## Transcription

```Are Tornadoes Getting Stronger?1
1
Notes for AGU Press Conference.
James B. Elsner @hurricanejim
December 10, 2013
Our research estimates tornado intensity from the size of the damage path. On average damage paths are getting larger resulting in
Thomas H. Jagger & Ian J. Elsner
helped with the research.
2
A tornado can destroy an entire town in minutes. Ferocious winds
exceeding 220 mph uproot trees and level buildings. It is important
to understand if climate change is making them stronger.
Problem
The EF damage scale used to rate tornado intensity is categorical. We
can count the number of tornadoes by EF rating. However, a plot of
the number of tornadoes by year and EF rating does not answer the
need an estimate of tornado intensity on a continuous scale.
Strong tornadoes occur from supercell thunderstorms. A supercell
thunderstorm is like a regular thunderstorm except the upward moving air is separated from the sinking air. This is because strong winds
tilt the top of the thunderstorm relative to its base. If the supercell
thunderstorm can survive for at least an hour or so, a tornado is
possible. Less than 20% of all supercell thunderstorms produce a
The tornado forms when the air flowing inward gets twisted because winds just above the ground are blowing faster than the winds
at the surface. The ribbon of spiraling winds gets lifted into the vertical by upward moving air in the southwest corner of the thunderstorm (see Fig. 2). Additional rotation occurs when the downdraft,
that originates at middle levels, wraps around the southwest corner of the thunderstorm. For this reason tornado chasers prefer to
position themselves to the south and east of the thunderstorm.
Tornadoes occur everywhere in the United States, but are most
prevalent east of the Rockies. Increasing awareness and improvements in technology lead to an increasing number of reported tornadoes.
Figure 2: Illustration of how a tornado
forms.
2
Tornado path length and path width are strongly correlated with
EF category. Tornadoes that have longer and wider paths tend to
reach higher damage categories. We model this relationship using a
categorical logistic regression.
Category
EF1
N
6179
Length (km)
Mean
Median
6.24
3.52
EF2
1843
13.05
EF3
543
EF4
120
EF5
13
(1.61,8.05)
Width (m)
Mean
Median
124.2
91.4
(45.7,137.2)
8.85
284.5
20.92
561.3
27.29
809.2
58.95
1389.9
182.9
(3.54,17.03)
26.89
(91.4,365.8)
(9.90,35.40)
42.58
(45.51,65.93)
402.3
(228.6,804.7)
(16.09,56.73)
67.30
Table 1: Damage path statistics. Data
are based on all reported tornadoes
in the United States (1994–2011). N is
the sample size. The lower and upper
quartile values are given in parentheses.
Since 1994 the U.S. has been almost
completely covered by NOAA’s WSR88D radar.
754.4
(443.5,1063.0)
1307.6
(1207.0,1609.3)
Let Wi and Li be the path width and path length of tornado i, then
logit[ P( Ti ≤ f )] =
(θ f − β 1 Li 1/3 − β 2 Wi 1/2 − β 3 Li 1/3 × Wi 1/2 )
exp(ζ 1 Li 1/3 + ζ 2 Wi 1/2 )
(1)
for i = 1, . . . , n and f = 1, . . . , 4, where P( Ti ≤ f ) is the probability of
tornado i having an EF category f or lower.
600
400
1
200
0
120
90
60
2
30
Frequency
0
25
20
15
3
10
5
0
10.0
7.5
5.0
4
2.5
0.0
4
3
2
5
We use the square root of the width and cube root of the length so
that the model conforms to the proportional odds assumption meaning that the relationship between the EF1 category and all higher
categories is the same as the relationship between the EF2 category
and all higher categories, and so on.
We compute the probability across the EF scale from path length
and width then take the product of these probabilities and the set
of characteristic wind speeds for each category. The probability in
each category is the weight in a weighted average of the characteristic
wind speeds. In this way we obtain a single tornado wind speed in
m s−1 .
We correlate our estimated wind speeds with wind speeds from
twelve tornadoes estimated from radar measurements that are independent of the damage. The derived radar wind speeds result from a
calibration of mobile radar (Doppler on Wheels) with nearby Weather
The wind speeds correlate at .82 (.46, .95) [95% CI]. Although
range from a low of 37.7 m s−1 to a high of 91.2 m s−1 suggesting the
1
0
50
60
70
80
90
Figure 3: Estimated wind speeds.
Figure 4: Doppler on wheels (DOW).
potential for our estimates to be broadly applicable throughout the
database.
Trends
Upward trends in path length and width result in upward trends
in estimated tornado wind speeds. Upward trends are noted in all
EF categories. Increasing effort on tornado surveys over time might
result in longer and wider damage paths. This is because the survey
typically starts with the most obvious damage and then investigates
outward from there, but more research is need to quantify to what
extent this has occurred.
Figure 5: Trends in path length, width,
and intensity.
a
2
3
4
5
100
50
2005
2010
2005
2010
2005
2010
2000
1995
2010
2005
2000
1995
2010
2005
2000
1995
2010
2005
2000
1995
2010
2005
2000
0
1995
Annual Mean
Path Length (km)
1
b
2
3
4
5
2
1
2000
1995
2010
2005
2000
1995
2010
2005
2000
1995
2010
2005
2000
1995
2010
2005
2000
0
1995
Annual Mean
Path Width (km)
1
3
c
2
3
4
5
80
A balance between the pressure gradient force and the centrifugal force produces the fastest tornado wind. The summation of the
centrifugal force from the center of the tornado to a radius where the
wind blowing the fastest is the mass-specific kinetic energy (E) given
by
Z
E=
ro
0
F (r )dr = v2 /2,
where v is the fastest wind inside the tornado.
The per-tornado kinetic energy by year is shown in Fig. 6. Upward
trends are noted at the 50th, 75th and 90th percentile levels.
Mass−Specific Kinetic Energy (J/kg)
2000
1995
2010
2005
2000
1995
2010
2005
2000
1995
2010
2005
2000
1995
2010
2005
2000
60
1995
Annual Mean
Intensity (m/s)
1
100
4000
3000
2000
1000
1995
2000
2005
2010
Year
Figure 6: Per tornado kinetic energy.
The quantile trends are shown for the
50th, 75th, and 90th percentile energy.
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Integrated Kinetic Energy
The fastest wind occurs over a relatively small percentage of the total
damage path area. The relationship between percent area covered
and EF rating is assumed to be logarithmic. Integrating the estimated
wind speed over the area covered by that wind speed provides an
estimate of the integrated kinetic energy for each tornado.
We total the integrated kinetic energy over all tornadoes for each
year and then plot the total integrated kinetic energy by year in
Fig. 7. A significant upward trend is noted starting at the turn of
the century.
Integrated Kinetic Energy (GJ)
Figure 7: Total integrated kinetic
energy.
1.0
0.5
0.0
1980
1990
2000
2010
Year
Final Words
• Our method and findings suggest an important new domain
within hazard research. How does climate change affect tornadoes and other severe local storms?
• We have organized the 1st International Summit on Tornadoes and
Climate Change to discuss this question with other experts. The
summit will be held in Crete, Greece from May 25–30, 2014.
• The code to reproduce our results including the intensity model
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