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

I was driving home from San Antonio so I had a lot of "me" time in the car.  Instead of thinking about non-work related stuff, my brain got busy thinking about the air dispersion model used for the Town of Dish, Texas, and for the "Fort Worth League of Neighborhoods" in their report to the Fort Worth Independent School District.

All of the modeling - modeling based on the science and math behind a Gaussian dispersion - is predicated on assumptions.  Not that there is anything wrong with that, it's just that if the assumption holds true in one part it must also hold true for the rest.

So my mind is mulling this over and over.  The math behind it is daunting, especially for a guy like me, but the premise, now that is something I think I do understand.

So in the Gaussian model, which is what Dr. Sattler uses, the premise is this:

If you know the wind direction, wind speed, stack height, atmospheric conditions, and emission rate, you can estimate the plume shape and concentration of the contaminant exiting the stack at any point within the plume.

It assumes that under fixed conditions for that run - fixed air speed, fixed emission rate, fixed atmospheric conditions, fixed exhaust stack height - the plume will behave in a Gaussian manner, that is, along a fixed center line (wind direction) the plume will behave the same on each side of that line.  What these models are used for is to say, that under the most ideal conditions it would be possible for a receptor so many meters away to be potentially exposed to this much of the contaminant at that stack height and that emission rate.

Since there is nothing we can do about the wind and weather, we can adjust the stack height or adjust the emission rate to decrease the intensity of the plume for that receptor.  The emission rate is often tweaked by adding pollution control devices on the stack or limiting the production the entity can produce.  No business likes to do less production so its mostly pollution control devices that are used - or sometimes - raising the height of the stack.

In order for Dr. Sattler to generate her models, she had to assume a fixed condition as well to plug into the computer model, a model that she says uses the Gaussian formula:

She had wind and atmospheric conditions for the day of sampling, so those could be plugged in.  She could reasonably estimate the stack hight for the compressors.  What she didn't have was the actual emission rate.  So it was her reasoning, that if she had the concentration from some point in the plume, she could back in that data and calculate the emission rate that must have been in place to generate that particular concentration under these known conditions (wind speed, direction, atmospheric, stack height, plume location "y").

Now this is completely reasonable in approach.  However it is only reasonable if you assume Gaussian dispersion was taking place.  The model is for Gaussian dispersion, so to calculate an emission rate "E", Gaussian dispersion must be in place for the sample "C" used to back in to the formula.

Again, there is nothing wrong with this premise, as long as a Gaussian dispersion was in operation when the sample was collected.  In order to back in the concentration "C" to get the emission rate "E", Dr. Sattler had to have assumed Gaussian dispersion was in place, since she used a Gaussian formula to calculate the emission rate "E."

So if Gaussian dispersion was in place, and a Gaussian formula was used to calculate the emission rate "E", then the other premise of the Gaussian model is also in place as well:

That at a given emission rate "E" and a wind speed "U", and atmospheric conditions "S" and a stack height "H", somewhere on either side of that center line at location "y" you will find the contaminant to be at concentration "C."

That's when it hit me.

Nothing else is in play here in these Gaussian models.  The chemical's properties, the impact of other agents, pooling, condensing, degradation, vortexes.. they do not exist for purposes of generating these plume models.  It looks at ideal conditions to generate the modeled plume.  The model predicts maximum distance where a particular concentration of the chemical might reasonably be found.

So to "back in" the actual concentration found in a canister, the assumption must be that nothing but a Gaussian plume was being produced when the contaminant was sampled.

If that were the case, the amount of contaminants found in each canisters would be proportional, since the emission rate was steady as was everything else.  Each canister was exposed to the same wind speed "U", the same wind direction "Center Line", the same atmospheric conditions "S", and the same stack height "H".  So taking the location of the canister "y" and the concentration of the contaminant "C" and backing it in to the formula would give you "E".  That's what Dr. Sattler did because that's what she said she did in her deposition.

And with that calculated emission rate "E" she was then able to model the air for 8760 individual plumes - the number of hours in a year for which she had historical data for "U" and "S."  With that data, the emission rate "E", and the estimated stack height "H" - she was able to plug all of that into the model, and using the Gaussian plume formula, calculate both the maximum distance where the dispersion model's plume would show a concentration above a threshold (she used the ESL) as well as calculate the highest possible concentration the source could theoretically produce to which a receptor (citizen in the Town of Dish) might be exposed to.

And that's just what she did for the report, producing Table 2:

Brilliant!  Except for one little bit of a problem.  If the calculated emission rate "E" was determined by backing in the concentration "C" in to the formula, it would produce a theoretical concentration (which she averaged in columns 2 and 5).  If that holds true, then that same emission rate "E" would also be able to produce the actual concentrations in canisters 1 - 6 shown in Table 1.

If it can produce a theoretical, it should also be able to reproduce the actual - since the emission rate "E" was derived from that particular actual data.

This means that canister with the highest amount of benzene - canister 4 - must have been located in the Gaussian plume at a location "y" where the benzene would theoretically be the highest (closer to the center line) when compared to all the other canisters.  Because canister 4 has the highest benzene - because of location "y" - the model holds that at a constant emission rate "E" for the other contaminants was in play as well.

For canister 4 to produce the highest benzene concentration its location in the plume would also produce the highest concentrations for all the other contaminants. Regardless of what "E" is calculated for each contaminant, that "E" was in effect for each canister at exactly the same rate for the six contaminants being discharged on that sample day.  If any of the parameters fluctuated at any time, that impact was felt by all.  The same with wind speed, wind direction, and atmospheric conditions.  The same with stack height.  Each canister was placed and collected under the exact same conditions.  Each canister had to be in the same plume when Dr. Sattler backed in data to generate that emission rate "E."  The conditions producing the actual amount of contaminants in the six canisters must be the same if Gaussian dispersion was in play.

Unless it wasn't.

And if you look at Table 2, you will clearly see it was not.  So if Gaussian dispersion was not taking place that day, then how can you back in the data to calculate an emission rate from a formula that is based on showing a Gaussian dispersion?  If the emission rate "E" that Dr. Sattler calculated cannot be used to calculate the actual concentrations seen, then how can it be used to calculate a theoretical maximum?

And if you ignore that by explaining it away saying the actual concentrations in the six canisters were impacted by other conditions, then you are admitting that Gaussian dispersion was not in play, therefore an emission rate "E" cannot be calculated since no other variables are considered in the formula.

And if you say the sample was collected over 24 hours and was diluted, well that doesn't affect Gaussian dispersion since all the samples were collected for that same period and would have been similarly diluted.

And if you say the wind conditions changed for each of the canisters throughout the day impacting the concentrations of some of the contaminants getting to the canisters, well then, you are really grasping at straws.  And besides, if that's the case, how do you know what concentration to back in to the model?

There are two equally valid reasons why Dr. Sattler's modeling and the subsequent "averaged concentrations" are incorrect:

1. It is impossible to calculate the exact concentration attached to a particular "y" to back into the model because - in real life - the plume is consistently changing over time.  Gaussian modeling assumes perfect and steady conditions in order to produce a plume.  So "E" can never accurately be calculated by backing in the concentration.
2. The concentrations captured in the six canisters came from multiple sources and not from one source as modeled.  In this case, backing those concentrations into the model will always generate an emission rate "E" that is higher than what it is.  This incorrect "E" will then generate plumes and concentrations that are also too high.

Bottom line is this:

If you assume Gaussian dispersion modeling can reasonably model possible concentrations within a plume....

....and you assume that the formula for ground level concentrations is correct:

....and you agree that the canisters were all under the same wind speed, wind direction, and atmospheric conditions...

....and the emission rate "E" was exactly the same for each of the contaminants detected in each of the six canisters...

....and you accept that the emission rate, along with all the other parameters, plugged into that formula will produce a plume that is Gaussian (see graphic at the beginning)....

....then the plume produced from that calculated emission rate "E" must accurately match the actual concentrations found in the six canisters in and around that modeled plume....

...and if the modeled plume - using to emission rate obtained by backing in the actual concentration - does not reproduce the actual concentration that were used to derive it....

....then either the model is wrong....

...or the samples have been impacted by conditions not considered in a Gaussian model....

...which means that the actual concentration found in the six canisters cannot be used to calculate the emission rate of the source....

....which means the data presented in Table 2 of the report, as well as any other report produced using backed in data to find an emission rate, is incorrect.

Bottom-bottom line.

As it stands now, Dr. Sattler's methodology of "backed in" data cannot be used to calculate an emission rate in order to generate plume data to show modeled average concentration levels and/or determine the proper setback for a source.

Bottom-bottom-bottom line:

You cannot use non-Gaussian data to determine the value needed in a formula that produces a Gaussian model.


Next post: The Fort Worth League of Neighborhoods Report to FWISD - Different place, same drummer


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