On the application and grid-size sensitivity of the urban dispersion model CAIRDIO v2.0 under real city weather conditions

. There is a gap between the need for city-wide air-quality simulations considering the intra-urban variability and mircoscale dispersion features and the computational capacities that conventional urban microscale models require. This gap can be bridged by targeting model applications on the gray zone situated between the mesoscale and large-eddy scale. The urban dispersion model CAIRDIO is a new contribution to the class of computational-ﬂuid dynamics models operating in this scale range. It uses a diffuse-obstacle boundary method to represent buildings as physical obstacles at gray-zone resolutions in 5 the order of tens of meters. The main objective of this approach is to ﬁnd an acceptable compromise between computationally inexpensive grid sizes for spatially comprehensive applications and the required accuracy in the description of building and boundary-layer effects. In this paper, CAIRDIO is applied on the simulation of black carbon and particulate matter dispersion for an entire mid-size city using an uniform horizontal grid spacing of 40m . For model evaluation, measurements from 5 operational air monitoring stations representative for the urban background and high-trafﬁc roads are used. The comparison 10 also includes the mesoscale host simulation, which provides the boundary conditions. The measurements show a dominant inﬂuence of the mixing layer evolution at background sites, and therefore both the mesoscale and LES simulation results are in good agreement with the observed air pollution levels. In contrast, at the high-trafﬁc sites the proximity to emissions and the interactions with the building environment lead to a signiﬁcantly ampliﬁed diurnal variability in pollutant concentrations. These urban road conditions can only be reasonably well represented by CAIRDIO while the meosocale simulation indiscriminately 15 reproduces a typical urban-background proﬁle, resulting in a large positive model bias. Remaining model discrepancies are further addressed by a grid-spacing sensitivity study using ofﬂine-nested reﬁned domains. The results show that modeled peak concentrations within street canyons can be further improved by decreasing the horizontal grid spacing down to 10m , but not beyond. Obviously, the default grid spacing of 40m is too coarse to represent the speciﬁc environment within narrow street canyons. The accuracy gains from the grid reﬁnements are still only modest compared to the remaining model error, which to a 20 large extend can be attributed to uncertainties in the emissions. Finally, the study shows that the proposed gray-scale modeling is a promising downscaling approach for urban air-quality applications. The results, however, also show that aspects other than the actual resolution of ﬂow patterns and numerical effects can determine the simulations at the urban microscale.

In this follow-up paper we shift the focus from idealized experiments to a more application-oriented use of the model for a real city and true atmospheric conditions, for which the mid-sized city of Leipzig in eastern Germany is selected as a showcase.
This allows us to include further processes in the model, which are paramount for realistic dispersion simulations within a real 95 urban canopy and realistic meteorology. For example, the stratification of the PBL does not necessarily have to be neutral and can be further modified locally in the model by a parameterized surface-heat flux from ground and building surfaces. Inflow conditions are in general not only turbulent but also transient, in order to account for an accurate evolution of the larger-scale meteorology. The complexity of the simulation is further increased by using a comprehensive emission inventory that includes all relevant sectors, which are modulated in time to account for diurnal and weekly changes in activity. While this study 100 aims not at analyzing individual processes in depth, its main objectives are to demonstrate the feasibility and practicability of the approach as a downscaling tool for a more accurate representation of the intra-urban air-pollution variability. Therefore, apart from static inputs, the model solely relies on the output fields of a host simulation conducted at the lower end of the mesoscale, for which the CTM COSMO-MUSCAT (Wolke et al., 2012) is used. For validation, we compare modeled PM 10 and/or BC concentrations with measurements at 5 different operational air-monitoring sites in Leipzig for a total period of two 105 consecutive days in spring 2020. To further estimate the sensitivity to the horizontal grid spacing, locally-nested sensitivity runs are performed, for which the horizontal grid spacing is decreased from a default ∆h = 40 m in steps down to ∆h = 5 m, enabling conventional building-resolved simulations.
The paper is structured as follows: Section 2 describes the methodology, in which all the general and technical aspects of the simulations and measurements are described. This also includes a detailed description of the mesoscale coupling. Section 3 110 includes the presentation and discussion of model results, which is subdivided into a part describing the modeled PBL evolution, a model evaluation with concentration measurements, including a comparison with results from the CTM COSMO-MUSCAT, and the grid-size sensitivity study. Section 4 summarizes the main findings of the study and highlights the advantages but also limitations of the demonstrated approach and the study itself.

Study time period
The model case study spans 2 consecutive days from 1 March 2020, 00:00 UTC to 3 March 2020, 00:00 UTC, to address the main objectives of this study. Yet, for a more significant model evaluation with observational data, a substantially longer simulation period needs to be simulated. While principally our approach is computationally much cheaper compared to a wellresolved urban microscale simulation, a compromise still had to be found, and we decided to invest computation resources 120 in a spatially more comprehensive simulation that fits better the aspect of a model case study. The specific simulation period was selected based on suitable properties for an investigation of the intra-urban air-pollution variability. Firstly, quality-assured observational data from all operational air-monitoring sites in Leipzig are available during this period. Secondly, significant impacts of the world-wide spreading Covid-19 pandemic had still not reached the German public by early March 2020, as data from the Google mobility report show a significant decline starting after 10 March (Google-LLC, 2020;Forster et al., 125 2020). This provided confidence that the traffic emissions had not to be adjusted for a reduced mobility, which is a potential source of additional uncertainty. Thirdly and most importantly, the meteorological conditions were suitable to focus on local air pollution and PBL processes affecting it. The large-scale synoptic pattern during the simulation period from 1 to 3 March 2020 was dominated by a large and deep low-pressure system situated over northwestern Europe, from which two troughs protruded southward and eventually moved across Germany (see Figure 1a-c). The associated unsettled weather conditions in Leipzig 130 resulted in diverse PBL characteristics and effects on local air quality, which are interesting to study. Moreover the influence of low pressure favored low background near-surface PM 10 concentrations over most of Germany, as suggested by results from an air-quality simulation for Europe depicted in Fig. 1d-f (cf. Section 2.3 for a detailed description of the mesoscale simulations).
According to this, highest PM 10 concentrations apart from the well-known air-polluted regions, like the Po Valley, occurred over the eastern half of Europe. There were also periods before and after the actual simulation period, when the Siberian high 135 pressure system extended westward and brought a polluted continental air mass to central Europe (not shown). During such periods with elevated background concentrations, the intra-urban air-pollution variability was quite insignificant and not worth to study.

Near-surface in-situ observations of air quality 140
A set of in-situ observations is used to evaluate the modeled air pollutant concentrations. The south-eastern German state Saxony operates 26 air-quality monitoring sites. Three of them are suitable for our model evaluation, as they are located within the city margins of Leipzig and provide PM 10 concentration measurements. One of the three stations considered is also cooperated by the TROPOS and provides BC retrievals too. Three stations are air quality stations operated by the Saxon State office while two additional stations belong to TROPOS. Three out of the five station measure also equivalent black carbon 145 (eBC) mass concentration, which are also relevant to our evaluation. Tab. 1 lists some basic information of the aforementioned measurement sites, while Fig. 2 shows their locations on horizontal maps of the simulation domains to provide a qualitative overview of the characteristic environment, like the distribution of buildings, parks and major roads highlighted by PM 10 line emissions. Finally, Fig. 3 gives a detailed mapping of the surrounding building environment in spherical coordinates at each exact measurement position, as well as the corresponding sky-view factors f sky . Based on these information, a brief introduc-150 tion of each measurement site is given in the following. Station Leipzig Lindenau (LL) measures PM 10 and is located in the western city district Leipzig Lindenau within a closed street canyon running in west-northwest east-southeast direction. The street canyon has average dimensions (height × width) of roughly 20 m × 25 m, which results in a sky-view factor of 0.34. The horizontal position of the measurement site is near the northern side of the canyon at a distance of only 5 m to a traffic-busy road, with an average daily traffic count (ADTC) of 20400 vehicles. This, in combination with an inlet height of 1.7 m leads 155 to a high exposure of this station to the exhaust gases from nearby traffic, which clearly classifies this station as roadside.
Station Leipzig Mitte (Leipzig Center, LC) provides PM 10 and eBC measurements. It is located southwest of the Leipzig main railway station at a junction of the inner-city ring, which is a multi-lane road (ADTC of 47600 vehicles). Therefore, also this 45 m. Furthermore, due to a local park adjoining to the east, the influence of traffic emissions at the measurement site can be expected to vary according to the prevailing wind direction. Station Leipzig West (LW), located within the western outskirts of Leipzig inside a park, is a background station for PM 10 , as it is also secluded by lines of trees from a nearby road (ADTC of 8600 vehicles). Station Leipzig Eisenbahnstr. (LE) has a long history as a scientific measurement site and is thus well documented from previous air-quality studies (see e.g. Klose et al. 2009, Wiesner et al. 2021. The measurement equipment 165 is located next to a window on the third floor of an apartment house (inlet height is approx. 6 m above the road) flanking a frequently traffic-congested street canyon (ADTC of 11500 vehicles). The cross section of the street canyon is symmetric (20 m × 20 m). Regularly occurring crossroads divide the street canyon into segments of 70 m − 110 m length, with the closest crossroad (ADTC of 11800 vehicles) being to the west at a horizontal distance of about 35 m from the measurement site. While this side is also classified as roadside, its inlet position high above the road makes it more representative to the average con-170 centrations within the street canyon. Depending on the development of the street-canyon vortex, however, it may be also more directly exposed to high pollution concentrations. Finally, the side Leipzig TROPOS (LT) is a background station for eBC, as it is located on the roof top of the TROPOS institute's building at a height of 16 m and at a distance of at least 100 m from any busy roads.
PM 10 concentrations are directly and near-continuously measured using the tapered element oscillating microbalance (TEOM) 175 system (scientific ambient particulate monitor TEOM 1405, Thermo Fisher Scientific Inc.). TEOM derives PM mass concentrations from the frequency-change of an oscillating hollow tube caused by deposited material at one end of the tube (Page et al., 2007). Real-time measurements are averaged to hourly-mean values with a stated precision of ±2.0 µg and an accuracy of 0.75 % (TFS, 2019). eBC is indirectly retrieved from optical principles with multi-angle absorption photometers (MAAP 5012,Thermo Fisher Scientific Inc.). MAAP estimated the absorption coefficient of an aerosol probe from the transmission 180 and back-scattering of light at a wavelength of 637 nm, where eBC is the main absorber (Petzold and Schönlinner, 2004). The eBC mass concentrations calculated with a mass absorption cross section of 6.6 m 2 g −1 are assumed to be directly comparable with modeled BC mass concentrations, and have an uncertainty between 5 % and 12 % according to different sources (Wiesner et al., 2021).  Figure 2. Map of the city area of Leipzig, which is also selected as the coarse-grid CAIRDIO simulation domain L0 introduced in Section 2.4.1. Each of the white boxes contains an operational air monitoring site used for model evaluation. In addition, a magnified view of the area within each box shows the local environment around the corresponding air-monitoring site, which is highlighted by a red circle. These areas also correspond to the CAIRDIO subdomains introduced in Section 2.5. Traffic-PPM10 emissions of major roads are represented by line sources.

In-situ and remote sensing meteorological observations
The evolution of the PBL has an important influence on the distribution and levels of urban air pollutants. To evaluate the properties and the vertical structure of the simulated PBL, a comprehensive set of in-situ and remote sensing measurements has been used.
At the TROPOS institutes site, lidar-based remote sensing instruments are routinely deployed to monitor aerosol composition 190 and dynamics within the PBL and also above. With the portable Raman lidar Polly-XT  as part of the ACTRIS subnetwork PollyNET , vertical profiles of aerosol optical properties are measured continuously.
From the vertical gradient in the profiles of the attenuated backscatter coefficient, the MLH can be estimated (Baars et al., 2008). While this method is reliable for the daytime with an aerosol-loaded PBL and a clean free troposphere above, with a well-differentiated aerosol layer, the vertical contrast in the backscatter profiles during night time is often much lower. The Additionally, the sky-view factors f sky are computed as the fraction of the solid angle of the hemisphere not blocked by buildings.
backscatter gradient from the nocturnal boundary layer to the residual layer (the remaining aerosol layer from daytime) is often week and the lower-height detection threshold of the lidar system (overlap issue, e.g. Wandinger and Ansmann 2002) decreases the confidence of the method then and often prohibits the determination of the nocturnal MLH. Besides the Polly XT lidar, a HALO photonics streamline XR Doppler lidar was also operated at the TROPOS site during the study period. n vertical staring mode (for dertmination of vertical air motions) but also in scanning mode (PPI) for the determination of the 200 horizontal wind velocity. In vertical staring mode, this lidar can be used to accurately observe vertical motions (uncertainty of less than 0.1 m s −1 ) in atmospheric regions with significant aerosol load (PBL, lifted aerosol layers, clouds) (Bühl et al., 2015). In scanning mode (PPI), it also allows to retrieve vertical profiles of the horizontal wind by the same Doppler principle.
Respective profiles were obtained with a frequency of 10 min throughout the simulation period. Data points with a relative uncertainty in one of the two wind components of larger than 20 % are discarded. The estimation of the night-time MLH is 205 based on the standard deviation of the observed vertical motions as indicator for turbulence: To make a single estimate, starting from the surface, the control volume of a box containing measurements (∆t × ∆z) is vertically increased until the computed standard deviation of contained measurements falls below a given threshold. The MLH is then determined from the height of the control volume. Results are sensitive to the selected time increment, the vertical resolution and the standard deviation threshold. Schween et al. (2014) give a relative change of the estimated MLH by 15 % for a variation of the threshold by 25 %.

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In addition to the MLH estimation, the thermal stratification of the boundary layer can be mapped using in-situ measurements from atmospheric soundings performed at the DWD meteorological observatories Lindenberg (150 km northeast of Leipzig, every 6 hours) and Meiningen (160 km southwest of Leipzig, every 12 hours). While these data cannot be used to evaluate the local city simulations, they can nevertheless be used to evaluate the coarser-scale meteorological simulations for central Germany.

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In addition to the air-quality measurements, hourly-averaged observations of wind speed, wind direction and air temperature from the sites LL and LC, respectively, are used to evaluate the urban wind field and urban heat island effect. This comparison can contribute to the confidence and discussion of the conducted dispersion simulations. To complete the set of surface observations, hourly precipitation totals from two meteorological sites operated by the German weather service (Deutscher Wetterdienst, DWD) are used to evaluate the model representation of precipitation and its impact on air quality. The first 220 site Leipzig/Halle is located 14 km northwest from the Leipzig city centre, and the second site Leipzig/Holzhausen is located 5.6 km southeast from the Leipzig city centre.

Mesocale air-quality modeling
As air pollution is not only influenced by local processes, all relevant larger scale sources and transport have to be considered in the city-focused, urban microscale simulations in terms of boundary conditions. Such a multiscale approach requires 225 tailored model setups with a scale-appropriate prioritization of the dominating processes. Besides the long-range transport, physico-chemical reactions contributing to significant secondary particulate matter (SPM) formation have to be considered on the continental and regional scales, for which in this study the online-coupled mesoscale CTM COSMO-MUSCAT (Wolke et al., 2012) is employed. COSMO-MUSCAT uses the regional model COSMO (Doms and Baldauf, 2018) as the meteorological driver, which was maintained and operationally used by the DWD until recently. Important multi-phase reactions in 230 MUSCAT leading to SPM involve the gaseous compounds ammonia, nitric acid, and sulfuric acid, which themselves are important air pollutants. Additionally, seasonally dependent secondary organic aerosol (SOA) formation is included in the set of chemical reactions composed by the mechanism RACM-MIM2 (Stockwell et al., 1997;Taraborrelli et al., 2009). The remaining fraction of PM 10 is primarily emitted (PPM), and approximated by chemically inert tracers that are only subjected to physical atmospheric removal processes. Figure 4 gives an overview of the bulk PM 10 decomposition in MUSCAT as it 235 is available from the model output. COSMO-MUSCAT is applied on a hierarchy of refined domains, with a one-way nesting technique providing the boundary condition for each consecutive simulation (see Figure 5 for an overview of the domains, which are referred to hereafter with "M<number>"). This model setup has already been used to provide quasi-operational air-quality forecasts for the citizen-science campaign WTImpact (Heinold et al., 2019;Tõnisson et al., 2021). The outermost domain M0 has a horizontal resolution of 14 km and covers entire Europe. This domain is initialized and driven by re-analysis 240 data from the global meteorological model ICON (Zängl et al., 2015), which is operationally run by DWD. Initialization and boundary conditions for air chemistry are interpolated from operational air-quality forecasts with the model system ECMWF IFS (Copernicus Atmosphere Monitoring Service) (Flemming et al., 2015). The domain M0 is simulated for an extended pe- A preprocessor is used to derive horizontal coverage of these segments in each grid cell, as well as probabilistic and geometric parameters of the canopy elements using a detailed building geometry dataset available for entire Saxony. LfULG. All of the aforementioned emission datasets are static in time, i.e. they represent annual mean emission rates per unit area, respective unit length. For time-depended emissions, the aforementioned static datasets are modulated with time profiles specific to each SNAP category (available from the TNO-MACC2 database). The time profiles incorporates different temporal scales, including monthly, weekly and diurnal changes. The temporal resolution is 1 h, with linear interpolation applied between clock hours. The spatially integrated and temporally modulated emissions are shown in Fig. 6 for the simulation period.

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Accordingly, the road transport category is by far the most important contributor to BC emissions, followed by other mobile sources and non-industrial combustion.  The local urban domains of the CAIRDIO model are hereafter denoted by "L<number>". For the city-wide simulation, domain L0 is horizontally resolved with uniform 40 m grid spacing. This resolution showed to be satisfactorily accurate in a first model validation study based on wind-tunnel data also presented in Weger et al. (2021). For DOB, the same geometric 295 building dataset as already used for deriving the parameters in DCEP is used. At the horizontal scale of 40 m, buildings are effectively represented as diffuse obstacles. As a consequence, the subgrid-scale mixing length is of similar magnitude or even larger than the average space between buildings. This implies that the simulation is mostly non-eddy resolving (similar to a RANS approach) within the urban canopy. For a more accurate representation of vertical gradients and mixing processes near the surface, the vertical dimension is kept much finer resolved, with 5 m grid spacing within the urban canopy. Increased grid 300 stretching is applied above, with a maximum stretching factor of 4 near the domain top. Note that vertical resolution is not as computationally expensive as horizontal resolution, because the Courant-Friedrichs-Lewy (CFL) criterion, which limits the explicit integration time step, is mostly determined by the horizontal wind speed. The horizontal coverage of domain L0 is roughly 18 km × 18 km, which is extensive enough to not only accommodate the complete city of Leipzig but also a sufficient fetch to allow for a relaxation of the lateral boundary conditions. The domain top is located at about 350 m height, which is 305 generally below the vertical extend of a typical convective PBL. However, a suitable boundary condition allows for vertical motions exiting/entering at the domain top, which is further explained in Appendix A0.3. While the surface orography within domain L0 is not mountainous, subtle effects from it can still influence meteorology. CAIRDIO can be used with terrainfollowing coordinates, which in this simulation are inferred from surface elevation data (DGM1) provided by the Staatsbetrieb für Geobasisinformation und Vermessung Sachsen (GeoSN). This dataset with a spatial resolution of 1 m has also been cor-of momentum, heat and moisture from vegetation, as well as other types of land cover (lakes, bare soil, subgrid-scale structure of buildings) are parameterized using Monin-Obukhov similarity theory (MOST). Note that this includes also urban trees, which are therefore most simply represented by the surface-roughness approach (see e.g. Salim et al. 2015 for a discussion of the limitations). In MOST, each surface type is characterized by a parametric roughness length z 0 . Table 2 lists the z 0 values 315 related to each land-cover class used in the model. Land-cover is based on a combination of the Pan-European land cover map for 2015 with 30 m spatial resolution (Pflugmacher et al., 2018), and the more detailed land-cover map by Banzhaf and Kollai (2018) (better than 5 m resolution) for most of the urban area. The combined dataset is depicted in Fig. 2 for domain L0, as well as for the finer resolved nested subdomains introduced in Section 2.5 addressing the LES-to-LES nesting.
The emissions used for domain L0 are on the same basis as the ones already used for mesoscale domain M3, which are, the 320 UBA area emissions for industry (SNAP 3, SNAP 4, SNAP 6, SNAP 9) and residential combustion (  Domain L0

Mesoscale forcings and boundary conditions
Simulation results from COSMO-MUSCAT mesoscale domain M3 are used to drive the meteorological and air-pollution fields of the city-scale domain L0. Initial and boundary conditions for the meteorological prognostic fields, which include the 3-D wind components, potential temperature Θ, specific humidity Q V , and subgrid-scale TKE E sgs , are spatially interpolated using 335 tricubic interpolation. Note that tricubic interpolation preserves spatial details better than trilinear interpolation, but is not wellsuited for positive scalar fields featuring large gradients. Therefore, trilinear interpolation is used for the air-pollution fields.
The 3-D interpolation procedure is carried out as a sequence of 2-D horizontal interpolation followed by vertical interpolation.
For the horizontal interpolation, the Climate Data Operators (CDO) software (Schulzweida, 2019) is used, which is convenient to remap data from rotated lat/lon coordinates of the COSMO-MUSCAT model directly to Lambertian azimuthal equal-area 340 coordinates (epsg:3035) of the L0 grid. Vertical interpolation is based on the 3-D height of half levels (HHL), which coincide with the locations of vertical velocity of the staggered grid. After horizontal remapping of the HHL field of the M3 grid, the vertical interpolation weights are generated by computing Lagrange polynomials of the desired accuracy from the HHL data.
As the CAIRDIO simulation employs a finer grid spacing near the ground than COSMO-MUSCAT, the first vertical levels need to be extrapolated, for which a level with zero-height is introduced. At this zero-height level, all wind components are set 345 to zero, and the potential temperature as well as specific humidity fields assume the respective surface values Θ S and Q S V . For the air-pollution fields, constant values from the first MUSCAT layer are extrapolated.
Lateral boundary conditions for the prognostic subgrid-scale TKE equation in the microscale model CAIRDIO are derived by applying a scale separation on the spatially interpolated subgrid-scale TKE of the COSMO-MUSCAT simulation (denoted by coarse) E c sgs . E c sgs is split into a part E f res that can be resolved on the CAIRDIO L0 grid (denoted by fine) and a still 350 unresolvable component E f sgs . The energy splitting can be approximated by integrating the well-known Kolmogorov spectrum for the inertial subrange E(k) ∝ k −5/3 up to the different cut-off wave-numbers k min of the fine and coarse grids. k min can be directly related to the subgrid-mixing scale ∆ sgs , then the following expression follows: (1) ∆ f sgs can be crudely approximated by twice the horizontal grid spacing (corresponding to the Nyquist wavenumber). Note 355 that the horizontal grid spacing in typical PBL simulations is equal or larger than the vertical grid spacing and is thus the dominant cut-off scale. ∆ c sgs , on the other hand, can be related to the master-mixing length of the mesoscale simulation. E f sgs is finally the lateral boundary condition for the prognostic subgrid-scale TKE equation, which determines the eddy diffusivities.
The lateral boundary condition for the 3-D wind vector is a Dirichlet/radiation condition that can flexibly distinguish inflow from outflow regions. For inflow regions, a superposition of the interpolated mesoscale wind field and recycled turbulence is 360 prescribed. The scale-separation applies in a similar way for the turbulence recycling scheme, as the cut-off wavelength of the extraction filter is chosen similar to ∆ c sgs . Consequently, the recycled turbulent fluctuations are scaled with the resolvable energy part E f res . At the domain top, a special boundary condition for velocity, which is quite similar to the turbulence recycling scheme for the lateral boundaries, is used. This boundary condition allows for a simultaneous prescription of the external mesoscale fields and small-scale turbulent motions reaching/extending beyond the domain top. Further details are addressed in 365 Appendix A0.3. As the turbulence recycling scheme can only extract and amplify existing turbulence, the potential temperature is disturbed by the cell-perturbation method of Muñoz-Esparza et al. (2015) across the full domain at model initialization.
Besides the initial and boundary conditions for the prognostic fields, another important forcing includes the heat and moisture fluxes from the land surface. For their parameterization in CAIRDIO, surface potential temperature Θ S and surface specific humidity Q S V are needed. Instead of employing an own land-surface model in CAIRDIO, a simpler approach is used in this 370 study, which consists of a downscaling of the respective prognostic surface fields from the mesoscale simulation M3. This can be referred to as a one-way coupling with the land surface, in contrast to a fully two-way coupling, which also considers the online feedback of the atmosphere on the land surface. A drawback of this neglected feedback is that the land-surface variables inherently lack the dynamic spatial variability at the finer scales that are only represented in the LES model. This may adversely impact the computed surface fluxes and as a final consequence the thermal stratification of the boundary layer.

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Also it is to point out that small-scale radiative effects, like partial shading inside a street canyon cannot be represented by this simple approach. Nevertheless, these potential sources of modeling error are accepted in favor of a simple solution, until an own land-surface for CAIRDIO is developed. The used down-scaling method essentially is a linear regression model that is based on the assumption of land cover being the most significant co-determinant of the small scale variability. This assumption applies only for limited horizontal domain extents with non-mountainous terrain, which, however, is quite well satisfied with 380 domain L0. For application outside these limits, the approach can be easily extended to a multiple linear regression model in order to consider other important explanatory variables, like, e.g., surface height, or the influence on horizontal position, which can be approximated by a bilinear function.
Explaining the method on the basis of surface potential temperature, in a first step, the mesoscale field is decomposed into a filtered or mean state Θ S and a fluctuating part Θ S . Additionally given are the different land-cover fractions on the same 385 mesoscale grid. These fractions are put in a m × n matrix L, whereas the dimension m states for the number of independent land-cover classes considered, and dimension n for the number of horizontal grid cells. Then, it is possible to solve for the unknown land-cover related potential temperature fluctuations Θ S Lc by minimization of the following least-square problem: The vector b contains the potential temperature contribution from a-priori determined land-cover classes, which are already 390 known for lakes and urban surfaces, the latter being direct outputs of the urban parameterization DCEP in COSMO. For more robust fitting results, we consider only forests, open vegetation (includes grass land, shrubs, and crops) and bare soil (minus the fraction of urban surfaces) as independent classes. After solving Eq. 2, the high-resolution field of domain L0 is composed by multiplying the obtained land-cover dependent fluctuations Θ S Lc (including b) with respective land-cover fractions given for domain L0 and addition to the horizontal mean state, respective horizontally interpolated filtered state Θ S .

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Because CAIRDIO uses a 3-D building structure, potential temperature values of these elevated horizontal and vertical surfaces are still missing. These values can, however, be directly inferred from the additional output fields of the mean roof and wall temperature computed with the DCEP parameterization. Q S V is fitted in a similar fashion like Θ S , with a further simplification that Q S V is set to zero for the impervious surface fraction, thus rain evaporation is neglected. Fig. 7 qualitatively shows the described downscaling approach based on an exemplary Θ S field for 2 March 2020, 12:00 UTC, when sunshine prevailed. For 400 the resulting reconstructed field of domain L0, a top-down projection is shown. The sun-lit roofs are the warmest surfaces with a quite even distribution due to a prescribed constant roof albedo of 0.16 in DCEP. Considerably cooler are the ground surfaces inside the partly shaded street canyons, followed by the forest areas, and finally by the seasonally cold lakes with the lowest surface potential temperature. While in the given example, surface orography is mostly flat and the surface elevation could be neglected as an additional disturbing factor, this approach may be an oversimplification for areas with more mountainous 405 terrain. For a limited quantitative evaluation of the downscaling method in the framework of this case study, we refer to the comparison of modeled near-surface air temperature with observations in Appendix B (Fig. B1e-f).

One-way LES to LES nesting
In order to quantify the influence of spatial resolution on results of the city-scale CAIRDIO simulations, spatially limited subdomains LW, LL, LC, LE, and LT, each of them centered around an air monitoring site, are offline-nested into the parent domain part E f res , which scales the inserted turbulent fluctuations at the inflow boundaries, a slightly modified formula is used in order to consider the missing contribution of numerical diffusion in E c sgs : where the extraction-filter width is set to λ cut = 140m, which is considerably larger than ∆ c sgs = 80 m. Note that the use of 420 an exponential filter function results in a smooth cut-off range, with λ cut defined as the wavelength that is scaled e −1 -fold.
In Figure 8 the described nesting method with the energy-scale separation is demonstrated by an example with domain LE and 5 m horizontal grid spacing, which features a stably-stratified, shear-driven PBL. The plots of the dominant velocity component v ( Fig. 8a and b) show that well-developed turbulence already exists near the southern inflow boundary, which qualitatively matches the turbulence more distant from the boundary well. This is also quantitatively shown by the derived energy spectra 425 shown for the x-dimension (Fig. 8c), which do not evolve much when moving further away from the inflow boundary. Note that the inertial subrange is followed by the dissipation range, which can be attributed to the combined (dissipative and dispersive) numerical error of the advection scheme at significant convective speeds (Yalla et al., 2021).
The surface fields Θ S and Q S V are again obtained from the corresponding mesoscale fields using the land-cover based method described in Sect. 2.4.2. An additional scaling is applied, such that the computed horizontally averaged values are independent @ inflow boundary @ 1/4 domain extend @ 1/3 domain extend @ 1/2 domain extend @ outflow boundary 2020-03-02 00:30 UTC z=95m 2020-03-02 00:30 UTC z=95m Plotted are, the energy spectra at various positions along the y-axis.

Synoptic and urban planetary-boundary layer meteorology
In the following, an overview of the meteorological conditions and resulting PBL characteristics during the simulation period from 1 March 2020, 00:00 UTC to 3 March 2020, 00:00 UTC is given. The implications of the variable PBL structure on the 435 modeled concentrations and transport of local air pollution are then qualitatively discussed based on model outputs from the CAIRDIO domain L0. As already briefly mentioned in Section 2, the weather in Leipzig during the simulation period was influenced by a low pressure system. The large pressure gradients ahead of the troughs (see again Fig. 1a-c) imply windy conditions over Leipzig for most of the time as it is shown by both model and lidar-based observational data in Fig. 11a.  (Fig. 9), a variable cloud cover prevailed during the first simulation day of 1 March, while on 2 March a significant sunshine period occurred around midday, before high-level cloud cover increased in the afternoon. Also 450 the mesoscale simulation shows a similar evolution of cloud fraction (gray line in Fig. 10). Based on additional ground-based observations, small amounts of rain fell on 1 March during 12:00 UTC (which is missing in the model), and during the night from 1 to 2 March, with measured and modeled totals reaching nearly 4 mm and 3 mm, respectively, at the end of the simulation period (Fig. 10). This amount is not considered to have a larger impact on the local air quality. The vertical Θ v distribution (area plot in Fig. 11b) indicates different influences on the PBL stratification. Intermittent cloudiness during nighttime allowed 455 for limited surface radiative cooling, while during the sunny periods surface heating caused the Θ v gradient to diminish as the result of convective conditions. Striking is the warm-air advection just before the trough axes crossed the area (around 2 March, 00:00 UTC, and after the end of the simulation), which resulted in a large Θ v -gradient within the lowermost 300 m.
The simulated PBL stratification from the coarsest mesoscale domain M1 was evaluated with in-situ measurements from radio sondes released at two meteorological sites in central Germany (also depicted in Fig. 11b). The comparison shows a generally  Figure   505 14. In the stably-stratified case, vertical mixing is limited near the surface and only gradually increases with height. In contrast, the vertical flux in the convective case already peaks close to the surface and then gradually decreases with increased height, indicating an efficient lifting of the near-surface air pollution. Also in the convective case, the flux is much larger compared to the stable case, partly also due to the higher traffic emissions during daytime. Lastly, the partitioning into the resolved and parameterized fluxes shows that while the resolved flux is always dominant outside the urban canopy (roughly the first 30 m), 510 the subgrid-scale flux has also a significant contribution, mainly close to the surface and in the stable case. This also indicates a significant model sensitivity to the mixing parameterization (e.g., the prescription of the static mixing length).

Quantitative model comparison with air-monitoring measurements
To quantitatively evaluate the model representation of the intra-urban variability of air pollution, hourly averaged model output of PM 10 and BC concentrations are compared to respective measurements at the different air-monitoring sites within the city 515 area of Leipzig. For an evaluation of the mean urban wind field and air temperature, according data from two urban airmonitoring sites is additionally compared with model data in Appendix B. Model output from mesoscale simulation M3 with 550 m horizontal resolution is added to the comparison to better quantify the benefit of the dynamic downscaling with 40 m horizontal grid spacing and explicit building representation with the CAIRDIO L0 domain.
In Figure 15, respective plots of PM 10 and BC concentrations are shown for all monitoring sites in Leipzig (see details in 520 Sect. 2.2). For the background station LT (Fig. 15a), the measured BC profile shows a clear diurnal cycle, with the lowest concentrations of about 0.1 µg m −3 during the morning hours of 1 March and 2 March around 06:00 UTC. Concentrations consistently peaked around 18:00 UTC on both days, which can be explained by the coincidence of high traffic emissions related to the rush-hour (see e.g., prescribed emission profile in Fig. 6) and a more shallow stably-stratified PBL during this time (see again Fig. 11e). In this respect, the morning peak on 2 March was damped by the increased PBL mixing height.

525
On the morning of 1 March, which was a Sunday, no peak occurred at all due to the negligible traffic emissions at this time.
Both the profiles from the mesoscale CTM and CAIRDIO simulations followed this observed evolution remarkably well. In the temporal mean, however, the COSMO-MUSCAT simulation tend to underestimate background BC concentrations based on the fractional bias (FB) = 0.28, which is improved in the CAIRDIO simulation to FB = 0.07. Nevertheless, the reasonably z=2.5m accurate model results can be considered to be a good basis for the following discussion of the roadside stations LE and LC 530 shown in Fig. 15b-c.
Compared to the background profile, the diurnal peaks are much more pronounced at the street-canyon site LE, with peak concentrations reaching up to 2.3 µg m −3 at 18:00 UTC on both days. The morning peak on 2 March is again much lower

590
where the brackets <> h denote for the horizontal averaging and c * i is the corrected snapshot. Note that the horizontal average within the canopy layer excludes the inaccessible grid-cell volume by using the volume-scaling field χ as weights. For the velocity components, the cell-face area scaling field η is used instead of χ. Vertical profiles of the computed horizontally and hourly averaged variables u, v, Θ v , c BC , u w , v w , Θ w , and c BC w are depicted in Figure 16 for the two contrasting PBL states already discussed in Section 3.1. Starting with the first case on 2 March at 00:30 UTC, strong southerly winds 595 along with a weakly stable stratification created a shear-driven, turbulent PBL. In the profiles of the mean horizontal wind components ( Fig. 16a-b), grid sensitivity is mainly restricted to the first 20 m within the canopy layer. Inside there, the run with default grid spacing of 40 m results in a slightly higher wind speed compared to the runs with a better resolution of buildings.
Profiles of Θ v show negligible sensitivity (Fig. 16c), while BC concentrations within the urban canopy are slightly higher in the 20 m and 10 m runs compared to the 40 m and 5 m runs (Fig. 16e). Significantly more sensitivity is observed in the vertical 600 turbulent fluxes of momentum (Fig. 16f-h), virtual potential temperature (Fig. 16i) and scalar BC (Fig. 16j). Although the subgrid-scale contributions (dotted lines) become larger as the resolution is decreased, they do not seem to compensate for the loss of resolved fluxes. Apparently, this issue is not restricted to the urban canopy, but may be influenced by an underestimation of vertical wind shear just above the roof tops in the coarser runs. Nevertheless, sensitivity in c BC and Θ v is very low, arguably because transport is mostly horizontal in the shear-driven case. Thus, the profiles of c BC and c BC w (respective Θ v and Θ v w ) 605 are only weakly related to each other.
For the featured convective case around 2 March 12:30 UTC, horizontal wind speeds are by one order of magnitude lower compared to the first case, but a positive vertical heat flux (Fig. 16s) is responsible for turbulence generation this time. Notably, the heat flux sharply increases from the surface up to the average roof height, which highlights the heating effects from building walls and roofs. The averaged wind profiles (Fig. 16k-l) show a similar sensitivity to the already discussed shear-driven case, 610 which may indeed indicate an increase of the prescribed roughness length of the subgrid-scale building structure for momentum transfer in future simulations with diffuse buildings. Compared to the shear-driven case, a more substantial sensitivity in Θ v of approximately 0.5 K and also in c BC can be observed for the height range within the urban canopy (Fig. 16m, o). In contrast, a negligible grid-sensitivity is observed for the respective vertical fluxes Θ v w and c BC w (Fig. 16s-t) across the full height range. The reason for this behavior in the given convective case is that scalar transport is dominated by vertical mixing. Since 615 the emissions are constant in all simulations, also no variations in the turbulent flux c BC w are expected when assuming an equilibrium state. This, however, does not imply that the profiles of eddy diffusivity are constant across the simulations, as the vertical gradients in c BC adjust to match the flux profile. In fact, there must be a significant sensitivity of the vertical eddy diffusivity within the height range where the scalar profiles start to diverge, which is not just by coincidence also the area with the largest instability (the largest super-adiabacity in Θ v ). In the currently used subgrid-scale model, the turbulent Prandtl 620 number P t , which relates the eddy diffusivity to the eddy viscosity, is not further decreased below the neutral value of 0.66 for unstable stratification. However, in unstable conditions P t may be actually much lower, implying a larger eddy diffusivity. An adjustment of the stability-dependent P t may be needed in future simulations.

Distribution of air pollutants
For the evaluation of grid sensitivity at the air-monitoring sites, the horizontal grid spacing of the locally nested domains 625 centered at roadside-classified air-monitoring sites (LE, LL, or LC, respectively) is varied between 40 m, 20 m, 10 m, and 5 m.
The finest grid spacing of 5 m permits conventional building-resolved simulations, but is omitted for the background stations LT and LW due to the expected low model sensitivity there. Model results are again hourly averaged and spatially interpolated to the exact locations of the measurement sites. In Figure 18, the obtained time series are plotted against each other and against the measurements as reference, similar to Fig. 15. In addition, the corresponding FB values in relation to the measurements 630 are listed in Tab. 3. For the BC background station LT (Fig. 18a), little grid-size sensitivity is found as to expect. At best, BC peak concentrations around 1 March 18:00 UTC tend to be slightly higher with increased resolution, which is mainly from the sensitivity of the subgrid-scale parameterization, as the PBL was stably stratified during this time. FB varies only slightly from 0.05 to 0.00 for the 10 m grid spacing. More interesting are the results for the roadside station LE (Fig. 18b). For this site, the 40 m grid spacing resulted in an underestimation of BC peak concentrations. In fact, decreasing the grid spacing 635 down to lower or equal 10 m results in a significantly better representation of both evening rush-hour peaks. However, absolute peak concentrations still cannot be fully recovered. Interestingly, no further improvements can be achieved with the finest grid spacing of 5 m, which points towards limitations with the used emissions. Nevertheless, the improved peak representation results in a slightly lower model FB ranging from 0.06 to 0.16. Aside from the discussed rush-hour peaks, model sensitivity is considerably lower, and it seems like the 10 m and 20 m grid spacings result in slightly higher concentrations compared to the 640 sites (e.g. LC in Fig. 18c), can be attributed to the static subgrid-scale mixing length ∆ sgs . In the 40 m run, ∆ sgs is 20 m near the ground, which is about the typical height of buildings, and thus adequate when considering that the eddies within the urban canopy cannot be resolved. In the 20 m run, however, ∆ sgs is significantly smaller than building size, while resolution is still too coarse to capture the most important eddies. This likely results in an underestimation of vertical mixing within the urban 645 canopy at such intermediate resolutions. By further decreasing the grid spacing down to 10 m or below, the largest eddies of the turbulent canopy flow are finally resolved.
For the station LC (Fig. 18c), a distinction of the evening rush-hour peaks from the remaining time series turns out to be reasonable too. For the two evening peaks, a decrease of peak BC concentrations with increasing spatial resolution can be observed, which is in contrast to the sensitivity at the station LE. A closer inspection of the spatial concentration gradients 650 in Figure 17 reveals the reason for this contrasting sensitivity. The station LC lies next to two traffic lanes to the north in the model. In the 40 m run, the exhaust plumes spread over a comparatively large area, causing a smearing of the gradient in the vicinity of the air-monitoring site. In the 5 m run, spatial gradients near the road are much sharper, which places the measurement site mostly outside the exhaust plumes. It is, however, questionable if the line-source representation of traffic emissions is still adequate in combination with such a fine grid spacing, as in reality emissions can be effectively spread over 655 a larger area by car-induced turbulence (Gross, 2016).
At the site LE, BC is directly measured above the traffic emissions. Here, the 40 m horizontal grid spacing is too coarse to keep the air pollution trapped within the narrow street canyon, as also part of the emissions are emitted outside of the canyon. This explains the observed positive sensitivity of modeled peak BC concentration with increased resolution. Obviously, the 10 m grid spacing is already adequate to contain all of the traffic emissions within the canyon. A similar observation is made with 660 respect to the wind direction at street-canyon site LL (see Fig. B1d in Appendix B).
Grid-sensitivity at the PM 10 -measurement site LW is negligible (Fig. 18d), while it is again much more significant at the streetcanyon site LL, where bulk PM 10 is influenced to a large degree by traffic emissions. Not surprisingly, decreasing the grid spacing to 20 m results in higher modeled peak concentrations compared to the 40 m grid spacing. A further decrease of the grid spacing leads to some indecisive changes for the first evening peak and no significant changes for the second peak. As a 665 result of the higher modeled peak concentrations in the higher resolved runs, an initially moderately positive FB = 0.21 of the 40 m is turned into slightly negative FB values ranging from -0.11 to -0.19. Finally at site LC, a quite similar behavior to the already discussed pollutant BC can be observed, albeit with an extenuated amplitude from the higher background influence of PM 10 . Hence, FB varies only slightly between -0.46 and -0.32 for the set of sensitivity runs.
Having discussed in detail the grid-sensitivity of modeled BC and PM 10 at the different measurement sites, it remains to 670 quantify this sensitivity in proportion to the simulation error in order to give a final conclusion. In addition, also the Pearson correlation coefficient r can serve as a criterion to judge the agreement of model results with observations. As metrics of the model error, both the root-mean-square error ( RMS , units of µg m −3 ) and the relative error ( r , units in %) are computed by the following equations: where c mod and c obs are the modeled and measured concentrations, respectively. t is the time index and n the number of time steps or observations. RM S , r and r values computed for all sensitivity runs are additionally listed in Tab

Conclusions
In this study, we applied the dispersion model CAIRDIO for the first time on a real mid-sized city to simulate dispersion of the pollutants PM 10 and BC using a realistic meteorological setup, which was interpolated from a hosting mesoscale simulation.
For the simulation period, two consecutive days in early March 2020 were selected. During this time, unsettled weather condi-695 tions with changing PBL characteristics and a generally pronounced magnitude of the intra-urban variability due to relatively low background pollution concentrations prevailed. The horizontal grid spacing of the model was set uniformly to 40 m, which permits only to resolve the largest building structures, like industrial sites, while the majority of buildings within the city is described as diffuse obstacles. Nevertheless, the LES approach allows for an explicit representation of the most important turbulent PBL processes, which also include effects from a thermal surface forcing essential to the evolution of the PBL. This 700 capability of the dynamical approach can be considered as a major advantage over more idealized models considering such thus provided further evidence for a realistic model representation of PBL transport processes. The model agreement with the measurements was also better for BC than PM 10 , as BC is more locally influenced, while PM 10 includes not only predominantly regional influences, but also uncertainties in the complex precursor chemistry. Ultimately, the model representation of the intra-urban variability of BC and PM 10 concentrations was evaluated using the measurements at the road sites. These were distinct from the measurements at the background sites by the significantly elevated concentrations throughout daytime Arguably, the sign of the sensitivity also depends on the distance to the nearby traffic lanes here. It is disputed, however, if the results with the finest grid spacing are more realistic, as turbulent diffusion might be underestimated by neglecting small scale processes like traffic motion. It became also apparent that buildings contribute importantly to turbulent vertical mixing 730 within the roughness sublayer. When decreasing the grid spacing, these turbulent motions are successively better resolved.
Especially in the shear-driven case, we observed a significant grid-size sensitivity of the vertical turbulent scalar flux just above the building roofs. The best explanation for the underestimation of this flux in the default 40 m simulation is a possible underestimation of the drag from the diffusely resolved buildings on the air flow, which would reduce vertical wind shear above the building roofs and also decrease the vertical turbulent flux in favor of the horizontal advective flux. In the convective case, 735 grid-size sensitivity of domain-averaged near-surface BC concentrations could also be traced back to an underestimation of the parameterized vertical diffusivity, especially in the super-adiabatic height range induced from the surface-heat flux. Here, a possible mismatch of the parameterized turbulent Prandtl number was pointed out. In order to further corroborate the reasons behind the observed sensitivity in the vertical scalar fluxes, additional sensitivity runs with variations of the parameters in question (e.g. r 0 , P t ) need to be carried out in future studies focusing mainly on such aspects. Also, we assumed the valid-740 ity of the downscaled surface potential-temperature fields prescribed in the simulation, which affect also the heat flux from building surfaces, mainly in lack of a more physically-based alternative. Here, the further comparison with a microscale model equipped with an own radiation and surface scheme could provide confidence, which was however out of the scope of this study. Finally, in spite of the observed and discussed sensitivity, the comparison of the error in modeled concentrations at the measurement sites showed only slight improvements with a decreasing grid spacing, if any at all. For a more significant model the necessity of more accurately representing other non-physical components in the model, in order to benefit from a more accurate representation of model physics with building-resolving grids. Most notably to mention are the traffic emissions with their currently limited accuracy and comprehensiveness, which may be improved in future simulations with the incorporation of real-time traffic-flux data. Nevertheless, with the currently available data the showcased modeling approach performed at 750 urban gray-zone horizontal resolutions showed to be a very promising tool for application on more targeted research questions that previously relied on mesoscale model outputs, like, e.g., urban population exposure to air pollution.
Code availability. The source code of CAIRDIO model version 2.0, as well as utilities for data pre-processing are accessible in release under the license GPL v3 and later at https://doi.org/10.5281/zenodo.6075354 (Weger et al., 2022).
Data availability. The data used in this study, which include model results and observations, are accessible at https://doi.org/10.5281/zenodo.6077050.

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Appendix A: CAIRDIO v2.0 improvements The actual model version 2.0 used in this paper features additional improvements over the published version 1.0, which apply to several model components and are listed in the following.

A0.1 Revised advection scheme
In CAIRDIO v.1.0, advection used linear 5 th -order reconstructions with additional limiting for positive scalars. It is well 760 known that such upwind-biased odd-order schemes result in numerical diffusion, as the leading error term is diffusive. In LES, numerical diffusion has a detrimental impact on the correct energy transfer, as excessive energy is drained from the smallest scales that feed on the larger eddies, thus affecting the entire energy cascade. The manifestation of excessive damping can be seen in the energy spectra of Figure A1. Nevertheless, some sort of numerical damping of the smallest wavelengths is necessary in order to maintain numerical stability, as these scales are flawed by large dispersion errors. Recognizing that the standard 765 5 th -order linear upwind formulation carried out in each dimension separately is simply the addition of a high-order diffusion term to a non-diffusive 6 th -order central scheme, directly leads to an opportunity to control numerical diffusion: Here, ∆ h is the grid spacing, u + the positive definite transport velocity component, and ∇ 5th a finite difference operator using 5 th -order reconstructions. The product u + ∆ h is called numerical diffusion coefficient, and mainly acts in the dominant 770 transport direction. In the revised scheme, u + is replaced by a constant parameter d = 0.05. Note that this results in isotropic diffusion, similar to the method proposed in Xue (2000) for high-order damping.

A0.2 Prognostic TKE formulation for subgrid-scale mixing
In version 1.0 an algebraic eddy-viscosity formulation was used. Therein, eddy viscosity was diagnosed from the strain-rate 775 tensor S without taking buoyancy effects into account. In order to simulate non-neutral PBLs, we implemented a prognostic subgrid-scale TKE formulation similar to Deardorff 1973 in version 2.0. This scheme not only takes buoyancy effects into account but also avoids the local-equilibrium assumption and thus may provide more accurate results with coarse grid spacings.
The prognostic equation for subgrid-scale TKE is given by The first two terms correspond to the advective-diffusive transport, which also incorporate the pressure-correlation term parameterized by a doubling of the diffusive flux. The shear-production term is parameterized with the squared magnitude of S and the buoyancy-production term results from the squared Brunt-Väisälä frequency N c multiplied with the eddy diffusivity k c . Finally, the dissipation term contains a stability-dependent subgrid-mixing length, which is formulated by

785
where ∆ = (∆ x ∆ y ∆ z ) 1/3 is the static (grid) mixing length. The eddy viscosity coefficient k m is parameterized according to: Note that we replaced l sgs with ∆ therein, as the original formulation resulted in a too small eddy diffusivity for stable stratifications within the roughness sublayer of diffuse urban canopies. We argue that in such a case, the mixing length is always at least as large as the typical building height, and thus not really stability dependent therein. c m and c e are model Lastly, the eddy diffusivity k h for heat and scalar transport is related to k m by the inverse turbulent Prandtl number: In Deardorff (1973), P r −1 t is parameterized according to However, as pointed out in paragraph 3.3.1, the neutral value of P r −1 t may be too low in unstable conditions (cf. Li et al. 2015), and if a negative impact from this is further corroborated, the stability dependency will be entirely replaced by another formulation in a future model version.

810
where <> wr is the filter operation with filter width w r . In a second step, the turbulent fluctuations are re-scaled to match a prescribed target intensity by: Here a max is a factor limiting the amplification of turbulence.  Figure A2 demonstrates the explained turbulent boundary condition based on a sensitivity study using domain L0, and with the same mesoscale forcings and lateral boundary conditions applied as in the main L0 simulation. The averaging period for the computed vertical fluxes w w , c BC w (Fig. A2 a-b) and the mean concentration profile of BC c BC (Fig. A2 c) (2014) was implemented, which considers the bulk-size categories PM 2.5 , PM 2.5−10 and PM 10+ . Accordingly, the deposition flux of a given particle category on a horizontal surface is given by the particle mass concentration c pm times the parameterized deposition velocity v d , which contains the contributions from gravitational settling v g , aerodynamic resistance r a and surface resistance r s : 845 v g primarily depends on particle size and can thus be set to a constant. For PM 2.5−10 a value of 10 −4 m s −1 is used, while for PM 2.5 gravitational settling is neglected. The aerodynamic resistance is computed according to where u * is the friction velocity and t h the surface-transfer coefficient for heat, also used in the parameterization of heat and moisture fluxes. Finally, Zhang and He (2014) provide empirical relationships for the surface-depostion velocity v ds , which is 850 the inverse of r s . For PM 2.5 , a linear dependency on u * is assumed while PM 2.5−10 uses a cubic formula for land-use classes with constant leaf-area index: The coefficients a 1 , b 1 , b 2 , and b 3 are adjusted to the different land-use classes considered by the scheme. To obtain the final and summed up.
Since clouds are not computed in CAIRDIO, wet deposition is solely based on precipitation (sub-cloud) scavenging, for which precipitation rates pr [kg m −2 s −1 ] of the mesoscale host simulation are inferred from. It is assumed that throughout the 860 simulated vertical range of the PBL, the precipitation rate is constant. As for the scavenging coefficients, 0.104 m 2 kg −1 and 0.418 m 2 kg −1 are assumed for the categories PM 2.5 and PM 2.5−10 , respectively.
Appendix B: Evaluation of modeled urban meteorology with near-surface observations For the evaluation of urban meteorology in the model, near-surface observations of hourly-averaged wind speed, wind direction and air temperature are additionally available to the air-quality measurements at the air-monitoring sites LL and LC, respec-865 tively. In Figure B1 respective observations are compared with outputs from the mesoscale model run COSMO M3, the default CAIRDIO simulation L0, and the concerning nested CAIRDIO simulation with 5 m grid spacing at the sites LC and LL. The nested model runs allow to discuss some aspects of the sensitivity to grid spacing. Wind speed and direction at site LC (Fig.   B1a, c), which is surrounded by more open areas, shows a much more complex evolution over time than suggested by the lidar observations aloft (cf. Fig. 11a). The measured wind speed is the highest (up to 5 m s −1 ) during the periods of a convectively 870 enhanced PBL around midday of both days, and generally lower during a nocturnal shallow PBL, which can be both explained by different rates of turbulent vertical momentum transport. The most frequent wind directions are either from the west or the east with quite abrupt turnings, which indicates a significant influence of nearby buildings. Since mesoscale simulation M3 contains only parameterized building effects in combination with a 550 m horizontal grid spacing, it is not surprising that the modeled profiles (blue lines) do not follow the observed profiles of wind speed and wind direction very well. Significantly 875 more realistic are, however, the according temporal profiles of the CAIRDIO simulation L0 (orange lines), as they follow the observed trend quite well, even though some underestimation of wind speed (up to 2 m s −1 ) is evident during the periods with the highest observed wind speeds. The locally nested simulation with 5 m grid spacing (red lines) shows little improvements at this site. For the street-canyon site LL (Fig. B1b), measured wind speeds are generally mostly below 2 m s −1 , while the wind direction (Fig. B1d) shows a jump profile with two possible wind directions either from the west or east, which is nearly paral-880 lel to the canyon orientation. All compared model runs show a quite good agreement with the measured profile of wind speed, however, the jump profile of the wind direction is neither reproduced by the COSMO M3, nor by the CAIRDIO L0 simulation.
Strikingly is, however, the nearly spot-on result of the nested CAIRDIO simulation with 5 m grid spacing. Note that the jumps are already seen in the nested run with 20 m grid spacing (not shown). Obviously, the 40 m run averages the wind field over a large area that is not yet representative to the specific location inside the street canyon, but nevertheless this simulation provided 885 accurate boundary conditions for the nested simulation. Lastly, in Fig. B1e-f also measured air temperature is compared with respective profiles from the models. Notably is that both measured profiles are quite similar, despite the significantly different environments the stations are located in. Generally speaking for both sites, the modeled profiles follow the measured trend quite well, even though some specific deviations are noticeable. Firstly, during the morning of the first day, the models show a delayed climb in temperature, and also underestimate air temperature by up to 2 K after midday of March 1 throughout the 890 rest of the day until early March 2. Secondly, a sudden short-term drop in temperature of 3 K is measured around 1 March 12:00 UTC, but is absent in the simulations. A comparison of modeled rain rates with observation ( Fig. 10) reveals that 1.2 mm of precipitation fell over a wider area during this specific time, while no precipitation occurred in the model at the same time.
While the observed precipitation totals had a negligible impact on air quality, an impact on near-surface air temperature could still be seen. Finally, it is still worth mentioning that the differences between the different models are small, i.e. the CAIRDIO 895 simulations do not significantly perform better than the COSMO simulation. This indicates that while the surface-temperature downscaling described in Section 2.4.2 satisfies it's purpose to represent the thermal effects of the surface, it's accuracy still very much depends on the accuracy of the mesoscale simulation. To overcome this limitation, an own land-surface model for CAIRDIO, including a detailed parameterization of radiative interactions, would be needed. Competing interests. All authors declare that they have no competing interests.
provided by the LfULG. Building geometries and orography (DGM1) are available from the State Enterprise for Geographic Information and Surveying Saxony (GeoSN). We thank Johannes Bühl for the Doppler-lidar based horizontal wind profiles used in the model validation.
The Doppler wind lidar was funded by BMBF under FKZ: 01LKL1603A. The precipitation measurements and radiosonde data used in the paper were downloaded from the CDC-OpenData platform of the Deutscher Wetterdienst (DWD). We thank the DWD for good cooperation and support.