed variability is not reproduced by the model and is consistent with the comparably lower correlation coefficients of the diurnal component compared with the synoptic and long-term components. relate this error to problems in comparing single point measurements with model grid cell values (incommensurability) and a disagreement in timing of modelled and observed concentrations, amongst others. The incommensurability can, in the case of NO2, come from NO2 observations being influenced by local sources that cannot be captured by WRF-Chem run at a horizontal resolution of 3 km × 3 km. The temporal variation of modelled NO2 concentrations, in the case of the diurnal component, can be influenced by the temporal profiles prescribed to the emission input data. Thus, the error is consistent with problems in the prescribed diurnal cycles of emissions including traffic emissions, but might also be related to a diurnally varying bias in emissions.

At rural near-city background stations, there is a relatively large contribution of the variance error of the diurnal component. This is probably caused by an overestimation of the standard deviation of observed diurnal components in autumn (Fig. S9 in the Supplement), particularly pronounced at the site Frohnau in the north or Berlin, slightly west of the main emission sources. This might be explained by the disagreement in modelled and observed wind direction in autumn, leading to higher than observed NO2 peaks in the model.

present a diagnostic model evaluation of the AQMEII phase 3 model simulations for the year 2010 and report the largest error of modelled NO2 in winter, both for the European and North American domains simulated in AQMEII. Our results show the opposite for urban background stations (Fig. S9 in the Supplement): the model error, and particularly the bias, is smallest in autumn and winter. While attribute the winter bias to a potential underestimation in residential combustion emissions, these seem to be captured comparably well by the TNO-MACC III inventory in the case of Berlin. The re-distribution of these emissions based on population density, as described in Sect. , may also have contributed to a better spatial representation in our study.

The results from the operational and diagnostic evaluation of modelled NO2 concentrations suggest that emissions within the urban area are a main source of model error, both contributing to the model bias and the lower correlation with observations. Traffic emissions have the largest contribution to urban NOx emissions. As traffic emissions have a distinct weekly and diurnal cycle, we additionally assess mean diurnal cycles of modelled and observed NO2 concentrations as well as the differences between weekdays and weekends. This also helps to further assess the contribution of problems in modelled mixing to the model error. In addition, we analyse the MQO and performance criteria separately for weekends (Saturday and Sunday) and weekdays (Monday through Friday). Public holidays that fall on a weekday are excluded from this analysis, as they were not treated separately from regular weekdays in the emission processing.

The comparison of mean modelled and observed NO2 diurnal cycles shows distinct differences between station classes and weekend and weekday diurnal cycles (Fig. ). The diurnal cycle of observed NO2 concentrations is modelled reasonably well for rural and suburban background stations. In particular, nighttime concentrations are simulated well for rural and suburban background stations, and mostly underestimated in the urban background. Other WRF-Chem modelling studies often report too little mixing at nighttime over urban areas leading to a strong overestimation of observed concentrations. In this study as in other modelling studies using WRF-Chem (Ravan Ahmadov, personal communication, 2017), a modification of the model code was applied in order to increase nighttime mixing. This, in combination with a more realistic vertical distribution of point source emissions (as described in Sect. ), seems to improve model performance for NO2 during nighttime. In addition, tests revealed that this change to the model code does not impact modelled daytime concentrations.

During weekdays, there is an underestimation of the observed morning peak in all seasons and at all station classes. Weekend diurnal cycles are modelled well at rural and suburban background stations. At urban background stations there is a larger disagreement between modelled and observed concentrations throughout the whole day on both weekends and weekdays. The underestimation of daytime urban background NO2 concentrations is particularly strong in summer and spring. This might be explained by mixing over urban areas during daytime that is too strong, caused for example by a turbulent diffusion coefficient that is too large during daytime over urban areas in the lowest model layer. Other modelling studies have reported similar problems, reducing the coefficient over urban areas e.g. of the CHIMERE model set-up used in. An onset of the deepening of the boundary layer that is too early (Sect. ) might further contribute to the disagreement in the modelled and observed morning peaks. Overall, this discussion shows that the representation of vertical mixing over urban areas might have to be improved to be physically more consistent in regional models, for example by better taking into account urban heat and momentum fluxes and treating the urban parameterization consistently with chemistry. Measurements of vertical profiles of NOx in cities, particularly in the planetary boundary layer, would be helpful in order to evaluate the models and improve the representation of surface NOx concentrations, as the NOx profile in the lowest model layer is not resolved at the model resolution used in this study.

The model underestimation of observed daytime NO2 concentrations at urban background stations is stronger on weekdays than on weekends, and is particularly noticeable during the morning hours. This is consistent with an overall underestimation of emission sources active in the morning hours on weekdays and potentially also a misrepresentation of the diurnal cycles of emissions in the model: traffic emissions are distributed in the model throughout the day using a linear scaling with traffic counts (Sect. ), which might fall short of accounting for relatively higher emissions during situations with high traffic and associated congestion. This issue is further assessed in Sect. .

Generally, throughout all seasons, the NO2 MQO is not met on weekdays for urban background stations, but is smaller than 1 on weekends (Fig. ). The patterns of the model–observation disagreement, and particularly the weekend–weekday differences, are consistent with traffic emissions as a main source of the bias, with a particularly large contribution to observed urban background concentrations.

The results from the operational and diagnostic evaluation of modelled NO2 concentrations suggest that traffic emissions are a main source of model error in the urban background: the bias and the mMSE of the diurnal component have the largest contribution to the model error in the urban background throughout all seasons, which is consistent with both an underestimation of the magnitude of traffic emissions, and a problem with their temporal distribution. This is further supported by the smaller (absolute and relative) daytime bias of modelled NO2 concentrations on weekends, where there is less traffic. In the following, we derive a correction factor based on this model bias, which represents the degree to which traffic emissions are underestimated in Berlin, but also takes into account that other sources of model error are likely to also contribute to this bias.

Besides biases in traffic emissions, problems in modelled mixing, which is particularly relevant in summer and spring when the mixed layer is deeper than in other seasons, might contribute to the model bias. Other contributions to the NO2 bias might come from deviations of modelled from observed wind speed in certain periods, and a potential overestimation of NO2 in the observations by detection of other nitrogen-containing compounds as discussed above. These sources of error are likely to impact the model results equally on both weekends and weekdays, whereas an underestimation of traffic emissions will have the largest impact on the results on weekdays. For the quantification of the underestimation of traffic emissions we assume that the weekend bias is entirely caused by non-traffic-emission-related sources of error and thus use the difference between weekday and weekend bias as an estimate for the traffic-related bias. We use the weekday–weekend difference of the relative biases (Fig. ), thus assuming that the model error due to other sources than traffic emissions roughly scales with the magnitude of modelled concentrations. These are both conservative assumptions, as the correction factor would be much larger if the whole weekday bias was regarded as caused by traffic emissions, and it would also be larger if the absolute weekday–weekend difference was used.

In order to estimate the correction factor for traffic NOx emissions, we combine the weekday increment of the model bias as defined above with the average fraction of NOx emissions from traffic to total NOx emissions in Berlin. The nighttime model bias on weekends and weekdays at urban background stations is of similar magnitude on weekends and weekdays (Fig. ). A t-test shows that the differences between weekday and weekend bias are not statistically significant at a 95 % confidence interval after ca. 17:00 UTC and before ca. 05:00 UTC (depending on the season). Furthermore, traffic emissions used in the model contribute only little to the total NOx emissions before 06:00 UTC. This suggests that an underestimation of traffic emissions is only likely to have a significant contribution to the bias in modelled NO2 concentrations between ca. 06:00 and 17:00 UTC. Within the core area of the city where traffic is high (all areas within the “S-Bahn ring”/main core of the city), the average contribution of traffic NOx to total NOx between 06:00 and 17:00 UTC is between ca. 30 and 55 %, depending on the month and hour of the day. Seasonal average values over the indicated time period are used for the calculation of the correction factor, with 37 % in winter, 47 % in summer and 42 % in autumn and spring.

With the above assumptions, we quantify the underestimation of traffic NOx emissions in the core urban area on weekdays between 06:00 and 17:00 UTC as follows, calculating a correction factor fNOx: fNOx=11+NMB⋅1st.

With the (negative) NMB = mod-obsobs, and st denoting the traffic share of NOx emissions. Averaged over all urban background stations, and all seasons, as well as the time period between 06:00 and 17:00 this results in a correction factor of ca. 3. When averaged over all hours of the day, this factor corresponds to an overall underestimation of NOx traffic emissions in the urban centre by a factor of ca. 2, and an underestimation of all-source NOx emissions in the urban centre by a factor of ca. 1.5.

In order to gain more insight into the underestimation of the NOx emissions, we calculate a separate correction factor for each hour and season based on hourly mean seasonal biases and traffic NOx emission shares (Fig. S10 in the Supplement). The seasonal correction factors show a small increase between 06:00 and 08:00 with a subsequent decrease, and then remain relatively constant from 11:00 to 17:00. The diurnal variations of the factors for the different seasons are qualitatively similar, and the factors vary in magnitude within a range of ca. 1 between the seasons, with the factors being larger in winter than in summer. The diurnal cycle of the correction factor could be due to a diurnally varying importance of other sources of the modelled NO2 bias than the traffic emissions, such as mixing, but might also be due to a disagreement in the prescribed diurnal cycle of traffic emissions with the real-world diurnal cycle of traffic emissions. The seasonal differences can at least partly be explained with the seasonally varying relevance of other sources of model error, such as mixing, which has a bigger impact in summer and thus also leads to a bigger bias on the weekends, reducing the weekday increment. The seasonal differences might also be influenced by the temperature dependence of NOx emissions in newer diesel cars , leading to higher NOx emissions at colder temperatures, which are not captured by the model.

Overall, the assumptions in these calculations are rather conservative: assuming the weekend bias is not caused by an underestimation of traffic emissions at all is likely to underestimate the effect of any traffic bias. As mentioned above, using the absolute weekday increment of the bias would also lead to higher correction factors. A further discussion of the model bias and correction factor looking into potential reasons contributing to an underestimation of traffic NOx emissions is presented in Sect. .

The weekday correction factor was applied to NOx traffic emissions for the core urban area of Berlin (within the “S-Bahn Ring”) and tested in two sensitivity simulations for January and July 2014. The results (Table  and Fig. ) show that the bias of modelled NO2 concentrations at urban background stations decreases on average by 2.6 µgm-3 (NMB decreases from -24 to -16 %) in January, and by 2.0 µgm-3 (from -43 to -34 %) in July when applying the correction factors for NOx emissions from traffic. The decrease is larger when only considering weekdays, with a mean bias lower by 3.4 µgm-3 (from -26 to -16 %) in January and by 2.7 µgm-3 (from -46 to -34 %) in July. NO2 concentrations on weekends are still represented reasonably well by the model in January (Fig. ). The weekend bias is only changed (decreased) by lower than 0.4 µgm-3 in both cases. Only a minor change would be expected, since emissions on the weekend are not changed in the sensitivity simulations, compared to the base simulation. In January, the correlation of modelled with observed NO2 concentrations in the urban background is improved by between 0.03 and 0.06 for urban background stations in the sensitivity simulation, but this is not the case in July (Table ). The lack of improvement in the July correlation coefficient could be related to nighttime concentrations in July that seem to be very sensitive to the increase in emissions during daytime (Fig. , lower panel). Despite an improved representation of nighttime concentrations compared to a previous study , this sensitivity suggests the need for further attention to mixing processes in urban areas in high-resolution chemistry transport models.

Bigger improvements are seen when comparing total NOx: the mean bias for urban background stations is reduced from -16.4 to -10.3 µgm-3 (NMB decreased from -35 to -22 %) in January and from -11.1 to -8.1 µgm-3 (from -45 to -33 %) in July. Only considering weekday concentrations, these are improved by 8.1 and 3.9 µgm-3 (from -37 to -12 and -48 to -33 %) in January and July, respectively. The differences in NO2 and NOx improvements suggest that the impact of the primary NO2 fraction in emitted NOx on modelled NO2 and NOx concentrations, as well as the influence of chemical processes such as NO titration and other relevant physical and chemical processes, might need to be assessed in greater detail.

While on average the normalized mean bias in a modelled rural and suburban background is only reduced by 1–2 % in both January and July, the simulation of NO2 and NOx concentrations downwind of the city centre is improved considerably in the sensitivity simulation. To analyse the change in modelled downwind concentrations, the results are broadly divided based on four main wind directions (N, W, S, E). For each wind direction bin, the results of two stations outside the core urban area are analysed, with Frohnau and Buch in the north, Johanna und Willi Brauer Platz and Mueggelseedamm in the east, Schichauweg and Blankenfelde-Mahlow in the south and Gross Glienicke and Grunewald in the west. Only situations with wind speeds above 2 m s-1 are considered. The statistics are calculated for stations where at least 72 hourly model–observation pairs exist in the respective wind direction bin, leaving four stations in January and six stations in July for the analysis, with between 91 and 228 model–observation pairs. With some differences between the stations, the bias of weekday downwind NO2 concentrations was reduced by between ca. 1.5 and 2.9 µgm-3 January and ca. 0.4 and 1.5 µgm-3 in July. Thus, downwind NO2 concentrations in the sensitivity simulation are only biased by ca. -4 % (January) and -14 % (July) on average (as compared to -12 and -22 % in the base run). This shows that the increase in traffic emissions also helps improve modelled downwind concentrations.

Overall, in both January and July, the bias in modelled urban background NO2 and NOx is improved but still negative. Modelled downwind NO2 concentrations are improved considerably, but with low negative biases remaining also in this case. The improvements are consistent with an underestimation of traffic emissions being a main source of error. However, the results also suggest that on the one side traffic emissions might still be too low, which is consistent with the correction factor being a rather conservative estimate. On the other side, a still negative bias is also consistent with other sources of error contributing considerably to the model–observation differences as discussed previously. A relatively large bias in July remains, consistent with the mixing being an additional main source of error, particularly in summer.

Modelled O3 concentrations are not very sensitive to the changes in NOx concentrations. On average, modelled O3 is reduced at urban background stations in January by 1.5 µgm-3 (NMB decreases from 29 to 22 %). In July, the increased NOx leads to a reduction in the already negatively biased O3 from the model, with the mean bias changing from -7.3 to -8.6 µgm-3 (-11 to -13 %). Similarly, simulated O3 concentrations downwind of the city (in analogue to the downwind NO2 concentrations described above) are biased negatively in both the base run and sensitivity study in July. The bias of downwind concentrations changes from -5.4 µgm-3 (-7 %) in the base run to -6.8 µgm-3 (-9 %) in the sensitivity run. The negative bias in both NOx and O3 in the base run is consistent with the model simulating insufficient NOx emissions in a NOx-limited ozone production regime. The reduction of O3 concentrations in response to increased NOx emissions is however consistent with the model actually being in a NOx-saturated (VOC-limited) ozone production regime. The representation of VOC emissions in the model could play a role in explaining this discrepancy, as for example biogenic VOC emissions in the Berlin–Brandenburg urban area are underestimated when using WRF-Chem and MEGAN . A comprehensive analysis of the simulated ozone production regime is beyond the scope of this work.

The model bias and the calculated correction factors show a diurnal cycle, with a larger model bias/correction factor in the morning hours. As explained in Sect.  and , one reason for this might be differences between prescribed and real-world diurnal cycles of the emissions. The diurnal cycle of traffic emissions in the model is calculated based on traffic counts for Berlin, assuming a linear scaling of traffic emissions with traffic counts, as done in many modelling studies.

Here, we use 3 years of hourly observations of roadside NOx concentrations and traffic counts measured at the same stations in order to get insights into the relationship between NOx concentrations and traffic counts. A linear regression model does not explain the variance of observed NOx concentrations at nighttime, as indicated by the R2 close to 0 in Fig. . However, during daytime, traffic counts alone explain up to ca. 40 % of observed NOx variance, particularly during the traffic rush hours. The explained variance is smaller during the afternoon peak. In comparison to a linear relationship, a quadratic relationship (NOx ∝ (traffic_count)2) does not explain more of the observed variance (not shown). An exponential relationship (NOx ∝ exp(traffic_count)), however, does explain a considerably larger share of the observed variance during daytime and particularly during the traffic rush hours, as depicted in Fig.  (up to ca. 60 % depending on the station).

This simple comparison suggests that roadside NOx concentrations, and thus most likely also road transport NOx emissions, scale more than linearly with traffic counts at times when the traffic intensity is high and underline that the assumption of a linear scaling of traffic emissions with traffic counts does not reflect the diurnal variation of traffic emissions sufficiently. More highly congested roads are typical in the morning, and emission factors (e.g. from HBEFA) are higher in congested situations compared to free-flowing traffic. Differences in congestion could contribute to explaining the non-linear scaling of NOx concentrations with traffic intensity. While the impact might not be large when simulating air quality with coarser models, it might play a more important role in high-resolution air quality modelling, and the temporal distribution of emissions could potentially be improved when taking these differences into account.

Based on a comparison of modelled and observed NO2 concentrations, we estimate that traffic emissions in the urban core of Berlin are underestimated by a factor of ca. 3 on weekdays between ca. 06:00 and 17:00 UTC. This corresponds to an overall underestimation of NOx traffic emissions (all-day average) in the urban centre by a factor of ca. 2, and an underestimation of total NOx emissions (all-day average) in the urban centre by a factor of ca. 1.5. Reasons for the underestimation of emissions used in this study can include limitations in the applicability of the emission inventory used here for high-resolution urban air quality modelling, problems in the temporal distribution of emissions, but also a general underestimation of traffic NOx emissions in the inventories. These three points are discussed further in the following.

First, while a reasonably good model performance can be achieved using the downscaled version of the TNO-MACC III inventory outside of the urban areas, the deviations of modelled from observed NO2 in the urban background might point to limitations in the applicability of these types of emission inventories for high-resolution modelling of NO2 in urban areas. The horizontal resolution of the original TNO-MACC III emission data is ca. 7 km × 7 km and national totals are disaggregated on the grid based on traffic intensities. Spatial differences in congestion, with emissions greatly varying between the different driving conditions and with car speed e.g., are probably not well resolved. A comparison of the downscaled version of the TNO-MACC III inventory for Berlin with a local inventory has, however, not revealed major differences in road transport emissions (see Sect. ), suggesting that a static highly resolved local inventory based on detailed local information is not likely to improve the model results by much.

Second, in addition to spatially unresolved differences in driving conditions and related emission factors locally increasing the underestimation of emissions, the diurnal cycle of the bias in all seasons suggest that the diurnal cycle of traffic emissions also does not sufficiently account for temporal differences in driving conditions. This is consistent with the observation-based analysis, suggesting that observed NOx concentrations do not scale linearly with traffic counts. While these assumptions might be valid for coarser model resolutions, they may need to be revisited when going to higher resolutions with a focus on urban areas. However, modelled NO2 concentrations are broadly underestimated throughout the day, which means that deviations of the model diurnal cycle from the real-world diurnal cycle alone cannot explain the underestimation of modelled NO2 and NOx concentrations.

Third, traffic NOx emissions may be underestimated generally by emission inventories. The correction factor calculated here is in line with the results from other studies quantifying traffic emission underestimations in Europe, reporting traffic NOx underestimations of around 80 % , a factor of 1.5–2 and up to a factor of 4 . A potential reason for the underestimation in NOx emissions from traffic can be discrepancies between real-world emission factors and those used in emission inventories. Even though HBEFA emission factors, which are often used for calculating emissions, are based on real-world driving conditions, the latest update of the handbook reports higher emission factors than previously assumed for Euro 6 and Euro 4 diesel cars , e.g. an increase by ca. 50 % in case of Euro 6 vehicles Fig. 14 in. In addition, the update assesses the temperature dependence of emission factors and concludes that it may lead to increases in NOx emissions of more than 30 %, compared with standard test conditions. NOx emissions from diesel cars increase with decreasing temperatures . This may also contribute to the larger correction factor calculated for the winter months. Finally, while some amount of congestion is included/assumed in the emission inventories, this might be an aspect that is underestimated in terms of severity and extent.

The first and second points of this discussion suggest that improvements might be achieved by combining high-resolution chemical transport models with more detailed approaches of calculating emissions. Coupling with a traffic model, for example, might allow for not only being able to take local differences in traffic conditions into account, but also prescribe a more realistic diurnal cycle of traffic emissions. Dispersion modelling and street canyon modelling e.g. OSPM, often already take a more detailed calculation of traffic emissions into account, and different emission modelling approaches exist e.g. traffic models such as MATSim,. The benefit of high-resolution chemistry transport modelling, e.g. their ability to assess the impact of different emission sources on air quality on larger scales and downwind of the main emission sources, could be further exploited if coupled with existing, more detailed approaches in calculating traffic emissions or general improvements in the accuracy and resolution of emission inventories.

The consistent findings that inventories of European traffic emissions may be underestimated, coming from studies using very different methodologies, suggest that further research is necessary in order to understand real-world traffic emissions and to represent them in the inventories accordingly. Alternative measurement approaches could help verify the assumptions underlying the calculation of emissions, and help identify potential systematic problems.