Elasticity of Tornado Casualties

Paper presented at the 2017 40th Annual Applied Geography Conference
Kent State University, Kent, OH

Transcript

1. Elasticity of Tornado Casualties Tyler Fricker (@TylerFricker) Department of Geography, Florida State University November 14, 2017
2. Problem
3. Objectives Establish statistical estimates (and margins of error) on how sensitive casualties are to: Changes in population and, Changes in tornado strength Examine these sensitivities across space
4. Casualties 1 10 100 1 10 Casualties Number of Tornadoes
5. Population Density 0 50 100 150 200 −5 0 5 10 Population Density Number of Tornadoes A
6. Energy Dissipation The equation for energy dissipation is E = Apρ J j=0 wj v3 j , (1) where Ap is the area of the approximate path (width times length), ρ is the air density (assumed to be 1 kg/m3 at the surface), vj is the midpoint wind speed for each damage rating j, and wj is the corresponding fraction of path area.
7. Energy Dissipation 0 50 100 150 108 1010 1012 1014 Energy Dissipation (W) Number of Tornadoes B
8. Addititve Model The model is given by: C ∼ NegBin(ˆ µ, n) (2) log(ˆ µ) = ˆ α log(P) + ˆ β log(E) + ˆ ν, (3) where NegBin(ˆ µ, n) indicates that the conditional casualty counts are described by negative binomial distributions with mean (rate) ˆ µ and size n. The coefficient ˆ α is the population elasticity, the coefficient ˆ β is the energy elasticity and ˆ ν is the intercept parameter.
9. Model Results Coefficient Value (95% Uncertainty) ˆ α .272 (.232,.311) ˆ β .411 (.384,.438) On average, a doubling of the population under the path of a tornado leads to a 21% increase in the casualty rate while a doubling of the energy dissipated by the tornado leads to a 33% increase in the casualty rate.
10. Interactive Model The model is given by: C ∼ NegBin(ˆ µ, n) (4) ˆ µ = ˆ β0 P ˆ βP E ˆ βE (E · P)ˆ βP·E , (5) where the coefficient ˆ βP is the population elasticity, the coefficient ˆ βE is the energy elasticity and ˆ βP·E is the interactive term.
11. Model Differences 1 2 5 10 20 50 1 2 5 10 20 50 100 Fixed Interaction Conditional Interaction .001 .1 10 1,000 .001 .1 10 1,000 .001 .1 10 1,000 Population Density [people per sq. km] Energy Dissipation [GW]
12. Model Differences 0.75 1 1.25 1.5 1.75 2 2.25 10 100 1,000 10 100 1,000 Population Density [people per sq. km] Energy Dissipation [GW]
13. Coefficients by State Rank State No. Tornadoes ˆ βP·E p-value 1 Arkansas 126 1.023 0.000 2 Tennessee 133 0.717 0.001 3 Missouri 109 0.607 0.010 4 Kentucky 94 0.493 0.053 5 Illinois 121 0.417 0.021 6 Oklahoma 108 0.404 0.023 7 Alabama 159 0.347 0.056 8 Mississippi 130 0.329 0.106 9 Texas 190 0.308 0.001 10 North Carolina 87 0.286 0.458 11 Louisiana 102 0.246 0.126 12 Georgia 125 0.128 0.663
14. Why is the Mid South so Vulnerable? 2010 2016 State Percent Elderly (65+) Percent Elderly (65+) 1 Arkansas 14.4 16.3 2 Tennessee 13.4 15.7 3 Missouri 14.0 16.1 4 Kentucky 13.3 15.6 5 Illinois 12.5 16.1 6 Oklahoma 13.5 15.0 7 Alabama 13.8 16.1 8 Mississippi 12.8 15.1 9 Texas 10.3 12.0 10 North Carolina 12.9 15.5 11 Louisiana 12.3 14.4 12 Georgia 10.7 13.1
15. Conclusions Using an additive model, on average, a doubling of the population under the path of a tornado leads to a 21% increase in the casualty rate while a doubling of the energy dissipated by the tornado leads to a 33% increase in the casualty rate. Using an interactive model, the percentage increase in casualty rates with increasing energy dissipation increases with population density. Controlling for energy dissipation, casualty rates are substantially higher in more densely populated areas of the Mid South than in similarly populated areas elsewhere