Basic Air Pollution Modeling Page

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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.

**Input Table**
Category Name	Input	Remarks
Stack Height	m	This is the height of the smokestack in meters (1 meter = 1.3 yds)
Weather Condition		Only A, B, C, D, E, F-- Click here for a guide to these codes
Wind Velocity	m/sec	This value is in meters per second
Downwind Distance	m	Please click here for help calculating this value
Offwind Distance	m	Please click here for help calculating this value
Rate of Pollutant Emission	g/sec	Click here for a comment on this value

Output Table
Category Name Output Remarks

Multiplier x 10^-10 This value tells you how much to multiply your emmissions amount by to get the concentration below (this value is unitless)

Pollutant
Deposition Rate x 10^-6 (g/sec) This is the pollutant deposition rate for the spot you described above using the Downwind and Offwind inputs

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.

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

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