Gaussian Equation:

The highest concentration is the center of the plume at ground level (y=0, z=0, h=0), where the equation is:

Step 1. Enter the input variables:

Q = emission rate =grams/sec

pi = 3.14159...

u = average wind speed =meters/sec

x = downwind distance =meters

Atmospheric Stability (A-F) =

Step 2. Record sigma values (note: ^ means "to the power of"):

sigma y = [*^] =

sigma z = [*^]- =

Step 3. Results

Conc. = / [ 2 * 3.14159 ***] = micrograms / m3

Sigma values

Sigma values are fundamental to all gaussian based air dispersion models. They can be determined very roughly by reading off a graph, but are more accurately determined by the following equations:

The value of x is always the distance downwind from the source. The values of a, c, d, and f are determined experimentally and amount to curve-fitting. These numbers are found in tables, and there are various sets of tables. It can be rather tedious to find the values of a,c,d,and f that correspond to the atmospheric stability being studied, so we can be thankful that various computer programs determine these values for us. However, if you want to see the tables used in this particular calculator and use a calculator to solve the above function, try the power function calculator.

One final comment: it's not difficult to see various discussions of gaussian air dispersion models on the internet. The approach I've presented here emphasizes the conceptual basics, and a brief search will show that there are various manipulations of this basic guassian equation. One of the most frequently used gaussian based models is aptly named "screen3", which we will discuss a little later on.