How To Build a Seasonal Tornado Model

James B. Elsner (@JBElsner)

Department of Geography, Florida State UniversityTallahassee, FL

March 10, 2016SC&C Workshop, Columbia University, New York, NY

Help: Thomas Jagger, Tyler Fricker, Holly M. WidenMoney: RPI2.0 (Mark Guishard, John Wardman)

Why are we doing this?

I Dynamical models can’t predict tornadoes

I They can predict conditions necessary

I But necessary does not imply sufficient

I Statistical models are needed, but how should they be made?

I Here I show you a way that is quite flexible

Spatial model (county level) ⇒ Space-time model (grid level)

Model must be spatial

Kansas Tennessee

1

10

100

El Nino Neutral La Nina

Annual Number of Tornadoes [1954−2014]

Model must deal with pathological tornado records

Enhanced Fujita Scale

Mobile Radar

Doppler Radar

Discovery of Microbursts

Fujita Scale

Tornado Spotter Network

Tornado Watch and Warning Program

Systematic Tabulation of Tornado Data

1900 1925 1950 1975 2000 2025Year

Annual number of tornado reports (Kansas)

50

100

150

200

1970 1980 1990 2000 2010Year

Num

ber

of E

F0+

Tor

nado

es

2012 Population Density [persons per square km]

Clark

Lyon

Gray

MarshallSmith

Rice

Thomas

Scott

Kiowa

Wichita

Clay

Cheyenne

Meade

Osborne

Franklin

Linn

Harvey

Sumner

Wilson

Cloud

Kearny

Sedgwick

Osage

Lincoln

Rush

RussellGove

Jewell

Mitchell

Republic

Trego

Stevens

Jackson

Stanton

Chautauqua

Stafford

McPhersonChase

Coffey

Ottawa

Saline

Butler

Wallace

Montgomery

Grant

Washington

Shawnee

Sheridan

Johnson

Haskell

Greenwood

Barton

Neosho

Rooks

Douglas

Elk

Labette

Pawnee

Graham

Ellsworth

Marion

Anderson

Logan

HodgemanFinneyHamilton

Comanche

Edwards

Riley

MortonBarber

Miami

Sherman

Reno

Crawford

Woodson

Doniphan

Wabaunsee

Pratt

BrownPhillips

Leavenworth

Ellis

Kingman

Decatur

Lane

Norton

Cherokee

Atchison

Allen

Geary

Cowley

Ness

Morris

Rawlins

Greeley

Ford

Pottawatomie

Dickinson

Harper

JeffersonWyandotte

Bourbon

Seward

Nemaha

1 3 10 40 158 631

Number of EF0+ Tornadoes (1970−2014)0 10 20 30 40 50 60 70 80

Observed Poisson

0

10

20

30

0 20 40 60 80 0 20 40 60 80Number of Tornadoes

Num

ber

of C

ount

ies

The number of tornado reports in each cell (Ts) is assumed tofollow a negative binomial distribution (NegBin) with mean (µs)and parameter rs .

Ts |µs , rs ∼ NegBin(µs , rs)

µs = exp(Asνs)

νs = β0 + β1 lpds + β2 (t − t0) + β3 lpds(t − t0) + us

rs = As n

where the mean of the distribution is linked to a structuredadditive response νs and the county area (As). The base-two logof county population density is lpds , t is the year, t0 is the baseyear set to 1991 (middle year of the record), n is the dispersionparameter, and us is the random effects term.

To account for spatial correlation the random effects term followsan intrinsic Besag formulation with a sum-to-zero constraint.

ui |{uj ,j 6=i , τ} ∼ N

1

mi

∑i∼j

uj ,1

miτ

,

where N is the normal distribution with mean 1/mi ·∑

i∼j uj andvariance 1/mi · 1/τ where mi is the number of neighbors of cell iand τ is the precision; i ∼ j indicates cells i and j are neighbors.Neighboring cells are determined by contiguity (queen’s rule).

Tornado (EF0+) Occurrence Rate [% Difference from Statewide Avg]−50 −40 −30 −20 −10 0 10 20 30 40 50

The model was used to show that tornadoes are significantly morelikely to occur over smooth terrain at a rate of 23%/10 m decreasein roughness.1

0.0

0.1

0.2

0.3

0 5 10 15% increase in tornado reports

per doubling of population

Pos

terio

r D

ensi

ty

a

0.0

0.3

0.6

0.9

0 1 2 3% increase in tornado reports

per meter decrease in elevation roughness

Pos

terio

r D

ensi

ty

b

1Elsner, J. B., T. Fricker, H. M. Widen, et al., The relationship betweenelevation roughness and tornado activity: A spatial statistical model fit to datafrom the central Great Plains, Journal of Applied Meteorology and Climatology,in the press.

Number of EF0+ Tornadoes (1970−2014)0 40 80 120 160 200 240

Number of EF0+ Tornado Days (1970−2014)0 20 40 60 80 100 120 140

Expected Annual Tornado (EF0+) Occurrence Rate [per 100 km square region]0.03 0.06 0.12 0.25 0.5 1 2 4 8

A space-time model

Number of Tornadoes

32°N34°N36°N38°N40°N42°N44°N

0 500 km

1999

0 500 km

2000

0 500 km

2001

0 500 km

2002

0 500 km

2003

0 500 km

2004

0 500 km

2005

0 500 km

2006

32°N34°N36°N38°N40°N42°N44°N

0 500 km

2007

0 500 km

2008

0 500 km

2009

0 500 km

2010

100°W 90°W 85°W

0 500 km

2011

0 500 km

2012

100°W 90°W 85°W

0 500 km

2013

0 500 km

2014

1 2 4 8 16 32 64 128

A

ENSO Effect on Tornadoes [% Change in Rate/S.D. Increase in ENSO Index]

32°N

34°N

36°N

38°N

40°N

42°N

44°N

100°W 95°W 90°W 85°W

0 500 km

−20 −15 −10 −5 0 5 10 15 20

B

Signficance Level

32°N

34°N

36°N

38°N

40°N

42°N

44°N

100°W 95°W 90°W 85°W

0 500 km

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Effect on Tornadoes [% Change in Rate/S.D. Increase in NAO]

30°N

35°N

40°N

100°W 95°W 90°W 85°W

−20 −15 −10 −5 0 5 10 15 20

Effect on Tornadoes [% Change in Rate/Deg. C Increase in WCA Temp]

30°N

35°N

40°N

100°W 95°W 90°W 85°W

−30 −20 −10 0 10 20 30

Elsner, J. B., and H. M. Widen, 2014: Predicting spring tornadoactivity in the central Great Plains by March 1st. Monthly WeatherReview, 142, 259–267.

According to Aon, the costliest U.S. thunderstorm outbreak onrecord occurred in late April 2011 across the Lower MississippiValley and cost insurers $7.7 bn in today’s dollars.

2011 Forecast (% of normal) enso = −2 nao = −0.5 td = 1.2

30°N

35°N

40°N

100°W 95°W 90°W 85°W

80% 90% 100% 110% 120% 130% 140% 150%

2015 Hindcast (% of normal) enso = 0.8 nao = 0.25 td = −0.56

30°N

35°N

40°N

100°W 95°W 90°W 85°W

85 90 95 100 105 110 115

1

10

El Nino Neutral La Nina

Annual Tennessee Tornado Fatalities by ENSO Phase [1954−2014]

Preliminary forecast for 2016

2016 Forecast (% of normal) enso = 0 nao = 0 td = 0.54

30°N

35°N

40°N

100°W 95°W 90°W 85°W

100 101 102 103 104