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  • View in gallery
    Fig. 1.

    Downtown Oklahoma City urban landscape with buildings shaded by building height. The measurement crane is marked with a triangle, and the release positions are marked with circles. The release positions are P for Park Avenue, W for the Westin Hotel, mW for modified Westin, B for botanical gardens, and F for intersection of 4th and Hudson Streets. The dates and IOPs for each release location are listed in Table 1.

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    Fig. 2.

    Instrumented crane system. Circles enclose the lowest two of the seven tracer inlets.

  • View in gallery
    Fig. 3.

    WSU TRAVERT profile system: 1) sampling bags and valves, 2) SF6 analyzer, and 3) control and data acquisition computer.

  • View in gallery
    Fig. 4.

    The SF6 vertical profiles from the crane site normalized by the maximum concentration measured during each 5-min profile during the (a) nighttime and (b) daytime IOPs are compared with (c) Briggs urban formulations for stability classes D and F. Only those measured profiles that had a maximum concentration of 500 ppt are plotted in (a) and (b).

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    Fig. 5.

    The 5-min-averaged tracer concentration profiles normalized by release rate from DOYs (a) 194, (b) 197, (c) 205, and (d) 207 (IOPs 5, 6, 8, and 9, respectively). The time stamps represent the endpoints of the 5-min sample period. The magnitudes of the error bars for selected concentration values are based on the percentages presented in Table 3.

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    Fig. 6.

    The 5-min-averaged tracer concentration profiles normalized by release rate from the mini-IOP (DOY 196) for (a) release period 1 and (b) release period 2. The time stamps represent the endpoints of the 5-min sample period. The magnitudes of the error bars for selected concentration values are based on the percentages presented in Table 3.

  • View in gallery
    Fig. 7.

    The SF6 concentrations normalized by release rate. These curves represent the maximum value over the depth of the profile. The y axis range for (j) is larger than the other panels because this was the mini-IOP, which had a much closer release point.

  • View in gallery
    Fig. 8.

    Normalized concentration for each of the seven tracer measurement levels and 42.5-m wind speed, and wind direction on DOYs 194, 197, 205, and 207 (IOPs 5, 6, 8, and 9, respectively). Error bars denote the ranges of values observed over the eight sonic anemometer levels and are positioned at the midpoints of the 10-min-averaging periods. The solid horizontal lines in the wind direction plots denote the azimuth connecting the release to the crane.

  • View in gallery
    Fig. 9.

    Instantaneous normalized concentrations from the mobile van on 4th and 8th Streets during IOPs (a) 5 and (b) 6. The abbreviations in the legend, such as R1P5, represents release 1, pass 5. The solid black line in the bottom half of the figure connects the release location with 8th Street and passes through the crane site. Van traverses were on 4th Street during releases 1 and 2, and on 8th Street during release 3.

  • View in gallery
    Fig. 10.

    Instantaneous normalized concentrations from the mobile van on 8th Street during IOPs (a) 8 and (b) 9. The abbreviations in the legend, such as R1P2, represents release 1, pass 2. The solid black line in the bottom half of the figure connects the release location with 8th Street and passes through the crane site.

  • View in gallery
    Fig. 11.

    Map of building-top meteorological station locations (black pentagons). The black triangle marks the crane location, and the stars mark each of the main IOP release locations.

  • View in gallery
    Fig. 12.

    The 5-min wind directions from building-top meteorological stations (St. Anthony’s, Civic Center, and DEQ) and 10-min wind directions from the 42.5-m LLNL sonic anemometer at the crane site during IOPs (a) 5, (b) 6, (c) 8, and (d) 9. The dashed horizontal line represents the azimuth connecting the release position to the crane site.

  • View in gallery
    Fig. 13.

    Plume channeling and dispersion pattern for a 210° wind direction case (heavy black line) are compared with the plume when no channeling occurs (dashed black line).

  • View in gallery
    Fig. 14.

    Average plume widths (σy) at 1000 m for each of the 12 continuous releases of IOPs 5, 6, 8, and 9 as a function of |β|, the angle of the winds with respect to the north–south streets. The fit line is the sum of a conventional empirical diffusion coefficient and the street channeling and diffusion component.

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Vertical Tracer Concentration Profiles Measured during the Joint Urban 2003 Dispersion Study

Julia E. FlahertyLaboratory for Atmospheric Research, Department of Civil and Environmental Engineering, Washington State University, Pullman, Washington

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Brian LambLaboratory for Atmospheric Research, Department of Civil and Environmental Engineering, Washington State University, Pullman, Washington

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K. Jerry AllwinePacific Northwest National Laboratory, Richland, Washington

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Eugene AllwineLaboratory for Atmospheric Research, Department of Civil and Environmental Engineering, Washington State University, Pullman, Washington

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Abstract

An atmospheric tracer dispersion study known as Joint Urban 2003 was conducted in Oklahoma City, Oklahoma, during July of 2003. As part of this field program, vertical concentration profiles were measured at approximately 1 km from the downtown ground-level tracer gas release locations. These profiles showed that the urban landscape was very effective in mixing the plume vertically. In general, the lowest concentration measured along the profile was within 50% of the highest concentration in any given 5-min measurement period. The general slope of the concentration profiles was bounded by a Gaussian distribution with Briggs’s urban equations (stability classes D and E/F) for vertical dispersion. However, measured concentration maxima occurred at levels above the surface, which would not be predicted by Gaussian formulations. Variations in tracer concentration observed in the time series between different release periods were related to changes in wind direction as opposed to changes in turbulence. This was demonstrated using data from mobile analyzers that captured the width of the plume by traveling east to west along nearby streets. These mobile-van-analyzer data were also used to compute plume widths. Plume widths increased for wind directions at larger angles to the street grid, and a simple model comprising adjusted open-country dispersion coefficients and a street channeling component, were used to describe the measured widths. This dispersion dataset is a valuable asset not only for developing advanced tools for emergency-response situations in the event of a toxic release but also for refining air-quality models.

* Current affiliation: Pacific Northwest National Laboratory, Richland, Washington

Corresponding author address: Julia E. Flaherty, Pacific Northwest National Laboratory, P.O. Box 999, MSIN K9-30, Richland, WA 99352. Email: julia.flaherty@pnl.gov

This article included in the Urban 2003 Experiment (JU2003) special collection.

Abstract

An atmospheric tracer dispersion study known as Joint Urban 2003 was conducted in Oklahoma City, Oklahoma, during July of 2003. As part of this field program, vertical concentration profiles were measured at approximately 1 km from the downtown ground-level tracer gas release locations. These profiles showed that the urban landscape was very effective in mixing the plume vertically. In general, the lowest concentration measured along the profile was within 50% of the highest concentration in any given 5-min measurement period. The general slope of the concentration profiles was bounded by a Gaussian distribution with Briggs’s urban equations (stability classes D and E/F) for vertical dispersion. However, measured concentration maxima occurred at levels above the surface, which would not be predicted by Gaussian formulations. Variations in tracer concentration observed in the time series between different release periods were related to changes in wind direction as opposed to changes in turbulence. This was demonstrated using data from mobile analyzers that captured the width of the plume by traveling east to west along nearby streets. These mobile-van-analyzer data were also used to compute plume widths. Plume widths increased for wind directions at larger angles to the street grid, and a simple model comprising adjusted open-country dispersion coefficients and a street channeling component, were used to describe the measured widths. This dispersion dataset is a valuable asset not only for developing advanced tools for emergency-response situations in the event of a toxic release but also for refining air-quality models.

* Current affiliation: Pacific Northwest National Laboratory, Richland, Washington

Corresponding author address: Julia E. Flaherty, Pacific Northwest National Laboratory, P.O. Box 999, MSIN K9-30, Richland, WA 99352. Email: julia.flaherty@pnl.gov

This article included in the Urban 2003 Experiment (JU2003) special collection.

1. Introduction

Atmospheric transport and dispersion field campaigns have been vital in the development and evaluation of air-quality and emergency-response models. Early experiments, such as Project Prairie Grass (Barad 1958) and the Wangara Experiment (Clarke et al. 1971), were fundamental to the study of plume dispersion. High-quality datasets such as those produced from these principal experiments continue to be referenced as a source of analysis and validation data. Some examples include Draxler’s (1976) and van Ulden’s (1978) work on diffusion coefficients as well as recent improvements to these diffusion parameters by Britter et al. (2003). Draxler (1984) presents an excellent summary of early dispersion experiments.

Many of these early atmospheric studies were conducted under relatively simple dispersion conditions. However, as Molina and Molina (2004) and Gurjar and Lelieveld (2005) have pointed out, nearly one-half of the world’s population now live in urban areas. Creating models that are more applicable for the complex urban landscape has increasingly become a research priority. Many people are exposed to a variety of urban pollutants daily; however, we still have an incomplete understanding of urban pollutant transport and diffusion. Britter and Hanna (2003) highlighted research that has investigated various components of urban flow. They mentioned that, although we have a fairly good understanding of the individual processes that take place in urban landscapes, how these processes combine and interact with one another is less clear.

In recent work, field studies, wind tunnel experiments, and numerical models have been used to investigate dispersion around individual buildings (e.g., Calhoun et al. 2004; Meroney et al. 1999), in single street canyons (e.g., Caton et al. 2003; Sagrado et al. 2002), and through small multibuilding industrial and urban areas (e.g., Guenther et al. 1990; Scaperdas and Colvile 1999). Additionally, large-scale dispersion studies have been performed for more complex settings. These include the Dispersion of Air Pollution and its Penetration into the Local Environment (DAPPLE) field experiment in London (Arnold et al. 2004), which studied a street canyon intersection as a potential hot spot for personal exposure; the Basel Urban Boundary Layer Experiment (BUBBLE), conducted in Basel, Switzerland (Rotach et al. 2004), which investigated dispersion over a fairly regular array of buildings; Urban 2000 in Salt Lake City, Utah (Allwine et al. 2002), which investigated the homeland security implications of atmospheric releases in an urban area; and the Barrio Logan study in San Diego (Venkatram et al. 2004), which was an environmental justice case that looked at the transport of emissions from an industrial area to a residential area 2 km downwind. This paper will discuss tracer vertical profile measurements from a recent urban dispersion study, Joint Urban 2003 (JU03), which was conducted in Oklahoma City, Oklahoma (OKC; Allwine et al. 2004).

The goal of this field study was to build a high-quality, comprehensive urban dispersion dataset to fill in the gaps in our understanding of these complex flows. These data are available for the characterization of urban flow and scalar dispersion as well as for the evaluation, modification, and improvement of dispersion models. This is important for the accurate prediction of urban air quality as well as for determining the impact of accidental or intentional releases of harmful materials.

In this study, over 20 principal investigators and 150 researchers collected meteorological and tracer data throughout Oklahoma City. The month-long field program included 10 intensive observation periods, or IOPs. Each IOP was 8 h long and generally consisted of three 30-min continuous sulfur hexafluoride (SF6) tracer releases and four instantaneous puff releases. Tracer releases were conducted at a height of approximately 2 m above ground level, and release rates were typically on the order of 3 g s−1 during the continuous releases and 500 g during puffs. The 10 IOP dates were selected based on predicted wind directions from the south or southeast, and three different release locations were utilized in order to maximize the data collected by the array of downwind receptors. Six of the releases occurred during the day, while four were conducted during the night. In addition to the 10 IOPs, a “mini-IOP” was conducted. In this case, the wind direction was not appropriate for conducting a complete IOP, so a new release position was selected about five blocks upwind of the Washington State University–Lawrence Livermore National Laboratory (WSU–LLNL) vertical profile site, which is described in a subsequent section. During the mini-IOP, several sonic anemometers and tracer analyzers were employed in addition to the instrumentation on the 90-m profile system. Table 1 presents a summary of the date, day of year (DOY), time, release position, 10-min vector-averaged wind direction and wind speed, persistence, friction velocity, and the distance from the source to the vertical profile site for the continuous releases of each IOP.

The objective of this paper is to present an analysis of the vertical concentration profile data collected downwind of the urban core of OKC using the Tracer Vertical (TRAVERT) system—a novel, automated profile sampling system. Section 2 briefly describes the study area, section 3 discusses the vertical profile system, section 4 presents the results of the data analysis, and a summary and conclusions are given in section 5.

2. Site description

Oklahoma City is situated in the middle of the state of Oklahoma on the flat terrain and grasslands of the Great Plains. During the summer, winds in OKC are generally from the south and the average wind speed for the month of July is 5.1 m s−1. July is OKC’s warmest month, with a mean temperature of about 28°C (82°F). The mean daily maximum temperature during this month is 34°C (93.4°F), while the mean daily minimum is 21.4°C (70.6°F) (NWS 2003). As mentioned in the previous section, tracer measurements were made during the hottest part of the day, when convection is likely to play a large role, as well as during the coolest part of the night.

Oklahoma City has a population of approximately 500 000, with 1 180 000 people within the metropolitan area (U.S. Census Bureau 2000). This dispersion study was conducted in the heart of downtown OKC, which contained all of the tallest buildings in the city as well as many shorter buildings of various shapes. The tallest building in the city is the Bank One Building, which is about 150 m tall. The central business district contains two other buildings that are at least 120 m tall, and eight additional buildings that are between 75 and 120 m tall. Other buildings in downtown Oklahoma City are less than 50 m, with many structures about 15 m tall. Figure 1 shows the urban landscape of downtown Oklahoma City. This range of building dimensions is characteristic of many medium-sized U.S. cities.

The role of the WSU Laboratory for Atmospheric Research in JU03 was to measure tracer concentrations using a vertical profile system, called TRAVERT, with inlets mounted on a 90-m crane located approximately 1 km from the downtown release points. This crane was also fitted with a series of three-dimensional sonic anemometers, which measure winds, operated by LLNL. The circular markers in Fig. 1 indicate the locations of the tracer release points, while the triangular marker near the top of the figure represents the crane (vertical profile) site. This site was near the southwest corner of the intersection of 8th Street and Harvey Avenue. Other obstacles that are not depicted in Fig. 1 that had minimal effect on the measurements made at this crane site include several shipping containers and trailers located on the southern half of the block occupied by the crane measurement system.

3. Profile system

a. Instrumentation

A ladder structure with two vertical cables in tension and eight horizontal crossbars was utilized to support the vertical profile system of sonic anemometers and tracer sampling lines. A large crane, approximately 90 m tall, suspended this ladder system while a smaller crane served to anchor it. The large crane was instrumented with a sonic anemometer on each of the eight crossbars. Researchers from LLNL collected 10-Hz sonic anemometer data continuously throughout the month-long study. During intensive observation periods, sequential 5-min-averaged concentrations of SF6 tracer gas were measured simultaneously at seven heights, from about 10 to 75 m above ground level. These inlets were mounted on the western guide cable as depicted in Fig. 2. (See Table 2 for the heights of the instrumentation on the crane.) The ladder system was very stable; however, in high winds, there was slight lateral movement. Time averaging the sonic anemometer wind measurements to 10-min averages minimized the effects of lateral movements.

The WSU TRAVERT profile system allowed for automated collection and analysis of 5-min-averaged samples. In operation, air was drawn simultaneously through seven 91.4-m- (300 ft) long polyethylene sample lines to the instrument. It was equipped with fourteen 10-L Tedlar bags, so while one set of seven bags was collecting air samples, and the second set of bags was sequentially analyzed. The SF6 concentration in a single bag was determined by drawing air from the bag to the analyzer for 30 s. Between the sample analysis and collection, the Tedlar bags were evacuated completely to ensure that the bags were “clean” for the next sampling period. Laboratory tests indicated that the bags did not require a flushing cycle.

The TRAVERT system also included an online calibration by incorporating a zero air and SF6 span gas into each 5-min analysis cycle. Calibration gases were sampled for 45 s each. The span gases utilized during the IOPs were either 527 parts per trillion by volume (ppt) or 4950 ppt (Scott-Marin, Inc.; ±5% certified accuracy).

The sequential bag analyzer used in this system was a modified Hewlett-Packard model 5890 gas chromatograph equipped with an electron capture detector (ECD). The analysis first involved combining the sample air with H2, then passing it through a packed bed of palladium catalyst. This converted the O2 in the air to H2O. Next, the air was passed through a nafion tube with a countercurrent flow of N2. This removed the H2O from the sample stream. The sample stream was then passed to the ECD, where the voltage changes due to the SF6 in the stream provided the signal for concentration. See Benner and Lamb (1985) for additional information about this type of detector system.

The final component of this system was the computer, which ran a LabVIEW program that regulated the pumps to ensure that samples were collected in the appropriate bags and that the samples were pumped to the detector in the correct sequence. The program was also responsible for capturing the 1-Hz signal from the ECD and writing the data files. See Fig. 3 for a photo of the TRAVERT profile system.

b. Measurement system characteristics

The lag time, or the time for the sample to travel down the tubing to the TRAVERT system, was calculated using the measured flow rate (approximately 101 standard L min−1), cross-sectional area of the polyethylene tubing (6.35-mm inner diameter), and its length (91.4 m). Although the inlet tubes were mounted at different heights, equal lengths of tubing were used for equal sample travel times. The lag time was approximately 12 s throughout the test periods. This was a small fraction of the 5-min sampling time and was, therefore, neglected in the data analysis.

The lower detection limit (LDL) for the SF6 concentration measurement was determined as three times the noise of the instrument. Table 3 presents the LDL for each of the intensive observation periods. The LDL normalized by a tracer release rate of 3 g s−1 is also given in Table 3 for comparison during subsequent discussions using normalized concentrations. Factors such as the duration since the tracer release, comparisons between concentrations at different profile levels, and the winds at the different levels were also considered when determining whether a low concentration was valid.

Actual calibration coefficients utilized in the postprocessing of these SF6 data were determined with several factors in mind. A suite of calibration gases was analyzed with this system during non-IOP periods. By considering an average response for calibration runs that were conducted on the non-IOP periods as well as the span checks that were run during each 5-min analysis cycle, an appropriate calibration factor was applied. Furthermore, when applying the calibration to the raw voltage data that was collected from the ECD, the zero air voltage that was subtracted from the sample response was the linearly interpolated zero between the current and previous analysis period to account for short-term instrument drift.

There were several sources of error in the measurement of tracer concentrations. First, there was a systematic error (±5%) associated with the concentration of the standard gas utilized for the calibration of the voltage signal from the ECD. Additionally, there was a random error from the instrument itself. This was quantified by determining the coefficient of variability (CV) of the span gas measurement. The CV was calculated as the ratio of the standard deviation of the signal to the mean signal, and was expressed as a percent. Table 3 lists the errors associated with the final reported SF6 concentration for each study day. The typical error was ±8%.

4. Tracer results

This field experiment included a total of 32 continuous releases (20 daytime, 12 nighttime) of SF6 tracer during the 11 IOPs. The meteorological conditions during these 32 release periods resulted in tracer concentrations from 26 of the releases (20 daytime, 6 nighttime) detected at the crane site. For ease of interpreting data from the day and night releases, all times in this paper are presented as central daylight time (CDT). Vertical profiles and time series graphs of the data collected at the crane site, as well as a horizontal plume traverse measured both north and south of the crane site, are presented.

a. Tracer vertical profiles

The vertical profiles of the SF6 tracer measured at the crane site show that the tracer was relatively well-mixed through the depth of the measurements. All 5-min-average profiles from the 10 main IOPs with a maximum concentration of at least 500 ppt are presented in Figs. 4a and 4b. There are approximately 30 nighttime profiles and 15 daytime profiles that fit this criterion. Although there were several more daytime continuous releases, the nighttime IOPs observed more consistent hits at the crane site, while the daytime IOPs resulted in intermittent hits. These profiles have been normalized by the maximum concentration measured during each 5-min profile, so the abscissa shows the fraction of the maximum concentration measured at each height. This figure shows that, generally, near-surface concentrations were not significantly higher than concentrations at greater heights. In some instances, the profile maximum was measured aloft, and the lowest concentrations were observed near the ground. Over the entire study, the lowest concentration measured along the vertical profile was typically within 50% of the maximum concentration. A recent experiment conducted in Basel, Switzerland (Rotach et al. 2004), also made tracer measurements in an urban street canyon. Although the profile measured in Basel was only about 20 m in depth as compared with the 75-m measurement made in this study, results from both experiments indicate very low gradients in the vertical tracer concentration profile.

The Briggs (1973) urban vertical dispersion coefficients for stability class D (σz = 122 m) and E/F (σz = 50 m), based on data from the St. Louis study (McElroy and Pooler 1968), roughly bound the upper portion of the measured normalized concentration profiles in Figs. 4a and 4b. Figure 4c shows the Gaussian vertical concentration distributions based on Briggs’s empirical formulations normalized by the computed concentrations at 11 m, which is the height of the lowest measurement. The distance to the crane, or x = 1000 m, was used to compute the Briggs vertical dispersion coefficients. Comparison of the measured vertical tracer profiles with results from a Gaussian plume equation using Briggs urban formulations is useful in demonstrating a generally favorable comparison between the vertical dispersion results from this study and the St. Louis study. However, it is clear from Fig. 4 that a Gaussian formulation will not predict concentration maxima above the surface, and additional parameterizations are necessary.

Figure 4 also shows that there is no consistent or characteristic difference in the profile shapes between the day and night IOPs. Both day and night profiles had concentration maxima at each measurement height, with the height of the maximum more often occurring in the lower half of the profile. Figures 5 and 6 show specific profiles to illustrate this more clearly. Five-minute-average tracer profiles from one 30-min continuous release for each of two daytime IOPs (IOP 5, DOY 194; IOP 6, DOY 197), and two nighttime IOPs (IOP 8, DOY 205; IOP 9, DOY 207), are presented in Fig. 5. The four release periods are 1300–1330 CDT for the two daytime IOPs, and 0100–0130 and 2300–2330 CDT for the two nighttime IOPs, respectively. These profiles were selected because they represent high-concentration release periods from both daytime and nighttime study periods. The time stamps in this figure mark the endpoint of the sampling period, so that 1305 represents a sample collected from 1300 to 1305 CDT.

In Fig. 5, as in Fig. 4, slight differences in the general features or trends in the 5-min-average profile shapes between day and night are evident. As might be expected from enhanced dispersion during convective conditions, the daytime profiles (DOYs 194 and 197) are generally of lower magnitude and exhibit a more uniform vertical distribution than do the nighttime profiles (DOYs 205 and 207). Specifically, the nighttime normalized concentrations for DOY 207 decrease by roughly 30%–50% through the depth of the profile during the period (2315–2340 CDT) when the continuous tracer plume is fully influencing the crane site.

Figure 6 shows vertical tracer concentration profiles from two of the 20-min continuous daytime releases (1200–1220 and 1230–1250 CDT) conducted during the mini-IOP from location F shown in Fig. 1. While many of the buildings in the CBD were between 70 and 120 m tall, there was only one building of significant height between release location F and the crane. During the mini-IOP, the tallest building was about 70 m tall, and the typical building height was less than 8 m. Concentrations from the mini-IOP were higher than those shown in Fig. 5 because the release position for the mini-IOP was about one-half of the distance (∼500 m) to the crane site in comparison with the regular IOPs. Another contrast to the previous figure is the distinct slope in the tracer profile. At 1245 CDT, the topmost concentration was less than half of the 11-m sample, and at 1235 CDT, the 76-m sample measured a tracer concentration that was a quarter of the 11-m sample. The maximum concentration during the mini-IOP also tended to be near the ground.

In general, 10-min-average wind profiles measured at the crane site were consistent over the duration of the four sampling periods covered in Fig. 5 and the one sampling period covered in Fig. 6. One-hour-average wind speed profiles were calculated for 1300–1400 CDT on DOYs 194 and 197, 0100–0200 CDT on DOY 205, 2300–2400 CDT on DOY 207, and 1200–1300 CDT on DOY 196. Wind speeds increased with height, closely following the conventional logarithmic wind profile at measurement heights above 20 m (top six sonic heights in Table 2). The wind speed profile data above 20 m (six points) were fit to the logarithmic wind profile for each of the five sampling periods using a least squares approach. The friction velocities determined from the fits to the logarithmic wind profile (correlation coefficients greater than 0.96) were typically within 20% (lower) of those values listed in Table 1 determined from sonic measurements of momentum fluxes. The average surface roughness value (∼2 m) resulting from the fit to the logarithmic wind profile was commensurate with accepted values for urban areas (Stull 1988).

It is not clear why the wind speeds at the lowest two measurement heights (7.8 and 14.6 m) were considerably higher than expected from the logarithmic profile (approximately 2.7 m s−1 measured versus 1.8 m s−1 expected at the lowest height). One possible explanation is local channeling (and increase) of winds between low buildings (generally below 20 m in height) along the north–south-oriented Harvey Avenue (see Fig. 1) adjacent to the crane site. The possibility of channeling is supported by measured wind direction profiles at the crane site. For example, the average wind direction above buildings during the mini-IOP was approximately 191° (see Table 1), which is comparable to the nearly uniform wind direction profile measured above 20 m (top six levels) at the crane site. However, the wind directions measured at the lowest two heights were closer to 180°, which is indicative of potential channeling along Harvey Avenue.

b. Tracer time series

Figure 7 presents a summary of normalized tracer concentration data collected at the crane site during the continuous tracer release periods. The concentrations (μg m−3) were normalized by the release rate (μg s−1). Only the highest concentration observed during each 5-min sampling period over the seven measurement heights is plotted. Previous figures have shown that there are small variations in concentration values over the depth of this profile. Figure 7 contains 10 panels, with DOY 199 (IOP 7) the only IOP omitted. The winds during IOP 7 were not favorable for a plume hit at the crane site, and very little data were collected at the crane site for this IOP. The ranges of the ordinate values for each of the panels in Fig. 7 are identical, except in the case of the mini-IOP (DOY 196), which had significantly higher observed concentrations relative to the other IOPs. Each panel in Fig. 7 also includes a plot of release rate versus time showing the relationship between the release start and end times with the maximum tracer concentrations observed in the profile.

For most of the continuous releases, the SF6 tracer was observed in the 5-min period immediately following the beginning of the release, and tracer levels were below the lower detection limit of the instrument within 30 min of the tracer shutoff. For a 4 m s−1 wind speed, the approximately 1-km distance between the release location and crane would take about 4 min, so the travel time for plume arrival that was observed at the crane site matches well with this rough approximation.

Inspection of all IOPs in Fig. 7 reveals that the range of normalized concentrations (from 1 × 10−6 to 7 × 10−6 s m−3) observed when there was a “hit” at the crane compares well to the urban data from Barrio Logan reported by Venkatram et al. (2004). The ranges of normalized maximum concentrations measured during the Barrio Logan study at 1000 m downwind of their release position were generally between 1 × 10−6 and 1 × 10−5 s m−3. Even though the urban landscape in the Barrio Logan study was more uniform and shorter than in OKC, the maximum observed concentrations at 1000 m are comparable.

As shown in Fig. 7, a wide range of normalized concentrations were observed at the crane site across the various IOPs as well as within each IOP. In general, several potential factors, including release rate, transport distance, wind speed, wind direction, and turbulence levels can potentially account for the range of observed concentrations. However, since the observed concentrations are normalized by the release rate and the release rate is constant with time during any given release, release rate is not a factor. Additionally, transport distance from the release to the crane has a minor influence in accounting for the large variations in observed concentrations because (excluding the mini-IOP) all transport distances are approximately 1000 m ± 15%.

Investigation of the effects of winds on tracer concentrations observed at the crane site are investigated by focusing on the two daytime IOPs (5 and 6) and the two nighttime IOPs (8 and 9) discussed previously. Figure 8 presents normalized SF6 concentration, scalar wind speed, and wind direction from the crane site during the continuous tracer releases for IOPs 5, 6, 8, and 9 (DOY 194, 197, 205, and 207). The sonic anemometer data are 10-min-average values from a midheight anemometer (42.5 m), while the error bars denote the range of values observed over the depth of the eight sonic anemometers. The horizontal lines in the wind direction plots represent the straight-line direction that connects the release point with the crane site. These plots also show the range of measured SF6 concentrations along the profile by plotting the time series for each of the seven levels.

The winds during the daytime IOPs (DOYs 194 and 197) were more variable than the two nighttime IOPs (DOYs 205 and 207). DOY 194 had a 45° shift in the wind direction at approximately 1200 CDT, while DOY 197 had 15°–30° wind direction shifts about every 30 min. As a result, days 194 and 197 had greater variability in measured concentrations than days 205 and 207. On day 194, the second release had essentially no observed plume at the crane site, which appears to be due to both a slightly increased wind speed, which diluted the plume, and a wind direction that is 30° west of the ideal direction. The first release period during DOY 194 resulted in hits for only two time periods, because of the rapid shift in wind direction just after 0900 CDT. Day 197, on the other hand, had wind directions that were 20°–30° from the ideal direction for the duration of the first continuous release period, and no SF6 was detected at the crane location. Winds were closer to the ideal direction during the second and third continuous release periods, and concentrations were therefore higher for these two releases.

Both of the two nighttime IOPs, on DOYs 205 and 207, had fairly constant winds that were near the ideal direction. Day 205 measured similar plume concentrations between each of the three tracer releases. Although DOY 207 had winds that were similar to DOY 205, the third continuous release period did not result in any observations of the plume at the crane site. The wind direction was consistently about 20° from the ideal wind during the third continuous release period.

c. Plume traverse

Additional information about the nature of the plume concentrations measured at the crane location can be gleaned by looking at plume traverses. During IOPs 5, 6, 8, and 9, a van-mounted mobile SF6 analyzer, operated by the National Oceanic and Atmospheric Administration Air Resources Laboratory, Field Research Division, was deployed along 4th and 8th Streets. The van drove 10–12 passes during each release period, and spent approximately 2–5 min to travel each pass. Figure 9 presents the concentrations normalized by release rate for each of the continuous release periods during IOPs 5 and 6. The measurements for these IOPs were taken along 4th Street for the first two release periods, and along 8th Street for the third release. Fourth Street is four blocks south of the crane site, at approximately 3926400 m northing (universal transverse Mercator grid zone 14, North American Datum 1983), while 8th Street is directly north of the crane site, at approximately 3926850 m northing. Figure 10 presents the concentrations measured during IOPs 8 and 9. For these two nighttime IOPs, the mobile van remained on 8th Street for the duration of the experiment. These concentration curves are superimposed on a map of the city to show the physical relationship among the release location, the crane site, and the plume.

Variations in the tracer concentrations measured at the crane site were shown in the previous discussion to be primarily the result of wind direction variations where the tracer plume from the release site would impact the crane site depending on the wind direction. As can be seen in Figs. 9 and 10, the tracer plume misses the crane site at times, which is supported by the minimal tracer concentrations observed at the crane site as shown in Fig. 8. The times of the individual van passes shown in Figs. 9 and 10 are given in Tables 4 –7 to facilitate direct comparisons of the tracer concentrations shown in Figs. 9 and 10 with the time series concentrations given in Fig. 8.

Because wind direction is critical to the influence of the released tracer at the crane site, the spatial variability of wind direction around downtown Oklahoma City is investigated later (in Fig. 12, where the time series of vector-average wind direction are shown for IOPs 5, 6, 8, and 9 at four measurement locations). Figure 11 shows the locations of three of the meteorological stations that were deployed by Pacific Northwest National Laboratory (PNNL). These three stations were well exposed to the ambient flow, located on the tops of buildings much higher than the surrounding buildings. Figure 12 shows the 5-min-average wind directions measured at the three PNNL meteorological stations and the 10-min-average 42.5-m level of the LLNL sonic at the crane site (as also shown in Fig. 8). The “ideal” wind direction, such that the tracer plume from the release would impact directly on the crane site, is shown in Fig. 12 by a dashed horizontal line.

Inspection of Fig. 12 shows that the wind direction variability at each station and across the region is greater during the daytime than nighttime, and area-wide wind direction shifts are consistent at all stations. For example, the wind direction shift from south-southwest to south-southeast at approximately 1200 on DOY 194 is measured at all stations. The variability in daytime wind directions is roughly ±15° among all stations and within individual stations, and roughly ±10° among all stations and ±5° within individual stations during nighttime. An especially interesting systematic difference was observed in the nighttime wind directions during IOP 8 (DOY 205). When the winds from stations on St. Anthony’s Hospital and the Civic Center Music Hall were approximately from the south-southeast, winds at the Department of Environmental Quality (DEQ) and the crane site were approximately from the southeast. We speculate that this difference in wind direction is a result of a local influence of the much taller central business district (CBD) causing a turning of the winds just downwind from the CBD, where the DEQ and crane instruments are located. In general, the small spatial variability in the wind directions as revealed by the observations presented in Fig. 12 did not significantly influence the tracer concentrations observed at the crane site. Rather, the general area-wide wind direction was the dominant factor.

Figure 9a shows that the first two tracer releases (top two sets of curves) during IOP 5 were observed as very wide plumes centered well east of the crane site. The plume centerline is farther east than what is expected from the measured wind direction (∼210°). In fact, the plume centerline for the first two releases is more commensurate with a wind direction from roughly 235°. We speculate that the reason for the tracer plume being farther east than expected from the observed wind direction is an initial translation of the tracer plume east caused by channeling of the tracer plume along Sheridan Avenue (see Fig. 1). The broader plume is then advected approximately to the north-northeast by the ∼210° winds. The initial channeling of the tracer plume is illustrated in Fig. 13, showing a plume influenced by channeling in comparison with a plume with no influence of channeling for ∼210° winds. The plume is not only shifted to the east, but it is also wider than the nonchanneled plume because the plume is dispersed from both the real point source and the resulting line source along Sheridan Avenue. The behavior of initial plume channeling along Sheridan Avenue is supported by field observations (Clawson et al. 2005) and by a computational fluid dynamics analysis (Coirier and Reich 2003). The third release, which was measured along 8th Street, resulted in a narrower tracer plume centered at the crane site in winds approximately from the south. The maximum concentration measured during each van pass fluctuated during this release, supporting the variability in concentration with time shown in Fig. 8a.

The plume centerline was much closer to the crane during IOP 6, as shown in Fig. 9b. The plume from the first release was too far to the east to be observed at the crane; however, the second and third releases were in line with the crane, as was seen by the crane measurements in Fig. 8b. See Table 8 for the average wind directions during the three release periods.

Figure 10a shows that the first two releases (top two sets of curves) during IOP 8 resulted in a plume that was centered near the crane site. During the third release; however, the plume centerline had shifted toward the east, and the crane saw only the western edge of the plume even though the wind data from the crane site indicated that the third release period of IOP 8 had ideal wind directions that should have resulted in the plume being centered at the crane. The plume centerline position shown in Fig. 10a matches more closely with the location of the plume transported in winds indicated by the three PNNL stations in Fig. 12. As discussed previously, we speculate that the wind direction indicated at the crane site was locally influenced by a turning of the winds downwind of the CBD and were therefore not indicative of the mean transport direction of the tracer plume during the third release during IOP 8.

Figure 10b shows the plume traverse measurements from IOP 9. During this IOP, the concentration measured at the crane decreased significantly between the first and second releases, and no tracer was observed for the third release period. The mobile van data show clearly that the plume centerline was near the crane for the first release, but as the wind direction shifted, only the edge of the plume was measured at the crane for the second release. The final release period had a wind direction of about 190° (from Fig. 12), so the plume missed the crane site completely.

These mobile van data (particularly the nighttime data) show that when the winds were within 20° of the ideal wind direction, the highest concentrations were observed at the crane site. Figure 10 shows that the width of the measurable concentrations was about 600–800 m, while the width of a 20° angle at 1 km is about 340 m. Therefore, the plume centerline could shift 20° (or 340 m) from the ideal wind direction, and the crane would still measure the edges of the plume (300–400 m from the centerline). Outside the 20° envelope, concentrations drop off rapidly as only the far edges of the plume are observed, or the plume misses the crane site completely.

d. Plume width

The plume width (Y) can be estimated from the mobile van tracer data by calculating the second moment about the mean of the data:
i1558-8432-46-12-2019-e1
where Y is the cross-plume coordinate in meters, C is the concentration (ppt) as a function of cross-plume distance, and Y0 and A are as follows:
i1558-8432-46-12-2019-e2
i1558-8432-46-12-2019-e3
The measured plume widths for each of the plume passes shown in Figs. 9 and 10 are presented in Tables 4 –7. It should be noted that the “plume width” determined from Eq. (1) is not the actual width (width perpendicular to the plume path centerline) but rather the width of the plume traversed by the van, where the van traverse is not typically perpendicular to the plume path. The actual plume width is determined from a cosine correction to the van-measured plume width. The “uncorrected” plume widths given in Tables 4 –7 generally reveal the daytime plume widths to be greater than nighttime, and the range of plume widths determined from all van passes to be greater during the daytime IOPs than the nighttime IOPs.
Table 8 presents a summary of the average plume width measured by the van for each of the continuous releases from Tables 4 –7. This table also lists the average of the scalar wind speed and wind direction from the St. Anthony’s and Civic Center meteorological stations. As mentioned previously, the van traverse is not measuring the true width of the plume, but along the plume length as well. Therefore, the measurements from the van traverses will reflect a larger value than the real width of the plume. The van traversed along 4th and 8th Streets, which are aligned east–west, and if we assume the plume centerline aligned with the mean wind direction, the angle α in Table 8 is the absolute value of the angle between the wind direction and south (180°). The “actual” plume width (Ya) given in Table 8 is determined as
i1558-8432-46-12-2019-e4

Inspection of the variation of Ya with changes in α in Table 8 for similar transport distances (x) reveals that plume width increases as α increases. In the Oklahoma City study area, the rectangular street grid is oriented north–south and east–west, and so α also represents the angle between the plume transport direction (i.e., 180° from wind direction) and the azimuth angle of the street within 45° of the plume centerline. Let us assign the variable β to this angle between transport direction and street grid, where 0 ≤ |β| ≤ 45. As an example, β for a release from point B (Fig. 1) in 210° winds would be 30° where the plume transport direction is 30° (210° − 180°) and the azimuth angle of the street (Robinson Avenue north) is 0°. The angle β would be 10° for a release from B in 260° winds where the plume transport direction is 80° (260° − 180°) and the street azimuth angle is 90° (Sheridan Avenue east).

To describe the apparent relationship indicated in Table 8 between plume width σy and the angle between the transport direction and street grid β (same as α in Table 8), we propose the following simple model:
i1558-8432-46-12-2019-e5
where x is the downwind distance and σyo is the Pasquill–Gifford–Turner lateral diffusion coefficient. Open-country diffusion coefficients moved up one stability class can roughly account for urban diffusion (Hanna et al. 1982); therefore, the equation for slightly unstable conditions (Scire et al. 1984) is used:
i1558-8432-46-12-2019-e6
The proposed component to diffusion from street channeling σyc is represented as
i1558-8432-46-12-2019-e7
where DC is a characteristic urban length scale where buildings have the potential to significantly influence lateral dispersion primarily through street canyon channeling. Thus, DC is likely a function of the building morphology and will require further investigation with data from other cities, which is not within the scope of this research. A proposed value of DC for OKC is 150 m, which was determined from the best fit of the model results to measured plume widths. This simple model is shown as the line in Fig. 14, with data points of measured plume widths given as a function of wind angle from the street grid. The plume widths Ya were translated to a common distance (1000 m) using a virtual distance approach, applying the Pasquill–Gifford–Turner lateral diffusion rate given by Eq. (6). The measured plume width translated to 1000 m (Y1kma) increases with wind angle.

5. Summary and conclusions

This paper discussed tracer concentrations measured at a seven-level vertical profile (crane) site during the Joint Urban 2003 atmospheric dispersion study. Wind speeds were relatively high throughout the study, and tracer concentrations 1 km from the release were detected within 5 min of the start of a tracer release. Vertical tracer concentration profiles that were collected at the WSU–LLNL crane site show that the plume was mixed well vertically. The slopes of both the daytime and nighttime concentration profiles were generally bounded by a Gaussian distribution using Briggs urban equations for vertical dispersion. The wind direction profiles were relatively constant for the upper 60 m of the sonic anemometer measurements, and the wind speed for these six measurements fit well with a logarithmic profile. Friction velocities and surface roughness lengths derived from the logarithmic profiles were commensurate with values expected in urban areas. Localized phenomena such as building wakes, chimney effects near buildings, and convection due to differential heating may have contributed to the low-gradient concentration profiles measured at the WSU–LLNL crane site.

The variability in the concentrations measured at the crane site for different release periods was due primarily to differences in wind direction. Cross-plume concentration measurements from mobile SF6 analyzers that traversed 4th and 8th Streets showed that the highest concentrations measured at the crane site occurred when the wind direction was within 20° of the ideal transport direction. Except in the case of wind directions at large angles to the street grid, the plume centerline location matched well with the direction of the winds, and the concentrations observed at the crane site during each of the three continuous releases were correlated to the shift in plume position with wind direction changes. When winds were highly oblique to the street directions and the release location was from the botanical gardens, channeling occurred to the east so that the plume centerline was offset from the wind direction transport location, and the plume width was enhanced by dispersion from a line source from the channeled plume.

The mobile cross-plume concentration measurements were also used to compute plume widths. These data showed that widths increase when winds are at large angles to the street grid. A simple model was presented to describe the relationship between the plume width and wind angle from the street grid that comprised the adjusted open-country and street channeling dispersion components. In this case, winds at large angles to the street grid resulted in double the lateral plume dispersion of winds that were oriented along the street grid.

The information gained from this study continues to improve our understanding of the mechanisms by which atmospheric contaminants disperse through an urban landscape. This OKC dispersion dataset is a valuable asset not only for developing advanced tools for emergency-response situations in the event of a toxic release but also for refining air-quality models.

Acknowledgments

This work was supported by the U.S. Department of Homeland Security under Contract DE-AC06-76RLO 1830 at the Pacific Northwest National Laboratory. Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle Memorial Institute. We appreciate the efforts of Dr. Alan Hills of the National Center for Atmospheric Research (NCAR) for his assistance in programming with LabVIEW. We also thank Dr. Kirk Clawson and his staff at the National Oceanic and Atmospheric Administration’s Air Resources Laboratory—Field Research Division for their work in the tracer study and Dr. Marty Leach and his colleagues at Lawrence Livermore National Laboratory for their sonic anemometer data. We thank the community of Oklahoma City for their overwhelming support and collaboration with this field project.

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Fig. 1.
Fig. 1.

Downtown Oklahoma City urban landscape with buildings shaded by building height. The measurement crane is marked with a triangle, and the release positions are marked with circles. The release positions are P for Park Avenue, W for the Westin Hotel, mW for modified Westin, B for botanical gardens, and F for intersection of 4th and Hudson Streets. The dates and IOPs for each release location are listed in Table 1.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 2.
Fig. 2.

Instrumented crane system. Circles enclose the lowest two of the seven tracer inlets.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 3.
Fig. 3.

WSU TRAVERT profile system: 1) sampling bags and valves, 2) SF6 analyzer, and 3) control and data acquisition computer.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 4.
Fig. 4.

The SF6 vertical profiles from the crane site normalized by the maximum concentration measured during each 5-min profile during the (a) nighttime and (b) daytime IOPs are compared with (c) Briggs urban formulations for stability classes D and F. Only those measured profiles that had a maximum concentration of 500 ppt are plotted in (a) and (b).

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 5.
Fig. 5.

The 5-min-averaged tracer concentration profiles normalized by release rate from DOYs (a) 194, (b) 197, (c) 205, and (d) 207 (IOPs 5, 6, 8, and 9, respectively). The time stamps represent the endpoints of the 5-min sample period. The magnitudes of the error bars for selected concentration values are based on the percentages presented in Table 3.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 6.
Fig. 6.

The 5-min-averaged tracer concentration profiles normalized by release rate from the mini-IOP (DOY 196) for (a) release period 1 and (b) release period 2. The time stamps represent the endpoints of the 5-min sample period. The magnitudes of the error bars for selected concentration values are based on the percentages presented in Table 3.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 7.
Fig. 7.

The SF6 concentrations normalized by release rate. These curves represent the maximum value over the depth of the profile. The y axis range for (j) is larger than the other panels because this was the mini-IOP, which had a much closer release point.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 8.
Fig. 8.

Normalized concentration for each of the seven tracer measurement levels and 42.5-m wind speed, and wind direction on DOYs 194, 197, 205, and 207 (IOPs 5, 6, 8, and 9, respectively). Error bars denote the ranges of values observed over the eight sonic anemometer levels and are positioned at the midpoints of the 10-min-averaging periods. The solid horizontal lines in the wind direction plots denote the azimuth connecting the release to the crane.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 9.
Fig. 9.

Instantaneous normalized concentrations from the mobile van on 4th and 8th Streets during IOPs (a) 5 and (b) 6. The abbreviations in the legend, such as R1P5, represents release 1, pass 5. The solid black line in the bottom half of the figure connects the release location with 8th Street and passes through the crane site. Van traverses were on 4th Street during releases 1 and 2, and on 8th Street during release 3.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 10.
Fig. 10.

Instantaneous normalized concentrations from the mobile van on 8th Street during IOPs (a) 8 and (b) 9. The abbreviations in the legend, such as R1P2, represents release 1, pass 2. The solid black line in the bottom half of the figure connects the release location with 8th Street and passes through the crane site.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 11.
Fig. 11.

Map of building-top meteorological station locations (black pentagons). The black triangle marks the crane location, and the stars mark each of the main IOP release locations.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 12.
Fig. 12.

The 5-min wind directions from building-top meteorological stations (St. Anthony’s, Civic Center, and DEQ) and 10-min wind directions from the 42.5-m LLNL sonic anemometer at the crane site during IOPs (a) 5, (b) 6, (c) 8, and (d) 9. The dashed horizontal line represents the azimuth connecting the release position to the crane site.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 13.
Fig. 13.

Plume channeling and dispersion pattern for a 210° wind direction case (heavy black line) are compared with the plume when no channeling occurs (dashed black line).

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Fig. 14.
Fig. 14.

Average plume widths (σy) at 1000 m for each of the 12 continuous releases of IOPs 5, 6, 8, and 9 as a function of |β|, the angle of the winds with respect to the north–south streets. The fit line is the sum of a conventional empirical diffusion coefficient and the street channeling and diffusion component.

Citation: Journal of Applied Meteorology and Climatology 46, 12; 10.1175/2006JAMC1305.1

Table 1.

Summary of continuous release periods during each of the IOPs. Release locations are marked in Fig. 1. The 10-min vector-average wind speed (WS), wind direction (WD), and friction velocity (U*) values from the z = 42.5 m level at the crane site were averaged over the duration of the continuous release measurements. The persistence P is the ratio of the vector-averaged wind speed to the scalar-averaged wind speed. Here, U* was computed from the momentum fluxes: (2 + 2)1/4. The distance is the straight-line distance between the release and crane locations.

Table 1.
Table 2.

Sonic anemometer and tracer sample inlet heights at the crane site.

Table 2.
Table 3.

Lower SF6 detection limits and estimated calibration errors during each IOP. The normalized lower detection limit (s m−3) assumes a release rate of 3 g s−1. Here, CV is the coefficient of variability of the span, which is the random error, and gas is the systematic error of the standard gas.

Table 3.
Table 4.

Summary of mobile van plume pass data from IOP 5 shown in Fig. 9a.

Table 4.
Table 5.

Summary of mobile van plume pass data from IOP 6 shown in Fig. 9b.

Table 5.
Table 6.

Summary of mobile van plume pass data from IOP 8 shown in Fig. 10a.

Table 6.
Table 7.

Summary of mobile van plume pass data from IOP 9 shown in Fig. 10b.

Table 7.
Table 8.

Summary of average plume widths from mobile van plume passes during IOPs 5, 6, 8, and 9. Scalar wind speed (WS) and wind direction (WD) are the averages for the pass periods from the PNNL meteorological stations at the St. Anthony’s and Civic Center Music Hall buildings; Y is the average plume width over the several van passes of each release period presented in Tables 4 –7. Here, |α| is the angle (obtained from the wind direction) that is used to compute Ya, the average plume width perpendicular to the assumed centerline. The average distance from the release point to the measured plume centerline is X. Here also, Y1kma is the measured plume width adjusted to a downwind distance of 1 km using the Pasquill–Gifford Turner dispersion coefficient equation for slightly unstable conditions.

Table 8.
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