The spatial distribution of the 1492 Airbase stations and the respective cluster number of their classification obtained after the first CA are shown in Fig. 3. Evidently, the five clusters do not simply represent different regions in Europe, although the members of cluster 1 (CL1) and cluster 2 (CL2) are concentrated in the Benelux and Ruhr regions and in the Po Valley region, respectively. CL1 extends from Slovenia to Great Britain through the Netherlands but also includes stations in France, Italy, Spain, and Eastern Europe. Besides the northern Italian stations CL2 also contains a few stations in the Alpine region, in the northwestern Balkans and in Spain. The third cluster (CL3) is much larger in its spatial extension and contains stations from almost all over Europe, including Scandinavia. The fourth cluster (CL4) spreads all over Europe with increased density along the Mediterranean coast and in the mountainous areas to the north and east of the Alps, the Bohemian Massif, and the Carpathian Mountains. Finally, the smallest cluster (CL5) largely overlaps with the mountainous regions of the Alps, the Pyrenees, Spain, and the Carpathians.

Table 2 presents a qualitative interpretation of the five clusters and shows the distribution of station altitudes for each cluster. The cluster descriptions were derived based on the geographical and altitude distribution together with a contingency analysis of the station type and station type of area attributes in the Airbase metadata. A contingency table with Airbase station attributes is provided in Table 1a, b. According to the Airbase classification (see Sect. 1) stations are marked as either “urban”, “suburban”, or “rural” depending on the area type and as “traffic”, “industrial”, or “background” according to the station type. Each row in Table 1 corresponds to one of the Airbase clusters and shows the number of stations related to each of nine Airbase classification pairs. Most of the stations that we retained in our data filtering procedure (Sect. 2) are background stations, which could indicate that there are no local pollution sources in their vicinity. Measured concentrations should ideally be representative for a larger area (and hence suitable for the evaluation of numerical models), except when local effects from orography, land use, or land–sea contrast confound the analysis. There is a relatively even split between rural, suburban, and urban background stations. Industrial and traffic stations constitute about 10–15 % each and are concentrated in the suburban and urban environments, respectively.

Table 3 presents the same information as Table 2 but for the second CA. There is some overlap between the cluster definitions of the first and second CA. The first cluster of the second CA corresponds to the second cluster of the first CA, with the exception that it does not contain stations from the Alpine region (Fig. 4). The second cluster is much larger and spreads over the Benelux and Ruhr regions in the center of Europe, partly covering France, Switzerland, and Eastern Europe and thus partially overlapping with the first cluster from the first CA.

The third cluster extends all over Europe and has several stations in Scandinavia. This cluster contains the largest number of stations. The fourth cluster includes high-mountain stations from the Alpine region and the Pyrenees, from the mountainous areas to the north and east of the Alps, the Bohemian Massif, and the eastern part of the Carpathian Mountains. Moreover, it includes low-altitude stations from Spain, France, Great Britain, Scandinavia, and the Mediterranean coast. Geographically it is a mix of stations from nearly all clusters of the first CA. The contingency tables with Airbase metadata (Table 1) and the geographical representation lead to the conclusion that the clusters from different CAs have some common features. For example, the first Po Valley cluster of the second CA, which is mostly concentrated in the north of Italy, is the same as the second cluster of the first CA. The second cluster of the second CA has the majority of stations, which were assigned to the first cluster in the first CA, and moreover also captures stations of the second and third clusters of the first CA. However, it appears as more elevated agglomeration. The third cluster shares 326 stations out of more than 500 with the third cluster of the first CA, resembling it also geographically and in altitude. It is the largest cluster in both CAs. The fourth cluster of the second CA contains both high- and low-altitude stations. It includes the entire fifth cluster and has some stations from the fourth and third clusters of the first CA. Therefore, on average the fourth cluster of the second CA with the mean altitude of 433 m is semi-elevated.

Figure 5 presents a comparison of the 5–25–50–75–95th percentiles distributions from the 3-hourly Airbase and MACC initial data sets for the period 2007–2010 (i.e., length of each data set = 1492 stations ⋅ 4 years ⋅ 365 days ⋅ 8 values per day). The mean and median volume mixing ratios averaged over the entire set of 1492 stations are 25 and 24 nmol mol-1 for Airbase and 34 and 33 nmol mol-1 for MACC, respectively. Thus the 50th percentile and the mean of the model data both show a positive bias of 9 nmol mol-1.

A more detailed pattern emerges when analyzing the station mean values using box-and-whisker plots separately for the five individual clusters of the first CA (Fig. 6). With the exceptions of CL2 and CL3, which show quite similar distributions, the distributions of the observed (Airbase) values are rather distinct for each cluster and increase from CL1 to CL5. In comparison, the MACC distributions are generally broader and exhibit a high bias of 5–12 nmol mol-1, except for CL5. MACC distributions also show increasing values from CL3 to CL5 but only little difference among CL1 to 3. Obviously, the model does not capture the differences among the somewhat more polluted sites very well. This is consistent with the distributions of simulated CO and NOx concentrations (there are too few observations available to make a meaningful comparison) shown in Fig. 7. While the MACC model results show a clear separation between clusters 1–3 on the one hand and clusters 4–5 on the other hand, they do not distinguish among CL1, 2, and 3. These results are not surprising given that ozone concentrations in CL1–CL3 are more likely influenced by local, small-scale pollution sources, which the model cannot simulate correctly with its grid point distance of approximately 80 km. It is, however, reassuring to see that the simulated mean values of ozone precursors are larger in those clusters that have been labeled more polluted according to the Airbase characterization tags.

Figure 8 shows the distributions of mean ozone mixing ratios in the clusters of the second CA. The MACC distributions of mean values are again broader than the observations and the model overestimates all clusters with the highest bias of 14 nmol mol-1 for CL1 and the lowest 4 nmol mol-1 for CL4. The distribution of observed ozone means of CL4 is broader than it is in the first CA. This can be explained by the mix of stations of various altitudes. For other clusters, the distributions are relatively narrow but still nearly twice as broad as those of the first CA, except for CL1 (Fig. 6). MACC model distributions of CO and NOx concentrations for the clusters of the second CA (not shown) are reflecting higher pollution levels in the first two clusters and moderate pollution conditions for CL3. CL4 is relatively clean and shows the lowest CO and NOx concentrations.

The comparison of ozone concentrations among the clusters and between the observations and the simulations was based upon quantiles characterizing the cumulative probability distribution. Another way is to estimate probability density functions or normalized frequency distributions computed by binning all available 3-hourly observations from both the Airbase and MACC data. Those frequency distributions are presented in Fig. 9 for each cluster of the first CA and distinguished between summer and winter.

In the Airbase wintertime data the three clusters with more urban characteristics (CL1, CL2, and CL3) contain a significant number of values with very low concentrations, which are primarily caused by ozone titration in the presence of large amounts of NOx from traffic and industries. Peak frequencies are decreasing from CL1 to CL4, though the last shows only a few incidents of “zero” ozone. For clusters CL1, CL3 and CL4 the MACC model is able to capture some of this titration, but not for CL2 (Po Valley). No ozone titration occurs in CL5, either in the observational data or in the model results.

MACC exhibits quite a good fit to CL4 and CL5 winter ozone concentrations and in general shows a greater similarity with the frequency distributions of the observations in winter compared to summer. During summer the measured ozone data are almost normally distributed (except for CL1), which is not seen for the MACC summer values. The model summer curves exhibit a high bias and contain two maxima for CL2 and CL4 (Fig. 9).

In order to quantitatively evaluate the model's ability to reproduce the observed frequency distributions in each cluster, we calculated the EMD (described in Sect. 3) (Table 4). As expected from Fig. 9, the largest EMD is found for CL1 and CL2 in summer, while the model shows greater skill in capturing the frequency distributions of CL4 and CL5 and to a lesser extent also CL3 (Table 4). This is again consistent with the previous characterizations of CL3 as a background, moderately polluted station and of CL4 and CL5 as (mostly rural) background stations (Table 2). From CL1 to CL5 the EMD values for summer are decreasing; thus model prediction of observations improves in that order. We note that in the same order the level of pollution of clusters is decreasing while mean ozone concentrations are increasing. The winter EMD values are smaller than summer ones and show no dependence from CL1 to CL5. In general the model describes winter ozone relatively well with the one exception of CL2, where MACC fails to predict the very low concentrations (Table 4, Fig. 9).

Frequency distributions of the 3-hourly surface ozone values of Airbase and MACC for each cluster of the second CA are presented in Fig. 10. As anticipated from the previous discussion, clusters with urban signatures CL1 and CL2 are expected to show a peak at low ozone concentrations, related to their higher pollution level. Indeed, the peaks of Airbase probabilities of zero ozone concentrations are pronounced for both clusters in comparison to the moderately polluted CL3, for example, where zero ozone occurs only half as often and the ozone maximum appears in the range 25–30 nmol mol-1. The shape of the relatively clean CL4 curve resembles a Gaussian distribution with maximum probability at ≈ 35 nmol mol-1. EMD calculated for comparison of observations to modeled frequency distributions (Table 5) show the strongest disagreement for CL1, followed by CL2 and CL3 with quite similar values, and finally is the smallest EMD value for CL4.

The mean seasonal amplitudes are defined as the difference between the highest and lowest 4-year average monthly mean ozone concentrations (Fig. 11). The amplitudes estimated from the Airbase stations within the clusters of the first CA are generally between 18 and 24 nmol mol-1 (25th to 75th percentiles), with the exception of CL2 (Po Valley stations), where seasonal amplitudes range from about 26 to 37 nmol mol-1 (25th to 75th percentiles). The MACC model data show a similar pattern among the clusters. However, the seasonal amplitude is often overestimated by 5–10 nmol mol-1 due to the overestimation of summertime ozone. The seasonal amplitude of CL2 stations is captured relatively well, although the mean values in CL2 exhibited the second highest bias (12 nmol mol-1, Fig. 6).

The seasonal cycles of the first CA cluster centroids are displayed in Fig. 12. In the observations CL1 and CL3 run almost parallel and show a broad maximum extending from April to July for CL1 and a slight maximum in April for CL3. More prominent spring maxima are evident in CL4 and CL5, but CL5 also exhibits a second small peak in July. The only cluster with a single pronounced maximum in summer (July) is CL2. The spring maximum is typical for seasonal cycles of western European sites and considered a northern hemispheric phenomenon (Monks, 2000). Indeed, a substantial subset of stations in CL3, CL4, and CL5 are situated along the western edge of the continent (see map, Fig. 3). The decline of ozone mixing ratios from spring until autumn in CL3 and CL4 suggests that summer photochemical ozone formation plays only a minor role at these sites. In contrast, the double peak of CL5 suggests a superposition of the “natural” spring maximum with the “anthropogenic” summertime photochemical ozone production. The stations in CL5 are more elevated and therefore can be influenced by ozone from the stratosphere–troposphere exchange, which is considered as a possible reason for the ozone spring maximum on high mountains (Elbern et al., 1997; Harris et al., 1998; Stohl et al., 2000; Monks, 2000; Zanis et al, 2003).

In contrast to the seasonal cycles of the Airbase cluster centroids, the cluster mean seasonal cycles of the MACC data all show a summer maximum of similar shape with peak in June. This suggests that either the summertime chemical ozone formation is exaggerated in the model or the largely transport-driven springtime maximum is underestimated. A potential influence from inconsistencies in the data assimilation (see Inness et al., 2013) is unlikely, but it cannot be excluded.

The seasonal cycles in Fig. 12 indicate that the MACC model performs better during winter than during the summer. This is particularly evident for CL3, 4, and 5, whereas a significant bias persists throughout the year for CL1 and CL2. In the Validation Report of the MACC reanalysis (Benedictow et al., 2013), a comparison with GAW (Global Atmosphere Watch program, http://www.wmo.int/pages/prog/arep/gaw/gaw_home_en.html) surface ozone data shows that in most regions of the world ozone mixing ratios are generally underestimated during winter and overestimated during summertime. Inness et al. (2013) present an evaluation with EMEP (European Monitoring and Evaluation Program, http://www.emep.int/) data which is also consistent with this analysis. EMEP stations are almost exclusively characterized as background sites and are partly contained in the Airbase database as well.

Diurnal amplitudes were calculated from averaged diurnal cycles of each station as an absolute difference between daily maximum and minimum and then gathered into distributions for each cluster. Box-and-whisker plots of ozone average diurnal amplitudes (Fig. 13) show a clear signature that appears to be correlated with the ozone precursor concentrations as simulated by the MACC model (see Fig. 7). The largest diurnal amplitudes (mean 27 nmol mol-1) are obtained for CL2 (Po Valley), followed by CL1 (mean 18 nmol mol-1), CL3 (mean 18 nmol mol-1), and CL4 (mean 17 nmol mol-1). CL5 (relatively clean elevated) stations exhibit the lowest diurnal amplitude (mean 9 nmol mol-1). This is consistent with earlier findings by Flemming et al. (2005) and Chevalier et al. (2007), who show the smallest diurnal amplitudes for clean sites. The average diurnal amplitudes of the MACC model are generally consistent with the measurement data, except that the distributions are somewhat broader, and there is no big difference between the diurnal amplitudes in CL2 compared to CL1 and CL3. We note that the MACC model does not prescribe a diurnal cycle for ozone precursor emissions.

The diurnal cycles of the Airbase cluster centroids show rather similar patterns with peak values between 12:00 and 15:00 LT for all clusters (Fig. 14). CL2 shows the most pronounced maximum, while CL5 exhibits the flattest curve. Ignoring the overall bias the model diurnal cycles are similar to the observations except that ozone mixing ratios show a lesser decline from 00:00 to 06:00 in all clusters except for CL5. This could indicate underestimation of ozone dry deposition, possibly in conjunction with errors in the calculation of mixing in the nocturnal boundary layer. Underestimation of the diurnal amplitude in CL2 (Fig. 13) is largely due to the model failure of capturing low ozone concentrations around 06:00 (Fig. 14).

Weekly amplitudes are shown in Fig. 15. These were calculated as the absolute difference between maximum and minimum ozone mixing ratios of averaged weekly cycles for each station and then grouped into clusters accordingly. Weekly amplitudes were not used as initial parameters in the CA, but interestingly the classification of Airbase data shows a clear tendency of the weekly amplitudes decreasing from CL1 to CL5, even though there is considerable overlap between the various box-and-whisker plots. The weekly cycles of all cluster centroids show growth from Friday to Sunday, but no significant change during the week (not shown). This confirms our characterization of the clusters from more to less polluted, meaning that the less polluted sites are less influenced by local precursor emissions with distinct weekday cycles, notably traffic emissions (Beirle et al., 2003). As for the MACC model, the boundary conditions of its chemical equation system do not contain weekly variations of ozone precursor emissions; therefore simulated ozone has no significant weekly cycle.

Schipa et al. (2009) and Pollack et al. (2012) concluded that for polluted areas the higher ozone values during the weekend result from the fact that reduced NO emissions and relatively small changes in volatile organic compound (VOC) emissions facilitate ozone production due to an increased VOC / NOx ratio. The median of weekly amplitudes in urban CL1 is 4 nmol mol-1, which is consistent with Murphy et al. (2007). The MACC model results exhibit much smaller weekly amplitudes (generally less than 1 nmol mol-1) with no apparent difference among clusters. It would be interesting to see how much of the weekly cycle can be produced by a global model if weekly variations of ozone precursor emissions were included, but this is beyond the scope of this study.

The large seasonal and diurnal amplitudes in the Airbase data of CL2 are consistent with the relatively large emissions and active photochemistry in the Po Valley region (Bigi et al., 2012). While ozone precursor concentrations at stations in CL1 may be as large as those in CL2 (based on emission inventories and the MACC simulation results for CO and NOx; see Fig. 7), the mean ozone concentrations at these stations are lower. As can be seen from the frequency distributions in Fig. 9, there are a lot more incidents with very low ozone concentrations at the stations in CL1, and these occur both in winter and in summer. In the northern and central parts of Europe, where the majority of CL1 stations are located, the photochemistry is slow especially during winter, so that not much NO2 is converted back to NO and ozone via photolysis. CL2 also exhibits ozone titration, but in summer to a lesser extent than for CL1 (Fig. 9). For CL2 ozone destruction by NO and dry deposition still occur during nighttime but the prevalence of the daily ozone production over the ozone titration is more obvious here than for CL1. Indeed, the seasonal and diurnal cycles of CL2 are more pronounced than for CL1 (Figs. 12 and 14) and are indicative of the intensive photochemistry in the Po Valley region. This may be explained by the basin type of the Po Valley region and by its partly subtropical climate with plenty of available UV light, which is favorable for summer diurnal photochemical ozone production.

The mean seasonal amplitudes for clusters of the second CA are presented in normalized units in Fig. 16. MACC data were normalized in the same way as the Airbase data and then grouped according to the clustering results. We notice narrowness of seasonal amplitudes distributions and the decrease of their average in order CL1 → CL2 → CL3 → CL4. MACC seasonal amplitudes follow the same dependence, but in a more “smoothed” way, and they have broader distributions. The means of modeled amplitudes slightly overestimate average observed amplitudes for CL3 and CL4 are nearly equal for CL2 and underestimate CL1.

The seasonal cycles in normalized values of the cluster centroids from the second CA are depicted in Fig. 17. In contrast to the results from the first CA, the seasonal cycles of centroids show gradual change from the smoothest cycle of CL4 (“background rural”) with only April maximum to the most prominent cycle of CL1 (“background urban”) with strong July maximum. CL2 presents an intermediate cycle with a broad maximum, and CL3, although it has a more pronounced amplitude than CL4, still preserves the same features with a dominant spring peak. While the annual amplitudes are generally well described, the model cannot distinguish different seasonal patterns, like spring maximum or July peak, but always presents broad symmetrical bell-shaped summer maxima. The model underestimates normalized seasonal cycles in the beginning of the calendar year (except for CL1) and springtime as well as overestimates in autumn for CL1 and 2 and also in summer for CL3 and 4.

With respect to seasonality the best match between model and observations is found in CL3 and CL4. Some underestimation in spring and winter is evident for CL3; though in summertime there is a good fit of diurnal cycles in daytime, the observations show more ozone titration during the night, which is not captured by the model. The least well-predicted centroid of CL1 has large differences between model and observations. Box-and-whisker plots of average diurnal ozone amplitudes expressed in normalized values (Fig. 18) are continuously decreasing in their mean from CL1 to CL4, likewise for the distributions of seasonal amplitudes (Fig. 16). For all clusters, modeled ozone diurnal amplitudes distributions are broader and underestimate the observed amplitudes.

In general the model performs better for the description of diurnal cycles rather than seasonal. The diurnal cycles (Fig. 19) show similar dependence on cluster number as seasonal cycles: the smoothest for CL4 and most pronounced for CL1. As expected from the first CA, all clusters exhibit diurnal minima at 06:00 and maxima between midday and 15:00, except for CL1, which maximizes in the late afternoon to after 15:00, similarly to CL2 of the first CA. Modeled diurnal minima and maxima are in accordance with the observations, except for CL1, where MACC shows daily maxima in between 12:00 and 15:00 like for other modeled groups.

Clustering based on the normalized set of properties shows a clear division of stations relevant to amplitudes of seasonal and diurnal cycles (Figs. 16 and 18). Further analysis (not presented here) of the second CA clusters have shown that they are also distinguished by the short-term variability, expressed as the difference between 95th and 5th percentiles of ozone mixing ratios (Lyapina, 2015). Both these amplitudes, as well as variability, decrease uniformly and gradually from CL1 to CL4 in accordance with the level of pollution of these clusters. In contrast, there are no substantial differences of variability between clusters of the first CA (Lyapina, 2015). And as mentioned earlier, the dominant clustering criteria of the first CA are the average ozone concentrations (Fig. 6), and only to a lesser extent the seasonal–diurnal amplitudes.