SSACgnp.TD883.DKM1.4
What are the Winds Blowing into
Mammoth Cave?
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 Issue
Modeling and estimation
Supporting Quantitative Literacy Topic
Basic arithmetic
Proportions
Graphical representation of data
USGS
Core Geoscience Subject
Air quality; Cave management
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.
1
Getting started
After completing this module you should
be able to:
•Define “modeling”.
•Be able to distinguish between modeling
and estimation.
•Be able to identify the variables needed
to construct an environmental model.
•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.
Kentucky
And you should also know where
Mammoth Cave National Park is.
2
The setting – Mammoth Cave National Park
Mammoth Cave National Park is the most extensive known cave system in the world and was
recognized as a World Heritage Site in 1981 and as an International Biosphere Reserve in
1990. The cave 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 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.
Sinkhole plain
Soda straw
Green River
Frozen Niagara
3
Geologic setting
Mammoth Cave was formed in Mississippian-aged limestone that was deposited 360 to 320
million years ago. This limestone is capped by the Pennsylvanian-aged Big Clifty Sandstone
(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 whole region was (and still is)
tilted to the northwest, water worked its way horizontally through the limestone layers to form
the large passages through which you traverse on most of the Mammoth Cave tours.
4
The Problem
In this module, you will construct a baseline model of air flow into and out of Mammoth Cave
using actual data collected by Mammoth Cave National Park at Houchin's Narrows, also known
as the Historic Entrance.
Question 1: What is the net volume
of air moving into Houchin's
Narrows in 1997?
Next, you will use the net volume of surface air moving into the cave and the concentrations of
O3, CO, and SO2 in that air to model the transport of pollutants into the cave.
Question 2: What’s the net amount of pollutants fluxing into
the cave in 1997? Is there any pattern to this flux?
5
Surface Air Quality
A report compiled by three environmental organizations cited Mammoth Cave National Park as
the third-most polluted park in the National Park Service system**. This designation was
established based on levels of haze, ozone, and acid precipitation measured by air quality
stations at the park. These pollutants drift into the park as emissions from interstates, power
plants, and industrial sites along the Ohio River Valley.
Pollutant
Sources
Environmental
impacts
Human impacts
EPA Standard Limits
Ozone
O3
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 monoxide
CO
Fossil fuel combustion;
chemical manufacturing;
Smog formation
Reduction of oxygen delivery
to body; loss of mental acuity;
respiratory irritation
Sulfur dioxide
SO2
Fossil fuel combustion; oil
refining; mining/ore
production
Reduction in visibility;
acid rain harming plants
& wildlife
Respiratory irritation
9 ppm (8-hour)*
35 ppm (1-hour)*
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.
**Report based on air quality data collected from 1991 to 2001 at ten national parks
with the most extensive monitoring protocols.
Return to Slide 16
6
Air Flow: Mammoth Cave & Houchin’s Narrows
At Mammoth Cave, seasonal changes in air flow occur such that air fluxes out of the cave’s
lower entrances during cooler periods, and into the cave’s lower entrances during warmer
periods, due to temperature and density differences. Cave air is cooler/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/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 affects of temperature & pressure on airflow, click here.
Return to Slide 16
Houchin’s Narrows the main entrance to Mammoth Cave, and the largest. Unlike other
entrances to the cave, it is not manmade and has therefore not been modified with door
systems to prevent unnatural air-flow patterns in the cave. Data have been collected here for
over 10 years to study the patterns of air movement in the cave.
7
Getting the data
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
migrating into and out of the cave, which receives some of the highest visitation than any other
area in the park.
A model in, scientific terms, is a basic representation of
a system upon which hypotheses are made to describe
or explain it. In this case, air flow and pollutant data are
compiled and analyzed to understand the
characteristics of both air flow and surface pollutants at
Mammoth Cave. Unlike estimation, which is an
approximate calculation of a specific variable, models
take into account numerous variables to help
understand and predict outcomes in a system.
Click on the Excel icon to the right and save the
file immediately to your computer. The
spreadsheet contains both air flow 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, and were averaged for each day.
Note: values might be missing from
some cells in your spreadsheet. This
is normal, as logging devices
sometimes malfunction and skip
measurements.
8
Calculating daily air volume
We can estimate the volume of air moving in or out of the cave on any given day using the 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 fast the air is moving, we see not only the
volume of air flow moving at any given point, but also it’s direction.
So if the average 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).
Note: For every cell in Column C that is
missing a measurement, your calculated
volume in Column D will be zero.
= cell with a given value
= cell with a formula
9
Calculating pollutant flux
To calculate the volume of pollutants fluxing into the cave, we first need to check our units to
make sure they are the same. The flux of air moving into the cave is measured in units of m3/s,
so the volume we are working with is m3. Pollutants are expressed as a concentration in units
of ppm (parts per million). If we convert ppm to mg/m3, we still have a concentration, but our
units of volume are the same.
Assuming standard temperature and pressure,
the conversion is easy:
where mw is the molecular weight of the
pollutant (g/mol), ppm is the concentration, and
22.45 is the volume in liters of an ideal gas at
standard temperature and pressure (STP at 25
°C and 1 atm). Note that the conversion from
grams in mw to mg in the concentration is
figured into this equation.
Add columns to your spreadsheet
converting each of the three pollutants
from ppm to mg/m3 using molecular
weights provided here.
Pollutant
Molecular Weight
O3
48 g/mol
CO
28.01 g/mol
SO2
64.06 g/mol
10
Calculating pollutant flux (cont’d)
Now that we have calculated both the volume of air moving in and out of the cave each day 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.
Add columns to your spreadsheet calculating the amount of surface pollutants fluxing 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.
11
Solving the problem
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 reflected throughout our flux calculations, this becomes a simple
matter of addition.
At the bottom of your
spreadsheet, calculate
the sum of all values for
daily air flow volume
and pollutant flux. At
the same time, convert
the net value of total
daily air flux to km3/yr
and to make it easier to
comprehend.
Return to Slide 16
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.
12
Assessing the results
Based on our calculations, we can estimate that a
whopping 49,380 km3 of surface air was imported into
the cave from the Houchin's Entrance in 1997, carrying
with it large amounts of pollutants, as summarized in the
table to the right.
This shows that the volume of air (and pollutants) coming
into the Houchin's Entrance far exceeds that moving out,
which could perturb the delicate balance of geochemistry
in the cave, threatening the stability and preservation of
both its geologic features and its unique biologic
assemblage.
Pollutant
g/yr
O3
163
CO
16,397
SO2
1,514
To understand more about the input of pollutants at
Houchin's Narrows, are there any seasonal effects on
airflow patterns here?
Graph both the air volume and pollutants over the course of 1997 to find out.
For help, click here.
13
Assessing the results (cont’d)
Both graphs support our calculations
that more air and the pollutants it
brings are fluxing into Houchin's
Narrows than are fluxing out.
Estimatd Air Volume (m3/day)
3500000
3000000
2500000
2000000
1500000
1000000
500000
0
12/1/96 1/20/97 3/11/97 4/30/97 6/19/97 8/8/97 9/27/97 11/16/97 1/5/98 2/24/98
-500000
-1000000
-1500000
800
600
Flux (g/day)
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 the 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 s as well.
Date
400
O3
200
0
12/1/96
SO2
CO
3/11/97
6/19/97
9/27/97
1/5/98
4/15/98
-200
Return to Slide 16
-400
Date
14
Wrap-up: assumptions in modeling
During the course of these calculations, you
should have noticed we’re making some
very important assumptions:
1.We are assuming standard temperature
and pressure when converting the
concentration of pollutants from ppm to
mg/m3.
2.We are assuming that missing data from
malfunctioning data loggers would not
contradict our results.
3.Trends seen at Houchin's Narrows in 1997
are indicative of long-term trends.
We are also ignoring some key points:
1.What’s 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’s the residence time of surface air
pollutants in the cave? Do they flux out as
rapidly as they flux 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’s often impractical, if
not impossible, to account for every variable in the system you’re trying to model. Uncertainty
is always a factor to consider when interpreting model results, and therefore you have to make
your model as complete as your datasets will allow, knowing your model results and
interpretations may change as new data becomes available.
What data would you add to make this model more complete?
Return to Slide 16
15
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 Houchins Narrows
changed over time and compare the results with your plot of air flux over time. How do air
flux and air temperature co-vary? 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). The dataset you have 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 ppm) 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?
16
End-of-module assignment, cont’d
5. Ozone is a pollutant of concern at Mammoth Cave National Park. Its ground levels are
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 ppm data). How do these three pollutants vary seasonally? If the major source
of these pollutants are power plants in the Ohio River Valley, can you explain these
variations? Why do you think ozone behaves differently?
Hint: pollutant information on Slide 6 and your answer for Question 5 may help.
17
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 cited for 8-hour increments (in the case of SO2, use the 24-hour increment).
You will find that the only pollutant that exceeded the value set by an EPA standard was ozone;
however, we do not know at this point whether it reached or exceeded the 0.075 ppm threshold
for 8 hours or more 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.
18
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 we stand 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 threshhold 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 a bit closer to identify when it has held those levels
for a period of 8-hours straight. Though we could examine the whole dataset, for this
exercise we will only do it for the first two weeks of August, One of the higher months. 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.
19
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
20
Endnote 1: introduction to air flow
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.
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
21
Endnote 2: inserting spreadsheet columns/rows
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.
Return to Slide 9
22
Endnote 3: creating x-y scatter plots
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.
Return to Slide 13
23