Population and energy elasticity of tornado casualties

Paper presented at the 2016 Southeastern Division of the Association of American Geographers Annual Meeting
University of South Carolina, Columbia, SC

Transcript

1. Population and energy elasticity of tornado casualties Tyler Fricker (@TylerFricker) Department of Geography, Florida State University November 21, 2016 James B. Elsner, and Thomas H. Jagger
2. Problem
3. Objective I Establish statistical estimates (and margins of error) on how sensitive casualties are to changes in population and on how sensitive casualties are to changes in tornado strength
4. Casualties I “Casualty” refers to either human death or injury as a direct consequence of tornado activity according to the NWS Storm Data Injury Type Number Frequency Soft tissue laceration 749 53.6% Fracture 406 29.1% Head injury 99 7.1% Blunt trauma 102 7.3% Minor strains 31 2.2%
5. Casualties 1 10 100 1 10 Casualties Number of Tornadoes
6. Casualties 10 100 1000 Number of Casualties
7. Population Density 0 50 100 0.0 2.5 5.0 7.5 Population Density Number of Tornadoes A
8. Energy Dissipation The equation for energy dissipation (atmosphere moment) is E = 1 2Av l ¯ ⇢ J X j =0 wj v2 j , (1) where Av is the area of the vortex (⇡ R2 ), l is the path length, ¯ ⇢ is air density, vj is the midpoint wind speed for each rating, and wj is the corresponding fraction of path area.
9. Energy Dissipation 0 30 60 90 120 106 108 1010 1012 1014 Energy Dissipation (J) Number of Tornadoes B
10. Population and Energy Elasticity I Tornado casualties are related to population and energy dissipation using the economic concept of ‘elasticity’. I This is an e cient way to explain the changes in casualties by focusing on the ratios of the percentage changes in population and energy to the percentage change in casualties.
11. Model I Consider a multiplicative model for casualties expressed as C ⇠ P ↵ · E , (2) where C is the number of casualties, P is the population density in persons per square km, and E is energy dissipation in joules.
12. Model I Taking logarithms and writing the relationship statistically, we have log( ˆ C ) = ˆ ↵ · log( P ) + ˆ · log( E ) (3) where ˆ C is the predicted number casualties and the coe cients ˆ ↵ and ˆ are called the output elasticities.
13. Bi-variate Relationships 10 1000 10 1000 Population Density Number of Casualties A
14. Bi-variate Relationships Tuscaloosa−Birmingham (2011−04−27) 10 1000 106 108 1010 1012 1014 Energy Dissipation (J) Number of Casualties B
15. Multiplicative Regression Model I The data are fit to the model (Eq. 3) using ordinary least squares. I The R2 from the model indicates that together population and energy dissipation explain 31% of the variability in the number of casualties. Coe cient Estimate Std. Error t value Pr(> |t|) ˆ ↵ .223 .024 9.474 < .0001 ˆ .206 .011 18.84 < .0001
16. Conclusions I A doubling of the energy dissipation leads to a 15% increase in the number of casualties, while a doubling of the population leads to a 17% increase in the number of casualties. I Energy dissipation is statistically as important as the expanding bull’s-eye e↵ect in explaining tornado casualties at the level of individual tornadoes.