Thermodynamics and

Statistical Mechanics of

Tornadoes

Sydnie Gjerald and Zachary Fahrendorff Advisor: Dr. Misha Shvartsman

August 31st, 2019

Center for Applied Mathematics, St. Paul, MN

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Abstract: The United States is affected by many types of natural disasters each year, but the astonishingly

large number of tornadoes that rip through the country is our focus. Meteorologists have a lot of

raw weather data to handle, and, of course, they want to be able to make inferences from that

data to aid in tornado prediction. These values that they find are often called indices or

parameters. Some of the parameters we focused on over the course of our research are CAPE—

convective available potential energy, SRH—storm relative helicity and STP—significant

tornado parameter. We would like to be able to better understand how these parameters indicate

tornado formation, how to use them, and if any are likely to be more significant than others.

Based on many of these values and their intuition about storms, meteorologists must decide

whether to issue a tornado watch/warning in a timely manner.

Problem Statement and Introduction: We all know of the infamous Tornado Alley that is situated in the middle of the United States,

and because of this phenomenon, the U.S. experiences more tornadoes than the rest of the world

combined. As mentioned earlier, tornado warnings need to be issued in a timely manner or they

really don’t matter at all. If you are warned only a few minutes before impact, it could be too late

for many people in the U.S. There is a fine balance between the accuracy of these predictions

and quickly releasing a warning. What makes tornado prediction so tricky is that two

thunderstorms that are nearly identical might produce different results—one storm a strong EF4

tornado and the other storm no tornado at all. Through the use of parameters and indices in

forecasting (Doswell and Schultz), we can attempt to analyze the atmosphere and make more

accurate predictions that give the public more time to prepare for these major events. So,

meteorologists often try to get as much data as possible to try to be accurate in their warning

without being too late in the warning lead time. Even an extra minute of lead time could save

many lives! Today,

tornadoes range from EF0-

EF5 on the EF scale,

which stands for Enhanced

Fujita scale (Figure 1).

This scale invented by Ted

Fujita considers the wind

speed of the storm and the

damage that occurred

during/after the storm. We

have chosen many

tornadoes from the last few

years to analyze and find

these parameters for. We

chose to focus on strong

tornadoes (EF3-EF5)

because we would like to

use data that is

significantly strong in

relation to other smaller tornadoes. Figure 1

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Goals: The goal of this research is that through the analysis of previous tornadoes, we would like to

understand how to more accurately predict tornadoes in the future by using indices and

parameters. Of course, we don’t have years of meteorology and storm chasing experience, so our

goals are relatively restricted to what we can learn from past tornadoes. We would like to draw

some conclusions about how we can more accurately calculate these values, and which values

are of most importance. In addition to the computational side of this research, we will discuss

how thermodynamics and tornadogenesis are related.

Thermodynamics of Tornadogenesis: To start this section, it is important to go over the generally accepted process in which most

midwestern tornadoes occur. Tornadogenesis begins with two wind shears going opposite

directions at two different heights (usually a warm front and cold front colliding). These

different wind shears cause horizontal rotation (Figure 2).

Horizontal rotation is relatively harmless, however, when it is tilted into a vertical spin it poses

the threat of becoming a deadly tornado. How does a horizontal spin become vertical? It has to

do with the sun and heated air. The sun’s rays don’t heat the air, but rather the sun heats up the

ground which in turn warms the air near the surface (Figure 3). We know that hot air rises, and

that updraft causes the horizontal spin to become tilted into two vertical spins (Figure 4). One

spin will die out or merge with the other, and that vertical column can possibly spawn a

tornado. This interaction between the heated surface air and the updraft that accompanies it is

why most tornadoes happen in the evening after warm days when the sun has had all day to heat

the ground.

Figure 2

Figure 3 Figure 4

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If a strong updraft persists and the downdraft

caused by rain stays far enough away a tornado can

occur (Figure 5).

Although this is a generally accepted process, the

exact conditions that cause tornadoes are still up for

debate. There are hundreds of theories regarding

tornadogenesis dealing with everything from

temperature and pressure differences within the

funnel to the significance of the rear-flank

downdraft to the implementation of roundabouts in

certain states (true story, look it up).

Most of the tornadoes that occur and almost all the

damaging ones are supercell tornadoes. This means

they form out of a supercell thunderstorm—a

rotating storm. These storms produce a lot of

energy. Given an average sized storm, for instance

10km x 10km x 15km, this storm will produce around 1.69 terajoules (1.69 x 1012 J) of energy. If

the storm lasts about an hour, it is possible that the storm has more energy than the Hiroshima

nuclear bomb. Not all of this internal energy is converted into mechanical work, in fact, most of

it is dispersed as heat (see 1st Law of Thermodynamics below). However, if even a small portion

of that energy is converted into mechanical work, we could have a large, deadly tornado on our

hands. We want to see which parameters indicate that more energy is being converted into

mechanical work rather than being dispersed as heat.

Latent heat is the source of most of the energy that is in the thunderstorm, and it is the energy

released when water vapor condenses into liquid in the clouds. The phase change of water vapor

to rain releases 2260 kilojoules of energy per kilogram and supercells have a lot of precipitation.

Thermodynamic theories play a big role in tornado formation, but they are still not well

understood. Thermodynamics simply means the branch of physical science that studies the

relationship between heat and other forms of energy and the transfer between the two. So,

thermodynamics helps explain why and how latent heat powers a tornado. There are 4 important

laws of thermodynamics:

0th Law: Absolute Temperature T exists

1st Law: Internal Energy U exists

𝛿𝑄 = 𝑑𝑈 + 𝛿𝑊 𝑤ℎ𝑒𝑟𝑒 𝛿𝑊 = 𝑃𝑑𝑉

𝛿𝑄 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 ℎ𝑒𝑎𝑡 𝑎𝑑𝑑𝑒𝑑 𝑡𝑜 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

𝛿𝑊 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑏𝑦 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚

2nd Law: Entropy S exists

𝑑𝑆 =𝛿𝑄

𝑇

3rd Law: As temperature goes to zero, so does entropy.

Figure 5

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𝑆 → 0 𝑎𝑠 𝑇 → 0

Internal Energy U plays a part in powering a tornado. What is important to us is how this energy

is changing, thus we take a total differential and focus on velocity. As you can see, U is a

function of entropy (level of disorder in our system on a microscopic level) and volume, which

are both extensive parameters meaning they are dependent on the size of the system.

So,

𝑑𝑈 = 𝑇𝑑𝑆 − 𝑃𝑑𝑉 =𝜕𝑈

𝜕𝑆𝑑𝑆 +

𝜕𝑈

𝜕𝑉𝑑𝑉

𝑤ℎ𝑒𝑟𝑒 𝑈(𝑆, 𝑉) 𝑖𝑠 𝑎 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑛𝑡𝑟𝑜𝑝𝑦 𝑎𝑛𝑑 𝑣𝑜𝑙𝑢𝑚𝑒

𝑎𝑛𝑑 𝑆, 𝑉 𝑎𝑟𝑒 𝑒𝑥𝑡𝑒𝑛𝑠𝑖𝑣𝑒 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠

𝑇, 𝑃 𝑎𝑟𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑣𝑒 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠

Helmholtz Free Energy (F) describes thermodynamic potential that measures the available

energy that could be used in the system, in this case a storm system that might produce a tornado.

Using the chain rule and partial derivatives:

𝐹 = 𝑈 − 𝑇𝑆

𝑑𝐹 = 𝑑𝑈 − 𝑇𝑑𝑆 − 𝑆𝑑𝑇 = 𝑇𝑑𝑆 − 𝑃𝑑𝑉 − 𝑇𝑑𝑆 − 𝑆𝑑𝑇 = −𝑃𝑑𝑉 − 𝑆𝑑𝑇

𝑑𝐹 = −𝑃𝑑𝑉 − 𝑆𝑑𝑇

𝑆𝑜, 𝑃 = −𝜕𝐹

𝜕𝑉 𝑎𝑛𝑑 𝑆 = −

𝜕𝐹

𝜕𝑇

Statistical Mechanics and Virtual Temperature: A term that is useful to understand before we get into our calculations and equations is parcel. A

parcel is a theoretical body of air to which any or all of the basic dynamic and thermodynamic

properties can be assigned. These bodies of air are big enough to be able to use the averaging

laws of statistical mechanics, but small enough to view their properties as functions of space and

time.

The air in our atmosphere is made of water vapor and dry air, and the two gases have very

different properties. Calculations for two-gas systems can easily become very tedious and

confusing, so we ideally would like to use a one-gas system. Thus, the concept of virtual

temperature was introduced to combat this issue. We will denote virtual temperature as theta, and

it will allow us to view our two-gas system as a one-gas system. Using Dalton’s Law and the

Ideal Gas Law, we have:

𝜌𝑚 = 𝜌𝑑 + 𝜌𝑣

where rho is density, and respectively m,d,v are mixed(moist) air, dry air, and water vapor.

Applying Dalton’s Law and the Ideal Gas Law:

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Pm = Pd + Pv = 𝜌dRd𝑇 + 𝜌vRv𝑇 = 𝜌dRd𝑇 (1 +Rv

Rd

𝜌v

𝜌d) = 𝜌mRd𝑇 (1 + (

Rv

Rd− 1)

𝜌v

𝜌m)

where respectively P is pressure, T is temperature and R is the universal gas constant. So,

𝑃𝑚 = 𝜌𝑚𝑅𝑑𝜃

where theta is virtual temperature.

Now to get to our anticipated result of representing the mixed gas system as a one gas system, a

short proof occurs:

𝜌𝑚𝑅𝑑𝜃 = 𝜌mRd𝑇 + Rd𝑇Rv − Rd

Rd𝜌v = 𝜌mRd𝑇 + 𝑇(Rv − Rd)𝜌 v

= (𝜌d + 𝜌v)Rd𝑇 + 𝑇(Rv − Rd)𝜌v

= 𝜌dRd𝑇 + 𝜌vRv𝑇 = Pm = Pd + Pv

To conclude, we can now represent the pressure of the mixed system as the sum of the pressures

of the dry air and water vapor,

𝑃𝑚 = 𝑃𝑑 + 𝑃𝑣

Now that we have settled some technicalities, we can introduce the equations for our parameters:

CAPE (convective available potential energy) is a measure of instability and potential energy in

the atmosphere, and this potential energy is the mechanical work that helps power a tornado if

the conditions are sufficient. There are a range of values for CAPE that suggest the possibility

for the formation of a tornado, but 2500-4000 J/kg shows strong instability, and greater than

4000 j/kg shows extreme instability, both of which indicate an increased probability of a tornado.

𝐶𝐴𝑃𝐸 = ∫𝜃 − 𝜃𝑒𝑛𝑣

𝜃𝑒𝑛𝑣𝑔 𝑑𝑧

𝑧2

𝑧1

𝑤ℎ𝑒𝑟𝑒 𝜃 = 𝑣𝑖𝑟𝑡𝑢𝑎𝑙 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑟𝑐𝑒𝑙 𝑎𝑛𝑑 𝜃𝑒𝑛𝑣 = 𝑣𝑖𝑟𝑡𝑢𝑎𝑙 𝑡𝑒𝑚𝑝 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡

𝑔 = 9.8 𝑚𝑠2⁄

SRH (storm relative helicity) is a measure of wind potential for cyclonic updraft rotation in right

moving supercells. SRH is usually calculated for the lowest 1km and 3km above the ground.

Values above 100 m2/s2 for 0-1km SRH and above 250 m2/s2 for 0-3km SRH suggest an

increased threat of tornadoes.

𝑆𝑅𝐻 = − ∫ 𝒌 ∙ [(𝑽h

z2

z1

− 𝑪) (𝛿𝑽h

𝛿z)]𝑑𝑧

Where C is a storm-relative motion vector, k is a unit vector in the upwards direction, and Vh is

horizontal wind velocity.

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STP (significant tornado parameter) is a multiparameter index (as shown below). STP values

greater than 1.0 are associated with “significant tornadoes,” i.e. EF2 or greater. We considered

STP, but since it is just an indexing number with no physical rationale, we decided to not devote

a lot of time to it, but it is still an important index to consider.

𝑆𝑇𝑃 = (𝑀𝐿𝐶𝐴𝑃𝐸

1000𝑗

𝑘𝑔⁄) (

SHR0−6km

20 ms2⁄

) (SRH0−1km

100 m2

s2⁄) (

2000m − MLLCL

1500m)

Calculating CAPE: CAPE is defined as the amount of energy available for convection measured in Joules per

kilogram. It is directly related to the maximum potential vertical speed in a thunderstorm’s

updraft. Higher values indicate an increased potential for severe weather, as mentioned earlier.

For this particular project we were interested in seeing if particular layers gave us any insight to

better predictions. In order to accomplish this layering effect, we needed to do some manual

calculations using soundings we found through the NOAA’s Air Resource Laboratory

department. A sounding (or Skew-T Log-P diagram) is a set of data evaluating the vertical

components (temperature, humidity, pressure, wind, etc…) of the atmosphere at a given place

and time. Below is the process of how we calculated the CAPE from these soundings:

Figure 6 (left)- From the bottom of

the dew-point temperature (green

line), draw a line upward parallel to

the saturation mixing ratio lines (thin

black lines near the bottom).

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Figure 7 (right)- From the bottom of

the temperature (red line), draw a line

upward parallel to the dry adiabatic

lines (long thin black lines). Where

this line and the line from the previous

step intersect is the Lifting

Condensation Level (LCL). The LCL

is the level at which a parcel of air

becomes saturated.

Figure 8 (right)- From the LCL, follow the

nearest saturated adiabat line (orange line)

with a curved line. If the temperature of the

theoretical parcel is less than the

temperature, then the area in between the

lines is known as Convective Inhibition

(CIN). However, if the theoretical parcel’s

temperature is greater than the temperature

than that area in between is our CAPE.

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Calculating SRH: When calculating SRH, we must take into account the motion of the storm itself in order to

understand how the storm is rotating in time and space. To do this, we calculate a storm motion

vector, C. This vector has many different opinions on how it should be calculated, but the

method we chose is to use 75% of the speed of the wind at the upper bound (height) and set

storm motion at 30 right of the wind direction at this same height.

Figure 10 demonstrates what our approximations might look like; we have vectors to indicate the

motion of each layer, and along with some other statistics we can then calculate the last two

columns of the data—the storm relative motion of the layers. This is done by subtracting our

storm-relative vector C from our original motion vectors {u,v}.

Figure 9 (left)- The theoretical parcel

temperature that we drew will eventually

cross the temperature line near the top of

the Skew-T Log-P graph. This place where

they intersect is known as the equilibrium

level (EL). The EL is the point where a

buoyantly rising parcel of air has the same

temperature as the environment. An

equilibrium level that sits high up in the

atmosphere allows thunderstorms to build

up high into the troposphere and maintain

high levels of CAPE.

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Results and Conclusions: The first three graphs shown (Figures 11-13) are an analysis of 4 tornadoes from the last 5 years,

all of them being of strength EF4. They took place in Texas in 2017, Kansas in 2016, Oklahoma

in 2016, and in Mississippi in 2014. The following two graphs (Figures 14-15) include

thunderstorm data and are for comparison purposes, which will be explained later.

Figure 11 indicates the total potential energy, in the neighborhood of the data

Figure 10

Texas-5954 J/kg

Kansas-3440 J/kg

Mississippi-3892 J/kg

Oklahoma-3850 J/kg

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Figure 12 indicates the total amount of rotation in the area of

measurements (0-1 km SRH)

Figure 13 again indicates the total amount of rotation in the area

of measurements (0-3 km SRH)

Texas-292.55 m2/s2

Kansas-143.67 m2/s2

Mississippi-65.38 m2/s2

Oklahoma-199.92 m2/s2

Texas-51.06 m2/s2

Kansas-22.96 m2/s2

Mississippi-109.66 m2/s2

Oklahoma-14.96 m2/s2

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All three of these graphs have values that are above the respective significance level, but they all

also have values that are low/below the significance level. This is why tornado prediction isn’t an

exact science; all of these storms were very strong and caused a lot of damage, yet not all of their

parameters make it seem this way. This is a prime example why many parameters need to be

taken into account when attempting to predict major storms, because focusing on one parameter

may occasionally give you accurate predictions, but most likely you will be wrong if you rely on

only one parameter/index.

Figure 14 shows many previous supercell thunderstorms and strong tornadoes. The purple points

are strong tornadoes, and the orange points are supercell thunderstorms that never produced any

tornadoes. The vertical axis is SRH and the horizontal axis is CAPE, so the graph as a whole is

showing us a relationship between the two parameters. Some important conclusions we drew

from this analysis is that a tornado tends to form when both SRH and CAPE have significant

values, as we expected. As we can see from the graph, if a storm had high SRH but a lower

CAPE, it tended to stay a thunderstorm. On the other hand, if the supercell had a high CAPE but

a low SRH, the same result, a thunderstorm, occurred most often. Although the data we collected

supports a combination of high CAPE and SRH for a strong tornado to form, it appears that SRH

is a deciding factor based on the data we collected. This does not mean that CAPE is not

important, it just means that our data favors SRH. As seen in Figure 15, a graph comparing the

CAPE values of tornadoes versus thunderstorms, you can see that the purple lines(tornadoes)

sometimes have higher CAPE values than the orange lines(thunderstorms), but there is a

considerable amount of overlap. Thus, we slightly favor SRH over CAPE, however, if one of the

parameters is too low, it does not seem to matter how high the other parameter is. It is still very

important to take into account many parameters/indices at once in order to have the most

accurate prediction strategy.

Figure 14

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Continuing on with our results, we look back at Figure 14. As we can see, there is an area near

both axes where if the value of either SRH or CAPE is low enough, then a tornado tends not to

form. Figures 16-17 show this, and we would like to point out there is no “line” separating if a

tornado will form or not, it is just for an easier visual.

Figure 15

Figure 16

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In Figure 16, almost all of the data points in the blue shaded area are only thunderstorms, which

lead us to conclude that if SRH is not high enough no matter what value CAPE is, a tornado is

unlikely to form. The same conclusion comes from Figure 17, where the data points in the green

shaded area tend not to form tornadoes since their CAPE values are not high enough regardless

of the SRH.

We have analyzed the areas of our graph in which it is unlikely for a tornado to form, and now

we can see that the red shaded area in Figure 18 has the highest likelihood of producing a

tornado. A combination of CAPE and SRH where both of the values are significant(and this isn’t

an exact number) gives the greatest chance of a tornado occurring.

Figure 17

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Limitations: Throughout the course of this research project, we came across numerous limitations when it

came to data collection and calculations.

Data collection and manipulation was a significant portion of our project; however, the data was

not easy to come by. The soundings and windgrams from which we calculated CAPE and SRH

are only provided every three hours, so that severely limited our choice in

tornadoes/thunderstorms and it added some variance to our data due to the fact some events

happened slightly before data was retrieved by the NOAA and some slightly after that

retrieval. We also have to take into account the location from which our data was taken. Slight

changes in latitude and longitude made slight changes to the data which is good and expected.

However, we know the data is not coming from inside the heart of the storm or directly

underneath the tornado’s funnel. The readings are proximal, but it is very difficult to know to

what extent. Not to mention the current doppler system is very sparse in certain regions of the

United States and some tornadoes and storms hit dead zones.

Another big limitation is the current U.S. doppler radar situation. Due to the curvature of the

earth and the sparseness of the radar stations, many storms are not accurately picked up by radar.

If a storm is far enough from the radar station, only some of the storm(the top) may be picked up.

As we can see in Figure 19, there are also dead zones where it is nearly impossible to get

accurate data.

Figure 18

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Manual calculations were another

large part of our summer

research. We manually calculated

CAPE and SRH. With

meteorological manual

calculations come a large number

of opinions on how these

parameters ought to be

computed. Meteorology is not

quite an exact science at this

point in time, so there are plenty

of opinions on how to calculate

certain quantities. A perfect

example of this in our calculation

of SRH. Some experts suggested

the storm relative motion be

adjusted by 75% wind speed and

30 degrees wind direction of the

upper bound while others said

adjust by the same values but use the mean height of the system instead of the upper bound and

still others had different ideas. To be impartial, we tried a couple of the most respected opinions

and went with the ones that made sense to us and did not give us skewed values.

Turbulence: Lastly, we cannot talk about our data without bringing up turbulence. Turbulence is the irregular

motion of particles that plagues all fluid motion and the atmosphere is no exception, in fact, it’s

the perfect example. Turbulence is characterized by gusts and lulls in the wind and seemingly

random spikes and drops in temperature or pressure or other parameters in the

atmosphere. Mathematicians and scientists have a slight grasp on two-dimensional turbulence,

but they have barely scratched the surface on understanding three-dimensional turbulence

(Lilly). There are theories on breaking down the three-dimensional turbulence of the atmosphere

into gravity waves and two-dimensional turbulence, however, these calculations are outside the

scope of our project. On the other hand, we cannot afford to ignore this irregularity for it plays a

significant role in our data. We discuss our plan to combat turbulence in the Future Thoughts

section.

Data Retrieval:

One of the most important aspects of this research is finding

reliable and accessible data for us to analyze. The best sites

we found were NOAA’s Storm Prediction Center, Air

Resources Laboratory, and National Center for

Environmental Information. We also found a lot of useful

location information via Weather.gov, in addition to

individuals states’ DNR websites. All of our data was

archived from previous years, and that is why we did not

analyze any tornadic events from this calendar year. As

Figure 19

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mentioned in the limitations section, these archives are not always user friendly and have many

time limitations, but we did our best to find archived data that fell on specific times so that we

could have to most accurate data readings as possible.

Future Thoughts: To further enhance our research, we have some ideas/goals for the future of this project. Adding

more tornadoes and thunderstorms to our analysis would strengthen our conclusions in addition

to the possibility of being able to find new trends in our data. We would use a wide variety of

new data, including but not limited to varying strengths of tornadoes, different locations and

different times of the year in which the tornado occurred.

We would also like to expand our knowledge of parameters/indices by analyzing other values

such as EHI(Energy Helicity Index), STP, BRN(Bulk Richardson Number), etc. In addition to

adding these new statistics, we could test them against the newly proven Sensitivity Conjecture.

Mathematician Hao Huang has recently proven a 30-year-old sensitivity conjecture about

combinatorics. This can apply to our research because this conjecture basically takes into

account how different variables will affect a system and which variables affect it the most—i.e.

have the most weight compared to the other variables. This way, we could confirm if there is a

parameter/index that has the most significance, or possibly even what combination of these

statistics will give the most accurate strategy for tornado prediction.

One of the biggest obstacles we had to tackle was inaccurate data and measurement errors caused

by possible mechanical errors in the instruments, but most commonly the turbulence mentioned

earlier. To combat this, we would like to model data fluctuations with pseudo-random number

generators to throw in volatility produced by turbulence. Turbulence is a topic that is not yet well

understood scientifically, so we are always looking for ways to shed new light on this issue.

Acknowledgments: Thank you to the University of St. Thomas, specifically The Center for Applied Mathematics, for

allowing us this opportunity to enhance our knowledge of mathematics and its applications

through this summer research. A very deserving thank you goes to our advisor Dr. Mikhail

Shvartsman, Dr. Patrick Van Fleet(Director, CAM), and Dr. Sarah Anderson(Associate Director,

CAM). What a great opportunity this was; we learned a lot and will continue to learn more!

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Bibliography/Appendix:

Doswell, C. A. III, and D. M. Schultz, 2006: On the use of indices and parameters in forecasting

severe storms. Electronic J. Severe Storms Meteor., 1, 1–14.

Lilly, D.K, 1983: Stratified Turbulence and the Mesoscale Variability of the Atmosphere.

National Center for Atmospheric Research., 749-761.

https://ready.arl.noaa.gov/READYamet.php?userid=85

https://www.spc.noaa.gov/

http://weather.gov

https://www.ncdc.noaa.gov/stormevents/eventdetails.jsp?id=685547

https://www.quantamagazine.org/mathematician-solves-computer-science-conjecture-in-two-

pages-20190725/