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The concentration of surface air pollutants is of growing concern at Mammoth Cave National Park, but what volume of

pollutants is making it into the cave?

Core Quantitative IssueModeling and estimation

Supporting Quantitative Literacy TopicBasic arithmeticProportionsGraphical representation of data

Core Geoscience SubjectAir quality; Cave management

USGS

Dorien K. McGee1, Bobby Carson2, and Jonathan Jernigan3; 1Department of Geology, University of South Florida, Tampa, FL 33620; 2Mammoth Cave National Park, Mammoth Cave, KY 42259; 3Cumberland Piedmont Network, Mammoth Cave National Park, Mammoth Cave, KY 42259© University of South Florida Libraries. All rights reserved. 2009.

What are the Winds Blowing into Mammoth Cave?

The module you are viewing is a PowerPoint slide presentation.

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You can and probably should have a spreadsheet open in a separate window, so you can try out things that are explained in the presentation.

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Getting started

After completing this module you should be able to:

•Define “modeling.”•Be able to distinguish between modeling and estimation. •Understand the benefits and drawbacks to using models to understand environmental processes and predict impacts. •Know how to perform unit conversions.•Know how to interpret trends represented in x-y scatter plots.

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Kentucky And you should also know where Mammoth Cave National Park is.

Mammoth Cave National Park is the most extensive known cave system in the world. It was recognized as a World Heritage Site in 1981 and as an International Biosphere Reserve in 1990. The cave, which has been forming in stages over the last 10 million years, contains almost every known type of cave formation and is the most biodiverse cave system known in the world. The relative stability of the cave environment helps preserve both its features and its organisms; however, this makes them more sensitive to perturbations such as changes in the flow and/or chemistry of the air and water. These perturbations are often triggered by anthropogenic activities at the surface. Air quality at the surface of Mammoth Cave is of utmost concern due to pollutants drifting south from coal processing and other industrial activities in the Ohio River Valley.

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The setting – Mammoth Cave National Park

Sinkhole plain Soda straw Green River Frozen Niagara

Geologic setting

Mammoth Cave formed in the last 10 million years in Mississippian-age limestone (deposited 360 to 320 million years ago). This limestone is capped by the Pennsylvanian-age Big Clifty Sandstone (deposited 320 to 300 million years ago). Because sandstones are more resistant to dissolution than limestone, the Big Clifty Sandstone protected much of the underlying limestone from dissolving; however, erosion took its toll on the Big Clifty Sandstone, and over the last 10 million years, water made its way into the limestone to dissolve it. Since the layered rocks of the region were (and still are) tilted to the northwest, water worked its way along the limestone layers to form the large passages through which you traverse on most of the Mammoth Cave tours.

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The Problem

In this module, you will construct a baseline model of air flow into and out of an entrance to Mammoth Cave using actual data collected by Mammoth Cave National Park personnel. The entrance is Houchin's Narrows and is also known as the Historic Entrance. Next, you will use the net volume air moving into the cave in 1997 and the concentrations of O3, CO, and SO2 in that air to model the transport of pollutants into the cave through that passageway.

Question 1: What is the net volume of air moving into Houchin's Narrows in 1997?

The term flux is useful in this module. The word is derived from flow. In the context of transport phenomena, which includes the flow of air, water and other fluids as well as the materials they contain, the term refers to the quantity of matter that moves across a unit area per unit time. That quantity can be measured in terms of volume (in which case we have a volumetric flux), mass (mass flux), or even molecules (diffusion flux).

Question 2: What is the net amount of pollutants flowing into the cave through that entrance in 1997? Is there any pattern?

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Surface Air Quality

A report compiled by three environmental organizations listed Mammoth Cave National Park as the third most polluted park in the National Park Service systems that they studied.** The report considered the amount of haze, ozone, and acid precipitation measured at air quality stations in the parks. These pollutants drift into the Mammoth Cave National Park as emissions from highways, power plants, and industrial sites along the Ohio River Valley.

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**Report based on air quality data collected from 1991 to 2001 at ten national parks with the most extensive monitoring protocols.

Pollutant SourcesEnvironmental

impactsHuman impacts EPA Standard Limits

OzoneO3

Produced from reactions of volatile organic compounds

with nitrogen oxides

Interference with photosynthetic processes

Respiratory irritation; lung damage; inflammation

0.075 ppm (8-hour)

Carbon monoxideCO

Fossil fuel combustion; chemical manufacturing;

Smog formationReduction of oxygen delivery to body; loss of mental acuity;

respiratory irritation

9 ppm (8-hour)*

35 ppm (1-hour)*

Sulfur dioxideSO2

Fossil fuel combustion; oil refining; mining/ore

production

Reduction in visibility; acid rain harming plants

& wildlifeRespiratory irritation

0.03 ppm (annual arithmetic mean) *

0.14 ppm (24-hours)

From EPA National Ambient Air Quality Standards (primary) in accordance with Clean Air Act* Not to be exceeded more than once per year.

Return to Slide 16

Air Flow: Mammoth Cave and Houchin’s Narrows

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At Mammoth Cave, seasonal changes in air flow occur such that air moves out of the cave’s lower entrances during cooler periods, and into the cave’s lower entrances during warmer periods. Cave air is cooler and denser than surface air during the summer months, causing it to flow out of the lower entrances (air is outcast), while pulling air in from upper entrances to replace it. Cave air is warmer and less dense than surface air in the winter months, causing the surface air to flow into the lower entrances, thus pushing some cave air out of the upper entrances (air is incast). This is a modified version of the chimney effect.

For more information on the effects of temperature and pressure on airflow, click here.

Houchin’s Narrows is the main entrance to Mammoth Cave, and the largest. Unlike other entrances to the cave, it is not manmade and has not been modified with door systems that prevent unnatural air-flow patterns in the cave. Data have been collected here for over ten years to study the patterns of air movement in the cave.

Return to Slide 16

Though there are numerous entrances to Mammoth Cave that accommodate and influence air flow, we will use data collected at Houchin’s Narrows to model the amount of pollutants moving into and out of that part of the cave, which receives some of the highest visitation of any other area in the park.

Getting the data

Click on the Excel icon to the right and save the file immediately to your computer. The spreadsheet contains both volumetric flux data for Houchin’s Narrows and surface pollutant data for Houchin’s Meadow for 1997. These data were originally collected at 5- or 15-minute intervals. Then they were averaged for each day.

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Note: values might be missing from some cells in your spreadsheet. This is normal, as logging devices sometimes malfunction and skip measurements.

A model, in scientific terms, is an interactive representation of a system which allows us to perform calculations that describe and explain what is happening within the system. In this case, the system is the cave, the air flowing through it, and the pollutants from the outside that the air is carrying. The data that go into the model are volumetric flux of air and concentration of pollutants in the air. The calculation involves multiplying the two together – with due allowance for consistency of units – to produce the max flow of pollutants into and out of Houchin’s Narrows.

We can estimate the total volume of air moving in or out of the cave on any given day using the volumetric flux data. A positive number indicates the air is incast, while a negative number indicates the air is outcast. Since the number itself indicates how much the air is moving, the number together with its sign tells us not only the rate of flow, but also its direction.

Calculating daily air volume

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= cell with a given value

= cell with a formula

Note: For every cell in Column C that is missing a measurement, your calculated volume in Column D will be zero.

So if the average volumetric flux of air on January 1, 1997 is 4.92 m3/s, what is the estimated volume of air moving into the cave that day? What unit conversion do you need to make this calculation?

Insert a column after Column C to calculate the average volume of air moving in or out of the cave daily (for help with inserting columns, click here).

To calculate the flow of pollutants we need to think about the units of our various quantities. The units of the volumetric flux of air have been m3/s and m3/day. The concentration of pollutant gases in the air (such as O3, SO2, and CO) are typically expressed in ppmv (parts per million per volume). One ppmv, for example is 1 microliter per liter, which is the same as 0.001 milliliters per liter. For amount of pollutants, it is customary to work with concentrations expressed in mg per cubic meter of air. Thus we need to convert our pollution concentrations from ppmv to mg/m3.

Calculating the flow of pollutants

Add columns to your spreadsheet converting each of the three pollutants from ppmv to mg/m3 using the molecular weights provided here. 10

Concentration in ppmv is a volume-per-volume quantity; in contrast, mg/m3 is a mass-per-volume quantity. To convert from one to the other, we need to take account of the density of the gas. Density in general is mass per unit volume. For gases, density is generally conceptualized in terms of a mole: the mass of a mole of the gas divided by the volume of a mole of the gas (a mole is 6.022 × 1023 atoms). The mass of the mole is easy: it’s the molecular weight (MW) of the gas. The volume is tougher, because it varies with temperature and air pressure. At standard temperature and pressure (STP: 25 C and 1 atm), the volume of a mole of gas is 22.45 L. Put all that together and the conversion we seek is

where C(mg/m3) and C(ppmv) refer to concentrations with the different units. We are assuming STP. To do otherwise would involve additional steps to take account of the expansion of air with increasing temperature and decreasing pressure.

Pollutant Molecular Weight

O3 48 g/mol

CO 28.01 g/mol

SO2 64.06 g/mol

Now that we have calculated both the volume of air moving in and out of the cave each day at Houchin’s Narrows and the concentration of pollutants contained in that air, we can calculate the amount of surface pollutants moving in and out of the cave each day by that entrance.

Calculating the flux of pollutants (cont’d)

Add columns to your spreadsheet calculating the flux of surface pollutants in and out of the cave each day. Since your units of mg/day will be rather large, convert your values to g/day to make them easier to comprehend.

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Now we can estimate both the net volume of air moving into Houchin's Narrows in 1997 as well as the amount of pollutants. Since our incast and outcast values are denoted by positive and negative numbers that are carried through our calculations, this becomes a simple matter of addition.

Solving the problem

At the bottom of your spreadsheet, calculate the sum of all values for daily air flow volume and pollutant flux.

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Hint: To make these numbers easier to interpret, insert comma separators by highlighting the row containing these calculated values and clicking the Comma Style icon in the Number panel on the Home tab.

Return to Slide 16

Based on our calculations, we can estimate that nearly 50 million m3 of surface air was imported into the cave through Houchin's Narrows in 1997, carrying pollutants with it, as summarized in the table to the right: about 160 g of ozone, more than 16 kg of carbon monoxide, and about 1½ kg of sulfur dioxide.

The positive sign of the flux shows that the volume of air (and amount of pollutants) coming into at Houchin's Narrows exceeds that moving out. This could perturb the delicate balance of geochemistry in the cave and threaten the stability of both its geologic features and its unique biology.

To understand more about the input of pollutants at Houchin's Narrows consider whether there are there any seasonal effects on airflow patterns.

Assessing the results

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Pollutant g/yr

O3 163

CO 16,397

SO2 1,514

Graph both the air volume and pollutants over the course of 1997 to find out. For help, click here.

Both graphs support our calculations. More air is flowing into Houchin's Narrows than is flowing out, and it is bringing in pollutants.

By graphing the data, we can see that, with some minor exceptions, air is flowing out of the cave from late spring to mid-fall, but that volume is less than that of air moving into the cave during the rest of the year. The same trend obviously exists for pollutant transport as well.

Assessing the results (cont’d)

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Return to Slide 16

While you worked through these calculations, you should have noticed that we are making some important assumptions:

1.We assumed standard temperature and pressure when converting the concentration of pollutants from ppmv to mg/m3.2.We assumed missing data from malfunctioning data loggers would not contradict our results.3.We assume trends seen at Houchin's Narrows in 1997 are indicative of long-term trends.

Wrap-up: assumptions in modeling

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We are also ignoring some key points:

1.What is the net volume of surface air imported to the entire cave (accounting for the chimney effect and all entrances)? Are the patterns at Houchin's Narrows reflective of air flow patterns at other entrances?2.What is the residence time of surface air pollutants in the cave? Do they flow out as rapidly as they flow in, or do they get trapped? Do they react with naturally occurring elements in the cave?

Making assumptions are a vital part of the modeling process because it is often impractical, if not impossible, to account for every variable in the system you are trying to model. Uncertainty is always a factor to consider when interpreting model results; therefore, you must make your model as complete as your datasets will allow and keep in mind that your model results and interpretations may change as new data become available.

What information or data would you add to make this model more complete? Return to Slide 16

End-of-module assignment

1. Construct the spreadsheet as described in Slides 9-12, and the x-y scatter plots as described in Slides 13-14.

2. Answer the question at the bottom of Slide 15.

3. Create another x-y scatter plot to illustrate how air temperatures at Houchin’s Narrows changed over time and compare the results with your plot of air flow over time. How do air flow and air temperature vary together? Explain in terms of the chimney effect described on Slide 7.

4. The EPA standards given on Slide 6 typically apply to 1- and 8-hour periods (with the exception of SO2). This dataset reports pollutant concentrations as daily averages but may still be used to estimate whether pollutants might have exceeded EPA standards in 1997. Calculate the yearly average of all three pollutants (in ppmv) at the bottom of your spreadsheet. Next, use the =MAX function to identify the highest daily average for each pollutant that year. Did any averages or maximum values come close to any of the EPA standards (regardless of the time duration)? If these calculations are based on daily averages, how might you interpret how the actual measured values varied?

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End-of-module assignment, cont’d

5. Ozone is a pollutant of concern at Mammoth Cave National Park. Ozone at ground level is related to vehicle and industrial emissions, but only indirectly. Using the Internet as a source, describe how ozone forms from emissions.

6. Create three new x-y scatter plots to illustrate how the pollutant concentrations change over time (using ppmv data). How do these three pollutants vary seasonally? If the major source of these pollutants is power plants in the Ohio River Valley, can you explain the variations? Why do you think ozone behaves differently? Hint: pollutant information on Slide 6 and your answer for Question 5 may help.

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End-of-module assignment – intermediate/advanced

In Question 3 of the End of Module assignment, we estimated whether any of the three pollutants exceeded EPA standards for 1997. Since we were using daily averages rather than raw data to assess this, we could not be certain of our results. Here we will work with raw pollutant data supplied by Mammoth Cave National Park to better address this question (it was from these data that daily averages were calculated and used earlier in this module).

Since data were recorded roughly every 5 minutes, the resultant dataset has nearly 102,000 entries for each pollutant! This is an exercise in narrowing and filtering your dataset to get the answers you need!

1.Use the =MAX function to determine which, if any, of the three pollutants exceeded the concentration limits set for 8-hour increments (in the case of SO2, use the 24-hour increment). You will find that the only pollutant that exceeded the EPA standard was ozone; however, we do not know at this point whether it reached or exceeded the 0.075 ppmv threshold for 8 hours or more on any given day. To determine the likelihood for this, use the =COUNTIF function to identify how many data measurements are greater than or equal to 0.075.

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End-of-module assignment – intermediate/advanced

2. Since ozone concentrations have met or exceeded 0.075 ppm just over 5,900 times during the course of the dataset there stands a good chance that it has done so over an 8-hour period. Highlight the column bearing the ozone data and select the Filter tool in the Data Panel. Click the down-arrow in the ozone column and select “Number Filters”, then “Greater Than Or Equal To” from the pop-up menu. Type in your threshold and click OK.

3. Now that you have filtered down your data to include only points where ozone exceeded 0.075 ppm, you may examine the data more closely to identify if it has held those levels continuously for 8-hours. Though we could examine the whole dataset, for this exercise we will do it only for the first two weeks of August. Filter the date to include only values for August, then further filter to include only the first 14 days.

4. There are 24 days in the month of August with high ozone concentrations. Scroll through these data and list which dates ozone met and/or exceeded the 8-hour EPA standard. Be sure you have full hours (i.e., if your data start at 14:30, you should have values for every 5 minutes until at least 22:30). Did any other days come close?

Record your results and hand in your spreadsheets.

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References

Slide 5 – images from Dr. Lindley Hanson, Salem State College Department of Geological Sciences

Slide 6 – Sources: USA Today, Appalachian Voice,

Slide 7 – image by Jonathan Jernigan: “Mathematical Modeling of Convective Heat Transfer in Mammoth Cave” (MS Thesis, Western Kentucky University, 1997).

Slide 22 – upper image from TechnicalEngineering.org; bottom left image from Charles Sturt University; bottom right image from Meteorological Monsters laboratory exercise (Science Education Resource Center).

Slide 23 – map from NPS

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Before we tackle this problem, we need to understand what causes air to move. Air moves primarily due to differences in temperature and pressure. As air becomes warmer, it becomes buoyant and rises. As it cools, it becomes denser and sinks. This is the science that drives the formation of convectional thunderstorms, as well as hot-air balloons.

Endnote 1: introduction to air flow

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Similarly, air flows from areas of high pressure to areas of low pressure. Together, differences in temperature and pressure at Earth’s surface drive the formation of winds, which are often deflected and/or rotated due to the rotation of Earth itself.

Return to Slide 7

Endnote 2: inserting spreadsheet columns/rows

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Return to Slide 9

Adding columns to spreadsheets is easy! In this case, we want to create a new Column D by shifting the ozone concentration data to Column E.

Right-click the Column D heading and select “Insert” in the pop-up menu. Because you right-clicked the column heading, Excel automatically interprets that you want to insert a new column. Likewise, if you were to click on a row heading, it would automatically interpret that you wanted to add a new row.

Note: Excel will automatically format the new column using the same formatting as the column to its immediate left. As a result, your cells will be yellow rather than orange, the normal color of cells requiring a calculation. You may change the cell colors using the color palette in the “Home” tab.

Endnote 3: creating x-y scatter plots

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Return to Slide 13

There are several ways to graph in Excel, but this one is simplest for those who’ve not graphed before. Highlight the data in the fields you wish to plot. Since these fields aren’t adjoined, here’s a little trick:

1.Highlight the field of dates first and hold down the Ctrl key.2.Without releasing the Ctrl key, highlight the Daily Air Flux data, being sure not to include the sum calculation at the bottom of the column (this will effect how your data plot).3.Select the Insert tab and in the Charts panel, click on the Scatter graph and choose “Scatter with smooth lines” in the pop-up menu (this option is best when plotting large datasets such as this. You may add axes labels and other visual elements to your graph using the “Layout” options in the Chart Tools tab.

Repeat this process to create a separate graph of pollutant flux over time, bearing in mind that you will be selecting the date and all three pollutant flux fields. Excel will recognize the pollutants as multiple y-axis values and plot them accordingly.