CASE STUDY: Transport of Atmospheric Pollutants

Source:

"Consider a Spherical Cow", John Harte. Narrative and case study design by Robert R. Gotwals, Jr.

Goal:

To learn about the flow of atmospheric pollutants between the northern and southern hemispheres.

Background Reading:

One of the main concerns of atmospheric chemists is to determine how do pollutants emitted into the atmosphere in one country or hemisphere flow into other countries or parts of the globe. Recently there have been significant political and diplomatic difficulties between the United States and Canada about this issue. Since pollutants know no boundaries, many of the pollutants that cause acid rain (mostly sulfur dioxide) are transported by winds in the upper atmosphere into Canada, where they mix with rain to produce acid rain.

In this case study, we are concerned with the flow of a particular pollutant, ethane, between the Northern and Southern hemispheres. Ethane (C₂H₆) is a part of natural gas that is emitted to the atmosphere whenever natural gas escapes unburned at wells and other sources. Ethane only enters the atmosphere in this fashion. In the atmosphere, ethane undergoes a number of chemical transformations (mostly oxidation with the hydroxyl radical, OH•) to form peroxyacetyl nitrate, also known as PAN. PAN is a part of the smog and ozone problems, and causes severe eye irritations and respiratory problems, particularly among the elderly and those with respiratory diseases.

In the Northern Hemisphere, ethane has a concentration of about 1.0 parts per billion (ppb). With a concentration of 1 ppb, that means there is one molecule of ethane for a billion molecules of air molecules. Using a golf analogy, if the concentration of red golf balls was 1 ppb, there would be one red golf ball for every 1,000,000,000 white golf balls. This may not seem like a problem, but this one little molecule of ethane reacts chemically with other stuff in the atmosphere, and eventually becomes a problem. It is like rolling a small snowball off a long hill - a little snowball won't hurt anyone, but if it rolls long enough, it becomes a snow boulder that can do serious damage!

In the Southern Hemisphere, the typical concentration of ethane is 0.5 ppb. Ethane can exit from the atmosphere by any of three methods, or mechanisms:

It can flow out of the lower atmosphere (the troposphere) where it does the most harm to the upper atmosphere (the stratosphere) where it does little or no harm.
It can wash out of the atmosphere through mixing with rain or snow.
It can react with other chemicals and be transformed to something different.

Ethane can also flow between hemispheres. Ethane can flow from North to South and South to North. The graphic below shows all of the possible mechanisms:

In this graphic, we show the Northern Hemisphere (X_N) on the left and the Southern Hemisphere (X_S) on the right. We show ethane coming into the two hemispheres from the bottom (E_N and E_S) . The graphic also shows ethane moving between hemispheres (aX_N and aX_N). In this case, the letter "a" is a rate that shows the number of ethane molecules transported per some period of time. For example, if "a" is 80%/year, then 80% of the ethane in the Northern Hemisphere and 80% of the ethane in the Southern Hemisphere change places every year. If the amounts in both are the same, then the net difference is zero -- this is called the steady-state or equilibrium condition. The politicians would love this to be true -- the stuff that is emitted in the North stays in the North, and the stuff emitted in the South stays in the South!

The graphic also shows ethane leaving both the North and the South through "wet deposition" -- pollutant mixes with the rain and snow and is deposited on the ground, where it may or may not do damage to people and things. Acid rain is the classic example of "wet deposition" - the stuff deposited is acid rain, which destroys buildings, plants, farm crops, and kills living things in ponds and lakes. The letter "b" is the rate constant for wet deposition from the atmosphere to the ground.

Building the Model:

You should be able to build a complete STELLA model based on the graphic and explanation of the graphic above. The question being asked by this model is:

For different inputs (amount of ethane, E_N and E_S, emitted by the nasty polluters!), how long does it take (in years) until the stuff emitted in the North stays there and the stuff emitted in the South stays there -- in other words, how long does it take for a steady-state/equilibrium condition to be in effect?

Initial Conditions:

For your model, assume there is no ethane in either hemisphere. We will also begin the model with identical rate constants for the transport of ethane between hemispheres (88.9% per year) and for wet deposition (b=88.9%). In this simulation, escape of ethane to the upper atmosphere is negligible, so we ignore it (you might ponder: what does that do to the accuracy of the model?).

Typical flows into the atmosphere of ethane are:

Northern Hemisphere: 1.2 x 10¹¹ molecules per year (120 ppb)

Southern Hemisphere: 0 molecules per year (0 ppb, since nearly all of the natural gas is mined and used solely in the Northern Hemisphere!)

Run your model for a period of 50 years. Experiment with a suitable choice of dt, striving for the fastest run with the best accuracy. Similar, experiment with various choices for integration method.

Investigate a number of plots, such as plots of the concentrations of the two hemispheres. You should also establish a converter -- "net interhemispheric flow" that is the difference between the flow from North to South and the flow from South to North. Plot this interhemispheric flow with the concentrations of the two hemispheres. You might also investigate the flows themselves.

Experimenting with the Model:

There are a variety of experiments that you can do with this model. Some possibilities:

Experiment with various flows to the northern hemisphere. What happens if the North increases its amount of emissions? What happens if, in Year 10, a large natural gas mine explodes, emitting an additional 2.35 x 10¹⁰ molecules of ethane into the Northern hemisphere? Does the system come back into steady-state? If so, how long does it take?
Suppose we still have the same amount of emissions: 1.2 x 10¹¹ molecules per year, but only 80% of that comes from the Northern Hemisphere (the other 20% from the Southern Hemisphere). What is the influence of that change on the time until steady-state? How does that affect the system as a whole?
Where does most of the ethane go? Between hemispheres? Deposited as wet deposition? Use your graph pad and/or table pad to get a sense of where the ethane is going.

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