A micro-scale dispersion model for motor vehicle exhaust gas in urban areas—OMG volume-source model

Atmospheric Environment Vol. 24B, No. 2, pp. 243-251, 1990. 0957 1272/90 $3.00+0.00 Printed in Great Britain. © 1990 Pergamon Press pie

A MICRO-SCALE DISPERSION MODEL FOR MOTOR VEHICLE EXHAUST GAS IN URBAN AREAS--OMG

VOLUME-SOURCE MODEL

HITOSHI KONO* a n d SHOZO I T o t * Planning and Coordination Department, Environment Division, Environment and Public Health Bureau of Osaka City, 1-3-20, Nakanoshima, Kita-ku, Osaka, 543 Japan and t College of Engineering, University of

Osaka Prefecture, Mozu-Umemachi, Sakai, Osaka, 591 Japan

(First received 28 December 1987 and in final form 10 February 1989)

Abstract--A micro-scale dispersion model is presented for estimating the concentration of pollutants from motor vehicle exhaust gas within an area extending 200 m from the side of the road in an urban area. The initial mixing of pollutants in a street canyon is modeled as a volume source employing an analytical solution to the Fickian diffusion equation.

Parameters for the model were determined based on data from experiments performed at five locations in Osaka. In the experiments, S F 6 w a s released as a tracer gas. The height for wind speed measurements for use as the advection speed of the plume was determined from an analysis of the flux of SF 6. The eddy diffusivities in the vertical and lateral directions were derived from statistics of the turbulent velocity fluctuations of the air. The sensitivity analysis of the model revealed that proper characterization of the thickness of the volume source is essential for proper estimation of the concentration of pollutants.

Key word index: Dispersion model, micro-scale, motor vehicle, urban area, volume source, OMG VOLUME-SOURCE model.

1. INTRODUCTION 2. MODEL

Several dispersion models for motor vehicle exhaust gas have been constructed (e.g. EPA HIWAY-2 Model by Petersen (1980) and CALINE-3 Model by Benson (1979)). Most of the models were developed for charac- terizing the dispersion of motor vehicle exhaust gas emitted along a highway in rural open terrain.

Few dispersion models are applicable to urban streets. The use of highway models developed for rural roadways is questionable as there are significant dif- ferences in the dispersive processes in urban areas vs rural areas. In urban areas, buildings stand along the streets, and the exhaust gas is mixed by eddies within the street canyons. The concentrat ion of pollutants in the vicinity of the street depends on the size of the street canyon. The mechanical turbulence resulting from the buildings should result in eddy diffusivities above buildings quite different from those seen in rural areas near roadways.

This paper describes the O M G * V O L U M E - SOURCE model, a micro-scale dispersion model for motor vehicle exhaust gas. The model is applicable for estimating concentrat ion of pollutants in an urban area within 200 m from the side of the road. We discuss the formulas for the O M G V O L U M E - SOURCE model, the data analysis for determining the parameters of the formulas, and the sensitivity of the concentrat ion estimates to the specification of each input parameter.

*Osaka Municipal Government.

2.1. Dispersion formula The concentration is estimated using the solution to

the Fickian diffusion equation obtained by Peters and Klinzing (197I)

=Qp /(m+l)(n+l)exp{ u,(m+l)y2~ C 4It ~/ KyK~x 2 4Kyx J

x [ e x p { u'(n+l)(z-z')2~ 4Kzx J

+exp{ 4Kzx J_] (1)

Ky = k, (x/L)"~ K z = k 2 (x/L)") (2)

where C = concentration of pollutant (m a m-3) , (x, y, z) = coordinates of receptor (m),

z' = point source release height (m), Qp = emission rate (m a s - 1), u a = advection speed of plume (m s - 1),

Ky, K, = eddy diffusivities in y and z directions (m2 s - l ) ,

kl , k2 = eddy diffusivities in y and z directions at x = L (m2s-1),

L = scaling parameter (10 m), m, n = empirical parameters.

In the model, the origin of the coordinate axes is fixed at the point on the imaginary boundary illustra- ted in Fig. 1. The direction of the x-axis is downwind

243

244 HITOSHI KONO and Snozo ITO

VOLUME S O U R C E

I 0 I I h i l i i i

_ _ L ' ' I !

BUILDING

F---; BOUNDARY

C--Cw, (-hs<z<O) Fig. 1. Schematic diagram of a volume source. The position margined with shadow illustrates a volume source. An imaginary boundary is placed at the bottom height of the volume source. H, D = depth and width of the volume source, h = height of

buildings, hs: height of base of volume source.

(horizontal); the y-axis is perpendicular to the x-axis and in the horizontal plane; and the z-axis is vertical to the ground.

When the wind direction is perpendicular to the road, the following equation given by Waiters (1962) for an infinite line source model is employed.

C=Q~. / , + l [expel u.(,+_l)(z-z'):~ 2 X[nu, k,xL t 4K,x J

+ e x p { ujn+-l)(z+z')2~] 4K,x J_} (3)

where Qe=emission rate from line source (m 3 m - 1 s - 1), and the other symbols are as defined in Equation (1).

A volume source is employed to model the effects of mixing of the pollutants within the street, see Fig. 1.

The concentration of pollutants emitted from the street is estimated by integrating Equation (1) and Equation (3) over the volume source. An imaginary boundary is placed at the bottom of the volume source. Based on the observed concentration distribu- tions of S F 6 leeward of the road, the concentration of pollutants under the imaginary boundary is assumed to be the same as that at the height of the imaginary boundary.

2.2. Eddy diffusivity The eddy diffusivity in the vertical direction, K=, is

related to the vertical turbulent velocity fluctuations a s

K, = l,o-,,, (4)

where aw is the standard deviation of the vertical turbulent velocity fluctuations, aw is representative of the magnitude of the turbulent velocity fluctuations in the vertical and 1~ represents the vertical mixing scale. We assume

1. = ~= (5 )

where at is the standard deviation of the concentra- tuon distribution in the vertical and u is an empirical parameter. The eddy diffusivity in the vertical can be defined as

K= = (1/2) (d tr~/dt) (6)

where t is travel time downwind and can be expressed as t = x/u,. If aw/u, and ct are independent of x, Equations (4), (5) and (6) can be used to express the eddy diffusivity in the vertical as

K= = ~2(%/u,)x%. (7)

The eddy diffusivity in the lateral direction, Ky, can be defined as

Kr = (u,/2) (da~/dx), (S)

where ay is the standard deviation of the concentration distribution in the lateral and we have again used t = x/ua. From Taylor (1921), % can be related to the lateral turbulent velocity fluctuations as,

ay = (a~/ua )x fy (9)

where av is the standard deviation of the lateral velocity fluctuations andfy is a universal function. For short travel times,fy is primarily a function of distance. Various expressions are available for fy, Irwin (1979) summarized Pasquill's (1976) as

fr = 1/(1 +0.031X°"6) , (10)

where x, in m, is less than 104 m. Substituting Equa- tions (9) and (10) into (8) provides the following expression for the lateral eddy diffusivity,

Ky = (0"2/Ua) {X/(1 + 0.031X0"46) 2

--0.014x°'46/(1 +0.031X°'46)3}. (11)

Since try is proportional to X 0"93 in Pasquill's empirical diagrams, we would anticipate from Equation (8) that Ky will be nearly proportional to x °'s6, and that by analogy to Equation (11),

Ky = (~2/Ua)XO'S6. (12)

Micro-scale dispersion model for exhaust gas 245

For 1 < x < 200 m, Equation (12) is generally within 15% of Equation (11). For simplicity, we used Equa- tion (12) in the model.

3. SENSITIVITY ANALYSIS

For practically applying the model, we have to distinguish those input parameters that most affect the estimated values of concentration For this purpose, using Equation (3), we performed a sensitivity analysis of the effect on the estimated concentration values to changes in the size of the volume source and in the vertical eddy diffusivity. The analysis was conducted for winds perpendicular to the roadway. Table 1 lists the input data employed in the sensitivity analysis and Figs 2 and 3 summarize the results.

Table 1. Input data for sensitivity analysis of the model

u = 2 ( m s -1) D = 15, 30 (m) H = 5, 10 (m)

( 1.3 (x/10) for unstable Kz=~O.55(x/lO) (m2s - l) forneutral

[0.26 (x/10) for stable

C/Qc

0.I D(m) H(m)

.,~ 15 5

. . . . . 30 5

• ! > , \ [ - . - 1 5 : ' \ l

• i \\k~ T stable Kz

---'~'-" "-~i : .~ '? .~: + n e u t r a l K, ' ~i " .L unstable K,

. . . . I .... i l

0 50 i00 150

Normal distance from the volume source (m)

Fig. 2. Normalized ground surface concentration of pollutant (c/Qt) vs volume source size and eddy diffusivity in

vertical direction (Kz)

Z Z

-H- ~ D (m) H (m) -H

2 " 'I', 15 5 2

'~ .... 30 5

\ " . . ~:o<m)

1 o 0 "'-.. " "'''~' 1

o o.05 o.i

C/Q [

The results can be summarized.

(1) The concentration estimate is more sensitive to changes in thickness of the volume source than to changes in the width of the volume source. (2) Near the road, the concentration estimate is more sensitive to changes in the thickness of the volume source than to changes in the eddy diffusivity due to stability variation. The sensitivity to the size of the volume source decreases as distance from the road increases, hence, the concentration estimates at larger distances are most sensitive to the specification of the eddy diffusivity.

4. EXPERIMENTAL DESIGN AND DATA

The parameters of the model were determined using data from dispersion experiments obtained at five locations in Osaka, Japan (Osaka Prefectural Govern- ment, 1979). Table 2 lists the characteristics and number of receptors at each location. As an example, Fig. 4 shows the arrangement of emission source, sampling points and location of meteorological instruments at Location O-2.

SF6 gas was released from a line source of 200 m in length, which was laid along the center of the street. The line source consisted of two pipes, each 100 m in length. SF 6 gas was released through holes on the pipes arranged at intervals of 5 m. The uniformity of SF6 concentration along the line source was checked before the dispersion experiments. It was ascertained that the concentration became uniform at 10 m downwind from the line source, if there was enough traffic mixing of the air. SF 6 was released for 30 min at a rate of 0 .005-0.006gm-*s-1. The amount of SF 6 released was measured using a weighing instrument. The release rate was monitored using a flowmeter. Before being released, SF6 gas was diluted to 10% (by volume) with air so that the density of the tracer gas became closer to that of the air. Pure SF6 gas was released in all experiments at Location 0-5 and at half

D(m)H(m)

15 5

.... 30 5

~:50 (m)

0 0.05 0.I

c/o

Fig. 3. Normalized concentration of a pollutant (c/Qt) in the vertical direction vs normalized height and volume source width. :~: normal distance from

the volume source.

246 HITOSHI KONO and SHOZO ITO

Table 2. Characteristics of location where trace gas was released, parameters of volume source and number of receptors

Building Volume source Number of Location p h (m) H (m) D (m) h s (m) H/h receptors

O-1 0.64 7 6 25 7 0.9 42 ~ 46 0-2 0.32 7 3 30 5 0.4 46 ~ 47 0-3 0.20 12 6 30 5 0.5 40 ~ 46 0-4 0.48 9 ~ 12 12 30 12 0.8 ~ 1 51 ~ 62 O-5 Open terrain: line source on G.L. 40

p = Building-to-land ratio around the street (*). h = Building height. H = Thickness of volume source in the vertical direction. D = Street canyon width and width of volume source. hs = Bottom height of volume source. G.L. = Ground level. * The aerial photographs were used to calculate p. In the areas of 100 m square on the both

sides of the street, p was investigated. The street where the line source was laid was not included in the area but the other small streets in the area were included in the area.

J_._J.

o_L____

7 I

c: j

159m >I< . -

{ , f ' 4 - 0

] . . . . . . . . - ~

P I . _

. ~ - ~ 7 " = l ' ~ - - I J l ~ , ~ ~ ~ ~)' | f - - ' l l ~ - . ( ~ - -

Fig. 4. An example of a line source and a sampling network for SF6 on the vertical and horizontal planes and a site for installing meteorological instruments in a residential area (Location 0-2): • = sampling point for SF 6 concentration; ® = site for meteorological instruments: [] = line source:

0 = wind direction/roadway orientation angle (deg).


of the experiments at Location O-3. Data obtained at Location 0-3 when pure SF 6 gas was released was excluded from the following analyses. The release rate of SF 6 was determined with the following objectives in consideration.

(1) SF 6 should be released at a rate that facilitates easy analysis. (2) SF 6 should be uniformly released through all of the holes. (3) The density of the tracer gas should be close to that of the air.

Sample air was collected using pumps and sample bags of 10 ~ capacity. The duration of sampling was 20 min. The sampling began 10min after the be- ginning of the release of SF 6. Sampled air was ana- lyzed using a gas chromatograph and an electron capture detector.

Using meteorological instruments as described in the Appendix, three components of atmospheric turbulence (u', v', w') were measured at a height of 15 m from ground level. Average wind speeds were determined from measurements at heights of 1, 4, 8 and 15 m. Solar radiation and radiation balance were measured to determine the Pasquill's stability category of each location. The meteorological instruments were sited in an open space of approximately 50 m square between buildings.

The Pasquill's stability categories were determined at each location using the method described by the Japan Experts Committee on Atomic Energy and Meteorology (Expert Committee on Atomic Energy and Meteorology, Nuclear Safety Research Associ- ation Japan, 1973). This method uses insolation during the daytime and net radiation (instead of the cloud amount) during the night-time.

The three wind speed components were recorded using an analogue data recorder. The signals were sampled at a rate of 5-10 times per second and averaged for the second to obtain one data per second. The observed average vertical velocity component did not equal zero. Furthermore, there was no evidence of a periodic variation in the average vertical velocity component as a function of horizontal wind directions 180 ° apart. We conclude that the phenomenon was caused by nearby obstacles and not by an inclination of the meteorological support mast. Accordingly, we did not revise the vertical velocity fluctuation data by a rotation of the axis.

A total of 124 dispersion experiments were conducted in Osaka. Of these, 36 experiments having a crosswind (wind direction/roadway angles between 65 ° and 90 °) and a wind speed at 15 m, u,5 1> 1 m s- *, were used to determine the height of the imaginary boundary and the size characterization of the volume source. 27 experiments conducted at Locations O- l - O - 4 were used to determine K z. And 94 experiments were used to calculate K r. The turbulence data from 40 experiments were used to check the value of K= in stable and unstable conditions.

5. DATA ANALYSIS

5.1. Mean advection speed of a plume

We determined the mean advection speed of a plume using, the following equation:

Qt u, sin0 = ® (13)

fh C(50, z) dz

where 0 is the wind direction/roadway orientation angle and C(50, z) indicates use of SF6 concentration values at x = 50 m downwind and the height of z m above ground. For determination of the mean advection speed, cases with wind direction nearly perpendicular to the roadway, 65 ° < 0 < 90 °, were selec- ted. The advection speed determined using Equation (13) was considered representative for use within the range from the roadside to distances 200 m downwind of the roadway. The parameter, h,, represents a level below which buildings interrupt the horizontal advection to the extent that the mean advection speed is zero. In the model, h, represents the height of the imaginary boundary shown in Fig. 1.

We calculated h, by using the following mass balance equation, which relates the amount of released SF6 per unit source length and unit time, Qe, to the vertical mass flux,

Qe = u(z) sin 0 C(x, z) dz. (14)

Values for C(x, z), u(z) and 0 in Equations (13) and (14) were obtained from observations collected during the tracer experiments. At three of the four urban experimental locations, we were able to obtain reasonable estimates of h,. These results are shown in Fig. 5, where the mean, maximum and minimum values were obtained from cases with crosswind flow where u,5 was >1 1 ms -* . At Location O-1, where buildings stand close together along the street, the mean h,

15

10

h, (m)

5

h(m) p

~ max. ave. 0 0-I 7 0.64

mln. O 0-2 7 o. 32

A 0 -3 12 0 .20

It t 0 I I i I

5 I 0 50 I 00 N o r m a l d i s t a n c e f r o m t h e c e n t e r o f t h e s t r e e t (m)

Fig. 5. Height of imaginary boundary h,.

248 HITOSHI KONO and SHOZO ITO

approximately equals the height of the buildings, h. We concluded from a comparison of the mean advection speed, u,, determined from Equation (13) to the observed vertical wind profile, u(z), that u, corresponds to the wind speed at several m above the buildings at Location O-1 where the building-to-land ratio, p, is high. At Location 0-3, where the building- to-land ratio is lower than at Location O-1, it was determined that u~ corresponds to the wind speed at the height of the buildings.

5.2. Size of the volume source

Table 2 list the thickness and bottom height of the volume sources determined at Locations O-1-O-5. Figure 6 shows the average normalized SF 6 concentration (uC/Qt), under neutral (B-C to D), crosswind conditions and u 15 f> 1 m s- *, as functions of normal distance from the center of each street. The average concentration was computed from observed values at heights less than half of the average building height. The results shown in Fig. 6 differ greatly in going from two-storey buildings at Location O-1, to taller buildings at 0-4, to open flat terrain at 0-5.

Our conclusions from these comparisons between estimated and measured concentrations at Locations O-1-O-5 are as follows.

(1) The width of a volume source equals that of the corresponding street canyon. (2) For streets with buildings close together, the depth of the volume source, H, equals the height of the street canyon. The height of the base of the volume source, h,, equals the height of the buildings.

O. L

uc/O~

• , • , I r e , g | . . . . . . . !

0 - 3 ~ .

°o°:

0.01 m m ' .... ! ' • , .... I i0 i00

X(m)

Fig. 6. Normalized concentration (uc/Ql) of SF 6 at O-1- 0-4, urban area, averaged between ground surface and the height of hi2, and normalized ground surface concentration of SF~ at 0-5, rural flat open terrain: x = normal distance from the center of street; solid line = observed concentration of SF 6, dotted line: predicted concentration of SF 6 at O-1, dashed line: predicted concentration of SF 6 at 0-4, dash-dotted line: predicted concentration of SF~ at 0-5; Kz = k 2 (x/10), n = 1 for urban areas, n = 0.7 for rural flat terrain. Parameter k 2 is determined by a least squares fit between

predicted and measured SF 6 concentration.

(3) At locations with buildings-to-land ratios, p, equals 0.20, both the depth and height of the base of the volume source are reduced to 1/2 of the height of the buildings.

5.3. Eddy diffusivity

We determined the parameters, n and k2, for determination of the eddy diffusivity in the vertical, for cases when u,5 i> 1 m s -*, using a least squares fit between the estimated and measured SF 6 concentrations. Measured SF~ concentrations above the imaginary boundary under crosswind conditions were used in determining n and k 2. In the most cases, except the experiments at Location 0-3, values for n were scat- tered within a range between 0.5 and 1.5. Therefore, in order to simplify the model, we assumed n = 1. We then redetermined the value of k 2 again, holding n = 1, using a least squares fit.

The eddy diffusivity, K,, was determined using Equation (7) for cases when u~5 ~> 1 m s-~. The parameter ct was determined by substituting k 2, n, ~rw, u, for the corresponding terms in Equations (2) and (7). Figure 7 shows the results. We conclude from the results shown in Fig. 7 that ~t varies as a function of atmospheric stability. However, there does not seem to be a systematic relation between ct and building size or building density. Therefore, in the model, we defined ~t as a function of atmospheric stability only. In the model, we employ the same values for ~, regardless of wind speed, as there were too few cases with u,5 < 1 m s -~ for analysis. Table 3 summarizes the values determined for parameterization of eddy diffusivities above buildings.

In the model development, Kz was related to Pasquill's stability category, for instances when on-site turbulence measurements are unavailable. With the following characterization of ~,,

_ ~2k2L-"x"+ * ~ 1/2 t r z - ( ( ~ 1 - ~ ) ' (15)

Equation (3) is converted to the form of a Gaussian plume equation for an infinite line source. The disper-

2

G

1

0.5

A &

°o~

O v A

00-i

O 0-2

"0-3

V 0-4 I I

A B

0 . 1 I I I I I

C D E F G

P a s q u l l l ' s s t a b i l i t y c lass

Fig. 7. Exchange coefficient ~ vs Pasquilrs stability class.


Table 3. Summary of parameters of eddy diffusivities above buildings

K z Ky Wind speed ~ B k 2 av /u a 6~,/u a (ms-l) all i>1 <1 i>1 <1

Unstable 1.1 0.76 1.6 0.59 (A ~ B) (2) (2) (6) (28)

Neutral 0.81 0.27 0.33 0.43 (BC ~ D) (11) (11) (4) (42)

Stable 0.55 0.17 0.31 0.39 (E ~ G) (3) (3) (1) (12)

0.56Ua -0"a2 (12)

( ) = Sample size In order to calculate the concentration of pollutants averaged for l-h, the

values of av/ua averaged for 20 minutes in Equation (17) were converted to those averaged for 1-h by using Gifford's formula:

¢7v/U a OCt 0"2,

where t is the averaging time.

sion parameters, az do not depend directly on wind speed, u, in the Pasquill and Gifford's diagram. With the following characterization of k 2,

k 2 = B((, Zo)U a, (16)

the right-hand side of Equation (15) becomes independent of ua. B is an empirical function of atmospheric stability, (, and surface roughness length, z o. Values determined for B for cases with u15 >t 1 m s -1 are listed in Table 3, where B has the units of m.

Equation (16) suggests that k2, and hence Kz, are proportional to ua. This is reasonable when u15 > 1 m s -1. When Uls < 1 (m s - l ) , other dispersive factors become important and K~ is not only proportional to wind speed. For instance, during low advection wind speeds, we would anticipate during unstable conditions to have greater heat convection than otherwise might be expected and during stable conditions to sometimes encounter gravity wave effects. Therefore, average values were calculated for k 2 for each stability category for use in modeling Kz when u15 < 1 m s- 1. Table 3 lists the mean k 2 value for each stability category.

In the model, Ky can also be calculated from Pasqtiill stability category and wind speed using the values of av/ua listed in Table 3. These values were determined for each stability-wind speed class, from the sonic data collected during the tracer experiments, when ul~ t> 1 m s -~.

Adachi and Ohta (1978) investigated the relation- ship between av/u and u during very low wind speeds, where av was the standard deviation of the lateral velocity fluctuations and u was the vector average wind speed. They determined that av/u is inversely proportional to u.

The following regression equation was obtained from our data of the 12 cases having u15 < 1 ms -1 with all measurements in m s- 1,

a v / U a = 0.45/U TM. (17)

The correlation coefficient (or explained variance), r 2,

between In av/u~ and In u~ for these 12 cases is equal to

0.79. As there was more dependence on u, than with stability category, we did not segregate by stability in determining Equation (17). The results suggest that during low wind speeds, av is only a weak function of wind speed.

6. DISCUSSION

The results of the sensitivity analysis show that pollutant concentration near a roadway are more dependent on the thickness of the volume source than on the eddy diffusivity. Therefore, the degree of irregu- larity in building heights along both sides of the road can affect the precision of the estimated concentration values. That is, the model is anticipated to obtain more precise estimates where building heights along the road are constant.

The bottom height of the volume source, hs, was defined to be the height where the vertically integrated SF6 flux, 50 m downwind from the road, equaled the tracer emission rate, Qe. Wind speeds measured at 1, 4, 8 and 15 m above the ground were used in determining the SF 6 flux. The average advection speed of the plume was then computed as a concentration weighted average over heights > h,. In general, it is difficult to represent wind speed between many buildings with one value measured at a specific location. However, the computed values of h~ did converge, though with some variations as shown in Fig. 5. It was concluded that the average value of h~, 50 m from the center of the road, is approximately equal to the building height in an area where buildings stand close together (p =0.64) and is 1/2 the building height where few buildings stand (p = 0.20). This is thought to be caused by the fact that the closer the buildings stand, the lower becomes the ratio of the flux that flows below the height of the buildings to the flux that flows above the buildings.

An important factor in modeling the dispersion is the height for wind speed measurements for best representation of the average advection speed of a plume. We concluded, that for a street along which

250 HITOSH! KONO and SHozo ITO

buildings stand close together, the best wind speed measurement height is several m above the buildings. This result is consistent with recommendation in the EPA HIWAY-2 model for use of wind speed measurements 2 m above ground level over open terrain. As the space between buildings increases, the representative height of the wind speed should be lowered (i.e. where p = 0.20, the height is the same as that of the buildings).

The typical mixing scale, l~, was determined to be 1.1 times as large as the vertical dispersion parameter, az, in unstable atmospheric conditions; 0.81 times a~ in neutral conditions; and 0.55 times az in stable conditions. These results suggest that in unstable and neutral conditions, eddies of size az are most effective in dispersal of the pollutants. And that in stable conditions, eddies of size smaller than az disperse the pollutants. These results are consistent with plume behavior reported by various researchers.

In the determination of values for ~ and B (for characterization of the vertical eddy diffusivity), there were too few crosswind orientation cases for analysis during unstable and stable stability conditions to accept the results as generally applicable. Considering only experiments with u15 > 1 m s -1, there were 28 experiments available for analysis in unstable conditions, and 12 in stable conditions. Comparing aw/ua measured with a crosswind orientation to that measured for all wind orientations, there was 3 % difference in stable conditions and 12% difference during unstable conditions. The degree of difference was relatively small, and we conclude that the values of B in unstable and stable conditions listed in Table 3 may be more generally applicable.

In calm conditions, it is difficult to define the mean transport direction of the pollutant because the wind direction changes frequently. In these situations, the average estimated concentration for 1-h involves large errors. A more representative estimate for practical use may be obtained by averaging the results from several tens of 1-h measurements.

7. CONCLUSIONS

The results obtained in determining the model parameters for the O M G VOLUME-SOURCE model are summarized as follows.

(1) The width of the volume source is equal to the width of the street canyon. For a street along which buildings stand close together, p = 0.64, the thickness of the volume source in the vertical is equal to the height of the street canyon, and the bottom level of the volume source equals the building height. As buildings become further apart, p = 0.20, both the thickness and bottom height of the volume source reduce to half the building height. (2) The measurement height of wind speed for best characterization of the mean advection wind speed of the plume, is several m above the buildings for a

street along which buildings stand close together. As the space between buildings increases, the representative height of wind speed should be lowered (i.e. where p = 0.20, the height is the same as that of the buildings). (3) The eddy diffusivity in the vertical direction is calculated as,

K~ = ot2(aw/u,)Xaw,

where 0t is 1.1 during unstable conditions (Pasquill categories A and B), 0.81 during slightly unstable to neutral conditions (categories B-C to D) and 0.55 during stable conditions (categories E-G). The lateral eddy diffusivity is calculated as,

K r = (0"2/Ua)X 0"86.

When turbulence measurements are not available, both K~ and Ky can be calculated using empirical parameters related to Pasquill stability category. (4) When applying the model, one is cautioned that the concentration estimates are highly sensitive to the specification of the thickness of the volume source. And that model performance will degrade in situations where there are large variations in building heights.

Acknowledoements--This research was supported by the Environment and Public Health Bureau of the Osaka Municipal Government. The programming and computer calculations were carried out in cooperation with the Japan Information Service Processing Cooperation and Staff mem- bers T. Matsui and A. Konishi. We thank them for their help in the data analysis, and we also thank K. Oda, T. Masuda, T. Shinohara, T. Matsumoto, K. Yamane and the staffmembers in the Planning and Coordination Department of the Osaka Municipal Government for assisting with this study.

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APPENDIX: METEOROLOGICAL INSTRUMENTS FOR EXPERIMENTS

Instrument Measurement Precision Manufacturer and model

Sonic anemometer Three components of wind < 4% (u, v) Kaijo-denki Co. speed of full scale Model SA-200 (u, v)

(20ms -1)

< 3% (w) Model PA-111-1 (w) of full scale (3 m s- 1)

< 0.3 m s- 1 Makino-ohyosokki-Research Institute Model S-11-1

Eikoseiki-Sangyo Co. Model CN-I 1

Eikoseiki-Sangyo Model Eppley

Cup anemometer Wind speed

Net-radiometer Radiation balance

Pyranometer Solar radiation

< 5% of reading

< 2.5% of reading

Documents

A micro-scale dispersion model for motor vehicle exhaust gas in urban areas—OMG volume-source model