Air Quality in the Barnett Shale - Part 21: If you assume E to be...

So in my last post I attempted to explain how the Gaussian model works based on my limited knowledge of the math - or math in general for that matter!

I am pretty sure that to "back in" to the model, the concentration "C" to obtain the emission rate "E," you have to know the values for all the other parameters in the formula:

So Dr. Sattler knows "C", she knows the distance from the stack where the sample was collected - "x".  She has the wind speed "U" and the meteorological data for the two S parameters.  She can estimate the height of the stack "H" and she knows, pi.  The only variable she does not know is "y" which needs to be calculated from the center line - required if the Gaussian principle is to be true - and the distance from the source "x."

The only way to get "y" is to fix the center line in one direction - which would be the wind direction - in order for the Gaussian model to hold true and a dispersion plume to be generated:

At a fixed wind direction, the stack at time = 0 will have the x,y coordinates of 0,0.  "y" is some distance from the stack - one side or the other (does not matter in a Gaussian model - both sides assumed equal in concentration) on the y-coordinate of the graph.

So in the Town of Dish example, here is what we are looking at.  Lets assume the wind is blowing in a Northwest direction.  That would be the center line.

Now I am going to orientate the map so it is in the same direction as the "Top View" plume graphic above:

If we know where the center line from the source is to be placed (wind direction), we can get the x,y coordinates.  With that data, the emission rate "E" can be calculated according to Dr. Sattler.

But that creates a problem....If we assume the Gaussian model to be true, and we assume the "backed in" data can calculate an emission rate "E", and the Gaussian model predicts a concentration at an x,y coordinate based on a wind speed "U" of meters per second and an emission rate "E" of grams per second, then logic would hold that the highest level of benzene would also show the highest levels of the other constituents in that sample point.

Look at Table 1:

In order to claim all of the contaminants in the six canisters came from one source at x,y = 0,0...then the model would predict similar ratios in every sample.  If you were to argue that the wind direction changed - thereby changing the center line - the same principle would hold true under the Gaussian model, that is, if you had low benzene you would also have low carbon disulfide, or if you had high carbon disulfide and low benzene in one sample you would have a similar ratio in the rest.  That's if you consider the Gaussian model to be true.

So either the Gaussian model is wrong in its "heart of the calculation" or the samples contain concentrations of chemicals from more than one source - which - if that the case, the emission rate "E" that was calculated is way too high thereby making all the dispersion model maps and concentrations calculated from it too high as well.

Or maybe wind direction moves all over the place changing the concentrations in the x,y coordinates where the samples were collected over a 24 hour period making it impossible to accurately "back in" to the model to get an emission rate since you would never know where the center line was.

I wonder which one it could be...

As ignorant as I most likely am on dispersion modeling, Dr. Sattler's premise and her emission calculations and dispersion modeling based on that value is wrong.  And that's not even bringing into the overall equation the use of TICs and the fact that all of this is based on a one time sampling event (n=1).

Somethin' aint right about all this.


Next Post: Air Quality in the Barnett Shale - Part 22: Gaussian for one, Gaussian for all.
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