The regional climate simulations were performed by the Regional Climate Model version 4.6 (RegCM4), which serves as a meteorological driver for the chemistry transport model simulations (see further). RegCM4 is a non-hydrostatic mesoscale climate model developed at International Centre for Theoretical Physics (ICTP) based on the MM4 model . RegCM4 offers multiple methods for calculating convection; here the Tiedtke scheme was chosen . Cloud and rain microphysics is computed using the explicit moisture scheme of , which offers a more comprehensive treatment of moisture and its transformations in air compared to the older SUBBEX scheme . For radiative transfer, the scheme from the National Center for Atmospheric Research (NCAR) Community Climate Model version 3 CCM3; was used.

The planetary boundary layer turbulence was parameterized using the scheme developed at the University of Washington by and (denoted “UW”). The UW is a local prognostic 1.5-order scheme and provides an alternative to the default non-local diagnostic Holtslag PBL scheme HOL; originally included in RegCM. made tests to identify the differences between these two PBL parameterizations and they found excessive vertical turbulent transfer in the HOL scheme for heat and water vapor leading to large biases in winter temperatures and problems capturing low-level stratus. The UW scheme seemed to overcome this shortcoming. Another reason for choosing this scheme in our simulations was that it provides prognostic turbulent kinetic energy (TKE) values on model output which enable to use TKE-based estimation of vertical eddy diffusion coefficient. Moreover, UW itself contains such a method (see further) and directly supplies Kv values upon model output readily usable in chemistry transport model calculations.

Fluxes of heat, radiation, water and momentum between the land surface and the atmosphere are calculated with the Community Land Model version 4.5 CLM4.5; implemented inside the driving regional climate model. To account for the specifics of urbanized surfaces, CLM4.5 contains the CLMU urban canopy module , which considers the classical canyon representation of urban geometry where cities are composed of street canyons. The canyon is bounded by roofs, walls and canyon floor, and trapping of solar and long-wave radiation within is considered.

Within the urban canyon, heat and momentum fluxes are calculated using the Monin–Obukhov similarity theory with roughness lengths and displacement heights typical for the canyon environment . Anthropogenic heat flux from air conditioning and heating is computed within the urban canopy model from the heat conduction equation based on interior boundary conditions corresponding to interior temperature of the building. To this heat flux, waste heat from air heating/conditioning is further added. It is parameterized directly from the amount of energy required to keep the internal building temperature between prescribed maximum and minimum values, assuming 50 % efficiency of the heating/cooling systems .

The chemical simulations were performed with the Comprehensive Air Quality Model with Extensions (CAMx) version 6.50 chemistry transport model (CTM) . CAMx is an Eulerian photochemical CTM that implements multiple gas-phase chemistry schemes (CB5, CB6, SAPRC07TC). The CB5 scheme was invoked in this study, having optimal complexity for long-term climate-scale simulations. Particle sizes are considered using a static two-mode approach. Dry deposition is solved using the approach, while for wet deposition the method is applied. The ISORROPIA thermodynamic equilibrium model is also activated in our setup to calculate the composition and phase state of the ammonia–sulfate–nitrate–chloride–sodium–water inorganic aerosol system in equilibrium with gas-phase precursors. Secondary organic aerosol (SOA) is computed with the semi-volatile equilibrium scheme SOAP .

CAMx is coupled offline to RegCM using the meteorological preprocessor RegCM2CAMx, originally developed by . For the diagnostic calculations of the vertical eddy diffusion coefficients, originally, the OB70 method was implemented in RegCM2CAMx, which uses a simple prescription of the Kv profile. extended RegCM2CAMx by the Community Multi-scale Air Quality model (CMAQ) scheme which applies the similarity theory for different stability regimes of the boundary layer. The stability regime in the CMAQ method is defined using the dimensionless ratio of the height above the ground and the Monin–Obukhov length. Here, we further extended the range of possible turbulent diffusion packages with a non-local Yonsei University (YSU) turbulent mixing scheme which contains an explicit treatment of entrainment processes at the PBL top. We also added the ACM2 method which is a new version of the original asymmetric convective model (ACM) and includes the non-local scheme of ACM combined with an eddy diffusion scheme. ACM2 is thus able to represent both the supergrid and subgrid components of turbulent transport. The fifth Kv calculation method (Mellor–Yamada–Janjić; MYJ) is based on the TKE approach of , as implemented by . MYJ implements 1.5-order (level-2.5) turbulence closure mode and determines the eddy diffusion coefficients from prognostic TKE. Finally, the last method of calculating Kv values for CAMx is to read them directly from RegCM output (denoted as the DIRECT method). In fact, DIRECT and MYJ differ only in the implementation but are based on the same physical principles. In summary, a range of six Kv calculation methods (CMAQ, DIRECT, ACM2, OB70, MYJ and YSU) are available to translate RegCM outputs to CAMx-ready Kv fields representing a wide range of values to drive vertical eddy diffusion (see further). It is clear that by this approach the calculation of Kv values is based sometimes on different concept than the calculation of PBL characteristics in the driving meteorological model (e.g., TKE-based PBL scheme in RegCM and similarity theory in CMAQ Kv scheme). However, all Kv methods use only large-scale characteristics from the meteorological model as input (wind, temperature, humidity, TKE profile, PBL height, etc.) without any a priori expectation on how these physical quantities have been obtained. In this regard, we assume this “non-consistency” a minor issue. Furthermore, showed too that using a “non-consistent” method in calculating Kv for CTMs does not implicate less accurate results than directly coupling the PBL parameters.

It has to be noted that the dry deposition scheme used in CAMx does not depend directly on the Kv values provided on CAMx inputs. Instead, for the aerodynamic resistance, calculation of diffusion through the first model layer to the ground is done using the scheme of based on the solar insolation, wind speed, surface roughness and near-surface temperature lapse rate. Consequently, different Kv computation methods do not directly impact dry deposition velocities.

Further developments of RegCM2CAMx here include that it takes cloud/rain/snow water directly from RegCM output, which in the version used already enables to output these variables. No feedbacks of the modeled species concentrations on RegCM radiation/microphysical processes were considered. , using a similar setup to the one here, showed that urbanization-induced chemical changes have a very small radiative feedback in long-term average.

For meteorological variables, the gridded E-OBS data, which enable spatial comparison, were chosen to reflect the model values. The modeled average summer (JJA) and winter (DJF) near-surface temperatures and precipitation are evaluated for all model resolutions. Note that from the 27 km model domain, results are shown only over a subdomain corresponding roughly to the 9 km domain area to facilitate comparison. In Fig. , the difference between the modeled and measured near-surface temperatures is presented. During summer, the 27 and 9 km resolution simulations tend to underestimate surface temperatures by 2 ∘C, while the 9 km one has smaller biases and even some overestimation occurs over the eastern part of the domain up to 1 ∘C. Largest differences are encountered over mountainous areas, where the main reason lies probably in the poor model representation of complex orography. The 3 km simulation shows a warm bias almost everywhere up to 1–2 ∘C (except a few areas near the Czech border). For the winter months, a warm model bias is seen at each resolution, being lowest in the 27 km one (up to 2 ∘C) and reaches 3 ∘C at 3 km resolution. Notably, the warm bias is largest over Prague (indicated by its borders), which suggests that the regional climate model used overestimates the urban temperature effects.

The difference between the model total precipitation and observation is shown in Fig.  in mmd-1. During winter, precipitation is overestimated in RegCM at each resolution, reaching up to 3–4 mmd-1 above mountains. The medium-resolution model simulation shows somewhat smaller bias, while at 3 km and around Prague, the model overestimated rain by 2–3 mmd-1. A different picture is seen during JJA: the low-resolution simulations show a strong overestimation of the precipitation by up to 2–3 mmd-1 all over the domain. A much smaller positive model bias is encountered for 9 km, with values usually lower than 1 mmd-1 (with even some negative bias over the domain edges). At the highest resolution, both positive and negative biases are present in the range of -3 to 2 mmd-1. For the area of Prague, the bias is however small, lying between -0.5 to 0.5 mmd-1.

The modeled surface concentrations were compared against the European Environment Agency AirBase (https://www.eea.europa.eu/data-and-maps/data/aqereporting-8, last access: 19 February 2020) station data. Rural and urban background stations were selected which are not affected by local sources unresolved by the models (i.e., traffic stations were not considered). The validation focuses on two key pollutants: O3 and PM2.5. Below, we use the term “modeled surface values” to mean the uniform concentration of the lowermost model layer at the corresponding grid box, which corresponds roughly to the urban canopy layer.

In Fig. , the scatter plots of measured and modeled ozone values are shown. It is seen that the vast majority of the values lie within a factor of 2 (i.e., conform to the FAC2). FAC2 is a robust measure, as it is weakly influenced by outliers . FAC2 is lower in winter when observations exhibit very low values that are not resolved by the model, regardless of the relatively high resolution (3 km). In summer, model values are usually overestimated, and the overestimation is slightly higher at 27 and 9 km resolutions. It is also evident that the model provides a narrower range of values than measurements, especially during summer when it is unable to capture low ozone situations (large number of observation near zero, while model values are around 50 to 150 µgm-3).

The deviations seen in the scatter plots are better understood looking at the comparison of seasonal average diurnal cycles in Fig. . For summer, the average daily maximum ozone is reasonably captured with a little positive bias around 3–5 µgm-3 at 27 and 9 km resolutions, while urban stations have this bias slightly larger. The daily maximum ozone values are almost perfectly captured for 3 km resolution with a small overestimation for urban stations. The timing of the maxima is reasonably captured too. However, the model tends to strongly overestimate nighttime values for all resolutions and especially for urban stations. This explains the overall overestimation of average daily values seen in the scatter plots. For winter, model biases are smaller. For rural stations, the model underestimates measured values for the 27 km resolution and slightly overestimates for the higher ones. Here, however, the daily ozone maxima are well modeled. The observed urban values are overestimated by the model, especially during morning hours by up to 10 µgm-3; however, again, daily maxima are reasonably captured. The comparison of monthly means in Fig.  confirms the overestimation of ozone values during JJA (by 10–20 µgm-3), where the main contributors are the too-high ozone values during the night, as seen from the previous figure. On the other hand, winter (and spring) averages are modeled with higher accuracy, and even some underestimation by model occurs for the 27 km resolution (seen also in the diurnal cycles). Again, the positive model bias is somewhat larger for urban stations than background ones.

The daily PM2.5 scatter plots in Fig.  and the corresponding normalized mean bias (NMB) values suggest that PM2.5 is underestimated in the model, except for summer over rural stations at 27 km resolution. On the other hand, very good agreement in terms of this metrics is achieved for the 3 km resolution during JJA. It is seen that the underestimation is caused mostly by the high end of the observed values which CAMx is not able to reproduce. The FAC2 statistic is about 0.6–0.7 at each resolution and season. The gain in using higher resolution is not clear and the model improvement depends on which metric is analyzed. For rural stations, however, the 3 km simulations seem to be more accurate than the lower-resolution ones.

The monthly values in Fig.  bring some light to the root of model biases seen in scatter plots. Winter concentrations are underestimated by the model in each case by about 5–10 µgm-3 over rural stations and 10–15 µgm-3 over urban ones. During JJA and for rural stations, model concentrations of PM2.5 tend to be higher than the measured ones by about 3–4 µgm-3 for the 27 km resolution, somewhat smaller for the 9 km one (about 2 µgm-3) and are in very good agreement for the fine-resolution simulations. Over urban stations, the model is consistently lower in PM2.5 concentrations; here, however, the highest underestimation for JJA occurs at 3 km resolution (around 3–5 µgm-3).

It has to be noted that many urban background stations selected in the analysis are taken from small urban areas and their emission is not resolved well by the model. Therefore, the average urban model concentrations are only slightly different from rural ones (higher values for PM2.5 in urban areas and lower ones for O3 due to titration effects).

Finally, to validate the model's ability to resolve the vertical transport and the sensitivity to the choice of Kv method, we contrasted the modeled pollutant profiles with available ozone sounding data for Prague, Czech Republic, measured for January to April at 12:00 UTC (see http://portal.chmi.cz/files/portal/docs/meteo/oa/sondaz_ozon.html, last access: 19 February 2020). Figure  shows a systematic underestimation of observed O3 values occurring for elevations (above sea level) higher than about 1000 m, reaching 10 ppbv or even exceeding it. It is also clear that the coarse-resolution experiment tends to agree with the sounding data best, at least for the two winter months. On the other hand, the lowest ozone values are systematically modeled at the highest model resolution (3 km). Near the surface, ozone is usually overestimated by different simulations, while the 3 km resolution shows the best match. From the shape of the modeled profiles, it is also clear that the TKE-based MYJ method results in the most straight curve (highest values near the surface, lowest at high elevations) meaning that it produces the strongest mixing for ozone (see further in Sec. ). On the other hand, the OB70 and YSU methods result in the most skewed ozone profiles at lower elevations (up to 1000 m) with the best agreement with observed values. In summary, it is difficult to conclude which resolution or Kv methods result in the best model–observation agreement. It seems that for higher elevations, coarse resolutions are more accurate, while at lower ones, the high-resolution simulations match observations better. Further, within the PBL, Kv methods producing lower Kv values (YSU and OB70) lead to ozone vertical patterns which most resemble the observations.

In Fig. , the spatial impact of urban canopy on near-surface temperature is shown. In general, the DJF impact on temperature is higher for both cities and exceeds 2 ∘C. In summer, the impact lies between 1.5 and 2 ∘C. Over Berlin, the 9 km simulation results in a more pronounced impact in both seasons. Over Prague, the impact is highest for the 27 km simulation in both seasons. It is also seen that if spatially averaged over coarse resolution, the high-resolution impact over Prague will be lower than over the 9 km and, especially, over the 27 km simulation. Further, the figure shows that most of the area analyzed exhibits statistically significant temperature impact, suggesting that even minor urbanized areas (small cities, villages) play a role in modulating near-surface temperatures.

The diurnal cycle of the urban canopy absolute temperatures and the difference compared to the non-urban case is shown in Fig. . It is seen that higher resolutions exhibit warmer urban canopy temperatures in accordance with the conclusions made in the validation. According to the expectations, maximum urban warming occurs during the evening at around 20:00–22:00 UTC (22:00 to 24:00 LT) for JJA. For DJF, the maximum difference occurs at different times over each city: for Berlin, it is around 00:00 UTC (01:00 LT); however, over Prague, it occurs earlier, around 04:00 to 08:00 UTC (05:00 to 09:00 LT). Over Berlin, the 9 km simulation results in almost 2 times higher impact (1 ∘C vs. 2 ∘C). Over Prague, the situation differs: the highest impact, in contrast to the absolute values, occurs for the 27 km simulation for DJF; however, for JJA, the results for the three resolutions are very close to each other and show maximum warming around 2.4 ∘C.

In Fig. , the JJA and DJF average impact on 10 m wind speed is shown for the three resolutions. It is seen that the wind is significantly decreased over urbanized areas, while the decrease is higher in DJF (around -1.5 to -2 ms-1 compared to -1 ms-1). The smallest decrease is modeled for the 27 km simulation for both cities and seasons. Statistically significant changes on the 98 % level are modeled over a large part of the analyzed region, suggesting that even small urban areas contribute to the wind reduction significantly.

Regarding the diurnal cycle of the wind speed and its urban-canopy-induced changes in Fig. , it is seen that the two analyzed cities behave somewhat differently; while, over Berlin, the 27 km simulation produces lower winds than the 9 km one, over Prague, the lowest wind speeds are modeled for the highest resolution. A more unique picture (in accordance with the spatial figures) is seen for the impact itself. The higher the model resolution, the stronger the impact on winds. For Berlin, it reaches -1.5 ms-1 for both seasons at noon. For Prague, the wind impact reaches -1.4 ms-1 for JJA and can be as strong as -1.8 ms-1 for DJF.

The main focus of this paper is the urban impact on the vertical eddy diffusion coefficient as a key factor determining urban pollution transport. Here, we present this impact for each of the Kv methods that are listed in Sect. . In Fig. , the urbanization-induced changes of the JJA eddy diffusion coefficient at the first model level (approximately 65 m, i.e., at urban canopy layer height) are shown for all three model resolutions (rows) and six Kv methods (columns). It is clear from each method/resolution that Kv values are affected the most over the two selected large cities (Berlin and Prague); however, statistically significant changes occur over rural areas too. The most striking feature is the wide range of Kv changes (predominantly increases). The smallest urbanization-induced increase is, in general, obtained for the CMAQ and YSU schemes: in both cases, the rural-to-urban transition results in about 1–2 m2s-1 increase of Kv over both cities. The strongest increase is modeled with the TKE-based DIRECT and MYJ methods, where it reaches 15 and 30 m2s-1, respectively. The ACM2 and OB70 methods lie in the middle range with increases up to 6–10 m2s-1. Regarding the sensitivity of the resolution, its effect seems to be small, and the three resolutions result in a comparable change of Kv values, while often the 27 km resolution produces the strongest impact, especially when spatially averaging the higher-resolution results to 27 km. In summary, the urbanization-induced Kv changes above the urban canopy layer during JJA encompass a relatively wide range from 1 to 30 m2s-1.

The DJF impact on Kv at the canopy layer height is shown in Fig. , and very similar patterns are seen when compared to JJA, both qualitatively and quantitatively. The strongest impact is obtained for the two TKE-based methods (DIRECT and MYJ), reaching 15 to 30 m2s-1. On the other hand, a 1 order of magnitude smaller impact is calculated for the CMAQ and YSU methods (up to 2 m2s-1). Similarly to the JJA impact, the ACM2 and OB70 methods lie in the middle range of the Kv methods, with the former one somewhat stronger. During both seasons, a few areas encounter a statistically significant Kv decrease in the DIRECT and MYJ methods. This might be connected to the general wind reduction over large areas and the corresponding reduced TKE generation resulting in lower Kv values, but this would require more analysis.

In order to understand the Kv evolution during the day, we plotted its diurnal cycle in Fig.  for Berlin. We are interested here not only in the urban canopy values but also in the impact on the whole Kv profile (within the PBL), and the absolute values from the URBAN model experiments are plotted as well as contour lines. Regarding the absolute values, it is seen that the largest Kv values are generated during early afternoon hours, in line with the expectations. The level of maximum Kv is higher in JJA (about 150–600 m) than during DJF (100–500) and also higher for the 9 km simulation compared to 27 km one. The TKE-based methods (DIRECT and MYJ) produce higher values, reaching 200 m2s-1 for the DIRECT method and 120 m2s-1 for MYJ in JJA. The lowest Kv values are calculated using the OB70 and YSU, reaching about 20 m2s-1 in JJA. Winter Kv values are much lower, as expected. It is also seen that Kv values are usually larger for the 9 km simulation in both seasons. Here, the MYJ and DIRECT methods are the exceptions, with sightly higher values for the 27 km resolution. Somewhat distinct diurnal distribution is obtained with the ACM2 method. Kv values remain relatively large throughout the whole day, and the maximum value is reached at much higher levels than for other methods (around 500–800 m). Turning our attention to the urban-canopy-induced Kv changes (shaded colors), it is seen, again, that the highest impact is obtained using the DIRECT and MYJ methods, reaching 100 m2s-1. It is also clear that the impact is higher during JJA and stronger for the 9 km resolution for all methods. The highest impact occurs at comparable levels to the absolute values and consistently around late afternoon to early evening hours for each method. This means that the maximum of the impact is shifted to 3 to 6 h later than the occurrence of the maximum absolute values. The smallest impact is simulated for the YSU and OB70 methods, reaching 10–20 m2s-1 at their maximum, which occurs in afternoon/early evening hours.

In Fig. , the absolute Kv values and the urban canopy impact are shown for Prague for JJA in the same manner as for Berlin, only extended by the 3 km simulation. In general, both the absolute Kv values as well as the impact is very similar to the impact over Berlin. The absolute eddy diffusion coefficient increases with increasing resolution and is, again, highest for the DIRECT and MYJ methods reaching 350 and 150 m2s-1, respectively. The lowest Kv values are obtained when calculated by the YSU and OB70 methods (up to 20 m2s-1). It is also clear that, at higher resolutions, the maximum Kv occurs at higher model levels. Regarding the impact, there is a very clear increase when going into higher resolutions, and the change is especially large between the 27 and 9 km resolutions.

During DJF (Fig. ), absolute Kv values are, of course, smaller compared to summer ones; however, one cannot clearly conclude an increase when turning to higher resolutions. For example, for the DIRECT and MYJ methods, the 27 km results are higher than those obtained for the 9 and 3 km simulations. However, these two methods still produce the largest vertical diffusivities (up to 40–50 m2s-1, with MYJ being higher). Regarding the urban canopy impact, the DIRECT and MYJ methods result in the strongest change. However, in contrast to Berlin (or to the Prague JJA results), the strongest impact is modeled at 27 km resolution, while for other Kv methods, the difference between individual resolution is not significant.

In Figs. –, we presented the range of Kv perturbation caused by the introduction of urban land surfaces, and it was seen that it covers 2 orders of magnitude (increases from a few m2s-1 to tens of m2s-1). Here, our attention moves to the range of perturbations of O3 and PM2.5 urban canopy concentrations this leads to (i.e., the kv-impact is evaluated for individual Kv methods).

Figure  presents the JJA changes of O3 due to the urbanization-induced Kv enhancement for the three resolutions and six Kv methods. Ozone is increased in all cases, ranging from 0.2 to 3 ppbv (about 5 %–10 %), as expected following . They showed that the main contributor to this increase is the reduced destruction due to the turbulence-enhanced vertical removal of NOx from the canopy layer and the increased turbulent flux from the RL during the night. The smallest increase is modeled by the CMAQ and YSU methods. At 27 km resolution, the largest effect is obtained using the DIRECT method; at 9 km, the four remaining methods give a rather comparable impact for both cities. At 3 km resolution, the largest impact is seen for the ACM2 and OB70 methods. For Berlin, higher resolution leads to a stronger impact for each method. For Prague, it is most often the 27 km resolution where the highest impact is modeled (expect YSU). In general, the impact over Berlin is stronger than that over Prague.

The DJF impact in Fig.  is stronger than the JJA one, often reaching 4–5 ppbv (up to 30 %–40 % change). Here, again, the smallest effect is obtained using the CMAQ and YSU methods. The strongest one is seen for the DIRECT, MYJ and ACM2 methods at each resolution. It is also clear that higher resolution usually leads to smaller modeled impact.

To gain a more detailed insight into the range of kv-impacts, we also plotted the diurnal cycle of the vertical profile above both analyzed cities along with the absolute values. In Fig. , we present the results for Berlin for both seasons. Regarding the absolute values in JJA, at higher levels, they are higher and this elevated maximum (usually around 200–500 m) “reaches” the surface as the usual early afternoon summer ozone maxima occur (about 40–50 ppbv). These are somewhat higher at 9 km resolution. Turning our attention to the impact, a very clear maximum is seen near the surface during early evening, reaching 6 ppbv, while the effect is stronger for the 9 km resolution. This maximum is not visible only for the OB70 method at 27 km resolution. Another striking feature is the ozone decrease up to -2 ppbv at higher levels (200–400 m) with maximum intensity coinciding with the maximum surface increase and slightly shifted compared to maxima of the absolute values. In general, the impact (similarly to the absolute values) is more pronounced for the 9 km resolution and reaches higher levels. A secondary ozone maximum in the daily cycle is detectable from noon to the evening at altitudes around 500–1500 m (higher altitudes at 9 km resolution), reaching 0.3–0.4 ppbv. During DJF, the pattern of absolute values is much simpler, with gradually increasing concentrations with increasing altitude including the expected weak afternoon maximum. The 9 km resolution profiles usually have lower values compared to 27 km ones, except near the surface when the ACM2 method provides higher values. The kv-impact on O3 is characterized by a clear increase at the surface model layer with a weak maximum during late afternoon up to 6 ppbv, while the strongest effect is modeled for the DIRECT and ACM2 methods. The diurnal amplitude of the impact is much smaller than during JJA and it is clearly stronger for the 9 km resolution than for the 27 km one. The O3 decrease at higher levels is well seen (around 300–400 m; up to -2 ppbv reduction) and it is much stronger for the 9 km resolution.

The pattern of the kv-impact on O3 as well as that of the absolute values is very similar for Prague compared to Berlin, as seen in Fig. . The O3 increase is limited to the lowermost layers and there is again a clear early evening maximum reaching 5–6 ppbv. The impact reaches almost zero values during midday near the surface, as seen for Berlin too. The decrease at higher levels (200–400 m) with maximum during late afternoon/early evening is evident from model results too and reaches -2 to -4 ppbv. Finally, the secondary maximum of O3 increase during noon hours at around 500–1500 m occurs as well and reaches 1 ppbv. The impact for the 3 km resolution seems to be the smallest, probably in connection with the fact that the absolute values are the smallest at this resolution.

During DJF, over Prague (Fig. ), both the absolute values and the kv-impact resemble the pattern seen for Berlin. The diurnal amplitude is much smaller for the impact, with maxima usually around early evening, and occasionally a weaker maximum is seen during morning hours for the DIRECT, ACM2, OB70 and MYJ methods. Again, the smallest impact is modeled for the CMAQ and YSU methods, and the values for the 3 km resolution are below those for lower resolutions. The ozone decrease at higher altitudes (around 200–500 m) is detectable too, reaching -2 ppbv.

In summary, different Kv methods lead to not only different average kv-impact on ozone values but substantially different vertical profiles and different shape of the daily cycle including the timing of the maximum value and occurrence of secondary maxima at higher altitudes.

Our attention now turns to the UCMF-induced PM2.5 changes, and we first look at the changes in near-surface concentrations due to the kv-impact. The results for JJA and DJF are presented in Figs.  and , respectively. For JJA and for Prague, there is a clear decrease of PM2.5, in line with the expectation of higher vertical turbulent removal (dispersion) of aerosol as well as their precursors from the urban canopy layer . In general, the 27 km resolution leads to stronger decrease of up to -2 µgm-3, especially for the DIRECT, ACM2 and OB70 methods. For higher resolutions, these methods result in the largest impacts too (-1 to -2 µgm-3), while very weak impact is modeled using the CMAQ and YSU methods (from -0.2 to -0.4 µgm-3). A slightly different picture is obtained for the kv-impact for Berlin. While at 9 km resolution, the conclusions are very similar to the ones seen for Prague (decreases of PM2.5 of similar magnitude; ACM2 and OB70 providing the strongest impact), at 27 km resolution, the impact is either a very small decrease (DIRECT and ACM2, up to -0.2 µgm-3) or a slight increase up to 0.3 µgm-3 for the remaining methods. It is seen that there is a general increase of PM2.5 over a large part of the analyzed region and this increase dominates the impact over Berlin. This is probably caused by the PM2.5 removed from the urban atmosphere (due to higher Kv values) and transported to and deposited in other regions, causing an opposite effect.

During DJF, the kv-impact leads to clear increase of PM2.5 concentrations for all resolutions, cities and methods. The strongest impact is seen for the DIRECT, ACM2 and MYJ methods, peaking at -2 µgm-3, while, again, the smallest impact is obtained for the CMAQ and YSU methods (below -1 µgm-3). It is also clear that the impact calculated for lower resolutions is usually slightly stronger, especially over Prague.

In order to see how the kv-impact on PM2.5 evolves during the day, we plotted in Fig.  the diurnal cycle of the impact of urbanization-induced Kv enhancement on the PM2.5 vertical profiles along with the absolute values. At the surface, the absolute values are higher during DJF (18 µgm-3) compared to JJA (up to 15 µgm-3) as expected due to the more stagnant meteorological conditions. However, at higher elevations, JJA concentrations are higher due to enhanced vertical transport from the canopy layer. It is also clear that for the 9 km resolution, PM2.5 decreases with height slower than in the 27 km run, which is in line with the slightly stronger vertical mixing in the 9 km resolution compared to 27 km one (see Fig. ). Further, it is seen that the Kv methods giving stronger vertical turbulent diffusivities (e.g., DIRECT) result in lower near-surface concentrations, and vice versa (e.g., OB70), especially for JJA. The diurnal cycle of the absolute values is characterized by a clear maximum during morning hours and a minimum (especially in JJA) during afternoon. Looking at the kv-impact on PM2.5 concentrations, it is seen that the near-surface values are characterized by decreases except the 27 km simulation values during JJA (in line with Fig. ). At 9 km resolution, during JJA, this decrease encompasses two peaks: a primary peak during the afternoon reaching -1 µgm-3 and a secondary one during morning (up to -0.6 µgm-3). The strongest impact is provided by the DIRECT, ACM2 and OB70 methods, as seen in the spatial figure above. At higher altitudes, the PM2.5 removed from the urban canopy layer causes a positive impact “region” (at about 100–300 m) up to 0.3–0.4 µgm-3 occurring during the afternoon. At 27 km resolution, however, this elevated maximum reaches the ground and leads to an almost complete disappearance of surface decreases. During DJF, the two resolutions behave qualitatively in a very similar way. Both lead to a well-pronounced surface PM2.5 decrease, while it is stronger in the 9 km resolution (up to -2 to -3 µgm-3). The DIRECT and ACM2 methods provide the largest impact. The double-peak shape of the near-surface impact is less clear or missing; instead, the kv-impact remains high from morning to evening hours. The elevated increase of PM2.5 is more pronounced during the cold season and is, similarly to JJA, stronger over at 9 km resolution, reaching 0.5–0.6 µgm-3 at about 200–500 m.

For Prague, the JJA absolute values in Fig.  look quantitatively and qualitatively very similar to those over Berlin, with peak values around 10–15 µgm-3 during morning hours, while higher values are modeled with Kv methods producing lower Kv values (e.g., OB70). The kv-impact manifests again as two maxima of the near-surface PM2.5 decrease, reaching -2 to -3 µgm-3. The strongest impact is seen for the DIRECT, ACM2 and OB70 methods, as is seen for Berlin too. The elevated positive impact seen for Berlin is present here too and reaches 0.5–0.6 µgm-3 with two maxima: one during morning hours and one during evening hours. In general, the impact over the 9 and 3 km resolutions (up to -3 µgm-3) is stronger than that over 27 km (up to -1.5 µgm-3).

Figure  presents the absolute Kv values and the kv-impact for DJF for Prague. It is clear that the 9 and 3 km resolutions result in higher near-surface concentrations and the vertical spread of the PM2.5 is stronger than that at 27 km. Regarding the impact, it reaches higher values in the 9 km and 3 km resolutions, and the maximum kv-impact is reached for the DIRECT, ACM2 and OB70 methods (up to -3 µgm-3 decrease) during daytime. For the 27 km resolution and for the YSU and CMAQ methods, the PM2.5 decrease is smaller (up to about -1 µgm-3). Similar to Berlin, the PM2.5 increase and higher levels are evident too and are stronger for the 9 and 3 km resolutions. They occur between 150 and 400 m, and reach 0.8–1 µgm-3, especially for the DIRECT, ACM2 and OB70 methods.

One of the most important questions to answer in this paper concerns the dominance of enhanced turbulence within the urban canopy impact on air quality via the urban meteorological effects. To answer this question, we evaluated also the total- or the t+q+uv+kv-impact for both analyzed pollutants as the difference between the URB_t+q+uv+kv and NOURBAN simulations for each resolution. As the NOURBAN model experiment is calculated using only the CMAQ Kv method; the total-impact is given also only for this method. Here, based on short 1-month test simulations, we verified that the t-, q- and uv-impacts depend on the choice of the Kv calculation only weakly (in contrast to the kv-impact itself, which is strongly dependent on the choice of the Kv scheme).

Figure  presents the total-impact of the urban meteorological changes on the mean canopy concentrations of O3 for each resolution and both seasons. predicted that near-surface O3 should increase due to the increased removal (turbulent dispersion) of NOx from urban areas and thus reduced titration, as well as due to enhanced turbulent transport from higher levels, although they pointed out that the overall effect is always a result of competitive impact of multiple influences. Indeed, in our results, ozone usually increases too, but the magnitude of the increase changes substantially across resolutions, and it is different for the two cities. For Berlin, it reaches around 0.2–0.3 and 0.4–0.6 ppbv for the 27 and 9 km simulations, respectively. For Prague, increases are encountered for the 9 and 3 km resolutions, reaching 0.3 and 0.8 ppbv, respectively. However, for the 27 km simulation, the overall urban impact turns out to be negative (about -0.2 ppbv). During DJF, ozone increases over both cities, mostly for the 27 km resolution (reaching 0.8 ppbv). However, for Prague, in the 3 km resolution, O3 decreases (up to -0.6 ppbv), in contrast to the JJA results.

In order to see whether the simulated total-impact is uniform during the day or if it behaves qualitatively and quantitatively differently during different hours, we plotted further the diurnal cycle of this impact along with the absolute concentrations for both cities and seasons, as shown in Fig. . For JJA, the absolute values (solid lines) are in line with the expectation of maximum during afternoon, while the difference between the different resolutions is not greater than 6–8 ppbv (greatest differences in the daily maxima and nighttime values). The impact (dashed lines) is characterized by a clear main maximum during afternoon hours reaching 3 ppbv for Berlin, while it is less pronounced in the coarse-resolution simulation. A secondary maximum is visible too during morning hours, especially for Prague. The minimum of the impact is encountered during early afternoon, and here, the differences between the resolutions are very large for Prague, ranging from -2 ppbv to almost 0, explaining the overall negative impact of the urban canopy meteorological forcing on ozone in the previous figure. During DJF, absolute ozone concentrations encounter two maxima: one during early morning and one during early afternoon. In DJF, ozone titration is the dominant process in cities, while ozone is transported here by turbulence from upper levels. The titration rate is highest when NOx emissions are peaking and this occurs in the morning and late afternoon, putting the two ozone maxima in between. In general, the 9 and 3 km resolutions result in higher absolute ozone for this season, especially during nighttime. The total-impact is, again, characterized by a clear late afternoon maximum reaching 2–3 ppbv and being strongest in the 27 km simulation. It is present also in the 3 km simulation for Prague; however, a negative peak forms here during morning (reaching -1.5 ppbv), which results in the overall negative impact on ozone seen in Fig. .

The total-impact on PM2.5 surface concentrations is presented in Fig. . The impact is negative in all cases, confirming the expectations that the effect of turbulent removal dominates . However, the magnitude of the change varies greatly between the cities and resolutions. It reaches -1.5 to -2 µgm-3 for Prague in both analyzed seasons and is strongest at 27 km resolution, while at 3 km, the decrease is only about -0.6 µgm-3. Over Berlin, the decrease is in the range of -0.4 to -1 µgm-3; in JJA, it is slightly stronger in the 9 km simulation, while in DJF, the opposite holds.

The diurnal cycle of the absolute near-surface PM2.5 concentrations as well as the total-impact over Berlin and Prague is presented in Fig. . A clear maximum occurs in the absolute values in JJA during morning hours over both cities, in line with the emissions' temporal evolution, while the difference between individual resolutions is within 5 µgm-3 and is highest during nighttime when the 27 km simulation produces the largest concentrations. Regarding the total-impact, in JJA, there is a clear negative peak during evening hours for both cities, reaching -2 µgm-3. However, at 3 km resolution, this peak is less pronounced and reaches only about -0.6 µgm-3. Here, another peak is present during morning hours and this is seen also at 27 and 9 km resolutions, especially for Berlin. During DJF, absolute concentrations exhibit a main maximum during morning hours, while a secondary peak is present during evening hours, probably in connection with the diurnal cycle of the emissions. The diurnal cycle of the impact is very similar between individual resolutions and cities with one main peak during morning hours when the impact is the smallest (it almost disappears over Berlin at 9 km resolution). Later, the impact increases, during noon to afternoon hours, reaching -2 µgm-3, similarly to the JJA impact. Again, the smallest impact is modeled at 9 km resolution (about -1 µgm-3).

In summary, when comparing the individual resolutions, it is clear that the total-impact for both O3 and PM2.5 can vary largely, in both the quantitative and qualitative sense. Further, it is evident that the kv-impact (evaluated in the previous section) will add further uncertainty to the results, as its spread is even larger than the spread seen in the total-impact due to different resolutions (bear in mind that the kv-impact represents a major component of the total impact). Further, the total-impact was evaluated using the CMAQ method. This resulted in one of the smallest kv-impacts. Even as such, it clearly dominates the total-impact. Consequently, using other Kv methods would lead to even stronger total-impact (increase of ozone and decrease of PM2.5) and thus confirms the dominance of the modifications in vertical turbulent transport among other components of the urban canopy meteorological forcing.