Using spatial analysis to establish a relationship

between hurricane attributes and damages

Adam Sachs

Harvard College Class of 2007

May 16, 2007

Contents

1 Introduction 2

2 Methods 3

3 Results 6

4 Figures 9

5 Appendix 18

6 Advisor Comments 21

7 Acknowledgments 22

1

Note: This paper is based on a portion of my undergraduate thesis, which I presented

to the Department of Earth & Planetary Sciences and the Department of Economics. The

thesis, entitled The Influence of ENSO on Hurricane Damages: A new methodology for pric-

ing risk, can be found here:

http://swell.eps.harvard.edu/~asachs/adamsachs_thesis

1 Introduction

For my thesis, I studied the influence of the El Nino–Southern Oscillation (ENSO), a global

climatic phenomenon, on short-term hurricane risk in the United States. The central diffi-

culty in analyzing this relationship—and, indeed, the main challenge in addressing almost

any question related to hurricane risk—is the extremely limited historical hurricane record,

which presents a problem of small sample size. The set of landfalling hurricanes for which we

have reliable data is simply too small to allow us to draw robust conclusions, even with meth-

ods of statistical extrapolation. I circumvented this obstacle by supplementing the sparse

data with our understanding of the physical mechanisms of hurricanes. In particular, I used

a physical hurricane model to generate three arbitrarily large sets of synthetic hurricane

tracks, one set for each of the three phases of ENSO (El Nino, La Nina, and the Neutral

phase.) To translate these synthetic storms into predictions of risk throughout the U.S.,

however, we require a function that maps each hurricane into the damages it causes along

its route. It was for this portion of my thesis—that is, the construction and application of a

damage function—that I made extensive use of GIS techniques.

2

2 Methods

A hurricane damage function is based fundamentally on the idea that the damage at some

location along a hurricane track will be related to the characteristics of the hurricane at

that location and the characteristics of the location itself. The total damage caused by

the hurricane, then, would be the integral of this locational damage along the entire track.

Relevant hurricane characteristics might include the wind profile and translational velocity,

and relevant locational characteristics might include the type and number of structures and

the topography. Since engineering was beyond the scope of this study, I chose to distill these

various characteristics down to the two that would seem to be of first-order importance:

the wind speed at a particular location, and the capital stock (henceforth, “wealth”) at

that location. Since one cannot actually integrate wealth continuously, I chose to discretize

each track by the counties it went through. Thus the idea for the damage function is the

following: for a particular hurricane, the total damage a hurricane causes should be a sum

over all counties it travels through of some function of the population and per capita wealth

in the county and of the hurricane’s wind speed as it travels through the county. This can

be represented mathematically as:

Damage =n∑i=1

f(Wealth Per Capitai, Populationi,Windi) (1)

where n is the number of counties the hurricane travels through. The hurricane damage

literature has tended to favor a power law relationship between wind speed and damages. I

therefore assumed the following functional form for the damage function:

3

Damagej = β1 ×n∑i=1

Populationij × (Wealth Per Capita) β2

ij ×Wind β3

ij (2)

where n is the number of counties that hurricane j travels through, β1 is a scaling factor,

β2 is the elasticity of damages with respect to wealth per capita, and β3 is the elasticity

of damages with respect to wind speed.1 Wealth Per Capitaij is the wealth per capita

in county i in the year of hurricane j, adjusted for inflation. Populationij is a measure of

the “affected population” of county i for hurricane j. Windij is the average wind speed of

hurricane j in county i.

The goal was to perform a nonlinear regression using data on historical hurricanes in order

to estimate the β parameters in equation (2). There have been 196 historical storms since

1925 for which we have an estimate of the total damage caused by the hurricane. I used this

data (adjusted for inflation) for the left-hand side of equation (2), and performed the following

GIS analysis to estimate the values of Populationij, Windij, and Wealth Per Capitaij for

each county i for each hurricane j to plug in to the right-hand side of equation (2).

The physical data for historical hurricanes, from the NOAA Hurricane Database (HUR-

DAT), gives the coordinates of the center of each hurricane at 6-hour intervals, as well as

the surface wind speed at these intervals. I plotted in the GIS (using ArcInfo 9.2) the 6-

hourly coordinates and wind speed over a layer of historical county boundaries for the year in

which the hurricane took place. These historical county boundaries were procured from the

Historical United States County (HUSCO) Boundary Files project, produced by the Depart-

1“Elasticity” is economics jargon for the proportional relationship between two variables. For example,the elasticity of damages with respect to wind speed is simply the percentage change in damages for eachpercentage change in wind speed, all else equal.

4

ment of Geography and Anthropology at Louisiana State University.2 For example, 1969’s

Hurricane Camille was plotted on top of the U.S. county boundaries in 1969 (Figure 1).

Next, I interpolated the position between the 6-hour observations with Bezier cubic splines,

resulting in a continuous track for each storm (Figure 2).

In a GIS, a line like that in Figure 2 can only be associated with a single attribute

(in this case, wind speed), so in order to approximate a continuous record of wind speeds

along the track, I divided each of these now-continuous hurricane tracks into a thousand

segments of equal length, and then linearly interpolated wind speeds between the HURDAT

observations.

I then added a 29-mile radius buffer on each side of the track (Figure 3). This buffer is

intended to represent the radius of maximum winds (RMW), which is the distance radially

outward from the hurricane’s center at which the hurricane achieves its maximum wind

speed.

For each county that intersected the buffer, I found a measure of the “affected population”

by multiplying the total population of the county in that year (taken from historical U.S.

census data) by the ratio of the county’s area that lay within the buffer to the total area of

the county. This, for county i and hurricane j, is Populationij (Figure 4). This calculation

assumes that the population is uniformly distributed within each county. This is surely

not generally the case—some counties have both major cities and rural areas—but without

higher resolution historical population data we have no reason to pick one particular spatial

distribution over another, and the uniform distribution is simplest. I found the average

maximum sustained surface wind speed in county i during hurricane j, Windij, by finding

2http://www.ga.lsu.edu/husco.html

5

the mean of the interpolated winds through that county (Figure 5). Finally, I estimated

the Wealth Per Capitaij for each affected county for the year in which hurricane j struck

using historical data from the United States Bureau of Economic Analysis, assuming that

all counties in a particular state have the same wealth per capita in any given year.

Table 1 shows a sample of the resulting data for Hurricane Camille. The actual table

produced has 230 rows–one per affected county–but Table 1 lists only the 10 affected coun-

ties with the highest average wind speed, for space considerations. I automated this string of

GIS functions with a Python script, which is reprinted in the Appendix, and ran this script

on 196 historical hurricanes, to produce one such table, including all affected counties, for

each hurricane. With the resulting data, I performed a nonlinear regression to estimate the

β parameters in equation (2).

3 Results

The estimated parameters and their estimated standard errors (SE) are:

β1 = 22.2 (SE = 9.6)

β2 = .83 (SE = .07) (3)

β3 = 6.3 (SE = .4)

Until recently, it has been commonly assumed that hurricane damages increase with the

cube of wind speed, because the power dissipated by a hurricane is related in part to the

cube of wind speed integrated over the lifetime of the storm. There is no reason, however,

6

to assume that wind affects structures in proportion to the power dissipated by those winds.

Instead, structures are governed by their own principles of materials and engineering. The

estimate of β3 shown in equation (3) suggests that damages are in fact much more sensitive

to wind speed than previously assumed: damages are estimated to increase with the sixth

power of wind speed. This extremely high sensitivity suggests a threshold behavior: up to a

certain wind speed, many structures remain standing and largely undamaged, but for more

intense winds these structures are destroyed.

A second notable result of the regression is that β2 is less than 1. In the hurricane damage

literature, there is no previous estimate of the elasticity of hurricane damages with respect to

wealth per capita. Many studies that attempt to normalize historical hurricane damages to

the present day make the assumption of unit elasticity for this value. This assumes that one’s

vulnerability to hurricane damages scales in direct proportion to one’s wealth. As a region

gets wealthier, however, it may gain access to better building materials, improved engineering

techniques, and superior weather forecasting. We might assume on theoretical grounds alone,

therefore, that a region’s vulnerability to hurricanes would increases less than one-to-one with

increases in its wealth, and the estimate of β2 of around .8 bears this out empirically. This

would suggest that normalization methodologies that assume unit elasticity of damages with

respect to wealth per capita are in fact overestimating the normalized damages of historical

hurricanes.

For each ENSO phase, the physical hurricane model produced 2,000 synthetic hurricane

tracks. The Python script in the Appendix was then run on the 2,000 synthetic tracks in each

phase, resulting in 6,000 tables—one per synthetic storm—listing the affected population,

average wind speed, and wealth per capita in each affected county. Using the damage

7

function (2), with the estimated β parameters from equation (3), I found the total estimated

damage for each synthetic storm, as well as the estimated damage each storm causes in each

affected county. This allowed me to produce far more robust estimates of how hurricane

risk varies by ENSO phase than would be possible with the limited historical record alone.

Figure 6 shows one result: the expected damage per county during a century of La Nina

phase years. Figure 7 shows the difference in the expected damage per county during a

century of La Nina years compared to a century of El Nino years. This figure demonstrates

that throughout most of the vulnerable coastal counties, expected damages per century are

clearly greater during La Nina. This much is not surprising: there is diminished Atlantic

wind shear during La Nina years, which tends to increase the frequency and intensity of

Atlantic hurricanes. More surprising are the exceptions: the expected damages in certain

parts of the U.S. appear to increase during El Nino years. In particular, the southwest coast

of peninsular Florida appears to experience increased risk during El Nino years. This seems

to be due to the influence of El Nino on the steering of hurricanes: the increased wind shear

during El Nino leads to an increased risk of landfalling hurricanes in southwest Florida.

Figure 8, which aggregates the expected damages by state, demonstrates that a similar

phenomenon may lead to increased hurricane risk in New England during El Nino years.

These are novel results; previous studies of the effect of ENSO on hurricane activity have

not examined the spatial distribution of risk in the U.S., partially because the number of

historical storms is simply too small to permit such an analysis. Synthetic hurricanes make

this kind of spatial analysis possible.

Please see my thesis (URL given at the beginning of this paper) for the complete analysis

of how hurricane risk varies with ENSO.

8

4 Figures

Wind Speed (m/s)12-1515-3030-5050-7070-85

Figure 1: HURDAT 6-hourly coordinates and maximum sustained surface wind speed forHurricane Camille, plotted on top of 1969 historical county boundaries.

9

Figure 2: Interpolated track for Hurricane Camille.

10

Figure 3: Interpolated track for Hurricane Camille with 29-mile radius buffer.

11

Affected Population(in thousands)

0 - 1010 - 2020 - 4040 - 60

60 - 120120 - 250250 - 500500 - 750

Figure 4: “Affected population” for each county affected by Hurricane Camille(Populationij). The county in red (500,000–750,000 affected people) is Shelby County, Ten-nessee, which contains Memphis. By the time Camille reached Shelby, however, it was quiteweak, as shown in Figure 5, and therefore caused negligible damages. Harrison County,Mississippi, on the other hand, had both high populations within 29 miles of the eye—it isthe county on the Gulf of Mexico colored in green, indicating 60,000-120,000 affected—andfaced high wind speeds, and so suffered extensive damage, including an area of total destruc-tion stretching 68 square miles (Source: Harrison County Library Website). Camille alsocaused considerable damage in Orleans Parish, in which New Orleans is located.

12

Avg. Wind Speed in County(m/s)

10 - 15

15 - 20

20 - 30

30 - 40

40 - 50

50 - 60

60 - 70

70 - 85

Figure 5: Average wind speed of Hurricane Camille in each affected county (Windij).

13

Damages (2005 $)

0

< 200 million

200 to 800 million

800 million to 2 billion

2 to 8 billion

8 to 12 billion

12 to 25 billion

25 to 40 billion

40 to 80 billion

80 to 160 billion

La Nina Phase Damages Per Century

Figure 6: Expected damage per county per century due to the synthetic La Nina phasestorms.

14

Difference in Damages (2005 $)

-23 to -12 billion-12 to -2 billion-2 billion to -700 million-700 to -100 million-100 to 700 million700 million to 2 billion2 to 7 billion7 to 15 billion15 to 30 billion30 to 60 billion

Difference in La Nina and El Nino Damages Per Century

Figure 7: Difference in expected damage per county during a century of La Nina yearscompared to a century of El Nino years. Positive numbers indicate greater damages duringa century of La Nina years, and negative numbers indicate greater damages during a centuryof El Nino years.

15

Difference in Damages (2005 $)

-1.5 billion to -500 million-500 to -150 million-150 to 150 million150 million to 1 billion1 to 5 billion5 to 15 billion15 to 60 billion60 to 130 billion130 to 450 billion

Difference in La Nina and El NinoDamages Per Century

Figure 8: Difference in expected damage per state during a century of La Nina years com-pared to a century of El Nino years. Positive numbers indicate greater damages during acentury of La Nina years, and negative numbers indicate greater damages during a centuryof El Nino years.

16

Table 1: Sample of affected population, wind speed, and wealth per capita data for HurricaneCamille. Note that wealth per capita, by construction, is the same for all counties in aparticular state in a particular year.

County State Affected Population Wind Speed (m/s) Wealth per capita (2005 $)

Plaquemines Louisiana 9,445 84.58 47,728

Orleans Louisiana 117,473 68.07 47,728

St Bernard Louisiana 39,569 76.75 47,728

Hancock Mississippi 17,356 60.74 40,261

St Tammany Louisiana 33,749 59.96 47,728

Harrison Mississippi 77,813 61.32 40,261

Stone Mississippi 2,871 51.40 40,261

Washington Louisiana 24,149 45.37 47,728

Pearl River Mississippi 27,754 50.82 40,261

17

5 Appendix

Python script to automate GIS procedure (next 3 pages)

# Import system modules import sys, string, os, arcgisscripting # Create the Geoprocessor object gp = arcgisscripting.create() # Load required toolboxes... gp.AddToolbox("ArcGIS/ArcToolbox/Toolboxes/Data Management Tools.tbx") gp.AddToolbox("DataEast/XToolsPro 4.1/Toolbox/XTools Pro.tbx") gp.AddToolbox("ArcGIS/ArcToolbox/Toolboxes/Analysis Tools.tbx") # Local variables... for i in range(1,2000): exec('hurr_%d_dbf = \"hurr\\hurr_%d.dbf\"' %(i,i)) exec('hurr_%d_Layer = \"hurr_%d_Layer\"' %(i,i)) exec('hurr_%d_line_shp = \"hurr_%d_line.shp\"' %(i,i)) exec('hurr_%d_split_shp = \"hurr_%d_split.shp\"' %(i,i)) exec('hurr_%d_join_shp = \"hurr_%d_join.shp\"' %(i,i)) # # Process: Make XY Event Layer... exec('gp.MakeXYEventLayer_management(hurr_%d_dbf, \"N1\", \"N2\", hurr_%d_Layer, \"\")' %(i,i)) # # Process: Make One Polyline from Points... gp.toolbox = "DataEast/XToolsPro 4.1/Toolbox/XTools Pro.tbx" exec('gp.XToolsPro_Points2Polyline(El_%d_Layer, El_%d_line_shp, \"\", \"USE_INPUT_FEATURES_ORDER\")' %(i,i))

18

# # Process: Split Polylines... gp.toolbox = "DataEast/XToolsPro 4.1/Toolbox/XTools Pro.tbx" exec('gp.XToolsPro_SplitPolylines(hurr_%d_line_shp, hurr_%d_split_shp, \"Split polylines into equal segments\", \"\",\"1000\", \"\", \"\", \"false\", \"\")' %(i,i)) # # Process: Spatial Join... exec('gp.SpatialJoin_analysis(hurr_%d_split_shp, hurr_%d_Layer, hurr_%d_join_shp, \"JOIN_ONE_TO_ONE\", \"KEEP_ALL\", \ "Id Id true false false 6 Long 0 6 ,First,#,hurr_%d_split.shp,Id,-1,-1;N1 N1 true false false 9 Double 2 8 ,First,#,hurr_%d_Features,N1,-1,-1;N2 N2 true false false 9 Double 2 8 ,First,#,hurr_%d_Features,N2, -1,-1;N3 N3 true false false 9 Double 2 8 , First,#,hurr_%d_Features,N3,-1,-1\", \"INTERSECTS\", \"0.001 DecimalDegrees\")' %(i,i,i,i,i,i,i)) if os.path.exists(eval('\"hurr_%d_join.shp\"' %(i))): print "analyzing " + eval('\"hurr_%d_join.shp\"\n' %(i)) fo = open('temp.py','w') fo.write('import sys, string, os, arcgisscripting\n') fo.write('gp = arcgisscripting.create()\n') # Local variables... fo.write('hurr_%d_join_shp = \"hurr_%d_join.shp\" \n' %(i,i)) fo.write('hurr_%d_line_shp = \"hurr_%d_line.shp\"\n' %(i,i)) fo.write('hurr_%d_join__2_ = \"hurr_%d_join.shp\"\n' %(i,i)) fo.write('hurr_%d_line__2_ = \"hurr_%d_line.shp\"\n' %(i,i)) fo.write('hurr_%d_join_buffer_shp = \"hurr_%d_join_buffer.shp\"\n' %(i,i)) fo.write('hurr_%d_line_buffer_shp = \"hurr _%d_line_buffer.shp\"\n' %(i,i)) fo.write(‘historical_wealth_shp = \" historical_wealth’.shp \"\n') fo.write('hurr_%d_intersect_shp = \"hurr_%d_intersect.shp\"\n' %(i,i)) fo.write('hurr_%d_intersect_shp__4_ = \"hurr _%d_intersect.shp\"\n' %(i,i)) fo.write('hurr_%d_intersect_shp__3_ = \"hurr_%d_intersect.shp\"\n' %(i,i)) fo.write('hurr_%d_intersect_shp__2_ = \"hurr_%d_intersect.shp\"\n' %(i,i)) fo.write('hurr_done_%d_shp = \"hurr_final_%d.shp\"\n' %(i,i)) # Process: Define Projection... fo.write('gp.DefineProjection_management(hurr_%d_join_shp, \"GEOGCS[\'GCS_WGS_1984\',DATUM[\'D_WGS_1984\',

SPHEROID[\'WGS_1984\',6378137.0,298.257223563]],PRIMEM[\'Greenwich\',0.0],UNIT[\'Degree\',0.0174532925199433]]\")\n' %(i))

# Process: Buffer... fo.write('gp.Buffer_analysis(hurr_%d_join__2_, hurr_%d_join_buffer_shp, \"29 Miles\", \"FULL\", \"ROUND\", \"NONE\", \"\")\n' %(i,i))

19

# Process: Define Projection (2)... fo.write('gp.DefineProjection_management(hurr_%d_line_shp, \"GEOGCS[\'GCS_WGS_1984\',DATUM[\'D_WGS_1984\',

SPHEROID[\'WGS_1984\',6378137.0,298.257223563]],PRIMEM[\'Greenwich\',0.0],UNIT[\'Degree\',0.0174532925199433]]\")\n' %(i))

# Process: Buffer (2)... fo.write('gp.Buffer_analysis(hurr_%d_line__2_, hurr_%d_line_buffer_shp, \"29 Miles\", \"FULL\", \"ROUND\",\"NONE\", \"\")\n' %(i,i)) # Process: Intersect... fo.write('gp.Intersect_analysis(\"hurr_%d_line_buffer.shp #; \‘historical_wealth’.shp\' #\", hurr_%d_intersect_shp,\"ALL\", \"\", \"INPUT\")\n' %(i,i)) # Process: Calculate Area (2)... fo.write('gp.toolbox = "DataEast/XToolsPro 4.1/Toolbox/XTools Pro.tbx"\n') fo.write('gp.XToolsPro_CalculateArea(hurr_%d_intersect_shp, \"Intersect_area\", \"DO_NOT_PROJECT_DATA\", \"\", \"\")\n' %(i)) # Process: Add Field (2)... fo.write('gp.AddField_management(hurr_%d_intersect_shp__2_, \"Wealth\", \"DOUBLE\", \"\", \"\", \"\", \"\", \"NON_NULLABLE\", \"NON_REQUIRED\", \"\")\n' %(i)) # Process: Calculate Field (3)... fo.write('gp.CalculateField_management(hurr_%d_intersect_shp__4_, \"Wealth\", \"( [Intersect_area]/ [Total_area])* [Year_Wealth]\", \"VB\", \"\")\n' %(i)) # Process: Spatial Join... fo.write('gp.SpatialJoin_analysis(hurr_%d_intersect_shp__3_, hurr_%d_join_buffer_shp, hurr_done_%d_shp, \"JOIN_ONE_TO_ONE\", \"KEEP_ALL\", \"COUNTY COUNTY true false false 25 Text 0 0, First,#,hurr_%d_intersect.shp,COUNTY,-1,-1;STATE STATE true false false 20 Text 0 0 ,First,#,hurr_%d_intersect.shp,STATE,-1,-1;ID_1 ID_1 true false false 19 Double 5 18 ,First,#,hurr_%d_intersect.shp,ID_1,-1,-1;Wealth Wealth true false false 19 Double 0 0 ,First,#,hurr_%d_intersect.shp,Wealth,-1,-1;N3 N3 true false false 11 Double 2 10 ,Mean,#,hurr _%d_join_buffer.shp,N3,-1,-1\", \"INTERSECTS\", \"0 DecimalDegrees\")\n' %(i,i,i,i,i,i,i,i)) fo.close os.system('Python24/python temp.py')

20

6 Advisor Comments

Thesis evaluation by Zhiming Kuang, Assistant Professor of Climate Science:

This project examines the influence of El Nino-Southern Oscillation (ENSO) on the

risks of hurricane damages. ENSO is a prominent climate signal that at the moment can be

forecasted with significant skill more than 6 months ahead, and potentially can be forecasted

more than a year ahead. Thus, if one could establish the influence of ENSO on hurricane

risks, one would be able to skillfully predict seasonal hurricane risks many months ahead,

which is of clear societal importance, and of great interest to the insurance industry as well

as public policymakers. This research makes two significant contributions on this issue;

both will affect future work in this field. The first is on the methodology: it demonstrated

clearly the inadequacy of relying on historical hurricane data alone (or with some statistical

extrapolation) for assessing hurricane risks, which has been the usual strategy in the field,

and presented a new methodology that supplements historical data with synthetic data based

on our physical understanding of hurricanes. The physical model is from work by Prof. Kerry

Emanuel at MIT, but Adam took it further and built a three-component (hazard, damage,

insurance) system that is able to produce information directly usable by the insurance-

reinsurance industry, such as the Industry Loss Warranty price, based on information on

ENSO. Applying this methodology to ENSO (note that the methodology is general and can

be applied to other climate variations such global warming as well) yields interesting and

significant results. This is the second contribution of this thesis. Adam’s results indicate

that vulnerability to hurricane damages scales sub-linearly with wealth, which is attributed

to improved technology, forecasts, and changes in the type of economy. This suggests that

21

previous studies may have overestimated normalized historical hurricane damages. He also

showed that ENSO affects not only the intensity distribution but also the spatial distribution

of the hurricane climatology. This has implications particularly to hurricane risks in New

England and southwest Florida.

The project started with a suggestion by Prof. Dan Schrag to do something related to

hurricanes, and it came to its present form mostly through Adam’s reading and discussions

with various people. I am extremely impressed by Adam’s originality and ability to work

independently. Adam came up with the design of three-component system and put the

different components together on his own. He required virtually no supervision. This is

particularly impressive given the scope of this thesis, which extends from the complicated

physics of hurricanes, to geographic information system, and to the even more complicated

(at least to me) working of the insurance industry. He was able to not only overcome the

technical challenges but also assess objectively the significance and robustness of his and

previous studies in the field. While I knew he was a good student from the very beginning,

what he has accomplished far exceeded my most optimistic expectations. Lastly, the thesis

is very well written and a pleasure to read.

7 Acknowledgments

I am indebted to my thesis advisor for this project, Prof. Zhiming Kuang. My academic

advisor, Prof. Daniel Schrag, was also a great help during the research and writing of this

paper. The physical hurricane model is courtesy of Prof. Kerry Emanuel at MIT. I am

also grateful to Wendy Guan and Guoping Huang at the Center for Geographic Analysis

22

and Scott Walker at the Harvard Map Collection for providing helpful and in-depth GIS

assistance during my research. Chris Walker, a research associate in the Department of

Earth & Planetary Sciences, assisted me in the writing of the Python code to automate the

GIS procedure.

23