Air Quality Models

Air quality models (AQMs) are models which in any way simulate a phenomenon or subject of interest that deals with air quality. Generally, this means modeling particle and gaseous dispersion in the atmosphere. The more advanced AQMs incorporate meteorological model output data into the input data for the AQM. There are several types of air quality models. We will discuss two here: the Gaussian plume and Gaussian puff models and the plume-in-grid model. These two are specific types of air quality models.

Gaussian Plume and Gaussian Puff Models

Gaussian Plume and Gaussian Puff models are those which model the dispersion of gases and particles from factories or other point sourcs, area sources, and volume sources. Based on the stability, stack height, and wind profile, the Gaussian dispersion models are used to predict pollution concentration downwind of the source. These models assume that the concentration is dispersed in the vertical and horizontal in a Gaussian, or bell-shaped, manner, with the highest concentrations in the center of the plume. You are encouraged to experiment with a real Gaussian Plume Model. We have developed a model interface that will run a model on a remote computer and then return to you a graph displaying the model results.A plume model (such as the Gaussian plume model) is good for tracking air parcels downwind and determining their pollution concentration. However, it is difficult to see how the plumes fit into the big picture. So, modelers have begun to use what is called a plume-in-grid model. This is the premise of the model:

Gaussian Plume Model

The Gaussian plume model is a (relatively) simple mathematical model that is typically applied to point source emitters, such as coal-burning electricity-producing plants. Occassionally, this model will be applied to non-point source emitters, such as exhaust from automobiles in an urban area. One of the key assumptions of this model is that over short periods of time (such as a few hours) steady state conditions exists with regard to air pollutant emissions and meteorological changes. Air pollution is represented by an idealized plume coming from the top of a stack of some height and diameter. One of the primary calculations is the effective stack height. As the gases are heated in the plant (from the burning of coal or other materials), the hot plume will be thrust upward some distance above the top of the stack -- the effective stack height. We need to be able to calculate this vertical displacement, which depends on the stack gas exit velocity and temperature, and the temperature of the surrounding air.
Once the plume has reached its effective stack height, dispersion will begin in three dimensions. Dispersion in the downwind direction is a function of the mean wind speed blowing across the plume. Dispersion in the cross-wind direction and in the vertical direction will be governed by the Gaussian plume equations of lateral dispersion. Lateral dispersion depends on a value known as the atmospheric condition, which is a measure of the relative stability of the surrounding air. The model assumes that dispersion in these two dimensions will take the form of a normal Gaussian curve, with the maximum concentration in the center of the plume.
The "standard" algorithm used in plume studies is the Gaussian plume model, develped in 1932 by O.G. Sutton. The algorithm is as follows:

where:

C(x,y,z) is the concentration of the emission (in micrograms per cubic meter) at any point x meters downwind of the source, y meters laterally from the centerline of the plume, and z meters above ground level.
Q is the quantity or mass of the emission (in grams) per unit of time (seconds)
u is the wind speed (in meters per second)
H is the height of the source above ground level (in meters)
and are the standard deviations of a statistically normal plume in the lateral and vertical dimensions, respectively

This algorithm has been shown in a number of studies to be fairly predictive of emission dispersion in a variety of conditions. If you look at some of the examples on other Web links, you will find its application in roadside, urban, and long-term conditions. In this algorithm, we are concerned with dispersion in all three dimensions (x, y, and z):

longitudinally (in the x direction) along a centerline of maximum concentration running downwind from the source
laterally (in the y direction) on either side of the centerline, as the pollution spreads out sideways
vertically (in the z direction) above and below a horizontal axis drawn through the source

The other major calculations for a simple Gaussian plume model are as follows:

Effective Stack Height:
Lateral and Vertical Dispersion Coefficients:
Ground-Level Concentrations:

The stability categories were developed in the late 1970s, and are based on wind speed, insolation, and extent of cloud cover. As shown above, we can calculate the values the standard deviations from the downwind axis for these six conditions or categories using the algorithms above. Initially, Gaussian plume models were used for pollutants such as carbon monoxide and other non-reactive species. The model has serious limitations when trying to account for pollutants that undergo chemical transformation in the atmosphere. Coupled with its dependence on steady state meteorological conditions and its short-term nature, this model has substantial limitations for use as a long-term airshed pollutant evaluator.
An interactive Gaussian plume case study and model are available to you through the next few sections. Use these to explore the types of inputs and outputs common to a Gaussian Plume Model.
A plume model is used to map the dispersion of pollutants from a stack. When the area of the plume reaches an equivalent grid cell size, the pollution concentration is approximated and then set as the concentration for the entire grid cell. In this way, the data from the plume model is encorporated into a grid model.
Plume-in-grid model

This type of model has many benefits. First, detail from a plume model can be transferred directly into a less detailed grid model. Ultimately, this allows an air quality model to yield a more accurate simulation than if there was no information on the plume. Second, the plume-in-grid model allows the plume to be mapped without placing a single, average concentration value for the grid in which the plume originates. In the diagram to the left, notice that the plume travels through a grid, but is not assimilated in to the grid model until the plume is same size as a the dimension of a grid cell. Again, this leads to a more accurate simulation.

Air Quality Models