Models, Models Everywhere
Your teacher has read your reports. It is obvious that, with hindsight, the Donora disaster could have be anticipated and avoided. With the advent of computer usage, it is even easier to predict performance and future possibilities through computer modeling. For the next part of your project, you are to investigate the concept of modeling, explore some representative samples and then explore the environmental models which might be useful for your primary task –– determining the concentration of pollutants that might be emitted at particular locations by new plants.
Your Assignment – How might models be used for environmental predictions.
Your team is looking for answers to these specific questions…
How might models have been used to prevent tragedies like the Donora disaster?
How might models be used to assist in site selection for a new factory?
The Action Plan – Procedures to follow
Print a copy of the worksheet to accompany Models, Models Everywhere.
Step 1 – Gather some basic information on modeling.
Computer models use mathematical formulas which use input data in order to make predictions or simulate behavior. Weather forecasting and hurricane path predictions rely heavily on a variety of computer models.
Step 2 – Investigate Environmental Models
The Gaussian Plume Model
A plume is the region of space containing the gases and particulates released from a smokestack as fuel is burnt. The Gaussian Plume Model is the most commonly used model to make the calculations
needed to predict the movement of a pollutant in complex situations. In order to
do this, several assumptions need to be made. It is assumed that certain things
will stay the same, i.e., remain in a "steady state." For example,
meteorological factors such as temperature and wind speed and direction are
assumed to remain fairly constant over the time period when the prediction is
being made.
Some limitations of the model - As a result the Gaussian plume model will only work well over short distances
of up to 50 km from the source of the pollutant to the receptor.
The receptor could be a measuring instrument, but it might well be a neighborhood in the path of the pollutant flow.
The model willalso not work well in areas where the terrain is very complex or in a coastal
area where sea and land-breezes can cause dramatic changes in meteorological
conditions.
Fuel is burned and a plume of emissions is produced. This may look like smoke and could contain one or more pollutants.
Because the plume is hot, it will rise,
since hot air is less dense. The plume will rise to a certain point and this is
called the "effective stack height". The effective stack height
depends on three main factors:
- the exit velocity of the gas from the stack
- the temperature of the plume
- the temperature of the surrounding air
After the plume reaches the effective stack height, the plume starts to disperse in three different directions.
1) The plume can move downwind. The amount that the plume moves is directly proportional to the wind speed and in the direction of the prevailing wind.
2) The plume can move in a cross-wind direction. This is determined by the Gaussian Plume equations.
3) The plume can move in a vertical direction, either up or down. This is also determined by the Gaussian Plume equations.
Gaussian Plume Model Simulations
Here are two options for working with the Gaussian Plume Model. If your computer accepts a
Java applet, the following link illustrates the model visually and is easy to
use.
Gaussian Plume Java Applet developed by the Shodor Foundation
This applet provides a
number of slider bars to change parameters:
- wind speed
- stack height
- stack diameter
- emission rate
- gas temperature
- gas velocity
- atmospheric temperature
- atmospheric conditions
- 3D coordinates and graphics resolution
To change the values,
simply slide the slider bar. Alternatively, you can type in a value and hit the
Enter/Return key.
Output is provided in several formats: x-y
graph, top and side view visualizations, and text-based output. In the side-view
format, the black bar on the left of the graphics window shows the stack,
changing in height as the stack height slider bar is modified. In the top-view
format, the stack is seen as a black dot, half-way up the y-axis.
The x-y-z contour plot range sliders help to
zoom in and out of the plume. The z-contour plot only modifies the side-view,
while the y-contour slider only modifies the top view. The x-contour modifies
both top and side views.
If you cannot
use the applet, the following Excel simulations allow you to manipulate
variables and observe outcomes.
Gaussian Plume Model Interface
Use one of the interactive simulations above
to change the variables in the table below and then observe the effect on the
concentration of the pollutant (mmg/m3). You can click on the
appropriate space to see the answer and explanation.
Team Report
Prepare a team report answering the original questions:
How might models have been used to prevent tragedies like the Donora disaster?
How might models be used to assist in site selection for a new factory?
