# Predicting Air Quality Near Roadways through the Application of a Gaussian Puff Model to Moving Sources {#predicting-air-quality-near-roadways-through-the-application-of-a-gaussian-puff-model-to-moving-sources .Awma-Title}

#  {#section .Awma-Head-2}

# 00-Abstract-65 {#abstract-65 .Awma-Head-2}

Roger L. Wayson

Brian Y. Kim

C. David Cooper

John M. Macdonald

Civil and Environmental Engineering

University of Central Florida

P.O. Box 162450

Orlando, FL 32816-2450

\(407\) 823-2480

wayson@pegasus.cc.ucf.edu

**Keywords: puff, model, dispersion, gaussian, air, roadway,
intersection, sigma, wake, modal, emission, multiplier, rise, traffic**

ABSTRACT

The Environmental Protection Agency (EPA) currently recommends the use
of CALINE3 or CAL3QHC for modeling the dispersion of carbon monoxide
(CO) near roadways. These models treat vehicles as part of a line source
such that the emissions are homogeneously spread out over the entire
line. And since the models use Gaussian plume equations, the results are
inherently steady-state values.

This paper describes a new simulation model entitled, TRaffic Air
Quality SImulation Model (TRAQSIM), developed at the University of
Central Florida. The basic concept in the model is that each vehicle is
considered a discrete moving point source rather than as part of an
overall line or area source. The model simulates traffic movement and
keeps track of the properties of each vehicle as it moves through a
traffic scenario. During each time-step, vehicles are moved and assigned
mode-varying emission factors. The dispersion in the atmosphere is
accomplished through the use of a Gaussian puff algorithm. Dispersion
parameters (σs) are determined from Pasquill stability classes and
combined with dispersion parameters corresponding to thermal buoyancy
and vehicle wake effects. Puff merging has also been implemented to
reduce computer processing time.

INTRODUCTION

The Environmental Protection Agency (EPA) currently recommends the use
of CALINE3 or CAL3QHC for modeling the dispersion of Carbon Monoxide
(CO) near roadways. These models distribute vehicle emissions and
traffic volumes along roadways which are modeled as line sources. This
approach is not realistic because only constant speed (not modal)
emission factors are applied to the line sources. Also, since the models
handle atmospheric dispersion through the use of steady-state Gaussian
equations, time-varying input and output information cannot be applied.

This paper describes a new roadway and intersection air quality model
developed at the University of Central Florida (UCF) entitled, TRaffic
Air Quality SImulation Model (TRAQSIM). The model takes a simulation
approach such that each vehicle is treated as a discrete moving point
source. Emissions from these moving sources are mode-specific since
modal multipliers are used to convert constant speed emission factors to
modal emission factors. The development of the modal multiplier
regression equations from the cooperative industry/government emissions
database collected in 1993-1994 is described elsewhere (1). Atmospheric
dispersion modeling is accomplished through the use of Gaussian puff
equations in order to provide transient concentrations. It is believed
that these theories provide a greater degree of accuracy and versatility
to the overall model than the current regulatory models.

COMPARABLE MODELS

Of the two EPA recommended models, CAL3QHC is more appropriate than
CALINE3 in comparing to TRAQSIM because unlike CALINE3, CAL3QHC can
model interrupted flow (intersections). CAL3QHC takes a macroscale
approach in determining queue lengths by using established methods from
literature such as the Highway Capacity Manual (2). Acceleration and
deceleration modes are approximated by using queue links. Therefore,
vehicle modes are not handled in a realistic manner. The cruise mode is
handled identical to constant speed travel along free-flow links, but
the idle mode is approximated by converting queue lengths into
equivalent free-flow line sources. Acceleration and deceleration effects
are approximated by the use of excess emissions which are derived by
converting queue links to equivalent free-flow links. All of the
emissions are used in Gaussian plume equations for line sources. CAL3QHC
essentially uses the CALINE3 model for atmospheric dispersion. Due to
the steady-state nature of the equations used, time-varying data (e.g.
meteorological) cannot be used during a model run. Although wind angles
can be varied and additional runs can be made for different conditions,
the results would still be steady-state concentrations. A well-known
shortcoming of CAL3QHC and most other air quality roadway models is that
dispersion in the near field due to vehicle wake effects and thermal
turbulence is difficult or impossible to accurately model. This is
because CALINE3 uses a mixing zone concept to account for the initial
dispersion directly over a roadway. The mixing zone is described by
setting an initial ~z~ three meters downwind of the nearest lane.

TEXIN2-4 is similar in scope to CAL3QHC in that it can model interrupted
flow and also employs the same equations used in CALINE3 to model
dispersion. However, the excess emissions arising from queues is handled
differently. TEXIN2-4 uses Critical Movement Analysis (CMA) to determine
a volume to capacity ratio (v/c) that leads to the determination of the
queue length. This queue length is then used along with derived emission
factors for vehicles slowing, stopping, and idling to determine the
total excess emission factor (3).

The CALINE4 model is essentially an expansion of CALINE3. Unlike its
predecessor, CALINE4 can be used to to model intersections. Queue
lengths are determined by using a vehicle spacing distance of seven
meters and modal activity input data. Modal emission factors are
determined from exponential functions obtained from regression analyses
involving modal multipliers and the product of speed and acceleration.
These factors are used to determine cumulative modal emission profiles
for each link. For use in dispersion modeling, the average distance rate
emission factor (e.g. g/mile) for a link is obtained by dividing the
difference between cumulative emissions at the link ends by the length
of the link. Similar to CALINE3, CALINE4 also incorporates a mixing zone
concept to account for the initial dispersion directly over a roadway.
But CALINE4 expands upon this methodology by incorporating an upward
heat flux algorithm that modifies the ~z~ values (4).

FLINT is another intersection air quality model that was developed at
the University of Central Florida. It uses macroscale traffic theory to
determine queue lengths and lengths of the acceleration/deceleration
zones. Modal emission factors are determined by applying fixed
multipliers to constant speed emission factors. The method FLINT uses to
model roadways is different than the aforementioned models in that the
roadways are treated as area sources and not as line sources. Dispersion
is accomplished through the use of the area source algorithm within the
PAL2 model. However, the  values in PAL2 were replaced with the ones in
CALINE3 (5).

MODEL DEVELOPMENT THEORY

# Vehicle Emissions {#vehicle-emissions .Awma-Head-2}

TRAQSIM currently requires constant speed emission factors determined
from MOBILE5a. These factors are converted to modal emission factors by
the use of modal multipliers. The development of the modal multiplier
regression equations is presented in another paper (1). The equations
relate modal multipliers (dependent variable) to the product of vehicle
speed and acceleration (independent variable). Emissions are categorized
in terms of vehicle type (cars, light-trucks, and heavy light-trucks)
and engine condition (cold transient, hot transient, and stabilized).
The condition of the engine is assumed to be constant for each vehicle
as it moves through a traffic scenario. This is considered reasonable
since travel times through an intersection are relatively short and the
condition of the engine is unknown prior to a vehicle's emergence into
the intersection being modeled.

# Atmospheric Dispersion {#atmospheric-dispersion .Awma-Head-2}

\(1\)

where c = concentration (g/m^3^)

Q = emission factor (g/s)

t = time interval between puff release (s)

x~p~, y~p~, z~p~ = center of puff (m, m, m)

x~r~, y~r~, z~r~ = receptor location (m, m, m)

H~m~ = height of mixing zone (m)

~x~ = standard deviation of puff in the x-direction (m)

~y~ = standard deviation of puff in the y-direction (m)

~z~ = standard deviation of puff in the vertical (z) direction (m)

The last two exponential terms in equation 1 represent reflections from
the ground and the top of the mixing zone, respectively. Due to the
conservative nature of CO, no deposition or decay is taken into account.
Although wind speed is not shown in the equation, it can be incorporated
into the puff location terms because a puff will be advected by the mean
wind. In addition to the wind, a puff's movement (or position) will be
affected by atmospheric rise and vehicle wake effects. These different
components also cause dispersion the magnitudes of which can be combined
as shown in equations 2-4.

> ~x~^2^ = ~ht~^2^ + ~hr~^2^ + ~xw~^2^ (2)

~y~^2^ = ~ht~^2^ + ~hr~^2^ + ~yw~^2^ (3)

> ~z~^2^ = ~zt~^2^ + ~zr~^2^ + ~zw~^2^ (4)

where ~x~ = x-composite horizontal dispersion parameter (m)

~y~ = y-composite horizontal dispersion parameter (m)

~ht~ = horizontal dispersion parameter corresponding to atm. turbulence
(m)

~hr~ = horizontal dispersion parameter corresponding to atm. rise (m)

~xw~ = x-horizontal dispersion parameter corresponding to vehicle wake
effects (m)

~yw~ = y-horizontal dispersion parameter corresponding to vehicle wake
effects (m)

~z~ = composite vertical dispersion parameter (m)

~zt~ = vertical dispersion parameter corresponding to atmospheric
turbulence (m)

~zr~ = vertical dispersion parameter corresponding to atmospheric rise
(m)

~zw~ = vertical dispersion parameter corresponding to vehicle wake
effects (m)

Dispersion parameters corresponding to atmospheric turbulence are
calculated from equations 5 and 6 which are based on parameters for
quasi-instantaneous sources that Turner developed from Slade (6).

σ~ht~ = ar^b^ (5)

σ~zt~ = cr^d^ (6)

where r = puff travel distance (m)

a, b, c, d = coefficients based on stability class (Table 1)

The parameters for these equations are shown in Table 1. This method of
determining dispersion parameters is similar to those used by current
regulatory line source models. Although theoretically simple, it is
advantageous over other methods when considering computation time. The
travel distance (r) in equations 5 and 6 is not necessarily the linear
distance from a current puff position to its original (release)
position. Rather, r is the total travel distance along the entire
pathway from the puffs original position to its current position in
time.

Atmospheric rise is modeled by the use of the solutions presented by
Hurley and Physick (7). Their equations for vertical rise and
corresponding dispersion parameters are reproduced as equations 7-11.

> z~r~ = 1.6\[(F~o~t^2^)/u~h~\]^1/3^ (7)

F~o~ = gw~s~r~s~^2^\[1-(T~a~/T~s~)\] (8)

R = z~r~ (9)

~hr~ = R (10)

~zr~ = R/2 (11)

where z~r~ = rise distance (current -- original) (m)

F~o~ = buoyancy factor (m^4^/s^3^)

t = time (s)

u~h~ = ambient horizontal wind speed (m/s)

g = gravitational constant = 9.81 m/s^2^

w~s~ = exit velocity (m/s)

r~s~ = exit radius (m)

T~a~ = ambient temperature (K)

T~s~ = exit temperature (K)

R = horizontal radius of puff = horizontal dispersion parameter (m)

 = constant ≈ 0.6

Equation 7 ignores momentum effects which is reasonable since buoyancy
is usually considered to be the dominant factor in atmospheric rise (8).
In addition, emissions from vehicles are usually horizontal and
therefore, do no contribute to vertical momentum. Although these
equations were derived for plumes, they are justified for use with puffs
since puffs can be used to model plumes.

Of all the movement and dispersion factors affecting puffs, vehicle wake
effects are probably the most complicated. A vehicle's wake can affect
nearby puffs through aerodynamic drag and turbulent dispersion. Drag
forces can carry emissions behind a vehicle resulting in a "channel" of
pollutants along the roadway. Although this can affect pollutant
concentrations at receptor locations, aerodynamic drag (also called wake
passing effect) is inherently non-dispersive. Its effect on dispersion
occurs indirectly through its contribution to the mean velocity. The
wake can be modeled as a self-preserving region generally behind a
moving vehicle where the velocity of a point in the region decreases
with distance away from the vehicle in three dimensions. The vehicle
wake theory was originally developed by Eskridge and Hunt and modified
by Eskridge and Thompson, and Eskridge and Rao (9, 10, and 11). Their
equations for the velocity field and the turbulent energy in the wake
are reproduced as equations 12-24.

> u~d~ = UA(S)^-3/4^f(N/l(s), Z/l(s)) (12)

S = s/H (13)

Z = z/(γAH) (14)

N = n/(λγAw~d~) (15)

A = \[Cd/(32πe^1/2^λγ^3^)\]^1/4^ (16)

l(s) = λAH(S)^1/4^ (17)

f(N/l(s), Z/l(s)) = \[Y(N/l(s))\]\[T(Z/l(s))\] (18)

Y(N/l(s)) = C~1~Exp\[-N^2^/(8l^2^(s))\] (19)

T(Z/l(s)) = T(ξ) = ∑b~i~ξ^i-1^ + b~0~, for i = 1 to 6 (20)

(u'^2^, v'^2^, w'^2^) = (a~1~, a~2~, a~3~)A^2^U^2^S^-1.2^F~c~(χ,ω) (21)

χ = n/(W~d~s^0.4^) (22)

ω = z/(Hs^0.4^) (23)

F~c~(χ,ω) = ∑~n~∑~m~ψ~2m,n~ω^n^χ^2m^, for m = 0 to 2 & n = 0 to 4 (24)

where u~d~ = velocity deficit (m/s)

U = wind speed relative to vehicle (m/s)

A = Strength of the wake

s = distance behind the vehicle along the wake centerline (m)

H = height of vehicle (m)

W~d~ = width of vehicle (m)

z = vertical distance above the wake centerline (m)

n = distance perpendicular to the wake centerline (m)

γ = constant ≈ 0.095

λ = constant ≈ 1.14

C~d~ = drag coefficient

u'^2^, v'^2^, w'^2^ = velocity variances

a~1~, a~2~, a~3~ = constants = 0.048, 0.040, 0.030

The velocity variances determined from equation 21 can be correlated to
dispersion parameters by using equation 25 which is derived from
Taylor's formula (12).

(σ~xw~^2^, σ~yw~^2^, σ~zw~^2^) = (u'^2^, v'^2^, w'^2^)t^2^ (25)

Equation 25 assumes that the travel time is much smaller than the
Lagrangian time scale which is typically on the order of 100 to 200
seconds (13). Since TRAQSIM uses a much smaller time step (one second)
during simulation, the use of equation 25 appears to be justified.

The coefficients for equations 20 and 24 are shown in Table 2. The wake
equations are based on a coordinate system relative to the moving
vehicle. This is evident in Figure 1 which shows a simplified view of a
wake that has been shifted from the centerline of a roadway due to the
mean wind. Using this coordinate system, the velocity deficit is defined
as the difference between the velocity of the ambient air moving past
the vehicle and the velocity of the air in the wake region. Therefore,
the air immediately behind the vehicle would have the highest velocity
deficit. Depending on the coordinate system used, the mean wind would
affect the velocity deficit and should be incorporated accordingly.

# Traffic Simulation {#traffic-simulation .Awma-Head-2}

The movement of vehicles is handled through a simulation module
originally developed for the Community Noise Model (CNM) developed at
UCF under sponsorship by the American Automobile Manufacturers
Association (AAMA) (14). The code creates, moves, and eliminates
vehicles according to the requirements set by the input data (e.g.
simulation time, roadway geometry, traffic volume, etc.). Random number
generators are implemented to affect vehicle creation time and their
initial deployment position on a roadway. This allows the simulation to
occur in a stochastic environment where each simulation run will likely
be unique even though consecutive runs may use the same input data.
However, this uniqueness only applies to the dynamics during the
simulation. Experiences from running the CNM model indicate that the
differences between concentrations determined under non-extreme
conditions (i.e. reasonable simulation time and traffic volumes) for
identical input data will likely be trivial.

The traffic simulation module includes several algorithms including
traffic follower, start-up loss time, acceleration rates, deceleration
rates, signal timing, etc. Most of the values for the parameters used in
these modules were taken from literature including those from the
Institute of Transportation Engineers (15).

MODEL STRUCTURE

The basic simulation scheme for the overall model is presented in Figure
2. The traffic simulation and modal emission factor modules are
condensed for simplicity. As previously mentioned, these modules have
been discussed elsewhere and will not be covered in detail here. The
simulation begins with an increment in time followed by traffic movement
and the determination of mode-specific emission factors. For newly
created puffs, initial dispersion parameters (σs) are set based on the
size of the exhaust outlet (i.e. tailpipe radius). Meteorological data
is read during each time step because the program allows more than one
record to be used during a simulation. This data affects all three
subroutines (atmospheric turbulence, atmospheric rise, and vehicle wake
effects) that control the movement and dispersion of puffs. Of these
three, the effects caused by vehicle wakes is the most complex due to
the geometry of the vehicle and wake. Since the program has to cycle
through each vehicle for each existing puff, wake effects are
computationally intensive. Once all of these effects are determined, new
dispersion parameters are calculated. This must be done at each time
step because some of the dispersion parameters (e.g. from wake effects)
must be cumulatively determined. The puffs are then moved horizontally
according to the mean wind and vehicle wakes, and vertically according
to atmospheric rise effects.

Puff merging is done mainly to reduce computation time. In a merging
process, two puffs are replaced by a single puff containing the sum of
the masses of the two puffs and average values for all other parameters
(σ values). Ludwig et al. suggest the merging of two puffs when the
distance between their centers is less than the sum of two σ values
(averages from each puff) (16).

Another option to reduce computation time is puff purging which
basically refers to the deletion of a puff. When a puff has moved far
enough from a receptor location, its contribution to the concentration
measured at that receptor may be low enough such that the puff can be
effectively purged from further analysis. This may appear to be a simple
process requiring only a decision to be made on the cutoff point when a
puff will be purged. But since vehicle wakes and changes in the wind
field may drag the puff back into the "relevance zone," purging becomes
more complicated. Therefore, purging has not been implemented in the
model and will not be used until a reasonable methodology based on
sensitivity studies is developed.

In addition to puff merging, Ludwig et al. also discusses the lag
(distance and time) between each puff release (16). The use of a
distance lag instead of one based on time may be more appropriate
because the latter option could be adversely affected by the strength of
the mean wind, vehicle wake, and buoyant forces. A fixed time lag may
result in an excessive amount of puffs being generated causing stiff
processing requirements. And at high wind speeds, not enough puffs would
be generated for a fixed time lag such that accuracy would be
compromised. Therefore, a constant distance lag would appear to be more
appropriate. However, the aforementioned scenarios are based on
stationary sources with a constant wind field. For the modeling
scenarios in TRAQSIM, any advantages of using constant distance lags for
the puffs during their release would eventually be negated by the
disruptive effects of vehicle wakes and a changing wind field (e.g. if
more than one meteorological record is used). Therefore, a constant time
lag of one second is used as the time step during simulation. This
approach has the advantage of being computationally simpler and
reasonable with respect to a puff being generated each second. But it
will eventually need to be validated through a sensitivity analysis.

SOFTWARE DESCRIPTION

The entire software was written in Microsoft Visual BASIC 6.0 for the
Windows (95, 98 and 2000) environment. The Visual BASIC compiler may not
produce executables that are as optimized as those generated by a C^++^
compiler, but the BASIC programming language clearly has the advantage
of clarity and simplicity due to its English-like commands. This is true
when comparing the BASIC language to any other language as well.
Therefore, the BASIC code is easier to learn and arguably, easier to
debug. This provides other novice programmers wishing to modify the
program with a shorter comprehension time. These advantages may
ultimately outweigh any gains in speed afforded by a more optimized
code. The actual losses of speed due to using Visual BASIC instead of a
more efficient language remains to be seen, and will not be known unless
the code is reproduced using a different language. However, the
possibility exists that certain parts of the code could be rewritten in
a more efficient language and compiled as a dynamic link library (DLL)
which could be used by the main Visual BASIC program as a subroutine.

Due to the Visual BASIC development environment, the model incorporates
a user-friendly graphical interface. The design of traffic layouts is
accomplished on a cartesian coordinate system and most of the design can
be accomplished graphically with minimal keyboard input of coordinates.
The graphical nature of the program, especially with the traffic layout
editor, simplifies the modeling process and will likely reduce user
input errors.

Once all of the input data is entered into the model, the simulation
window can be opened to start a run. Once a simulation is started, the
traffic layout is reproduced on screen and the traffic animation is
shown during the simulation. This allows for a visual check of the
modeled scenario. At the end of the simulation, CO concentrations can be
obtained for each of the receptor locations from an output window.

TEST RUNS AND VALIDATION

Due to the simulation nature of the model, run time is significantly
longer than steady-state models such as CAL3QHC. For example, on a
Pentium II 300 megahertz computer with 96 megabytes of ram, the run time
for a one hour simulation involving a 400 feet, one-lane roadway with a
traffic volume of 300 vehicles per hour came out to be a little over two
hours. The run time increases dramatically when the number of traffic
elements (e.g. roadways, traffic signals, vehicles etc.) increases. A
one hour simulation involving an intersection with 8 major roadway links
and 12 minor links (e.g. for turning movements) with about 700 to 800
total vehicles per hour on each of four approach links took
approximately 74 hours (over three days). Since run times vary with
traffic layout and the computer system used, no average values can be
provided. Trial runs with traffic animation features turned off have
been previously conducted on the CNM model and results indicate that the
animation doesn't make a significant difference in the overall run time.
As a result, the animation feature is currently being kept as an
integral feature (not optional) in TRAQSIM. TRAQSIM's code is also being
modified on an on-going basis in an effort to optimize it, and
therefore, the aforementioned run times are likely to be reduced.

Since the validation of any new model is a requirement for its usage, a
few preliminary simulations have been conducted using some of the data
from the Melrose Park and College Station databases (5). The initial
results appear to indicate good correlation with actual CO readings.
However several assumptions had to be made with respect to the
meteorological and emissions data due to the differences in the models.
A more comprehensive validation involving these databases is planned in
the near future. It is also hoped that the data collected by Systems
Applications International (SAI) under contract to the National
Cooperative Highway Research Program (NCHRP) will be made available so
that TRAQSIM can be validated with more recent data (17).

CONCLUSION

Taking a simulation approach to modeling air quality near roadways may
not be new, but the incorporation of modal emission factors, atmospheric
rise, and vehicle wake effects in a single program that uses Gaussian
puff dispersion algorithms is unique. The basic advantages that TRAQSIM
has over the existing models stem from the simulation approach which is
more versatile and realistic than the steady-state algorithms in such
models as CAL3QHC. The use of modal multipliers and vehicle wake effects
is also more realistic than using equivalent queue lengths and the
mixing zone concept, respectively. Although TRAQSIM's current run times
on a PC are extremely long (especially for full intersection analysis),
code-optimization efforts will likely improve run time in the near
future.

RECOMMENDATIONS

There are several recommendations that can be made concerning the new
model:

1.  The model is being made freely available from the authors to allow a
    wider range of testing and validation. Validation with data from SAI
    needs to be done.

2.  Sensitivity analyses involving the individual modules (e.g.
    atmospheric rise, wake effects, etc.) need to be conducted.

3.  The use of DLLs created with a more efficient compiler (such as the
    one used with Visual C^++^) should be investigated.

4.  Incorporating the output from a more complex traffic model (such as
    CORSIM) should be investigated.

5.  TRAQSIM can be merged with the CNM noise model. This would be ideal
    since the composite model would be able to predict both air and
    noise quality using the same input data.

REFERENCES

1.  Wayson, Roger L. and Brian Y. Kim. "Development of a Modal Emissions
    Model Using Data from the Cooperative Industry/Government Exhaust
    Emission Test Program." A paper presented to the Air & Waste
    Management Association, 93^th^ Annual Meeting, Salt Lake City, Utah,
    June 18-22, 2000.

2.  *User\'s Guide to CAL3QHC Version 2.0: A Modeling Methodology for
    Predicting Pollutant Concentrations Near Roadway Intersections*.
    EPA-454/R-92-006. September 1995.

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3.  Bullin, Jerry A., Michael W. Hlavinka, John J. Korpics, James H.
    Schroeder, Roderick D. Moe, and Guy R. Donaldson. *Modeling and
    Measurement of Vehicle Emissions from Roadways, Volume I*. Texas
    State Department of Highways and Public Transportation. Research
    Report 283-3F, Research Study No. 2-8-80-283. July 1987.

4.  Benson, Paul. "CALINE4 -- A Dispersion Model For Predicting Air
    Pollutant Concentrations Near Roadways." State of California
    Department of Transportation. Final Report November 1984, Revised
    June 1989.

5.  Cooper, C. David, Roger L. Wayson, Haitham Al-Deek, Linda C. Malone,
    Pwu-Sheng Liu, Debra K. Keely, Richard Traynelis, Mahmoud Heriba,
    and Fouad Matar. FLINT, The Florida Intersection Model. A Final
    Report of a Research project. Florida Department of Transportation.
    WPI 0510676, State Job No. 99700-3521-119. December 10, 1997.

6.  Turner, D. Bruce. *Workbook of Atmospheric Dispersion Estimates*.
    CRC Press, Inc., Boca Raton, Florida, 1994.

7.  Hurley, Peter and William Physick. "Lagrangian Particle Modelling of
    Buoyant Point Sources: Plume Rise and Entrapment Under Convective
    Conditions." *Atmospheric Environment.* 27A, no. 10 (1993):
    1579-1584.

8.  Cooper, C. David and F. C. Alley. *Air Pollution control*. Waveland
    Press, Inc., Prospect Heights, Illinois, 1994.

9.  Eskridge, Robert E. and J. C. R. Hunt. "Highway Modeling. Part I:
    Prediction of Velocity and Turbulence Fields in the Wake of
    Vehicles." *Journal of Applied Meteorology*. 18, no. 4 (April 1979):
    387-400.

10. Eskridge, Robert E. and Roger S. Thompson. "Experimental and
    Theoretical Study of the Wake of a Block-Shaped Vehicle in a
    Shear-Free Boundary Flow." *Atmospheric Environment*. 16, no. 12
    (1982): 2821-2836.

11. Eskridge, Robert E. and S. Trivikrama Rao. "Measurement and
    Prediction of Traffic-Induced Turbulence and Velocity Fields Near
    Roadways." *Journal of Climate and Applied Meteorology*. Volume 22
    (August 1983): 1431-1443.

12. Dobbins, Richard A. *Atmospheric Motion and Air Pollution*. John
    Wiley & Sons, Inc., New York, 1979.

13. Zannetti, Paolo. *Air Pollution Modeling*. Van Nostrand Reinhold,
    New York, 1990.

14. Wayson, Roger L. and John M. MacDonald. "Version 4.0 of the AAMA
    Community Noise Model." Technical Manual. Draft. University of
    Central Florida. April 1997.

15. Institute of Transportation Engineers. *Traffic Engineering
    Handbook*. 4^th^ Edition. 1992.

16. Ludwig, F. L., L.S. Gasiorek, and R. E. Ruff. "Simplification of a
    Gaussian Puff Model for Real-Time Minicomputer Use." *Atmospheric
    Environment*. Volume 11 (1977): 431-436.

17. Carr, Edward L., Robert G. Ireson, and Chris Biltoft. "Analysis of
    Dispersion Characteristics and Induced Turbulent Flows Near Roadway
    Intersections from Mobile Sources." A Paper to the Air & Waste
    Management Association, 89^th^ Annual Meeting, Nashville, Tennessee,
    June 23-28, 1996.

Table 1

Power Function Coefficients for Dispersion Parameter Equations

  ----------------------- ------------ ----------- ----------- -----------
  Stability Class         a            b           c           d

  A                       0.18         0.92        0.72        0.76

  B                       0.14         0.92        0.53        0.73

  C                       0.1          0.92        0.34        0.72

  D                       0.06         0.92        0.15        0.70

  E                       0.045        0.91        0.12        0.67

  F                       0.03         0.90        0.08        0.64

  G                       0.02         0.89        0.05        0.61
  ----------------------- ------------ ----------- ----------- -----------

**Table 2**

**Coefficients for Wake Modeling Equations 19 and 23**

  --------- ---------------------------- --- --------- --------------------
            Surface Fit                                Curve Fit

  ψ~00~     0.3511237 X 10^-1^               b~0~      0.0179349

  ψ~01~     0.1255308 X 10^2^                b~1~      2.576580

  ψ~02~     -0.4796241 X 10^2^               b~2~      -2.3062584

  ψ~03~     0.6732523 X 10^2^                b~3~      0.8951468

  ψ~04~     -0.3572466 X 10^2^               b~4~      -0.1758604

  ψ~20~     -0.1890581                       b~5~      0.0169970

  ψ~21~     -0.9345507 X 10                  b~6~      -0.0006404

  ψ~22~     -0.1821427 X 10^3^                         

  ψ~23~     0.5617911 X 10^3^                          

  ψ~24~     -0.3995373 X 10^3^                         

  ψ~40~     0.2649465                                  

  ψ~41~     -0.9434068 X 10^2^                         

  ψ~42~     0.1034830 X 10^4^                          

  ψ~43~     -0.2348153 X 10^4^                         

  ψ~44~     0.1510437 X 10^4^                          
  --------- ---------------------------- --- --------- --------------------

> Source: (12)

**Figure 1**

**Simplified View of a Wake Behind a Vehicle**

**Figure 2**

**Model Simulation Scheme**