Rapid Cost Estimation for Storm Recovery Using Geographic Information System

by Rolando A. Berríos-Montero

B.S. in Industrial and Systems Engineering, June 1998, The Ohio State University M.S. in Engineering Management, June 2001, Polytechnic University of Puerto Rico B.S. in Civil Engineering, June 2012, Polytechnic University of Puerto Rico M.S. in Economics, June 2014, University of Puerto Rico

A Dissertation submitted to

The Faculty of The School of Engineering and Applied Science of The George Washington University in partial satisfaction of the requirements for the degree of Doctor of Philosophy

May 15th , 2016

Dissertation directed by

Jason Dever Professional Lecturer of Engineering Management and Systems Engineering

and

Steven M. F. Stuban Professional Lecturer of Engineering Management and Systems Engineering

The School of Engineering and Applied Science of The George Washington

University certifies that Rolando A. Berríos-Montero has passed the Final

Examination for the degree of Doctor of Philosophy as of March 18 th , 2016. This is the final and approved form of the dissertation.

Rapid Cost Estimation for Storm Recovery Using Geographic Information System

Rolando A. Berríos-Montero

Dissertation Research Committee:

Shahram Sarkani, Professor of Engineering Management and Systems Engineering, Dissertation Co-Director

Thomas Mazzuchi, Professor of Engineering Management and Systems Engineering & Decision Sciences, Dissertation Co-Director

Steven M. F. Stuban, Professorial Lecturer in Engineering Management and System Engineering, Committee Member

Pavel Fomin, Professorial Lecturer in Engineering Management and Systems Engineering, Committee Member

E. Lile Murphree, Professor Emeritus of Engineering Management and Systems Engineering, Committee Member

iii

Dedication

To my beloved wife Ana Ligia and my daughter Ana Cristina…

“…, there are three things we all should do every day. We should do this every day of our lives. Number one is laugh. You should laugh every day. Number two is think.

You should spend some time in thought. And number three is, you should have your emotions moved to tears, could be happiness or joy. But think about it. If you laugh, you think, and you cry, that's a full day. That's a heck of a day. You do that seven days a week, you're going to have something special.”

James Thomas Anthony "Jim" Valvano (March 4 th , 1993)

…because this is how the three of us live every day.

Acknowledgments

I am deeply appreciative of my mother, father and my sister for their continued interest and support of my doctoral journey.

I would like to express my gratitude to my advisors Dr. Stuban and Dr.

Dever for their positive guidance and patience. Their direction and feedback really gave me insight and motivation to continue on this journey.

I am grateful to my classmates who constantly checked on my progress over the last two years. A special thanks to George Wilamowski and Thembani Togwe for caring and for all the influential discussions and support toward the dissertation path. Their support made the world of difference.

Abstract

Rapid Cost Estimation for Storm Recovery Using Geographic Information System

The present research introduces a new approach to estimate the recovery costs of public property in the aftermath of a storm, by integrating Geographic Information

Systems (GIS). Estimating recovery costs for a disaster is a current concern for emergency responders. This work focuses on applying economic indicators, population data, and storm event tracking to GIS for rapidly estimating recovery costs. Firstly, recovery costs of historical events are normalized and adjusted for inflation, wealth, and population. Geospatial analysis is used to predict, manage, and learn political boundaries and population density. Secondly, rapid recovery cost estimation is accomplished by defining population, personal income, and gross domestic product. Finally, a jurisdiction fiscal capacity (JFC) is calculated illustrating the economic capability of jurisdictions to finance public property recovery, based on their economy size. The variability of estimated absolute errors between cost estimates and actual normalized costs are also examined. The results reveal that JFC is a more suitable metric for rapidly estimating recovery costs of public properties than the method presently followed by the Federal Emergency

Management Agency. This new approach effectively aids the local government in providing quick cost guidance to recovery responders, while offering the ability to construct accurate recovery cost estimates.

Table of Contents

Dedication ...... iii

Acknowledgments...... v

Abstract ...... vi

Table of Contents ...... vii

List of Figures ...... ix

List of Tables ...... xi

List of Acronyms ...... xii

Chapter 1. Introduction ...... 1 1.1 Systems Engineering Cost Estimation ...... 1 1.2 Problem Statement ...... 2 1.3 Purpose ...... 3 1.4 Approach ...... 4 1.5 Significance ...... 7 1.6 Limitation ...... 7 1.7 Outline ...... 8

Chapter 2. Literature Review ...... 10 2.1 Actual cost estimation models ...... 10 2.1.1 Components of actual cost estimating models ...... 12 2.1.2 Florida public hurricane loss projection model ...... 16 2.2 Cost estimation...... 19 2.3 GIS-based cost estimate ...... 22

Chapter 3. Data ...... 29 3.1 Storms ...... 30 3.2 Historical recovery cost ...... 32 3.3 Population and economic indicators ...... 32

vii

Chapter 4. Methodology ...... 35 4.1 Methodology approach ...... 35 4.2 Storm analysis ...... 38 4.3 Normalized Cost ...... 42 4.4 Jurisdiction fiscal capacity ...... 43 4.5 Recovery cost estimation ...... 44

Chapter 5. Results and Analysis ...... 48 5.1 Mahalanobis Distance (MD) ...... 52 5.2 Hurricane Georges as outlier ...... 56 5.3 Median absolute deviation (MAD) ...... 58 5.4 GIS output ...... 71 5.5 Cost exceedance probability ...... 82 5.5.1 Random sampling methodology ...... 83 5.6 Log-normal distribution ...... 86

Chapter 6. Conclusion ...... 89 6.1 Recommendations for future research ...... 91

References ...... 92

Appendix A: Jurisdictions affected per storm ...... 103

Appendix B: Mahalanobis Distance MATLAB ® code ...... 133

Appendix C: Cost exceedance probability MATLAB ® code...... 135

viii

List of Figures

Figure 4.1 GIS Model Flow Diagram ...... 36

Figure 4.2 ArcMap® Attribute table implemented for hurricane Irene ...... 38

Figure 4.3 Count per month of storms ...... 39

Figure 4.4 Cumulative distribution function of storms ...... 39

Figure 4.5 Puerto Rico’s storm count ...... 41

Figure 4.6 ArcMap ® Fields Calculator window for recovery cost estimation ...... 44

Figure 5.1 7Bar graph of the normalized recovery cost and the recovery cost estimate. .. 51

Figure 5.2 8Mahalinobis distance plot ...... 55

Figure 5.3 9Euclidian distance plot ...... 55

Figure 5.4 10 Mahalinobis distance scatterplot ...... 57

Figure 5.5 11 Actual FEMA estimates and the Rapid Cost Estimates Error Bound Plot..... 65

Figure 5.6 12 Adjusted FEMA estimates and the Rapid Cost Estimates Error Bound Plot . 65

Figure 5.7 13 Error absolute values deviation from median: Rapid Cost Estimate ...... 66

Figure 5.8 14 Error absolute values deviation from median: Actual FEMA estimate ...... 67

Figure 5.9 15 Error absolute values deviation from median: Adjusted FEMA estimate ..... 67

Figure 5.10 16 Normal probability plot: Rapid Cost Estimate ...... 69

Figure 5.11 17 Normal probability plot: Actual FEMA Estimate ...... 69

Figure 5.12 18 Normal probability plot: Adjusted FEMA Estimate ...... 70

Figure 5.13 19 NOAA-Historical Hurricane Tracks Hugo (1989) ...... 72

Figure 5.14 20 ArcMap® Hugo GIS-based model output ...... 73

Figure 5.15 21 NOAA-Historical Hurricane Tracks Hortense (1996) ...... 74

Figure 5.16 22 ArcMap® Hortense GIS-based model output ...... 75

Figure 5.17 23 NOAA-Historical Hurricane Tracks Georges (1998) ...... 76

Figure 5.18 24 ArcMap® Georges GIS-based model output ...... 77

Figure 5.19 25 NOAA-Historical Hurricane Tracks Jeanne (2004) ...... 78

Figure 5.20 26 ArcMap® Jeanne GIS-based model output ...... 79

Figure 5.21 27 NOAA: Historical Hurricane Tracks Irene (2011) ...... 80

Figure 5.22 28 ArcMap® Irene GIS-based model output ...... 81

Figure 5.23 29 Cost exceedance probability curve ...... 85

Figure 5.24 30 Log-normal distribution ...... 87

Figure 5.25 31 Kolmogorov-Smirnov Test MATLAB® output ...... 88

Figure 6.1 32 Puerto Rico storm recovery cost trends...... 90

List of Tables

Table 3.1 GIS database by layer...... 29

Table 3.2 Storm and hurricane events ...... 31

Table 3.3 Economic indicators ...... 33

Table 4.1Population...... 46

Table 5.1 Comparison between actual costs normalized to year 2012, FEMA estimate, and the rapid costs estimates...... 50

Table 5.2 Percentage and error difference between normalized cost and the rapid cost estimation as an input to analyze MAD...... 59

Table 5.3 Percentage and error difference between normalized cost and the FEMA estimation as an input to analyze MAD...... 60

Table 5.4 Rapid Cost Estimate sorted data per percentile and the MAD...... 61

Table 5.5 FEMA Estimation sorted data per percentile and the MAD output per storm. 62

Table 5.6 6Comparison between new adjusted FEMA estimate MAD and Rapid Cost Estimate MAD ...... 63

Table 5.7 Regression Analysis R 2's ...... 70

List of Acronyms

CDF Cumulative Distribution Functions

C.F.R. Code of Federal Regulations

ECDF Empirical Cumulative Distribution Functions

DLI Damage Loss Indicator

FEMA Federal Emergency Management Agency

GAO U.S. Government Accountability Office

GDP Gross Domestic Product

GIS Geographic Information Systems

H Hurricane

JFC Jurisdiction Fiscal Capacity kn knots

MAD Median Absolute Deviation mb millibars

MD Mahalinobis Distance

N North

NOAA National Oceanic and Atmospheric Administration

PDA Preliminary Damage Assessment

PI Personal Income

PREMA Puerto Rico Emergency Management Agency

R2 R-Square

SS Severe Storm

TS Tropical Storm

xii

TTR Total Taxable Resources

USD U.S. Dollar

W West

xiii

Chapter 1. Introduction

1.1 Systems Engineering Cost Estimation

Systems engineering is a disciplined approach to design, plan, specify, integrate, implement, operate, and maintain complex systems. Any system development relies on a planning process, however one significant task that makes the planning process difficult is cost estimation. Cost estimation provides necessary information to facilitate a decision making process regarding resources, equipment, materials, and supplies needed. Cost estimation information can even have a direct impact on a schedule or vice versa. More importantly, cost estimation is the fundamental process that allows the development of systems.

Certainly, decisions made while restoring public properties after a storm disaster drive emergency management systems’ recovery and operation costs. In order to receive adequate recovery funding, it is imperative to know and understand how to accurately estimate potential expenses to restore public properties. A well-developed cost estimation approach is a decision-support tool within systems engineering.

1.2 Problem Statement

A system to rapidly estimate the cost of restoring public properties after a storm disaster would assist state and local governments by providing an indicator of resilience. A recovery cost estimation includes the cost of restoring public properties to their original condition, prior to the physical damage caused by the storm (Fujimi & Tatano, 2012). Such estimations tend to be onerous and time- consuming tasks for emergency management officials, because the costs of a natural disaster are linked to several factors and vary according to storm categories. Zandbergen (2009) states that the storm surge presents the greatest hazard to low-lying coastal areas, but the wind and rain hazards can have a greater impact because they can reach further inland. Therefore, these natural events often cause damage extending hundreds of miles inland, destroying public buildings, roads, and bridges.

Estimating the reconstruction costs in the aftermath of a storm requires a careful and time-consuming analysis (Dorra, Stafford, & Elghazouli, 2013; Fujimi

& Tatano, 2012; Coffman & Noy, 2011; Huang et al., 2008; Tatano & Tsuchiya,

2008; Dutta, Herath, & Musiake, 2003). This research concentrates on rapid recovery cost estimation using a Geographic Information Systems (GIS), and includes costs related to public property assets such as public buildings, roads, bridges, water systems, and the power transmission infrastructure. The recovery cost estimate assumes that public properties physically affected by a storm are to be restored to their original condition.

1.3 Purpose

This research considers the cost estimation approach of the U.S. Federal

Emergency Management Agency (FEMA), which is based on a preliminary damage assessment (PDA). Then, a proposed method is demonstrated to estimate this cost by applying jurisdiction economic indicators, population, and storm tracks to a GIS.

Currently, each jurisdiction affected by a storm event sends local private contractors, government representatives, and FEMA officials to visually inspect damage sites and provide early cost estimates under disaster conditions. These cost estimates are considered by FEMA when completing a PDA, which is a joint assessment to determine the impact of the storm damage and to decide whether federal assistance is needed. The PDA considers statewide and countywide per- capita indicators, which are adjusted annually for inflation. The statewide and countywide indicators for the United States in 2012 were 1.35USD and 3.39USD, respectively (GAO, 2012). These indicators are determined by FEMA based on

1983 per capita personal income nationwide. Moreover, the actual recovery costs are recorded and maintained by FEMA, because this information is a necessary part of its Public Assistance Grant Program. This program assists all U.S. jurisdictions in responding to and recovering from major disasters or emergencies declared by the President (GAO, 2012).

The purpose of this research is to identify and propose a more accurate method to estimate recovery costs of physically damaged public properties. The

3 integration of GIS-readable database, including jurisdiction economic indicators, public building locations, political boundaries, municipality population, and storm track is a more suitable approach than FEMA-used statewide per capita indicator for rapidly estimating recovery costs of public properties in the aftermath of a storm event.

1.4 Approach

This investigation presents a systematic approach to rapidly estimating the recovery costs for public properties by incorporating the jurisdiction fiscal capacity (JFC), population, and event track data in a GIS. The GIS-readable database includes public jurisdiction economic indicators, building locations, political boundaries, municipality populations, and storm intensity profiles. Using the database, the systematic cost estimate model simulates storm damages based on historical storm data and normalized damage costs. Then, the JFC is determined in U.S. dollars by calculating the total taxable resources (TTR). This provides a more sensitive adjustment for growth over time in a jurisdiction than does an adjustment for inflation based on personal income (GAO, 2001). A more suitable public property cost estimation can be obtained from the JFC because it reflects a jurisdiction’s current fiscal reality, as well as its response and recovery capabilities (GAO, 2012). TTR is a comprehensive measure of all sources of income that a state could conceivably tax, irrespective of the state’s actual tax policies (Compson, 2003). Therefore, integrating the JFC into the model enables us to estimate recovery costs and improves our ability to assess a jurisdiction’s capacity to respond and recover on its own.

This research presents a new approach to estimating the costs of restoring public properties that have suffered physical damage. It is shown that integrating a

GIS-readable database is a more suitable approach to rapidly estimating recovery costs than is the statewide per capita indicator used by FEMA. Moreover, this results from the proposed model better reflecting actual recovery costs than does the current FEMA method.

A GIS-based cost estimation model requires parameters that describe the subject geography in the geodatabase. Similarly, the GIS-based application provides resources to display storm event tracks. These data are then overlaid with maps of the population, industrial public properties, and estimated costs in order to provide a rapid recovery cost estimate. GIS layers such as storm tracks, political boundaries, industrial public properties, population, and historical recovery costs have been developed into a geodatabase to rapidly and more accurately estimate costs in the aftermath of a storm event. For instance, Elsner (2003) and Camargo et al. (2007) used GIS layers in cluster methods on storm locations to construct storm tracks.

First, the GIS software is used to obtain shapefiles that describe the basemap of the study area. These shapefiles include political boundaries, storm tracks, jurisdictions affected by storms, and public buildings. Second, attribute tables are loaded with economic indicators, recovery costs, and population data.

Population and economic indicators are essential to adjusting recovery costs over time to a notional economic value in year 2012. The cost estimations are normalized to adjust for inflation, wealth, and population. Then, the JFC

5 measurement is calculated to rapidly and more accurately estimate the recovery costs. Recovery cost estimations are important for the accountability of emergency responder officials. These officials develop a general framework that implements appropriate analytical models to estimate the recovery costs (FEMA, 2011). This research also includes an exceedance probability analysis to estimate yearly recovery costs that exceed specified amounts. Using a GIS provides several benefits to emergency responders, including quick access to prior recovery cost data, data analyses, and the presentation of results (Burrough, 2001). This systematic GIS-based cost estimation approach interacts with a geodatabase of economic indicators and storms in order to rapidly estimate the costs of recovery for public properties. Moreover, an exceedance probability analysis determines the likelihood of a recovery cost occurring. Then, the JFC analysis provides new insights into how jurisdictions have responded to needs and services, while still being able to analyze variations across states (Mikesell, 2007).

The cost exceedance probability is calculated by fitting the normalized cost data set to an exponential distribution, and then calculating the storm event values from a cumulative distribution function. Because the frequency of a storm event is unknown, this event is defined as a random variable x, with an exponential distribution. In other words, an exponential distribution is used to estimate the relevant costs when a storm occurs. Hence, considering an exponential and a

Poisson distribution, with specified parameters, random variables for each storm can be generated in order to estimate the recovery costs based on a simulation with a large set of events. This process is repeated in a simulation at least 20,000 times

6 in order to obtain a cost exceedance probability curve and its 95% confidence band. An exponential fit uses the mean value to create an exponential distribution, from which the cost estimates may be sampled. The simulation is used to develop the cost exceedance probability curve. This curve shows the probability of any given recovery cost being exceeded after a storm, within a given cost range.

1.5 Significance

The significance of this work relies on the accuracy of cost estimations, within the time limitation constraint on emergency responders. Recovery cost estimation is important for the accountability of emergency responder officials, who develop a general framework implementing analytical models appropriate to estimating these costs. Using a GIS provides several benefits to emergency responders, including rapid access to prior recovery costs, data analyses, and the presentation of results (Burrough, 2001). Moreover, the JFC analysis provides insights into how jurisdictions have responded to needs and services, while still being able to analyze variations across states (Mikesell, 2007). This systematic

GIS-based cost estimation approach interacts with a geodatabase of economic indicators and storms to rapidly estimate the costs associated with the recovery of public properties.

1.6 Limitation

Emergency response agencies currently use a variety of approaches to assess the overall damage, loss, and recovery costs after a storm event (Nadi et al.,

2010). This research is limited to accurate recovery cost estimations for public

7 properties, and presents a finite approach to rapidly estimating these costs by applying GIS technology. A geospatial approach is applied to identify municipality boundaries and population densities, as part of the cost estimation calculation. Storm intensity characteristics, such as precipitation and sustained winds, are beyond the scope of this research. The investigation focuses on the jurisdiction of Puerto Rico to validate the GIS-based cost estimate model, and considers only those storm events that damaged public properties.

1.7 Outline

The dissertation is organized as follows:

Chapter 2 presents the literature review. This is an exhaustive exposition of previous research on cost estimation, as well as recovery based on GIS-based cost estimations. Examples of previous recovery cost applications are presented. In addition, this chapter explores the links between previous solutions and the proposed GIS-based cost estimate approach in order to rapidly estimate the recovery costs for public properties.

Chapter 3 presents the data and data sources used during the research.

Types of data and domains are analyzed to demonstrate the capability of the formulation to estimate recovery costs. Some data are overlaid with population maps, public building properties, economic indicators, and estimated costs to rapidly provide cost information for the identified storm events.

Chapter 4 discusses the rapid recovery cost estimation method, including using a GIS. Then, the chapter discusses applying a statistical analysis to evaluate the storm occurrence distribution. Moreover, it presents using the quantitative formulation to determine a recovery cost estimate in a timely manner using a

ArcMap ®, a GIS software.

Chapter 5 presents and analyzes the results of the GIS-based cost estimation model. The results and GIS outcomes are presented for various storms, and the major finding are discussed. The outcomes show that incorporating a fiscal capacity indicator in the GIS-based cost estimation analysis produces estimated costs that are close to the actual costs.

Chapter 6 concludes the dissertation with a discussion of the GIS-based cost estimation, applying the JFC, and provides recommendations for possible future work.

Chapter 2. Literature Review

This chapter presents an exhaustive exposition of current cost estimation models, previous research on cost estimation, and applying GIS to recovery cost management. This includes introducing concepts such as loss and recovery costs.

Moreover, the GIS-based model for rapid recovery cost estimation is introduced because this is the focus of the research described here.

2.1 Actual cost estimation models

Cost estimation techniques are widely employed to estimate the financial value of the probable damage to properties caused by storms. These techniques help government emergency responders and insurance companies to identify how much damage has occurred and estimate how much claimants will apply to recover for losses.

Watson and Johnson (2004) describe the actual components of prediction models. However, these are highly abstracted because the models are proprietary and mostly used by insurance companies and mortgage holders, which limits government agencies and insurance companies in conducting exhaustive benchmark analyses on the effectiveness of the models. Nevertheless, these models include a number of common components. This section describes a few cost estimation models by applying them to real scenarios.

Storm models have always attracted a lot of attention among practitioners and academic researchers. Storms models are quite different to traditional actuarial models or methods used to determine rates based on previous recovery costs for a given set (Watson & Johnson, 2004). In terms of modeling low probability and high severity events such as windstorms, Watson and Johnson (2004) have also noted that actuarial methods lose credibility. Theoretically, cost estimation models based on current storm exposures should be able to produce more accurate results.

However, it is difficult for emergency responders or others involved in the process to assess the validity of these models. For instance, insurers find it challenging using these models to establish fair and accurate rates (Watson & Johnson, 2004).

A wide variety of research is available on the differences among storm models, including studies by engineers, insurance researchers, and meteorological researchers. These researchers have been able to establish differences based on meteorological assumptions, such as topography, decay rates, wind fields, and landfall frequencies. A few other factors have also been identified as important, including changes in global climate, surges in demand, insurance contracts, and expenses based on loss adjustments (Canabarro, 2000). For instance, the Florida

Commission on Hurricane Loss Projection Methodology (2007), in a report to the

Florida House of Representatives, examined the variations in model outputs across all models, using county level as the benchmark. They found that two models, namely the Public Model and ARA Model, had the most observations outside the set benchmark. A few other researchers have found differences in the ultimate loss cost models, based on the assumptions in the models. For example, the range of

11 loss costs can be quite large, with a 3 to 1 ratio, or higher (Watson et al., 2004).

This ratio could be even higher for inland areas. These variations in loss costs cause disparities in pricing models for some locations.

For instance, insurance companies have developed catastrophe models, which use complex computer simulations. Insurers worldwide use these models to predict potential recovery costs after hurricanes, tornadoes, or earthquakes. They use the simulations to help manage portfolios and make decisions on risk and pricing. Currently, four private companies offer storm recovery cost estimation models that have been approved for use in Florida: AIR Worldwide, Applied

Research Associates, EQECAT, and Risk Management Solutions (Jeanine-Brown,

2011).

The implications of these models are wide. Variations among the models affect the recovery costs, pricing, and premiums and, ultimately, on insurance- linked securities. There is an increasing need for in-depth research in this area in order to develop better models and, thus, better estimates with less variation

(Jeanine-Brown, 2011).

2.1.1 Components of actual cost estimating models

Storm cost estimation models usually consist of five critical components (Watson

& Johnson, 2004):

1. Input databases

2. Wind models

3. Boundary layer models

4. Damage function

5. Frequency of occurrence models

A description of each component follows.

Input databases: Existing cost estimation models use an input database with a minimum of three input data sets (Watson & Johnson, 2004):

a) Land cover data sets include information on the general coverage of

the area within the scope of exposure. This may vary in the level of

detail, from basic information (e.g., is it land or sea) to more

sophisticated categorizations, such as the trajectory-based model with

72 land type classifications.

b) Exposure data sets contain data that describe the location and the

value of the risk. These data sets also contain information on the

types of structures within the scope of exposure, as well as the

effectiveness of code enforcement, which significantly influences the

extent of damage during impact. Because the complete range of

construction types in an area may be unknown, data sets are based on

the typical construction mix in the area.

c) Historical storm tracks and intensities are usually maintained in the

library for simulations of historical events and analyses of their

frequency.

Wind models: Like the land models, wind models range in complexity, from the simple Rankine Vortex model to complex parametric models to full three- dimensional physics models. Almost all wind models used by insurance companies are parametric (Malmquist & Michaels, 2000). These models employ simple storm parameters such as forward speed, minimum central pressure, radius of maximum winds, and so forth.

Boundary layer models: These models correct the results produced by the wind models when the raw winds hit the surface conditions. In theory, this model adjusts the results using a multiplication factor. However, there is no consensus in the literature on what the correct factor should be. It is generally about 0.85 over water, and 0.7 over land, but varies greatly in complexity for various terrain types.

Damage function: The damage function associates the wind deposited on an exposure site to the damage expected at the site. Damage functions may generally be grouped into three broad classes (Malmquist & Michaels, 2000):

a) Claims based

b) Engineering judgment

c) Theoretically based

Claims-based functions analyze actual claims submitted to insurance companies. Despite their logical simplicity, such estimates are largely subjective, and depend on several administrative, political, and other considerations that differ between storms (Watson & Johnson, 2004).

Engineering judgment-based functions are based on the damage to structures, as determined by an engineering survey. Here too, individual interpretation may vary substantially (Chen et al., 2009).

Theoretical functions are based on the physics of the behavior of structures.

Although human judgment in this model is minimal, this model must be compatible with the other components of the overall loss estimation model

(Dunion et al., 2003).

Frequency of occurrence: The components mentioned so far are used to estimate the magnitude of the loss for a single occurrence of an event. In order to estimate holistic levels of losses from hurricanes in a particular area, the frequency component is used. There are three common approaches to including frequency information:

a) Rely on historical events

b) Fit and smooth probabilities along coastal segments

c) Reproduce hurricane formation and movement in a realistic fashion

Relying on historical events presumes that future tropical cyclone activity will follow patterns similar to those that have occurred previously. The second approach involves fitting the frequencies of historical events by coastal segments in order to match modeled landfalls (Schwerdt, Ho, & Watkins 1979). The third approach can be accomplished using either statistical or climate models. The statistical methods can be summarized as follows (Watson & Johnson, 2004):

a) Historic storm set estimation

b) Monte Carlo simulation and estimation

c) Maximum likelihood estimation approach

2.1.2 Florida public hurricane loss projection model

In this section, the discussion moves away from the theory to examine models being used in practice. As an example, the Florida loss prediction model is considered. In terms of design, the model is composed of three components (FIU Public Hurricane Loss

Projection Model, 2014, cited by Johnson & Watson, 2004):

a) Wind vulnerability (engineering)

b) Insured loss cost (actuarial)

c) Hazard (meteorology)

This computer platform has further sub-components, and is designed to accommodate additional hook-ups, if required (FIU Public Hurricane Loss Projection

Model, 2014). Apart from assessing hurricane risks, the model can predict expected 16 annual losses for insured residential areas in Florida, up to the zip code level. The complete model for risk assessment has been built from several parts, including: the wind field model, the vulnerability model, the exposure study, actuarial components, and the computer platform. Most models use a regression analysis of claims data to define the vulnerability of homes. Instead, this model defines damage using a different component approach that considers the resistance capacity of each component of a home and the wind forces produced at increasing increments of wind speed (Pinelli et al., 2004).

The estimated loss can be broken down into components of structure, content, and additional living expenses. Further portfolio classifications by construction type and territory ratings, and combinations thereof, are also possible in this model. For a given portfolio of policies, the model can generate the probability of exceedance, return time, and probable maximum loss (Pita et al., 2013).

Components of the wind models include the following (FIU Public Hurricane Loss

Projection Model, 2014):

a) Storm track and intensity model: Generates storm tracks and intensity for

simulated hurricanes based on historical initial states

b) Inland storm decay model: Calculates decay after landfall

c) Wind field model: Creates open terrain wind speeds for hurricane-affected

zip codes

d) Gust factor model: Generates peak wind speeds

e) Terrain roughness model: Corrects wind speed for terrain roughness

f) Wind probabilities model: Creates wind probabilities

Components of the vulnerability model include the following (FIU Public

Hurricane Loss Projection Model, 2014):

a) Engineering simulation model: Simulates possible wind damage to the

structure, interior, and content

b) Engineering damage model: Produces damage matrices and ratios for a

structure

c) Engineering mitigation model: Creates vulnerability functions (damage

matrices) for mitigated structures

Components of the insured loss model include the following (FIU Public

Hurricane Loss Projection Model, 2014):

a) Policy modifications model: Models deductibles and policy limits

b) Insured loss actuarial model (probabilistic): Estimates annual loss costs for

each policy, or portfolio of policies, or by area and construction type,

including adjustments for deductibles and limits

c) Insured loss actuarial model (scenario based): Creates expected loss costs for

a specific hurricane affecting a given area.

The reliability of a model has significant implications for several institutions, and their major decisions. However, in their current state, these models do not show consistently accurate results (Watson & Johnson, 2004). Although the primary improvement scope lies in the field of meteorology, substantial steps in related fields, such as computational statistics, and disclosure efforts will help to make the science of recovery cost estimation more reliable.

2.2 Cost estimation

Cost estimations for public property damage occur shortly after a natural disaster. Certainly, states and local governments need cost information to make budgetary and feasibility decisions in order to complete a recovery system plan.

Estimating costs tends to be an onerous and time-consuming task for emergency management officials, because the cost of a natural disaster depends on several factors and varies according to the type of disaster. In addition, a GIS is a valuable tool in a natural disaster recovery cost estimation system because it can provide summarized information on demand.

AACE International, formerly known as the American Association of Cost

Engineering, defines cost estimating as “the predictive process used to quantify, cost, and price the resources required by the scope of an investment option, activity, or project.” From the literature, some studies use this process when determining economic loss or economic cost. Even though economic cost considers tangible and intangible damage (Dorra et al., 2013; Fujimi & Tatano,

2012; Coffman & Noy, 2011; Huang et al., 2008; Tatano & Tsuchiya, 2008; Dutta

19 el at., 2003), this investigation concentrates on cost estimation for tangible public properties. Tangible property includes physical public property assets such as public buildings, roads, bridges, water systems, and the power transmission infrastructure. On the other hand, intangible losses refer to the loss of human life, business interruption, ecosystem services, physical and psychological impacts, evacuation and rescue operations, health-care assistance, and traffic disruption, among others. The recovery costs for tangible properties include repair and replacement expenses to restore public properties to their original condition after suffering physical damage (Fujimi & Tatano, 2012).

However, the most appropriate measure of the economic cost is the market value of a property just before the disaster hit versus the replacement cost to rebuild it (Kousky, 2011). The replacement cost could be higher or lower, for several reasons. For instance, in a post-disaster scenario, some materials may be in short supply and more expensive substitutes might need to be used. In addition, labor may be in short supply, making wages higher, and driving the cost of rebuilding above what it would have been before the disaster (Olsen & Porter,

2008).

Cost estimation concepts have been tested previously. However, possible gaps in the accuracy of recovery cost estimations for infrastructure remain in the literature (Cheng & Yang, 2001; Tatano & Tsuchiya, 2008). In some cases, buildings and infrastructure may seem totally destroyed, but then turn out to be only partially damaged. One characteristic common to all natural disasters is that damage estimates calculated shortly after a disaster tend to be significantly

20 underestimated. In order to successfully complete a cost estimate, estimators need to understand clearly the project deliverables required to prepare estimates

(Dysert, 1997).

Cost estimation should depend on good systems of methods and procedures that meet the disaster recovery requirements (Hallegatte, 2014). For instance,

Franco et al. (2010) use a mathematical algorithm based on field surveys to obtain approximate cost estimates for repairs to components that tend to drive the overall repair cost. Algorithms provide specific steps to record the variables to be considered within the estimation methods and procedures.

Empirical studies and cost estimation methodologies have been completed.

For instance, the construction cost trend for the Louisiana Highway Department after Hurricane Katrina was studied by Cheng and Wilmot (2009). The authors showed how construction costs increased 51% in the aftermath of the storms, whereas the same construction costs decreased in other parts of the state. Even though they acknowledge that the trend in construction costs lasts for approximately two quarters, this economic competitive market behavior demonstrates a classic relationship between demand and supply. They conclude that the Louisiana Highway Cost Index trends show that Hurricanes Katrina and

Rita had a significant influence on Louisiana’s highway construction costs.

Similarly, Padgett et al. (2008) evaluated bridge damage patterns after Katrina, including damage attributed to wind, water inundation, and impact from debris, as well as examples of transportation system reconstruction and recovery measures to restore functionality. An analysis of their data indicated a relationship between the

21 surge elevation, damage state, and resulting repair costs. It was also shown that the normalized repair cost was typically highly nonlinear, as a function of damage state (Padgett et al., 2008). Karlaftis, Kepaptsoglou, and Lambropoulos (2007) developed an algorithm to support a three-stage approach for allocating repair funds to an urban bridge network following a natural disaster. Their methodology allocates available funds to repair bridges to their lowest acceptable operational level. Then, they estimate the bridge network repair costs.

To conclude, a rapid recovery cost estimation offers a better understanding of the impacts of a tropical storm disaster. In addition, it provides guidance for recovery management systems and the ability to construct an accurate cost estimation process, with built-in accountability for emergency responders. Here, a new recovery cost estimation model, including a GIS, is presented. This systematic GIS-based cost estimation approach interacts with a geodatabase of economic indicators and storms to rapidly estimate the cost of recovering and restoring public properties.

The link between cost estimation and the GIS application for rapid recovery cost estimation is discussed in more detail in the next section.

2.3 GIS-based cost estimate

In the previous section, we investigated the term cost estimation. In this section, we focus on using a GIS as a tool in cost estimation. Martin et al. (2001) estimated the road maintenance cost per kilometer by characterizing pavement maintenance costs using a GIS. The GIS-based model includes a road network

22 represented as connections of nodes and links. ArcView ® routing algorithms were developed to calculate the minimum distance path and minimum maintenance cost.

Similar applications have been adopted for emergency responders. When disaster strikes, a GIS helps responders assess emergency management and resilience activities. Reliable data on economic indicators and the recovery costs for public properties after storms, as well as how these costs differ spatially, would be valuable to disaster responders. A GIS is an excellent tool to maintain data and help provide rapid cost estimations, as well as to improve the communication and performance of management systems. GIS-based cost estimate applications also help to improve emergency response government agencies, hold government officials accountable, and promote responder effectiveness.

Integrating a GIS into the recovery cost estimation process provides a visual structure for conceptualizing different storm scenarios, and facilitating resiliency and recovery decision-making (Shrestha & Shrestha, 2014).

A GIS-based cost estimating system to support recovery cost estimations after a storm event is an excellent tool to facilitate decision-making at all levels of government. In fact, recovery cost estimation can be used to review and evaluate disaster recovery planning, construction codes, and future economic and land development.

During the past few decades, GISs have created opportunities for more detailed and rapid analyses of natural hazards. When weather-related disasters impact a jurisdiction, many states, counties, and cities use a GIS for emergency

23 response and disaster recovery. For instance, a GIS is used to create specialized maps, enabling emergency responders to make sense of the ruins left behind by a natural event (Nadi et al., 2010). A notable recent application was documented by

Armenakis and Nirupama (2013), where they include a GIS-based tool for disaster risks by integrating a spatial analysis with disaster management for the Toronto propane explosion in 2008. The study shows how including spatial overlays and attribute information related to people’s vulnerability helped to identify evacuation zones and critical infrastructure. Specifically, they cite Carr and Zwick

(2005), Church and Murray (2009), Kar and Hodgson (2008) with regard to geospatial information science and GIS technologies, which support site- suitability analyses in relation to the surrounding locations and population. Spatial analysis is a key technique when using a GIS as a tool for natural disaster recovery, because it locates various facilities in a given area, at the local and national level, depending on the area under consideration (Bansal, 2014).

Eveleigh, Mazzuchi, and Sarkani (2007) state that GIS technology is an excellent tool for managing data with a spatial component and exploiting spatial operators, such as contiguity, intersection, proximity, shape, and position, to support advanced data query, processing, and fusion. Furthermore, Yamamoto (2012) points out that a GIS has four major functions: (1) a database construction function; (2) an information analysis function; (3) an information sharing function; and, (4) a decision-making support function. These functions provide the information system with the link between the real world and the virtual world.

Moreover, he notes that GISs have such superior and unique functions that they

24 may become the basis for an information infrastructure that plays an important role in recovery and reconstruction.

Cost estimations for public properties can be extremely difficult to determine accurately in the aftermath of a storm disaster event. The cost assessment varies depending on the perceptions of the respondent and on site accessibility. Though a number of studies on recovery cost estimations have been completed over the years, there is insufficient research on applying a GIS to rapidly determine recovery costs. Cheng and Yang (2001) suggest a system that integrates a GIS-based cost estimation with construction-planning processes.

Similar GIS-based cost estimations can be achieved by integrating geographical systems into the information management of a population, storm tracks, and minimum pressure, in conjunction with economic cost damage indicators, in order to rapidly estimate recovery costs after a storm.

GIS capabilities allow an analysis of the relationship among the socioeconomics characteristics and physical features of a jurisdiction (Taupier &

Willis, 1994). For instance, FEMA uses Hazus as a GIS solution, which contains residents’ socioeconomic characteristics data, as well as structural industrial, commercial, and residential buildings (Schneider & Schauer, 2006). Hazus can model a hypothetical storm event and analyze the damage states of both residential and commercial properties. However, it is intensive in terms of data input, and takes a significant length of time to complete (Pan, 2014).

The Hazus–MH Hurricane Wind Model enables users to estimate the economic and social losses from a storm, and facilitates a more accurate way of preparing for eventualities from all spheres. Relevant stakeholders, primarily state officers, often use the information provided by this model to evaluate, plan for, and mitigate the effects of hurricanes. The Hazus–MH Hurricane Wind Model makes this possible by employing a state-of-the-art wind field model, which has been calibrated and validated using full-scale hurricane data. This version of the

Hazus–MH model incorporates sea surface temperatures in the boundary layer analysis, and calculates wind speed as a function of translation speed, central pressure, and surface roughness (Hazus-Multi Hazard Hurricane Wind Model,

2014).

Currently, the recovery costs for public properties are estimated by the local government and FEMA by applying personal income per capita. An independent auditor’s report, GAO-12-838, from the U.S. Government

Accountability Office (GAO), states that FEMA relies on the personal income indicator to determine and estimate whether to recommend to the President that a jurisdiction needs public assistance funding after a natural disaster (p. 2). This indicator has been 3.50USD per capita since 2013. Geographic indicator differences affect the level of need in each jurisdiction (Compson, 2003). FEMA’s current PDA approach does not accurately reflect public property recovery costs or whether a jurisdiction can recover from a disaster without federal assistance

(GAO, 2012).

A systematic approach that rapidly adjusts cost estimations would more accurately reflect the variations in costs (GAO, 2013). This can be achieved by integrating a geographical system into reliable data of a storm’s profile, recovery costs, political boundaries, population, and economic indicators, which include inflation, personal income, gross domestic product (GDP), and wealth. These data can be utilized as the key input to providing a storm event recovery solution. The fact that public infrastructure grows as an economy develops (Imran & Niazi,

2011) gives us a reason to consider a jurisdiction’s economic indicators in a GIS analysis. This links the analysis to GDP and population, which relates to public infrastructure literature. GDP is a measure of a jurisdiction's current production of goods and services in a certain period, and its fluctuations can be explained by changes in the population. In macroeconomics, GDP is the broadest economic indicator measuring a country's economy, and is often considered a lagging indicator (Kitchen & Monaco, 2003). In addition, GDP is considered the basic economic indicator of the wealth of a region. The literature on public infrastructure and growth focuses on how the demand for a physical infrastructure has direct and indirect effects on economic growth (Agénor & Moreno, 2006;

Hashimzade & Myles, 2010; Imran & Niazi, 2011). In fact, public property reconstruction increases GDP because there is an increase in construction spending in affected jurisdictions in the years following a natural disaster (Cashell &

Labonte, 1992).

The GIS-based cost estimate solution described here demonstrates how to rapidly estimate recovery costs for public properties. The results show clear

27 evidence that incorporating a fiscal capacity indicator into a GIS-based cost estimation analysis produces a recovery cost that is close to actual recorded costs.

Chapter 3. Data

This research presents a GIS-based model to rapidly estimate the recovery costs for public properties after a storm event. As an application, we focus on the island of Puerto Rico, which is located in the Caribbean Sea and has an area of

3,425 square miles. The island is centered at 18.15° N, 66.30° W. This application requires parameters to describe the subject geography and the storm in the geodatabase. Similarly, the GIS application involves mapping rare and storm event tracks. Then, these data are overlaid with maps of the population, public building properties, and estimated costs in order to rapidly provide cost information on storm events. GIS layers such as storm tracks, political boundaries, public building properties, and population have been developed into a geodatabase to rapidly and accurately estimate costs in the aftermath of a storm event. The GIS layers are described in Table 3.1.

Table 3.1 GIS database by layer

Field GIS Layer Type Format Description and Data Sources Attribute Event track Line Vector Type Storm and hurricane tracks, data extracted from NOAA, FEMA, PREMA, and National Weather Service Forecast Office Political Polygon Vector Length Administrative areas extracted boundaries from topographic data Building properties Polygon Vector Type Public buildings shapefiles from Puerto Rico Industrial Development Company (PRIDCO) Population Polygon Vector Value Population data collected from US Bureau of Labor

Estimated cost Polygon Vector Value Dollar value based on population and JFC

3.1 Storms

Historical data of storm profiles and tracks are extracted from the Historic

Hurricane Track database maintained by the National Oceanic and Atmospheric

Administration (NOAA) (NOAA/Office for Coastal Management, 2014). The

Hurricane Track database contains storm event names, dates, coordinates, storm categories, and storm profiles, such as minimum pressure in millibars (mb). The storm historical data for this work consider the following event classifications: severe storms (SS), tropical storms (TS), and hurricanes (H). These storms all occurred from 1950 to 2011 and within 65 nautical miles of Puerto Rico. The scale used to differentiate the severity of types of storms and hurricane is based on wind intensity. For instance, an (SS) is a natural event in which one-minute sustained surface winds are less than 33 knots (kn). Then, a (TS) has a maximum one-minute sustained surface wind speed ranging from 34 kn to 63 kn, (H1) has a one-minute sustained surface wind of at least 64 kn, (H2) has a one-minute sustained surface wind speed of at least 83 kn, (H3) has a one-minute sustained surface wind speed of at least 96 kn, (H4) has a one-minute sustained surface wind speed of at least

113 kn, and (H5) has a one-minute sustained surface wind speed of 137 kn, or more (NOAA/National Weather Service, 2014).

The attributes of storms considered in this study are those reported by

FEMA or the Puerto Rico Emergency Management Agency (PREMA) public records since 1950, and are shown in Table 3.2. Despite several storms striking

30 and making landfall in Puerto Rico before 1950, the lack of data and records on public property damage probably resulted in an undercount prior to 1950.

Table 3.2 Storm and hurricane events within 65 nautical miles of Puerto Rico. Historic Hurricane Track database maintained by the National Oceanic and Atmospheric Administration. *The closest storm location to Puerto Rico centroid.

Max. Min. Julian Name or Location* Wind Date Pressure Category Day FEMA ID N W Speed (mb) (kn) 8/23/1950 236 Baker 18 67 1007 35 TS ⁰ ⁰ 9/11/1955 254 Hilda 19.2 65.6 1002 40 TS ⁰ ⁰ 8/12/1956 225 Betsy 17.8 65.7 991 80 H1 ⁰ ⁰ 9/15/1975 258 Eloise 19.0 65.6 1007 30 TS ⁰ ⁰ 9/4/1979 247 Frederic 18.1 65.8 1003 45 TS ⁰ ⁰ 10/10/1985 283 DR-597 18.3 66.1 1019 25 SS ⁰ ⁰ 11/26/1987 330 DR-746 18.3 66.0 1009 40 SS ⁰ ⁰ 9/18/1989 261 Hugo 18.2 65.5 958 110 H2 ⁰ ⁰ 9/16/1995 259 Marilyn 18.5 65.2 952 95 H2 ⁰ ⁰ 9/10/1996 284 Hortense 18.0 66.9 989 70 H1 ⁰ ⁰ 9/21/1998 264 Georges 18.2 66.3 968 100 H2 ⁰ ⁰ 5/7/2001 127 DR-1372 18.2 66.2 1015 34 SS ⁰ ⁰ 11/8/2001 312 DR-1396 18.1 66.1 1016 31 SS ⁰ ⁰ 11/15/2003 319 DR-1501 18.2 66.0 1010 34 SS ⁰ ⁰ 9/15/2004 320 Jeanne 18.3 66.2 991 60 TS ⁰ ⁰ 10/9/2005 282 DR-1613 18.1 66.4 1007 35 SS ⁰ ⁰ 10/1/2008 274 DR-1798 18.3 66.0 1005 37 SS ⁰ ⁰ 5/27/2010 147 DR-1919 18.0 66.0 1015 28 SS ⁰ ⁰ 10/6/2010 279 Otto 18.7 66.1 1004 38 TS ⁰ ⁰ 5/20/2011 140 DR-4004 19.0 66.0 1014 23 SS ⁰ ⁰ 8/22/2011 234 Irene 18.3 66.2 990 65 H1 ⁰ ⁰

3.2 Historical recovery cost

Historical storm event damage costs are also considered in the GIS database. Damage costs caused by a storm to public properties are recorded and maintained in FEMA public records, because it is a necessary information as part of its FEMA’s Public Assistance Grant Program. This program provides assistance to all U.S. jurisdictions in order to quickly respond to and recover from major disasters or emergencies declared by the President (GAO, 2012).

3.3 Population and economic indicators

Data related to population and economic indicators were acquired from the

US Bureau of Labor Statistics and the Puerto Rico Planning Board, respectively.

Economic indicators include inflation, real wealth per capita, GDP, and personal income, actual recovery cost is recorded and maintained by FEMA since such information is necessary to the Public Assistance Grant Program. This program is meant to provide assist all U.S. jurisdictions by assuring prompt response and recovery from presidential declared major disaster or emergencies (GAO, 2012).

Recovery costs before FEMA (1975) were obtained from PREMA regarding years with storm events. Table 3.3 summarizes the considered economic data for actual cost normalization. This recovery expense adjustment will be explained in detail in the methodology section.

Table 3.3 Economic indicators applicable to the jurisdiction of Puerto Rico. Data sources include the U.S. Bureau of Labor Statistics and the Puerto Rico Planning Board. Recovery cost data sources include FEMA and PREMA Recovery Real Wealth Population Name or Inflation Year Cost per capita (thousand) FEMA ID (It) (Ct) (RWPC t) (Pt) 1950 Baker $2,543,747 -1.79 -2.35 2,206 1955 Hilda $5,739,836 -0.95 -3.23 2,232 1956 Betsy $5,889,482 1.23 2.43 2,250 1975 Eloise $9,374,393 8.56 0.18 2,914 1979 Frederic $2,398,533 6.46 0.21 3,141 1985 DR-597 $5,716,498 0.21 6.66 3,363 1987 DR-746 $8,528,283 2.08 0.67 3,420 1989 Hugo $40,609,290 2.82 0.50 3,479 1995 Marilyn $2,925,362 1.92 0.67 3,666 1996 Hortense $34,828,047 3.31 0.40 3,704 1998 Georges $117,911,767 0.05 25.36 3,770 2001 DR-1372 $5,147,725 0.58 1.92 3,815 2001 DR-1396 $4,853,317 0.58 1.92 3,815 2003 DR-1501 $6,996,153 1.38 0.83 3,825 2004 Jeanne $41,301,481 2.54 0.45 3,826 2005 DR-1613 $11,822,936 5.61 0.21 3,824 2008 DR-1798 $14,931,386 5.21 0.22 3,772 2010 DR-1919 $5,308,114 2.48 0.43 3,731 2010 Otto $16,337,825 2.48 0.43 3,731 2011 DR-4004 $7,397,528 1.09 0.96 3,714 2011 Irene $55,664,884 1.09 0.97 3,714

All data required to successfully apply the cost estimation model are administered, and calculations are made using the geospatial analysis software

ArcMap ®. ArcMap ® can manage and store data in attribute tables in order to facilitate the data entry process. Attribute tables are database components similar 33 to a spreadsheet, including a field calculator tool to create new data from historical data stored in a table. Integrating population, economic indicator, and historical cost data into a GIS-based cost estimation model provides new input data, such as normalized costs and the JFC, which can be used to rapidly estimate damage costs after a storm.

Chapter 4. Methodology

The objective of this research is to provide a method of rapid cost estimation for recovery after a storm, using a GIS. The claim made in this investigation is as follows: applying a JFC is more suitable than applying statewide per capita indicators from FEMA when rapidly estimating recovery costs for public properties in the aftermath of a storm.

4.1 Methodology approach

GIS solutions employ geographic data sets such as contours, storm tracks, political boundaries, and population, among others. These data may be in the form of a shapeﬁle, geodatabase, or spreadsheet. They also incorporate jurisdictions’ economic indicators to normalize historical recovery costs and to calculate the

JFC.

The GIS model in this research involves 5 stages as depicted in Figure 4.1:

(1) data collection and classification; (2) frequency of storms and analysis; (3) geodatabase development; (3) data processing to normalize cost and to calculate the JFC; (4) recovery cost estimation; and, (5) geographical representation information.

Start

Load data (Attribute Tables)

Personal County/City/ Population Municipality Income

Real Wealth Storm GDP per capita

Frequency of storms and analysis

Geodatabse

Shapefiles; Maps and storm tracks New Field

GIS visualization interface

Rapid recovery cost estimation

Geographical representation information

Figure 4.1 GIS Model Flow Diagram

First, an examination of the frequency of storms is performed. Second, the historical recovery costs reported by FEMA are normalized. The normalization calculation estimates the damage that would occur if storms from the past resulted in recovery costs for public properties in 2012. Third, the JFC is determined to show the economic capability of the jurisdiction of Puerto Rico to finance public property recovery based on the size of its economy. Then, the JFC is multiplied by the population size to rapidly estimate the recovery costs.

Cost estimation calculations are based on the data described in Chapter 3, which is stored using ArcMap ®. ArcMap® can manage and store data in attribute tables in order to facilitate the data entry process (Figure 4.2). Attribute tables are database components similar to a spreadsheet, including a field calculator tool to create new data from historical data already stored in a table. Integrating population, economic indicators, and public property recovery cost data into a

GIS-based cost estimation model provides new input data, such as normalized costs and the JFC, to rapidly estimate recovery costs for public properties after a storm. Finally, the cost exceedance probability is developed to provide guidance on recovery cost estimations.

Figure 4.2 ArcMap® Attribute table implemented for hurricane Irene

4.2 Storm analysis

This work relies on data of storms that have occurred within 65 nautical miles of Puerto Rico and that have physically affected public properties. The data are acquired from NOAA: National Hurricane Center – Historical Hurricane

Tracks, FEMA: Disaster Declarations for Puerto Rico, and the Puerto Rico

Emergency Management Agency (PREMA): Disaster Historical Records.

Puerto Rico’s hurricane season runs from June 1 to November 30. Figure

4.3 shows the storm counts per month. Figure 4.4 illustrates the cumulative distribution functions (CDF) of these storms. The CDF graph shows that the probability value increases from zero to one (vertical axis), and the Julian days for

38 the assigned storms go from left to right on the horizontal axis. Figure 4.3 and

Figure 4.4 show that the peak storm activity period is September.

Figure 4.3 Count per month of storms that affected public properties in Puerto Rico. Data source: NOAA: National Hurricane Center – Historical Hurricane Tracks, FEMA: Disaster Declarations for Puerto Rico, and Puerto Rico Emergency Management Agency (PREMA). Figure similar to Malmstadt, Scheitlin, and Elsner (2009).

Storm Count since 1950 10 8 8

6 4 4 3 3 3 2 Count (since (since 1950) Count 0 0 0 May Jun Jul Aug Sep Oct Nov Month

Figure 4.4 Cumulative distribution function of storms from Figure 4.3. Figure similar to Malmstadt, J., Scheitlin, K., and Elsner, J. (2009).

1.00

0.80

0.60

0.40 Cumulative Cumulative Distribution 0.20

0.00 100 200 300 400 Julian Day

A storm data distribution analysis is implemented to fit the data to the correct distribution. First, a storm frequency analysis is performed. The frequency of storms per year, which is a discrete distribution, is suspected to fit the Poisson distribution.

According to Chiasson (2013), a continuous random variable x is said to have an exponential λ distribution if it has the following cumulative density function (p. 238):

0, < 0 (4.1) = 1 − , ≥ 0 where x denotes independent events that occur at a constant average cost rate λ.

The Poisson distribution is suggested because storm events are independent, and the occurrence of an event increases or decreases the chance of another

(Malmstadt, Scheitlin & Elsner, 2009). The illustrated data set can be characterized well by a Poisson distribution, because its plot is skewed toward the end (i.e., the distribution is not symmetrical). See Figure 4.5.

The Poisson distribution is discrete. Given a certain storm event that occurs at a rate l , it models the probability that k of these events will occur within a specified period. The probability mass function is shown in equation (4.2):

; = =

, (4.2) = !

40 where k is the number of events. The function is evaluated at k ={0,1,2,...}, and the function value f(k ; l ) is the probability that the event occurs.

Figure 4.5 Puerto Rico’s storm count which public properties cost estimates are demonstrated since 1950.

Annual Storm Counts, 1950-2011 45 40 35 30 25 20 Count 15 10 5 0 0 1 2 Number of storms occuring in a given year

The storm activity assumes a Poisson distribution (Jagger and Elsner,

2012). A Poisson distribution is suggested because storm events are independent, as noted earlier. The illustrated Poisson distribution is skewed toward the one end.

2 Moreover, the Chi-Square (χ ) test is performed to prove the null hypotheses (Ho) that the frequency of storms per year fits the Poisson distribution. The probability level alpha (α) is equal to 0.05, with one degree of freedom, and with the following categories of storms {0, 1, 2+}. Since the χ 2 statistic of 1.208 does not

2 2 exceed the critical value of 3.841 (χ < χ Crit ), H o cannot be rejected. Therefore, the frequency of storms per year fits the Poisson distribution with parameter l .

4.3 Normalized Cost

ArcMap ® is used to obtain shapefiles describing the basemap of the study area. These shapefiles include political boundaries, storm tracks, jurisdictions affected by storms, and public buildings. Attribute tables are loaded with economic indicators, recovery costs, and population data. These data (e.g., Table

3.3) are also used in the field calculator in ArcMap ® to normalize public property recovery costs. This method provides a cost if storms from the past resulted in property and facility damages under another year’s societal conditions (Pielke et al., 2008). Population and economic indicators are required to adjust recovery costs to a notional economic value in 2012. The estimated costs of recovering public properties are normalized to adjust for inflation, wealth, and population, in the following way:

(4.1) = × × × where C denotes the normalized public properties recovery cost, Ct denotes the public property cost reported by FEMA or PREMA in the current year, It denotes the inflation adjustment as per the Puerto Rico Planning Board, RWPC t is the real wealth per capita adjustment as per the Puerto Rico Planning Board, and Pt is the

Puerto Rico population adjustment as per the U.S. Bureau of Labor Statistics. The subscript t denotes the year under consideration.

4.4 Jurisdiction fiscal capacity

The JFC measurement is calculated by applying equation 4.2 in order to rapidly and more accurately estimate the cost of recovering public properties after a storm:

. (4.2) = ∗ 100

where JFC t stands for Jurisdiction Fiscal Capacity for recovery in a given year, based on Puerto Rico total taxable resources, PI PR personal income of Puerto Rico,

PI US the U.S. personal income, GDP PR gross domestic product of Puerto Rico,

GDP US U.S. aggregate gross domestic product, TTR US U.S. total taxable resource dollars per capita in a given year. All necessary data for JFC determination was obtained from the U.S. Department of the Treasury, Federal Reserve Bank of St.

Louis Economic Research (n.d.) and the Puerto Rico Planning Board (2013).

These economic indicators are stored in attribute tables and the JFC calculation is executed using the field calculator in ArcMap ® to create a new field in the attribute table. See Figure 4.6.

Figure 4.6 ArcMap ® Fields Calculator window for recovery cost estimation

Calculating a JFC enables rapid cost estimation by plugging the following values (in millions) into equation (2): PI PR =10,021USD; PI US =13,887,700USD;

GDP PR =10,395USD; GDP US =16,160,000USD; and TTR US =58,274USD, resulting in 18.92USD per capita index. The JFC, an indicator applied per capita, shows the economic capability of a jurisdiction to finance its public property recovery, based on the size of its economy.

4.5 Recovery cost estimation

Recovery cost estimation is important for the accountability of emergency responder official, who develop a general framework that implements appropriate analytical models to estimate recovery costs. Using a GIS provides several benefits to emergency responders, including rapid access to prior recovery costs, data analyses, and the presentation of results (Burrough, 2001). Moreover, the analysis of the JFC provides new insights into how jurisdictions have responded to

44 needs and services, while still being able to analyze variations across states

(Mikesell, 2007). This systematic GIS-based cost estimation approach interacts with a geodatabase of economic indicators and storms to rapidly estimate the costs of restoring and recovering public properties. Multiplying the JFC by the population size in an affected jurisdiction (equation 4.3) provides better cost estimations than when applying the FEMA indicator.

(4.3) = ∑ ∗

where JFC t is the jurisdiction fiscal capacity in year t, and Population x is the affected jurisdiction population.

Table 4.1 shows the populations of jurisdictions where public properties were affected by a storm. Similarly, Appendix A shows all the jurisdictions where public properties were affected.

Table 4.1Population associated to those jurisdiction where public properties were affected by a storm as reported by FEMA Declaration Report.

STORM NAME POPULATION OR FEMA ID ELOISE 735,055 FREDERIC 248,104 DR-746 403,372 DR-805 1,291,324 HUGO 3,007,310 MARILYN 276,178 HORTENSE 2,961,506 GEORGES 3,725,788 DR-1372 388,725 DR-1396 580,542 DR-1501 610,643 JEANNE 2,385,806 DR-1613 627,090 DR-1798 943,435 DR-1919 429,164 OTTO 764,777 DR-4004 505,466 IRENE 2,819,950

Eventually, the following is expected as a result of providing an indicator of resilience and integrating economic indicators into GIS:

1. The application of GIS-based cost estimation will provide accurate recovery cost

estimation for the accountability of emergency responder officials.

2. The use of GIS-based cost estimation will allow state and local government to

rapidly estimate the costs associated with the recovery of public properties in the

aftermath of a storm event.

Chapter 5. Results and Analysis

This chapter discussed the results and analysis performed in this research.

ArcMap ® output for hurricane Hugo, Hortense, Georges, Jeanne, and Irene are shown to understand spatial information and analysis applied.

Details of methods performed are included for calculation comparison with the estimated amount, based on a physical damage assessment of the public buildings and infrastructure. If a cost estimate is suspect of being an outlier because it appears to deviate significantly from the data set, then the Mahalanobis distance (MD) approach is implemented to identify outliers. Then, variation between rapid recovery cost estimation and normalized cost is analyzed using median absolute deviation (MAD) since it is not sensitive to the presence of outliers.

Furthermore, this chapter includes discussion regarding cost exceedance probability curve that communicates the probability of potential recovery cost or greater recovery cost in the aftermath of a storm event. The exceedance probability curve provides benchmark for estimate comparison over time. Finally, normalized cost data distribution is analyzed through the log-normal method because of the connection between additive effects and the normal distribution parallels that of multiplicative effects and the log-normal distribution (Limpert,

Stahel, & Abbt, 2001). The use of the log-normal model is equivalent to first

48 subjecting the storm data to the log transformation and then proceeding with methods based on the normal distribution.

Calculating a JFC facilitates the rapid cost estimation process. The JFC measures a state’s fiscal capacities (Compson, 2003). For a reasonable cost estimation, a JFC for Puerto Rico of 18.92USD should be developed to rapidly estimate the cost of recovering public properties in order to assess public assistance from both local government and federal agencies. Currently, FEMA’s public property assistance per capita indicator is set at 3.50USD (U.S. Government

Publishing Office, 2013), which is multiplied by the population of the jurisdiction to arrive at a threshold amount. The result of that calculation is compared with the estimated amount, based on a physical damage assessment of the public buildings and infrastructure (44C.F.R. § 206.48). FEMA uses the comparison as an indicator of the jurisdiction’s need for federal assistance. Hence, the GAO-12-838 specifically states, “This damage indicator, which FEMA has used since 1986, is essentially a proxy fiscal measure of a state’s capacity to respond to and recover from a disaster, rather than a more comprehensive assessment of a state’s fiscal capacity.” (p. 24). The proposed 18.92USD per capita cost impact indicator implies that Puerto Rico would be less likely to receive public assistance funding from FEMA, because the fiscal capacity is based on the JFC, which determines a jurisdiction’s ability to recover without federal assistance (GAO, 2012). However, a JFC of 18.92USD per capita is a more suitable indicator than FEMA’s current indicator because it supports a more accurate rapid cost estimate, as shown in

Table 5.1. Of course, using a recovery cost impact indicator less than 18.92USD

49 per capita, such as 3.50USD, results in a spurious rapid damage loss estimation.

Appendix A breaks down all jurisdictions affected per storm.

Table 5.1 Comparison between actual costs normalized to year 2012, FEMA estimate, and the rapid costs estimates (U.S. dollar).

Jurisdiction FEMA/ Rapid Name/ Normalized Date affected PREMA Cost FEMA ID Cost population Estimate Estimate 8/23/1950 Baker 740,917 $18,041,686 $6,246,681 $14,018,172 9/11/1955 Hilda 1,455,740 $29,366,058 $15,549,528 $27,542,590 8/12/1956 Betsy 2,016,694 $29,108,503 $9,267,565 $38,155,844 9/15/1975 Eloise 735,055 $18,182,248 $2,572,693 $13,907,241 9/4/1979 Frederic 248,104 $3,855,415 $1,868,364 $4,694,127 10/10/1985 DR-746 403,372 $8,839,290 $4,411,802 $7,631,798 11/26/1987 DR-805 1,291,324 $12,940,042 $6,192,850 $12,333,550 9/18/1989 Hugo 3,007,310 $60,690,764 $34,584,065 $56,898,305 9/16/1995 Marilyn 276,178 $3,826,467 $1,769,976 $5,151,991 9/10/1996 Hortense 2,961,506 $46,267,262 $9,527,535 $51,503,134 9/21/1998 Georges 3,725,788 $147,343,051 $47,503,797 $70,491,908 5/7/2001 DR-1372 388,725 $5,593,914 $1,360,537 $7,354,667 11/8/2001 DR-1396 580,542 $5,273,988 $3,192,981 $10,983,854 11/15/2003 DR-1501 610,643 $7,819,146 $3,541,729 $11,553,365 9/15/2004 Jeanne 2,385,806 $45,481,760 $32,208,381 $45,139,449 10/9/2005 DR-1613 627,090 $13,255,031 $5,957,355 $11,864,542 10/1/2008 DR-1798 943,435 $17,228,509 $0.00 $17,849,790 5/27/2010 DR-1919 429,164 $5,700,969 $6,074,262 $8,119,782 10/6/2010 Otto 764,777 $17,546,991 $8,794,935 $14,469,580 5/20/2011 DR-4004 505,466 $7,764,829 $5,828,522 $9,563,416 8/22/2011 Irene 2,819,950 $58,429,938 $4,905,003 $53,353,454

Recall that the JFC analysis provides insights into how jurisdictions have responded to needs and services (Mikesell, 2007). The results in Table 5.1 show that the rapid cost estimation approach is more suitable than using the normalized recovery costs. Figure 5.1 shows a graphical view of the outcome once the actual recovery costs are normalized and the JFC is applied per jurisdiction and per storm.

Figure 5.1 7Bar graph of the normalized recovery cost and the recovery cost estimate.

Recovery Cost Estimate Normalized Actual Recovery Cost $160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 US US Dollar (in Thousands) $20,000 $0 Otto Irene Hilda Hugo Betsy Baker Eloise Jeanne DR-746 DR-805 Marilyn Frederic Georges Hortense DR-1372 DR-1396 DR-1501 DR-1613 DR-1798 DR-1919 DR-4004 Storm Events

Note that for Hurricane Georges, there is a big difference between the rapid cost estimate (70,491,908USD) and the normalized cost (147,343,051USD).

Hurricane Georges is a suspected outlier. An outlier is an observation that deviates markedly from other observations (Hawkins, 1980). Therefore, in this research a statistical method to measure the distance between an observed points and a distribution is taking into account to identify outliers.

5.1 Mahalanobis Distance (MD)

This research applies the MD approach to identifying outliers because the normalized costs and the rapid cost estimates are jointly distributed. After reviewing the output, Hurricane Georges deviates from the structured data. The

MD is suitable for identifying data points that lie a long way from the centroid of the data distribution. The MD considers the distances of the variables, as well as the relative distances, using the dispersion between each of the original variables

(Mahalanobis, 1936). This approach is used in clustering and discriminant analyses (Tipping & Bishop, 1999; Mkhadri, 1995).

The MD is also considered a generalized Euclidian distance. This is a function D(x, y) if the following conditions hold:

(5.1) , ≥ 0; ∀, (5.2) , = 0, = (5.3) , = , (5.4) , ≤ , + ,

The Euclidian distance is a most common metric, which is merely the distance between any two points. The Euclidian distance equation (DE(x,y)) between two points x = [ x1 , x 2], y = [y1 , y2] in a two-dimensional space is expressed as follow:

(5.5) , = − + −

The Euclidian distance is also referred to the Euclidian norm or 2-norm. A norm is a special metric that obeys a specific form. For any real number p ≥ 1 , the “ p- norm ” of a vector z is denoted and is equal to: ‖‖p

(5.6) ‖‖ = ∑

where zi, i = 1,…,n are the elements of the vector z . Any p-norm satisfies the conditions that are necessary for a metric.

However, the MD can be thought of as a measurement of separation between a point and the centroid of a distribution. In one dimension, it measures the number of standard deviations a point lies away from the mean. The concept extends to higher dimensional spaces as well. The MD DM(µ,S,x) between a distribution centered at μ, with covariance matrix S and a vector x is:

(5.7) , , = − −

In each dimension, the separation between the centroid and vector is weighted by entries in the covariance matrix. Because the off-diagonal terms of the covariance matrix are included, the metric accounts for correlation between the variables (i.e. trends in the data).

The MD metric is most commonly used to measure the distance between vectors and the centroid of multidimensional Gaussian distributions. Therefore, it is often used to detect outliers. For instance, consider the following two- dimensional example comparing the use of these two distance metrics as outlier detectors. One hundred points are generated from the bivariate normal distribution, with the following parameters:

3 10 3 (5.8) = = 5 3 1

Five of the data points are randomly distorted to represent measurement error or extraneous influence. Figure 5.2 and Figure 5.3 plot the data and color code the points based on their MD and Euclidian distance from the mean, respectively. Note that the two plots contain all the same data points, but are labeled using different metrics. The circled points represent outliers that fall more d = 4.605 units away from the centroid, using either metric. The ellipses are contour lines for the distribution N(μ, S) (i.e., all the points that fall on a certain ellipse centered at the mean have the same pdf value).

Figure 5.2 8Mahalinobis distance plot

Figure 5.3 9Euclidian distance plot

The MD remains small for some points that have a large Euclidian distance away from the centroid. The MD contour lines are ellipses with axes defined by the covariance matrix. In other words, they are the same as the contour lines of the distribution. The Euclidian contour lines are circles. It is clear that the MD outlier identification is more appropriate for this distribution, because the Euclidian detector rejects several additional data points that are not perturbed, and even fails to reject one point that is perturbed near (5, 2).

Note the following:

o For the standard normal distribution, or any multivariate Gaussian

distribution with covariance matrix that is the identity matrix, the Euclidian

and Mahalanobis distances are the same.

o The Euclidian distribution is not dependent on the distribution parameters.

The distance is only dependent on the number-line distances between

points.

5.2 Hurricane Georges as outlier

The normalized cost of 147,343,051USD for public property damage versus the rapid cost estimate (70,491,908USD) for Hurricane Georges is shown as an outlier. The MD is used to measure the distance between Georges’ normalized cost data point and the data set distribution, and code is written in MATLAB ® to identify outliers (See Appendix B).

Applying the MD helps to successfully identify outliers to detect cost estimate failures, as shown in the scatterplot (Figure 5.4) along both primary axes

56 of variance. Hurricane Georges’ data point is circled and colored according to its

Mahalanobis values. It has been demonstrated that Georges has distance of 18.209, while the threshold is at 13.816. Hurricane Georges is a statistical outlier for two degrees of freedom and p = 0.999. In other words, Hurricane Georges is not indicative of the usual performance of the rapid recovery cost estimation method.

Figure 5.4 10 Mahalinobis distance scatterplot of Puerto Rico’s storm data for public property cost estimates and normalized costs since 1950. Hurricane Georges is identified as outlier.

The estimated recovery cost for hurricane Georges is likely caused by the storm moving exceptionally slowly, and reaching a peak intensity of 135 kn

(Kepert, 2006). Moreover, three tornadoes where reported by the Doppler weather radar (Bennett & Mojica, 2009). The cost estimation was unable to account for this effects. Therefore, the rapid recovery cost estimate for restoring public properties after Hurricane Georges is a significant outlier, because it deviates markedly from

57 the distribution of the other estimates. There are opportunities to extend this scope and adjust the recovery cost estimates to consider storm intensity, sustained winds, and rainfall.

5.3 Median absolute deviation (MAD)

The application of the MAD has suggested 1,580,101USD as an absolute deviation from the median cost estimation. The MAD is a measure of variability in a data set. In this application, the data points are the absolute errors between cost estimates and actual normalized damage costs. Refer to Table 5.2 and Table 5.3 for the absolute errors between the cost estimates and actual normalized costs.

Table 5.4 and Table 5.5 display the sorted data per percentile and the MAD output per storm.

Moreover, MAD is more resilient to a distant observation or outliers because the presence of outliers does not change the value of the MAD. MAD is expressed as follows:

, (5.9) = − −

where xi is the rapid cost estimate; xj is the normalized cost of damage; xij is the difference absolute value between the rapid cost estimate and the normalized cost of damage.

Table 5.2 Percentage and error difference between normalized cost and the rapid cost estimation as an input to analyze MAD.

Name or Normalized Rapid Cost Percentage ERROR FEMA ID Cost Estimate Difference DR-1919 $5,700,969 $8,119,782 29.79 $2,418,813 Hilda $29,366,058 $27,542,590 -6.62 -$1,823,468 DR-4004 $7,764,829 $9,563,416 18.81 $1,798,587 DR-1372 $5,593,914 $7,354,667 23.94 $1,760,753 Otto $17,546,991 $14,469,580 -21.27 -$3,077,411 DR-1613 $13,255,031 $11,864,542 -11.72 -$1,390,489 Marilyn $3,826,467 $5,151,991 25.73 $1,325,524 DR-746 $8,839,290 $7,631,798 -15.82 -$1,207,492 DR-1501 $7,819,146 $11,553,365 32.32 $3,734,219 Hugo $60,690,764 $56,898,305 -6.67 -$3,792,459 Frederic $3,855,415 $4,694,430 17.87 $838,712 Baker $18,041,686 $14,018,172 -28.70 -$4,023,514 DR-1798 $17,228,509 $17,854,595 3.48 $621,280 DR-805 $12,940,042 $12,333,550 -4.92 -$606,492 Eloise $18,182,248 $13,907,241 -30.54 -$4,275,008 Jeanne $45,481,760 $45,139,449 -0.76 -$342,311 Irene $58,429,938 $53,353,454 -9.51 -$5,076,484 Hortense $46,267,262 $51,503,134 10.17 $5,235,872 DR-1396 $5,273,988 $10,983,854 51.98 $5,709,866 Betsy $29,108,503 $38,155,844 23.71 $9,047,341 Georges $147,343,051 $70,491,908 -109.02 -$76,851,143

Table 5.3 Percentage and error difference between normalized cost and the FEMA estimation as an input to analyze MAD.

Name or Normalized Percentage FEMA Estimate ERROR FEMA ID Cost Difference Otto $17,546,991 $8,794,935 -99.51 -$8,752,056 DR-1613 $13,255,031 $5,957,355 -122.50 -$7,297,676 DR-805 $12,940,043 $6,192,850 -108.95 -$6,747,193 Baker $18,041,687 $6,246,681 -188.82 -$11,795,006 DR-746 $8,839,290 $4,411,802 -100.36 -$4,427,488 DR-1501 $7,819,147 $3,541,729 -120.77 -$4,277,418 DR-1372 $5,593,915 $1,360,537 -311.15 -$4,233,378 Jeanne $45,481,761 $32,208,381 -41.21 -$13,273,380 Hilda $29,366,059 $15,549,528 -88.85 -$13,816,531 DR-1396 $5,273,989 $3,192,981 -65.17 -$2,081,008 Marilyn $3,826,467 $1,769,976 -116.19 -$2,056,491 Frederic $3,855,415 $1,868,364 -106.35 -$1,987,051 DR-4004 $7,764,830 $5,828,522 -33.22 -$1,936,308 Eloise $18,182,249 $2,572,693 -606.74 -$15,609,556 DR-1919 $5,700,969 $6,074,262 6.15 $373,293 DR-1798 $17,228,510 $0 0 -$17,228,510 Betsy $29,108,503 $9,267,565 -214.09 -$19,840,938 Hugo $60,690,764 $34,584,065 -75.49 -$26,106,699 Hortense $46,267,263 $9,527,535 -385.62 -$36,739,728 Irene $58,429,939 $4,905,003 -1091.23 -$53,524,936 Georges $147,343,052 $47,503,797 -210.17 -$99,839,255

Table 5.4 Rapid Cost Estimate sorted data per percentile and the MAD output per storm.

Name or Error Absolute Value Percentile MAD FEMA ID DR-1919 $2,516,431 2.4% $0 Hilda $2,418,814 7.1% $97,617 DR-4004 $3,077,411 11.9% $560,980 DR-1372 $1,823,468 16.7% $692,962 Otto $1,760,752 21.4% $755,679 DR-1613 $1,390,489 26.2% $1,125,942 Marilyn $1,325,525 31.0% $1,190,906 DR-746 $3,734,219 35.7% $1,217,788 DR-1501 $3,792,459 40.5% $1,276,028 Hugo $1,207,492 45.2% $1,308,939 Frederic $4,023,514 50.0% $1,507,083 Baker $838,712 54.8% $1,677,719 DR-1798 $4,275,008 59.5% $1,758,577 DR-805 $621,280 64.3% $1,895,151 Eloise $606,492 69.0% $1,909,939 Jeanne $342,311 73.8% $2,174,120 Irene $5,076,485 78.6% $2,560,054 Hortense $5,235,872 83.3% $2,719,441 DR-1396 $5,709,866 88.1% $3,193,435 Betsy $9,047,341 92.9% $6,530,910 Georges $76,851,144 97.6% $74,334,713* *Outlier

Table 5.5 FEMA Estimation sorted data per percentile and the MAD output per storm.

Name of Error Absolute Value Percentile MAD FEMA ID Otto $8,752,056 2.4% $0 DR-1613 $7,297,676 7.1% $1,454,380 DR-805 $6,747,193 11.9% $2,004,864 Baker $11,795,006 16.7% $3,042,949 DR-746 $4,427,488 21.4% $4,324,568 DR-1501 $4,277,418 26.2% $4,474,639 DR-1372 $4,233,378 31.0% $4,518,679 Jeanne $13,273,380 35.7% $4,521,323 Hilda $13,816,531 40.5% $5,064,474 DR-1396 $2,081,008 45.2% $6,671,049 Marilyn $2,056,491 50.0% $6,695,565 Frederic $1,987,051 54.8% $6,765,005 DR-4004 $1,936,308 59.5% $6,815,749 Eloise $15,609,556 64.3% $6,857,499 DR-1919 $373,293 69.0% $8,378,764 DR-1798 $17,228,510 73.8% $8,476,453 Betsy $19,840,938 78.6% $11,088,882 Hugo $26,106,699 83.3% $17,354,643 Hortense $36,739,728 88.1% $27,987,671 Irene $53,524,936 92.9% $44,772,879 Georges $99,839,255 97.6% $91,087,198* *Outlier

Consider a new FEMA estimate by adjusting its current estimation by a factor phi ( f) .

∑ (5.10) = ; % = 1 −

62 where xi is the actual FEMA estimates, yi is the normalized recovery cost, and n is the total number of events.

(5.11) =

Table 5.6 shows the new adjusted FEMA estimates and the comparison between the Adjusted FEMA Estimate MAD and the Rapid Cost Estimate MAD.

Table 5.6 6Comparison between new adjusted FEMA estimate MAD and Rapid Cost Estimate MAD (in thousands U.S. dollar)

Actual New Rapid Normalized New Error Storm FEMA % FEMA Cost Cost FEMA Absolute Name Estimate Diff Estimate Estimate (yi) Estimate Value (xi) MAD MAD Baker $18,042 $6,247 0.65 $11,135 $6,907 $4,271 $1,605 Hilda $29,366 $15,550 0.47 $27,718 $1,648 $987 $595 Betsy $29,109 $9,268 0.68 $16,520 $12,589 $9,953 $6,629 Eloise $18,182 $2,573 0.86 $4,586 $13,596 $10,961 $1,856 Frederic $3,855 $1,868 0.52 $3,330 $525 $2,111 $1,580 DR-746 $8,839 $4,412 0.50 $7,864 $975 $1,661 $1,211 DR-805 $12,940 $6,193 0.52 $11,039 $1,901 $735 $1,812 Hugo $60,691 $34,584 0.43 $61,648 $957 $1,679 $1,374 Marilyn $3,826 $1,770 0.54 $3,155 $671 $1,964 $1,093 Hortense $46,267 $9,528 0.79 $16,983 $29,284 $26,648 $2,817 Georges $147,343 $47,504 0.68 $84,678 $62,665 $60,029 $74,432 DR-1372 $5,594 $1,361 0.76 $2,425 $3,169 $533 $658 DR-1396 $5,274 $3,193 0.39 $5,692 $418 $2,218 $3,291 DR-1501 $7,819 $3,542 0.55 $6,313 $1,506 $1,130 $1,315 Jeanne $45,482 $32,208 0.29 $57,413 $11,931 $9,296 $2,077 DR-1613 $13,255 $5,957 0.55 $10,619 $2,636 $0 $1,028 DR-1798 $17,229 $0 1.00 $0 $17,229 $14,593 $1,798 DR-1919 $5,701 $6,074 -0.07 $10,828 $5,127 $2,491 $0 Otto $17,547 $8,795 0.50 $15,677 $1,870 $766 $659 DR-4004 $7,765 $5,829 0.25 $10,390 $2,625 $11 $620 Irene $58,430 $4,905 0.92 $8,743 $49,687 $47,051 $2,658 = fff =f == 0.56 MEDIAN $2,636 $2,111 $1,580

It is demonstrated that the MAD for the new adjusted FEMA estimation method is greater than the Rapid Cost Estimate ($2,110,787 > $1,580,101). Therefore, the

Rapid Cost Estimate method is more accurate than the corrected FEMA estimation.

Figure 5.5 illustrates a comparison of the actual FEMA estimates and the

Rapid Cost Estimates. Notice that the plot presents error bounds for both estimates, Actual FEMA estimate and the Rapid Cost Estimate. Similarly, Figure

5.6 shows a comparison plot between the corrected FEMA estimation and the

Rapid Cost Estimate. Figures 5.5 and 5.6 demonstrate that the Rapid Cost

Estimation method is more accurate than both FEMA estimations, the actual method and the adjusted method. These graphical illustrations reflect the closeness between the Normalized Cost and the Rapid Cost Estimate values.

Figure 5.5 11 Actual FEMA estimates and the Rapid Cost Estimates Error Bound Plot

The errors deviate from the estimate by the MAD MAD Actual FEMA Estimate = ±$6,695,565 MAD Rapid Cost Estimate = ±$1,580,101

Figure 5.6 12 Adjusted FEMA estimates and the Rapid Cost Estimates Error Bound Plot

The errors deviate from the estimate by the MAD MAD Adjusted FEMA Estimate = ±$2,110,787 MAD Rapid Cost Estimate = ±$1,580,101

Figures 5.7, 5.8 and 5.9 illustrate the sorted storm data based on absolute error values in order to develop an empirical CDF, which essentially demonstrates that 50% of storms differed from the median. However, outliers are identified and eliminated from this analysis in order to provide a readable plot.

Figure 5.713 Error absolute values deviation from median: Rapid Cost Estimate

Rapid Cost Estimate Absolute Deviation from Median

Median Emperical CDF Linear (Emperical CDF) 100% 90% 80% 70% 60% 50% 40% y = 3E-07x 30% R² = 0.9574 20% 10% Absolute Deviation from Median ($) Medianfrom Deviation Absolute 0% $0.00 $0.50 $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 Millions Percentile

Figure 5.8 14 Error absolute values deviation from median: Actual FEMA estimate

Actual FEMA Estimate Absolute Deviation from Median

Median Emperical CDF Linear (Emperical CDF) 100% 90% 80% 70% 60% 50% 40% 30% y = 5E-08x 20% R² = 0.3932 10% Absolute Deviation from Median ($) Medianfrom Deviation Absolute 0% $0.00 $5.00 $10.00 $15.00 $20.00 $25.00 $30.00 Millions Percentile

Figure 5.9 15 Error absolute values deviation from median: Adjusted FEMA estimate

Adjusted FEMA Estimate Absolute Deviation from Median

Median Series1 Linear (Series1) 100% 90% 80% 70% 60% 50% y = 5E-08x R² = -0.234 40% 30% 20% 10% Absolute Deviation from Median ($) Medianfrom Deviation Absolute 0% $0.00 $10.00 $20.00 $30.00 Percentile Millions

Figures 5.10, 5.11, and 5.12 are normal probability plots, which show that the data might reasonably be assumed to be normal (i.e., the closer to a straight red line, the better).

Note that this plot shows absolute errors, not median deviations, and shows a good fit for the data. The good fit is demonstrated by a statistical measurement,

R-Square (R 2). R 2 concludes how close or how well data is fitted to a regression line. The rapid cost estimation model proposed in this research fits the data well if the differences between the actual costs and the costs estimated are small and unbiased. Therefore, the higher the result of the R2 the better the model fits the data.

Figure 5.10 16 Normal probability plot: Rapid Cost Estimate Rapid Cost Estimate Normal Probability Plot y = 1.0979x $2.50 R² = 0.9173 $2.00 $1.50 $1.00 $0.50 $- $(2.50) $(2.00) $(1.50) $(1.00) $(0.50) $- $0.50 $1.00 $1.50 $(0.50) $(1.00) $(1.50)

Normalized Error Normalized Error Statistics $(2.00) $(2.50) Standard Normal

Figure 5.11 17 Normal probability plot: Actual FEMA Estimate

Actual FEMA Estimate Normal Probability Plot

$4.00 y = 0.9042x R² = 0.6222 $3.50 $3.00 $2.50 $2.00 $1.50 $1.00 $0.50 $- $(2.50) $(2.00) $(1.50) $(1.00) $(0.50) $(0.50) $- $0.50 $1.00 $1.50 Normalized Error Statistics Error Normalized $(1.00) $(1.50) $(2.00) $(2.50) Standard Normal

Figure 5.12 18 Normal probability plot: Adjusted FEMA Estimate

Adjusted FEMA Estimate Normal Probability Plot

$4.00 y = 0.859x R² = 0.5616

$3.00

$2.00

$1.00

$- $(2.50) $(2.00) $(1.50) $(1.00) $(0.50) $- $0.50 $1.00 $1.50 Normalized Error Statistics Error Normalized

$(1.00)

$(2.00) Standard Normal

The good fit results obtained after plotting the absolute error values validates the hypothesis previously claimed in this research. The hypothesis states that the rapid cost estimate using GIS is a more accurate method to estimate recovery costs of physically damaged public properties than the FEMA estimation method. Table 5.7 illustrates the R 2 results to accept the hypothesis.

Table 5.7 Regression Analysis R 2's

Cost Estimation Method Error absolute values Normal probability plot R2 deviation from median Rapid Cost Estimation 95.74% 91.73% Actual FEMA Estimation 39.32% 62.22% Adjusted FEMA Estimation 23.40% 56.16%

In general, the absolute deviation from median regression model for the

Rapid Cost Estimate accounts for 95.74% of the variance while the FEMA

Estimation accounts for 39.32% and Adjusted FEMA Estimate for 23.40%.

Similarly, the normal probability plot for the Rapid Cost Estimate accounts for

91.73% while Actual FEMA Estimation accounts for 62.22% and Adjusted FEMA

Estimate for 56.16%.

Therefore, the Rapid Cost Estimate is a better estimation method since it has the higher R 2 which is closer to 100%. If the regression analysis performed for the Rapid Cost Estimate model could explain 100% of the variance, the fitted values would equal the actual recovery costs of physically damaged public properties in the aftermath of the storms.

5.4 GIS output

The GIS output model is shown in this section. The outputs consider all jurisdictions that receive public property assistance funding, as declared by

FEMA. For instance, Hurricane Hugo (category 2) recovery cost is determined to be 56,898,305USD; the Hurricane Hortense (category 1) recovery cost is

51,503,134USD; the Hurricane Georges (category 2) recovery cost is

70,491,908USD; the tropical storm Jeanne recovery cost is 45,139,449USD; and the Hurricane Irene (category 1) recovery cost is 53,353,454USD. The geospatial analysis displays a color-coded distribution table based on the recovery costs

(damages) reported by FEMA’s disaster declarations.

5.4.1 Hugo

NOAA (1990) reported that research aircraft measured winds of 160 MPH and a central pressure of 918 mb at one point east of Guadeloupe which rated Hugo as a Category 5.

When Hugo struck the Virgin Islands, Puerto Rico and the Carolinas, it was classified as a Category 4. The following is recorded:

1. Wind and Pressure Data: Wind recorded at 120 MPH. Sustained winds hit 98

MPH. Lowest surface pressure at 946mb at Roosevelt Roads.

Figure 5.13 19 NOAA-Historical Hurricane Tracks Hugo (1989)

Figure 5.14 20 ArcMap® Hugo GIS-based model output

5.4.2 Hortese

Hurricane Hortense crossed the Puerto Rico in the southwest side of the

Island as category one (Avila, 1996). Hortense devastated portions of Puerto Rico but most of the damage was not done by winds or storm surge. Instead, damage was caused by torrential rains producing flash floods and mud slides (Avila, 1996).

From Avila’s Preliminary Report October 23 rd , 1996, the following is recorded:

1. Wind and Pressure Data: Maximum wind speed reported was 95 kn at 989mb

by the NOAA aircraft.

2. Puert Rico Landfall: Southwest of Puerto Rico with sustained surface winds of

95 kn.

3. Rainfall: 15 – 20 inches.

Figure 5.15 21 NOAA-Historical Hurricane Tracks Hortense (1996)

Figure 5.1622 ArcMap® Hortense GIS-based model output

5.4.3 George

Guiney (2014) describes hurricane George as “the second deadliest and second strongest hurricane within the Atlantic basin during the 1998 season”. From Guiney’s

Preliminary Reports updated 9 September 2014 for U.S. damage, the following is recorded:

4. Wind and Pressure Data: Maximum wind speed reported was 152 kn at 700mb

by the NOAA aircraft. The lowest central pressure reported was 937mb

5. Storm Surge Data: 10 feet in Fajardo, Puerto Rico

6. Puert Rico Landfall: Southeast of Puerto Rico with sustained surface winds of

100 kn. Two tornadoes were also reported in Puerto Rico.

7. Rainfall: 10 – 15 inches.

Figure 5.1723 NOAA-Historical Hurricane Tracks Georges (1998)

Figure 5.1824 ArcMap® Georges GIS-based model output

5.4.4 Jeanne

Tropical storm Jeanne on 14 September continue its circulation slowly over the

Virgin Islands and the center moved inland over southeastern Puerto Rico with a maximum sustained surface winds reached 60 kt. From Lawrence and Cobb (2005)

Preliminary Reports updated January 7 th, 2005, the following is recorded:

1. Wind and Pressure Data: Maximum wind speed reported was 60 knots at

991mb.

2. Puert Rico Landfall: Southeast of Puerto Rico with sustained surface winds of

45 knots.

3. Rainfall: 23.75 inches.

Figure 5.1925 NOAA-Historical Hurricane Tracks Jeanne (2004)

Figure 5.20 26 ArcMap® Jeanne GIS-based model output

5.4.5 Irene

Huuricane Irene became a hurricane while moving over the island of Puerto Rico, but the hurricane-force winds occurred only over water north of the center (Avila &

Casigialosi, 2011). From Avila and Casigialosi (2011) Tropical Cyclone report the following is recorded:

8. Wind and Pressure Data: Maximum wind speed reported was 65 knots at

990mb.

9. Puert Rico Landfall: Southeast of Puerto Rico with sustained surface winds of

65 knots.

10. Rainfall: 8 inches.

Figure 5.2127 NOAA: Historical Hurricane Tracks Irene (2011)

Figure 5.22 28 ArcMap® Irene GIS-based model output

5.5 Cost exceedance probability

Consequently, a probability analysis can be conducted to determine the potential costs of recovering after a storm. Cost exceedance probabilities anticipate the likely recovery cost being exceed and not accurate cost estimation.

A cost exceedance probability describes the behavior of individual extreme events (Jagger & Elsner, 2006) and the probability that a determined monetary value will be exceeded. Similar works have been performed by Malmstadt,

Scheitlin, and Elsner (2009) to estimate the potential losses in Florida, where the loss exceedance curve is based on a generalized Pareto distribution to forecast a yearly total loss amount. However, this work employs normalized costs as input parameters because these correspond with the recovery cost incremental data.

After normalizing the available cost data, a cost exceedance probability analysis should be used to define the probability of a cost estimation for any given storm event. The appropriate cost exceedance method can then be used to extend the cost curve to illustrate extreme recovery costs after a storm event.

The cost exceedance model for Puerto Rico storms is based on the provided empirical storm cost data. The model is developed in MATLAB ®. See Appendix C for the code reference. The provided data points, including storm dates and adjusted/normalized costs, were provided and manually entered into the m-file.

The actual cost exceedance model is based on a modified version of the model presented by Malmstadt, Scheitlin, and Elsner (2009) in Florida Hurricanes and Damage Costs. Specifically, the proposed model is similar in spirit, but uses a

82 fundamentally different statistical analysis to develop the model. The Malmstadt,

Scheitlin, and Elsner (2009) model uses a generalized Pareto distribution to estimate the cost exceedance probability. The analysis in this research uses a two- stage approach, where the number of storms in a given year is drawn from a

Poisson distribution (fit from the data), and the cost of each hurricane is drawn from a lognormal distribution (also fit from the data). For instance, based on

Poisson distribution fit from empirical storm count data, Puerto Rico has a 33% probability of having at least one storm strike each year.

Next section will cover the random sampling methodology used to develop the exceedance probability curve including 95% confidence interval. Random sampling is used to analyze sample results. In other words, incorporating random sampling in this analysis will allow to use statistical methods to define a confidence interval around the sample mean.

5.5.1 Random sampling methodology

MATLAB ® provides a built-in function for randomly sampling from a

Poisson distribution with a specified parameter: poissrnd(param). Additionally, by creating a distribution object:

lndist = fitdist(costs, 'exp' ); a vector n random samples can be drawn from lndist as follows:

indiv_cost = lndist.random(1,n);

A Monte Carlo simulation was performed to develop the cost exceedance probability model. Set Ctotal = $0 and Ktotal = 0. For trial i = 1,…, n:

a) Random sampling from the Poisson distribution with parameter λ=62/21.

This will yield an integer number of storms Ki > 0.

b) If Ki==0, trial i has ended.

Else, for storms k = 1,…, Ki, sample the exponential distribution with parameter

μ=$18,858,379 to obtain cost ck. Ci = Σk {c k}.

From the n = 20,000 costs Ci , create an empirical probability plot. This process is then repeated for parameters that lie at the bounds of a 95% confidence interval about μ: [12,821,196USD, 30,465,103USD], to develop a 95% confidence interval band.

The result of these three Monte Carlo simulations is the cost exceedance probability plot in Figure 5.23, which is obtained by sorting the annual cost results and plotting them against an equally-sized vector that contains the numbers from 0 to 1 in n equal steps. The right tail end of the data is not shown on the plot because the cost exceedance rapidly collapses to zero as the probability approaches the empirical probability that any storms occur in a given year (approximately 21/62 for the given data). The exceedance probability curve in Figures 5.23 illustrates

Puerto Rico’s cost probability estimation for yearly cost estimation in the aftermath of a storm event exceeding specified amounts.

Figure 5.23 29 Cost exceedance probability curve. The red curve represents the results of the Monte Carlo simulation performed with the nominal exponential cost distribution. The dashed curves represent the 95% confidence interval around the nominal result.

Also, from the cost exceedance probability curve (Figure 5.23), the frequency of a storm resulting in a certain cost for recovery can be estimated. The exceedance cost probability is a valuable tool that incorporates the normalized damage costs into the decision making process and assessment of rapid cost estimation.

It is expected that a storm produces at least $10 million to recover public properties once in every 66 months, on average. This finding should be a matter of concern for the local government to better define and understand the disaster and emergency response budget to enable a more efficient recovery system.

5.6 Log-normal distribution

Normalized cost data distribution is analyzed through the log-normal method because of the connection between additive effects and the normal distribution parallels that of multiplicative effects and the log-normal distribution

(Limpert, Stahel, & Abbt, 2001). Log-normal distribution is based on a variety of forces acting independently of one another having a multiplicative effect. The use of the log-normal model is equivalent to first subjecting the cost data to the log transformation and then proceeding with methods based on the normal distribution. However, the Kolmogorov-Smirnov Test (KS-test) is applied to decide if the cost data comes from log-normal distribution.

KS-test is used to compare an empirical CDF to either a reference CDF

(one-sample) or another empirical CDF (two-sample). The purpose is to test the null hypothesis that the two datasets come from the same underlying distribution.

KS-tests are non-parametric, as they make no assumption about the parameters of the data set (i.e. the setup of the test does not depend on the actual parameters of what was measured or collected). In the one-sample KS-test, it was compared the cost data of an empirical CDF (ECDF) to a reference CDF whose parameters may or may not be computed from the data set. The test statistic is the largest difference between two CDF and the empirical distribution function.

Mathematically, the test statistic KS is given by:

(5.10) = | − |

86 where “sup” is the supremum function. This is similar to “maximum”, but it is defined to include a limit which the maximum may be approaching, and provides an important correction for this statistic.

Recovery cost data shows a mean score of μ = 15.7231, with a standard deviation of σ = 1.29396. Therefore, the hypotheses for the KS-test are:

Ho: the cost data come from the lognormal distribution N(15.7231, 1.2939²)

Ha: the cost data do not come from the lognormal distribution N(15.7231, 1.2939²)

The one-sample KS-test is used to test whether these costs fits log-normal distribution p = 0.1406 with mean μ and standard deviation σ. The KS-test does not the reject the null hypothesis that the cost data comes from log-normal distribution. Figure 5.24 shows the lognormal distribution tested.

Figure 5.24 30 Log-normal distribution

The value of the KS-test statistic is 0.2552, which is equal to the height of the thick black bar. The MATLAB ® output (Figure 5.25) of

[H,P,KSSTAT,CV]=KS-test is:

Figure 5.25 31 Kolmogorov-Smirnov Test MATLAB® output

KSSTAT_manual = 0.2552 H = 0 P = 0.1406 KSSTAT = 0.2552 CV = 0.3014

The output includes the following:

1. H (if 0, do not reject the null hypothesis);

2. P (p-value of the test),

3. KSSTAT (KS-test statistic);

4. CV (critical value of KS-test statistic).

If KSSTAT < CV, then do not reject the null hypothesis.

Based on the KS-test above, the cost data for all historical storm cases come from the lognormal distribution.

Chapter 6. Conclusion

This work incorporates various components to an integrated GIS-based model to provide a systematic way to rapidly cost estimate public properties recovery after a storm event. The GIS-based model and the data have shown that a

JFC is a more suitable metric than the actual statewide per-capita estimator used by FEMA to estimate public property damage in the aftermath of a storm event.

The recovery cost estimation solution implies that it is important for emergency responder’s accountability to develop a general framework that implements appropriate analytical models to rapidly estimate recover cost.

Moreover, a systematic GIS-based cost estimation approach that interacts with a spatial mapping of storms to estimate cost for public properties recovery.

The rapid cost estimation results demonstrate that GIS-based model approach effectively complements the local government to implement a methodology that provides a more accurate public property cost estimate to recover from a storm disaster event. It also has been shown that $1.5 million, approximately, is the variability of the rapid cost estimate and that potential public property damages will continue to increase. The relationships between these storm event and recovery cost are demonstrated based on quartile regression analysis.

Figure 6.1 shows an increase trend in normalized costs. Quartile regression provides an equally convenient method, which breaks up the data into groups where a certain percentage of the time-series data falls within each bin. Negative

89 trends show that a value is decreasing over time, and positive trends show the opposite. Figure 6.1 evidences that the mean and the recovery cost upper quartile are seen as upward trends. This indicates that on an average, storms cost estimates for Puerto Rico are increasing over time.

Figure 6.1 32 Puerto Rico storm recovery cost trends with quartile regression lines. From top to bottom, the regression lines represent regression for the 3 rd quartile, median, and 1st quartile as functions of time.

Finally, it has been demonstrated that this approach improves upon current public property cost estimation for recovery and can provide emergency responders with a GIS-based model to integrate economic factors and storm intensity characteristics to develop better cost estimates. This GIS-based model offers the ability to construct accurate cost estimation process, built accountability for emergency responders, and provides relevant information to the concern of government and insurance companies.

6.1 Recommendations for future research

This section provides recommendations of future research.

1. Research should expand the rapid cost estimate model to incorporate storm

intensity characteristics, such as minimum pressure, precipitation, and

maximum sustained winds.

2. Additional comparison should be undertaken to consider probable scenario

if an event diminishing power as it crosses the interior features of a wider

region (i.e. Florida, South Carolina, and Louisiana).

3. Integrate this rapid cost estimation approach with FEMA's HAZUS which

computes detailed wind-shear, debris, and flooding to evaluate if the

recovery estimate costs modeled from those effects further qualify the

earlier estimate.

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102

Appendix A: Jurisdictions affected per storm

Storm Eloise Incident Place Declared County/Area Population End Date Code 9/19/1975 99001 Adjuntas (Municipality) 19,483

9/19/1975 99003 Aguada (Municipality) 41,959

9/19/1975 99009 Aibonito (Municipality) 25,900

9/19/1975 99015 Arroyo (Municipality) 19,575

9/19/1975 99027 Camuy (Municipality) 35,159

9/19/1975 99029 Canovanas (Municipality) 47,648

9/19/1975 99033 Catano (Municipality) 28,140

9/19/1975 99045 Comerio (Municipality) 20,778

9/19/1975 99049 Culebra (Municipality) 1,818

9/19/1975 99054 Florida (Municipality) 12,680

9/19/1975 99059 Guayanilla (Municipality) 21,581

Hormigueros 9/19/1975 99067 17,250 (Municipality)

9/19/1975 99079 Lajas (Municipality) 25,753

9/19/1975 99083 Las Marias (Municipality) 9,881

103

9/19/1975 99089 Luquillo (Municipality) 20,068

9/19/1975 99093 Maricao (Municipality) 6,275

9/19/1975 99095 Maunabo (Municipality) 12,225

9/19/1975 99099 Moca (Municipality) 40,109

9/19/1975 99101 Morovis (Municipality) 32,610

9/19/1975 99103 Naguabo (Municipality) 26,720

9/19/1975 99105 Naranjito (Municipality) 30,402

9/19/1975 99107 Orocovis (Municipality) 23,423

9/19/1975 99109 Patillas (Municipality) 19,277

9/19/1975 99111 Penuelas (Municipality) 24,282

Quebradillas 9/19/1975 99115 25,919 (Municipality)

9/19/1975 99117 Rincon (Municipality) 15,200

Sabana Grande 9/19/1975 99121 25,265 (Municipality)

9/19/1975 99133 Santa Isabel (Municipality) 23,274

9/19/1975 99141 Utuado (Municipality) 33,149

9/19/1975 99143 Vega Alta (Municipality) 39,951

104

9/19/1975 99147 Vieques (Municipality) 9,301

Frederic Incident End Place Declared County/Area Population Date Code 9/2/1979 99011 Anasco (Municipality) 29,261

9/2/1979 99015 Arroyo (Municipality) 19,575

9/2/1979 99017 Barceloneta (Municipality) 24,816

9/2/1979 99023 Cabo Rojo (Municipality) 50,917

9/2/1979 99037 Ceiba (Municipality) 13,631

9/2/1979 99039 Ciales (Municipality) 18,782

9/2/1979 99049 Culebra (Municipality) 1,818

9/2/1979 99073 Jayuya (Municipality) 16,642

9/2/1979 99079 Lajas (Municipality) 25,753

9/2/1979 99081 Lares (Municipality) 30,753

9/2/1979 99083 Las Marias (Municipality) 9,881

9/2/1979 99093 Maricao (Municipality) 6,275

FEMA ID: DR-746 Incident End Place Declared County/Area Population Date Code 10/7/1985 99001 Adjuntas (Municipality) 19,483

10/7/1985 99035 Cayey (Municipality) 48,119

10/7/1985 99041 Cidra (Municipality) 43,480

105

10/7/1985 99053 Fajardo (Municipality) 36,993

10/7/1985 99061 Guaynabo (Municipality) 97,924

10/7/1985 99067 Hormigueros (Municipality) 17,250

10/7/1985 99073 Jayuya (Municipality) 16,642

10/7/1985 99095 Maunabo (Municipality) 12,225

10/7/1985 99105 Naranjito (Municipality) 30,402

10/7/1985 99107 Orocovis (Municipality) 23,423

10/7/1985 99111 Penuelas (Municipality) 24,282

10/7/1985 99141 Utuado (Municipality) 33,149

FEMA ID: DR-805 Incident End Place Declared County/Area Population Date Code 12/9/1987 99001 Adjuntas (Municipality) 19,483

12/9/1987 99009 Aibonito (Municipality) 25,900

12/9/1987 99029 Canovanas (Municipality) 47,648

12/9/1987 99031 Carolina (Municipality) 176,762

12/9/1987 99043 Coamo (Municipality) 40,512

12/9/1987 99049 Culebra (Municipality) 1,818

12/9/1987 99053 Fajardo (Municipality) 36,993

12/9/1987 99059 Guayanilla (Municipality) 21,581

12/9/1987 99063 Gurabo (Municipality) 45,369

12/9/1987 99069 Humacao (Municipality) 58,466

12/9/1987 99075 Juana Diaz (Municipality) 50,747

106

12/9/1987 99077 Juncos (Municipality) 40,290

12/9/1987 99079 Lajas (Municipality) 25,753

12/9/1987 99085 Las Piedras (Municipality) 38,675

12/9/1987 99087 Loiza (Municipality) 30,060

12/9/1987 99095 Maunabo (Municipality) 12,225

12/9/1987 99103 Naguabo (Municipality) 26,720

12/9/1987 99107 Orocovis (Municipality) 23,423

12/9/1987 99109 Patillas (Municipality) 19,277

12/9/1987 99111 Penuelas (Municipality) 24,282

12/9/1987 99113 Ponce (Municipality) 166,327

12/9/1987 99119 Rio Grande (Municipality) 54,304

Sabana Grande 12/9/1987 99121 25,265 (Municipality)

12/9/1987 99123 Salinas (Municipality) 31,078

12/9/1987 99125 San German (Municipality) 35,527

12/9/1987 99129 San Lorenzo (Municipality) 41,058

12/9/1987 99133 Santa Isabel (Municipality) 23,274

12/9/1987 99141 Utuado (Municipality) 33,149

12/9/1987 99147 Vieques (Municipality) 9,301

12/9/1987 99149 Villalba (Municipality) 26,073

12/9/1987 99151 Yabucoa (Municipality) 37,941

12/9/1987 99153 Yauco (Municipality) 42,043

107

Hugo Incident End Place Declared County/Area Population Date Code 9/18/1989 99001 Adjuntas (Municipality) 19,483

Aguas Buenas 9/18/1989 99007 28,659 (Municipality)

9/18/1989 99009 Aibonito (Municipality) 25,900

9/18/1989 99013 Arecibo (Municipality) 96,440

9/18/1989 99015 Arroyo (Municipality) 19,575

9/18/1989 99017 Barceloneta (Municipality) 24,816

Barranquitas 9/18/1989 99019 30,318 (Municipality)

9/18/1989 99021 Bayamon (Municipality) 208,116

9/18/1989 99025 Caguas (Municipality) 142,893

9/18/1989 99027 Camuy (Municipality) 35,159

9/18/1989 99029 Canovanas (Municipality) 47,648

9/18/1989 99031 Carolina (Municipality) 176,762

9/18/1989 99033 Catano (Municipality) 28,140

9/18/1989 99035 Cayey (Municipality) 48,119

9/18/1989 99037 Ceiba (Municipality) 13,631

9/18/1989 99039 Ciales (Municipality) 18,782

9/18/1989 99041 Cidra (Municipality) 43,480

9/18/1989 99043 Coamo (Municipality) 40,512

9/18/1989 99045 Comerio (Municipality) 20,778

108

9/18/1989 99047 Corozal (Municipality) 37,142

9/18/1989 99049 Culebra (Municipality) 1,818

9/18/1989 99051 Dorado (Municipality) 38,165

9/18/1989 99053 Fajardo (Municipality) 36,993

9/18/1989 99054 Florida (Municipality) 12,680

9/18/1989 99057 Guayama (Municipality) 45,362

9/18/1989 99061 Guaynabo (Municipality) 97,924

9/18/1989 99063 Gurabo (Municipality) 45,369

9/18/1989 99065 Hatillo (Municipality) 41,953

9/18/1989 99069 Humacao (Municipality) 58,466

9/18/1989 99073 Jayuya (Municipality) 16,642

9/18/1989 99077 Juncos (Municipality) 40,290

9/18/1989 99081 Lares (Municipality) 30,753

9/18/1989 99085 Las Piedras (Municipality) 38,675

9/18/1989 99087 Loiza (Municipality) 30,060

9/18/1989 99089 Luquillo (Municipality) 20,068

9/18/1989 99091 Manati (Municipality) 44,113

9/18/1989 99095 Maunabo (Municipality) 12,225

9/18/1989 99101 Morovis (Municipality) 32,610

9/18/1989 99103 Naguabo (Municipality) 26,720

9/18/1989 99105 Naranjito (Municipality) 30,402

9/18/1989 99107 Orocovis (Municipality) 23,423

9/18/1989 99109 Patillas (Municipality) 19,277

109

9/18/1989 99111 Penuelas (Municipality) 24,282

9/18/1989 99113 Ponce (Municipality) 166,327

9/18/1989 99119 Rio Grande (Municipality) 54,304

9/18/1989 99123 Salinas (Municipality) 31,078

9/18/1989 99127 San Juan (Municipality) 395,326

San Lorenzo 9/18/1989 99129 41,058 (Municipality)

9/18/1989 99135 Toa Alta (Municipality) 74,066

9/18/1989 99137 Toa Baja (Municipality) 89,609

Trujillo Alto 9/18/1989 99139 74,842 (Municipality)

9/18/1989 99141 Utuado (Municipality) 33,149

9/18/1989 99143 Vega Alta (Municipality) 39,951

9/18/1989 99145 Vega Baja (Municipality) 59,662

9/18/1989 99147 Vieques (Municipality) 9,301

9/18/1989 99149 Villalba (Municipality) 26,073

9/18/1989 99151 Yabucoa (Municipality) 37,941

Marilyn Incident End Place Declared County/Area Population Date Code Aguas Buenas 9/17/1995 99007 28,659 (Municipality)

9/17/1995 99029 Canovanas (Municipality) 47,648

110

9/17/1995 99037 Ceiba (Municipality) 13,631

9/17/1995 99049 Culebra (Municipality) 1,818

9/17/1995 99053 Fajardo (Municipality) 36,993

9/17/1995 99077 Juncos (Municipality) 40,290

9/17/1995 99087 Loiza (Municipality) 30,060

9/17/1995 99103 Naguabo (Municipality) 26,720

San Lorenzo 9/17/1995 99129 41,058 (Municipality)

9/17/1995 99147 Vieques (Municipality) 9,301

Hortense Incident End Place Declared County/Area Population Date Code 9/11/1996 99001 Adjuntas (Municipality) 19,483

9/11/1996 99003 Aguada (Municipality) 41,959

9/11/1996 99005 Aguadilla (Municipality) 60,949

Aguas Buenas 9/11/1996 99007 28,659 (Municipality)

9/11/1996 99009 Aibonito (Municipality) 25,900

9/11/1996 99013 Arecibo (Municipality) 96,440

9/11/1996 99015 Arroyo (Municipality) 19,575

9/11/1996 99017 Barceloneta (Municipality) 24,816

Barranquitas 9/11/1996 99019 30,318 (Municipality)

111

9/11/1996 99021 Bayamon (Municipality) 208,116

9/11/1996 99025 Caguas (Municipality) 142,893

9/11/1996 99029 Canovanas (Municipality) 47,648

9/11/1996 99031 Carolina (Municipality) 176,762

9/11/1996 99035 Cayey (Municipality) 48,119

9/11/1996 99039 Ciales (Municipality) 18,782

9/11/1996 99041 Cidra (Municipality) 43,480

9/11/1996 99043 Coamo (Municipality) 40,512

9/11/1996 99045 Comerio (Municipality) 20,778

9/11/1996 99047 Corozal (Municipality) 37,142

9/11/1996 99051 Dorado (Municipality) 38,165

9/11/1996 99055 Guanica (Municipality) 19,427

9/11/1996 99057 Guayama (Municipality) 45,362

9/11/1996 99059 Guayanilla (Municipality) 21,581

9/11/1996 99061 Guaynabo (Municipality) 97,924

9/11/1996 99063 Gurabo (Municipality) 45,369

9/11/1996 99069 Humacao (Municipality) 58,466

9/11/1996 99073 Jayuya (Municipality) 16,642

9/11/1996 99075 Juana Diaz (Municipality) 50,747

9/11/1996 99077 Juncos (Municipality) 40,290

9/11/1996 99081 Lares (Municipality) 30,753

9/11/1996 99083 Las Marias (Municipality) 9,881

9/11/1996 99085 Las Piedras (Municipality) 38,675

112

9/11/1996 99087 Loiza (Municipality) 30,060

9/11/1996 99091 Manati (Municipality) 44,113

9/11/1996 99095 Maunabo (Municipality) 12,225

9/11/1996 99101 Morovis (Municipality) 32,610

9/11/1996 99103 Naguabo (Municipality) 26,720

9/11/1996 99107 Orocovis (Municipality) 23,423

9/11/1996 99109 Patillas (Municipality) 19,277

9/11/1996 99111 Penuelas (Municipality) 24,282

9/11/1996 99113 Ponce (Municipality) 166,327

9/11/1996 99117 Rincon (Municipality) 15,200

9/11/1996 99119 Rio Grande (Municipality) 54,304

9/11/1996 99123 Salinas (Municipality) 31,078

9/11/1996 99127 San Juan (Municipality) 395,326

9/11/1996 99133 Santa Isabel (Municipality) 23,274

9/11/1996 99135 Toa Alta (Municipality) 74,066

9/11/1996 99137 Toa Baja (Municipality) 89,609

Trujillo Alto 9/11/1996 99139 74,842 (Municipality)

9/11/1996 99141 Utuado (Municipality) 33,149

9/11/1996 99143 Vega Alta (Municipality) 39,951

9/11/1996 99149 Villalba (Municipality) 26,073

9/11/1996 99151 Yabucoa (Municipality) 37,941

9/11/1996 99153 Yauco (Municipality) 42,043

113

Georges Incident End Place Declared County/Area Population Date Code 10/27/1998 99001 Adjuntas (Municipality) 19,483

10/27/1998 99003 Aguada (Municipality) 41,959

10/27/1998 99005 Aguadilla (Municipality) 60,949

Aguas Buenas 10/27/1998 99007 28,659 (Municipality)

10/27/1998 99009 Aibonito (Municipality) 25,900

10/27/1998 99011 Anasco (Municipality) 29,261

10/27/1998 99013 Arecibo (Municipality) 96,440

10/27/1998 99015 Arroyo (Municipality) 19,575

10/27/1998 99017 Barceloneta (Municipality) 24,816

Barranquitas 10/27/1998 99019 30,318 (Municipality)

10/27/1998 99021 Bayamon (Municipality) 208,116

10/27/1998 99023 Cabo Rojo (Municipality) 50,917

10/27/1998 99025 Caguas (Municipality) 142,893

10/27/1998 99027 Camuy (Municipality) 35,159

10/27/1998 99029 Canovanas (Municipality) 47,648

10/27/1998 99031 Carolina (Municipality) 176,762

10/27/1998 99033 Catano (Municipality) 28,140

10/27/1998 99035 Cayey (Municipality) 48,119

114

10/27/1998 99037 Ceiba (Municipality) 13,631

10/27/1998 99039 Ciales (Municipality) 18,782

10/27/1998 99041 Cidra (Municipality) 43,480

10/27/1998 99043 Coamo (Municipality) 40,512

10/27/1998 99045 Comerio (Municipality) 20,778

10/27/1998 99047 Corozal (Municipality) 37,142

10/27/1998 99049 Culebra (Municipality) 1,818

10/27/1998 99051 Dorado (Municipality) 38,165

10/27/1998 99053 Fajardo (Municipality) 36,993

10/27/1998 99054 Florida (Municipality) 12,680

10/27/1998 99055 Guanica (Municipality) 19,427

10/27/1998 99057 Guayama (Municipality) 45,362

10/27/1998 99059 Guayanilla (Municipality) 21,581

10/27/1998 99061 Guaynabo (Municipality) 97,924

10/27/1998 99063 Gurabo (Municipality) 45,369

10/27/1998 99065 Hatillo (Municipality) 41,953

Hormigueros 10/27/1998 99067 17,250 (Municipality)

10/27/1998 99069 Humacao (Municipality) 58,466

10/27/1998 99071 Isabela (Municipality) 45,631

10/27/1998 99073 Jayuya (Municipality) 16,642

10/27/1998 99075 Juana Diaz (Municipality) 50,747

10/27/1998 99077 Juncos (Municipality) 40,290

115

10/27/1998 99079 Lajas (Municipality) 25,753

10/27/1998 99081 Lares (Municipality) 30,753

10/27/1998 99083 Las Marias (Municipality) 9,881

10/27/1998 99085 Las Piedras (Municipality) 38,675

10/27/1998 99087 Loiza (Municipality) 30,060

10/27/1998 99089 Luquillo (Municipality) 20,068

10/27/1998 99091 Manati (Municipality) 44,113

10/27/1998 99093 Maricao (Municipality) 6,275

10/27/1998 99095 Maunabo (Municipality) 12,225

10/27/1998 99097 Mayaguez (Municipality) 89,080

10/27/1998 99099 Moca (Municipality) 40,109

10/27/1998 99101 Morovis (Municipality) 32,610

10/27/1998 99103 Naguabo (Municipality) 26,720

10/27/1998 99105 Naranjito (Municipality) 30,402

10/27/1998 99107 Orocovis (Municipality) 23,423

10/27/1998 99109 Patillas (Municipality) 19,277

10/27/1998 99111 Penuelas (Municipality) 24,282

10/27/1998 99113 Ponce (Municipality) 166,327

Quebradillas 10/27/1998 99115 25,919 (Municipality)

10/27/1998 99117 Rincon (Municipality) 15,200

10/27/1998 99119 Rio Grande (Municipality) 54,304

116

10/27/1998 99121 Sabana Grande 25,265 (Municipality) 10/27/1998 99123 Salinas (Municipality) 31,078

10/27/1998 99125 San German (Municipality) 35,527

10/27/1998 99127 San Juan (Municipality) 395,326

San Lorenzo 10/27/1998 99129 41,058 (Municipality)

San Sebastian 10/27/1998 99131 42,430 (Municipality)

10/27/1998 99133 Santa Isabel (Municipality) 23,274

10/27/1998 99135 Toa Alta (Municipality) 74,066

10/27/1998 99137 Toa Baja (Municipality) 89,609

Trujillo Alto 10/27/1998 99139 74,842 (Municipality)

10/27/1998 99141 Utuado (Municipality) 33,149

10/27/1998 99143 Vega Alta (Municipality) 39,951

10/27/1998 99145 Vega Baja (Municipality) 59,662

10/27/1998 99147 Vieques (Municipality) 9,301

10/27/1998 99149 Villalba (Municipality) 26,073

10/27/1998 99151 Yabucoa (Municipality) 37,941

10/27/1998 99153 Yauco (Municipality) 42,043

117

FEMA ID: DR-372 Incident End Place Declared County/Area Population Date Code 5/11/2001 99001 Adjuntas (Municipality) 19,483

5/11/2001 99011 Anasco (Municipality) 29,261

5/11/2001 99023 Cabo Rojo (Municipality) 50,917

5/11/2001 99055 Guanica (Municipality) 19,427

5/11/2001 99059 Guayanilla (Municipality) 21,581

Hormigueros 5/11/2001 99067 17,250 (Municipality)

5/11/2001 99079 Lajas (Municipality) 25,753

5/11/2001 99081 Lares (Municipality) 30,753

5/11/2001 99083 Las Marias (Municipality) 9,881

5/11/2001 99093 Maricao (Municipality) 6,275

5/11/2001 99099 Moca (Municipality) 40,109

5/11/2001 99117 Rincon (Municipality) 15,200

Sabana Grande 5/11/2001 99121 25,265 (Municipality)

5/11/2001 99125 San German (Municipality) 35,527

5/11/2001 99153 Yauco (Municipality) 42,043

FEMA ID: 1396 Incident End Place Declared County/Area Population Date Code

118

Aguas Buenas 11/9/2001 99007 28,659 (Municipality)

Barranquitas 11/9/2001 99019 30,318 (Municipality)

11/9/2001 99021 Bayamon (Municipality) 208,116

11/9/2001 99039 Ciales (Municipality) 18,782

11/9/2001 99047 Corozal (Municipality) 37,142

11/9/2001 99073 Jayuya (Municipality) 16,642

11/9/2001 99077 Juncos (Municipality) 40,290

11/9/2001 99101 Morovis (Municipality) 32,610

11/9/2001 99105 Naranjito (Municipality) 30,402

11/9/2001 99107 Orocovis (Municipality) 23,423

San Lorenzo 11/9/2001 99129 41,058 (Municipality)

11/9/2001 99141 Utuado (Municipality) 33,149

11/9/2001 99143 Vega Alta (Municipality) 39,951

FEMA ID: DR-1501 Incident End Place Declared County/Area Population Date Code 11/23/2003 99035 Cayey (Municipality) 48,119

11/23/2003 99037 Ceiba (Municipality) 13,631

11/23/2003 99043 Coamo (Municipality) 40,512

11/23/2003 99049 Culebra (Municipality) 1,818

119

11/23/2003 99055 Guanica (Municipality) 19,427

11/23/2003 99057 Guayama (Municipality) 45,362

11/23/2003 99077 Juncos (Municipality) 40,290

11/23/2003 99079 Lajas (Municipality) 25,753

11/23/2003 99089 Luquillo (Municipality) 20,068

11/23/2003 99103 Naguabo (Municipality) 26,720

11/23/2003 99109 Patillas (Municipality) 19,277

11/23/2003 99119 Rio Grande (Municipality) 54,304

Sabana Grande 11/23/2003 99121 25,265 (Municipality)

11/23/2003 99123 Salinas (Municipality) 31,078

San German 11/23/2003 99125 35,527 (Municipality)

San Lorenzo 11/23/2003 99129 41,058 (Municipality)

11/23/2003 99141 Utuado (Municipality) 33,149

11/23/2003 99147 Vieques (Municipality) 9,301

11/23/2003 99151 Yabucoa (Municipality) 37,941

11/23/2003 99153 Yauco (Municipality) 42,043

120

Jeanne Incident End Place Declared County/Area Population Date Code 9/19/2004 99003 Aguada (Municipality) 41,959

9/19/2004 99005 Aguadilla (Municipality) 60,949

Aguas Buenas 9/19/2004 99007 28,659 (Municipality)

9/19/2004 99009 Aibonito (Municipality) 25,900

9/19/2004 99011 Anasco (Municipality) 29,261

9/19/2004 99013 Arecibo (Municipality) 96,440

9/19/2004 99015 Arroyo (Municipality) 19,575

Barceloneta 9/19/2004 99017 24,816 (Municipality)

9/19/2004 99021 Bayamon (Municipality) 208,116

9/19/2004 99025 Caguas (Municipality) 142,893

9/19/2004 99027 Camuy (Municipality) 35,159

9/19/2004 99029 Canovanas (Municipality) 47,648

9/19/2004 99031 Carolina (Municipality) 176,762

9/19/2004 99033 Catano (Municipality) 28,140

9/19/2004 99035 Cayey (Municipality) 48,119

9/19/2004 99037 Ceiba (Municipality) 13,631

9/19/2004 99039 Ciales (Municipality) 18,782

9/19/2004 99041 Cidra (Municipality) 43,480

9/19/2004 99043 Coamo (Municipality) 40,512

121

9/19/2004 99045 Comerio (Municipality) 20,778

9/19/2004 99047 Corozal (Municipality) 37,142

9/19/2004 99051 Dorado (Municipality) 38,165

9/19/2004 99053 Fajardo (Municipality) 36,993

9/19/2004 99054 Florida (Municipality) 12,680

9/19/2004 99057 Guayama (Municipality) 45,362

9/19/2004 99065 Hatillo (Municipality) 41,953

9/19/2004 99069 Humacao (Municipality) 58,466

9/19/2004 99071 Isabela (Municipality) 45,631

9/19/2004 99075 Juana Diaz (Municipality) 50,747

9/19/2004 99077 Juncos (Municipality) 40,290

9/19/2004 99081 Lares (Municipality) 30,753

9/19/2004 99085 Las Piedras (Municipality) 38,675

9/19/2004 99087 Loiza (Municipality) 30,060

9/19/2004 99091 Manati (Municipality) 44,113

9/19/2004 99095 Maunabo (Municipality) 12,225

9/19/2004 99099 Moca (Municipality) 40,109

9/19/2004 99101 Morovis (Municipality) 32,610

9/19/2004 99103 Naguabo (Municipality) 26,720

9/19/2004 99105 Naranjito (Municipality) 30,402

9/19/2004 99107 Orocovis (Municipality) 23,423

9/19/2004 99109 Patillas (Municipality) 19,277

122

Quebradillas 9/19/2004 99115 25,919 (Municipality)

9/19/2004 99117 Rincon (Municipality) 15,200

9/19/2004 99119 Rio Grande (Municipality) 54,304

9/19/2004 99123 Salinas (Municipality) 31,078

San Lorenzo 9/19/2004 99129 41,058 (Municipality)

San Sebastian 9/19/2004 99131 42,430 (Municipality)

Santa Isabel 9/19/2004 99133 23,274 (Municipality)

9/19/2004 99135 Toa Alta (Municipality) 74,066

9/19/2004 99137 Toa Baja (Municipality) 89,609

9/19/2004 99141 Utuado (Municipality) 33,149

9/19/2004 99143 Vega Alta (Municipality) 39,951

9/19/2004 99145 Vega Baja (Municipality) 59,662

9/19/2004 99147 Vieques (Municipality) 9,301

9/19/2004 99149 Villalba (Municipality) 26,073

9/19/2004 99151 Yabucoa (Municipality) 37,941

FEMA ID: DR-1613 Incident End Place Declared County/Area Population Date Code 10/15/2005 99001 Adjuntas (Municipality) 19,483

123

10/15/2005 99009 Aibonito (Municipality) 25,900

10/15/2005 99035 Cayey (Municipality) 48,119

10/15/2005 99059 Guayanilla (Municipality) 21,581

10/15/2005 99073 Jayuya (Municipality) 16,642

10/15/2005 99075 Juana Diaz (Municipality) 50,747

10/15/2005 99081 Lares (Municipality) 30,753

10/15/2005 99093 Maricao (Municipality) 6,275

10/15/2005 99107 Orocovis (Municipality) 23,423

10/15/2005 99111 Penuelas (Municipality) 24,282

10/15/2005 99113 Ponce (Municipality) 166,327

10/15/2005 99123 Salinas (Municipality) 31,078

Santa Isabel 10/15/2005 99133 23,274 (Municipality)

10/15/2005 99141 Utuado (Municipality) 33,149

10/15/2005 99149 Villalba (Municipality) 26,073

10/15/2005 99151 Yabucoa (Municipality) 37,941

10/15/2005 99153 Yauco (Municipality) 42,043

FEMA ID: DR-1798 Incident End Place Declared County/Area Population Date Code 10/3/2008 99001 Adjuntas (Municipality) 19,483

10/3/2008 99015 Arroyo (Municipality) 19,575

10/3/2008 99023 Cabo Rojo (Municipality) 50,917

124

10/3/2008 99055 Guanica (Municipality) 19,427

10/3/2008 99057 Guayama (Municipality) 45,362

10/3/2008 99059 Guayanilla (Municipality) 21,581

10/3/2008 99063 Gurabo (Municipality) 45,369

10/3/2008 99069 Humacao (Municipality) 58,466

10/3/2008 99073 Jayuya (Municipality) 16,642

10/3/2008 99077 Juncos (Municipality) 40,290

10/3/2008 99079 Lajas (Municipality) 25,753

10/3/2008 99083 Las Marias (Municipality) 9,881

10/3/2008 99085 Las Piedras (Municipality) 38,675

10/3/2008 99103 Naguabo (Municipality) 26,720

10/3/2008 99109 Patillas (Municipality) 19,277

10/3/2008 99111 Penuelas (Municipality) 24,282

10/3/2008 99113 Ponce (Municipality) 166,327

10/3/2008 99121 Sabana Grande 25,265 (Municipality) 10/3/2008 99123 Salinas (Municipality) 31,078

San German

10/3/2008 99125 (Municipality) 35,527

San Lorenzo

10/3/2008 99129 (Municipality) 41,058

Santa Isabel

10/3/2008 99133 (Municipality) 23,274

10/3/2008 99141 Utuado (Municipality) 33,149

125

10/3/2008 99149 Villalba (Municipality) 26,073

10/3/2008 99151 Yabucoa (Municipality) 37,941

10/3/2008 99153 Yauco (Municipality) 42,043

FEMA ID: DR-1919 Incident End Place Declared County/Area Population Date Code 5/31/2010 99013 Arecibo (Municipality) 96,440

Barranquitas 5/31/2010 99019 30,318 (Municipality)

5/31/2010 99043 Coamo (Municipality) 40,512

5/31/2010 99047 Corozal (Municipality) 37,142

5/31/2010 99051 Dorado (Municipality) 38,165

5/31/2010 99105 Naranjito (Municipality) 30,402

5/31/2010 99107 Orocovis (Municipality) 23,423

5/31/2010 99141 Utuado (Municipality) 33,149

5/31/2010 99143 Vega Alta (Municipality) 39,951

5/31/2010 99145 Vega Baja (Municipality) 59,662

Otto Incident End Place Declared County/Area Population Date Code 10/8/2010 99001 Adjuntas (Municipality) 19,483

10/8/2010 99009 Aibonito (Municipality) 25,900

10/8/2010 99011 Anasco (Municipality) 29,261

126

10/8/2010 99055 Guanica (Municipality) 19,427

10/8/2010 99057 Guayama (Municipality) 45,362

10/8/2010 99073 Jayuya (Municipality) 16,642

10/8/2010 99081 Lares (Municipality) 30,753

10/8/2010 99083 Las Marias (Municipality) 9,881

10/8/2010 99093 Maricao (Municipality) 6,275

10/8/2010 99097 Mayaguez (Municipality) 89,080

10/8/2010 99101 Morovis (Municipality) 32,610

10/8/2010 99107 Orocovis (Municipality) 23,423

10/8/2010 99109 Patillas (Municipality) 19,277

10/8/2010 99113 Ponce (Municipality) 166,327

10/8/2010 99121 Sabana Grande 25,265 (Municipality) 10/8/2010 99123 Salinas (Municipality) 31,078

San German 10/8/2010 99125 35,527 (Municipality)

10/8/2010 99141 Utuado (Municipality) 33,149

10/8/2010 99149 Villalba (Municipality) 26,073

10/8/2010 99151 Yabucoa (Municipality) 37,941

10/8/2010 99153 Yauco (Municipality) 42,043

FEMA ID: DR-4004 Incident End Place Declared County/Area Population Date Code 6/8/2011 99011 Anasco (Municipality) 29,261

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6/8/2011 99025 Caguas (Municipality) 142,893

6/8/2011 99027 Camuy (Municipality) 35,159

6/8/2011 99039 Ciales (Municipality) 18,782

6/8/2011 99065 Hatillo (Municipality) 41,953

6/8/2011 99085 Las Piedras (Municipality) 38,675

6/8/2011 99101 Morovis (Municipality) 32,610

6/8/2011 99107 Orocovis (Municipality) 23,423

San Lorenzo

6/8/2011 99129 (Municipality) 41,058

San Sebastian

6/8/2011 99131 (Municipality) 42,430

6/8/2011 99141 Utuado (Municipality) 33,149

6/8/2011 99149 Villalba (Municipality) 26,073

Irene Incident End Place Declared County/Area Population Date Code Adjuntas 8/24/2011 99001 19,483 (Municipality)

Aguada 8/24/2011 99003 41,959 (Municipality)

8/24/2011 99007 Aguas Buenas 28,659 (Municipality) Aibonito 8/24/2011 99009 25,900 (Municipality)

128

Anasco 8/24/2011 99011 29,261 (Municipality)

Arecibo 8/24/2011 99013 96,440 (Municipality)

8/24/2011 99015 Arroyo (Municipality) 19,575

8/24/2011 99019 Barranquitas 30,318 (Municipality) Bayamon 8/24/2011 99021 208,116 (Municipality)

8/24/2011 99025 Caguas (Municipality) 142,893

8/24/2011 99029 47,648 Canovanas (Municipality) Carolina 8/24/2011 99031 176,762 (Municipality)

8/24/2011 99033 Catano (Municipality) 28,140

8/24/2011 99035 Cayey (Municipality) 48,119

8/24/2011 99037 Ceiba (Municipality) 13,631

8/24/2011 99039 Ciales (Municipality) 18,782

8/24/2011 99041 Cidra (Municipality) 43,480

8/24/2011 99043 Coamo (Municipality) 40,512

Comerio 8/24/2011 99045 20,778 (Municipality)

Corozal 8/24/2011 99047 37,142 (Municipality)

129

Culebra 8/24/2011 99049 1,818 (Municipality)

Fajardo 8/24/2011 99053 36,993 (Municipality)

Guayama 8/24/2011 99057 45,362 (Municipality)

8/24/2011 99061 97,924 Guaynabo (Municipality) Gurabo 8/24/2011 99063 45,369 (Municipality)

Humacao 8/24/2011 99069 58,466 (Municipality)

8/24/2011 99073 Jayuya (Municipality) 16,642

8/24/2011 99075 50,747 Juana Diaz (Municipality) 8/24/2011 99077 Juncos (Municipality) 40,290

8/24/2011 99083 9,881 Las Marias (Municipality) 8/24/2011 99085 Las Piedras (Municipality) 38,675

8/24/2011 99087 Loiza (Municipality) 30,060

Luquillo 8/24/2011 99089 20,068 (Municipality)

Maricao 8/24/2011 99093 6,275 (Municipality)

Maunabo 8/24/2011 99095 12,225 (Municipality)

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Morovis 8/24/2011 99101 32,610 (Municipality)

Naguabo 8/24/2011 99103 26,720 (Municipality)

Naranjito 8/24/2011 99105 30,402 (Municipality)

Orocovis 8/24/2011 99107 23,423 (Municipality)

8/24/2011 99109 Patillas (Municipality) 19,277

Penuelas 8/24/2011 99111 24,282 (Municipality)

8/24/2011 99113 Ponce (Municipality) 166,327

8/24/2011 99117 Rincon (Municipality) 15,200

8/24/2011 99119 54,304 Rio Grande (Municipality) 8/24/2011 99121 Sabana Grande 25,265 (Municipality) 8/24/2011 99123 Salinas (Municipality) 31,078

San Juan 8/24/2011 99127 395,326 (Municipality)

San Lorenzo 8/24/2011 99129 41,058 (Municipality)

8/24/2011 99133 Santa Isabel 23,274 (Municipality) 8/24/2011 99139 Trujillo Alto 74,842 (Municipality) 8/24/2011 99141 Utuado (Municipality) 33,149

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8/24/2011 99145 59,662 Vega Baja (Municipality) Vieques 8/24/2011 99147 9,301 (Municipality)

Villalba 8/24/2011 99149 26,073 (Municipality)

Yabucoa 8/24/2011 99151 37,941 (Municipality)

8/24/2011 99153 Yauco (Municipality) 42,043

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Appendix B: Mahalanobis Distance MATLAB ® code

% Normalized Cost vectors CostData=fliplr([27542590,29366058;13907241,18182248;5151991,3826467;14469580, 17546991;51503134,46267262;56898305,60690764;14018172,18041686;53353454,584 29938;4694127,3855415;38155844,29108503;45139449,45481760;70491908,14734305 1;7631798,8839290;12333550,12940042;7354667,5593914;10983854,5273988;1155336 5,7819146;11864542,13255031;17849790,17228509;8119782,5700969;9563416,776482 9])/1e6;

% compute the Mahalanobis distances from the centroid M = mahal(CostData,CostData);

% find the cutoff for an outlier df = 2;

% 2 degrees of freedom b/c two variables p = 0.999;

% confidence level cutoff = chi2inv(p,df);

% chi squared distribution cutoff (Mahalanobis distances follow chi2 dist). % find the outliers non_outlier = find(M <= cutoff); outlier_ind = find(M > cutoff);

% create scatterplot scatter(CostData(non_outlier,1),CostData(non_outlier,2),50, M(non_outlier), '*' ,'LineWidth' ,2) hold on

133 scatter(CostData(:,1), CostData(:,2), 50, M, '*' ,'LineWidth' ,2) scatter(CostData(outlier_ind,1), CostData(outlier_ind,2), 200, M(outlier_ind), 'o' )

% Graph and axis labels xlabel( 'Normalized Cost (Millions of USD)' ) ylabel( 'Rapid Cost Estimate (Millions of USD)' ) title( 'Outlier Identification with Mahalinobis Distance' ) hb = colorbar; ylabel(hb, 'Mahalanobis Distance' ) grid on colormap jet axis([0 160 0 80]) text(137,67, 'Georges'

134

Appendix C: Cost exceedance probability MATLAB ® code

%%Empirical Probability Plot costs=[18041686;29366058;29108503;18182248;3855415;8839290;12940042;60 690764;3826467;46267262;147343051;5593914;5273988;7819146;45481760;13 255031;17228509;5700969;17546991;7764829;58429938];

%LogCost logsp_costs = logspace(log10(min(costs)),log10(max(costs))); logsp_costs_above = zeros(1, length(logsp_costs)); for i = 1: length(logsp_costs) thresh = logsp_costs(i); logsp_costs_above(i) = sum(costs > thresh); end

% COST MODEL % 1. Fit to exponential curve expdist = fitdist(costs, 'exp' ); CI = expdist.paramci;

% 2. Condifence bands expdist_lower = makedist( 'exp' ,'mu' ,CI(1)); expdist_upper = makedist( 'exp' ,'mu' ,CI(2));

% 3. Create CDFS from each one expcdf = cdf(expdist, logsp_costs); expcdf_lower = cdf(expdist_lower, logsp_costs); expcdf_upper = cdf(expdist_upper, logsp_costs);

% FREQUENCY MODEL % 1. Count annual storm frequency

135 year_no = [ 1950.64615; 1956.617567; 1971.646041; 1973.68032; 1975.709123;1979.679115; 1979.547695; 1981.691491; 1984.856533; 1988.651298;1989.719089; 1995.712408; 1996.698062; 1998.726865; 2000.64615; 2001.645493;2004.71197; 2007.948198; 2007.822254; 2008.627204; 2011.644398] year = floor(year_no); nH = zeros(1, min(year)-min(year)+1); for i = min(year):max(year) j = i - min(year) + 1; nH(j) = sum(year == i); end [freq,nH_freq] = hist(nH,0:3);

% Simulation trials = 20000; [annual_cost, annual_cost_lower, annual_cost_upper] = deal(zeros(1,trials)); for i = 1:trials

% how many storms this year - parameter is empirical mean nH_emp = poissrnd(count/(max(year)-min(year)+1));

% find a cost for each one if nH_emp > 0

% simulate with mean and CI models indiv_cost = expdist.random(1,nH_emp); indiv_cost_lower = expdist_lower.random(1,nH_emp); indiv_cost_upper = expdist_upper.random(1,nH_emp);

% add up the costs for each model in each year

136 annual_cost(i) = sum(indiv_cost); annual_cost_lower(i) = sum(indiv_cost_lower); annual_cost_upper(i) = sum(indiv_cost_upper); end end

% sort the costs and convert to millions to prepare for plotting sort_AC = sort(annual_cost)/1e6; sort_AC_lower = sort(annual_cost_lower)/1e6; sort_AC_upper = sort(annual_cost_upper)/1e6;

% identify the index of first non-zero cost ind = min(find(sort_AC>0));

% vector of relevant probabilities prob_vect = 1-(ind:trials)/trials;

% plot figure semilogy(prob_vect, sort_AC(ind:end), 'k' , 'LineWidth' , 2) hold on semilogy(prob_vect, sort_AC_lower(ind:end), 'k--', 'LineWidth' , 2) semilogy(prob_vect, sort_AC_upper(ind:end), 'k--', 'LineWidth' , 2) grid grid minor axis([0 0.25 1 1000]) xlabel( 'Annual Probability' ) ylabel( 'Cost Exceedance (Million of Dollars)' )

137