Large-eddy simulation of the optimal street-tree layout for pedestrian-level aerosol particle concentrations – A case study from a city-boulevard

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Road traffic is one of the main sources for urban air pollution (Fenger, 2009) and as a result the largest pollutant 2.1.1. Canopy model 126 The aerodynamic effect of vegetation on flow is taken into account by an embedded canopy model. Vegetation decelerates the flow by acting as a momentum sink, the magnitude of which depends on the wind velocity, leaf area density (LAD, m 2 m −3 ) and the aerodynamic drag coefficient following: where represents the wind components ( 1 = , 2 = , 3 = ). Furthermore, the effect on the SGS-TKE ( ) 127 is considered with an additional sink term in its prognostic equations: LAD is defined as the total one-sided leaf area per unit volume and quantifies the form and viscous drag forces on solid surfaces and vegetation. The advection and diffusion of aerosol number and mass are solved in the Eulerian 141 framework.

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Dry deposition on vegetation produces a sink term in the prognostic equations of concentrations where is the aerosol number concentration in size bin and , is the dry deposition velocity, which can be solved using the parametrisation either by Zhang et al. (2001) or Petroff and Zhang (2010). On solid surfaces, dry deposition is implemented by means of a surface flux: The same equations apply for mass concentrations , , where is the chemical component.  The simulations are performed for a realistic city boulevard and its generalised surrounding neighbourhood (Fig. 1).

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Five street-tree layout scenarios (S1-S3) in addition to a baseline scenario without any trees (S0) are studied (Table 1   161 and Fig. 2). In scenarios S0, S2A, S2B and S2C the boulevard is 54 m wide, while it is 4 m wider in S1 and 4 m 162 narrower in S3. The scenarios were decided together with local urban planners and the different street widths are 163 suitable for each of the street-tree layout varying from two to four rows of trees. In all scenarios, there are in total eight 164 traffic lanes. Tram lines are located in the middle and cycle lanes and pavements on both sides of the boulevard. As 165 a default, the street trees are 15-m-tall Tilia × vulgaris (deciduous) trees, but in S2C the outermost trees are 9-m-tall 166 Sorbus intermedia (deciduous). In S2B with three rows of trees, uniform hedges of 1 m in width and 0.75 m in height 167 are set below the canopies of the outermost trees. In addition to the boulevard, some Tilia × vulgaris trees are also 168 added to the surroundings (see Fig. 1).

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The city blocks along the boulevard are manually constructed into a three-dimensional model based on a develop-    186 Traffic-related emissions are treated as area sources from the eight 3-m-wide traffic lanes (Fig. 2) Table 1 for details. is the plan area fraction (i.e., fraction of the building plan area to the total plan area) and is the frontal aspect ratio (i.e., ratio of the building facade area in the direction of the mean wind to the total plan area).

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The sectional representation of the size distributions is shown in Fig. S3.  Table 2. aerosol size distribution is modelled for a size range 3 nm-10 µm using ten size bins (see Table S1). Dry deposition  Surface roughness equal to the idealised generic roughness elements (Table 2)  stepping scheme (Williamson, 1980). The pressure term in the prognostic equations for momentum is calculated using 251 the iterative multigrid scheme (Hackbusch, 1985).

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All simulations are first run for = 600 s after which data output is collected for the following = 1 h. Simulations  used to refer to pedestrian areas on the side of streets which in American English would be referred to as sidewalks.

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To represent the magnitude of the mean circulation within the street canyon, a volumetric flow rate across the street canyon per unit length is calculated for the perpendicular wind direction (WD = 82 • ). The mean circulation is defined from the stream function averaged along the boulevard in rotated coordinates so that -axis is perpendicular and -axis is parallel to the boulevard, is the height above Vertical turbulent flux measures pollutant ventilation due to turbulent transport. In this study, is calculated only for the aerosol size bin 6 ( = 303.3 nm) because this size range has the lowest deposition velocity (Kurppa et al., 2019) and is thus least affected by dry deposition. Hence, bin6 is the covariance between and aerosol number concentration where ′ ( , , , ) and The mean (MKE) and turbulent kinetic energy (TKE) of the flow at tree heights ( = 1.9 − 14.6 m) were studied independently. MKE was calculated as N WD where , and are the one-hour averaged wind components in ( , , ) direction, and TKE as where ( ′ ) 2 , ( ′ ) 2 and ( ′ ) 2 are the one-hour averaged variances of the wind components.   Table   292 3) and PM 2.5 by 1-72 % ( Table 4). The scenario S2C with three rows of trees and smaller outermost trees shows least  Table 3 Relative difference in mean (median in brackets) PM 10 (%) concentrations on the pavements compared to baseline scenario S0 at = 1.9 m.

Table 4
Relative difference in mean (median in brackets) PM 2.5 (%) concentrations on the pavements compared to baseline scenario S0 at = 1.9 m.
If the relative differences of the mean and median values are calculated, S2C shows the lowest concentrations 300 relative to the treeless case S0 and increases PM 10 by 69 % and PM 2.5 by 33 % compared to >75 % and >35 %, 301 respectively, in other scenarios. One should notice that besides the tree layout, the street widths are different in scenarios 302 S0, S2A, S2B and S2C, S1 and S3 and thus the pure effect of trees can be revealed only by comparing the scenarios with 303 the same street-canyon width (S0, S2A, S2B and S2C). The three rows of uniform trees in S2A create the highest mass 304 concentrations on the pavements (+88 % and +42 % for PM 10 and PM 2.5 ), yet the increase in concentrations is smaller 305 when hedges are introduced below the tree canopies in S2B (+75 % and +35 % for PM 10 and PM 2.5 , respectively). The 306 effect of trees is stronger on PM 10 than on PM 2.5 concentrations. Slightly higher mass concentrations are observed in 307 S3 (narrower) than in S1 (wider). concentrations when compared to the three rows of uniform trees (in S2A). The influence of trees on aerosol number is 319 much less (the maximum difference compared to the treeless scenario 53 %) than those on aerosol mass (the maximum 320 difference 120 % for PM 10 and 71 % for PM 2.5 ).

Table 5
Relative difference in mean (median in brackets) tot (%) concentrations on the pavements compared to baseline scenario S0 at = 1.9 m.
The lowest concentrations observed in S0 are concurrent with, on average, the most effective vertical dispersion 322 of aerosol particles (see vertical profiles in Fig. S5-S7). Similarly, the notably low values in S2C on the eastern side 323 with perpendicular wind coincide with clearly more effective vertical dispersion (Fig. S5b, S6b and S7b). The relative 324 differences in the vertical profiles between the scenarios are larger for tot than PM 2.5 and PM 10 , which is consistent 325 with the spread in the mean values and variation (Fig. 5, 6 and S4).

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To compare the street-tree scenarios without the impact of varying street widths, the relationship between the crown 327 volume fraction (CVF, the total tree crown volume divided by that of the entire street canyon; Table 1) and the mean 328 concentrations (PM 10 and tot ) on the pavements (Fig. 7) is examined. CVF varies from 0 to 0.19, with the smallest 329 non-zero CVF in S2C with variable tree heights and the largest in S1 with four rows of trees and a slightly wider street  > 800 nm (see Fig. S3).

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With parallel wind, S2C shows the smallest and S1 the largest differences compared to S0, while with perpendicular 352 wind |Δ⟨ ⟩| is generally the smallest in S1. Especially for aerosol particles > 1 µm, Δ⟨ ⟩ are higher for the 353 parallel than the perpendicular wind direction. Interestingly, ⟨ ⟩ for this size range is still noticeable higher above the 354 mean building height when the wind is parallel to the boulevard (Fig. 8g). This is observed both for the upwind and 355 downwind part of the boulevard (see Fig. S9).

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Comparing CVF and Δ⟨ ⟩ for different aerosol size ranges over the whole boulevard shows that for UFP ( < 357 100 nm), Δ⟨ ⟩ decreases with increasing CVF with no systematic difference in wind directions (down to -20 %, see   The mean values and variation of vertical turbulent exchange ⟨ bin6 ⟩ (see Eq. 6) over the whole boulevard at two 365 heights are shown in Fig. 9 and Table 6. The lower level ( = 14.6 m) is located near the crown top of Tilia × vulgaris 366 trees (Fig. 3) and the upper level ( = 23.6 m) around 3 m above the highest buildings (Table 2). With parallel wind 367 ( Fig. 9a and c), introducing trees to the boulevard increases ⟨ bin6 ⟩ at both levels by 13-70 %. On average, ⟨ bin6 ⟩ is and hence also fluxes are slightly higher in the northern end (not shown).

Table 6
Relative difference in hourly mean (median in brackets) ⟨ bin6 ⟩ (%) compared to S0 over the whole boulevard at = 14.6 m and = 23.6 m. ⟨...⟩ denotes the average over the whole boulevard. With perpendicular wind ( Fig. 9b and d), ⟨ bin6 ⟩ at the lower level is clearly highest in S0 without trees (mean 375 6.3 × 10 5 m −2 s −1 ) and lowest in S1 with four rows of trees (-65 %). Thus, trees disturb the vertical turbulent transport 376 from the boulevard with perpendicular wind. Actually, the 25-percentile of ⟨ bin6 ⟩ is even negative for S1, S2A and 377 S2B indicating entrainment of more polluted air to the street canyon on the eastern side of the boulevard (not shown).

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However, above rooftop the hourly averaged fluxes become very uniform and the impact of trees on the average fluxes 379 nearly disappears. Only difference is the slightly lower variation in S1 and S2C.

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For the mean flow transport of aerosols, Fig. 10 shows the pedestrian-level a) ⟨PM 10 ⟩ and b) ⟨ tot ⟩ as a function which shows how the dry deposition is more effective for the smaller particle size ranges.

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To further assess the relationship of the mean flow and turbulence with ventilation, pedestrian-level ⟨PM 10 ⟩ is 389 analysed as function of ⟨MKE⟩ and ⟨TKE⟩ at several heights (Figs. 11 and 12). Generally, larger ⟨MKE⟩ values 390 are observed with wind parallel to the boulevard than with perpendicular wind. Also, the mean ⟨MKE⟩ within the 391 street canyon is clearly largest in S0, which can be expected as trees act as momentum sinks. With parallel wind, 392 the pedestrian-level ⟨PM 10 ⟩ shows negative linear relationship with ⟨MKE⟩, especially with ⟨MKE⟩ 14.6 m . Instead, 393 no linear relationship between ⟨MKE⟩ and ⟨PM 10 ⟩ can be observed with perpendicular wind and all scenarios with 394 trees show nearly equal ⟨MKE⟩ values. But as shown above, increasing , which specifically measures the mean 395 circulation under perpendicular wind, is shown to decrease pedestrian-level concentrations (Fig. 10). Similar behaviour 396 between ⟨PM 10 ⟩ and ⟨MKE⟩ is observed also when focusing only on concentrations on the pavements, except that the 397 relationship is slightly weaker (see Fig. S11 ans S12). Furthermore, results are also alike for tot (see Fig. S13-16).

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The relationship of ⟨TKE⟩ and ⟨PM 10 ⟩ is more complicated (Fig. 12). In general, trees decrease TKE as also 399 shown in Santiago et al. (2019). No linear relationship between ⟨TKE⟩ and ⟨PM 10 ⟩ can be observed with parallel 400 wind, whereas with perpendicular wind ⟨PM 10 ⟩ is shown to systematically decrease with increasing ⟨TKE⟩. With 401 parallel wind, ⟨TKE⟩ is clearly highest in S2C and around threefold compared to S0 at = 14.6 m, which corresponds  vegetation mass closer to the emission source can be beneficial for ventilation and/or dry deposition.

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In all scenarios, dry deposition is observed to be important only for smallest particles. This was also shown in Tong  as well as further work to improve the parametrisations, especially in local scale modelling, is required.

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As for the quantitative analysis, the modelled situation represents a dry, spring-time morning rush hour in an urban 432 neighbourhood in a northern country, where studded tyres are applied in winter. These initial conditions lead to high 433 PM 10 concentrations with peaks >300 µg m −3 , which are up to 6-7-fold compared to PM 2.5 . Nevertheless, the hourly and thermal impact. Also the biogenic volatile organic compounds are not considered and they will complicate the 443 situation further by participating to aerosol particle formation and growth. Furthermore, vehicle-induced turbulence 444 (VIT) is omitted as no efficient VIT parametrisation for neighbourhood-scale LES is currently available.

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The purpose of this study was to understand the net effect of street trees on pedestrian-level aerosol particle met-447 rics in a boulevard-type street canyon, and to find out which of the studied street-tree layout scenario minimises the 448 concentrations over pavements and maximises vertical transport in the boulevard. We use the large-eddy simulation

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Of all scenarios with trees, the lowest mass concentrations over pavements are observed in S2C (three rows of 464 trees with smaller outermost trees) with parallel wind and S1 (four rows of trees) with perpendicular wind. For aerosol 465 number, lowest concentrations are observed in S1. Generally, S2C displays smallest concentration variability as well 466 as highest vertical turbulent transport and TKE, but also weakest dry deposition. Hedges below the outermost rows of 467 trees in S2B were not shown significant (5-7 % decrease) for the pedestrian-level aerosol particle concentrations over