The air pollution
model on this page is most popular for calculating the direction and rates
that pollution will travel given weather, distance, and emission rates. The
model is based on theories of statistical probability. The location of particular
chemical molecules are determined following a set of assumptions regarding
weather, topographic features, characteristics of the various chemicals. This
model works best for short term modeling. When looking at the long term, the
model's results must be averaged to account for time.
Another
problem with using this particular type of model is the inavailability of
real time release data. Toxic Release Inventory data is only made available
after two or three years. So today, if you wanted to model the air pollution
of a particular facility, the most recent data available is already two or
three years old. The pollution source may have retooled and might be releasing
less, or their production levels may have risen along with the amount of pollution
being released into the atmosphere.
Given these disclaimers,
use the following table carefully. Use it to raise questions about your local
situation.
Explanations:
What happens when
you press the submit button? A little JavaScript program I wrote called calculateIt
and hidden in the page head uses the data inputs you provide to calculate
the multiplier and the pollutant deposition rate for the point you described
(the x, y, coordinates).
Let's
first go over each data input. Below that, I'll (re)construct the dispersion
equation.
Data
Needs:
- Stack Height:
describes the height of Smokestack in meters. Our calculations are conservative
in that we are assuming that the released gasses start to disperse as soon
as they hit the ambient air. This is not always the case. Usually the gasses
are hotter than the ambient air and they sometimes are released with a determinable
velocity. They rise until they reach a thermal and gravitational equilibrium
(called the effective stack height).
- Weather Condition:
Different conditions change the dispersion variables in the dispersion equation
below. These variables are used to calculate other important intermediate
variables called sigma_y (the crosswind plume standard deviation) and sigma_z
(the vertical plume standard deviation).
- Wind Velocity:
this input is given as the velocity of the wind over 10 meters. The unit
is meters per second.
- Downwind
and Crosswind Distances: See this page
for help calculating this information. The unit for this category is meters.
- Rate of Pollution
Emission: this is the amount of pollutant that is being released per
a defined time period. For this model we are using grams per second. Use
this page to help you determine this.
You will also find toxicity data for different pollutants at the Scorecard
site.
The
Equations:
We first need to
caclulate sigma_y and sigma_z. We need weather condition, and downwind distance
to do this. Using the information from the weathercondition
page to calculate the weather condition. We use the following table to
find other intermediary variables I will call a_sigma, c_sigma, d_sigma, and
f_sigma. The values in the first table apply when the downwind distance is
less than 1 kilometer (1000 meters). The second table is for distances greater
than 1 km.
Downwind Distance Less Than 1 km
Weather
Condition |
a_sigma |
c_sigma |
d_sigma |
f_sigma |
| A |
213 |
440.8 |
1.941 |
9.27 |
| B |
156 |
106.6 |
1.149 |
3.3 |
| C |
104 |
61.0 |
.911 |
0 |
| D |
68 |
33.2 |
.725 |
-1.7 |
| E |
50.5 |
22.8 |
.675 |
-1.3 |
| F |
34 |
14.35 |
.740 |
-.35 |
Downwind
Distance Greater Than 1 km
Weather
Condition |
a_sigma |
c_sigma |
d_sigma |
f_sigma |
| A |
213 |
459.7 |
2.094 |
-9.6 |
| B |
156 |
108.2 |
1.098 |
2.0 |
| C |
104 |
61 |
.911 |
0 |
| D |
68 |
44.5 |
.516 |
-13 |
| E |
50.5 |
55.4 |
.305 |
-34 |
| F |
34 |
62.6 |
.180 |
-48.6 |
We'll
use the default input data as the source for our example.
sigma_y
= a_sigma * (downwind distance in kilometers ^ .894)
sigma_y
= 156 * (1.5 ^ .894) = 224.25
and,
sigma_z
= (c_sigma * (downwind distance--km) ^ d_sigma) + f_sigma
sigma_z
= (108.2 * (1 ^ 1.098) + 2 = 170.88
After calculating
sigma_y and sigma_z we then use the primary assimilation equation, sometimes
called the Gaussian Plume Model.
Multiplier
= (1/(pi*sigma_y*sigma_z*wind velocity))* e ^ {-.5[(y/sigma_y)^2) + (Stackheight/sigma_z)^2]}
Multiplier
= (1/(3.14*224.25*170.88*3))* 2.718 ^ {-.5[(1000/224.25)^2) + (30/170.88)^2]}=1.3x10^-10
Using this
multiplier we can now calculate the rate of pollutant deposition on the coordinates
you input. In our case we are using an emission rate of 15 grams per second.
This gives us:
Rate
of deposition (x, y) = Multiplier * Rate of Pollutant Emission
Rate
of deposition (1500, 1000) = 1.3x10^-10 * 15 g/sec = .0000000196 g/sec
or 1.96
* 10^-8 g/sec
One
can now search Scorecard's
Databases for information on how this particular compound affects you given
this concentration.
- Intel's
Pollution levels vs. other New Mexico Industry
(www.scorecard.org)
- Intel:
What are we breathing??? (chemical list)
- Volatile
Organic Chemical Concentrations Near Intel Plant
- Air
Dispersion of Emissions from an Industrial Facility--Animation
- How
to model air pollution-a primer
- A
Primer Proposal for Community Air Monitoring
Use the menu bar to the left to
volunteer.
This
page was constructed by Xavier Morales from Arizona State University's Center
for Urban Inquiry he can be contacted at x-man@asu.edu
