Neutral Boundary Layer Urban Dispersion in Scaled Uniform and Nonuniform Residential Building Arrays

Abstract

Dispersion within idealized urban environments was studied in a simulated neutrally buoyant, 1:200 scale boundary layer with the Meteorological Wind Tunnel at the EPA’s Fluid Modeling Facility. The measurements are used to offer a baseline of performance for the mechanical turbulence formulation and concentration predictions of AERMOD, the EPA’s preferred Gaussian dispersion model. Scaled meteorological conditions and dispersion characteristics were studied for both uniform and nonuniform building arrays oriented at 0° and 30° with respect to the flow and were compared to baseline, “rural”, measurements without the presence of buildings. Particle image velocimetry (PIV) measured velocity and shear stress profiles within each model configuration, whereas hydrocarbon analyzers (HCAs) measured ethane concentrations at defined points throughout the model. Four source locations were examined for each building array, with two in the urban core and two in a street canyon, each with a source within and above the building canopy. Experimental profiles, regardless of their shape, were fitted to Gaussian profiles to determine lateral and vertical plume spread and shift from the wind tunnel centerline. These parameters were compared against a no-building reference case. Concentration predictions using the formulations in AERMOD are computed for 3 variations of modeled velocity profiles for each source, using factor of 2 ($FAC2$) and fractional bias ($FB$) as the governing model evaluation parameters. The two urban configurations were found to decrease the $FAC2$ performance by 34.1% and 30.1% from the no-building reference for the uniform and nonuniform cases, respectively, while producing modeled concentrations of only 48.1% and 62.4% of the 10 highest observed concentrations. These results encouraged simple first-order corrections to improve model performance with an emphasis on predicting maximum concentrations for regulatory purposes. These corrections proved successful for the uniform cases, mitigating $FB$, and improving the $FAC2$ percentage by 11.4% with more mixed results in nonuniform configurations, highlighting the difficulty in applying uniformly derived parameterizations in realistic, nonuniform environments.

1. Introduction

Most of the Earth’s population lives in urban areas, yet many algorithms developed for dispersion models that aim to protect human health make crude horizontally homogenous assumptions that do not apply within or near the canopy of urban environments. Dispersion modeling of an urban area is inherently complex and site-specific, combining additional convective and mechanical considerations through the change in material and geometric structures used to construct the urban area. A handful of field studies are aimed to directly diagnose the fundamental physics governing dispersion (Chang and Hanna 2010), including several urban-specific cases such as: St. Louis (Clarke et al. 1982), Indianapolis (Murray and Bowne 1988), Salt Lake City (Allwine et al. 2002), Oklahoma City (Allwine and Flaherty 2006), Basel, Switzerland (Rotach et al. 2005), and others. Planned experiments with the US Department of Energy’s Urban Integrated Field Laboratory initiative (U.S. Department of Energy 2024) demonstrate the importance of this topic and will provide further urban meteorological data to assist model development. While these field studies remain the standard for model evaluation (Hanna and Chang 2012), they are expensive, laborious, and can be limited in time or scope. Therefore, it is often better to isolate variables in controlled laboratory settings, or within high-fidelity models, to inform the development of faster reduced-order models used for regulatory dispersion modeling.

There have been numerous urban-focused studies in micrometeorological wind tunnels (Pirhalla et al. 2021; Cheng and Castro 2002; Shig et al. 2023) or water tunnel (Huq and Franzese 2013; Eisma et al. 2018; Moltchanov et al. 2011) facilities. Most of these experiments were neutrally stratified to isolate mechanical turbulence leading to key early parameterizations that are commonly found in dispersion models (Macdonald et al. 1998). Many initial studies focused on various arrays of regular cube-shaped structures, although inhomogeneous domains have been shown to drastically alter the dispersion, even with only a single large building (Fuka et al. 2018; Heist et al. 2009). Insights into urban canopy velocity and turbulence profiles were traditionally obtained with pointwise laser Doppler anemometry measurements (Cheng and Castro 2002). Currently, particle image velocimetry (PIV) offers increased spatial resolution and coverage to capture entire measurement planes. Transparent buildings (Hirose et al. 2022) and an automated stereo PIV system are implemented together to provide three-dimensional characterization within street canyons (Monnier et al. 2018).

To couple with experimental efforts, urban dispersion large eddy simulations (LES) are also common in the literature, offering the ability to study a variety of idealized (Sützl et al. 2021; Cheng and Porté-Agel 2016) and realistic (Akinlabi et al. 2022) urban geometries as detailed case studies. While computational time is restricting the widespread use of LES, these simulations offer high-resolution flow and concentration fields over large domains from which one can reduce and parameterize, leading to recommendations for reduced-order single-column models (Xie and Fuka 2018; Tian et al. 2023; Nazarian et al. 2020).

Even with these tools, the input meteorology in Gaussian dispersion models is often limited to one station or single column of data. This reduction in resolution remains problematic in complex environments, particularly when applied for regulatory purposes. Gaussian models are not inherently building-aware and, therefore, offer a low accuracy baseline to compare against more specialized models (Hertwig et al. 2018), raising concerns for their use in complex regulatory environments (Richter 2016). As illustrated in Fig. 1, most formulations that exist in these models are derived for horizontally homogenous “rural” areas (left side) that are then used, potentially with slight modifications, in urban areas using urban canopy options (right side). The key issue is the lateral spatial averaging in a single column model required to produce vertical profiles of the meteorological properties, but how does one accomplish this with so much variation within the averaging region? This lack of representation of flow, turbulence, and dispersion between and around buildings, or building awareness, is limiting and leads to oversimplifications that must be understood when applying the model for regulatory applications in urban areas.

Fig. 1.

Illustration of the single column model in horizontally homogenous and urban domains with a depiction of the “column” from a top (top row) and side view (bottom row). Representative velocity profiles are shown as a function of height, $U\left(z\right)$, for rural $\left(r\right)$ and urban ($u$) cases

This work aims to first understand and then suggest improvements upon the existing formulation in the EPA’s preferred Gaussian dispersion model, AERMOD (Cimorelli et al. 2005), on complex urban environments. We do so by introducing and analyzing two new wind tunnel experiments in the EPA’s Meteorological Wind Tunnel: (1) an idealized uniform urban environment, and (2) a realistic nonuniform urban environment. Both experiments are intended to represent medium-density suburban-style areas where many people in the United States reside. Suggested boundary layer parameterizations from literature are implemented in the model toward achieving improved model performance.

1.1. Concentration Formulation in AERMOD

Given the troubles with single column meteorology in modeling inhomogeneous urban areas, we must first understand the predictive performance of the existing formulations with the measured profiles in the laboratory. Gaussian dispersion in AERMOD for stable and neutral environments is modeled by the following expression (Cimorelli et al. 2005), which provides concentration predictions $\left(C_s\right)$ at locations downwind $\left(x\right)$, laterally $\left(y\right)$, and vertically ($z$) from a source:

$$C_s\left(x,y,z\right)=\frac{Q}{\sqrt{2\pi }\tilde{u}{\sigma }_{zs}}{F}_y\sum _{m=-\mathrm{\infty }}^{\mathrm{\infty }}\left[\exp \left(-\frac{{\left(z-h_{es}-2m{z}_{ieff}\right)}^2}{2{\sigma }_{zs}^2}\right)+\exp \left(-\frac{{\left(z+h_{es}+2m{z}_{ieff}\right)}^2}{2{\sigma }_{zs}^2}\right)\right],$$ (1)

where $Q$ is the emission rate, m is a summed index to account for plume reflections off the effective mechanical mixed layer height $\left(z_{ieff}\right),{\sigma }_{zs}$ is the total vertical dispersion, $h_{es}$ is the plume height (source height plus the plume rise), $\tilde{u}$ is the average wind speed between the source height and the receptor height, and $F_y$ is the lateral distribution function with meander given by:

$$F_y=\frac{1}{\sqrt{2\pi }{\sigma }_y}\exp \left(-\frac{{\left(y-y_P\right)}^2}{2{\sigma }_y^2}\right).$$ (2)

The lateral shift $\left(y_P\right)$ is not used in AERMOD (e.g., $y_P=0$) but is included here as a reference for the analysis in this work. The lateral dispersion $\left({\sigma }_y\right)$ is estimated by:

$${\sigma }_y=\frac{{\sigma }_{v}x}{\tilde{u}{(1+\delta X)}^P},$$ (3)

where $\delta$ and $P$ are constants of 78 and 0.3, respectively, $X={\sigma }_{v}x/\tilde{u}{z}_{\mathit{ieff}}$, and ${\sigma }_v$ is the lateral turbulence given as a function of the friction velocity $\left(u_{\mathrm{*}}\right)$ by ${\sigma }_v^2=3.6u_{\mathrm{*}}^2$. Limiting the analysis to the surface portion of the vertical dispersion (see (Cimorelli et al. 2005) Eq. 24), we can write ${\sigma }_{zs}$ as:

$${\sigma }_{zs}=\sqrt{\frac{2}{\pi }}\left(\frac{u_{\mathrm{*}}x}{\tilde{u}}\right){\left(1+0.7\frac{x}{L}\right)}^{-\frac{1}{3}},$$ (4)

where $L$ is the Obukhov length, which is infinite for this neutral simulation.

AERMOD does offer an urban option, but the formulations are based only on an increase in sensible heat flux that produces a convective-like boundary layer that, in turn, modifies variables related to mechanical turbulence (Cimorelli et al. 2005). Given the stability in this wind tunnel study is inherently neutral, these expressions are not representative of this work and are, therefore, not examined.

2. Model and Experimental Setup

This section overviews the physical model and experimental observation campaign. Both a traditional uniform building arrangement commonly seen in literature and a nonuniform building arrangement were analyzed for the geometry and meteorological effects on urban dispersion.

2.1. Uniform and Nonuniform Residential Models

Two 1:200 scale models were studied in the EPA’s Meteorological Wind Tunnel (Snyder 1979), featuring uniform and nonuniform distributions of buildings oriented in city blocks to represent residential areas. The boundary layer was developed by use of five large Irwin spires at the start of the fetch with staggered roughness elements (38 × 76 mm tabs) spaced 305 mm laterally and 305 mm axially (measured center-to-center) throughout the fetch of the wind tunnel to maintain a turbulent boundary layer through the experimental domain. The nominal freestream velocity of the wind tunnel was set to 5.2 m/s, resulting in a Reynolds number of ~10,600 using the uniform building height $\left(H\right)$ of 60 mm as the characteristic length and the velocity at this height, $u_H=2.65\mathrm{m}/\mathrm{s}$, which is near the critical Reynolds number in the wind tunnel of 11,000 for fully developed turbulent flow (Snyder 1981). The reference, no building approach flow features a surface roughness of 0.6 m, friction velocity of 0.33 m/s, and a depth of $~25H$ as estimated from velocity measurements.

Figure 2 and Fig. 3 represent an overview of the geometry for the uniform and nonuniform building cases, respectively. Both feature an array of streets to separate the city columns (x-direction) and avenues to delineate the city rows (y-direction). Including one of each of the bounding streets ($\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=0.75H$) and avenues ($\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}=H$), each city block was $17.67H\times 7.83H$ (1060 mm × 470 mm). Each block of the uniform model featured two rows containing 16 columns of $1.25H\times 0.75H\times H(\mathrm{L}\times \mathrm{W}\times \mathrm{H})$ wooden buildings in each city block with the building length mounted parallel to the wind direction, which reflects a 0° incoming wind configuration. This array of 15 m ×9 m × 12 m rectangular buildings is intended to represent plats of three-story residential neighborhoods commonly found outside the urban core of many US cities. For the 30° incoming wind case, the model was rotated about the tracer source origin location (more details below) and cut to maintain the original spacing to the tunnel side walls. The cut panels were used to backfill in the geometry at the front of the fetch to maintain a uniform transition in the mock urban area. The building plan area ratio $\left({\lambda }_p\right)$, the sum of the building top area within a block over the total area of the block, was 0.217, with a frontal area ratio $\left({\lambda }_f\right)$, the sum of the front facing building area over the total area of the block, of 0.173 and 0.295 for the 0° and 30° cases, respectively.

Fig. 2.

The uniform model a 0° and b 30° configurations and measurement locations along with pictures in the actual model in the wind tunnel c–d. Note that for the 30° case, the location of sources 3 and 4 was above a support beam. Therefore, they were relocated downstream by one block and were relabeled as sources 5 and 6. Source locations and HCA measurement profiles are denoted with colored points and lines, respectively, which correspond to the source denoted in the legend. Locations of PIV planes are shown by dark green lines

Fig. 3.

The nonuniform model restricted to the geometry of the turntable at a 0° and b 30° with overlays of the measurement locations along with pictures of the actual model in the wind tunnel c–d. The sources, PIV, and HCA measurements are denoted by the same coloring scheme stated in Fig. 2

The nonuniform configuration follows the same basic city-block layout, only with a more realistic array of building types and shapes that may represent a more typical urban or suburban environment, including buildings such as small apartment buildings, stores, and houses of various sizes and shapes. The basic shapes and variation in height are shown in Fig. 3. Each block consisted of one of two nonuniform configurations installed in various orientations throughout the model: an L-shaped building block (B1 in Fig. 3a) and a $1.67H$ (100 mm) tall building block (B6 in Fig. 3a). The buildings were constructed from 3D printed plastic and wood and were limited to the geometry of the turntable for ease of rotation, compared to the uniform configuration. The plan area ratios were ${\lambda }_p=0.304$ and 0.256 for the tall building and L-shaped building blocks, respectively, with frontal area ratios of ${\lambda }_f=0.201$ and 0.283 for the $1.67H$ tall building block and ${\lambda }_f=0.155$ and 0.248 for the L-shaped building block for 0° and 30° configurations, respectively.

Four different point source configurations were considered for each building geometry. Two $x-y$ locations were selected and are denoted with a colored circle in both figures: source 1 was in the center of a designated avenue or street and shown as a black dot near the middle of the building arrays in Figs. 2 and 3. Source 3 is plotted as a purple dot in the same figures at a crosswise intersection. These locations were chosen to study the immediate effect of frontal area and potential channeling effects, respectively, as observed from previous work (Pirhalla et al. 2021). Sources 1 and 3 were positioned at a height of $\mathrm{z}=0.5H$, while sources 2 and 4 were colocated at the same coordinate, respectively, but generally above the building canopy at $\mathrm{z}=1.5H$. Sources 2 and 4 are identified in orange and green dots stacked on top of the other two source points.

Measurements were gathered while the front faces of the buildings were perpendicular to the approach flow, representing a $\theta =0^{\circ }$ incoming wind direction. Both model configurations were rotated $\theta ={30}^{\circ }$ about $\mathrm{x}=0,\mathrm{y}=0$, or the location of sources 1 and 3 to examine channeling effects from a variation in approach flow. The downstream concentration measurement planes for each source are marked in Figs. 2 and 3 as horizontal-colored lines that match each respective source color. At a minimum, for the uniform building cases, all sources included downstream concentration measurements at distances relative to the source at $\mathrm{x}=3.9H,15.67H$, and 47 H (235-, 940-, and 2820 mm). For the nonuniform building cases, concentration measurements were recorded in $\mathrm{y}-\mathrm{z}$ planes at $\mathrm{x}=3.9H,7.83H,15.67H$, and $23.5H$ (235-, 470-, 940-, and 1410 mm) relative to each source. PIV measurement planes are also denoted in dark green perpendicular lines in these plots. Due to the complex nature of the geometry, eight vertical measurement planes were recorded to illustrate the breadth of flow fields for this geometry.

The flow direction and the coordinate systems for the wind tunnel ($x_T,y_T$) and model $\left(x_M,y_M\right)$ are also marked in Figs. 2 and 3. For the 30° uniform building case, the location of sources 3 and 4 was above a wind-tunnel support beam; therefore, they were relocated downstream by one block and were relabeled as sources 5 and 6. This slight modification is still representative as being in the similar release location at street intersections.

2.2. Particle Image Velocimetry System

The PIV system featured a dual-head ND:YAG laser (Big Sky Laser CRF400 PIV, Bozeman, MT) operating near 150 mJ/pulse and Powerview Plus 4MPix charge-coupled device (CCD) dual framing cameras (TSI Instruments, Shoreview, MN). The cameras were replaced with pco.panda sCMOS detectors toward the end of the testing period. Sheet forming optics for vertical profiles were −25 mm cylindrical and +2000 mm spherical lenses. Horizontal planes utilized a −125 mm cylindrical lens with a + 2000 mm spherical lens. Image pairs were captured with a pulse delay of 500 μs and processed using Insight 4G software (TSI Instruments, Shoreview, MN). Figure 4 highlights the two main configurations used in this work of a vertical (measuring u, w) and horizontal (measuring u, v) laser sheet with cameras mounted perpendicular to the laser sheet to demonstrate the camera’s field of view (FOV). Due to the geometry of the wind tunnel, no direct line-of-sight was available into the street canyons; therefore, the cameras viewed the model through a periscope assembly positioned inside the wind tunnel to acquire 2-dimensional velocimetry measurements within the street canyons. Measurement positions of the PIV vertical planes are displayed earlier in Figs. 2 and 3. At least 400 image pairs were recorded at ~1-Hz for all measurement locations.

Fig. 4.

Illustrations of the PIV experimental setups for a vertical and b horizontal measurement planes with photograph inserts of the laser sheet configuration

The processing steps included background subtraction, image masking, and a double-pass cross-correlation scheme from 64 × 64 to 32 × 32 pixel windows with 25% overlap (8-pixel resolution) in Insight4G. The imaging resolution ranged from ~175–240 μm/pixel depending on the measurement location. General statistics and Reynolds normal and shear stresses were calculated from the processed velocity fields for each spatial coordinate using a custom script in R (R Core Team 2024). Horizontal data (not shown) are referenced only with respect to potential corrections seen in Sect. 4.3. For the angled building cases, both model frame and wind tunnel frame images were recorded (also not shown).

2.3. Hydrocarbon Analyzers

Six Rosemount Analytical Model 400A Hydrocarbon Analyzers (HCAs) (Emerson, St. Louis, MO) were used in parallel to measure 2-min time average concentrations of a nonbuoyant 1 g/min ethane tracer gas released from a porous 10 mm diameter sphere (see Fig. 5a) at 6 discrete points. Figures 5b, c depict the horizontal (40 mm spacing) and vertical (30 mm spacing) sample probes, used for the $\theta =0^{\circ }$ and $\theta ={30}^{\circ }$ model configurations, respectively. A LabVIEW acquisition system (National Instruments, Austin, TX) controlled the position of the sample probe and storage of the measured concentration. The HCAs were calibrated once a month to six known ethane-air mixtures across the desired measurement range. Daily checks at zero (air only) and the full measurement range were recorded along with backgrounds to account for any day-to-day changes in the analyzers or the measurement environment.

Fig. 5.

a Source height for z/H = 0.5 (30-mm) and different orientations of gas sampling probes: b horizontal with 40-mm spacing used for the 0° cases, and c vertical with 30-mm spacing used for all 30° measurements

Concentration results are presented as the dimensionless variable, $\chi$, as:

$$\chi =\frac{C{U}_{ref}{H}^2}{Q},$$ (5)

where $C$ is the measured concentration (g/m³), $U_{ref}$ the reference velocity (m/s) selected as 3.24 m/s (from pretest laser Doppler velocimetry (LDV) measurements at $z=2H$; see Perry et al. (Perry et al. 2016) for details on the LDV system), $H$ is the building height (60 mm), and $Q$ is the flow rate of the tracer gas at the source (g/s). The mass flow controller drifted throughout the study, requiring daily monitoring and corrections to the flowrate for each observed concentration measurement.

3. Results

The PIV and HCA measurements are presented here and summarized for each case before a discussion on their comparison to the modeled results from AERMOD in Sect. 4. For brevity, only the 0° PIV cases are presented here.

3.1. Flow Field Measurements

Planar velocimetry measurements were performed throughout the developed urban flow field to obtain estimates of the mean velocity and friction velocity to be used as inputs to AERMOD’s dispersion algorithm. Revisiting the locations of the PIV planes in Figs. 2 and 3 denoted in dark green lines, one can see the strategic locations selected for the uniform case to highlight representative flow fields: (1) directly behind a building, (2) between two buildings, and (3) in the center of the street. Figure 6a, b depicts these mean velocity fields and the Reynolds shear stress with average vertical profiles over each slice in Fig. 6c, d. Gray-colored regions are void of measurements due to the buildings effecting the camera perspective through the periscope. The mean profiles are contrasted against the dataset for the no-building case, illustrating the importance of considering a displacement height or even a separate parameterization below the average building height and the large change in magnitude of the shear stress. The dataset for the no-building case is an average of three vertical planes to account for the geometry of the boundary layer tabs on the floor of the wind tunnel.

Fig. 6.

Uniform building array a mean velocity planes in the flow direction and b Reynolds shear stress planes for (top) $y=0H$, (middle) $y=4.67H$, and (bottom) $y=8.83H$. Average profiles corresponding to each plane are shown in c and d along with profiles recorded without buildings present shown in black. The inflection point for the shear stress peak in d) is denoted by a vertical line for each corresponding plane

The measurement plane between the two buildings $(y=0H)$ features a weak recirculation zone before the next row of buildings but otherwise exhibits positive velocities, whereas flow over the buildings has a large recirculation region behind the building, resulting in a negative average velocity near the surface. However, the shear stress profiles for these two building cases coincide in location and magnitude with peak values at $z=1H$, suggesting a common representative friction velocity for these location environments. The measurement plane in the street canyon, however, is fundamentally different from the building cases with an always-positive mean-velocity profile for $z<1H$ and a maximum shear stress of only 60% of the two building cases. The height of maximum shear stress also appears well above the canopy near $z=1.7H$. These two extreme cases within the uniform environment represent the local conditions for sources 1 and 2 in the buildings and sources 3 and 4 in the street.

Representative velocity profiles for the nonuniform building array are not as straightforward. Therefore, a breadth of planes was recorded to illustrate the range of flow conditions present in this residential array, with the locations marked with dark green lines on the model in Fig. 3. With a format similar to the uniform case in Fig. 6, the nonuniform results are displayed in Fig. 7 where, once again, the mean profiles are overlaid on profiles recorded without any buildings present. Each street canyon features a unique mean velocity profile, heavily governed by the heights of the building encompassing the avenue. All planes except the plane at $y=0H$ (the location of sources 1 and 2) feature reverse flow on average near the surface, including the plane in the street at $y=8.89H$. This change in behavior from the uniform case is likely due to the combined effects of three $1.67H$ tall buildings and an L-shaped building defining the intersection at that measurement location, which is also the location of sources 3 and 4. Unlike the uniform case, flow at $y=0H$ is positive due to the ventilation downstream from the lack of immediate buildings. Mean profiles in Fig. 7c demonstrate the variance in local displacement height and profile shape, particularly for $z<3h$.

Fig. 7.

a Mean velocity and b shear stress planar measurements for eight unique PIV planes along with the average c velocity profiles and d shear stress profiles for the nonuniform building geometry against the no-building case

Shear stress profiles are likewise quite varied, with the height of the maximum stress ranging from $z=1H$ to $z=1.67H$ (the respective minimum and maximum building heights), with mean values less than the values seen for the uniform case. However, local values exceed the values from the uniform configuration, specifically at $y=11.46H$. One case of interest is the $y=6.18H$ plane in the bottom right of the contour plots of Fig. 7c, denoted in pink in Fig. 7d, where the shear layer from an upstream $1.67H$ tall building out of the field of view propagates above the buildings in the measurement plane, highlighting the complexity of the local shear stress that is evident in the average profiles of Fig. 7d. Unlike the uniform case, selection of a representative mean velocity and friction velocity is not trivial.

Since both properties (a mean shear stress and friction velocity) are required as inputs for AERMOD’s dispersion calculation, we attempt to use these measurement planes and those for the 30° case to provide a best estimate for the entire urban area for each configuration. A summary of this effort is shown in Table 1. For this analysis, we limit the determination of the friction velocity to the time-averaged Reynolds shear stress, although spatially averaged dispersive stresses may also contribute due to the heterogeneous spatial domain and will be the focus of future work. Also, note for all 30° data, only wind tunnel frame measurement planes are considered in the velocity profile and calculation of $u_{\mathrm{*}}$ to eliminate rotation errors with measurements recorded in the model frame. Weight factors for the uniform case were based on geometric considerations. The spatial area in the x-direction for each block was comprised of 68% buildings, 25% between buildings, and 7% roads. The nonuniform case is too diverse to bias any weighting on the eight velocity fields (NU1 through NU8), so a simple average of 1/8 is used. These mean values for the friction velocity, highlighted in bold in Table 1, are used along with average velocity profiles and a mixing height estimated to be $25H$ to predict the vertical and lateral spread of the plume using the expressions in AERMOD.

Table 1.

Inferred friction velocity for the no-building (NB), uniform (U), and nonuniform (NU) building cases. Colors represent the measurement planes that combine to form one estimate of the friction velocity

Case	$\theta$	$\sqrt{-u^{\prime }{w}^{\prime }}$	W	$u_{\mathrm{*}}$	Case	$\theta$	$\sqrt{-u^{\prime }{w}^{\prime }}$	W	$u_{\mathrm{*}}$	Case	$\theta$	$\sqrt{-u^{\prime }{w}^{\prime }}$	W	$u_{\mathrm{*}}$
NB	-	0.33	1	0.27	NU.1	0	0.46	1/8	0.39	NU.1*	30	0.40	0	0.41
U.l	0	0.44	0.25	0.42	NU.2	0	0.34	1/8		NU.2*	30	0.37	0
U.2	0	0.43	0.68		NU.3	0	0.34	1/8		NU.3*	30	0.39	0
U.3	0	0.34	0.07		NU.4	0	0.34	1/8		NU.4*	30	0.45	0
U.1*	30	0.40	0	0.43	NU.5	0	0.42	1/8		NU.5*	30	0.45	0
U.2*	30	0.41	0		NU.6	0	0.40	1/8		NU.6*	30	0.41	0
U.3*	30	0.42	0		NU.7	0	0.37	1/8		NU.7*	30	0.41	0
U.4	30	0.43	1		NU.8	0	0.43	1/8		NU.8*	30	0.42	0
										NU.9	30	0.41	1

^*Recorded in the model frame, W = weight term, $\theta$ = incoming wind direction

3.2. Concentration Profiles

A representative selection of the crosswind concentration profiles is presented in Fig. 8 a, b for the uniform and nonuniform cases, respectively. The x - and y-coordinates are presented as relative to the respective source, whereas the z-coordinate remains in the tunnel frame. Note that there are occasional gaps in the y-axis of the data for the 30° case, as the path of the profile occasionally intersects with buildings.

Fig. 8.

a Uniform and b nonuniform dispersion results on selected planes. Note that the purple curves represent source locations 3 and 4 for the nonuniform case, but 5 and 6 for the uniform case

The raw data from the uniform building array dispersion study immediately suggest a Gaussian dispersion model that could, in principle, be used to accurately model the time-averaged concentration profile. Even near the source, there is a clear Gaussian shape over a range of heights and source locations. The highest magnitude concentrations near the surface are unsurprisingly associated with sources 1 and 3 at $z=0.5H$. There is also clear evidence of channeling effects, as the lateral edges of the plume tend to drift up in magnitude to the left for the 30° cases (open symbols), specifically for all heights at $x=15.67H$, indicative of the more open side of the model, with less building-induced blockage.

The nonuniform geometry, however, is not immediately supportive of a Gaussian dispersion model, as the time-averaged profiles are not trivial single-Gaussian shapes, especially at $x=3.9H$ and $7.83H$ where bi-Gaussian profiles are common. Even for the farthest downstream plane at $x=15.67H$, the profiles are biased in the $+y$ direction for the 0° case yet biased in the $-y$ direction for the 30° case.

Regardless, we fit these concentration observations to Gaussian profiles to understand how these urban geometric features may translate the center (e.g., $y_P\ne 0$) and broaden or restrict the plume as it propagates downstream. Figure 9 demonstrates representative fits for the same physical location in the tunnel for both uniform (Fig. 9a, c) and nonuniform (Fig. 9b–d) cases in both the y and z planes for source 1. Both building arrays are at $\theta ={30}^{\circ }$, highlighting the time-averaged bias of the uniform plume to the left of the domain with respect to a classical Gaussian profile (9a) due to channeling through the avenues. For the nonuniform array (9b), the profile measurement height of $1.5H$ is lower than the tallest building at $1.67H$ and, therefore, experiences significant building effects leading to three concentration peaks with a large shift away from the centerline (9b). Revisiting the model in Fig. 3b and the relationship of source 1 to the first measurement plane explains this behavior. The strongest peak near $y/H=-4$ appears directly downwind of a $1.25H$ (75 mm) building where the flow is altered by the building wake coupled with channeling through the avenue. The central peak is near $y/H=0$ directly downwind of the source, and finally, the small peak near $y/H=+5$ is due to flow relief from the gap in $1H$ buildings upwind working against the direction of flow channeling. A clear consequence of using a single Gaussian model in this domain is the underprediction of the peak measured concentration.

Fig. 9.

Representative Gaussian profile fits for the uniform a and c and nonuniform b and d model configurations at 30°. Lateral profiles are from source 1 at $\mathrm{x}=3.9H$ and $\mathrm{z}=1.5H$. Vertical profiles are at $\mathrm{y}=0\mathrm{m}\mathrm{m}$ and normalized to 1, with blue vertical lines illustrating the vertical center of mass

The vertical observations are fit to a reflected Gaussian profile, denoted as:

$$\chi =A\left[\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\left(z-z_p\right)}^2}{2{\sigma }_z^2}\right)+\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{{\left(z+z_p\right)}^2}{2{\sigma }_z^2}\right)\right],$$ (6)

where $A$ is a constant, ${\mathrm{z}}_{\mathrm{p}}$ is the vertical offset from the plume centerline, and ${\sigma }_z$ is the vertical plume spread term. AERMOD adopts this reflected plume approach to conserve mass, seen earlier in Eq. (1), assuming no tracer gas is deposited on the surface. Fits to reflective Gaussian profiles, which can produce ${\sigma }_z$ and $z_p$, are insensitive and unreliable; therefore, the more physically intuitive vertical center of mass, $\bar{z}=\frac{1}{C_{\mathit{total}}}\left(\sum _{i=1}^N{C}_i{z}_i\right)$, where $C_{\mathit{total}}$ is the total concentration for a given profile, is discussed here and shown in blue in Fig. 9c, d.

Fits like those in Fig. 9 for all lateral and vertical profiles are made using Eq. 2 for tabulation of ${\sigma }_y$ and $y_p$ and the vertical center of mass, all of which are summarized in Fig. 10 for the uniform model and Fig. 11 for the nonuniform model as a function of downwind distance. Both are compared to data recorded with no buildings (shown in black) to illuminate any inherent biases in the wind tunnel and to isolate the effects of the building configurations and source locations. Results of the fits are shown as points, whereas the trendlines for the lateral properties are fit to the functional form $~\sqrt{x}$, whereas $\bar{z}$ lines are linear to each mean. The no building case shows a slight bias in the $+y$ direction of ~13 mm over 1402 mm, or an ~0.5° deviation from the wind tunnel center line. The formulations in AERMOD, as currently configured, cannot handle a lateral translation in the plume center. Both ${\sigma }_y$ and $\bar{z}$ increase with downwind distance, offering a baseline to compare against the building cases.

Fig. 10.

a Lateral shift $\left(y_p\right)$, b lateral spread (${\sigma }_y$), and c vertical center of mass ($\bar{z}$) of the plume for the uniform building array. Individual points are fits to single profiles that meet a residual cut off, with smoothed lines illustrating general trends for each source. Color combinations match for common source x-y locations, with the bold colors representing source heights of $\mathrm{z}=0.5H$ (odd sources) and faded/lighter colors representing $\mathrm{z}=1.5H$ (even sources)

Fig. 11.

a Lateral shift $\left(y_p\right)$, b lateral spread (${\sigma }_y$), and c vertical center of mass ($\bar{z}$) of the plume for the nonuniform building array. Individual points are fits to single profiles that meet a residual cutoff, with smoothed lines illustrating general trends for each source. Color combinations match for common source x–y locations, with the bold colors representing source heights of $\mathrm{z}=0.5H$ (odd sources) and faded/lighter representing $\mathrm{z}=1.5H$ (even sources)

The uniform buildings produce orderly trends that appear consistent with building configuration and source height. All 0° sources have similar $+y$ direction lateral bias with sources 3 and 4 in the street featuring a lower bias than the no-building data, suggesting that some downstream geometric channeling of the buildings helps overcome the inherent wind tunnel bias seen in the no-building data. The30° sources are all biased in the $-y$ direction, due to channeling through the avenues, with source 1 featuring the most significant channeling due to the origin within an avenue and without the flow relief through a perpendicular street awarded to source 3. The 0° and 30° lateral spread bound the no-building case from below 30°and above, respectively, suggesting enhanced mixing and lower concentrations for the case.

The vertical center of mass also distinguishes the two uniform angled configurations, where the 0° plumes are distinctly lower than all 30° cases, with only source 3 lower than the no-building reference. The 0° plumes are aided by gaps between buildings (sources 1 and 3) and a street canyon (sources 3 and 4) parallel to the flow direction, whereas the 30° plumes all must translate above the canopy height potentially for the lack of flow pathways parallel to the freestream direction.

Compared to the uniform building array case, the behavior of the plume through the nonuniform building array is more dependent on the local building geometry seen earlier in Fig. 3. For example, in Fig. 11a, sources 2–4 of the 0° sources maintain the slight positive lateral bias, but source 1 has a strong negative bias due to the influence of: (1) the 1.25 Hm tall building just before the source entrapping flow near the $\mathrm{z}=0.5H$ source in its wake, and (2) the longer $1.25H$ tall building one block downstream acting as flow blockage and encouraging lateral spread of the plume. The 30° sources maintain a negative bias, where again source 1 features alley channeling leading to the largest bias for all cases. The lateral spread appears initially larger than the no-building case for the 0° sources at $\mathrm{z}=0.5H$ but recovers with downwind distance to match the elevated sources at or below the no building reference data. For the 30° sources at the center of the model, the spread is significantly larger than the uniform case, suggesting even more mixing and decreased centerline concentrations.

Like the uniform case, the vertical center of mass in Fig. 11c illustrates how all nonuniform plumes are located physically higher than the no building reference, but with less of a separation between 0° and 30° configurations than the uniform case. Sources 3 and 4 experience the highest center of mass for the nonuniform 30° case, albeit with the point at $\mathrm{x}=3.9H$ blocked by buildings overlapping the desired measurement region. In addition, considering the buildings encompassing the street-avenue intersection for these sources seen in Fig. 3, three out of four of them are the largest height seen in the model $\left(1.67H\right)$, leading to a recirculation zone within the street canyon as seen in NU. 4 in Fig. 7. This height would increase the initial vertical spread of the plume with respect to a street without a recirculation region that promotes channeling. Parameterizing this level of detail into a model is difficult and often case-specific. Therefore, most implementations considered in the next section are based on observations in the uniform case with a model performance review in the nonuniform case.

4. Discussion

We now compare concentration predictions using the AERMOD formulations to the dispersion results in the wind tunnel, examine the consequences of using the existing formulations for urban plumes, and provide recommendations for future updates to the AERMOD dispersion algorithm in urban environments.

4.1. Velocity Profiles Compared to AERMOD Formulations

We first discuss the necessary meteorological inputs from the wind tunnel experiment for input to AERMOD. The urban option in AERMOD enforces a surface roughness length ($z_0$) of $z_o=1\mathrm{m}$ with no displacement height $\left(d_o=0\mathrm{m}\right)$ to generate a velocity profile using the canonical log-law formulation of:

$$U(z)=\frac{u_{\mathrm{*}}}{k}ln\left(\frac{z-d_o}{z_o}\right),$$ (7)

where $k$ is the dimensionless von Karman constant set to 0.4. Figure 12 illustrates the effect of applying this expression explicitly using the weighted mean friction velocity determined experimentally in Table 1 to model the velocity profile for both building configurations, as shown by the black curve. AERMOD will scale the profile to match a measured wind speed at a reference height, effectively changing $u_{\mathrm{*}}$ from Eq. (7) for the velocity profile, but not for other calculations that involve friction velocity. Taking the uniform 0° model case as an example in Fig. 12, a scaling factor of 0.83 would be required to match the velocity at a height of $\mathrm{z}/\mathrm{H}=2$ (represented as the dashed profile shown).

Fig. 12.

Example comparison between the AERMOD log law velocity profile, a scaled profile set to match the measured value at $z=2H$, and an experimental fit profile with the surface roughness (${\mathrm{z}}_0$) and displacement height $\left({\mathrm{d}}_0\right)$ embedded in each plot for a uniform 0°, b nonuniform 0°, c uniform 30°, and d nonuniform 30°

Attempting to acquire a representative wind speed from these profiles to use in the dispersion calculation will result in an inaccurate value compared to the true wind speed. Alternatively, fitting the mean PIV profiles using the standard log law and an exponential profile below the canopy height, $h_c$, we obtain improved fits to the velocity profile to use in the dispersion calculation. The exponential expression is taken from Weil et al. (Weil and Alessandrini 2023) and is defined as a function of the velocity at the canopy height, $U_c$, as:

$$U(z)=U_c\mathrm{e}\mathrm{x}\mathrm{p}\left[\gamma \left(\frac{z}{h_c}-1\right)\right]forz\le h_c,$$ (8)

with the attenuation coefficient, $\gamma$, defined as:

$$\gamma ={\left(\left(1-\frac{d_o}{h_c}\right)\mathrm{l}\mathrm{n}\left[\frac{h_c-d_o}{z_o}\right]\right)}^{-1}.$$ (9)

While previous work from Castro (Castro 2017) highlighted the lack of an exponential profile in urban canopies with nonuniform drag, which is true for our nonuniform building array, the previous work provides a sufficient fit that improves upon the default AERMOD profile. The value of $h_c$ is 1.0 for uniform and 1.4 for nonuniform geometries, selected to produce the best fit for the urban profiles in Fig. 12.

The results of these fits for each of the four main configurations are shown in Fig. 12 in green and the best fit surface roughness and displacement heights are listed in Table 2 along with the reference, no building case. The consequences of using different velocity profiles are examined in the following section when we compute concentrations with these profiles. The displacement height and surface roughness are inherently negatively correlated. Therefore, positive errors in the fit to one component will lead to negative errors in the other. The average building height for the nonuniform planes is z/H = 1.29 (or z = 15.48 m full scale), indicating that the displacement heights are 67%, 77%, 53%, and 40% of the average building height, respectively, using this specific definition of the average flow field.

Table 2.

Recommended displacement heights (${\mathrm{d}}_0$) for each building case based on ${\mathrm{z}}_0$ and $u_{\mathrm{*}}$

Case	$u_{\mathrm{*}}(\mathrm{m}/\mathrm{s})$	$z_0(\text{m})$	$d_0(\text{m})$
NB	0.33	0.6	0
U 0°	0.42	1.24	8
U 30°	0.43	1.82	6.4
NU 0°	0.37	1.01	12.2
NU 30°	0.41	1.58	6.2

NB = no building, U = uniform, NU = nonuniform, 0° = 0° incoming wind direction, 30° = 30° incoming wind direction

These vertical velocity profiles are critical in the selection of a representative velocity, $\tilde{u}$, for use in Eq. 1, where the current implementation for point sources requires the average velocity from the source height to the receptor height. As is clear from Fig. 12, this procedure results in different values depending on which velocity profile is used.

4.2. Concentration Profiles Compared to AERMOD Formulations

With the measured and modeled meteorological parameters from the wind tunnel, we compute the expected concentration profiles using the formulations in AERMOD (see Eqs. 1–3) at the same locations as the experimental profiles. To be clear, the AERMOD model itself was not used, merely the formulations found in the model. The velocity profiles from Sect. 4.1 are used to determine the representative velocity, as an average in height from the source to the receptor, and the friction velocity as determined earlier from Sect. 3.1 and repeated in Table 2. Three different iterations are shown as follows, to understand the consequences of neglecting a displacement height: (1) the original AERMOD computed wind profile, (2) the scaled AERMOD profile, and (3) the urban velocity profile using an exponential profile in the canopy with the inputs shown in Table 2.

4.2.1. No Building Reference Case

To begin, we reference the concentration profiles from the no-building case to the AERMOD formulations to understand any potential bias in the wind tunnel for this boundary layer setup. The velocity profile was shown previously in Figs. 6c and 7c. The porous 10 mm diameter sphere used for the point source in the work is not negligible in size compared to the environment and is therefore not a true “point”. To distinguish this situation, an initial dispersion at $x=0\mathrm{m}\mathrm{m}$ is implemented in the vertical (${\sigma }_{zo}$) and lateral dimensions (${\sigma }_{yo}$) and is summed in quadrature with the existing dispersion from Eqs. 3–4 to provide an initial offset as:

$${\sigma }_{yeff}=\sqrt{{\sigma }_y+{\sigma }_{yo}},\mathit{and}{\sigma }_{zeff}=\sqrt{{\sigma }_z+{\sigma }_{zo}},$$ (10)

where ${\sigma }_{yeff}$ and ${\sigma }_{zeff}$ replace the equivalent variables in Eq. 1. As seen in Fig. 13, the model results with initial dispersion values of ${\sigma }_{yo}={\sigma }_{zo}=10\mathrm{m}$ provide good agreement with the no-building observations; therefore, these initial dispersion values are used for all residential building cases. A 35% correction factor to $Q$ from Eq. 5 was included, due to a discrepancy in the mass flow controller during the time of measurements. This value for the emission rate was estimated from mass flux estimates using the mean velocity profile and concentration profiles downstream of the source. The mass flow controller issue was resolved for all urban building cases, and therefore, those data do not require an offset.

Fig. 13.

Comparison of AERMOD formulation to wind tunnel results for the no-building case. Scatter plots with dashed lines representing FAC2 error with respect to the observations for a log–log scale and b normal scale

4.2.2. Residential Building Dispersion

We now expand the comparison of the AERMOD formulation to the building cases. Note that the same vertical velocity profile is used for each of the four sources considered for each wind direction from Fig. 12. Two cases are highlighted in Fig. 14 to illustrate different phenomena. Figure 14a–c depicts the results for the uniform building 0° source 3 case to illustrate belowcanopy channeling that constricts the lateral growth of the plume, while Fig. 14d–f depicts the nonuniform 30° source 1 case to illustrate the deflection of the plume from the approach wind direction caused by buildings. For the first case, the modeled concentrations level off with respect to the observations (see Fig. 14b), producing near horizontal lines due to the lateral and vertical spread dependence on the local velocity (i.e., lower velocities closer to the ground yield higher modeled lateral spread). Figure 14c illustrates how the lateral spread of the observed plume remains nearly constant with height, suggesting that effects independent of local velocity govern the lateral spread, such as the width of the street canyon parallel to the wind direction. For the nonuniform case, the model misses the “center” of the plume, resulting in inverted U-shaped distributions about the 1-to-1 line. As seen in Fig. 14f, the plume splits into a bi-Gaussian shape which is intractable with the current model formulation. In both cases, the model struggles to match the performance seen in Fig. 13 from the no building data.

Fig. 14.

Representative uniform $\theta =0^{\circ }$ scatter plots a–c and nonuniform plots d–f with respective lineouts at $x=3.9H$ with AERMOD formulations in black and observations in red

To better compare the performance of the model for all the cases, we examine the Factor of 2 $\left(FAC2\right)$ error and the fractional bias $\left(FB\right)$ of each model compared to the experimental value. The error and bias are defined in Eqs. 11–12 with the results displayed in Fig. 15a, b for all sources using the initial AERMOD velocity profile (open circles), the AERMOD profile scaled to match at $\mathrm{z}/\mathrm{H}=2$ (open triangles), and the experimental fit of “urban profile” value (closed circles). These measures offer a simplified path to compare all model runs and are commonly used in the dispersion community:

$$FAC2=\frac{1}{N}\sum _i{F}_i,F_i=\left\{\begin{array}{c}1,if0.5\le \frac{{\chi }_{\mathrm{m}\mathrm{o}\mathrm{d}}}{{\chi }_{\mathrm{e}\mathrm{x}\mathrm{p}}}\le 2.0\\ 0,\text{otherwise}\end{array},\right.$$ (11)

$$FB=2\frac{\left({\chi }_{\mathrm{e}\mathrm{x}\mathrm{p}}-{\chi }_{\mathrm{m}\mathrm{o}\mathrm{d}}\right)}{\left({\chi }_{\mathrm{e}\mathrm{x}\mathrm{p}}+{\chi }_{\mathrm{m}\mathrm{o}\mathrm{d}}\right)}.$$ (12)

Fig. 15.

FAC2 and FB for each source and velocity profile for the a uniform and b nonuniform building arrays compared against the no-building model performance shown in black. Quantile–quantile plots for the c uniform and d nonuniform model runs where again the black points illustrate the no-building case. Dashed lines are FAC2 error and open circles are within the canopy. Large points are within $|y/H|<3.33$ of the tunnel centerline, whereas small points represent the entirety of the data

Figure 15 displays the model performance for all building cases with the no-building case represented by the points in black. Performance statistics computed using all the data are shown with small points, whereas results limited to $|y/H|<3.33\left(\right|y|<200\mathrm{m}\mathrm{m})$ are shown with large points. The no-building reference offers values of $FAC2=80.8\mathrm{\%}$ and $FB=0.031$ for all data and $FAC2=97.6\mathrm{\%}$ and $FB=0.047$ for $|y/H|<3.33$. All building configuration cases fare worse than the no-building reference in both categories, and all model results are biased low. The continued improvement of the velocity profile (from the original AERMOD fit to the scaled AERMOD fit to the urban profile) decreases the magnitude of the FB of the model but only maintains or decreases the FAC2 percentage. Comparing the original AERMOD profile to the urban profile, this improvement leads to a 43.4% and 54.5% decrease in FB to −0.3 and −0.2 on average for uniform and nonuniform cases, respectively. The $FAC2$ decreased by 2.5% to 63.5% on average for the uniform case and remained at 67.5% for the nonuniform case. This determination is curious, as using the actual velocity profile should improve the model performance, not degrade it, suggesting additional formulation issues are present that must be resolved. The decrease in $FAC2$ performance from the no building data is 34.1% and 30.1% on average for the uniform and nonuniform cases.

Apart from general model accuracy, given the uses of AERMOD, we must also consider a regulatory perspective where the time and space of observations are ignored, and the maximum sorted concentrations are used exclusively for permitting applications. These results are visualized in a quantile-quantile (Q-Q) plot in Fig. 15c, d against the no-building data in black, where observed values within the canopy are presented as open circles with closed circles above the canopy. The urban velocity profile data are used for these comparisons. While the no-building data follow the 1:1 line, the maximum building observations are categorically underpredicted by the existing AERMOD formulation. The highest modeled values for the uniform case approach or drop below 50% of the observations, all of which are within the canopy for the lowest-positioned odd-numbered sources. Considering the highest ten observed values for each source location, the AERMOD formulations, even with the best fit urban velocity profiles, are only 48.1% and 62.4% of the observations for uniform, and nonuniform cases, respectively. These results offer the baseline of model performance to benefit future model development.

4.3. Suggested Improvements

Our findings encourage future urban model development in AERMOD to improve both general model and regulatory model performance seen in Fig. 15. Without true building awareness, there are limited parameterizations that can improve performance in generic urban environments, and true predictions will remain dominated by the geometry local to the source. However, we highlight four physically-based modifications to incorporate in the model. They include:

1. Implementation of a displacement height in the velocity profile (accomplished above) or an urban-type profile as suggested by Weil and Alessandrini (Weil and Alessandrini 2023).

2. Corresponding to the mean velocity profile, scale the velocity variance below the canopy to account for the presence of the buildings, following the work of Stockl et al. (Stöckl et al. 2022), with details in Appendix A.

3. Incorporate a lateral shift, $y_P$, if information on the ratio of freestream to lateral flow velocity near the source is known.

4. Apply first order corrections based on the local geometry of buildings by accounting for the volume into which the plume can physically disperse based on plan and frontal area ratios on the vertical and lateral spread, respectively. We additionally impose the width of the street canyon aligned with the wind direction to put a limit ${\sigma }_y$ in the near field.

The addition of a displacement height was discussed previously and resulted in varied model performance with respect to the existing AERMOD formulation, as shown in Fig. 15. Scaling of the velocity variance within the canopy is a coupled argument and is encouraged by many observations suggesting the peak variance occurs near the top of the canopy and decays toward the surface (Huq and Franzese 2013). We chose to follow the guidance of Stockl et al. (Stöckl et al. 2022) with details presented in Appendix 1. The introduction of $y_P$ was inspired by the work of Hertwig et al., who utilized averaged LES velocity components near the source to induce a lateral shift (Hertwig et al. 2018). We took available horizontal PIV data representative of the source y-z location to ratio the lateral to freestream direction velocity to parameterize a lateral shift as:

$$y_P=c\frac{v_T}{u_T}\sqrt{x},$$ (13)

where the square root functional form was supported by the experimental data from the uniform building array in Fig. 10a, and c is a constant.

Finally, first order geometric corrections are considered based on the reduced volume the plume can disperse into laterally and vertically. Effective spread parameters within the canopy for the lateral spread by the frontal area was defined as ${\sigma }_{yeff}={\sigma }_y\left(1-{\lambda }_f\right)$ for $\mathrm{z}<H$, and considering the presence of buildings that limit the vertical spread through the plan area was defined as ${\sigma }_{zeff}={\sigma }_z\left(1-{\lambda }_P\right)$ for all z. We use the average frontal and plan areas of the two different nonuniform blocks as representative values. To account for channeling through the street canyon, we strictly impose a limit on the lateral variance for cases when the flow direction is parallel to the direction of the street, as is the case for sources 3 and 4 in this study for a wind direction of 0°. Imposition of this limit would require the modeler to have more intimate knowledge of the surrounding area to encourage such a restriction in a regulatory model evaluation.

The results of these efforts are summarized in Table 3 with the best-performing values in bold and shown as “x“ shapes in Fig. 16, where the model evaluation points from Fig. 15 are repeated as solid circles for comparison purposes along with recalculated regulatory Q-Q plots. Viewing the mean values from all sources in Table 3, the suggested modifications do help mitigate $FB$. The gains in $FAC2$ are modest on average, with only an 11% and 1.4% improvement for the uniform and nonuniform cases, respectively. In fact, the nonuniform scaled AERMOD velocity profile still outperformed the urban profile with the suggested improvements. This (1) highlights continued issues with applying Gaussian schemes in urban canopies if incorrect inputs produce the best result, and (2) reiterates how lessons learned from uniform arrays do not necessarily apply in nonuniform arrays.

Table 3.

Summarized FAC2 and FB for different velocity profiles and model formulations for $|y/H|<3.33$

	Case	AERMOD	AERMOD scaled at z = 2H	Urban Profile	Urban Profile with suggestions
Uniform	FAC2	66.0%	69%	63.5%	74.5%
	FB	− 0.53	− 0.40	− 0.30	− 0.073
Nonuniform	FAC2	67.5%	71.3%	67.5%	68.9%
	FB	− 0.44	− 0.29	− 0.20	+ 0.02

Fig. 16.

Same as Fig. 15, with model performance values for the urban velocity profile (closed circles) compared to the suggested improvements (“X” shape) for $|y/H|<3.33$ for a uniform and b nonuniform configurations. Q-Q plots for c uniform and d nonuniform configurations where open circles are within the canopy

Figure 16 allows the examination of each source location independently. The model performance is improved for all sources in the uniform configuration, evidenced by a shift towards $FB=0$ and an increase in $FAC2$. The uniform Q-Q plot now straddles the 1:1 line for difference source locations, void of a underprediction bias. However, these improvements do not translate to the nonuniform configuration. The only source locations that definitively improved in both $FB$ and $FAC2$ are source 2 for 0° and 30°, and source 4 for the 0° case, all of which are mounted higher to mitigate the effect of the canopy. All sources within the canopy decreased model performance. The nonuniform Q-Q plot also now straddles the 1:1 line, juxtaposed to earlier in Fig. 15d, but now with a high bias driven by locations within the canopy. Considering the average of the top 10 observations for all sources, the new suggestions produce model values 95.7% and 134% of the observed values for uniform and nonuniform configurations, respectively.

5. Conclusions and Future Work

A wind tunnel study was constructed at 1:200 scale to analyze the performance of the EPA’s preferred Gaussian dispersion model, AERMOD, in mock uniform and nonuniform building arrays. Four unique source locations for incoming wind directions of 0° and 30° were studied to examine the effects of frontal area and channeling in comparison to a representative no-building case. PIV and HCA measurements provided local meteorological and concentration observations for each configuration. Results were compared to the model formulations in AERMOD.

Measured velocity profiles encouraged the use of a piecewise velocity profile, incorporating a displacement height in the canonical log-law profile to best represent the average flow field, with an exponential profile to model the flow within the canopy. Values of peak Reynolds shear stress varied significantly based on the local environment, encouraging a weighted sum to generate a column averaged value of $u_{\mathrm{*}}$ for each model configuration. Dispersion profiles obeyed general trends for the uniform case, including both a bias and translation towards the more “open” side of the urban model for all source positions in the 30° wind case. Lateral spread for source positions in streets with a parallel wind direction was limited by channeling through the width of the street canyon. Trends observed in the uniform array were not as applicable in the nonuniform configurations, as the local building geometry generated dual Gaussian plume profiles that are currently intractable in the AERMOD formulation.

Model performance using AERMOD formulations for a no-building reference case produced model performance metrics of $FAC2=97.6\mathrm{\%}$ and $FB=0.047$ for $|y/H|<3.33$ to provide a baseline to compare against model accuracy in residential urban areas. As an average for all source positions, $FAC2=63.5\mathrm{\%}$ and 67.5% and $FB=-0.3$ and −0.2 for the uniform and nonuniform cases, respectively, using the urban velocity profiles from PIV measurements. Regarding peak observed concentrations, the AERMOD formulations were unable to predict the maximum concentrations observed in the wind tunnel, most of which occurred within the urban canopy. The mean of the ten highest modeled concentrations were only 48.1% and 62.4% of the observations for uniform and nonuniform cases, respectively.

These results illuminated the high accuracy of AERMOD in a horizontally homogenous no-building environment, coupled with the inability of the AERMOD formulation to predict concentrations in idealized building environments. The AERMOD formulation does not account for the reduction in turbulence and general air volume within an urban canopy, incorporate a lateral shift, or account for geometric-constrained channeling effects. Simple improvements were suggested, resulting in a mitigation of FB on average and modest only 11% and 1.4% improvements to the $FAC2$ for the uniform and nonuniform cases, respectively. These results highlight how improvements derived from simple, regular arrays do not always translate to realistic, nonuniform environments.

Future work will entail higher resolution datasets from a coinciding LES effort, providing finely resolved outputs of all meteorological and dispersive parameters as opposed to the discrete observations offered here to better isolate how far downwind a Gaussian model would be representative. Such data, when properly validated against this wind tunnel experiment, will further aid the development of parameterized urban formulations in AERMOD or other fast-running Gaussian dispersion models.

Appendix 1: Lateral and Vertical Velocity Variance

Following the work of Stockl et al. (Stöckl et al. 2022), we compared their suggested profiles with our data before applying them as a modification to the AERMOD formulation. With planar PIV oriented along the axis of the freestream direction, we do not have $\overline{v^{\prime }{v}^{\prime }}$ available, but we can view $\overline{u^{\prime }{u}^{\prime }}$ and $\overline{w^{\prime }{w}^{\prime }}$ for comparison purposes. Stockl et al. suggest the following formulations, after comparison with a variety of spatially averaged wind tunnel experiments, full scale experiments, and simulated flow fields:

$${\sigma }_u^2=\overline{u^{\prime }{u}^{\prime }}={\left.\overline{u^{\prime }{u}^{\prime }}\right|}_{z=h}\exp \left[1.30\left(\frac{z}{h}-1\right)\right],$$ (14)

$${\sigma }_v^2=\overline{v^{\prime }{v}^{\prime }}={\left.\overline{v^{\prime }{v}^{\prime }}\right|}_{z=h}\mathrm{e}\mathrm{x}\mathrm{p}\left[0.72\left(\frac{z}{h}-1\right)\right],$$ (15)

and:

$${\sigma }_w^2=\overline{w^{\prime }{w}^{\prime }}={\left.\overline{w^{\prime }{w}^{\prime }}\right|}_{z=h}{\left(\frac{z}{h}\right)}^{\frac{1}{2.06}},$$ (16)

for $z\le h$ with values decaying linearly for $z>h$ to the height of the mixing layer estimated at $z=25h$. However, for this analysis we limit the discussion to the surface release and therefore constant velocity variance values. Figure 17 compares these functional forms to the PIV data obtained from this work for the uniform and nonuniform 0° cases. There are small differences in magnitude between this model and our measurements, but note the general agreement in functional form of the fit to the experiment within the canopy. Therefore, these expressions are added to the formulation in hopes of improving the comparison. For implementation in AERMOD, a few changes are required to maintain consistency in the formulation. Lateral spread (Eq. 3) is a direct function of ${\sigma }_v$, with ${\left.\overline{v\prime v\prime }\right|}_{z=h}=3.6u_{\mathrm{*}}^2$. Vertical spread is not clearly derived from ${\sigma }_w$ in Eq. (4), but we can utilize the canonical relationship ${\sigma }_w=1.3u_{\mathrm{*}}$ to relate the variables to apply Eq. (15) with ${\left.\overline{w^{\prime }{w}^{\prime }}\right|}_{z=h}={\left(1.3u_{\mathrm{*}}\right)}^2$. Applying this expression as a direct substitution in Eq. (4), we obtain the following:

$${\sigma }_{zs}=\frac{{\sigma }_w}{1.3}\sqrt{\frac{2}{\pi }}\left(\frac{x}{\tilde{u}}\right){\left(1+0.7\frac{x}{L}\right)}^{-\frac{1}{3}},$$ (17a)

$${\sigma }_{zs}=\frac{1.3u_{\mathrm{*}}{\left(\frac{z}{h}\right)}^{\frac{1}{4.12}}}{1.3}\sqrt{\frac{2}{\pi }}\left(\frac{x}{\tilde{u}}\right){\left(1+0.7\frac{x}{L}\right)}^{-\frac{1}{3}},$$ (17b)

$${\sigma }_{zs}={\left(\frac{z}{h}\right)}^{\frac{1}{4.12}}\sqrt{\frac{2}{\pi }}\left(\frac{u_{\mathrm{*}}x}{\tilde{u}}\right){\left(1+0.7\frac{x}{L}\right)}^{-\frac{1}{3}}.$$ (17c)

This expression is similar to the existing expression, only now with a ${\left(\frac{z}{h}\right)}^{\frac{1}{4.12}}$ modifier as a function of receptor height at or below the average building height.

Fig. 17.

a-b Uniform zero-degree normal stress profiles compared to the suggested model from Stockl et al. c-d, similarly for the nonuniform zero-degree case. Faded colors represent individual profiles, black points are an average over all profiles, and the solid red line is the fit

Data Availability

Data from this work are available after publication at https://doi.org/10.23719/1531139.