Annex 5.1 Urban dispersion models

An urban area contains thousands, or even millions, of individual sources. The application of a diffusion model to each source is impractical. Consequently most of the small sources are combined into larger area sources of strength Q_a (mass per unit time per unit area), and it is assumed that the emissions from the ground surface are uniform over that particular area.

Diffusion from the largest point sources can be calculated individually and the resulting concentrations at a receptor point can be added to the contribution from the area sources.

A. AREA SOURCE MODEL

In order to estimate by hand calculations the 1hr average air concentration at an arbitrary receptor point (o) due to area source emissions, a modified expression of the ATDL urban diffusion model (Hanna, 1972; Gifford and Hanna, 1973) may be used:

(A.1)

where

C, the concentration (micrograms m^-3)

o, denotes the location of the receptor point

n, is the number of grid blocks (of size), necessary to reach the upwind edge of the urban area, starting from the receptor point.

Q, for i=o,1,2,...,n, are source strengths (microgram sec^-1 m^-2), constant over a distance .

u, is the wind speed, assumed constant within the mixing layer.

c,d are the Brookhaven National Laboratory parameter values, (Smith, 1968), as listed in Table 1.

Table A.1. Brookhaven National Laboratory parameter values a, b, c and d in equation (A.1) and in the formulas for the dispersion parameters ,  and 

Basic assumptions

• The pollutants are assumed to be uniformly mixed in a layer, whose height is proportional to the vertical dispersion parameter , where x is the total distance from the urban area.

When the distribution of emissions is quite smooth, as it is often the case in residential urban areas, the calculated concentration (C) at any receptor point is usually proportional to the emissions Q_ao in the grid square in which the receptor is located. In this case it is sufficient to use the following simpler relation:

(A.2)

the expression  denotes the distance to the edge of city.

The following values for the dimensionless factor A are suggested:

Note, however, that A is slightly dependent on .

Additional contribution from other sources

The urban area source model can give the average concentration over a broad area. In a street canyon or adjacent to a highway in an urban area, there is an additional contribution to the concentration from local sources. In this case the total concentration C_t is the sum of the spatial average C (calculated from equation (A.1)) and the local C_l component. Finally, the concentrations resulting at a receptor point from large point sources, C_p, can also be added to the spatial average concentration C.

B. ELEVATED POINT SOURCES

In order to estimate the contribution from an elevated point source C_p, (Fig. 1) of strength Q, the following Gaussian relation can be used:

(A.3)

where

C is the concentration (micrograms m^-3);

Q is the source strength (micrograms sec^-1);

u is the wind speed at the plume height;

y refers to the horizontal direction at right angles to the plume axis with y equal to zero on the axis;

z is the height above the ground;

are standard deviations of the concentration distribution C, in the y and z direction and are calculated from table A.1;

h is the effective plume height (stack height plus plume rise). The plume rise can be calculated by using the appropriate formulas, summarised in table A.2
.

Figure A.1 Diagram of plume, illustrating concepts important in the Gaussian plume formula.

Table A.2. Plume rise formulas according to the plume characteristics and atmospheric conditions

plume type	1	atmospheric conditions	formulas
bent-over	buoyant    jet	stable    strong wind     neutral,    unstable     strong wind  neutral
vertical	jet  buoyant	low wind          stable

is the buoyancy flux , ;

M is the momentum flux, M=wV;

s is the atmospheric stability, ;

V is the plume volume flux (V=wR² for vertical plume and V=uR² for bent over plume);

w is the plume vertical speed;

x is distance from the stack;

D is the stack diameter;

T is the temperature.

Subscripts p and e denote plume and environment.

Note that alternative formulations for the plume rise exist.

Limitations

Although the Gaussian plume formula in general is appropriate to calculate the dispersion of elevated continuous major point sources, it has been demonstrated that it can lead to misleading results in special cases, such as in inhomogeneous terrain. For other simple models which could be used, see for instance Kretzschmar et al.,1994; Kretzschmar and Cosemans, 1996.
 
 
 

Longer averaging times

The diffusion parameters  are directly related to the standard deviations of the turbulent velocity fluctuations. Thus, as averaging time increases, the turbulent velocity fluctuations increase and hence  increase. Gifford suggests accounting for the effects of sampling time trough the empirical formula:

(A.4)

where,

d and e represent two different averaging times, and q is in the range 0.25 to 0.3 for 1hr_sd<100hr and equals approximately 0.2 for 3min_sd<1hr.

The standard dispersion parameters given in table A.1, represent a sampling time T_se of about 10 min.

Extension to longer averaging times is made by solving the above equations for a variety of wind directions and then weighting each result by the frequency with which the wind blows from that direction.
 

C. STREET CANYON SUBMODEL

Consider the street canyon in figure A.2, where the important variables are defined. Depending on the wind direction, at roof level, the following relations can be used.

Figure A.2 Schematic of cross-street air circulation in a street canyon. [From Johnson et al, 1977)

Wind direction normal to the street axis

If the wind direction is nearly normal to the street, the equations for the concentration C_l in the street canyon are:

• lee side,  (A.5)

• windward side,  (A.6)

Cl	is the concentration (µg/m3);
N	is the traffic flow (vehicles/hr);
q	is the emission factor (g/km);
u	is the wind speed at roof level (m/sec);
W	is the street width(m);
x and z	are horizontal distance and height (both in m) of the receptor point relative to the traffic lane;
K	is a dimensionless "best fit" constant (K7 is suggested).

If the wind direction is nearly parallel to the street axis, the equations for the concentration C_l in the street canyon are:

(A.7)

Limitation: The model as such is not suitable for calculation of NO₂ concentrations, which are mainly determined by chemical reaction of NO with ozone.

D. HIGHWAY SUBMODEL

The excess concentration C_l contributed by a major highway in an urban area is important for a distance less than 300m downwind of the highway. Consider the highway in figure A.3, the concentration at some distance x from the highway can be estimated from the relation:

(A.8)

where

C is the concentration (µg/m³);

Q is the line source strength (µg/s/m);

h is the effective height of emissions due to initial dispersion (2-3m);

is the angle between the wind direction and the highway;

is the vertical dispersion parameter.

F() Function of ; for around 90 degrees, F() is close to 1.

Figure A.3 Infinite line source pattern.

Limitation: This formula cannot be used to calculate concentrations on the highway, or in case the wind blows in the direction of the highway .

Meteorological data and emissions

All the models in this annex are best suitable for estimation of long term average concentrations. They should not be used for short term high percentile values, which are highly dependent on critical meteorological conditions.

For long term average concentrations, calculations can be made with average meteorological conditions. For wind speed, the annual average can be used. For wind direction, the most frequent direction can be taken. For point sources, neutral atmospheric conditions should be selected.

Appropriate choices must also be made for emission estimates, to make sure that they reflect typical conditions.
 

References

Gifford F.A. and Hanna S.R., (1973) Modelling urban air pollution. Atmospheric Environment, 7, 131-136.

Hanna S.R., (1972) Description of ATDL computer model for dispersion from multiple sources. Proc. of second annual industrial air pollution control conference. Knoxville, Tn. ATDL Report 56, NOAA, Oak Ridge.

W. B. Johnson, R. C. Sklarew, and D. B. Turner, Urban Air Quality Simulation Modeling in Air Pollution, vol. 1, 3rd ed. Chapter 10, p. 530, A. G. Stern (Ed.), Academic Press, New York, 1977.

Kretzschmar, J.G., Cosemans G.(1996) 4th workshop on harmonization within atmospheric dispersion modelling for regulatory purposes, vol. 1 and 2. E&M.RA9603, VITO, Mol, Belgium.

Kretzschmar, J.G., Maes, G. Cosemans G.(1994) Operational short range atmospheric dispersion models for environmental impact assessment in Europe, vol 1 and 2. E&M.RA9416, VITO, Mol, Belgium.

Smith, M. E. (ed.) (1968) Recommended Guide for the Prediction of the Dispersion of Airborne Effluents, Am. Soc. of Mech. Engineers, New York