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Electronic Theses, Treatises and Dissertations
The Graduate School
2015
Estimating Kinetic Energy of U.S.
Tornadoes
Tyler Anthony Fricker
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FLORIDA STATE UNIVERSITY
COLLEGE OF SOCIAL SCIENCES AND PUBLIC POLICY
ESTIMATING KINETIC ENERGY OF U.S. TORNADOES
By
TYLER FRICKER
A Thesis submitted to the
Department of Geography
in partial fulfillment of the
requirements for the degree of
Master of Science
Degree Awarded:
Spring Semester, 2015
c 2015 Tyler Fricker. All Rights Reserved.
Copyright Tyler Fricker defended this thesis on March 20, 2015.
The members of the supervisory committee were:
James B. Elsner
Professor Directing Thesis
Victor Mesev
Committee Member
Stephanie Pau
Committee Member
The Graduate School has verified and approved the above-named committee members, and certifies
that the thesis has been approved in accordance with university requirements.
ii
To my parents whose love, support, and encouragement never waivers.
iii
TABLE OF CONTENTS
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
1 Introduction
1
2 Literature Review
7
2.1 Modeling tornado damage and intensity . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Calculating the kinetic energy of tornadoes . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Understanding the climatology of tornadoes . . . . . . . . . . . . . . . . . . . . . . . 12
3 Materials and Methods
3.1 Data . . . . . . . . . .
3.2 Method . . . . . . . .
3.2.1 Validation . . .
3.2.2 Limitations . .
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15
15
16
18
20
4 Results
22
5 Discussion
32
6 Conclusions
38
Appendix
A Comparison of Destruction Indexes
41
B R Source Code
42
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
iv
LIST OF TABLES
1.1
The F-scale.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
Correlations between physical variables, indexes of destruction, and casualties and
losses. The 90% confidence intervals are shown in parentheses. . . . . . . . . . . . . . 20
3.2
Median percent area by maximum EF rating between estimates made from the NWS
DAT and the NRC model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1
Top ten tornadoes ranked by TKE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.1
United States census regions and TKE . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
A.1
Comparison of known indexes of destruction . . . . . . . . . . . . . . . . . . . . . . . 41
v
3
LIST OF FIGURES
1.1
1.2
Damage path of the Washington, Illinois EF4 tornado. The storm resulted in three
fatalities, 121 injuries, and $800 million of damage. Photo by Jon Erdman [21]. . . . .
2
FR12: DOD 10: Total destruction of entire building. Redrafted from McDonald and
Mehta [37]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
3.1
Web-based view of the National Weather Service’s Damage Assessment Toolkit. . . . 16
3.2
Sample tornado polygon available from the NWS’s DAT. In Fricker et al. [24] polygons
are downloaded and mapped for tornado-specific damage area. . . . . . . . . . . . . . 17
3.3
NRC model of fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4
Model versus empirical estimated total kinetic energy. Redrafted from Figure 4 in
Fricker et al. [24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5
Distribution of TKE over the years 2007-2013. . . . . . . . . . . . . . . . . . . . . . . 19
3.6
Variability among individual tornadoes and the NRC model. . . . . . . . . . . . . . . 21
4.1
Average TKE of tornadoes by EF-scale category. The values are given in terajoules
(TJ). The number of tornadoes by category is given along the horizontal axis. . . . . 23
4.2
The top 10 tornadoes ranked by TKE on a United States map. The line segments
show the track of each tornado. The different colors indicate EF-scale rating. . . . . 24
4.3
Top ten days ranked by daily TKE. The number of tornadoes is used as a color fill on
the bars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.4
Daily cumulated TKE for the years 2007-2013. . . . . . . . . . . . . . . . . . . . . . . 25
4.5
TKE ranked by year. The color ramp indicates the number of tornadoes. . . . . . . . 27
4.6
TKE ranked by month. The color ramp indicates the number of tornadoes. . . . . . . 27
4.7
TKE distributed over the United States. The color ramp indicates the kinetic energy
in joules (J). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.8
TKE and Frequency by month. The color ramp for the top subplot indicates the
number of tornadoes. The color ramp for the bottom subplot indicates kinetic energy
in TJ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.9
TKE and Frequency distributed over the United States. The color ramp for the top
subplot indicates kinetic energy in J. The color ramp for the bottom subplot indicates
the number of tornadoes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
vi
5.1
United States census regions. The color ramp indicates region including: Midwest
(MW), Northeast (NE), South (S), and West (W). . . . . . . . . . . . . . . . . . . . . 35
vii
LIST OF ABBREVIATIONS
F-scale
EF-scale
DI
DOD
DPI
TDI
KE
NWS
DAT
SPC
TKE
A-bomb
TJ
NRC
A-scale
SS
GIS
NIST
CAPE
NCDC
GJ
PJ
Fujita Scale
Enhanced Fujita Scale
Damage Indicator
Degree of Damage
Destructive Potential Index
Tornado Destruction Index
Kinetic Energy
National Weather Service
Damage Assessment Toolkit
Storm Prediction Center
Total Kinetic Energy
Atomic Bomb
Terajoules (1012 )
U.S. Nuclear Regulatory Commission
Area Scale
Saffir-Simpson Scale
Geographic Information Systems
National Institute of Standards and Technology
Convective Air Potential Energy
U.S. National Climate Data Center
Gigajoules (109 )
Petajoules (1015 )
viii
ABSTRACT
Perhaps nothing on Earth is so uniquely majestic, yet destructive as the tornado. A violent tornado can level a town in minutes, causing death, injuries, monumental property losses and lasting
emotional damage. To better understand the power behind tornadoes this research estimates the
per-tornado total kinetic energy (TKE) for all tornadoes in the Storm Prediction Center (SPC)
database over the period 2007-2013. TKE is estimated using the fraction of the tornado path
experiencing Enhanced Fujita (EF) damage and the midpoint wind speed for each EF damage
rating. TKE is validated as a metric of destruction by comparing it to other indexes of destruction
including the Destruction Potential Index (DPI) and Tornado Destruction Index (TDI). Results
showed that the Tallulah-Yazoo City-Durant tornado was the tornado with the most energy over
the period, that 2011 was the year with the most energy, and that April and May were the months
of the year with the most energy. The difference between frequency and energy was investigated
and showed that while parts of “Tornado Alley” experienced the most tornadoes, it was the Deep
South that experienced the most powerful tornadoes. Future work on TKE should look to compare environmental parameters (convective air potential energy (CAPE), helicity, and vertical wind
shear) and TKE values. It should also look to disaggregate the scale at which TKE is possible and
focus on the social implications of powerful tornadoes. TKE as a metric of destruction has value in
its potential ability to spark new considerations about insurance rates, building codes, and public
policy concerning tornadoes.
ix
CHAPTER 1
INTRODUCTION
Perhaps nothing on Earth so uniquely combines spectacle, terror, and random violence as the
tornado [29]. Few other weather phenomena have the ability to develop as quickly, diminish as
suddenly, yet cause as much misery. A tornado by definition has undergone a succession of understanding from: 1) 1959 - “a violently rotating column of air, pendant from a cumulonimbus
cloud,” 2) 2000 - “a violently rotating column of air, in contact with the ground, pendant from a
cumuliform cloud,” and 3) 2013 - “a rotating column of air, in contact with the surface, pendant
from a cumuliform cloud, and often visible as a funnel cloud and/or circulating debris/dust at the
ground” [2].
A tornado physically is nothing more than insubstantial air and water vapor, combined in a
rotating vortex. However, there is a complexity of fluid dynamics, air/moisture interactions, and
energy transfers at work. Interestingly, tornadoes have almost life-like qualities [29] with their
own birth-to-death life cycles. Small tornadoes are powerful enough to cause damage to buildings
and automobiles, while large tornadoes can level a town in minutes causing numerous injuries and
fatalities (Fig. 1.1).
For example, the Super Outbreak of April 3-4, 1974 killed 319 people and produced $600 million
in damage (1974 USD). The Super Outbreak included 30 F4/F5 tornadoes [19], which is the most
in United States (U.S.) history. The Xenia, Ohio tornado caused 34 fatalities, 1,150 injuries, and
an estimated $100 million (1974 USD) in damages alone [29]. More recently, the Moore, Oklahoma
tornado of May 20, 2013 caused 24 fatalities, 377 injuries, and $2 billion in damages [46]. These
numbers make understanding the destructiveness of tornadoes vital.
Much of what we know about tornadoes comes from surveying damage. Meteorologists and other
experts have been keeping historical records since the 17th century [29], with primitive information
limited to the size and location of an event. Early surveyors were able to differentiate between large
and small-scale storms. They were also able to determine locations of tornadoes due to damage
1
Figure 1.1: Damage path of the Washington, Illinois EF4 tornado. The storm resulted in
three fatalities, 121 injuries, and $800 million of damage. Photo by Jon Erdman [21].
left behind. The data collected at sites were matched to newspaper and eyewitness accounts, and
formatted into lists, most famously published by John Park Finley.
As advancements in technology and surveying techniques progressed, so did tornado data quality. The creation and subsequent acceptance of the Fujita Scale (F-scale) in 1971 opened periods of
unprecedented progress in tornado research culminating in a Storm Data collection. The F-scale is
a tornado rating system from 0-5 based primarily on damage with estimated wind speeds attached.
The six categories are labeled F0, F1, F2, F3, F4, and F5. Rankings increase in intensity, meaning
that an F5 tornado is more intense than and F4 tornado.
The F-scale is detailed in Table 1.1. An F0 tornado typically has light damage including: some
damage to chimneys; branches broken off trees; shallow rooted trees pushed over; sign boards
damage. It has estimated wind speeds of less than 73 mph. An F5 tornado typically has incredible
damage including: strong frame houses leveled off foundations and swept away; automobile-sized
missiles flying through the air in excess of 100 meters; trees debarked [27]. It has estimated wind
speeds between 261-318 mph.
While the F-scale was not an ideal system for linking damage and wind speed, it did have several
advantages. It was simple enough to use in daily practice without the need to exhaust additional
2
Table 1.1: The F-scale.
Scale
F0
Wind estimate [ms−1 ]
<32
F1
33-50
F2
51-70
F3
72-94
F4
95-118
F5
119-143
Typical damage
Light damage. Some damage to chimneys; branches broken off trees;
shallow-rooted trees pushed over; sign boards damaged.
Moderate damage. Peels surface off roofs; mobile homes pushed off foundations
or overturned; moving autos blown off roads.
Considerable damage. Roofs torn off frame houses; mobile homes demolished;
boxcars overturned; large trees snapped or uprooted; light-object missiles generated;
cars lifted off ground.
Severe damage. Roofs and some walls torn off well-constructed houses;
trains overturned; most trees in forest uprooted; heavy cars lifted off the ground
and thrown.
Devastating damage. Well-constructed houses leveled; structures with weak
foundations blown away some distance; cars thrown and large missiles generated.
Incredible damage. Strong frame houses leveled off foundations and swept away;
automobile-sized missiles fly through the air in excess of 100 meters (109 yds);
trees debarked; incredible phenomena will occur.
time and money, and was practical enough to gain widespread support [29]. This widespread
support waned, however, as critics focused on two flaws: 1) the damage scale was too subjective and
too prone to large errors in judgment to provide useful quantitative results, and 2) the reliance on
building damage meant that many tornadoes, especially in the rural Great Plains, went undetected
or underrated.
These shortcomings and other considerations led to the creation and adoption of the Enhanced
Fujita Scale (EF-scale) in 2007. The EF-scale, much like the F-scale, is a tornado rating system
from 0-5 based on the damage associated with a tornado. However, the EF-scale is based on
better and more extensive examinations of tornado damage, which allows for wind speeds to better
align with associated damage. Today, when a tornado touches down, surveyors are able to record
a damage rating based on 28 Damage Indicators (DI) and different Degrees of Damage (DOD),
which maintain some conformity to the original F-scale [37]. The DIs range from small barns/farm
outbuildings to softwood trees. For example, if damage is done to a one-or-two-family residency
(FR12) it is ranked on ten DODs from a threshold of visible damage to total destruction of entire
building. An FR12 with a DOD of 10 is seen in Figure 1.2.
Yet there remain flaws with the current EF-scale. Inconsistencies continue to exist in surveying
techniques and there is a level of subjectivity in every damage survey. Additionally, the EF-scale,
3
Figure 1.2: FR12: DOD 10: Total destruction of entire building. Redrafted from McDonald and Mehta [37].
like the F-scale, is directly related to damage. This causes problems due to the poorly understood
relationship between wind and damage [16]. While DIs and DODs have increased the accuracy and
applicability of tornado intensity ratings, they still fail to provide overwhelming consistency. Future
consideration may have to be given to regional DIs and DODs which rely on a wind speed range
categorization that encompasses the full range of wind speeds physically possible in tornadoes [16].
Post storm surveys of damage allow engineers to make determinations about individual tornadoes and rate them on a scale from zero to five. Historically a damage rating was directly related to
tornado wind speed [25, 26]. Currently this damage rating is determined by connecting wind speed
with observed damage [22]. However, damage rating is not the only data collected at a survey. Path
length, path width, building damage, and tree damage are also recorded. Injuries and fatalities are
added to the record after the survey and the data are made available for public use.
While this collected data is useful for a basic understanding of tornado power, it is the more
advanced characteristics such as total area, area by EF category, and duration of a tornado that
allow for deeper knowledge of these storms. Using total area and area by EF category allows
for calculations of tornado power to be undertaken, progressing from previous work that uses
4
wind speed and damage rating [47, 1]. However, total area varies by storm. For instance, the
EF4 Tallulah-Yazoo City-Durant, LA tornado had a damage path area of about 530,000 squared
kilometers while the EF4 Smith-Jasper-Clarkem, MS tornado had a damage path area of about
148,000 squared kilometers.
For some time, researchers in meteorology and engineering have focused on measuring the
intensity of tornadoes [47, 40, 1]. For example, Thompson and Vescio [47] multiply the path area
by the damage rating and then sum over all tornadoes in a given day to define an index useful
for comparing destruction across different tornado days and outbreaks. This destructive potential
index (DPI) allows for differences in energy between weak and violent tornadoes to be accounted for
better than damage rating alone. Similarly, Agee and Childs [1] introduce the tornado destruction
index (TDI) by squaring the product of a damage rating wind speed and the path width. The DPI
and TDI are useful for outlining a collection of tornadoes (tornado days for the DPI and tornado
years for the TDI) and for comparing different outbreak.
Although these indexes have expanded our understanding of tornado power (energy), they leave
open questions to the tornado power (energy) of individual storms. This research focuses on the
kinetic energy (KE) of individual tornadoes. It relies on information found in available datasets
(National Weather Service’s (NWS) Damage Assessment Toolkit (DAT), and Storm Prediction
Center’s (SPC) tornado database) to calculate an estimate of total kinetic energy (TKE) from
all U.S. tornadoes from 2007-2013. Here the objectives are: 1) calculate a TKE for all available
tornadoes, and 2) make climatological comparisons of TKE in space (e.g. by state) and time (e.g.
by month).
These objectives result in the creation of a database that includes a per tornado estimate of
TKE and new knowledge about the climatology of these severe convective storms. Each estimate
of TKE is calculated in joules, which gives a physical variable to compare individual tornadoes.
Joules are a derived unit of energy congruent with kgm2 s−2 . For reference, the first atomic bomb
(A-bomb) produced an explosion of 80 terajoules (TJ). With energy being an extensive variable,
the results can be averaged and summed to give comprehensive climatological analysis of these
storms in both space and time. This analysis can be used to answer questions such as: where are
storms most powerful; what year is the most energetic of the past seven years; and what months
of the year are the most energetic?
5
Furthermore, this research has both physical and social implications. Understanding these
storms in terms of a physical variable such as TKE allows for future research to be devoted to connecting tornado power (energy) with environmental factors. Additionally, it allows for a comparison
of individual storms to be made across different parts of the country, with different topographies,
socioeconomic factors, and community structures. That stated, this work also creates results that
have the potential to affect or at least provoke new thoughts about insurance rates, building codes,
and tornado safety policy. Knowing when and where the most powerful tornadoes hit has the potential to allow communities to better prepare for emergency management response, risk assessment,
or preemptive safety measures.
With estimates of TKE available for every tornado between 2007-2103, this research stands to
bridge the gap between previous work, like the DPI and TDI, and to create results of tornado power
(energy) in physical units (joules). Using TKE as a variable for tornado power (energy) allows for
deeper insight into the nature of these destructive storms, which will be discussed in the following
chapters.
6
CHAPTER 2
LITERATURE REVIEW
This research is grounded in the literature of: the modeling of tornado damage and intensity, the
kinetic energy of tornadoes, and the climatology of tornadoes. These strands together provide a
knowledge base with which to attack many questions within the subfield of climatology, particularly,
tornado climatology. This knowledge base is not only robust in its ability to make sense of both
modeling and calculating tornado damage and intensity, but in its ability to recognize the potential
effects of tornado damage.
2.1
Modeling tornado damage and intensity
The use of modeling in the representation of tornado damage and occurrence has long been
understood as something that is of great benefit to many people throughout the U.S. [38]. While
there are different forms of tornado modeling, it is the previous work done concerning the modeling
of tornado damage, damage potential, and intensity that is of importance to this research.
Reinhold and Ellingwood [42] model tornado damage risk by looking at the damage of a tornado
based on its differing F-scale category [27]. Through the analysis of 149 tornadoes, which occurred
on April 3 and 4, 1974, the authors are able to calculate the variation of both length and width
over the five F categories of the original Fujita scale.
Boissonnade et al. create a probabilistic tornado wind hazard model [7], similar to Reinhold
and Ellingwood [42] for the continental U.S.. The model incorporates both random and epistemic
uncertainties to quantify tornado wind hazard parameters. It is an areal probability model that
takes into account the size and orientation of any facility, the length and width of tornado damage
area, and wind speed variation within the damage area [7].
With the collection of more information and better data on tornado damage, a new EF-scale
was established in the U.S. in 2007 [11]. This new EF-scale created a need for updated tornado
intensities along length and across width of an expected tornado path. That need was fulfilled with
the release of the United States Nuclear Regulatory Commission’s (NRC) NUREG/CR-4461 [40].
7
The report assesses the risk of a tornado at any location. It examines the implications of moving
from the F-scale to the EF-scale on wind speed estimates of tornadoes.
The NRC reclassifies tornado intensity and percent damage by EF category through the use of
a stationary Rankine vortex and table 7c from Reinhold and Ellinwood’s [42] work. By using both
theoretical and empirical evidence of recent storms, the NRC concludes that damage decreases in
percent by area as EF category rises, unlike previous estimations of intensity, which labeled the F1
category as the highest damage zone by percent area, followed by F0, F3, F4, and F2 [42].
A tornado is not only important for the damage it creates; it also holds some amount of
damage potential and power that perplexes meteorologists, physicists, engineers, and geographers
alike. Thompson and Vescio [47] model the power behind tornadoes using the DPI. With the goal of
improving upon tornado categorization by damage alone with an index that incorporates a measure
of tornado intensity with a measure of the damage area, they introduce the DPI with an ad hoc
method to combine damage amount with damage area, using the equation:
DP I =
X
a(F i + 1)
(2.1)
where a = damage area (length x width), and F i = Fujita rating [47]. The index is believed to
allow for more consistent comparisons between different tornado days and for a better account
of long-track, violent tornadoes. It was introduced with the hope of finding some discrimination
between storms, other than just F-scale ranking. Additionally, the authors propose combining path
length and mean widths into a simple tornado damage area scale (A-Scale) that is analogous to
the widely used Fujita Scale (F-Scale).
Sample DPI calculations are performed for historical tornado outbreaks in Thompson and Vescio
[47]. They find that the Super Outbreak of April 3, 1974 stands out in terms of tornado numbers
and DPI. The DPI total of 2647 is around 40% higher than the DPI total from the next closest
outbreak, the Palm Sunday outbreak of April 11, 1965.
The DPI is further discussed and evaluated in Doswell et al. [15] where the authors look to
measure and rank severe weather events. By creating a scheme that includes: 1) using multiple
variables, 2) providing reproducible results, 3) yielding rankings similar to what subjective thought
would rank, 4) accounting for the known large secular trends, and 5) results that are reasonably
robust to any arbitrary parameter choice, they work to systematically find a way to rank weather
8
events according to the specific requirements of any project or variable [15]. Successfully, the authors
are able to rank events for both tornado outbreaks (7+ tornadoes) and non-tornadic outbreaks (6+
severe storms). They conclude that the DPI is nonlinear and even through detrending techniques,
is unable to create any trend for climatological use.
The index was reformulated in Agee and Childs [1] by multiplying the square of the damage
path width by the square of the mean wind speed for maximum EF rating under the assumption
that every location in the damage path receives the worst wind damage. The TDI is seen in the
equation:
T DI = (v · W )2
(2.2)
where v is the midpoint wind speed for the highest EF rating and W is the path width. The authors
find annual cumulative TDI (TDIc ) through the equation:
T DIc =
n
X
(Nn v 2 ) · (W )2
(2.3)
n=0
where Nn is the number of tornadoes per damage rating (n ), v is the midpoint wind speed for the
highest EF rating and W is the path width. Using Eq. 2.3 the authors rank tornado seasons. They
find that 2011 had the highest value of TDI, followed by 2008 and 2007. They also note that the
ratio of significant tornadoes has increased from 7.2% in 2004 to 13.2% in 2012, while there has
been a decrease in significant tornadoes [1].
While modeling the damage potential of a tornado may aid researchers in measuring and ranking
storms, it does not directly address whether or not tornadoes are getting stronger. This is done
through the modeling of tornado intensity. Dotzek et al. [17] address the issue by determining an
appropriate statistical model of tornado intensity distributions. The authors conclude that tornado
intensity distributions are not described properly by exponentials, but rather satisfied by Weibull
distributions. They also show that the U.S. has statistically comparable tornado data to current
German data using Weibull parameters b and c [17].
Brooks [8] investigates the relationship between tornado path length and path width to tornado
intensity. Using a Weibull distribution for different F-scale values, the author shows that the fits are
good over a wide range of lengths and width. He identifies that path length and path width tend to
increase with increasing F-scale values and that as path length and path width increases, so does
9
the F-scale value [8]. However, even for long or wide tornadoes, there is a significant probability of
a range of possible F-scale values, which makes only path length or path width an insufficient way
to make an estimate of F-scale value.
A more recent attempt at estimating tornado intensity is seen in Elsner et al. [20], where damage
path dimensions are used to develop a method for estimating the intensity of any tornado in the
SPC database. The authors use a statistical model assuming a Weibull distribution to quantify
the relationship between damage rating wind speeds and path length and path width. The model
is able to generate samples of predictive intensity when EF rating, path length, and path width
are included. In some cases, path length and path width do not provide information of tornado
intensity beyond the EF-scale rating. For tornadoes with damage ratings of EF1-EF3, path length
and path width suggest a lower-end intensity [20]. The authors discern that the modeled intensity
allows for new analyses to be performed on the tornado database not possible with the current
categorical system.
2.2
Calculating the kinetic energy of tornadoes
For this research, an estimate of TKE is needed for every tornado available in the dataset. Yet,
the amount of research committed to studying tornado power and intensity is relatively small, with
much of the literature seen in recent publications [17, 18, 8, 44, 20]. Dotzek et al. [17] determine an
appropriate statistical model of tornado intensity distributions; Brooks [8] compares the relationship
between tornado path length and path width to tornado intensity; Dotzek et al. [18] find strong
evidence for exponential tornado intensity distribution in wind speed squared (v 2 ), or Rayleigh
distributions in wind seed (v); Schielicke and Névir [44] incorporate a mass-specific kinetic energy
calculation on global tornado intensity distributions; Elsner et al. [20] use damage path dimensions
to develop a method for estimating the intensity of any tornado in the SPC database.
The kinetic energy of any object is the energy that is possessed during motion. Kinetic energy can exist as translational energy, rotational energy, vibrational energy, or any combination
of motions. However, a tornado is not a purely rotational object. Tornadoes have both volume
and density components to their mass, and because of this, any estimate of kinetic energy must
substitute different variables for the mass of a tornado in the form of cylindrical mass or V = πr2 h,
where r = radius, and h = height, while assuming that the density of air is 1 kgm−3 [12]. After
10
substituting this volume and density into the translational equation of KE, the KE of a tornado,
which is in a quasi-fluid state, is seen in the equation:
1
KE = πr2 hv 2
2
(2.4)
From a theoretical standpoint, Kurgansky shows that kinetic energy distributions of tornadoes
are Rayleigh distributed by wind speed (v) and exponentially distributed in mass-specific kinetic
energy [33], using tornado data from the former USSR [45]. Dotzek et al. [18] test this theory on
worldwide data. As mentioned earlier, the authors find strong evidence for Rayleigh distributed
wind speeds (v) and exponentially distribution in wind speed squared (v 2 ). Schielicke and Névir [44]
expand upon this understanding of tornado energy by incorporating a mass-specific kinetic energy
calculation on global tornado intensity distributions. They calculate the mass-specific kinetic energy
through the eqaution:
1
KE = v 2
2
(2.5)
where v is the damage scale wind speed. They find that tornado intensity classes have a non-uniform
distribution.
Building on Eq. 2.5, it is possible to compute a weighted average on the wind speeds using
corresponding fractions of total damage as weights. To convert mass-specific kinetic energy to
joules, its value can be multiplied by by both air density and height of the storm. This allows for
a physical variable to be attached to an estimate of tornado energy.
Each estimate of TKE presented in this work is similar to the integrated kinetic energy (IKE)
examined by Powell and Reinhold [39]. While not focused on tornadoes, the authors suggest that
a better way to understand the destructive nature of an impending hurricane is through the IKE
equation of:
IKE =
Z
1 2
πv dV
2
(2.6)
where v = wind speed, and dV = volume elements. Powell and Reinhold [39] present a way to
think about severe convective storms beyond real-time diagnostics, and into explanatory results.
They are able to rank past hurricanes based on different damage characteristics, much like the
11
research presented here. For example they find that hurricane Isabel had an IKE of 174 TJ at a
Saffir-Simpson (SS) rating of 2, while hurricane Andrew had an IKE of 20 TJ at a SS rating of
5. The SS system is a hurricane rating system from 1 to 5 based on a hurricane’s sustained wind
speed [10], much like the F-scale or EF-scale.
2.3
Understanding the climatology of tornadoes
This work has a foundation set in the climatology of tornadoes. It is well known that tornadoes
are phenomena which create large amounts of damage and destruction. They are intense, rare,
localized events that can lead to injury and death. Unfortunately, these storms are not usually
considered in the design of ordinary buildings and structures. The risk of damage from these
storms have long been considered an insurance problem [42], and the large-scale research devoted
to tornadoes is mostly tied to nuclear structures. Moving forward, there is a need to increase the
understanding of the vulnerability attached to these severe phenomena.
Ashley [4] compiles and analyzes a dataset of killer tornadoes to assess vulnerability throughout
the U.S. from 1880 to 2005. Results show that most tornado fatalities occur in the southeastern
U.S., which is outside the traditional “Tornado Alley.” The spatial distribution of killer tornadoes
suggest that above average numbers of mobile homes in the southeast U.S. may be a reason for
the larger fatality maximum found in the area [4]. Additionally, results show that middle aged and
elderly populations are at much greater risk than younger people during tornadoes.
Ashley et al. [5] evaluates the vulnerability of people in large urban cities such as Chicago,
Illinois. Using population and housing grid construction, the authors create an areal weighting
algorithm with datasets conflated in geographic information systems (GIS). They utilize historical
and synthetic tornado tracks to represent the totality of each tornado, and find that violent tornadoes (EF4 or above) have theoretical damage footprints that are four to five times the size of
significant tornadoes (EF2 or above). By using block and block group census data, the authors
were able to evaluate micro-scale changes in Chicago’s exposure to tornadoes and run worst-case
scenarios for both: 1) full-dimension synthetic scenarios, and 2) 10-km synthetic scenarios. They
conclude that an increasing and spreading population is leading to substantial growth in tornado
hazard exposure rates, offsetting mitigation techniques and expanding the bull’s eye effect, or the
relative risk that people in large urban centers face. They find that population is not solely re-
12
sponsible for an increasing bull’s eye effect, but rather connected to a population’s affiliated built
environment and that lastly, and most interestingly, the root cause of escalating disasters is not necessarily due to climate change, but rather likely due to 1) increased density and spread of humans
and property in harm’s way, and 2) increasing vulnerability of the population [5].
Ashley et al’s [5] research has several implications, including an understanding that large populated areas in places vulnerable to tornadoes may see an increase in risk, which they call the bull’s
eye effect. With more people at risk in sensitive areas, such as large urban centers, the possibility
of stronger and more energetic tornadoes becomes an issue impossible to ignore.
However, large populated areas are not the only places at risk to tornadoes. The vulnerability of
smaller populated centers can be seen in the tragic aftermath of the Joplin, Missouri 2011 tornado.
On May 22, 2011 an EF-5 tornado swept through the small town of Joplin killing 161 people and
creating over $ 3 billion worth of damage [32]. In the aftermath of the storm, the National Institute
of Standards and Technology (NIST) produced a detailed report analyzing virtually every aspect of
the event [32]. They evaluate tornado characteristics, building performance, human behavior, and
emergency communication of the storm. They state that nationally accepted standards for building
design and construction, public shelters, and emergency communications could significantly reduce
deaths and the steep economic costs of property damage caused by tornadoes.
While the U.S. experiences more tornadoes than any other country in the world, it is not the
only country affected by these severe convective storms. Tornado climatologies exist for Finland
[41], Italy [28], Germany [6], Turkey [31], Lithuania [35], and Greece [36]. For example, Rauhala et
al [41] construct a tornado climatology for Finland from 1796 to 2007 using both a historical dataset
(1796-1996) and a recent dataset (1997-2007). Many (86%) of the 298 tornadoes in Finland were of
F1 intensity or less, with only a total of 43 significant tornadoes being observed. In Finland, there
have only been six F3 tornadoes, one F4 tornado, and no F5 tornadoes. All of the documented
tornadoes in Finland have occurred between April and November [41], with maximum frequency
occurring in July and August.
Giaiotti et al [28] use 10 years (1991-1999) of reports collected by weather amateurs to define
a preliminary climatology of tornadoes and waterspouts in Italy. Interestingly, tornadoes and
waterspouts are more frequent in late summer and autumn than in other season. The authors
note that convective air potential energy (CAPE) Storm-Relative-Helicity diagrams show different
13
behaviors than observed in the U.S. Particularly, CAPE values are lower in Italy than in the U.S.,
perhaps due to the Mediterranean climate [28].
Bissolli et al [6] use the TorDACH network to analyze the tornadoes in Germany from 19502003. The authors find that the numbers of reported tornadoes in Germany have increased since
1990. During the period, most years consisted of fewer than 20 tornadoes, with zero tornadoes
occurring in 1991. The highest frequencies (>25 tornadoes) occurred in the recent 6-year period
of 1998-2003. 468 tornadoes were reported in the database, with more than 15% of this number
occurring in years 2000 and 2003. The majority (55%) of tornadoes in Germany are weak ones (F1
or less), with 18% of tornadoes ranked as F2. 13 tornadoes are documented as F3 and one tornado
is documented as F4 (Pforzheim tornado) [6]. The seasonality of tornadoes in Germany is closest
to the U.S. with tornadoes occurring in all months. However, many of the tornadoes occur between
May and September, especially in June, July, and August.
Kahraman and Markowski [31] present a climatology of tornadoes in Turkey using a variety of
sources (e.g. the Turkish State Meteorological Service, European Severe Weather Database, etc.).
385 tornado cases are examined. The authors find that tornadoes in Turkey range from F0 to F3,
with F1 being the most frequently documented damage rating. May and June are the peak months
for tornadoes in Turkey, with a secondary peak seen in October and Novermber [31].
These climatologies indicate that anyone, living anywhere that can encounter a tornado is at
risk. These small-scale phenomena do not discriminate with respect to destruction, and annihilate
anything in their path. The disconnect between tornado literature, its risks, and public policy,
then, is alarming and something that must be considered when researching these severe events.
While climate change and high-impact tornado events have sparked new interest in tornado
climatology [14, 1, 50], there is still much to learn about the nature of tornadoes with respect to a
warming earth. New methods in tornado climatology may be needed to overcome inconsistencies in
current data. Widen et al. [50] examine a few statistical methods to overcome the data limitations.
These include using the proportion of tornadoes occurring on big tornado day, estimating tornado
energy, and modeling count spatially. The methods move beyond traditional analyses of occurrences
by damage ratings and spatial smoothing to inspire more research on tornado climatology [50]. By
moving beyond traditional methods, more confident physical interpretations of tornadoes can be
attained, leading to better understandings of the link between tornadoes and climate.
14
CHAPTER 3
MATERIALS AND METHODS
3.1
Data
The SPC currently holds the most readily available tornado database in the world, compiled
from the NWS’s Storm Data and reviewed by the U.S. National Climate Data Center (NCDC)
[49]. It contains information on occurrence time, location, damage rating, path length, path width,
injuries, fatalities, and property loss dating back to 1950. For this work, all tornadoes between
2007 and 2013 are used, consistent with the adoption of the EF-scale by the NWS.
Storm surveys allow engineers to rate damage on a scale from zero to five. In the past. a
damage rating was directly related to tornado wind speed [25, 26], while today, this damage rating
is determined by connecting wind speed with observed damage [22]. The estimated wind speed
comes from different DIs that are connected to different DODs [37]. For example, EF0 damage
corresponds to wind speeds between 29 and 38 m s−1 , and EF5 damage corresponds to wind speed
greater than 89 m s−1 .
The EF rating a tornado receives is based on the highest damage category found within a
damage path [16]. The EF-scale has some conformity to the previous F-scale, but includes more
extensive DI and DOD. The EF-scale was adopted by the NWS in 2007, and is presently the damage
scale used to rate all tornadoes occurring in the U.S.
The DAT is a NWS initiative to standardize and streamline the collection of damage assessment
data following severe weather. The DAT facilitates the collection of data using the EF-scale criteria,
where wind speeds are estimated by comparing damaged structures to DI and associated DOD [51].
The DAT consists of four components, including a geospatially enabled database which stores the
data [24]. During an assessment, data are collected and sent to the central database via mobile apps
and/or laptop software. The software allows for GPS positioning and the inclusion of photographs
from the damage site. Once in the central database, data are quality-controlled through a web-based
interface [24]. This quality-controlled data are available for dissemination through Open Geospatial
Consortium compliant web services, and through a web-based data viewer [24] (Fig. 3.1).
15
Figure 3.1: Web-based view of the National Weather Service’s Damage Assessment Toolkit.
3.2
Method
This research focuses on a way to distinguish individual tornadoes based on a physical unit
of energy. Estimates of tornado energy have been made before [44]. Specifically, Fricker et al.
[24] estimate TKE for 18 tornadoes between 2011-2013 using damage information available from
the NWS’s DAT (Fig. 3.2). They compute TKE through a weighted average using the squared
midpoint wind speed from corresponding damage rating and the total damage area by each damage
rating as weights. The equation is seen in:
1 X
TKE = m
wj vj2 ,
2
J
(3.1)
j=0
where J is the highest EF rating, vj is the midpoint wind speed for each rating (e.g., v0 = 33.8
m s−1 , v1 = 44.0 m s−1 , etc), wj is the corresponding fraction of path area, and m is the tornado
mass, which is estimated as air density (1 kg m−3 ) times the volume (total path area times height).
Due to no upper bound on EF5 wind speeds, the midpoint wind speed is maintained at 97 m s−1 ,
which is 7.5 m s−1 above the threshold windspeed consistent with the EF4 wind speed relative to
its threshold. It is acknowledged that tornado height may vary between individual storms by as
16
35.5
EF−scale
EF0
35.4
EF1
lat
EF2
EF3
35.3
EF4
EF5
35.2
−97.7
−97.6
−97.5
−97.4
−97.3
lon
Figure 3.2: Sample tornado polygon available from the NWS’s DAT. In Fricker et al. [24]
polygons are downloaded and mapped for tornado-specific damage area.
much as a factor of 10 or more, but with no better data available for tornado height, the height is
fixed at 1 km.
With no tornado-specific fractions of area by EF rating available in the SPC database, the
NRC model of fractions (Fig. 3.3) is used here instead. The NRC model fractions are based on a
weighted average of a theoretical model (Rankine vortex) [ 13 weighting] and empirical estimates [ 32
weighting] taken from the Reinhold and Ellingwood [42] report on tornado damage risk assessment
[24]. This model was used in Fricker et al. [24] to compare TKE estimated from percent area
fractions available in the DAT. When compared, the empirical estimates (DAT estimates) and
NRC derived values showed excellent correlation. The correlation between the two exceeded 0.99
17
NRC EF0
NRC EF1
NRC EF2
NRC EF3
NRC EF4
NRC EF5
EF
EF0
EF1
EF2
EF3
EF4
EF5
Figure 3.3: NRC model of fractions.
(Fig. 3.4).
TKE is computed for the 8752 tornadoes in the SPC database from 2007-2015. There are many
more weak tornadoes than strong tornadoes, leading to a skewed median TKE of 62.1 gigajoules
(GJ). When put on a log scale, TKE distribution is symmetric (Fig. 3.5). Ten percent of the
tornadoes have TKE values above 1.97 TJ. Five percent have TKE values above 5.53 TJ, and one
percent have TKE values above 31.9 TJ.
3.2.1
Validation
The method to estimate TKE is validated by comparing the resulting values to other indexes
of tornado destruction, such as the DPI and TDI. Per-tornado DPI is computed using the equation
found in Thompson and Vescio [47]
DPI = A · (J + 1),
where J is the highest EF rating and A is the path area estimated by multiplying the path length
by the path width. Per-tornado TDI is computed using the equation found in Agee and Childs [1]
18
Model Estimated Total KE (TJ)
100
1
1
100
Empirical Estimated Total KE (TJ)
Figure 3.4: Model versus empirical estimated total kinetic energy. Redrafted from Figure
4 in Fricker et al. [24].
Number of Tornadoes
1500
1000
500
0
106
108
1010
1012
1014
Total Kinetic Energy (J)
Figure 3.5: Distribution of TKE over the years 2007-2013.
19
Table 3.1: Correlations between physical variables, indexes of destruction, and casualties
and losses. The 90% confidence intervals are shown in parentheses.
Variable
Total kinetic energy (TKE)
Destructive potential index (DPI)
Tornado destruction index (TDI)
Path Length
Path Width
No. of fatalities
.415
(.401,.430)
.445
(.430,.459)
.350
(.334,.365)
.295
(.279,.311)
.227
(.210,.244)
No. of injuries
.394
(.379,.409)
.408
(.394,.423)
.332
(.316,.347)
.277
(.261,.293)
.229
(.212,.245)
Loss amount
.366
(.351,.381)
.390
(.375,.405)
.338
(.323,.354)
.233
(.216,.249)
.210
(.193,.227)
TDI = (vJ · W )2 ,
where vJ is the midpoint wind speed for the highest EF rating (J) and W is the path width.
To validate TKE as a useful measure of destruction, its relationship to fatalities, injuries, and
loss amount are compared to similar relationships using path length and path width, DPI and TDI
(Table 3.1). TKE is positively correlated to fatalities, injuries, and property loss. TKE explains
about 16% of the variation in destructive measures, which is significantly larger than path length
and path width. The remaining variation most likely exists in where the tornadoes hit. The power
of DPI for statistically explaining destructive measures exceeds that of TKE by a small amount,
but the difference is not significant. The explanatory power of TDI is considerably less than that
of TKE and DPI. In summary, TKE is an improvement on the physical variables available in the
SPC database and has the same or greater explanatory power as other indexes of destruction.
3.2.2
Limitations
Some limitations exist with the method. As previously mentioned, there are no damage characteristics available in the SPC database. Although the empirical estimates in Fricker et al. [24]
correlate nicely with the NRC estimates (Fig. 3.4), there is still variability involved (Fig. 3.6). For
example, in an EF1 tornado, the percent area ranged from 4.1 - 33.9 in the DAT, while the NRC
model was fixed at 22.8 (Table 3.2). This can make a significant difference in TKE at a per-tornado
level. Additionally, using the DPI and TDI for per-tornado estimates of tornado energy moves beyond their initial uses of tornado days and tornado years respectively. While using both indexes of
20
destruction as validation for TKE makes sense from a comparison standpoint, it could be argued
that using each at a per-tornado level is not warranted.
Hayleyville
Sawyerville−Eoline
EF
EF0
EF1
NRC Model
EF2
EF3
Figure 3.6: Variability among individual tornadoes and the NRC model.
Table 3.2: Median percent area by maximum EF rating between estimates made from the
NWS DAT and the NRC model
Rating
EF1
EF2
EF3
EF4
EF5
Wind Speed
[m s−1 ]
38.4–49.6
49.6–60.8
60.8–74.2
74.2–89.4
89.4–104.6
Midpoint Speed
[m s−1 ]
44.0
55.2
67.5
81.8
96.1
Number of
Tornadoes
6
2
4
4
2
21
Median
% Area
20.7
6.1
2.3
.9
.8
Range
% Area
(4.1, 33.9)
(.7, 11.5)
(.5, 7.0)
(.1, 1.9)
(.1, 1.6)
NRC
% Area
22.8
11.5
6.7
3.2
1.7
CHAPTER 4
RESULTS
In the previous chapter, TKE is defined as a variable of tornado destructiveness in physical units.
Here, variations of TKE are examined in both space and time. Since energy is an extensive property,
TKE values can be averaged and summed. For example, the average energy of the nine EF5
tornadoes in the study was 102 TJ (Fig. 4.1). The average energy of the 57 EF4 tornadoes was
just over half of that at 51.3 TJ. The average energy of the 232 EF3 tornadoes was less than half
of the EF4 total at 18.9 TJ, followed by an average energy of 4.27 TJ (EF2 tornadoes), .844 TJ
(EF1 tornadoes), and .086 TJ (EF0 tornadoes).
Over the period 2007-2013, the top ten tornadoes ranked by TKE were the Tallulah-Yazoo CityDurant, LA tornado, the Hackleburg-Phil Campbell, AL tornado, the Tuscaloosa-Birmingham,
AL tornado, the Cordova, AL tornado, the Argo-Shoal Creek-Ohatchee-Forney, AL tornado, the
Clinton, AR tornado, the Vilonia, AR tornado, the Picher, OK tornado, the Smith-Jasper-Clarkem,
MS tornado, and the West Liberty, KY tornado (Fig. 4.2). Details are seen in Table 4.1. The
tornado with the most energy was the Tallulah-Yazoo City-Durant tornado of April 24, 2010 with
a TKE of 516.7 TJ. It tracked more than 240 km (149 miles) and was more than 2.8 km (1.75 miles)
wide at its widest. The storm resulted in ten fatalities and 146 injuries. The most commonly known
tornado on the list was the Tuscaloosa-Birmingham tornado of April 27, 2011. It occurred during
the April 25-28, 2011 tornado outbreak, which was the largest tornado outbreak in U.S. history.
The tornado tracked more than 128 km (80 miles), and was more than 2.4 km (1.5 miles) wide at
its widest. The storm resulted in 65 fatalities, and over 1500 injuries, while producing about $2
billion of insured losses [43].
Combining per-tornado TKE over all tornadoes in a day produces an estimate of daily kinetic
energy. There were 1185 days with at least one tornado between 2007-2103. The day with the
most energy over the period was April 27, 2011, with more than 2.6 petajoules (PJ) of energy from
207 tornadoes (Fig. 4.3). April 27, 2011 was the deadliest day of the April 25-28, 2011 tornado
outbreak. The day had a total of 122 tornadoes that resulted in 316 deaths across Mississippi,
22
Average Kinetic Energy (TJ)
100
75
50
25
0
4994
2642
818
232
57
9
0
1
2
3
4
5
EF Category
Figure 4.1: Average TKE of tornadoes by EF-scale category. The values are given in
terajoules (TJ). The number of tornadoes by category is given along the horizontal axis.
Alabama, Tennessee, Virginia, and Georgia. There were 15 violent tornadoes reported (EF-scale 4
or 5) and eight of the tornadoes had a path length larger than 80 km (50 miles) [30]. The day with
the second most energy was April 24, 2010 with 655 TJ of energy from 37 tornadoes.
When daily TKE is divided by the number of tornadoes in a given day, a measure of daily
efficiency is created. Of the top ten days with the most energy, April 24, 2010 was the most
efficient day with a per-tornado average TKE of 17.7 TJ, followed by April 27, 2011 with an
average TKE of 12.7 TJ, and May 5, 2007 with an average TKE of 9.7 TJ.
Daily cumulative energy varies by year. This is shown in Figure 4.4. The time axis is in days
with tic labels on the first day of the month. The vertical axis is the sum of all tornado energy up
to and including that day in unites of petajoules (PJ). Spikes in energy were generally seen in both
April and May, but occured in other months as well. For instance, in 2008, February was an active
month. Similarly, in 2012, March was an active month. The 2010 season had a slow beginning,
but was very active toward the end of April lasting through the middle of June. With graphs like
Figure 4.4 becoming increasingly more popular with the NWS, the use of TKE as a variable to
23
50
EF−scale
2
40
lat
3
4
30
5
20
−120
−110
−100
−90
−80
−70
lon
Figure 4.2: The top 10 tornadoes ranked by TKE on a United States map. The line
segments show the track of each tornado. The different colors indicate EF-scale rating.
show changes in energy throughout different seasons has value. Seeing the differences in TKE for
tornado seasons temporally provides visual evidence for potential shifts in tornado seasonality.
When TKE is accumulated over an entire calendar year, an estimate of yearly kinetic energy
is produced. Over the period of study, 2011 had the most energy by year (Fig. 4.5) with a TKE
of 5.16 PJ. The 2011 season was an unusually active and deadly year for tornadoes across the U.S.
It included the first ranked day by energy in this study (April 27, 2011), as well as the third and
eighth ranked days by energy (May 24, 2011 and April 15, 2011 respectively). 2011 was the fourth
deadliest season on record, and totaled estimated losses of around $10 billion.
24
2011−04−27
Date (Year−Month−Day)
2010−04−24
Number of
Tornadoes
200
2011−05−24
2012−03−02
2010−05−10
150
2012−04−14
100
2008−02−05
50
2011−04−15
2008−05−23
2007−05−04
0
1
2
Total Kinetic Energy of U.S. Tornadoes (petajoules)
Ranked by Day
Figure 4.3: Top ten days ranked by daily TKE. The number of tornadoes is used as a
color fill on the bars.
Cumulative Tornado Energy (PJ)
5
Year
4
2007
2008
3
2009
2010
2
2011
2012
2013
1
0
Jan
Feb Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov Dec
Jan
Figure 4.4: Daily cumulated TKE for the years 2007-2013.
25
Table 4.1: Top ten tornadoes ranked by TKE
Name
Tallulah-Yazoo City-Durant, LA
Hackleburg-Phil Campbell, AL
Tuscaloosa-Birmingham, AL
Cordova, AL
Argo-Shoal Creek-Ohatchee-Forney, AL
Clinton, AR
Vilonia, AR
Picher, OK
Smith-Jasper-Clarkem, MS
West Liberty, KY
Date (Y-M-D)
2010-04-24
2011-04-27
2011-04-27
2011-04-27
2011-04-27
2008-02-05
2011-04-25
2008-05-10
2011-04-27
2012-03-02
EF
4
5
4
4
4
4
2
4
4
3
TKE [TJ]
516.7
353.7
236.2
202.7
192.9
181.1
179.4
149.7
144.3
142.7
The year with the second most energy over the period of study was 2008 with a TKE of 2.59
PJ, which is roughly half the total of the 2011 season. 2008, much like 2011, was an active season.
It ranks as the third most active year in U.S. history, behind only 2004 and 2011. The 2008 season
had an unusually active January and February (Fig. 4.4) with multiple outbreaks taking place. It
also contained the seventh and ninth ranked days by energy (February 5, 2008 and May 23, 2008
respectively). The year with the least amount of energy was 2009 with a TKE of 0.86 PJ. Typically
years that had more energy had more tornadoes, although 2013 was an exception with relatively
high energy totals from relatively few tornadoes.
The seasonality of tornadoes is seen in greater detail through the accumulation of monthly
kinetic energy. Over the period of study, April (5.89 PJ) and May (3.56 PJ) were the months of
the year with the most energy (Fig. 4.6). Interestingly, February and March were the months with
the next highest energy values with a TKE of 0.99 PJ and 1.19 PJ respectively. This information,
along with global climate models suggesting an increase in greenhouse gas concentration that will
likely result in an increase in the number of days with conditions favorable to severe convection
[48], may signal a shift in tornado activity to earlier months on the year [34].
Tornado energy also varies spatially throughout the U.S. The state with the most energy over the
period was Alabama with a TKE of 2.48 PJ. The state with the second most energy was Oklahoma
with a TKE of 1.45 PJ, followed by Mississippi (1.41 PJ), Kansas (1.36 PJ), and Arkansas (1.17 PJ).
A nice swath of energy was seen throughout the contiguous states of Kansas, Oklahoma, Arkansas,
Mississippi, and Alabama (Fig. 4.7). Three of the top five states ranked by energy were in the Deep
26
2011
Number of
Tornadoes
2008
2010
Year
1500
2007
1300
2012
1100
2013
2009
0
1
2
3
4
5
Kinetic Energy (PJ)
Ranked by Year
Figure 4.5: TKE ranked by year. The color ramp indicates the number of tornadoes.
Kinetic Energy (TJ)
6000
Number of
Tornadoes
4000
1500
1000
2000
500
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Month
Figure 4.6: TKE ranked by month. The color ramp indicates the number of tornadoes.
27
Kinetic
Energy (J)
1011 1012 1013 1014 1015
Figure 4.7: TKE distributed over the United States. The color ramp indicates the kinetic
energy in joules (J).
South - the cultural and geographic subregion of the southern U.S. including Alabama, Arkansas,
Georgia, Louisiana, Mississippi, and South Carolina - which differs from the current location of
“Tornado Alley” throughout much of the Great Plains.
A major theme seen in this research was the difference between tornado frequency and tornado
energy. While the relationship between frequency and energy tends to be positive (more tornadoes
results in higher energy levels), there are exceptions. At the yearly level, 2011 was the season
with the most energy with a TKE of 5.16 PJ, followed by 2008 with a TKE of 2.59 PJ. Yet when
frequency was compared, both had almost identical tornado counts (1690 for 2011 and 1689 for
2008). 2012 and 2013 had almost identical TKE totals at 1.22 PJ and 1.21 PJ respectively, but
differed in tornado counts with totals of 938 and 905.
When frequency and energy were compared at a monthly level, stark differences were seen.
(Fig. 4.8). April had more energy (5.89 PJ) than May (3.56 PJ), but had fewer tornadoes (1770
tornadoes for April, 1935 tornados for May). March had more energy than June, but experienced
far fewer tornadoes (694 tornadoes in March, 1405 tornadoes in June). September had the least
28
amount of energy, but November and December had the fewest amount of tornadoes.
Differences between frequency and energy were also apparent at a spatial scale (Fig. 4.9). The
top five states ranked by energy over the period were Alabama (2.48 PJ), Oklahoma (1.45 PJ),
Mississippi (1.41 PJ), Kansas (1.36 PJ), and Arkansas (1.17PJ). The top five states ranked by count
were Texas (855), Kansas (734), Oklahoma (523), Alabama (461), and Mississippi (398). While
four of the top five states were the same for both energy and frequency, the glaring difference was
the large amount of tornadoes seen in Texas. Texas ranked first by count, but ninth by energy.
This means that on average, Texas experienced many weaker and shorter lived storms than other
states. It was also apparent that states like Alabama and Mississippi, which ranked first and third
in energy, yet had about half the total number of tornadoes as Texas, experienced stronger and
longer lived storms. These findings suggest that future work on tornadoes should move beyond
frequency in the Great Plains into the potential destruction of the Deep South.
29
Kinetic Energy (TJ)
6000
Number of
Tornadoes
4000
1500
1000
2000
500
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Month
Number of Tornadoes
2000
Kinetic
Energy (TJ)
1500
5000
4000
1000
3000
2000
500
1000
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Month
Figure 4.8: TKE and Frequency by month. The color ramp for the top subplot indicates
the number of tornadoes. The color ramp for the bottom subplot indicates kinetic energy
in TJ.
30
Kinetic
Energy (J)
1011 1012 1013 1014 1015
Count
200
400
600
800
Figure 4.9: TKE and Frequency distributed over the United States. The color ramp for
the top subplot indicates kinetic energy in J. The color ramp for the bottom subplot
indicates the number of tornadoes.
31
CHAPTER 5
DISCUSSION
Tornadoes are agents of destruction. Their powerful winds cause havoc and can level a town in a
matter of minutes. This research estimates the per-tornado TKE of every U.S. tornado between
2007 and 2013 available in the SPC database. Doing so creates results that influence knowledge
from both a physical and social standpoint with respect to tornadoes.
TKE is used as a metric of destruction that has physical units of energy. Unlike previous
destruction indexes, such as the DPI and TDI, TKE is computed in joules and relies on both
theoretical considerations and empirical data. Furthermore, TKE is calculated at a per-tornado
level, as opposed to the DPI (tornado days) and the TDI (tornado years).
When compared to variables present in the SPC database (path length and path width), TKE
shows an improvement in explanatory power with the number of fatalities, the number of injuries,
and property loss. This means that if TKE was added to the database, there would be a variable
present that better explains the number of fatalities, the number of injuries, and property loss.
When compared to other indexes of destruction (DPI and TDI), TKE shows the same or greater
explanatory power with the number of fatalities, the number of injuries, and property loss.
TKE as an index of destruction has advantages over both the DPI and TDI. First, TKE is
created to compare individual tornadoes, unlike previous indexes of destruction which have focused
on ranking either tornado days or tornado years. Second, TKE results in an energy value measured
in joules, as opposed to the dimensionless quantities of DPI and TDI. Third, values of TKE can be
averaged and summed due to energy being an extensive variable. Through this research, there is
now a variable of destruction that can compare tornado energy from the bottom up. TKE is unique
in its ability to rank individual storms (Table 4.1), tornado days (Fig. 4.3), as well as tornado years
(Fig. 4.5). It can also move beyond temporal comparisons into spatial comparisons, such as state
kinetic energy (Fig. 4.7).
Due to its ability to measure energy in joules, TKE can be compared and evaluated with other
environmental parameters. There are a number of conditions that control the birth of a tornado,
32
including CAPE, helicity, and vertical wind shear. Measurements of each are available through
NOAA. By comparing estimates of TKE to CAPE, helicity, and/or vertical wind shear, connections
to conditions needed to create powerful and strong tornadoes can occur. This can bridge the gap
between tornadoes and climate, and provide insight into tornado-parent environments.
Beyond the creation of an index of destruction with physical units of energy, this research
is valuable through the potential social implications of its findings. High levels of TKE typically
results in higher numbers of fatalities, injuries, and property loss. For example, the top 10 tornadoes
ranked by TKE had 10, 72, 64, 13, 22, 3, 7, 8, 7, and 6 fatalities respectively. The 30-year (19842013) average annual fatality rate of tornadoes is 75, which means that tornadoes with high levels
of energy can cause above average annual fatalities in a single event.
TKE varies spatially across the U.S. Specifically, Kansas, Oklahoma, Arkansas, Mississippi, and
Alabama (Fig. 4.7) resulted in high levels of energy. The most powerful and dangerous tornadoes
in this study appeared over most of the Deep South. While “Tornado Alley” is synonymous to
states across the Great Plains, recent tornado activity may suggest a shift in tornado risk toward
the Deep South. Dixon et al. [14] investigates this further through a risk-assessment of “Dixie
Alley” - the term given to the “Delta Region” of Arkansas, Mississippi, Alabama, and Tennessee.
The authors find that “Tornado Alley” experiences more tornadoes than “Dixie Alley,” but that
the Deep South has more killer tornadoes than does the Great Plains, an idea echoed from Ashley
[4].
This research showed that there is a high amount of energy throughout “Dixie Alley” and that
in terms of TKE, Alabama ranked number one in energy by state in the U.S. This drives a need for
more in-depth analysis of “Dixie Alley” from a risk-assessment view. People in the Deep South are
at more risk to injury and death than the rest of the country, Yet, there are plenty of socio-economic
restraints in the Deep South that prevent excess money from being spent on structures to protect
constituents. For example, by TKE, Alabama ranks first in energy by state from 2007-2013, but
ranks 45th for median annual income at $23,680 per capita [9]. Similarly, Mississippi ranks third
in energy by state over the period, but ranks last in median annual income at $20,618 per capita
[9]. This is potentially a problem for state-wide initiatives to increase tornado safety, and signals a
need for either federal governmental aid or private sector help.
33
At an individual level, many choices for tornado safety are made based on either perceived risk
or disposable income. People who live in areas with a high frequency of tornadoes are more apt
to take precautionary measures to ensure a safety plan is in place for a tornado. However, the
effectiveness of safety precautions can come down to availability, location, and price. One option is
the building or use of a safe room which is a hardened structure providing near-absolute protection
in extreme weather events, including tornadoes and hurricanes. Other options include the building
or use of an underground storm shelter/storm cellar, or the building or use of a basement. The
cost of a safe room depends on a variety of factors including building materials used, location, type
of door use, type of foundation on which the home is built, etc., but typically will cost over $3,000
at a minimum [3]. Similarly, the cost of an underground storm shelter/storm cellar will vary based
on building materials used, location, type of foundation on which the home is built, etc., but on
average will cost around $6,000.
This presents a problem for many in rural areas throughout the Great Plains and Deep South. As
mentioned above, many of the states most affected by tornadoes rank in the bottom half of median
annual income per capita in the U.S. This puts a strain on the amount of disposable income that
can be used toward upgraded safety measures. An individual in Mississippi would theoretically be
spending about 15% of their total annual income to build a safe room, and about 30% of their total
annual income on an underground storm shelter/storm cellar. Similarly, an individual in Alabama
would theoretically be spending about 13% of their total annual income to build a safe room, and
about 26% of their total annual income on an underground storm shelter/storm cellar.
As with any mainstream economic system, an emphasis is put on the short-term benefit over
the long-term success. This makes spending a large portion of total income on preemptive measures
difficult to rationalize. Although there are grants available through the Federal Emergency Management Agency to aid in the building of safe rooms or storm shelters/storm cellars, the process
to obtain one is difficult, and dependent on federal, state, and local funding sources.
Moving forward, it will be imperative to educate and convince communities and individuals on
the need for tornado safety. Here, TKE is used to express the energy and power that individual
tornadoes possess. Other information such as the number of fatalities, the number of injuries, and
property loss connected to these severe convective storms should spark some motivation to protect
34
Region
MW
NE
S
W
Figure 5.1: United States census regions. The color ramp indicates region including:
Midwest (MW), Northeast (NE), South (S), and West (W).
society from the destructive potential tornadoes have. This research reiterates that much of the
southern Great Plains and Deep South are affected by powerful tornadoes.
However, much of the current research on tornadoes has been focused on the Great Plains, not
the Deep South. For example, from 2007-2013 over $65 million was granted by the National Science
Foundation (NSF) for tornado-specific projects. $10.1 million was awarded to Oklahoma, and $5.7
million awarded to Texas [23]. Yet, only $1.7 million was awarded to Alabama and $824,000
awarded to Mississippi [23]. While this allocation is reasonable based on tornado frequency, it is
disproportionate based on tornado energy.
When TKE is separated into regions based on the U.S. census map (Fig. 5.1), the South ranks
first in energy by region with a TKE of 9.92 PJ (Table 5.1). The next closest region is the Midwest
with a TKE of 4.00 PJ, a difference of 148%. More attention will need to be given to people living
in the South regarding tornado safety and safety accessibility to ensure that injuries and deaths
are limited in the future.
35
Table 5.1: United States census regions and TKE
Region
Northeast
South
Midwest
West
Number of tornadoes
219
4523
3419
591
TKE [PJ]
.196
9.92
4.00
.277
The study of TKE is also of value from a risk-assessment standpoint. There have been other
climatologies that focus on risk associated with tornadoes based on frequency [4, 5]. However, the
use of TKE as an index of destruction with physical units of measure may be advantageous moving
forward. If TKE is able to compare nicely with other environmental parameters, spatial patterns
of energetic and powerful tornadoes may be found. This can potentially signal where and what
populations are at the most risk to powerful tornadoes.
Future work of TKE should be devoted to disaggregating the scale at which energy can be
estimated. Currently, TKE is averaged and summed at the state level. Although this can help
with identifying which states are at the most risk and where aid should be allocated for safety
measures, it makes identifying specific at-risk communities and cities difficult. By moving TKE to
a county or block-level, local communities and populations can be considered. This can allow for
socioeconomic and population density data to be used in conjunction with TKE estimates and may
potentially help strengthen current literature devoted to at-risk populations, such as the expanding
the bull’s-eye effect [5].
The main idea of this research is to create an index of destruction (TKE) with physical units
of energy. While this creates an ability to compare and differentiate individual tornadoes, it also
creates potential influences for improving building codes, insurance rates, and public policy. TKE
may not change the face of tornado safety, and it may not directly impact building codes, but it
may be useful for echoing the already heard cries for tornado safety and policy improvements.
States throughout “Dixie Alley” and the southern Great Plains face real issues connected to
tornado risk. Should building codes be made stronger in these areas? Should we raise insurance
premiums due to the risk of severe storms? These are the questions that policymakers face yearly
with respect to tornadoes. Should tornado safety be improved in local communities and schools?
Should a more advanced warning system be in place for these areas? These are the questions that
36
affect real human beings; that impact lives. TKE alone is not a cure or an answer for all these
concerns, but it does help spark new thinking about the power of tornadoes and the devastating
results these severe convective storms create. It does create the potential for future work to be
devoted to producing an even clearer picture of the power behind tornadoes and the environment
that spawns them.
37
CHAPTER 6
CONCLUSIONS
Tornado damage varies widely by event. To better understand the power behind tornadoes this
research estimates the per-tornado TKE for all tornadoes in the SPC database over the period
2007-2013. TKE is estimated using the fraction of the tornado path experiencing EF damage and
the midpoint wind speed for each EF damage rating. The fraction of the path is found using the
NRC model that uses both theoretical considerations and empirical data. The results of TKE from
the model correlated strongly (0.99) with those computed using recent tornado damage outputs.
The method is validated as a useful metric of destruction by comparing it to other indexes of
destruction including the DPI and TDI. Additional validations is shown by comparing TKE, DPI,
and TDI to fatalities, injuries, and property loss. Due to energy being an extensive variable, TKE
values can be averaged and summed to produce a new climatology of tornadoes. The average energy
of the nine EF5 tornadoes in the study was 102 TJ. The average energy of the 57 EF4 tornadoes
was just over half of that at 51.3 TJ, followed by the average energy of the 232 EF3 tornadoes at
18.9 TJ.
The tornado with the most energy was the Tallulah-Yazoo City-Durant tornado which was
Louisiana’s worst natural disaster since Hurricane Katrina in 2005. Also in the top ten tornadoes
ranked by energy was the Hackleburg-Phil Campbell tornado and the Tuscaloosa-Birmingham
tornado, both from the April 27, 2011 outbreak. April 27, 2011 was the day with the most energy
over the period with a TKE of more than 2.6 PJ, followed by April 24, 2010, May 5, 2011, and
March 2, 2012.
Spikes in energy were generally seen in both April and May, with February and March having
high energy totals as well. This may be evidence to support a shift in earlier tornado activity
[34]. Tornado energy varies spatially throughout the U.S. with a swath of energy seen throughout
Kansas, Oklahoma, Arkansas, Mississippi, and Alabama. Three of the top five states ranked by
energy were in the Deep South, which suggests an active “Dixie Alley” [14].
38
A theme seen throughout this study was the difference between tornado frequency and tornado
energy. While the relationship between frequency and energy tends to be positive, there are exceptions. For example, 2011 had roughly twice the amount of energy as 2008 with almost identical
counts. April had more energy than May with fewer tornadoes and March had more energy than
June with half as many tornadoes.
The use of TKE influences knowledge from both a physical and social standpoint with respect
to tornadoes. TKE shows improvement in explanatory power with the number of fatalities, the
number of injuries, and property over current SPC variable (path length and path width). It also
has the same or greater explanatory power when compared to the DPI and TDI. The advantage of
TKE over these other indexes of destruction is the extensive variable of energy attached to each
computation.
TKE can be compared and evaluated with other environmental parameters such as CAPE,
helicity, and vertical wind shear. By comparing estimates of TKE to these factors, more knowledge
about the conditions needed to create powerful and strong tornadoes can be had.
High levels of TKE typically results in higher numbers of fatalities, injuries, and property loss.
This is important when considering tornado risk-assessment. Results showed high energy values
throughout “Dixie Alley,” an area with socioeconomic restraints that prevents excess money from
being spent on structures to protect constituents. For instance, Alabama ranked first in energy by
state from 2007-2013, but ranks 45th for median annual income. Mississippi ranked third in energy
by state, but ranks last in median annual income.
TKE can be used as a tool to advance thinking about tornado safety, building codes, insurance
rates, and policy. Though it may not be an answer for many of the issues surrounding society and
tornado destruction, TKE can be helpful in sparking new ways of thinking about the power behind
tornadoes.
Future work of TKE should look to connect it to environmental parameters. It should also
attempt to disaggregate the scale at which energy can be estimated. By making TKE estimates at
the county or block-level, more in-depth analysis can be performed for at-risk populations. This
may aid current literature devoted to risk-assessment, such as the expanding bull’s-eye effect [5].
Recent climate models have suggested a future with more days of high wind shear coinciding
with high values of CAPE, creating the possibility for more powerful tornadoes [13]. TKE as an
39
index of destructiveness with physical units of energy should help scientists better understanding
the nature and climate of tornado activity.
40
APPENDIX A
COMPARISON OF DESTRUCTION INDEXES
Table A.1: Comparison of known indexes of destruction
Index
DPI
TDI
TKE
Units of measure
No units and dimensionless
No units and dimensionless
joules
Advantages
Compares tornado days beyond counts and damage rating
Compares tornado years beyond counts and damage rating
Allows for individual estimates of tornado energy
Compares tornado energy seasonality (e.g. years, months, days)
Compares tornado energy spatial distribution
41
APPENDIX B
R SOURCE CODE
--title : " Thesis Code "
author : " Tyler Fricker "
date : " March 30 , 2015 "
output : html _ document
--Set working directory and load packages .
‘ ‘ ‘{ r w or ki ng Di rP ac ka ge s }
date ()
setwd ( " ~ / Dropbox / Tyler / Thesis " )
require ( MASS )
require ( ggplot2 )
require ( rgdal )
library ( plyr )
library ( reshape2 )
library ( lubridate )
require ( gamlss . cens )
library ( ggthemes )
library ( wesanderson )
library ( dplyr )
library ( rgeos )
library ( ggmap )
library ( maps )
library ( maptools )
library ( grid )
library ( SDMTools )
‘‘‘
Tornado Data
‘ ‘ ‘{ r }
TornL = readOGR ( dsn = " . " , layer = " tornado " ,
stringsAsFactors = FALSE )
TornL $ OM = as . integer ( TornL $ OM )
TornL $ Year = as . integer ( TornL $ YR )
TornL $ Month = as . integer ( TornL $ MO )
TornL $ EF = as . integer ( TornL $ MAG )
42
TornL $ Date = as . Date ( TornL $ DATE )
TornL $ Length = as . numeric ( TornL $ LEN ) * 1609.34
TornL $ Width = as . numeric ( TornL $ WID ) * .9144
TornL $ FAT = as . integer ( TornL $ FAT )
TornL $ SLON = as . numeric ( TornL $ SLON )
TornL $ SLAT = as . numeric ( TornL $ SLAT )
TornL $ ELON = as . numeric ( TornL $ ELON )
TornL $ ELAT = as . numeric ( TornL $ ELAT )
TornL $ INJ = as . numeric ( TornL $ INJ )
TornL $ LOSS = as . numeric ( TornL $ LOSS )
Torn . df = as . data . frame ( TornL )
‘‘‘
TKE
‘ ‘ ‘{ rTKE }
Torn . df = Torn . df % >%
filter ( Year >= 2007) % >%
mutate ( Area = .5 * Length * .5 * Width * pi )
dim ( Torn . df )
perc = c (1 , 0 , 0 , 0 ,
.772 , .228 ,
.616 , .268 ,
.529 , .271 ,
.543 , .238 ,
.538 , .223 ,
percM = matrix ( perc ,
0, 0,
0, 0, 0, 0,
.115 , 0 , 0 , 0 ,
.133 , .067 , 0 , 0 ,
.131 , .056 , .032 , 0 ,
.119 , .07 , .033 , .017)
ncol = 6 , byrow = TRUE )
threshW = c (29.06 , 38.45 , 49.62 , 60.8 , 74.21 , 89.41)
midptW = c ( diff ( threshW ) / 2 + threshW [ - length ( threshW )] ,
threshW [ length ( threshW )] + 7.5)
midptW
ef = Torn . df $ EF + 1
EW2 = numeric ()
for ( i in 1: length ( ef )){
EW2 [ i ] = midptW ^2 % * % percM [ ef [ i ] , ]
}
Torn . df = Torn . df % >%
mutate ( TKE = .5 * EW2 * Area * 1000 ,
DPI = Area * ( EF + 1) ,
TDI = ( midptW [ ef ] * Width )^2)
‘‘‘
Correlation with SPC variables
43
‘ ‘ ‘{ rcorrelation }
cor . test ( Torn . df $ TKE , Torn . df $ FAT , conf . level = .9)
cor . test ( Torn . df $ TKE , Torn . df $ INJ , conf . level = .9)
cor . test ( Torn . df $ TKE , Torn . df $ LOSS , conf . level = .9)
cor . test ( Torn . df $ Length , Torn . df $ FAT , conf . level = .9)
cor . test ( Torn . df $ Length , Torn . df $ INJ , conf . level = .9)
cor . test ( Torn . df $ Length , Torn . df $ LOSS , conf . level = .9)
cor . test ( Torn . df $ Width , Torn . df $ FAT , conf . level = .9)
cor . test ( Torn . df $ Width , Torn . df $ INJ , conf . level = .9)
cor . test ( Torn . df $ Width , Torn . df $ LOSS , conf . level = .9)
‘‘‘
Correlation with indexes of destruction
‘ ‘ ‘{ rcorrelation2 }
cor . test ( Torn . df $ TKE , Torn . df $ FAT , conf . level = .9)
cor . test ( Torn . df $ TKE , Torn . df $ INJ , conf . level = .9)
cor . test ( Torn . df $ TKE , Torn . df $ LOSS , conf . level = .9)
cor . test ( Torn . df $ DPI , Torn . df $ FAT , conf . level = .9)
cor . test ( Torn . df $ DPI , Torn . df $ INJ , conf . level = .9)
cor . test ( Torn . df $ DPI , Torn . df $ LOSS , conf . level = .9)
cor . test ( Torn . df $ TDI , Torn . df $ FAT , conf . level = .9)
cor . test ( Torn . df $ TDI , Torn . df $ INJ , conf . level = .9)
cor . test ( Torn . df $ TDI , Torn . df $ LOSS , conf . level = .9)
‘‘‘
Distribution of TKE
‘ ‘ ‘{ rdistr }
library ( scales )
ggplot ( Torn . df , aes ( TKE )) +
geom _ histogram ( binwidth = .5 , color = " white " ) +
scale _ x _ log10 ( breaks = trans _ breaks ( " log10 " ,
function ( x ) 10^ x ) ,
labels = trans _ format ( " log10 " ,
math _ format (10^. x ))) +
xlab ( " Total Kinetic Energy ( J ) " ) +
ylab ( " Number of Tornadoes " )
‘‘‘
Top Ten tornadoes
‘ ‘ ‘{ r }
df = Torn . df % >%
arrange ( desc ( TKE ))
df = df [1:10 ,]
map = get _ map ( location = " united states " , zoom = 4 ,
44
source = " google " )
ggmap ( map ) +
geom _ segment ( data = df , aes ( x = SLON , y = SLAT ,
xend = ELON , yend = ELAT ,
color = factor ( EF ))) +
scale _ color _ manual ( name = " EF - scale " ,
values = wes _ palette ( " Zissou " ))
‘‘‘
By EF category
‘ ‘ ‘{ rEF }
df = Torn . df % >%
group _ by ( EF ) % >%
summarize ( Count = n () ,
TKEef = sum ( TKE ) ,
avgTKE = mean ( TKE ) ,
sd = sd ( TKE ) ,
se = sd / sqrt ( Count ) ,
ciMult = qt (.95 / 2 + .5 , Count - 1) ,
ci = se * ciMult )
ggplot ( df , aes ( x = factor ( EF ) , y = avgTKE / 10^12 , fill = EF )) +
geom _ histogram ( stat = " identity " ) +
xlab ( " EF Category " ) +
ylab ( " Average Kinetic Energy ( TJ ) " ) +
scale _ fill _ continuous ( low = " # fff7bc " ,
high = " # d95f0e " , guide = " none " ) +
geom _ text ( aes ( label = Count , x = factor ( EF ) , y = 0) ,
data = df ,
vjust = 1.3 , size = 4)
‘‘‘
By Day
‘ ‘ ‘{ rbyday }
df = Torn . df % >%
group _ by ( Date ) % >%
summarize ( count = n () ,
tKE1 = sum ( TKE ) ,
EFF = tKE1 / count ) % >%
arrange ( desc ( tKE1 ))
or = order ( df $ tKE1 , decreasing = FALSE )
df $ DateF = factor ( df $ Date ,
levels = as . character ( df $ Date [ or ]))
45
ggplot ( df [1:10 ,] , aes ( x = DateF , y = tKE1 / 10^15 , fill = count )) +
geom _ histogram ( stat = " identity " ) +
coord _ flip () +
xlab ( " Date ( Year - Month - Day ) " ) +
ylab ( " Total Kinetic Energy of U . S . Tornadoes
( petajoules )\ nRanked by Day " ) +
scale _ fill _ continuous ( low = " # ccece6 " , high = " #005824 " ,
name = " Number of \ nTornadoes " ) +
# scale _ fill _ gradientn ( colours = pal (20) ,
# name = " Number of \ nTornadoes ") +
theme _ bw ()
‘‘‘
Daily aggregated total
‘ ‘ ‘{ raggregated }
library ( scales )
df = Torn . df % >%
group _ by ( Year ) % >%
mutate ( TKEc = cumsum ( TKE ) ,
DoY = as . numeric ( Date as . Date ( paste ( Year , " -01 -01 " , sep = " " ))) +
1,
Date2 = as . POSIXct ( as . Date (
DoY , origin = " 2015 -01 -01 " ))) % >%
select ( Date2 , Year , TKEc )
df $ Year = as . character ( df $ Year )
ggplot ( df , aes ( x = Date2 , y = TKEc / 10^15 , color = Year )) +
geom _ line ( size = 2 , alpha = .75) +
scale _ x _ datetime ( labels = date _ format ( " % b " ) ,
breaks = date _ breaks ( width = " 1 month " )) +
xlab ( " " ) +
ylab ( " Cumulative Tornado Energy ( PJ ) " ) +
scale _ color _ manual ( values = c ( " # e41a1c " ," #377 eb8 " ,
" #4 daf4a " , " #984 ea3 " , " # ff7f00 " ,
" # ffff33 " , " # a65628 " ))
‘‘‘
By Year
‘ ‘ ‘{ rbyyear }
df = Torn . df % >%
group _ by ( Year ) % >%
summarize ( TKEy = sum ( TKE ) ,
Count = n ()) % >%
46
arrange ( desc ( TKEy ))
or = order ( df $ TKEy , decreasing = FALSE )
df $ YearF = factor ( df $ Year , levels = df $ Year [ or ])
ggplot ( df , aes ( x = YearF , y = TKEy / 10^15 , fill = Count )) +
geom _ histogram ( stat = " identity " ) +
coord _ flip () +
xlab ( " Year " ) +
ylab ( " Kinetic Energy ( PJ )\ nRanked by Year " ) +
scale _ fill _ continuous ( low = " # bae4bc " , high = " #43 a2ca " ,
name = " Number of \ nTornadoes " )
ggplot ( df , aes ( x = YearF , y = Count , fill = TKEy )) +
geom _ histogram ( stat = " identity " ) +
coord _ flip () +
scale _ fill _ continuous ( low = " # bae4bc " , high = " #43 a2ca " ,
name = " TKE " )
‘‘‘
By Month
‘ ‘ ‘{ rbymonth }
df = Torn . df % >%
group _ by ( Month ) % >%
summarize ( TKEm = sum ( TKE ) ,
Count = n ()) % >%
mutate ( Ma = factor ( month . abb [ Month ] , levels = month . abb [1:12]))
ggplot ( df , aes ( x = Ma , y = TKEm / 10^12 , fill = Count )) +
geom _ histogram ( stat = " identity " ) +
xlab ( " Month " ) +
ylab ( " Kinetic Energy ( TJ ) " ) +
scale _ fill _ continuous ( low = " # a6bddb " , high = " #1 c9099 " ,
name = " Number of \ nTornadoes " ) +
theme ( legend . position = " none " )
ggplot ( df , aes ( x = Ma , y = Count , fill = TKEm / 10^12)) +
geom _ histogram ( stat = " identity " ) +
xlab ( " Month " ) +
ylab ( " Number of Tornadoes " ) +
scale _ fill _ continuous ( low = " # a6bddb " , high = " #1 c9099 " ,
name = " Kinetic \ nEnergy ( TJ ) " ) +
theme ( legend . position = " none " )
‘‘‘
47
By State
‘ ‘ ‘{ rbystate }
df = Torn . df % >%
group _ by ( ST ) % >%
summarize ( Count = n () ,
TKEst = sum ( TKE ) ,
TKEstpT = TKEst / Count ) % >%
arrange ( desc ( TKEst ))
states . df = map _ data ( " state " ) % >%
filter ( region ! = ’ alaska ’ ,
region ! = ’ district of columbia ’) % >%
mutate ( ST = state . abb [ match ( region , tolower ( state . name ))]) % >%
merge ( df , by = " ST " ) % >%
arrange ( order )
ggplot ( states . df , aes ( x = long , y = lat , group = group ,
fill = log10 ( TKEst ))) +
geom _ polygon () +
geom _ path ( color = " gray75 " ) +
coord _ map ( project = " polyconic " ) +
theme ( panel . grid . minor = element _ blank () ,
panel . grid . major = element _ blank () ,
panel . background = element _ blank () ,
axis . ticks = element _ blank () ,
axis . text = element _ blank () ,
legend . position = " bottom " ) +
# labs ( title = " Total Tornado Kinetic Energy \ n [1994 -2013]") +
xlab ( " " ) + ylab ( " " ) +
scale _ fill _ continuous ( " Kinetic \ nEnergy ( J ) " ,
low = " yellow " , high = " red " ,
breaks = 11:15 ,
labels = c ( expression (10^11) ,
expression (10^12) ,
expression (10^13) ,
expression (10^14) ,
expression (10^15)))
ggplot ( states . df , aes ( x = long , y = lat ,
group = group , fill = Count )) +
geom _ polygon () +
geom _ path ( color = " gray75 " ) +
coord _ map ( project = " polyconic " ) +
theme ( panel . grid . minor = element _ blank () ,
panel . grid . major = element _ blank () ,
48
panel . background = element _ blank () ,
axis . ticks = element _ blank () ,
axis . text = element _ blank () ,
legend . position = " bottom " ) +
# labs ( title = " Total Tornado Kinetic Energy \ n [1994 -2013]") +
xlab ( " " ) + ylab ( " " ) +
scale _ fill _ continuous ( " Count " , low = " yellow " , high = " red " ,
breaks = waiver ())
‘‘‘
Map the Regions
‘ ‘ ‘{ rregionsmap }
for ( i in 1: length ( Torn . df $ ST )){
if ( Torn . df $ ST [ i ] == " OH " | Torn . df $ ST [ i ] == " MI "
| Torn . df $ ST [ i ] == " IN " | Torn . df $ ST [ i ] == " IL "
| Torn . df $ ST [ i ] == " WI " | Torn . df $ ST [ i ] == " MN "
| Torn . df $ ST [ i ] == " IA " | Torn . df $ ST [ i ] == " MO "
| Torn . df $ ST [ i ] == " ND " | Torn . df $ ST [ i ] == " SD "
| Torn . df $ ST [ i ] == " NE " | Torn . df $ ST [ i ] == " KS " ) {
Torn . df $ Region [ i ] = " MW "
}
else if ( Torn . df $ ST [ i ] == " DE " | Torn . df $ ST [ i ] == " MD "
| Torn . df $ ST [ i ] == " VA " | Torn . df $ ST [ i ] == " WV "
| Torn . df $ ST [ i ] == " KY " | Torn . df $ ST [ i ] == " TN "
| Torn . df $ ST [ i ] == " NC " | Torn . df $ ST [ i ] == " SC "
| Torn . df $ ST [ i ] == " GA " | Torn . df $ ST [ i ] == " FL "
| Torn . df $ ST [ i ] == " AL " | Torn . df $ ST [ i ] == " MS "
| Torn . df $ ST [ i ] == " LA " | Torn . df $ ST [ i ] == " AR "
| Torn . df $ ST [ i ] == " OK " | Torn . df $ ST [ i ] == " TX " ){
Torn . df $ Region [ i ] = " S "
}
else if ( Torn . df $ ST [ i ] == " MT " | Torn . df $ ST [ i ] == " WY "
| Torn . df $ ST [ i ] == " CO " | Torn . df $ ST [ i ] == " NM "
| Torn . df $ ST [ i ] == " ID " | Torn . df $ ST [ i ] == " UT "
| Torn . df $ ST [ i ] == " AZ " | Torn . df $ ST [ i ] == " NV "
| Torn . df $ ST [ i ] == " WA " | Torn . df $ ST [ i ] == " OR "
| Torn . df $ ST [ i ] == " CA " ){
Torn . df $ Region [ i ] = " W "
}
else if ( Torn . df $ ST [ i ] == " ME " | Torn . df $ ST [ i ] == " NH "
| Torn . df $ ST [ i ] == " VT " | Torn . df $ ST [ i ] == " MA "
| Torn . df $ ST [ i ] == " CT " | Torn . df $ ST [ i ] == " RI "
| Torn . df $ ST [ i ] == " NY " | Torn . df $ ST [ i ] == " NJ "
| Torn . df $ ST [ i ] == " PA " ){
Torn . df $ Region [ i ] = " NE "
49
}
}
df = Torn . df % >%
group _ by ( ST , Region ) % >%
summarize ( Count = n () ,
TKEst = sum ( TKE ) ,
TKEstpT = TKEst / Count ) % >%
arrange ( desc ( TKEst ))
states . df = map _ data ( " state " ) % >%
filter ( region ! = ’ alaska ’ ,
region ! = ’ district of columbia ’) % >%
mutate ( ST = state . abb [ match ( region , tolower ( state . name ))]) % >%
merge ( df , by = " ST " ) % >%
arrange ( order )
ggplot ( states . df , aes ( x = long , y = lat ,
group = group , fill = Region )) +
geom _ polygon () +
geom _ path ( color = " gray75 " ) +
coord _ map ( project = " polyconic " ) +
theme ( panel . grid . minor = element _ blank () ,
panel . grid . major = element _ blank () ,
panel . background = element _ blank () ,
axis . ticks = element _ blank () ,
axis . text = element _ blank () ,
legend . position = " bottom " ) +
xlab ( " " ) + ylab ( " " ) +
scale _ fill _ manual ( values = wes _ palette ( " Royal1 " ))
# scale _ fill _ continuous (" Kinetic \ nEnergy ( J )" ,
# low = " yellow " , high = " red " ,
# breaks = 11:15 ,
# labels = c ( expression (10^11) , expression (10^12) ,
# expression (10^13) , expression (10^14) ,
# expression (10^15)))
‘‘‘
NRC models
‘ ‘ ‘{ rNRC models }
# EF3
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 , 50 , 50 , 0 , 0) ,
nrow = 5 ,
ncol = 2)
50
EF0
EF1 = matrix (
c (52.9 , 52.9 , 147.1 , 147.1 , 52.9 , 13.225 ,
36.775 , 36.775 , 13.225 , 13.225) ,
nrow = 5 ,
ncol = 2)
EF1
EF2 = matrix (
c (80 , 80 , 120 , 120 , 80 , 20 , 30 , 30 , 20 , 20) ,
nrow = 5 ,
ncol = 2)
EF2
EF3 = matrix (
c (93.3 , 93.3 , 106.7 , 106.7 , 93.3 , 23.325 ,
26.675 , 26.675 , 23.325 , 23.325) ,
nrow = 5 ,
ncol = 2)
EF3
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
p1 = Polygon ( EF1 )
ps1 = Polygons ( list ( p1 ) , 1)
p2 = Polygon ( EF2 )
ps2 = Polygons ( list ( p2 ) , 2)
p3 = Polygon ( EF3 )
ps3 = Polygons ( list ( p3 ) , 3)
spsNRC3 = SpatialPolygons ( list ( ps0 , ps1 , ps2 , ps3 ))
gArea ( spsNRC3 , byid = TRUE )
spsNRC3 . df = fortify ( spsNRC3 )
spsNRC3 . df $ DM = rep ( " " , dim ( spsNRC3 . df )[1])
spsNRC3 . df $ EF = spsNRC3 . df $ id
pal = wes _ palette ( " Moonrise3 " , 4)
ggplot ( spsNRC3 . df , aes ( x = long , y = lat , fill = EF )) +
geom _ polygon () +
coord _ fixed () +
ggtitle ( " NRC EF3 Model " ) +
xlab ( " " ) + ylab ( " " ) +
scale _ fill _ manual ( values = wes _ palette ( " Moonrise3 " )) +
theme ( panel . grid . minor = element _ blank () ,
panel . grid . major = element _ blank () ,
panel . background = element _ blank () ,
axis . ticks = element _ blank () ,
51
axis . text = element _ blank () ,
strip . background = element _ blank () ,
legend . position = " bottom " ) +
facet _ wrap ( ~ DM )
‘‘‘
All NRC models
‘ ‘ ‘{ rall }
# EF0
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 , 50 , 50 , 0 , 0) ,
nrow = 5 ,
ncol = 2)
EF0
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
spsNRC0 = SpatialPolygons ( list ( ps0 ))
gArea ( spsNRC0 , byid = TRUE )
# EF1
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 , 50 , 50 , 0 , 0) ,
nrow = 5 ,
ncol = 2)
EF0
EF1 = matrix (
c (77.2 , 77.2 , 122.8 , 122.8 , 77.2 , 19.3 ,
30.7 , 30.7 , 19.3 , 19.3) ,
nrow = 5 ,
ncol = 2)
EF1
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
p1 = Polygon ( EF1 )
ps1 = Polygons ( list ( p1 ) , 1)
spsNRC1 = SpatialPolygons ( list ( ps0 , ps1 ))
gArea ( spsNRC1 , byid = TRUE )
# EF2
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 , 50 , 50 , 0 , 0) ,
nrow = 5 ,
ncol = 2)
EF0
EF1 = matrix (
52
c (61.6 , 61.6 , 138.4 , 138.4 , 61.6 , 15.4 ,
34.5 , 34.5 , 15.4 , 15.4) ,
nrow = 5 ,
ncol = 2)
EF1
EF2 = matrix (
c (88.4 , 88.4 , 111.6 , 111.6 , 88.4 , 22.1 ,
27.8 , 27.8 , 22.1 , 22.1) ,
nrow = 5 ,
ncol = 2)
EF2
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
p1 = Polygon ( EF1 )
ps1 = Polygons ( list ( p1 ) , 1)
p2 = Polygon ( EF2 )
ps2 = Polygons ( list ( p2 ) , 2)
spsNRC2 = SpatialPolygons ( list ( ps0 , ps1 , ps2 ))
gArea ( spsNRC2 , byid = TRUE )
# EF4
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 , 50 , 50 , 0 , 0) ,
nrow = 5 ,
ncol = 2)
EF0
EF1 = matrix (
c (54.3 , 54.3 , 145.7 , 145.7 , 54.3 , 13.575 ,
36.425 , 36.425 , 13.575 , 13.575) ,
nrow = 5 ,
ncol = 2)
EF1
EF2 = matrix (
c (78.1 , 78.1 , 121.9 , 121.9 , 78.1 , 19.525 ,
30.475 , 30.475 , 19.525 , 19.525) ,
nrow = 5 ,
ncol = 2)
EF2
EF3 = matrix (
c (91.2 , 91.2 , 108.8 , 108.8 , 91.2 , 22.8 ,
27.625 , 27.625 , 22.8 , 22.8) ,
nrow = 5 ,
ncol = 2)
EF3
EF4 = matrix (
53
c (96.8 , 96.8 , 103.2 , 103.2 , 96.8 , 24.2 ,
26.225 , 26.225 , 24.2 , 24.2) ,
nrow = 5 ,
ncol = 2)
EF4
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
p1 = Polygon ( EF1 )
ps1 = Polygons ( list ( p1 ) , 1)
p2 = Polygon ( EF2 )
ps2 = Polygons ( list ( p2 ) , 2)
p3 = Polygon ( EF3 )
ps3 = Polygons ( list ( p3 ) , 3)
p4 = Polygon ( EF4 )
ps4 = Polygons ( list ( p4 ) , 4)
spsNRC4 = SpatialPolygons ( list ( ps0 , ps1 , ps2 , ps3 , ps4 ))
gArea ( spsNRC4 , byid = TRUE )
# plot ( spsNRC4 )
# EF5
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 , 50 , 50 , 0 , 0) ,
nrow = 5 ,
ncol = 2)
EF0
EF1 = matrix (
c (53.8 , 53.8 , 146.2 , 146.2 , 53.8 , 13.45 ,
36.55 , 36.55 , 13.45 , 13.45) ,
nrow = 5 ,
ncol = 2)
EF1
EF2 = matrix (
c (76.1 , 76.1 , 123.9 , 123.9 , 76.1 , 19.025 ,
30.975 , 30.975 , 19.025 , 19.025) ,
nrow = 5 ,
ncol = 2)
EF2
EF3 = matrix (
c (88 , 88 , 112 , 112 , 88 , 22 , 28 , 28 , 22 , 22) ,
nrow = 5 ,
ncol = 2)
EF3
EF4 = matrix (
c (95 , 95 , 105 , 105 , 95 , 23.75 , 26.25 ,
26.25 , 23.75 , 23.75) ,
54
nrow = 5 ,
ncol = 2)
EF4
EF5 = matrix (
c (98.3 , 98.3 , 101.7 , 101.7 , 98.3 , 24.575 ,
25.425 , 25.425 , 24.575 , 24.575) ,
nrow = 5 ,
ncol = 2)
EF5
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
p1 = Polygon ( EF1 )
ps1 = Polygons ( list ( p1 ) , 1)
p2 = Polygon ( EF2 )
ps2 = Polygons ( list ( p2 ) , 2)
p3 = Polygon ( EF3 )
ps3 = Polygons ( list ( p3 ) , 3)
p4 = Polygon ( EF4 )
ps4 = Polygons ( list ( p4 ) , 4)
p5 = Polygon ( EF5 )
ps5 = Polygons ( list ( p5 ) , 5)
spsNRC5 = SpatialPolygons ( list ( ps0 , ps1 , ps2 , ps3 , ps4 , ps5 ))
gArea ( spsNRC5 , byid = TRUE )
‘‘‘
Plot together
‘ ‘ ‘{ rplottogether }
spsNRC0 . df = fortify ( spsNRC0 )
spsNRC0 . df $ DM = rep ( " NRC EF0 " ,
spsNRC1 . df = fortify ( spsNRC1 )
spsNRC1 . df $ DM = rep ( " NRC EF1 " ,
spsNRC2 . df = fortify ( spsNRC2 )
spsNRC2 . df $ DM = rep ( " NRC EF2 " ,
spsNRC3 . df = fortify ( spsNRC3 )
spsNRC3 . df $ DM = rep ( " NRC EF3 " ,
spsNRC4 . df = fortify ( spsNRC4 )
spsNRC4 . df $ DM = rep ( " NRC EF4 " ,
spsNRC5 . df = fortify ( spsNRC5 )
spsNRC5 . df $ DM = rep ( " NRC EF5 " ,
dim ( spsNRC0 . df )[1])
dim ( spsNRC1 . df )[1])
dim ( spsNRC2 . df )[1])
dim ( spsNRC3 . df )[1])
dim ( spsNRC4 . df )[1])
dim ( spsNRC5 . df )[1])
sps . df = rbind ( spsNRC0 . df , spsNRC1 . df , spsNRC2 . df ,
spsNRC3 . df , spsNRC4 . df , spsNRC5 . df )
sps . df $ EF = paste ( " EF " , sps . df $ id , sep = " " )
ggplot ( sps . df , aes ( x = long , y = lat , fill = EF )) +
55
geom _ polygon () +
coord _ fixed () +
# ggtitle (" NRC Model Fractions ") +
xlab ( " " ) + ylab ( " " ) +
scale _ fill _ manual ( values =
wes _ palette ( " Zissou " , 7 ,
type = " continuous " )) +
theme ( panel . grid . minor = element _ blank () ,
panel . grid . major = element _ blank () ,
panel . background = element _ blank () ,
axis . ticks = element _ blank () ,
axis . text = element _ blank () ,
strip . background = element _ blank () ,
legend . position = " bottom " ) +
facet _ wrap ( ~ DM )
‘‘‘
Show variability
‘ ‘ ‘{ rvariability }
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 ,
nrow = 5 ,
ncol = 2)
EF0
EF1 = matrix (
c (52 , 52 , 148 , 148 , 52 ,
nrow = 5 ,
ncol = 2)
EF1
EF2 = matrix (
c (86 , 86 , 114 , 114 , 86 ,
21.5 , 21.5) ,
nrow = 5 ,
ncol = 2)
EF2
EF3 = matrix (
c (98 , 98 , 102 , 102 , 98 ,
24.5 , 24.5) ,
nrow = 5 ,
ncol = 2)
EF3
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
p1 = Polygon ( EF1 )
50 , 50 , 0 , 0) ,
13 , 37 , 37 , 13 , 13) ,
21.5 , 28.5 , 28.5 ,
24.5 , 25.5 , 25.5 ,
56
ps1 = Polygons ( list ( p1 ) , 1)
p2 = Polygon ( EF2 )
ps2 = Polygons ( list ( p2 ) , 2)
p3 = Polygon ( EF3 )
ps3 = Polygons ( list ( p3 ) , 3)
spsH = SpatialPolygons ( list ( ps0 , ps1 , ps2 , ps3 ))
gArea ( spsH , byid = TRUE )
EF0 = matrix (
c (0 , 0 , 200 , 200 , 0 , 0 , 50 , 50 , 0 , 0) ,
nrow = 5 ,
ncol = 2)
EF0
EF1 = matrix (
c (30 , 30 , 170 , 170 , 30 , 7.5 , 42.5 ,
42.5 , 7.5 , 7.5) ,
nrow = 5 ,
ncol = 2)
EF1
EF2 = matrix (
c (55 , 55 , 145 , 145 , 55 , 13.75 , 36.25 ,
36.25 , 13.75 , 13.75) ,
nrow = 5 ,
ncol = 2)
EF2
EF3 = matrix (
c (93 , 93 , 107 , 107 , 93 , 23.25 , 26.75 ,
26.75 , 23.25 , 23.25) ,
nrow = 5 ,
ncol = 2)
EF3
p0 = Polygon ( EF0 )
ps0 = Polygons ( list ( p0 ) , 0)
p1 = Polygon ( EF1 )
ps1 = Polygons ( list ( p1 ) , 1)
p2 = Polygon ( EF2 )
ps2 = Polygons ( list ( p2 ) , 2)
p3 = Polygon ( EF3 )
ps3 = Polygons ( list ( p3 ) , 3)
spsS = SpatialPolygons ( list ( ps0 , ps1 , ps2 , ps3 ))
gArea ( spsS , byid = TRUE )
spsNRC3 . df = fortify ( spsNRC3 )
spsNRC3 . df $ DM = rep ( " NRC Model " , dim ( spsNRC3 . df )[1])
spsH . df = fortify ( spsH )
57
spsH . df $ DM = rep ( " Hayleyville " , dim ( spsH . df )[1])
spsS . df = fortify ( spsS )
spsS . df $ DM = rep ( " Sawyerville - Eoline " , dim ( spsS . df )[1])
sps . df = rbind ( spsNRC3 . df , spsH . df , spsS . df )
sps . df $ EF = paste ( " EF " , sps . df $ id , sep = " " )
neworder = c ( " Hayleyville " ,
" Sawyerville - Eoline " , " NRC Model " )
library ( plyr )
sps2 . df = arrange ( transform ( sps . df ,
DM = factor ( DM , levels = neworder )) , DM )
ggplot ( sps2 . df , aes ( x = long , y = lat , fill = EF )) +
geom _ polygon () +
coord _ fixed () +
# ggtitle (" NRC EF3 Model ") +
xlab ( " " ) + ylab ( " " ) +
scale _ fill _ manual ( values = wes _ palette ( " Moonrise3 " )) +
theme ( panel . grid . minor = element _ blank () ,
panel . grid . major = element _ blank () ,
panel . background = element _ blank () ,
axis . ticks = element _ blank () ,
axis . text = element _ blank () ,
strip . background = element _ blank () ,
legend . position = " bottom " ) +
facet _ wrap ( ~ DM )
‘‘‘
Damage characteristic ( Moore , OK )
‘ ‘ ‘{ r r ea d T or n a do P a th D a ta }
setwd ( " ~ / Dropbox / Tyler " )
require ( rgdal )
require ( rgeos )
require ( maptools )
require ( ggplot2 )
require ( ggmap )
library ( GISTools )
library ( maps )
library ( SDMTools )
TornS = readOGR ( dsn = " DamagePaths / Moore _ OK _ Tornado _ Shape " ,
layer = " ex tr ac tD am ag eP ol ys " )
plot ( TornS , col = rainbow ( nrow ( TornS )))
‘‘‘
58
Geolocate and get map .
‘ ‘ ‘{ r geolocateMap }
loc = geocode ( " Moore , OK " )
loc = unlist ( loc )
Map = get _ map ( location = loc , source = " google " ,
maptype = " roadmap " , zoom =11)
‘‘‘
Plot map and paths .
‘ ‘ ‘{ r mapWithPaths }
mapdata = fortify ( TornS )
TornS@data $ id = rownames ( TornS@data )
mapdata = join ( mapdata , TornS@data , by = " id " )
ggmap ( Map ) +
geom _ polygon ( aes ( x = long , y = lat , fill = efscale , color = id ) ,
data = mapdata , alpha =0.7) +
guides ( color = FALSE ) +
scale _ color _ manual ( values =
wes _ palette ( " Zissou " , 13 ,
type = " continuous " )) +
scale _ fill _ manual ( name = " EF - scale " ,
values = wes _ palette ( " Zissou " , 7 ,
type = " continuous " ))
‘‘‘
59
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BIOGRAPHICAL SKETCH
Tyler Fricker was born in Cincinnati, Ohio and received his Bachelor of Science in Environment and
Natural Resources from The Ohio State University in 2013. His research interests include climate
change, weather systems, and human-environment interactions.
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