The results from the outputs from the five runs were assessed following the suggestions provided by on the evaluation of the quality of model simulations. These authors stated that Pearson's correlation coefficient (r), the fractional bias (FB) and the normalised mean square error (NMSE) were the most relevant statistical parameters to be analysed for O3 simulations with CTM. Table  shows a coloured grid indicating the values of r, FB and NMSE obtained in the comparison between the observations from background monitoring stations and the simulated O3. The colour scale is independent for each parameter and serves as an indication of the agreement between observations and model predictions.

All five configurations presented good correlations with observations with an average r of 0.752, although lower values were obtained for the five-layer schemes (0.695±0.077 and 0.745±0.044) than for the configurations using the hybrid-layer scheme (0.750±0.062–0.801±0.034). Among these multiple-layer-scheme simulations, the one showing the best r is ECMWF_70, which was the configuration with the coarser spatial resolution for LOTOS-EUROS among the three. Therefore, regarding the degree of correlation for multilayer configurations, increasing horizontal resolution to very fine grid sizes in the photochemical model does not improve results (provided that no changes are implemented in the emission inventory). This is known in meteorological modelling as the “double penalty” issue and occurs when evaluating simulations using point observations. The high-resolution runs may be penalised twice, for not capturing the occurrence of the event and also for not predicting the right location of the event, while a low-resolution simulation can only fail in predicting the event.

LOTOS-EUROS tends to moderately overestimate ground-level O3 concentrations varying widely in the five set-ups. It was clear that deviations with respect to observations declined with the use of a higher number of vertical levels and finer spatial resolution. The absolute values of the averaged FB for WRF_70 (0.079±0.059) and ECMWF_HR_70 (0.088±0.060) were substantially lower than those of the other three configurations (0.260±0.095–0.117±0.095). Clear improvements were observed using finer spatial resolution in LOTOS-EUROS (either WRF simulations or ECMWF_HR_70), while ECMWF_5 and, especially, ECMWF_70 presented systematic but moderate overestimations (Fig. S3). In consequence, the best configurations for adjusting the model bias were WRF_70 and ECMWF_HR_70.

A major reason for the overestimation detected for ECMWF runs with coarser spatial resolution was associated with an excessive O3 formation in the noon hours of the day in situations of low wind speed as shown in Fig. . This plot shows the correlation between the model bias and the modelled wind speed in the location of El Retiro (see location in Table ) in Madrid for the five runs. In the plots corresponding to ECMWF_5 and ECMWF_70 runs we observe systematic positive bias especially in the period 14:00–20:00 UTC when the formation is strong, although it only spiked with low wind speed. This feature was not so marked in the three remaining configurations, and, in particular, in the two WRF runs the bias values were randomly distributed around zero. The ECMWF_HR_70 run showed a subtler systematic overestimation during daytime, but the correlation with low wind speeds was not observed in this case. Analysing the night-time period (00:00–06:00 UTC) we detect that the systematic overestimation was only present in the ECMWF_70 execution.

Regarding the simulation errors quantified via the NMSE (Fig. ), the results were satisfactory because the values of this parameter remained low for the five configurations (means ranging between 0.082±0.046 and 0.122±0.068 with the WRF_70 run showing the best performance). The relevant information extracted from NMSE values in Fig.  was that the errors of the model were consistently lower in rural areas (0.063±0.038) than in suburban (0.096±0.033) and urban (0.135±0.077) sites. This might be an effect of the simulation of the interaction between O3 and NOx, which acquires more relevance as a source of errors in the vicinity of traffic sources. Other authors suggest that the use of an urban canopy model (not used in this simulation) improves model predictions in densely built areas by reducing the overestimation of wind speed.

Systematic features characterised the modelled mean daily cycles of the 35 stations (Fig.  shows the plots for the El Pardo site as a typical example). The daily cycles obtained with the simulations performed with the mixed-layer scheme of five levels (ECMWF_5 and WRF_5) presented a sharp increment in O3 concentrations from 06:00 to 07:00 UTC which was not present in the simulations performed with the hybrid scheme of 70 levels. In these runs, the morning increment of O3 after the rush hour was delayed 1 or 2 h (WRF_70 and ECMWF_HR_70 runs) and clearly smoothed. The observations reflected that the timing of the increase was better represented in the mixed-layer-scheme runs, although the increase was excessively abrupt. The occurrence of this steep increase in the concentrations in the executions performed with the mixed-layer scheme coincided with the first steps of the boundary layer development. In the mixed-layer scheme, a rise of the boundary layer leads immediately to complete mixing of NOx emitted at the surface over the (increased) boundary layer and thus limits titration of ozone; in the 70-layer schemes, however, the mixing over the boundary layer seems to take place more gradually. A more extensive validation including other tracers than the chemically active ozone should provide insight into which scheme performs better under which conditions, and it should preferably lead to better characterisation of the vertical diffusion.

The evaluation of CTMs in the vertical direction has always been a difficult task due to the small number of high-resolution vertical observations to compare with. In this work, data from O3 free soundings launched from Madrid airport at 12:00 UTC every 7 d on 6, 13, 20 and 27 July 2016 were used for this purpose. Comparisons between the vertical profiles of modelled O3 with the five different set-ups and the observations are presented in Fig. . The corresponding profiles of wind direction and speed (modelled data are taken from the input meteorological datasets) can be found in the Supplement (Fig. S4). As suggested by , the enrichment of O3 in the lower troposphere during episodes without ventilation is high as a consequence of the intense photochemical formation and the development of convective circulations. This typically results in vertical profiles in which O3 concentrations are relatively high near the surface up to 2000 m a.s.l. at midday soundings in Madrid, as shown also here in Fig. a and d. During venting episodes, the more intense surface dispersion explains why O3 vertical profiles have lower values in the mixing layer (Fig. b and c).

The event of 27 July was characteristic of an accumulation scenario with high concentrations near the surface, while on 13 July (a typical venting event), O3 in the lower levels was moderate and increased with altitude as described above. These two profiles were correctly simulated by most runs. However, the modelled profiles for 6 and 20 July showed overestimation in the lower levels with respect to observations, and for the 20 July case, all the high-resolution simulations overestimated the observed values. In Fig. S4, we can also check how the input meteorological data used to feed the simulations (ECMWF and WRF fields) closely reproduced the wind profiles obtained during the soundings of those 4 d both on speed and direction. Because of the complexity of the vertical mechanisms, further research should be conducted to investigate the causes of this mismatch in some events.

From the qualitative perspective, the first obvious conclusion was that a larger number of vertical levels in the model considerably improved the capability for capturing the vertical gradients of O3 concentrations, with the exception of the lowest level on 20 July. However, even in the simplest vertical scheme (five layers), the model was able to reproduce the general vertical trends. A particular meteorological scenario was present during 13 July. We can observe two O3 layers centred around 3000 and 4300 m a.s.l. The two multilayered WRF runs captured these two layers at, approximately, the correct altitudes, although the 3000 m layer was not as marked as in the observations. The ECMWF runs also presented these two features but were displaced in altitude by around 200–300 m with respect to observations.

In all the WRF_5 runs and on 27 July WRF_70 simulations a steep drop in surface concentrations was noticed. This is probably associated with the emission model configuration, the fine spatial resolution of the runs (3km×3km) and the vertical mixing in these set-ups. The O3 soundings were released from Adolfo Suárez Barajas Airport, which is one of the major airports in Europe with more than 53 million passengers and 470 t of goods transported in 2017 (http://www.aena.es/, last access: 15 November 2019) as well as significant NOx emissions. The emission model employed by LOTOS-EUROS allocates at the surface level all the air traffic emissions in the grid cell where the airport is located. These emissions, added to those produced by road traffic, lead to a grid cell that has the highest NOx emissions in the domain. As a consequence, and given the fine size of the grid cells in the WRF runs, O3 levels were excessively reduced compared with reality in the aforementioned cases. Regarding ECMWF runs, the coarser spatial resolution did not allow observation of this feature because the modelled emissions from the airport were distributed on a larger surface.

Quantitatively, the model generally showed the ability to reproduce the same order of magnitude of the concentrations observed in the O3 soundings at all altitude levels. The values of the statistical parameters that indicate the quality of the simulations (FB and NMSE) of the vertical profiles of O3 are shown in Table , where generally satisfactory values can be observed with poorer results especially for 20 July. The FB showed a majority of positive values indicating overestimation, although, in most cases, it was moderate (the range of averages for the five configurations was -0.5 to 0.11). The NMSE data in Table  support this conclusion because the average errors were small (0.023–0.042).

Summarising, the configuration that presented the best overall performance among the five tested in the previous sections was WRF_70, so it was employed for interpreting the variability of O3 in the MAB during July 2016.

These events correspond to the pattern sketched by in which wind direction turns clockwise during the day, aided by the effect of the blocking effect of the Guadarrama range, while described that the mixing layer growth at midday was reduced favouring vertical recirculation at the eastern slopes of the Guadarrama range (see Sect. ). In July 2016 four REC periods were identified: 1–6, 8–11, 15–17 and 25–28. To illustrate the main features of REC episodes, the period 15–17 July will be used as an example (Figs.  and ). A complete pattern of simulated fields of O3, wind and relative humidity (RH) for July 2016 can be consulted in Fig. S5.

Surface wind speeds registered during REC episodes were weak (Figs.  and S5), and the change in direction associated with recirculation is observed. However, despite the local circulation, air masses remain inside the basin during REC days aided by a relatively thin mixing layer at 12:00 UTC (Fig. S4).

A stable band of high RH centred at around 4000 m is observed in Figs.  and S5, which can be associated with the evapotranspiration caused by the intense heating registered during these events. The presence of a high-altitude trough located to the west of the IP during the 3–6 July REC period induced moist south-westerlies at altitude resulting in the development of convective clouds in the evenings (Fig. S5).

Surface O3 concentrations generally reach high values at the central time of the day during REC episodes (Fig. ). During the 17 REC days registered in July 2016, 37 exceedances of 180 µgm-3 were recorded in all the monitoring stations in the study area. The sectors suffering the greatest impact of O3 are the W–N belt of the MMA (MAJ, PAR, COL, ALC and ALG) and, more episodically, the Henares valley (AZU, AHE and GUA) or the south-east of the basin (ORT and VSA). Occasionally, when SW winds in the evening reached sufficient intensity (for example on 16 July), the O3-enriched air masses reach rural stations located in the north-east of the basin (ATA and CAM) late in the day. LOTOS-EUROS surface concentration maps show that at 12:00 UTC O3 begins to rise, reaching the maximum concentrations around 18:00 UTC. Time series of O3 also support this conclusion because the highest O3 levels are observed in the evening (Fig. ).

To study the three-dimensional variability of O3 during a typical REC event, Fig.  presents longitudinal and latitudinal cross sections of simulated O3 and NO2 for 4 different hours during 16 July. The use of NO2 plots allows observation of the evolution of fresh emissions from the Madrid conurbation in the course of the day. This figure illustrates the strong photochemical formation of O3 followed by the accumulation during a typical REC episode. In the first hours of the day, a very shallow boundary layer combined with the stagnant conditions allows locally emitted precursors to accumulate inside the basin. Ozone is then effectively eliminated by titration with NO coming mainly from traffic emissions. This explains the steep drop in O3 time series during the rush hours (Fig. ), with the exception of rural stations far from the Madrid conurbation like SPM, which showed a more stable behaviour in their O3 concentrations.

From the simulation results, we can interpret the evolution of O3. At 18:00 UTC of 16 July, we can see how O3 levels increased drastically, and the boundary layer depth grew up to 3500 m a.s.l. aided by convection at 18:00 UTC. Normally, REC events show higher planetary boundary layer (PBL) heights in the evening. Figure  shows how the strong convection during REC events injected ground-level pollutants at high altitudes during the late afternoon and the evening reaching up to 3500 m a.s.l. as illustrated in the NO2 plots. When the night-time stable boundary layer forms after sunset, air masses with high O3 that originated near the surface during the previous day were decoupled and remained in the residual layer at altitudes ranging between 2000 and 4000 m a.s.l., forming reservoir layers (00:00 and 06:00 UTC cross sections in Fig. ) which can fumigate the following day. These reservoir layers can also be observed as a relatively thin band at an altitude of 2000–4000 m a.s.l. during every night of the REC period (Figs.  and S5).

We will refer to NAD events as those during which the dominant situation consisted of the advection of air masses coming from the north over the MAB. During July 2016, the following two periods matched that description: 12–14 and 22–24.

During NAD periods, surface wind is channelled following the NE–SW axis parallel to the Guadarrama range resulting in prevailing north-easterlies in the lowest tropospheric layers while in the upper levels the dominant component is north-west (Figs. ,  and S5) and often associated with the passage of cold fronts from the Atlantic. Winds are generally stronger than in REC events, which implies a renovation of air masses and lower temperatures.

Humidity during NAD events is conditioned by the arrival of air masses off the Atlantic, which are generally moist. During the period 12–14 July, a band of high RH (in the order of 50 %–60 %) that reaches an altitude of approximately 3000 m a.s.l. can be observed (Fig. ). Moreover, a diagonal band of low RH can be observed descending from an altitude of 8000–9000 m a.s.l. at around 10:00 UTC on 12 July, reaching the surface by midday of 14 July. This structure was associated with layers of high O3 detached from the lower stratosphere as shown in Fig. . These low-RH stratospheric intrusions were observed also on 22 and 23 July during the third NAD episode (Fig. S5).

The northern winds during NAD episodes push surface air masses with high O3 towards the south and south-west of the MAB. However, ground-level O3 concentrations are lower than those observed during REC events. The highest O3 levels were registered on 12 July at the south-eastern part of the domain (AHE and ORT) with concentrations below 160 µgm-3. Meanwhile, the maximum concentrations in the rest of stations that day fell below 130 µgm-3, which is consistent with LOTOS-EUROS surface concentration maps for 12 July (Fig. ). The next 2 d, winds intensified and veered north, resulting in concentrations that did not exceed 130 µgm-3 along with noteworthy O3 increments in the rural station of SPM located in the southernmost part of the basin, in accordance with LOTOS-EUROS surface concentration maps of 13 and 14 July (Fig. ). Only one hourly exceedance of 180 µgm-3 was registered during the 6 NAD days in all the air-quality stations in the study area in July 2016.

Figure  shows how increased advection reduced the residence time of polluted air masses over the region, resulting in lower and less variable O3 concentrations throughout the day as observed in observations presented in Fig. . Moreover, the formation of reservoir layers during NAD episodes was less common due to the lower convection, relative to that of REC cases presented before.

It is also remarkable in Fig.  that above 3000–3500 m a.s.l. O3 concentrations were very high (in the order of 100 ppb according to the model). This was associated with the stratospheric intrusion of very dry air described above. LOTOS-EUROS reproduced this stratospheric intrusion that was detected from data obtained with free and tethered O3 soundings for the same period during a field campaign . The actual impact of this stratospheric intrusion on surface levels remains unclear. In the referenced paper, the authors estimate a possible but limited impact of the intrusion on surface levels assuming that the boundary layer could exceed the 3000 m a.s.l. during the day. As shown in Fig. , LOTOS-EUROS predicts that the maximum altitude of the boundary layer according to LOTOS-EUROS reached its maximum values of 2500–2700 m a.s.l. limited by the wind ventilation, so, probably, the impact on the surface should be low (if any) in this case.

Southern transport implies the arrival of warm air masses, sometimes, coming from northern Africa (maximum temperatures at El Retiro during SAD events in the study period varied between 35.1 and 38.1 ∘C while during NAD periods they ranged from 27.1 to 35.1 ∘C). In July 2016, two SAD periods were observed: 18–21 and 29–31. The first of these two periods has been chosen to illustrate the main features of SAD episodes (Figs. –).

SAD events are characterised by constant southerly winds at the surface and at altitude as shown in the simulated fields of U and V (Figs.  and S5). Because the southern coast of the IP is a densely populated area (especially in summer due to the strong touristic pressure) and anthropogenic emissions of O3 precursors are high, including industrial emissions around the cities of Huelva, Seville and Algeciras, regional contribution of external O3 may acquire importance at the basin during SAD events.

High RH values in the middle troposphere are observed during SAD periods (Figs.  and S5) where relevant increments were registered in the period 19–20 July. Although southerly winds are often associated with rain in the MAB, only small amounts of precipitation were collected during this period.

Analysing the 18–21 July case as a typical example of a SAD episode, we observe in the O3 time series that concentrations increased in the entire basin earlier in the day than in the other two scenarios. While ground-level O3 peaks around 18:00 UTC for REC conditions, daily maxima are found around 12:00 UTC under SAD patterns, as confirmed in Fig. . After the intense photochemical formation observed at midday, O3 is transported towards the north-east in the afternoon. This explains the concentration peaks registered at the rural stations located on that side of the basin (ATA and CAM) for example on 19 or 29 July (no figure shown of this day). Other days, such as on 18 July, the model still produces a peak in the mid/late afternoon and the shift of the O3 daily maxima is biased by the spatial distribution of stations, which miss the plume that has been advected north-west at 18:00 UTC. SAD episodes are then periods in which O3 produced at the MAB can be exported towards the north of the IP. Less often, if winds blow from the south-east in SAD events, O3 can be transported across the Guadarrama range towards the north-west as happened on 18 July (Fig. ).

The effect of southern winds ventilating the area and some weak rainfall events limited the increase of O3, although considerable levels were recorded in monitoring stations during SAD events. In general, O3 concentrations during SAD periods are slightly lower than during REC events (with specific exceptions like 19 July) but higher than in NAD episodes. In the stations located in the basin, hourly concentrations rarely exceeded 180 µgm-3 during SAD days (twice in July 2016 in the 7 SAD days), but concentrations above 120 µgm-3 were more frequent (1083 in total in all the stations in the study area or 155 per day) especially in the stations like ATA and CAM located on the north-east of the basin (see 19 July in Fig. ). This proportion of records above 120 µgm-3 is higher than during NAD events (average of 56 per day) and lower than the rate registered during REC events (203 per day).

Vertical cross sections of O3 and NO2 on 2 consecutive days (18 and 19 July) from a SAD period have been used to illustrate the different behaviours observed (Figs.  and ). The intense accumulation of NO2 observed in the 00:00 and 06:00 UTC plots points out that, on these days, ventilation was not as effective as in NAD events. As a consequence, the O3 daily cycles showed a considerable drop associated with titration in the morning rush hour unlike on NAD days and closer to the situation of REC episodes (Fig. ). Likewise, for NAD events, vertical mixing is limited as shown in the NO2 vertical cross sections of 18 and 19 July, preventing the formation of reservoir layers during SAD events. The higher O3 registered on 19 July seems to be related to the fact that a deeper boundary layer (maximum heights above 4000 m a.s.l. on 18 July, 3200 m a.s.l. on 19 July) allowed larger dilution, lowering surface concentrations.

Figure a presents a comparison between observed (data from ) and simulated (WRF_70 configuration) BLH at 12:00 UTC. We can observe that the model tends to overestimate the BLH at midday, although the general trends are captured. In particular, the gradual decrease in the 12:00 UTC BLH from 11 to 14 July that allowed O3 to accumulate smoothly in the basin, which was described in the aforementioned work, is also observed in the simulated data. The overestimation is slight on most days, although larger differences are observed in certain periods (5–10 and 29–31 July).

describe lower midday BLH in O3 accumulation episodes (equivalent to REC events described here) than in venting episodes (NAD or SAD). The simulations with LOTOS-EUROS confirm that finding as observed in Fig. b. The mixing layer is deeper on 13 July (NAD) than on 16 July (REC) from 00:00 to 16:00 UTC, which includes the period of most effective photochemical formation of O3. This allows a more effective formation of reservoir layers during REC events that fumigate to the surface as the diurnal convective circulation develops. After 16:00 UTC the BLH during the REC event grows higher than during the NAD day due to the larger convection in the second scenario.