The WS700 meteorological sensors (Lufft GmbH) provided air temperature, relative humidity, wind direction, wind speed, global radiation, pressure, and precipitation data. Different trace gas sensors measured O3, CO2, NO2, and SO2 gas compositions. An aethalometer (AE51; Aethlabs Inc.) measured the temporal variability of equivalent black carbon (eBC) concentrations . An HR-ToF-AMS equipped with an aerodynamic lens was installed in a mobile container to continuously measure total non-refractory particle mass as a function of size (up to 2.5 µm particle aerodynamic diameter) at a temporal resolution of 30 s. The AMS inlet was connected to a PM2.5 head (flow rate 1 m3h-1; Comde-Derenda GmbH) and a stainless-steel tube of 3.45 m length. The AMS data were analysed with AMS data analysis software packages SQUIRREL (version 1.60C) and PIKA (version 1.20C). Positive matrix factorization PMF; was applied for AMS data to identify different aerosol source factors for source appointment . This allows us to differentiate organic aerosol in terms of, for example, hydrocarbon-like OA (HOA), cooking-related OA (COA), nitrogen-enriched OA (NOA), biomass burning OA (BBOA), semi-volatile oxygenated OA (SV-OOA), and low-volatility oxygenated OA (LV-OOA). The mass spectra of these five OA factors resolved from the PMF analysis are shown in Fig. S2. These in situ data were averaged over 10 min. Detailed information about in situ measurements and aerosol chemical composition is introduced in .

In addition to in situ container measurements, radiosondes at Schnarrenberg meteorological station (SB; see Fig. b) were launched by the German weather service (DWD) to measure the vertical profile of meteorological parameters (e.g. temperature, humidity, pressure, and wind). The vertical profiles of temperature and humidity were used to determine boundary layer heights. Detailed descriptions of boundary layer retrieval methods were introduced in previous publications .

Figure S5a, e, and i show the correlation between boundary layer heights and PM10, eBC, and BBOA concentrations for three different subsets of data, respectively. The colour of the scatter points indicates the relative humidity. For all PM10 data points, an anti-correlation, as shown in Fig. S5a, was found for boundary layer heights above 900 m (R=-0.44, Pearson correlation coefficient, same hereafter). This anti-correlation means that a deeper boundary layer diluted the aerosol, while a shallower boundary layer concentrated aerosol at the ground level. The aerosols were diluted by transporting them from a near-ground level to higher altitudes during boundary layer mixing process. However, we also found a positive correlation between PM10 and boundary layer heights for boundary layer heights below 900 m a.s.l. (R=0.32). This positive correlation is also reported in and typically coincided with low wind speed and high relative humidity, indicating typical properties of the nocturnal boundary layers.

Then, the data were divided into three groups for three different time periods – morning (04:00–10:00 UTC) (b, f, j), afternoon (12:00–18:00 UTC) (c, g, k), and night (18:00–04:00 UTC) (d, h, l). The correlation between the boundary layer and surface aerosol concentrations (PM10) in the these three subplots (b–d) is positive for PBL heights below 900 m a.s.l. (R=0.31 (Fig. S5b), 0.58 (Fig. S5d)) and weaker but negative for larger PBL heights (R=-0.64 (Fig. S5b), -0.49 (Fig. S5c), -0.22 (Fig. S5d)). The correlation between boundary layer heights and eBC, as well as BBOA concentrations shown in Fig. S5, revealed that the eBC and BBOA concentrations are always anti-correlated with the boundary layer heights (R=-0.25 (Fig. S5e), 0.21 (Fig. S5i)). The reason for the positive correlation between PM10 and boundary layer height below 900 m a.s.l. is the fact that the local emissions and aerosol water are taken up during the night and in the early morning. The reason for only anti-correlation between the boundary layer heights and eBC, as well as BBOA concentrations, is that the eBC and BBOA emitted particles from sources like biomass burning or traffic are smaller and less hygroscopic and thus could be diluted by boundary layer evolution.

A good case to illustrate this phenomenon is shown in Fig. . The chemical composition measured by the AMS is shown in Fig. b. From this figure, we found that the mass concentration of various aerosol components (e.g. ammonium sulfate, ammonium nitrate) increased from 13 February at 18:00 to 14 February at 05:00 UTC, while the boundary layer heights increased slowly during this time period, which caused a positive correlation between the boundary layer and PM10 concentration. However, the eBC and BBOA concentrations shown in Fig. c and d are constant in the night-time. Hence, the PM10 concentrations can be correlated with boundary layer heights, while eBC and BBOA concentrations are always anti-correlated with boundary layer heights.

The above statistical data analysis of the correlation between ground-level aerosol concentrations and the boundary layer heights is based on data collected during 1 month. More data were analysed to support this relationship. Figure S6 shows the diurnal variations of PM10 and the boundary layer heights based on 2-year data from 1 January 2020 to 31 December 2021 in Stuttgart. The PM10 concentrations are the hourly reported data by LUBW, and the boundary layer heights are from the ERA5 dataset. Figure S6 shows a positive correlation between boundary layer heights and PM10 concentrations between 04:00 and 08:00 UTC as shaded in Fig. S6, and this positive correlation is possibly related to local morning emission or water take up during the morning rush hour. In addition, the increasing boundary layer after sunrise (08:00–12:00 UTC) diluted the aerosol within the boundary layer, thus causing a decrease in PM10 concentrations.

The diurnal variations of PM10 concentrations and the boundary layer heights are shown in Fig.  for the winter of 2018 based on our measurement (top panel) as well as different seasons based on LUBW and ERA5 data. This also shows that the ground-level PM10 concentrations are correlated with boundary layer heights from 04:00 to 08:00 UTC for all datasets. However, the strength of the correlation is different for different seasons. The spring (MAM) shows the strongest correlation (Pearson correlation coefficient: 0.83), while the winter (DJF) shows the weakest correlation (Pearson correlation coefficient: 0.26). In addition, the summer has the highest mixing layer height (1283 ± 399 m) while the winter has the lowest mixing layer height (682 ± 542 m) as expected due to the solar radiation being strongest in summer while weakest during winter. The ground-level PM10 aerosol concentrations are anti-correlated with mixing layer heights and show the highest concentrations during winter (33 ± 32 µgm-3) and the lowest concentrations during summer (16 ± 7 µgm-3). From the correlation between PM10 concentrations and boundary layer heights, we conclude that the ground-level PM10 concentrations are anti-correlated with mixing layer heights but correlated with nocturnal boundary layer heights.

In Fig. , the evolution of the boundary layer heights and their effect on surface aerosol mixing processes is illustrated for the whole measurement period. In this section, two cases (13–14 and 24–25 February 2018) are selected to demonstrate these processes in detail. The case from 13 to 14 February was selected due to the low wind speed (0.76 ± 0.35 ms-1). The low wind speed minimizes the impact of horizontal transport, allowing for more accurate analysis of local atmospheric conditions. Additionally, the clear skies during this 2 d period ensured sufficient solar radiation to fully engage the boundary layer dynamics. In contrast, the case from 24 to 25 February was chosen due to the presence of clear skies but with relatively stronger wind speeds (2.2 ± 0.6 ms-1). This selection allows for a comparative analysis of these two cases, highlighting the differences that wind speed can introduce to atmospheric conditions under otherwise similar solar radiation conditions.

Figure a shows the time series of lidar-retrieved vertical backscatter coefficients, the boundary layer heights (solid white line), the residual layer (RL) heights (dashed white line), and the boundary layer heights from the ERA5 dataset (dashed grey line), as well as the boundary layer heights retrieved from radiosondes (yellow triangles). Please note that the altitude used here is the height above sea level. The reason for using altitude instead of height above ground level is that the altitudes of these three observation stations are different, as shown in Fig. a. The vertically distributed backscatter coefficients are shown from the ground level to the free troposphere by merging zenith and near-horizontal (5° above the horizon) measurements. The time series of aerosol chemical composition measured by AMS is shown in Fig. b, and the PMF analysis result of the organic aerosol with five factors is shown in Fig. c. In addition, the potential temperatures (θ) from the microwave radiometer and turbulent kinetic energy (TKE) from wind lidar data are shown in Fig. e and f, respectively. Finally, the eBC concentrations and solar radiation are shown in Fig. d and g, respectively.

The vertically extended backscatter coefficients in this figure show that most of the aerosol only stayed within the boundary layer or residual layer and could not reach the free troposphere, as stated in previous publications . We also found that the mixing layer heights measured by lidar and radiosondes show good agreement in this case.

A decreasing trend of the residual layer height and a weakly increasing PBL height at around 550 ± 93 m a.s.l. can be seen during night-time. The shallow and nocturnal boundary layer and increased emissions during the morning rush hour (05:00–10:00 UTC) caused a rapid accumulation of aerosol near the surface, as can be seen from the low-altitude backscatter coefficients and ground-level in situ measurements. Driven by increased solar radiation after 10:00 UTC on 14 February, the boundary layer height increased and diluted the aerosol within the boundary layer, thus causing a decrease in aerosol concentrations at ground level. Furthermore, we found that the aerosol concentrations increased more during the morning rush hour (05:00–10:00 UTC) than during the evening rush hour (17:00–20:00 UTC), mainly due to the shallow boundary layer in the morning. The increased aerosol during the morning and evening rush hour is related to the emissions of traffic (HOA) and industry (amine-based OOA) as can be seen from the PMF analysis results shown in panel (c). At night-time, the potential temperature inversion shown in panel (e) and a small value of turbulent kinetic energy (TKE) shown in panel (f) indicate a stable and shallow boundary layer.

In order to investigate the effect of local emission on ground-level aerosol concentration, we need to normalize aerosol concentration by the boundary layer. The normalization was conducted in two following steps: (1) The boundary layer height was normalized to get unitless boundary layer height. (2) The aerosol concentration was multiplied by the unitless boundary layer height. Figure S7 shows a similar plot to Fig.  but with the ground-level aerosol concentration normalized by the boundary layer heights (daytime) or residual layer height (night-time) . This figure shows that the nitrate aerosol particle mass increased from 3.9 to 10.8 µgm-3 in the morning rush hour (06:00–12:00 UTC) on 14 February 2018. While during the night-time (18:00–04:00 UTC), the nitrate aerosol particle mass increased from 2.5 to 3.9 µgm-3, the eBC concentrations decreased by more than 50 % from 1048 to 464 ngm-3. However, we need to be careful with this result, especially during night-time, as the aerosols are not well mixed but instead accumulate near the ground level. Hence, this normalization would be underestimated when considering the total aerosol concentration within the boundary layer. The aerosol horizontal transport source was not considered because the wind speed was 0.76 ± 0.35 (less than 1 ms-1 in most of time) from 18:00 13 February 2018 to 12:00 UTC 14 February 2018. The only considered source during this period is local emission. The reason for the increase in non-refractory particles concentrations but the decrease in eBC concentration is that the non-refractory particles were emitted during the night-time or take up water due to high relative humidity, while the emissions of eBC particles were diluted due to a slight increase in the nocturnal boundary layer during the night-time .

Interestingly, we found in this case that the boundary layer height increased more slowly on the second day (14 February) than that on the first day (13 February). There was a time delay in the boundary layer convection during the second day despite the solar radiation being the same in this 2 d period (Fig. 4g). The reason for these different boundary layer evolutions is different vertical thermal structures, as can be seen in the vertical temperature profiles given in Fig. e and h. On the first day, the temperature inversion is weaker, and the TKE is larger than on the second day, as can be seen from Fig. e and f, which means that it takes a shorter time to transform the nocturnal boundary layer into the convective boundary layer. Hence, the boundary layer grew faster on the first day than on the second day. One explanation of these thermal structure differences for this 2 d period is the presence of clouds during the first night. They prevented longwave emissions and weakened the temperature inversion, which caused a neutral boundary layer during night-time. Furthermore, the boundary layer grew faster after sunrise due to this neutral boundary layer in the morning. Finally, the delay of the boundary layer convection process on the second day prevented diffusion of aerosol during the morning rush hour (05:00–10:00 UTC, 14 February), thus causing accumulation of aerosol at ground level, as shown in Fig. a–c. The conceptual schematic for this phenomenon is summarized in Fig. . The different boundary layer mixing in this 2 d period has a substantial impact on ground-level aerosol concentrations. As can be seen from Fig. , significantly more aerosol accumulated on 14 February due to lower boundary layer heights before 12:00 UTC. Here we assume similar emissions on these 2 weekdays.

Figure  shows the results during case 2, in which the same methods as in case 1 were applied, but different patterns were shown. The most obvious phenomenon is that a sharp decrease in aerosol concentrations from 07:00 to 12:00 UTC on 24 February was observed, even though the boundary layer heights only increased from 1042 to 1280 m a.s.l. In addition, the boundary layer heights did not decrease after sunset of 24 February, as shown in the red rectangle. Furthermore, the boundary layer heights measured by radiosondes are higher than those derived from lidar measurements, in contrast to case 1 (Fig. 4). The possible reason for the differences in boundary layer height for case 2 could be as follows: the radiosonde site (SB; 321 m a.s.l) is at a relatively higher altitude compared to the lidar site (RSP; 247 m a.s.l.), as shown in Fig. 1b. Additionally, the wind speed is much higher (2.2 ± 0.6 ms-1) for case 2, as shown in Fig. S8. This higher wind speed can induce updrafts, causing an increase in the boundary layer height. We also found that the aerosol concentrations at ground level were much lower on 25 February than those on 24 February, corresponding to a higher boundary layer on 25 February. Finally, the PMF analysis result shown in panel (c) shows a large fraction of LV-OOA for organic composition, which is typically more related to regional transport .

Figures  and  showed different boundary layer evolution and different patterns of aerosol concentrations at ground level, even with a similar evolution of solar radiation, as shown in panel (g) of both figures. However, the evolution of temperature and wind is different, as shown in Fig. S8. Comparing the meteorological background in these two cases, we found that the temperature decreased more rapidly for case 2, as shown in the bottom panel of this figure. This decrease caused a lower temperature on 25 February. The temperature was below 0 °C, even during the day on 25 February. In addition, a higher wind speed was observed from 07:00 on 24 February to 16:00 UTC on 25 February for case 2. Then, the wind speed began to decrease, and the wind direction also changed from east to north from 16:00 UTC on 25 February. All this meteorological information indicates that a cold front passed by the observation station from 24 and 25 February, affecting local temperature and wind, thus having an impact on the boundary layer evolution and aerosol distributions in the boundary layer. The high wind speed during this cold front causes strong turbulence in the boundary layer, thus increasing the boundary layer heights, especially at night-time. In addition, this high wind speed also blew the local aerosol away and caused a low aerosol concentration on 25 February.

From the above two cases, we conclude that the evolution of the boundary layer was affected by related meteorological factors such as solar radiation, clouds, wind speed, and wind direction, which in turn affect the aerosol distribution in the boundary layer.

Case 1 outlined above is a good example of boundary layer evolution and aerosol mixing processes for 2 consecutive days. The comprehensive dataset collected during this case provided us a good opportunity to evaluate the LES model PALM-4U. To simplify, we use the altitude above the ground level (a.g.l.) to compare observational results with model simulations as the coordinate used in the model is the height above ground level.

The diurnal development of the boundary layer temperature fields as simulated by PALM-4U is shown in Fig.  as the time–height section above the RSP site, as indicated in Fig. b. Nocturnal cooling near the surface underneath the residual heat from the daytime and the stabilization of the boundary layer were captured by the model dynamics. During daytime, neutral, convective conditions were simulated with reoccurring stabilization, after longwave radiative cooling outweighed shortwave radiative heating at the surface. We found these thermally driven circulation processes to be simulated in a plausible way qualitatively, based on the observational data we compared the simulation results to. An exact quantitative comparison and an attribution of deviations have not been part of this study, as the focus was on the measured data. More detailed comparisons between two more scanning Doppler wind lidars and PALM-4U were conducted but will be published elsewhere, as this analysis of the model dynamics is not within the scope of this paper. Turbulence was evaluated for summer cases by .

To compare aerosol spatial concentration between the PALM-4U simulation and observations, we convert lidar-derived extinction coefficients to PM2.5 concentrations using a conversion factor calculated from ground-level PM2.5 concentrations (OPC, Fidas200) and ground-level lidar-derived extinction coefficients. Figure S9 shows a good linear correlation between extinction coefficients and PM2.5 concentrations, with a slope of 78 182.0 ± 1132.0 and Pearson correlation coefficient of 0.822; this good correlation ensures the quality of this conversion. Figure  shows the time series of the PM2.5 concentrations retrieved from lidar measurements and PALM-4U. Figure c shows time series of PM2.5 concentrations from ground-level OPC measurements and from a PALM-4U simulation, which indicates that the simulated PM2.5 concentrations show a similar trend to the observational data except for the spin-up period (before 12:00 UTC 13 February) but underestimate the PM2.5 concentrations by a factor of 4.5 ± 2.1. The spin-up period ensures that the atmosphere is in balance with the new surface temperature and soil properties and that the atmospheric chemistry approaches an equilibrium state. The comparison of vertical extended PM2.5 concentrations from lidar measurement and the model simulation shows that PALM-4U agrees well with lidar observation in terms of boundary layer evolution and aerosol transport and mixing processes. This is in line with our objectives and the scope this study.

Several factors of uncertainty contribute to this underestimation, namely emissions, transformation processes, and initial and lateral boundary conditions (ICs and LBCs). Residential emissions are not included in this simulation, which we expect to be a significant source in winter. Furthermore, traffic emissions are parameterized based on street type and time of day . These very simple assumptions cannot accurately simulate the true emissions, especially if traffic congestion amplifies true emissions. High levels of HOA (traffic related aerosol) were identified in the PMF analysis of organic aerosol, as shown in Fig. c, which substantiates the assumption that this is a large source of uncertainty in our simulation. Finally, the IC and LBC for this simulations were based on the nocturnal profile on 14 February 2018 at 00:00 UTC. Providing spatially and temporally variable IC and LBC would most likely improve agreement of the regional background concentrations and allow us to disentangle this contribution to the total uncertainty from the local emissions. We found that the large distance from the outer domain boundary to the inner domain boundary (> 3 BLH during daytime) allowed sufficient “spin-up” mixing upstream of the child domain, such that turbulence and vertical distribution behaved plausibly. Depending on the grid spacing of 40 m, the spatial heterogeneity transported into the child domain was however quite diffuse, as expected. It is also noteworthy that only road emissions, transport, and dry deposition were simulated here. Particulate processes like aggregation, wet deposition, chemical transformation or secondary aerosol formation are not accounted for, with the underlying assumption being that on local scales and 24 h timescales, primary emissions and transport are more dominant. As mentioned in the Introduction, 58 % of the PM10 has been attributed to road emissions . This being an annual average, the omission of residential heating emissions most likely accounts for a large fraction of the simulated underestimation during this cold winter period. Additionally, most smaller roads are not fully represented in the parent domain with 40 m grid spacing, such that the regional urban background road emissions might be underrepresented with contributions only from highways and other large road structures. This is substantiated by our finding that HOA is dominant in these periods, as shown in Fig. d.

Figure  shows a range–height cross section of PM2.5 concentrations derived from lidar measurements and the PALM-4U simulation during two different periods (09:12–09:20; 16:07–16:15 UTC) on 14 February 2018. As we already know that the PALM-4U underestimated the PM2.5 concentrations by a factor of 4.5 ± 2.1, we scaled up the PM2.5 concentrations from the PALM-4U simulation by a factor of 4.5 to better demonstrate aerosol spatial distribution. The figure panels in the first row demonstrate the aerosol spatial distribution in the early morning, which reflect a similar shallow boundary layer and high ground-level aerosol loading. The figure panels in the second row show the aerosol spatial distribution in the afternoon, which reflects a well-mixed boundary layer and relatively low-concentration and homogeneous aerosol distributions. Compared with the observational data, PALM-4U simulated the aerosol spatial distribution and boundary layer structure well. However, there is still some inconsistency that needs to be cleared up. Compared to observational data, the model shows more homogeneous spatial and temporal aerosol distribution, especially for the case in the afternoon, as shown in the second row of Fig. 9. One possible reason for this inconsistency is that the PALM-4U did not resolve all turbulent eddies (i.e. limited by 10 m grid spacing) as stable winter conditions might require finer grid spacings. The lack of spatial and temporal detail in the emissions also contributes to the diffuse characteristic of the simulated concentration fields. Another reason for this lack of structure could be associated with the time averaging; 10 min might be long enough to blur many small-scale instantaneous structures that the instrument might detect in a scan.