FLORIDA PUBLIC HURRICANE LOSS PROJECTION MODEL. Engineering Team Final Report. submitted to: Dr. Shahid Hamid. Director

Transcription

1 FLORIDA PUBLIC HURRICANE LOSS PROJECTION MODEL Engineering Team Final Report submitted to: Dr. Shahid Hamid Director LABORATORY FOR INSURANCE, FINANCIAL, AND ECONOMIC RESEARCH INTERNATIONAL HURRICANE RESEARCH CENTER FLORIDA INTERNATIONAL UNIVERSITY Volume III Development Calibration and Validation of Vulnerability Matrices of the Florida Public Hurricane Loss Projection Model May 2005

2 Principal Investigators ENGINEERING TEAM Kurtis Gurley, Ph. D. Associate Professor Civil and Coastal Engineering Department University of Florida Jean-Paul Pinelli, Ph.D., P.E. Team leader Associate Professor Civil Engineering Department Florida Institute of Technology Chelakara Subramanian, Ph.D., P.E. (UK) Professor Aerospace Engineering Department Florida Institute of Technology Graduate Research Assistants Anne Cope, Ph. D. Currently with Reynolds, Smith, and Hills Florida Liang Zhang, M.S. Currently with Risk Management Solutions California Joshua Murphree, M.S. Arnoldo Artiles Graduate Research Assistant Civil Engineering Department Florida Institute of Technology

3 Pranay Misra Graduate Research Assistant Civil Engineering Department Florida Institute of Technology Consultants: Dr. Sneh Gulati Associate Professor Department of Statistics Florida International University Dr. Emil Simiu NIST Fellow Building and Fire Research Laboratory National Institute of Standards and Technology

4 Abstract Hurricane force winds pose a potentially devastating threat to the $1.5 trillion dollars of existing real estate in the state of Florida. With rapidly increasing populations in coastal regions where this risk is highest, the need for insurance companies operating within the state to predict future losses from these events is critical. These circumstances prompted the Florida Department of Financial Services (FDFS) to request that a group of researchers develop a public hurricane loss projection model to estimate damage to residential structures when subject to high winds associated with hurricanes. Several models of this sort exist however almost all are developed for insurance companies for ratemaking purposes and being proprietary models the public has no access to the results which they produce. The complete risk assessment model is built from several distinct parts including: the wind field model, the exposure study, the vulnerability model, actuarial components, and the computer platform. The work presented in this report deals primarily with the development of the vulnerability model and its integration with the other components. Rather than using regression analysis of claims data to define the vulnerability of homes like other models, this vulnerability model uses a component approach that explicitly considers the resistance capacities of each component of a home and the wind forces produced at increments of wind speed to define damage. Variability in both the resistance capacities and wind forces are modeled using Monte Carlo simulation techniques. Monte Carlo simulation models are developed based upon what were determined from an exposure study to be the typical structural types in each region of the state. The Monte Carlo simulations only model physical damage to the major components of each home type. From the modeled damages to these components damage to the remainder of the home (the interior and utilities), likely contents damage, and repair times are extrapolated. The cost of repairing all damage is calculated based upon typical repair costs, defined by various costing resources, for each structural type. A separate model is also developed to predict damages to appurtenant structures. The repair cost predictions are organized in vulnerability matrices, which define the probability of any iii

5 increment of damage given a particular wind speed, or the probability of contents and additional living expense damage given an increment of structural damage. These damage predictions are validated using historical claims data from recent Florida hurricanes and inspections of structures damaged during the 2004 hurricane season. Actuarial considerations are applied to the vulnerability model predictions to define insured losses. All components are integrated together to form the complete insurance loss projection model, which can be used to simulate historical or hypothetical storm events or to predict average annual insured losses to a home covered by an insurance policy, a zip code, region, the entire state, or complete insurance portfolio file. iv

6 Table of Contents Abstract... iii List of Figures... viii List of Tables... xv Chapter 1 Introduction Background Goals and Objectives Scope...4 Chapter 2 Literature Review Cost Estimation Resources Loss Projection...6 Chapter 3 Vulnerability Model Development Modeled Structural Types Site-Built Homes Manufactured Homes Damage Matrices Site-Built Homes Manufactured Homes Replacement Cost Ratios Site-Built Homes Manufactured Homes Summary...28 Chapter 4 Cost Estimation Explicit Costing Florida Building Code Requirements / Replacement Thresholds General Requirements Windborne Debris Region High Velocity Hurricane Zone Implicit Costing Interior Damage Two-Story Homes Utilities Damage...60 v

7 4.3 Total Building Damage Site-Built Homes Manufactured Homes Other Coverage s Contents Additional Living Expenses Appurtenant Structures Summary Chapter 5 Vulnerability Model Results Model Vulnerability Matrices Site-Built Homes Vulnerability for Weak and Medium Models Manufactured Homes Weighted Vulnerability Matrices Standard or Strong Site-Built Homes Weak and Medium Site-Built Homes Weak, Medium, and Strong Model Distributions Manufactured Homes Summary Chapter 6 Model Validation Claims Data Processing Hurricane Andrew Hurricane Opal Damage Surveys Hurricane Charley Hurricane Frances Hurricane Jeanne Other Model Results Other Model/Regression Comparisons HAZUS Comparisons Summary Chapter 7 Model Integration Program Design Florida Commission Requirements Summary Chapter 8 Conclusions and Recommendations Current Research Conclusions Recommendations vi

8 References Appendix A Replacement Ratios Appendix B Programs Appendix C Results Appendix D Zip Code Classifications Appendix E ISO Structural Types Appendix F Use Cases Appendix G Claims Data Appendix H Mitigation Summary Definitions and Required Procedures Base case models Mitigated models Form V-2 base case, mitigated case, and individual mitigation measures Procedure for completing form V Modeling the base case and mitigation measures Vulnerability matrices and curves vii

9 List of Figures Figure Hurricane Jeanne making landfall (NOAA)... 1 Figure 3-1 Regional boundaries for exposure studies Figure 3-2 Performance of metal roof during Hurricane Charley Figure Performance of shingle roof during Hurricane Charley Figure Performance of tile roof during Hurricane Charley Figure Undamaged shingle roof following Charley Figure 3-6 Central FL manufactured home distribution Figure 3-7- South FL manufactured home distribution Figure FL Keys manufactured home distribution...17 Figure North FL manufactured home distribution...17 Figure HUD wind zone map Figure ASCE 7-98 basic wind speed map and windborne debris regions Figure 4-2 Shapes of Weibull distribution function Figure Interior damage as a function of sheathing damage, no random distribution (mean values) Figure Interior damage as a function of sheathing damage using Weibull distribution, mean=1 variance= Figure Sheathing damage and resulting interior damage Figure Interior damage as a function of roof sheathing damage Figure 4-7 Cover damage resulting in interior damage Figure 4-8 Cover damage exposing plywood Figure Interior damage as a function of roof cover damage Figure Port Charlotte manufactured home destroyed during Hurricane Charley Figure Punta Gorda home destroyed during Hurricane Charley Figure Wall damage of a poorly constructed home, majority of interior undamaged...48 Figure Interior damage as a function of wall damage...50 Figure Window damage from flying debris or wind pressure Figure Broken kitchen window, little or no interior damage just clean up Figure Interior damage as a function of window damage Figure Door damage and resulting interior damages Figure Interior damage as a function of door damage Figure Gable end damage viii

10 Figure Interior damage as a function of gable end damage Figure Sliding of manufactured home, likely light interior damage as a result Figure Overturned manufactured home in Hurricane Frances Figure Overturned manufactured home in Hurricane Charley Figure Electrical damage vs. sheathing damage Figure Electrical damage vs. interior damage resulting from sheathing damage Figure Electrical damage caused by exterior wall failure Figure Plumbing damage resulting from structural failures Figure Wind damaged air condition unit Figure Mechanical damage resulting from structural failures Figure Contents damage a complete bedroom set lies under the debris Figure Contents damage to a manufactured home Figure Contents damage - the whole roof is lost and some furniture may need to be replaced...71 Figure Modeled contents damage vs. structural damage, each point is one model simulation...71 Figure Time home is unlivable vs. Interior Damage Figure Modeled ALE damage vs. building damage Figure Typical plot of appurtenant structure vs. building claims Figure Highly susceptible appurtenant structure - the screened patio, and low susceptible - the pool Figure Moderately susceptible appurtenant structure - the pool house, and low susceptible - the pool Figure Appurtenant structure vulnerability curves Figure APS damage ratio vs. wind speed, exponential distribution Figure APS damage ratio vs. Building Damage ratio, assuming a random distribution of 5% high, 5% moderate, and 90% low (this figure was developed using a normal distribution, an update is intended) Figure Vulnerability and Fragility plots of a model vulnerability matrix...83 Figure Sub region vulnerability comparisons of South FL homes...84 Figure Vulnerability comparison of gable and hip roofs...84 Figure Vulnerability comparison of shuttered and not shuttered homes Figure Vulnerability comparison of shingle and tile roofs Figure Vulnerability comparison of concrete and wood homes...86 Figure Vulnerability comparison of 1 and 2 story homes...86 Figure Contents vulnerability and fragility curves...89 Figure ALE vulnerability and fragility curves...89 Figure Type 2 contents vulnerability curve Figure Type 2 ALE vulnerability curve ix

11 Figure Appurtenant structure vulnerability curve Figure 5-13 Weak wood structure vulnerabilities in the South high velocity hurricane zone Figure 5-14 Weak wood structure vulnerabilities in Central wind borne debris region Figure 5-15 Weak wood structure vulnerabilities in the North wind borne debris region Figure 5-16 Weak masonry structure vulnerabilities in the South high velocity hurricane zone Figure 5-17 Weak masonry structure vulnerabilities in Central wind borne debris region...98 Figure 5-18 Weak masonry structure vulnerabilities in North wind borne debris region Figure Vulnerability and fragility of pre-1994, not tied-down, manufactured homes Figure Vulnerability and fragility of pre-1994, tied-down, manufactured homes Figure Vulnerability and fragility of post-1994, zone 2, manufactured homes Figure Vulnerability and fragility of post-1994, zone 3, manufactured homes Figure Contents vulnerability and fragility: pre-1994, not tied-down, manufactured Figure Contents vulnerability and fragility: pre-1994, tied-down, manufactured Figure Contents vulnerability and fragility: post-1994, zone 2, manufactured Figure Contents vulnerability and fragility: post-1994, zone 3, manufactured Figure ALE vulnerability and fragility: pre-1994, not tied-down, manufactured Figure ALE vulnerability and fragility: pre-1994, tied-down, manufactured 105 Figure ALE vulnerability and fragility: post-1994, zone 2, manufactured Figure ALE vulnerability and fragility: post-1994, zone 3, manufactured Figure Type 2 contents vulnerability curve for manufactured homes Figure Type 2 ALE vulnerability curve for manufactured homes Figure Weighted building vulnerability and fragility curves Figure Weighted type 1 contents vulnerability and fragility curves Figure Weighted type 1 ALE vulnerability and fragility curves Figure Weighted type 2 contents vulnerability curve Figure Weighted type 2 ALE vulnerability curve x

12 Figure 5-38 Weighted masonry structure vulnerabilities in the South high velocity hurricane zone Figure 5-39 Weighted timber structure vulnerabilities in the South high velocity hurricane zone Figure 5-40 Weighted Masonry structure vulnerabilities in the North wind borne debris region Figure 5-41 Weighted timber structure vulnerabilities in the North wind borne debris region Figure Manufactured homes vulnerability curves Figure Company B, Hurricane Georges contents losses Figure Company B, Hurricane Georges appurtenant losses Figure Company B, Hurricane Georges additional living expense claims Figure Company A, Hurricane Andrew contents losses Figure 6-5- Satellite image of Hurricane Andrew making landfall (NOAA) Figure The destruction left behind, Naranja Lakes (NOAA) Figure Masonry structural claims from Hurricane Andrew and model results (note: the curve fit starts at 95 mph rather than zero because it is a parabolic curve and a point of inflection occurs prior to 95 mph) Figure Masonry contents claims from Hurricane Andrew and model results. 134 Figure Masonry contents vs. structural claims, Andrew data and model results Figure Timber structural claims from Hurricane Andrew and model results 135 Figure Timber contents claims from Hurricane Andrew and model results Figure Manufactured home claims from Hurricane Andrew and model results Figure Manufactured home contents claims from Hurricane Andrew and model results Figure Manufactured home ALE claims from Hurricane Andrew and model results Figure Manufactured home ALE claims from Hurricane Andrew and type 2 model results Figure Masonry structural damage probability distribution plot, mph139 Figure Masonry structural damage probability distribution plot, mph Figure Masonry structural damage probability distribution plot, mph Figure Masonry structural damage probability distribution plot, mph Figure Masonry structural damage probability distribution plot, mph Figure Masonry contents damage probability distribution plot, mph 141 xi

13 Figure Masonry contents damage probability distribution plot, mph Figure Masonry contents damage probability distribution plot, mph Figure Masonry contents damage probability distribution plot, mph Figure Masonry contents damage probability distribution plot, 0-5% building loss Figure Masonry contents damage probability distribution plot, 7-13% building loss Figure Masonry contents damage probability distribution plot, 15-22% building loss Figure Masonry contents damage probability distribution plot, 26-38% building loss Figure Masonry contents damage probability distribution plot, 42-54% building loss Figure Masonry contents damage probability distribution plot, 58-70% building loss Figure Masonry contents damage probability distribution plot, 74-86% building loss Figure Masonry contents damage probability distribution plot, % building loss Figure Hurricane Opal making landfall in the Florida Panhandle (NOAA) Figure Storm surge damage caused by Hurricane Opal Figure Opal wood structure claims data vs. model results Figure Opal wood contents claims vs. model results Figure Opal masonry structure claims data vs. model results Figure Wood structural damage probability distribution plot, mph, Opal Figure Wood structural damage probability distribution plot, mph, Opal Figure Wood structural damage probability distribution plot, mph, Opal Figure Charley making landfall (NOAA) Figure Wind swath of hurricane Charley (NOAA) Figure Manufactured home park in Port Charlotte following Charley, every manufactured home in sight is destroyed, average damage of pre 1994 homes in the park 75-85% Figure Typical manufactured home damage in Port Charlotte: complete interior, and utilities loss, although buried some contents may be salvageable xii

14 Figure Severe site-built home damage in Punta Gorda, the poor quality of construction is evident in that most other nearby homes suffered far less damage Figure In Punta Gorda the average home had a similar extent of roof damage, this most likely caused some interior damage and possibly contents losses Figure More typical roof damage in Punta Gorda Figure Model manufactured home vulnerability curve and observed points 160 Figure Site-built home modeled vulnerability and observed damage (the other home matrix is used because it encompasses all structural types) Figure Sheathing damage and resulting interior and contents damage Figure The model average at 15% sheathing damage results in about 20% interior damage, and this case falls well within the modeled range Figure Frances making landfall (NOAA) Figure Wind swath of hurricane Frances (NOAA) Figure Roof Cover damage to Indian Harbor Beach Home, typical in the area probably about 1 in 8 (or more) homes needed a new roof following the storm Figure Manufactured home damage in Indian Harbor Beach, recorded peak wind gust 78 mph approximately 1 mile north Figure Manufactured home in Indian Harbor Beach, this home experienced greater damage than any other in the park, it was the only one not shielded by nearby structures Figure Fort Pierce, garage door damage caused internal pressurization resulting in loss of roof sheathing Figure Site-built home damage in one of the hardest hit areas of Fort Pierce, beachside near the inlet state park, wind gusts in the area measured up to 108 mph Figure Collapsed roof in Fort Pierce Figure More site-built home damage in Fort Pierce, the overhang prior to the storm extended 5 feet beyond the front wall, severe interior damage also occurred Figure Manufactured home damage in Fort Pierce, on U.S. 1 near Indrio Rd Figure Severe manufactured home damage in Fort Pierce Figure Site-built model vulnerability curve compared with observations from Frances Figure Manufactured home vulnerability curves compared with observations from Frances Figure Hurricane Jeanne approaching the Florida East Coast (NOAA) xiii

15 Figure Wind swath of hurricane Jeanne (NOAA) Figure story Fort Pierce Home, both garage doors damaged, extensive roof and interior damage Figure Vero Beach home, severe roof damage Figure Vero Beach, severe roof and interior damage Figure Wabaso 2 story home, severe wall, roof, and interior damage Figure More typical extent of damage seen in Vero (also more representative of the modeled home types) Figure Vero, destroyed manufactured home Figure Probability distribution for other structure at 120 mph (the other structure distribution is used because it encompasses all structural types) Figure Falling tree damage Figure Effects of storm surge in Satellite Beach Figure Total loss comparison Bhinderwala (company 1 data) vs. Florida Public model Figure Comparison with Bhinderwala data (company 2) aggregated data by zip code Figure Comparison of Florida Public model results with HAZUS Figure Matrix selection process for site-built homes Figure Insurance algorithm flowchart part Figure Insurance algorithm flowchart part Figure Matrix selection process for manufactured homes xiv

16 List of Tables Table 3-1- Four most common structural types Table Population of most common structural types in defined geographic regions...11 Table 3-3 Additional Structural types...11 Table Population of additional structural types in defined geographic regions Table Structural Types modeled for each geographic region Table Description of values given in the damage matrixes for site built homes...20 Table Description of values given in the damage matrixes for manufactured homes Table Replacement Cost Ratios for a concrete block home type in north FL Table Unit Costs for Residential Homes Table 3-10 Typical new home construction costs Table Unit Costs for Manufactured Homes Table New construction costs for single and double-wide manufactured homes Table Replacement ratios for single and double-wide manufactured homes..28 Table 4-1 Typical cost distribution of interior Table Interior damage equations Table Interior damage as a function of sheathing damage, using Weibull distribution...38 Table Derivation of interior damage equation as a function of roof sheathing damage Table Derivation of interior damage equation as a function of roof cover damage Table Derivation of interior damage equation as a function of wall damage Table Derivation of interior damage equation as a function of window damage Table Derivation of interior damage equation as a function of door damage Table Derivation of interior damage equation as a function of gable end damage Table Electrical damage as a function of sheathing damage equation Table 4-11 Calculation of Weibull distribution for content predictions xv

17 Table Estimation of repair times Table Appurtenant structure damage estimation per wind speed Table Partial example of a vulnerability matrix (columns: wind speed, rows: damage ratio)...82 Table Partial example of type 2 contents matrix Table Characteristics of the 3 site built models Table List of different weighted matrices created Table 5-5 Age classification of the models per region Table 5-6: Year-built statistics for the different regions Table 6-1- Summary of processed claims data (number of claims provided) Table Hurricane Andrew open terrain wind speeds per zip code Table Hurricane Opal open terrain wind speeds per zip code xvi

18 1.1 Background Chapter 1 Introduction Hurricanes are among the most destructive and costliest of all natural disasters. In the Untied States, within the last century more Hurricanes have made landfall in Florida than in any other state. It was well-publicized throughout the media that the 2004 hurricane season was extremely active and ravaged many portions of the Southeast, and in particular Florida. Four storms threatened the state in 2004, three (Charley, Frances, and Jeanne) made direct landfall while one other (Ivan) came ashore in southern Alabama, but still had a major impact on the Florida panhandle. Total insured losses resulting from these hurricanes are estimated to be over $20 billion, with over 2 million claims filed. Many researchers confirm that we are in the midst of a cycle of increased hurricane activity in the Atlantic basin, and suggest that years similar to 2004 may become increasingly common. For these reasons it has become essential to project the potential economic impact from future such events. Figure Hurricane Jeanne making landfall (NOAA) 1

19 These circumstances have prompted the Florida Department of Financial Services (FDFS) to request that a group of researchers develop the Florida Public Hurricane Loss Prediction Model, a computer model used to project annual expected insurable losses to residential structures subject to high winds associated with hurricanes. The team consists of Engineers, Meteorologists, Statisticians, Computer and Actuarial Experts from the Florida Institute of Technology (FIT), University of Florida (UF), Florida International University (FIU), Florida State University (FSU), the National Oceanic and Atmospheric Administration (NOAA), and the National Institute of Standards and Technology (NIST). The model is being developed using the best available data from historical events, methodologies, theories, and scientific principles. This model is nonproprietary, completely transparent, and subject to the review of the Florida Commission on Hurricane Loss Projection Methodology, of whose standards it must comply. The complete risk assessment model is built from several distinct parts including: the wind field model, the exposure study, the vulnerability model, actuarial components, and the computer platform. The work presented in this report deals primarily with the vulnerability model and its integration with the other components. The meteorological team has developed the wind field model [15] to predict the probabilities of occurrence of a range of wind speeds at the centroid of each zip code in the state of Florida. This information is used in the computation of expected average annual insured losses for a particular location. Also, the wind field model is used to simulate historical or hypothetical hurricane events, so that scenario based portfolio analyses can be performed. The exposure study is presented in detail in Public Hurricane Loss Prediction Model: Exposure and Vulnerability Components, Zhang 2003 [5]. The exposure study was conducted to define the statistical distribution of typical residential building types throughout the different regions of Florida. Important statistical information regarding the distribution of common roof types, exterior wall construction, building areas, etc. was gathered from an analysis of tax appraiser databases and various other resources. The vulnerability model uses these statistics to define building models relevant to the different regions of Florida and for weighting the vulnerability matrices, as will be explained in this report. Vulnerability as used in this context can be defined as the susceptibility of a particular structural type to physical damage or monetary damage expressed as a function of wind speed. To provide consistent estimates of monetary damage for homes of different values, damage is computed as damage ratios. The damage ratio is defined as the cost of replacing the damaged components of a home divided by the replacement value of that particular home. 2

20 The vulnerability model is based on a component approach rather than regression analysis of insurance claims data from historical hurricanes, a method adopted by many commercial loss projection models. The problem with the regression approach is that it is highly dependent on the type of construction and construction practices common to the areas represented in the claims data. Recent changes in building codes cannot be accurately reflected in data from past storms. Also, in many cases after a major hurricane reliable wind speed data may not be available due to the destruction of observation equipment, as was the case with Hurricane Andrew. On the other hand, the component approach used for damage prediction explicitly accounts for both the resistance capacity of the various building components and the load effects produced by the wind at various speeds and angles. When the loads acting on a particular component exceed its given capacity, damage is computed. Because the resistance capacities of the various building components and the load effects produced by the wind cannot be explicitly defined for all structures, the vulnerability model uses a Monte Carlo simulation engine to generate values for these variables. The simulations are an analytical method meant to imitate the variability of a real-life system (different homes), systems that maybe far too complex to analyze by any other means. The Monte Carlo simulations are only a part of the vulnerability model. The result of these simulations is physical damage to exterior and structural components of the modeled home, while the final result of the vulnerability model is the vulnerability matrices, which give the probability of different damage ratios occurring at wind speeds of incremental velocities. The work of this report builds upon the Monte Carlo simulation results to complete the objectives of the vulnerability model. One of the ultimate goals of the complete risk assessment model is to analyze portfolio files of various insurance companies operating in the state of Florida to compute expected annual losses of their insured policies. This analysis could be used for rate making, validation of other models, to assess the efficiency of mitigation measures, etc. The vulnerability matrices are combined in this analysis with the wind speed probabilities and insurance portfolio parameters into an actuarial algorithm to compute expected insured yearly losses. The actuarial methods used in the model comply with all standards set forth by the Florida Commission on Hurricane Loss Projection Methodology [12]. Finally, all parts of the model are integrated together into a computer platform that includes user friendly graphics. 3

21 1.2 Goals and Objectives The work of reported in this report is a component of the engineering model and focuses primarily on damage projection, cost estimation, integration of the various components, and validation. Basically, a link is developed between the component based probabilistic damage estimations generated by the engineering team at the University of Florida and the actuarial science and software development teams at Florida International University. The objectives of this research are as follows: Develop an accurate and reliable method to project un-modeled damage as a function of the physical damage to the exterior and structural building components modeled by the Monte Carlo simulations. Create a general procedure to convert the combined physical damages into monetary damage or damage ratios, similar to the way an insurance adjuster would assess damage to a home after a storm, taking into account typical variations in construction materials, structural characteristics, and Florida Building Code requirements Define vulnerability matrices for specific home types (considering different construction materials, structural characteristics, and Florida Building Code requirements) and weighted regional vulnerability matrices based on the results of the building exposure study for use in the analysis of insurance files. Provide a logical explanation and accurate method for predicting damage to contents, appurtenant structures, and additional living expenses. Develop a procedure for analyzing and making use of all available and relevant insurance portfolio file information for the process of selecting and applying the most appropriate vulnerability matrix for use in loss projection computations. Validate the model results by comparisons with insurance claims data from historical storm events, the results of other models, and site inspections of homes damaged during Hurricane Charley, Frances, and Jeanne. 1.3 Scope The objectives discussed above are described in detail in chapters 3 through 8. Chapter 2 provides a review of literature devoted to the field of hurricane loss projection. Chapter 3 describes the cost estimation procedures developed for residential and manufactured homes and explains how these procedures are applied to the probabilistic damage estimations provided by the Monte Carlo simulations. Chapter 4 4

22 presents the methods used to predict interior and utilities damage, as well as losses to contents, appurtenant structures, and additional living expenses. In chapter 5 a detailed explanation of the model results and there significance is given. In chapter 6 the model results are validated using the best available data. The complete loss projection process and the models compliance with the Florida Commission on Hurricane Loss Projection Methodology are discussed in chapter 7. Finally, conclusions of the model, uncertainties, and potential areas for future improvement are provided in chapter 8. 5

23 Chapter 2 Literature Review This chapter is a review of literature in two different areas. Cost estimation resources are discussed in the first section. These provide the basis for the prediction of repair costs of modeled physical damage. Other hurricane loss projection methods and models are presented in the second section. A more exhaustive literature survey on the general topic of loss prediction and modeling is contained in the master thesis of Liang Zhang [5] and the doctoral dissertation of Anne Cope [19]. 2.1 Cost Estimation Resources Cost estimation resources are collections of typical unit costs for materials and labor obtained from successful bids on actual construction jobs. These tools provide the basis for our repair cost predictions. There is a whole market of these resources available. Obviously, each may have its advantages and disadvantages. RSMeans is the resource used by the HAZUS manual; however it did not offer any distinct advantages over similar resources that would justify the much higher cost. The primary resource used for this project was the 2004 National Renovation & Insurance Repair Estimator [10]. This manual was selected because it best suited our needs for predicting insurable repair costs. It also contains a section on manufactured housing costs that is not available in other books. To provide validation of the estimates in the first resource the CEIA Cost 2002 [11] was also referenced. This manual maybe slightly outdated. However, because it was only used to double check the estimates it proved sufficient. Also, many resources are available online. A quick internet search will reveal several home repair cost calculators that may also be used for the validation of these other references. 2.2 Loss Projection Several studies have been conducted in recent years following devastating hurricanes such as Hugo and Andrew, to asses the vulnerability of structures in the event of similar 6

24 storms. Most of these studies involve regression techniques to fit a vulnerability curve to insurance claims data. A master s thesis by Bhinderwala [3] is one such widely referenced document. In his thesis he establishes a relationship between the gradient (or flight level, there appears to be some confusion regarding the wind speed terms) wind speed and the average insurance loss ratio by the analysis of 770 insurance claims from Hurricane Andrew. Despite the limited data used in the analysis a reasonable vulnerability curve is developed. However, a vulnerability curve can only predict the mean loss per wind speed. The probability of other degrees of damage cannot be established based on just a curve or analysis of this small amount of data. Furthermore, the vulnerability of a home is at least somewhat dependant upon the construction type and practices of an area, considerations not accounted for. A similar event in another area with different code and construction practices may produce a significantly different curve. Papers by Huang, Rosowsky, and Sparks [18] based on a dissertation by Huang present findings similar to Bhinderwala but based on a much greater amount of data from not only Andrew but also Hurricane Hugo. An analytical expression to determine the vulnerability of structures is given in the risk assessment model developed by Huang [17]. This expression appears to greatly over predict losses when compared with the results of other models and our own results. Also, similar statements can be made regarding the limitations of only producing a curve and not considering construction types or practices. These considerations of construction type are taken into account in the vulnerability curves developed by Khanduri and Morrow [22]. These curves were also developed from insurance loss data and present a logical relationship, similar to that developed by this model, between the vulnerability of different construction types. Other research by Sparks, Schiff, and Reinhold [16] and a paper by Sill and Kozolowski [8] attempt to discern wind induced damage and losses from those that result because of rain penetrating the structure. They both use the concept of a loss magnifier that increases exponentially at some estimated wind speed. This magnifier is a ratio of rain induced damage to wind induced damage. This works in a way similar to the interior loss equations developed in this report. However, there is no randomness accounted for in their expressions for defining this magnifier. Also, an increase in losses resulting from rain would not occur as drastically as represented in these papers, and little if any validation of the results is presented. The HAZUS Wind Loss Estimation Methodology Report [7] documents the development of another component based loss projection model very similar to the Florida public model. This document covers all aspects of the model development, and also like the Florida public model there are several parts including a wind field model, terrain model, missile impact model, physical damage model, and economic loss model. Because the focus of this report is primarily economic losses this is the portion of the HAZUS model that is being addressed. 7

25 The HAZUS economic loss model uses methods very similar to those presented in this report. However, in many ways the work that will be presented here is an attempt to improve upon these methods. For instance, when the HAZUS model predicts interior losses as a function of modeled building components simple linear equations are used without taking into account any possibility of random variations, although hurricane damage is very random in nature and might not be better defined by simple linear expressions. Also, the HAZUS model was not developed with the goal of predicting losses for insurance companies, but rather as a tool for emergency planning and mitigation, so the validity of using the HAZUS model for this purpose maybe questionable. 8

26 Chapter 3 Vulnerability Model Development 3.1 Modeled Structural Types The vulnerability of a structure can be affected by a wide range of uncontrollable variables. These may include wind direction, duration, shielding by nearby structures, channeling of wind or vortexes created by nearby structures, terrain roughness, falling trees, size and geometry of the structure, roof pitch, quality of construction, age, mitigation measures, etc. Since the goal here is to predict insured losses to structures over a large area (the entire state of Florida) an idealized model must be created based on typical conditions that can be expected throughout a region of the state. Because wind loads and the resulting damage computed by the Monte Carlo simulations, as well as the repair costs associated with the predicted damages are heavily dependent upon the size, shape, and component make up of a given structure, a step of critical importance was to define the structural types that are representative of the typical homes that can be found in each region of Florida. To determine the predominant structural types that make up the majority of the Florida residential building stock and their statistical distribution in each region an extensive study of several counties tax appraisers databases, the Florida Hurricane Catastrophe Fund (FHCF) database, and the HAZUS report with statistics of Miami- Dade County were conducted [7]. Regional boundaries were defined as shown in Figure 3-1. Tax appraiser data used for this study was obtained from the highlighted counties shown in this figure. 9

27 North Central South Keys Figure 3-1 Regional boundaries for exposure studies Site-Built Homes The exposure study revealed the majority of residential site-built homes in the state are one of 4 structural types given in Table 3-1. The distribution of these structural types, along with the average area (under air) is presented in Table 3-2. The study also revealed many other structural types that make up a much smaller percentage of the Florida building stock, Table 3-3 and Table 3-4. Structural Type CBG CBH WG WH Table 3-1- Four most common structural types Characteristics Concrete block gable roof one story home with shingles or tile Concrete block hip roof one story home with shingles or tile Wood frame gable roof one story home with shingles or tile Wood frame hip roof one story home with shingles or tile 10

28 Table Population of most common structural types in defined geographic regions North Region Central Region South Region Florida Keys Structural Type p ) A (ft 2 ) p ) A (ft 2 ) p ) A (ft 2 ) p ) A (ft 2 ) CBG 12% 42% 46% 23% CBH 6% 22% 23% 11% WG 39% 12% 4% 12% WH 20% 6% 2% 6% Sum of most common 77% 82% 75% 52% Unknown 14% 13% 11% 23% Total coverage 91% 95% 86% 75% * Large standard deviation from observed data 3295* 2771* Structural Type 2CBWG 2CBWH 2WG 2WH 2Keys CBGM CBHM WGM WHM Table 3-3 Additional Structural types Characteristics Concrete block 1 st story, wood frame 2 nd story, gable roof home with shingles or tile Concrete block 1 st story, wood frame 2 nd story, hip roof home with shingles or tile Wood frame two story gable roof home with shingles or tile Wood frame two story hip roof home with shingles or tile Two story home of unspecified frame and roof cover Concrete block gable roof one story home with metal roof Concrete hip gable roof one story home with metal roof Wood frame gable roof one story home with metal roof Wood frame hip roof one story home with metal roof 11

29 Table Population of additional structural types in defined geographic regions North Region p ) Central Region p ) South Region p ) Structural Type 2CBWG 1% 2% 8% 2CBWH 1% 1% 4% 2WG 5% 1% 1% 2WH 2% 1% 1% Florida Keys p ) 2Keys 3% CBGM 8% CBHM 4% WGM 7% WHM 3% Sum of most common types (from Table 3-2) 77% 82% 75% 52% Unknown 14% 13% 11% 23% Total 100% 100% 100% 100% Because the additional structural types given in Table 3-3 and Table 3-4 make up just a small percentage of the population, individual models were developed for only the most common structural types given in Table 3-1. To account for the two story home distribution in each region models were developed based on the framework of the one story homes with increased wind speeds to more accurately represent forces that would be experienced at the higher elevation. The metal roof types that comprise a significant portion of the building stock in the Keys (and that are becoming increasingly popular in other parts of Florida) are not modeled separately. This is because little information exists regarding the strength of a metal roof compared to that of tile or shingle, and based on post storm damage investigations of hurricanes Charley, Frances, and Jeanne none of the roof types appeared to perform significantly better than the others. This point is illustrated in Figure 3-2 through Figure 3-5. These four homes (2 shingle, 1 metal, and 1 tile roof) located on the same street in Punta Gorda, FL experienced very similar wind conditions during Hurricane Charley. The random nature of the damage can be seen in that a shingle roof was unharmed while most others saw extensive damage; yet, on average all roof types in a given location experienced similar degrees of damage. Therefore, since the cost of replacing a metal roof is approximately the same as replacing a tile roof, it is assumed that the homes in the Keys with metal roofs have the same vulnerability as homes in the Keys with tile roofs. 12

30 Figure 3-2 Performance of metal roof during Hurricane Charley Figure Performance of shingle roof during Hurricane Charley Figure Performance of tile roof during Hurricane Charley 13

31 Figure Undamaged shingle roof following Charley Plan dimensions were selected for each single story home model such that the square footage remains close to the mean area plus a garage of approximately 400 ft 2, while providing the largest number of whole sheathing panels on the roof surface. Unusually shaped sheathing panel cuts are avoided. The resulting site-built models for single story homes are described in Table 3-5, where the plan dimensions represent the wall lengths. An overhang of two feet on each side adds a total of four feet to both plan dimensions to give the size of the roof surface. All model home types have 15 windows, a two-car garage, a front entrance door, and a sliding glass back door. Identical models are created for homes that are equipped with hurricane shutters, window capacities are increased such that failure is much less likely. Table Structural Types modeled for each geographic region Structural North Region Central Region South Region and Florida Keys Region Type Plan (ft) Area (ft 2 ) Plan (ft) Area (ft 2 ) Plan (ft) Area (ft 2 ) CBG or CBH 56x x x WG or WH 60x x x Tables 3-1 through 3-5 were all obtained from Predicting the Vulnerability of Typical Residential Buildings to Hurricane Damage, a Dissertation by Anne Cope [19] Manufactured Homes The most current information available regarding the distribution of manufactured home types is found in the 2002 Florida Hurricane Catastrophe Fund (FHCF) Industry Data [20]. This database gives exposure statistics aggregated by type of business, line of 14

32 business, construction type, deductible group, county code, and zip code. It includes exposure of residential, manufactured homes, tenants (renters), and condominium unit owners. The manufactured home data was extracted and processed to obtain the relevant information required for our modeling purposes. The manufactured home data was first aggregated by construction type. The exposures of all deductible groups of the same construction type in each zip code were summed to give the exposure of each construction type in each zip code. The deductible group is not needed for this analysis. This data covers the five manufactured home construction types of: Manufactured Home - Fully Tied Down, manufactured before 7/13/94 Manufactured Home - Fully Tied Down, manufactured on or after 7/13/94 Manufactured Home Partially Tied Down Manufactured Home - Not Tied Down Manufactured Home Unknown This first processing step revealed the exposure of these five home types per zip code. However, not all the zip codes represented in this data contain an exposure large enough to assume that it is indicative of the actual building population; the data for some zip codes had only one or two insured risks. So knowing which zip codes lay within each county, and the counties that lay within each region, the data was aggregated by region. The distribution percentages were then determined by dividing the total insured building exposure of each construction type in the region by the total insured building exposure of the entire region. The results of this processing are shown in Figure 3-6 through Figure

33 Central Florida Manufactured Home Building Exposure 0.1% 1.4% 3.3% 20.0% Full TD <94 Full TD >94 Partial TD No TD Unknown 75.2% Figure 3-6 Central FL manufactured home distribution South Florida Manufactured Home Building Exposure 0.0% 0.9% 2.6% 14.6% Full TD <94 Full TD >94 Partial TD No TD Unknown 81.8% Figure 3-7- South FL manufactured home distribution 16

34 Florida Keys Manufactured Home Building Exposure 9.8% 0.0% 0.0% 0.1% Full TD <94 Full TD >94 Partial TD No TD Unknown 90.0% Figure FL Keys manufactured home distribution North Florida Manufactured Home Building Exposure 0.2% 3.0% 11.3% 42.2% Full TD <94 Full TD >94 Partial TD No TD Unknown 43.4% Figure North FL manufactured home distribution 17

35 The 1994 cutoff date given in this data is of great significance. After the widespread destruction of manufactured homes during Hurricane Andrew in 1992, the Department of Housing and Urban Development (HUD) passed federal regulations to ensure more uniform and higher quality construction standards of manufactured homes. These regulations that took effect on June 13, 1994 defined three wind zones. Manufactured homes constructed for each of these zones must be designed to withstand wind forces that can be expected in the region. A map detailing the HUD specified wind zones is shown in Figure It can be seen in this figure that only two wind zones fall within the state of Florida, zone II and zone III. The delineation of the these zones by county within FL is explicitly stated in HUD , this is important in the analysis of the insurance portfolio files as will be discussed in chapter 7. Figure HUD wind zone map Based on these and other studies it was decided to model four manufactured home types. These types include: Pre Fully Tied down Pre Not Tied down Post HUD Zone II Post HUD Zone III The partially tied down homes are assumed to have a vulnerability that is a weighted average of the vulnerabilities of fully tied down and not tied down homes. Because little information is available regarding the distribution of manufactured home types by size or geometry all model types are of a single wide manufactured home and it is assumed that the vulnerability of these home types is similar to those of other geometry. The 18

36 modeled single wide manufactured homes are 56 ft x 13 ft, have gable roofs, 8 windows, a front entrance door, and a sliding glass back door. 3.2 Damage Matrices Now that development of the Monte Carlo Simulation models and their characteristics has been explained, the output of these models can be discussed. As stated earlier, the output of the Monte Carlo simulation model is physical damage to structural and exterior components of the modeled home. The results are in the form of a damage matrix. Each row of the matrix is one model simulation, the amount of damage to each modeled component for a simulation is given in the columns, and each column represents a different component. Each damage matrix gives the results of 5000 Monte Carlo simulations. A separate matrix is created for each peak 3-second gust wind speed between 50 and 250 mph in 5 mph increments (50, 55, 60, etc.) at angles between 0 and 315 degrees in 45-degree increments (50 mph at 0 degrees, 50 mph at 45 degrees, 50 mph at 90 degrees, etc.). The components represented in the columns and the meaning of the values given for both site built and manufactured homes will be discussed in the remainder of this section Site-Built Homes The engineering team from the University of Florida developed the Monte Carlo simulation models and is in control of producing the results. For each site-built home model the complete set of results is given in a zip file called, for example, Results_South_CB_gable_60204.zip, where the name of the file name tells the region, construction type, roof type, and date of the model run. When this file is unzipped a folder named output is created. Contained within this folder are MATLAB files which contain the Monte Carlo simulation results at each wind speed and angle, 328 files total, with names that give the region, date of the model run, roof type, construction type, wind speed, and angle, for example, south_602041g_concrblkv100at0.mat. When these files are opened in MATLAB two double array matrices are created in the workspace, one called damage and the other dimensions. The vulnerability model does not use the dimensions matrix so it is disregarded. The damage double array is the 5000 x 15 matrix that contains the results of the Monte Carlo simulations for that particular home type at the given wind speed and angle. The values given in the columns of the damage matrix represent damage to each modeled component as described in table

37 Table Description of values given in the damage matrixes for site built homes Column # Description of Value Min Value Max Value 1 % failed roof sheathing % failed roof cover % failed roof to wall connections # of failed walls # of failed windows # of failed doors y or n failed garage door 0 = no 1 = yes 8 y or n envelope breached 0 = no 1 = yes 9 # of windows broken by debris impact % of gable end panels broken internal pressure 0 Not defined 12 % failed wall panels - front % failed wall panels - back % failed wall panels - side % failed wall panels - side * Note: For columns 12-15, % of failed wall panels, an error was discovered in the model results, the percentage loss values ranged from 0-200%. It was determined that the problem could be most easily corrected by simply dividing the values in these columns by 2. This error was corrected in the Monte Carlo simulation model; however, because of time constraints a new set of results for each model was not produced. The results produced by the corrected Monte Carlo simulation model and using the division by 2 are identical. So, all results presented in this report use the division by Manufactured Homes The way that the results are produced and stored for the manufactured home models is very similar to the site built models. The complete set of results for a model type is given in a zip file called, for example, Results_MH _1pre _TD_ zip, where the name of the file name tells if the results are for the pre or post 1994 models, if pre 1994 tied down or not tied down, if post 94 wind zone II or III, and date of the model run. Unzipping these files again creates the output folder containing individual MATLAB files that hold the results of the Monte Carlo simulations for each wind speed and angle for that construction type. When these files are opened in MATLAB a 5000 x 9 damage matrix is created in the workspace. A description of the values in each column of the damage matrix is given in Table

38 Table Description of values given in the damage matrixes for manufactured homes Column # Description of Value Min Value Max Value 1 # of failed windows (out of 8 for single wide) # of broken windows that were broken by impact load case # of failed doors (front and back = 2 total) % of roof sheathing failed % of roof cover failed % of wall sheathing failed # of failed roof to wall connections (out of 58) sliding (0 = no sliding, 1 = minor sliding, 2 = major sliding) overturning (0 = not overturned, 1 = overturned) Replacement Cost Ratios Up to this point only background information pertaining to development of the Monte Carlo simulation models and output that they produce has been discussed. Previous graduate students from UF and Florida Tech have completed the majority of this work [5] [19]. From here forward procedures and methods developed to build upon this prior work will be presented. The goal is to take the modeled physical damage of each Monte Carlo simulation for each wind speed and angle, assign an estimated repair cost expressed as a percentage of the homes value to this predicted damage, and then determine the probability of a given percentage of damage occurring at each wind speed. Replacement cost ratios provide a key link between modeled physical damage and the corresponding monetary losses. Replacement cost ratios can be defined as the cost of replacing a damaged component or assembly of a home divided by the cost of constructing a complete new home of the same type. These are similar to the subassembly cost ratios used by the HAZUS model, however the subassembly cost ratios are determined by calculating the cost of constructing a new assembly divided by the cost of constructing a complete new home, and then the additional costs of removal, repair, and remodeling of the damaged assembly is accounted for by multiplying the ratio by a factor of 1.4. For our model these additional costs are included in the replacement cost so a similar factor is not needed, this is also the reason that the sum of these ratios is greater than 100%. Table 3-8 presents an example set of replacement cost ratios for one site-built home type. The complete set of replacement cost ratios used for each vulnerability model type is given in Appendix A. 21

39 Table Replacement Cost Ratios for a concrete block home type in north FL Construction Type Region Roof Type Tile or Shingle Sub region Concrete Block North Gable Tile Neither Sheathing 4% Cover 14% Trusses 9% Exterior Walls 24% Windows (with or w/o shutters) 6% Entrance Door and Sliding Back Door 1% Garage Door 1% Gable Ends 1% Interior 31% Mechanical 6% Electrical 8% Plumbing 9% Wall Sheathing 0% Total 113% Replacement ratios are calculated for all modeled components of a home as well as the components or assemblies that comprise a significant portion of the homes value. The methods used to derive the replacement cost ratios for site-built and manufactured homes are very similar, however because the geometry, modeled components, and unit cost values used to calculate these ratios are different each will be discussed in a separate section Site-Built Homes The replacement ratios for residential homes are all based on what could be considered an average home. It is true that these ratios may vary depending on the quality of construction, uniqueness, or special features of the components, etc. but remember that our goal is to predict losses on a large scale so we are concerned only with typical conditions. In addition, the replacement ratios may only vary by a matter of a few percent when these other factors are considered, and with all the uncertainty that is already inherent to the model these differences are almost irrelevant. However, this could be an area for future improvement or research. 22

40 The first step in calculating the replacement ratios of any home type is to compute the construction costs of the new home for which the ratios are based. A complete description of the model home types including geometry and component make up was given in Section Using this description the unit costs are obtained from the 2004 National Renovation & Insurance Repair Estimator [10], given in Table 3-9. The unit costs are multiplied by the unit values to determine the new construction cost of each component or assembly, as shown in Example 3-1. These values are then summed to determine the complete new home construction cost, Table

41 Table Unit Costs for Residential Homes Item Residential Homes Unit $/Unit Foundation sf 2.99 Roof and Wall Sheathing sf 1.42 Remove Sheathing sf 0.37 Roof Cover - Shingle sf 1.96 Roof Cover - Tile sf 5.03 Remove Roof Cover - Shingle sf 0.29 Remove Roof Cover - Tile sf 0.99 Trusses Hip - Shingle sf 2.98 Trusses Hip - Tile sf 3.92 Trusses Gable - Shingle sf 2.40 Trusses Gable - Tile sf 3.34 Remove Trusses sf 0.60 Exterior Walls - Masonry sf 9.90 Exterior Walls - Frame sf 6.54 Remove Exterior Walls - Masonry sf 2.51 Remove Exterior Walls - Frame sf 0.17 Windows ea Remove Windows ea Shutters ea Remove Shutters ea 4.49 Exterior Doors - Entrance and Sliding Back ea Remove Exterior Doors - Entrance and Sliding Back ea Garage ea Remove Garage ea Gable Ends ea Remove Gable Ends ea Interior sf Remove Interior sf 4.05 Mechanical sf 3.61 Remove Mechanical sf 0.20 Electrical sf 3.72 Remove Electrical sf 1.25 Plumbing sf 4.67 Remove Plumbing sf

42 Example Calculation of new shingle roof cost Area of roof cover x Unit Cost of roof cover = New roof cost 3072 (ft^2) x 1.96 ($/ft^2) = $6,021 Table 3-10 Typical new home construction costs Sheathing $ 4,362 Cover $ 6,021 Trusses $ 9,155 Exterior Walls $ 26,136 Windows (with or w/o shutters) $ 6,525 Entrance Door and Sliding Back Door $ 1,404 Garage $ 1,484 Gable Ends $ - Interior $ 35,168 Mechanical $ 8,086 Electrical $ 8,333 Plumbing $ 10,461 Foundation $ 9,185 Wall Sheathing $ - Total $ 126,320 To be more descriptive of the unit costs in Table 3-9 the electrical system includes the complete house wiring, outlets, switches, and permanent fixtures. The plumbing system includes complete supply lines, waste lines, and finish fixtures. Mechanical includes all permanent or semi-permanent mechanical systems within the home. These may include the air condition and heating system, hot water heater, air handler, garage door opener, etc. Now that we know the denominator of the replacement ratio (the complete new home construction cost) we must calculate the numerators (the replacement costs). This is done using the same method shown in Example 3-1 however the additional costs of removing the damaged components is added, as illustrated in Example 3-2. Once these values are determined the replacement ratios are calculated, Example 3-3. Example Calculation of replacement shingle roof cost Area of roof cover x (Unit cost roof cover + Unit removal costs) = Replacement roof cost 3072 (ft^2) x (1.96 ($/ft^2) ($/ft^2)) = $6,912 25

43 Example Calculation of shingle roof cover replacement ratio Replacement roof cost / New home construction cost = Roof cover replacement ratio $6,912 / $126,320 = 5.5% This method of costing allows for a wide range of modeling possibilities. Differences in the quality of construction, material alternatives, building code requirements, mitigation measures, etc. can easily be reflected in the unit cost values used to compute the ratios. Currently, replacement ratios are computed for 112 different home types. For each model, replacement ratios are calculated to consider additional common variables including tile or shingle roof cover, with or without shutters, and within the windborne debris region or high velocity hurricane zone (defined by the Florida Building Code), for each region. A summary of this procedure is given in the use case in Appendix F Manufactured Homes The procedure used for calculating the replacement ratios of manufactured homes is identical to the procedure for site-built homes. However, the different unit cost values and geometry used for the calculations obviously affect the results. The unit cost values are given in Table The new construction costs are given in Table 3-12 and the replacement ratios in Table Notice that the replacement ratios have been calculated for both single and double wide manufactured homes. This is because originally Monte Carlo simulation models had been developed for double wide homes, however as research progressed these models were not updated along with the single wides. So the framework for the double wide costing model is still in place but currently results are only valid for single wides. Future work on the model could include further development of the double wide model as well as possibly a triple wide model. Also note that there is no cost difference made for pre 1994 homes and post 1994 homes (zones II or III), this is because if any pre 1994 manufactured home is destroyed in a hurricane it must be built to the post 1994 standards and it can be assumed that there is very little difference in cost between the zone II and III homes. The replacement ratios are calculated to represent the typical manufactured home built after A summary of this procedure is given in the use case in Appendix F.2. 26

44 Table Unit Costs for Manufactured Homes Item - Manufactured Homes Unit $/Unit Foundation - Single Wide ea Foundation - Double Wide ea Roof and Wall Sheathing sf 1.42 Remove Sheathing sf 0.37 Roof Cover - Shingle sf 1.96 Remove Roof Cover - Shingle sf 0.29 Trusses Gable - Shingle (assume 14 ft 24" o.c.) ea Remove Trusses ea Exterior Walls lf Remove Exterior Walls lf 1.32 Windows ea Remove Windows ea 9.83 Shutters ea Remove Shutters ea 2.30 Exterior Doors - Entrance and Sliding Back ea Remove Exterior Doors - Entrance and Sliding Back ea Interior sf Remove Interior sf 4.05 Mechanical sf 3.61 Remove Mechanical sf 0.20 Electrical sf 3.72 Remove Electrical sf 1.25 Plumbing sf 4.67 Remove Plumbing sf 1.25 Table New construction costs for single and double-wide manufactured homes Single Wide Double Wide Windows $ 920 $ 1,150 Doors $ 630 $ 630 Roof Sheathing $ 1,034 $ 2,068 Roof Cover $ 1,427 $ 2,854 Wall Sheathing and Siding $ 1,660 $ 3,320 Trusses $ 1,383 $ 2,766 Interior $ 11,430 $ 22,859 Mechanical $ 2,628 $ 5,256 Electrical $ 2,708 $ 5,416 Plumbing $ 3,400 $ 6,800 Foundation $ 589 $ 785 Wall Framing $ 3,574 $ 4,248 Total $ 31,382 $ 58,151 27

45 Table Replacement ratios for single and double-wide manufactured homes Single Wide Double Wide Windows 3% 2% Doors 2% 1% Roof Sheathing 4% 4% Roof Cover 5% 6% Wall Sheathing and Siding 7% 7% Trusses 5% 5% Interior 46% 49% Mechanical 9% 10% Electrical 12% 12% Plumbing 14% 15% Total 106% 112% 3.4 Summary In this chapter development of the Monte Carlo simulation models along with the research and reasoning behind the model selection were presented. The form and meaning of the model output and calculation of replacement ratios for all home types were discussed. These items form the basis of the vulnerability model. In the proceeding chapter the methods and equations developed to link modeled physical damage to monetary insured losses is introduced. 28

46 Cost Estimation In chapter 3 the main components of the vulnerability model (the Monte Carlo models, damage matrices, and replacement ratios) were introduced. In this chapter the methods and considerations used to convert the modeled physical damages into monetary damage will be presented. This includes the development of equations that link modeled damage to interior and utilities damage, as well as contents, appurtenant structures, and additional living expenses, taking into account Florida Building Code regulations that apply to the repair of existing structures. Explicit Costing A very simple and explicit procedure is used to convert physical damage of the modeled components to monetary repair costs. Since the replacement ratio of each modeled component is known, the monetary damage resulting from damage to a component expressed as a percentage of the homes value can be obtained by multiplying the percentage of the component damaged by its replacement ratio. For example, if 30% of the roofs cover is damaged and for this particular home type the replacement ratio of roof cover is 14%, the value of the home lost as a result of the damaged roof cover would be 0.30 x 0.14 = 4.2%. If the value of this home were say $150,000, the cost to replace 30% of the roof would be $150,000 x = $6,300. This procedure allows for an effective and fairly accurate way to determine insurable damage to modeled building components. However, when computing the total value of a home lost due to the damage of all the modeled components some issues arise. For instance, if 30% of the roof cover were damaged would insurance pay to have all of the cover replaced or only the portion damaged? According to the Florida Building code in some regions windows are required to have glazing protection (shutters, shatter proof glass, films, etc.). If windows are damaged in an existing home that did not have glazing protection must insurance pay the additional costs to comply with the building code? Also, it can be seen from the replacement ratio tables in Appendix A that the interior and utilities of a home comprise the majority its value, typically around 55%. Water and wind entering the structure through damaged exterior components can cause significant 29

47 interior and utilities damage, none of which are modeled. How can we predict interior damage resulting from damage to the modeled building components? Answers to these questions will be presented in the following sections. Florida Building Code Requirements / Replacement Thresholds Several Florida Building Code (FBC) requirements apply to the repair of existing structures that may have a substantial effect on the cost of replacing damaged building components. Some of these requirements are taken into account when computing the repair costs of each model simulation. Additionally, in many cases it is not practical to replace only a portion of a damaged assembly. If 75% of the shingles blow off a roof insurance will obviously pay to have the whole thing replaced not just the damaged portion. These considerations will be addressed in this section. The FBC defines two distinct regions of the state in which even more stringent building regulations apply. These areas are referred to as the windborne debris region and the high velocity hurricane zone. The windborne debris region encompasses all portions of the state within 1 mile of the coast and areas that have a 120 mph or higher basic wind speed as defined by ASCE 7-98, Figure 0-1. The high velocity hurricane zone includes Miami-Dade and Broward counties, the areas previously regulated by the South Florida Building Code. The FBC requirements maybe subject to interpretation, yet their significance cannot be overlooked. Some requirements generally apply to all buildings within the state while others apply just to a specific sub-region. In the following sections excerpts from the FBC will be presented along with explanations of how each requirement is considered when computing modeled repair costs. 30

48 Figure ASCE 7-98 basic wind speed map and windborne debris regions General Requirements Chapter 34 of the FBC presents the regulations imposed upon existing structures. The section of most concern to us is Repairs and Alterations. In this section thresholds are placed on the extent of repairs that can be completed with or without regard to the FBC requirements. A portion of the code that is relevant to the modeling purposes is as follows: Structural repairs and alterations, the cost of which does not exceed 25 percent of the value of the existing building or structure, shall comply with the requirements for new buildings or structures except that minor structural alterations, with the approval of the building official, may be made of the same material and degree of fire-resistivity of which the building or structure is constructed Non-structural repairs and alterations exclusive of fixtures and furniture, the cost of which does not exceed 25 percent of the value of the existing building or structure and which do not affect egress or fireresistivity, may be made of the same material of which the building or structure is constructed. 31

49 The replacement of garage doors, exterior doors, skylights, operative and inoperative windows shall be designed and constructed to comply with Chapter 16 of this code. OPENING PROTECTION EXCEPTION: For one-and two-family dwellings constructed under codes other than the Florida Building Code and located in windborne debris regions, the replacement of garage doors and exterior doors with glazing, sliding glass doors, glass patio doors, skylights, and operable and inoperable windows within any 12 month period shall not be required to have opening protection, but shall be designed for wind pressures for enclosed buildings provided the aggregate area of the glazing in the replaced components does not exceed 25 percent of the aggregate area of the glazed openings in the dwelling or dwelling unit Repairs and alterations amounting to over 25 percent but not exceeding 50 percent of the value of the existing building may be made during any 12 month period without making the entire existing building comply provided such repairs and alterations comply with the requirements of this code for a building of like area, height and occupancy When repairs and alterations amounting to more than 50 percent of the value of the existing building are made during any 12 month period, the building or structure shall be made to conform to the requirements for a new building or structure or be entirely demolished. To summarize, if repairs to a structure constitute less than 25% of the structures value they do not have to comply with the FBC requirements for new homes. If repairs costs are between 25% and 50% of the structures value only the portions under repair need to comply with the FBC requirements for new homes. When repair costs exceed 50%, the whole structure must either be demolished or made to comply with all FBC requirements for new homes. Now, the enforcement of these codes may be of question especially in the event of a hurricane when nearly every home in an area must be repaired. For the modeling of repair costs it would be best to assume strict enforcement of the code. At this time no consideration for these requirements are made in the cost estimation program. The reason these requirements are not considered is that it is not possible to evaluate the existing structures compliance with the FBC given only information available in an insurance policy file. Therefore, any increase in repair costs made to satisfy FBC requirements would just be arbitrary. Again this could be an area for future improvement or further research. However, some replacement thresholds are generally applied to all structures. These thresholds are not based so much on the FBC but deal more with practicality of construction and insurance adjuster guidelines. Thresholds are applied to the replacement of roof sheathing and roof cover for all homes in Florida. For homes that do not fall within either the windborne debris region or the high velocity zone theses thresholds are set at 35%. This means that if any home experiences greater than or 32

50 equal to 35% roof cover or roof sheathing damage the repair cost is equal to replacing 100%. The value of 35% was estimated based on judgment and the FBC threshold set for the high velocity zone. The thresholds used in the windborne debris region and high velocity zone will be discussed in the next two sections. Windborne Debris Region According to the FBC new homes constructed within the windborne debris region are required to have protected openings or they must be designed as an open structure. This doesn t necessarily mean that all new homes in this region must have opening protection however it is assumed that this is typically the case. This protection could include shutters, shatter proof glass, glazing films, pre-cut plywood, a reinforced garage door, etc. It is not possible or worthwhile to consider all the possible effects on construction costs that these various alternative opening protection measures could have. For simplicity it is assumed that windows of all homes in the windborne debris region will be replaced with shutters. It is stated in section existing structures that experience less than 25% opening damage need not be made to comply with the FBC requirement for glazing protection. Again for simplicity this requirement is ignored; in the model if damage occurs to any window it must be replaced with shutters. In addition if greater than 50% of the openings are damaged it is assumed that all must be replaced with shutters. Although explicitly stated in the FBC, from a practical standpoint some of these requirements may not seem completely realistic. However, as will be presented in Chapter 5 these considerations have a very minimal effect on the final result. High Velocity Hurricane Zone Since the entire high velocity hurricane zone falls within the windborne debris region the same threshold on openings applies to homes in both regions. One additional threshold is applied to homes in the high velocity zone based on section of the FBC that states: Roofing. Not more than 25 percent of the roof covering of any building or structure shall be replaced in any 12 month period unless the entire roof covering is made to conform to the requirements of the code. Based on this code the threshold on roof covering and roof sheathing is decreased to 25% in this region. Therefore, if any home experiences greater than or equal to 25% roof cover or roof sheathing damage the repair cost is equal to replacing 100%. 33

51 Implicit Costing For the interior and utilities of a home there is no explicit means by which to compute damages and resulting repair costs. Unlike the modeled exterior components where we know that for each wind speed loads in excess of the capacity will cause damage and the cost of replacing these components is fairly certain, damage to the interior and utilities results primarily from rain and wind entering the building and the cost of repairing this damage could be highly variable. An attempt was made quantify interior damage as a function of damage to each modeled component of the home that causes a breach of the envelope. Utilities damage is then estimated as a function of the predicted interior damage. Interior Damage Damage to the interior of a home occurs when the building envelope is breached allowing wind and rain to enter. Of the modeled components for site-built homes damage to roof sheathing, roof cover, walls, windows, doors, and gable ends present the greatest threat of causing interior damage. For manufactured homes additional interior repair costs could be caused by sliding or overturning off the foundation. The basic components that comprise the interior of a typical home include the kitchen, carpets/flooring, interior walls, ceiling, painting, interior doors, and insulation. Based on unit values obtained from the 2004 National Renovation & Insurance Repair Estimator [10] an estimation of the percentage that each of these components contributes to the total interior value of a typical home was determined as listed in Table 0-1. It is assumed that these percentages are similar for both manufactured and site-built homes. Table 0-1 Typical cost distribution of interior Interior Component % of Value Kitchen 15% Carpets/Flooring 15% Interior Walls 34% Ceiling 30% Painting 3% Interior Doors 2% Insulation 1% Total 100% Interior damage equations are derived as a function of each of the modeled components previously mentioned. These equations are developed primarily based on experience and engineering judgment. Observations of homes damaged during the 2004 hurricane season helped to validate the predictions. The interior equations are derived by estimating typical percentages of damage to each interior component given a 34

52 percentage of damage to a modeled component. For example, 25% sheathing damage may typically result in 10% kitchen damage, 75% carpet/flooring damage, 15% interior wall damage, etc. or a total value interior damage of 35%. This estimation is repeated for several degrees of component damage, the % interior damage vs. the % component damage is plotted and an equation is fit to the data points. The details of these derivations are given in the subsections of this section. The interior equation for each component is shown in Table 0-2. Although the costs are of course different in each case, the equations that relate % interior damage to component damage in each case are the same for site built and manufactured homes. However, because the manufactured homes are much smaller than site built, the same component damage would lead to a greater interior damage, so that we multiply the equations by a factor of 1.1 for manufactured homes. Table Interior damage equations Modeled Component Interior Equation Roof sheathing: y=1.29*x Roof cover: y=0.62*x 2-0.2*x Walls or wall sheathing: y=7.91*x * x *x Windows: y=0.39*x *x Doors: y=0.26*x Gable Ends: y=0.38*x *x y=% interior damage x=% component damage Obviously these equations must be viewed cautiously. In fact so much uncertainty exists that a consistent estimation of the interior damage as a function of any modeled component is nearly impossible. The extent of interior damage could be dependant upon the amount of total exterior damage, location of the damage, composition of the interior in the vicinity of the damage, rainfall associated with a storm, wind speed, and many other factors. Interior damage could even result from leaking around windows and doors without any damage to the structure. To add even more uncertainty, the monetary repair costs associated with these damages is determined based on the subjective decision of an insurance adjuster or contractor. What if a portion of a homes roof is damaged in a storm and water leaks in on the carpets? Will insurance pay to have the carpets cleaned or replaced, or neither? What if the home has tile flooring? Wood flooring? Say insurance decides to pay to replace the flooring, you can t just replace a section that was damaged, the flooring in the whole room must be replaced. What if it s a large room? A small room? Connected to other 35

53 rooms? Maybe the existing carpet was top of the line or maybe it was the cheapest available. We could ask similar questions about the rest of the interior as well. Clearly, there is no way to answer all of these questions with a simple mean value equation. So to account for all this uncertainty some random distribution must be applied to these equations defined in Table 0-2. There are many different types of distributions that may be used for accomplishing this. Based on engineering judgment, and the fact that it is the most commonly observed distribution of data for these kinds of problems, a Weibull distribution was adopted. As will be seen later, this produced satisfactory agreement with the available claims data. The Weibull distribution offers great flexibility in the shape of the probability distribution functions that can be obtained. Any statistics book such as reference [21] should provide a detailed discussion on Weibull distributions. Figure 0-2 illustrates possible different shapes of the Weibull probability distribution function; these shapes are easily modified by changing the scale and shape factors α and β (in Figure 0-2 gamma = β). The density function for a Weibull distribution is given in Equation 0-1. Figure 0-2 Shapes of Weibull distribution function Equation 0-1- Density function of a Weibull distribution f ( x) = α β x β 1 exp( α x β ) A simple way to apply this distribution to the interior equations is to define a shape parameter β and calculate a scale parameter α such that the mean of the distribution is equal to 1 and then multiply random variables having these characteristics by the 36

54 interior damage equations. This results in the interior damage equation having a mean defined by the equation with a random distribution defined by the shape and scale parameters. Based on engineering judgment the value of the β (or gamma in Figure 0-2) parameter was chosen to be 2, for a resulting mean equal to 1 the α parameter must equal to , which gives a variance to the distribution. This distribution produces fairly good agreement with the claims data. A much more rigorous calculation of the shape and scale parameters to provide exact agreement with the distribution of the claims data was not performed. To do this the probability distribution function of structural damage ratios must be analyzed at each modeled wind speed, since interior damage contributes to the total structural damage and the distribution of structural damage varies as a function of wind speed. Therefore applying the same distribution of the claims data at each wind speed to the interior damage equations should produce a similar distribution of the total structural damage ratio. However, for one this calculation is very difficult and cumbersome. Yet, more importantly just because these distribution parameters are in exact agreement does not mean the distribution of our model results will exactly match that of the claims data. We are only applying this distribution to the un-modeled components of the home which only account for a portion of the homes value. The total structural damage ratio distribution is heavily dependent upon the physical damage modeled by the Monte Carlo simulations, and if this damage does not fit this same distribution (which it does not) there will not be an exact agreement. Based on the results of the model the choice of the Weibull parameter is assumed to be reasonable, but a sensitivity study is planned with a view of confirming this assumption or revising the choice. Functions available in Matlab Statistics toolbox make generating a random Weibull distribution a simple matter of defining the shape and scale parameters. The form of the interior equations with the applied distribution is illustrated in Table 0-3, this is the equation used to predict interior damage resulting from sheathing loss. The difference between the standard equation and the equation with the Weibull distribution applied is shown in Figure 0-4 and Figure

55 Table Interior damage as a function of sheathing damage, using Weibull distribution β=2 α = (1/ Γ(1+β -1 )) -β R=weibrnd(α,β) y = 1.29*x Int=R*y if Int>=1.0 Int=1.0 if Int<=0.001 Int=0 where: β = Weibull beta parameter (for future improvements could vary as a function of wind speed) α = Weibull alpha parameter (calculated so that the mean of the distribution is equal to 1) R = Random Weibull variable (generated by Matlab using the function weibrnd by defining β and α) x = % sheathing damage y = mean % interior damage Int = % interior damage with distribution applied 38

56 Figure Interior damage as a function of sheathing damage, no random distribution (mean values) Figure Interior damage as a function of sheathing damage using Weibull distribution, mean=1 variance= To compute the total interior damage for each model simulation first all values in the damage matrices (5000 simulations for each of 41 wind speeds at 8 different angles, 5000 x 41 x 8 = 1,640,000 simulations) are converted to percentages of component damage. The interior equations are applied to each component that causes a breach of envelope (Table 0-2) and the total interior damage for each model simulation is taken to 39

57 be the maximum interior damage value produced by these equations. The maximum value is taken to avoid the possibility of replacing the interior items more than once. It may be possible that for instance, the roof is damaged on one side of a home resulting in some interior damage and windows blew out on the other causing even more. However any attempt to combine these interior damages using some sort of weighted equation based on the output given in the damage matrices would just be arbitrary and introduce an even higher probability of error. A summary of the interior damage prediction method is given in the use case in Appendix F.3. Validation of these equations is discussed in chapter six. Homes damaged during the 2004 hurricane season were inspected to verify that the interior damage estimates produced by these equations agree with actual occurrences. Based on these inspections the equations seem to produce fairly good results. Interior damage appears to consistently fall within the range predicted by these equations. The results were also compared against extensive claims data over a large population of damaged homes from hurricane Andrew and others. There are probably many alternatives to the interior damage prediction method proposed here. One such alternative could be to define the interior area impacted from damage to each modeled component thought to cause interior damage. For example, damage of 20 ft 2 of roof sheathing with 100 mph wind speeds will impact 40 ft 2 of interior, or damage of 2 windows at 120 mph will impact 60 ft 2 of interior. We know from costing resources that the average cost to replace the interior is $/ft 2, so the interior repair costs caused by 20 ft 2 of sheathing loss would be approximately equal to 40 ft 2 x $/ft 2 = $790. Again some sort of distribution must be used to account for uncertainties. The advantage of this method is that it could possibly be easier to validate with inspections or even wind tunnel tests. Unfortunately, because of time constraints this and other alternative methods were not fully explored but these could be topics of future research. Function of Sheathing Damage Damage to any portion of a homes roof sheathing inevitably results in some interior damage. Logically, the more sheathing lost the more extensive the damage. The derivation of the interior damage equation is shown in Table 0-4. Based on observations and intuition, typically if a home suffers some sheathing damage the area of interior impacted will be greater than the area of sheathing loss. This is because with hurricane force winds rain does not fall vertically; it blows through the opening and affects a large area. Once the ceiling becomes saturated it can no longer support it own weight and collapses. After this happens rain falls freely into the interior, flooding occurs and everything in the vicinity becomes damaged. Again the repair costs associated with this damage depend on exactly what is in this vicinity. Figure 0-5 illustrates interior damage resulting from sheathing loss. 40

58 Figure Sheathing damage and resulting interior damage 41

59 Table Derivation of interior damage equation as a function of roof sheathing damage Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 10% 15% % Sheathing Loss Carpets/Flooring 75% 15% 11% 25% Interior Walls 15% 34% 5% Ceiling 50% 30% 15% Painting 20% 3% 1% Interior Doors 30% 2% 1% Insulation 100% 1% 1% Total 100% 35% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 25% 15% % Sheathing Loss Carpets/Flooring 100% 15% 15% 50% Interior Walls 35% 34% 12% Ceiling 75% 30% 23% Painting 100% 3% 3% Interior Doors 50% 2% 1% Insulation 100% 1% 1% Total 100% 58% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 100% 15% % Sheathing Loss Carpets/Flooring 100% 15% 15% 75% Interior Walls 100% 34% 34% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 100% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 100% 15% % Sheathing Loss Carpets/Flooring 100% 15% 15% 100% Interior Walls 100% 34% 34% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 100% 42

60 100% Sheathing 90% 80% 70% y = x % Interior Loss 60% 50% 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % Component Loss Figure Interior damage as a function of roof sheathing damage Function of Cover Damage In some cases when a homes roof cover is damaged rain is able to penetrate the structure causing interior damage. This damage is able to occur more readily when the tarpaper beneath the cover is also removed exposing the bare plywood. Typically the damage is limited to minor leaks in the ceiling resulting only after substantial cover has been lost. In many cases significant cover can be lost with no interior water damage. However, if cover damage becomes more severe and all or nearly all of the plywood sheathing is exposed interior water damage could become great. These considerations are reflected in the derivation of the interior damage equation for roof cover shown in Table 0-5. Figure 0-7 and Figure 0-8 depict two homes that experienced roof cover damage during the 2004 hurricane season, the owners of these homes also reported interior water damage. Yet, in some cases with similar degrees of cover loss no water damage was reported. 43

61 Figure 0-7 Cover damage resulting in interior damage Figure 0-8 Cover damage exposing plywood 44

62 Table Derivation of interior damage equation as a function of roof cover damage Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Cover Kitchen 0% 15% % Component Loss Carpets/Flooring 0% 15% 0% 25% Interior Walls 0% 34% 0% Ceiling 5% 30% 2% Painting 0% 3% 0% Interior Doors 0% 2% 0% Insulation 0% 1% 0% Total 100% 2% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Cover Kitchen 0% 15% % Component Loss Carpets/Flooring 25% 15% 4% 50% Interior Walls 5% 34% 2% Ceiling 25% 30% 8% Painting 50% 3% 2% Interior Doors 10% 2% 0% Insulation 25% 1% 0% Total 100% 15% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Cover Kitchen 15% 15% % Component Loss Carpets/Flooring 75% 15% 11% 75% Interior Walls 10% 34% 3% Ceiling 50% 30% 15% Painting 75% 3% 2% Interior Doors 15% 2% 0% Insulation 50% 1% 1% Total 100% 35% Envelope Breach Interior Component % Damaged % of Value % of Value Lost Cover Kitchen 30% 15% % Component Loss Carpets/Flooring 100% 15% 15% 100% Interior Walls 15% 34% 5% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 25% 2% 1% Insulation 100% 1% 1% Total 100% 59% 45

63 100% Cover % Interior Loss 90% 80% 70% 60% 50% 40% 30% 20% 10% y = x x 0% 0% 20% 40% 60% 80% 100% % Component Loss Figure Interior damage as a function of roof cover damage Function of Wall Damage Without question when wall damage occurs the interior of a home is severely damaged. Everything inside maybe directly exposed to the elements leading to total destruction. Complete wall failure is typically a rare occurrence seen only in poorly constructed buildings or in the extreme winds associated with a strong category three hurricane or higher. Also, wall damage is usually a progressive failure where first the roof sheathing is removed, then the trusses or roof to wall connections begin to fail weakening the structure, and finally the walls just collapse. So total interior damage may occur prior to any wall damage whatsoever. Regardless, an equation was developed to predict interior damage resulting from wall damage as shown in Table 0-6. Figure 0-10, Figure 0-11, and Figure 0-12 illustrate some examples of wall damage seen in recent Florida hurricanes. 46

64 Figure Port Charlotte manufactured home destroyed during Hurricane Charley Figure Punta Gorda home destroyed during Hurricane Charley 47

65 Figure Wall damage of a poorly constructed home, majority of interior undamaged 48

66 Table Derivation of interior damage equation as a function of wall damage Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Walls Kitchen 50% 15% % Component Loss Carpets/Flooring 75% 15% 11% 25% Interior Walls 50% 34% 17% Ceiling 75% 30% 23% Painting 100% 3% 3% Interior Doors 75% 2% 2% Insulation 50% 1% 1% Total 100% 63% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Walls Kitchen 80% 15% % Component Loss Carpets/Flooring 100% 15% 15% 50% Interior Walls 85% 34% 29% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 92% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Walls Kitchen 100% 15% % Component Loss Carpets/Flooring 100% 15% 15% 55% Interior Walls 100% 34% 34% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 100% Envelope Breach Interior Component % Damaged % of Value % of Value Lost Walls Kitchen 100% 15% % Component Loss Carpets/Flooring 100% 15% 15% 100% Interior Walls 100% 34% 34% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 100% 49

67 100% Walls %Interior Loss 90% 80% 70% 60% 50% 40% 30% 20% 10% y = x x x 0% 0% 20% 40% 60% 80% 100% % Component Loss Figure Interior damage as a function of wall damage Function of Window Damage Windows of a home are damaged wind and rain is free to enter the structure. It is assumed that loss of a few windows will cause only minor interior damage, while damage to the majority of the windows will cause substantial damage. When surveying homes damaged during the Florida hurricanes of 2004 this appeared to be the case. One problem however is that many of the homes that experienced severe window damage also had heavy roof damage and the interior damage could not be solely attributed to the loss of windows. Some pictures of window damage and subsequent interior damage are shown in Figure 0-14 and Figure The derivation of the interior damage equation as a function of window damage is shown in Table

68 Figure Window damage from flying debris or wind pressure Figure Broken kitchen window, little or no interior damage just clean up 51

69 Table Derivation of interior damage equation as a function of window damage Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Windows Kitchen 0% 15% % Component Loss Carpets/Flooring 35% 15% 5% 25% Interior Walls 10% 34% 3% Ceiling 0% 30% 0% Painting 50% 3% 2% Interior Doors 15% 2% 0% Insulation 0% 1% 0% Total 100% 10% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Windows Kitchen 15% 15% % Component Loss Carpets/Flooring 50% 15% 8% 50% Interior Walls 25% 34% 9% Ceiling 10% 30% 3% Painting 75% 3% 2% Interior Doors 50% 2% 1% Insulation 25% 1% 0% Total 100% 25% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Windows Kitchen 40% 15% % Component Loss Carpets/Flooring 75% 15% 11% 75% Interior Walls 50% 34% 17% Ceiling 20% 30% 6% Painting 100% 3% 3% Interior Doors 70% 2% 1% Insulation 50% 1% 1% Total 100% 45% Envelope Breach Interior Component % Damaged % of Value % of Value Lost Windows Kitchen 65% 15% % Component Loss Carpets/Flooring 100% 15% 15% 100% Interior Walls 75% 34% 26% Ceiling 45% 30% 14% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 70% 52

70 100% Windows %Interior Loss 90% 80% 70% 60% 50% 40% 30% 20% 10% y = x x 0% 0% 20% 40% 60% 80% 100% % Component Loss Figure Interior damage as a function of window damage Function of Door Damage Door damage may result in damage similar to that of window loss. Since the Monte Carlo simulations model only 2 doors the derivation of the equation is a based on the damage of one or both doors. An example of door damage and resulting interior damage is shown in Figure The derivation of the interior equation is shown in Table 0-8. Figure 0-18 illustrates the interior equation without the Weibull distribution applied. Figure Door damage and resulting interior damages 53

71 Table Derivation of interior damage equation as a function of door damage Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Doors Kitchen 0% 15% % Component Loss Carpets/Flooring 35% 15% 5% 50% Interior Walls 10% 34% 3% Ceiling 0% 30% 0% Painting 100% 3% 3% Interior Doors 15% 2% 0% Insulation 0% 1% 0% Total 100% 12% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Doors Kitchen 25% 15% % Component Loss Carpets/Flooring 80% 15% 12% 100% Interior Walls 20% 34% 7% Ceiling 0% 30% 0% Painting 100% 3% 3% Interior Doors 50% 2% 1% Insulation 0% 1% 0% Total 100% 27% 100% Doors % Interior Loss 90% 80% 70% 60% 50% 40% 30% 20% 10% y = x 0% 0% 20% 40% 60% 80% 100% % Component Loss Figure Interior damage as a function of door damage Function of Gable End Damage Gable end damage is assumed to impact the interior in a similar manner and proportion as sheathing damage. Based on inspections of areas in Florida impacted by hurricanes in 2004 this type of damage seems to occur most frequently in structures with a large gable situated normal to the quadrant of stronger winds, and many cases of this type of damage were observed in residential homes. Figure 0-19 illustrates a home with gable end damage. The derivation of the interior equation is shown in Table 0-9 and the equation without the Weibull distribution applied is shown in Figure

72 Figure Gable end damage 55

73 Table Derivation of interior damage equation as a function of gable end damage Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Gable Ends Kitchen 0% 15% % Component Loss Carpets/Flooring 35% 15% 5% 25% Interior Walls 5% 34% 2% Ceiling 5% 30% 2% Painting 50% 3% 2% Interior Doors 15% 2% 0% Insulation 0% 1% 0% Total 100% 10% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Gable Ends Kitchen 15% 15% % Component Loss Carpets/Flooring 50% 15% 8% 50% Interior Walls 10% 34% 3% Ceiling 10% 30% 3% Painting 75% 3% 2% Interior Doors 30% 2% 1% Insulation 50% 1% 1% Total 100% 20% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Gable Ends Kitchen 30% 15% % Component Loss Carpets/Flooring 75% 15% 11% 75% Interior Walls 25% 34% 9% Ceiling 35% 30% 11% Painting 75% 3% 2% Interior Doors 50% 2% 1% Insulation 100% 1% 1% Total 100% 39% Envelope Breach Interior Component % Damaged % of Value % of Value Lost Gable Ends Kitchen 60% 15% % Component Loss Carpets/Flooring 100% 15% 15% 100% Interior Walls 50% 34% 17% Ceiling 50% 30% 15% Painting 100% 3% 3% Interior Doors 75% 2% 2% Insulation 100% 1% 1% Total 100% 62% 56

74 100% Gable Ends % Interior Loss 90% 80% 70% 60% 50% 40% 30% 20% 10% y = 0.38x x 0% 0% 20% 40% 60% 80% 100% % Component Loss Figure Interior damage as a function of gable end damage Function of Sliding for Manufactured Homes When wind loads on a manufactured home exceed the resistance capacity of the anchoring system (if tied down) and the frictional resistance of the foundation on which it rests sliding occurs. Two types of sliding are modeled by the Monte Carlo Simulations: minor and major. Minor sliding is said to occur when wind loads are just greater than the resistance capacities. Major sliding occurs when the wind loads on a manufactured home are greater than 120% of the resistance capacities. Based on these definitions it is assumed that when minor sliding occurs the home has only slightly shifted position but still remains on its foundation. When major sliding occurs it is assumed that the home has been completely moved off the foundation. These types of sliding are likely to cause some interior damage to a home. The degree of this interior damage is a big question and could be highly variable. From surveys of numerous manufactured home parks subject to hurricane force winds during the 2004 season a few instances of sliding (either major or minor) were seen. It is thought and was observed that very little interior damage will result if only minor sliding occurs. Much more interior damage could possibly occur in the case of major sliding. There are probably two extreme cases of interior damage resulting from major sliding. On one end no interior damage could occur, the home just slid of the foundation and it is simply picked up, put back, and re-anchored. On the other hand the impact experienced from sliding of the foundation could cause severe structural damage destroying the entire home. The average is probably somewhere in between these extremes. Based on these ideas it is assumed that on average minor sliding will cause 10.0% interior damage, and an overall increase of external damage of 10%. Major sliding will cause 40% interior damage, and an overall increase of external damage of 20%. The same random Weibull distribution applied to the other interior equations is also applied to these values. 57

75 Figure Sliding of manufactured home, likely light interior damage as a result Function of Overturning Overturning of manufactured homes is modeled much like sliding. However there is no minor or major overturning, it either happened or it didn t. The question again is how much interior damage will result if a manufactured home overturns? Again, like sliding it can be assumed that there are two extreme cases, moderate damage or complete destruction. Figure 0-22 depicts a manufactured home that overturned during Hurricane Frances, it can be seen that the home is almost completely intact other than the fact that it is on its side. Repair of this home is probably just a simple matter of flipping it back over and replacing the damaged siding. Most likely moderate interior damage occurred. The manufactured home in Figure 0-23 wasn t so lucky. This home is completely destroyed even if some of the interior may still be ok the structural damage is so severe that the condition of the interior is irrelevant. When overturning occurs it is assumed in most cases that some significant interior damage will result therefore the model assumes a total loss when overturning occurs. Like all other interior equations a random distribution is applied to account for uncertainty and the possibility extreme cases. 58

76 Figure Overturned manufactured home in Hurricane Frances Figure Overturned manufactured home in Hurricane Charley Two-Story Homes As was mentioned in Section a separate physical Monte Carlo simulation model has not been developed for two-story homes. Instead the one story models are modified to account for the likely increased wind forces experienced at the higher elevation. In 59

77 addition to theses considerations applied to the Monte Carlo models, it may be logical to make adjustments to the interior damage projections as well to account for the likelihood of increased interior damage resulting from some breach of the building envelope, since this breach of envelope may impact a larger area of the interior of a twostory home than a one-story home. There is no data or basis by which to justify the magnitude of this adjustment other than engineering judgment. Yet, to provide a means by which to modify the predictions based on these considerations a factor k2 is defined and multiplied by each interior equation. The value of k2 is current set at So for the same breach of envelope, the model predicts 10% greater interior damage for two story homes than 1 story. Utilities Damage Potential damage to the utilities of a home presents another modeling puzzle. The utilities of a home include the electrical, plumbing, and mechanical systems as described previously in chapter 3. Combined these assemblies comprise a significant portion of a homes cost, typically around 25%. It is quite possible that these systems will be damaged in an intense hurricane, not only from the direct effects of the wind but also, like the interior, resulting from rain and wind entering the structure. In addition when damaged portions of the interior such as the wall partitions must be replaced, electrical and plumbing supply lines may also require attention. If these repair costs are neglected in some cases there could be a drastic underestimation of insured loss. The simplest and most logical method to estimate utilities damage is based upon the prediction of interior damage. The other alternative first explored was to develop separate equations for each type of utility damage as a function of each modeled component and take the total damage to be the maximum, the same way the interior damage prediction is made. The problem with this method is that so many equations are defined based on nothing more than pure judgment that any physical meaning is completely lost. On the other hand, interior equations are defined based on the best possible physical reasoning, verified by inspecting homes that suffered damage during recent hurricanes, and then damage to the utilities is extrapolated from the predicted interior damage. To extrapolate the utilities damage, a coefficient is defined for each utility (electrical, plumbing, and mechanical) then multiplied by the interior equation defined for each component and the total damage is taken to be the maximum value. The utilities coefficients are based on engineering judgment but it is much easier to justify and validate one judgment call than eight. The small number of parameters allows for a simple means by which to calibrate the model. When compared with validation data; if the repair costs predicted by the model seem high these coefficients can be reduced; if low, increased. The selection of the utilities coefficients for the electrical, plumbing, and mechanical systems will be 60

78 presented in the following sections. A summary of these methods is given in the use case in Appendix F.4. Electrical Damage In both site-built and manufactured homes it is assumed that electrical damage occurs at about half the rate of interior damage. For site-built homes and manufactured home, each interior equation is multiplied by a coefficient, ke equal to 0.5. The total electrical damage is the maximum value of all interior equations multiplied by ke. The question could be raised; why isn t the coefficient ke just multiplied by the total interior damage (which is the maximum of all interior damage equations) to save computation time? If that was done the maximum possible electrical damage could only be 50%, since the maximum interior damage is 100%. But when ke is multiplied by each interior equation the results can range up to 100%, Figure 0-24, since the equation predicts interior damages in excess of 100%, but is logically capped at 100%. The point is that even after 100% interior damage has occurred utilities damage could continue to increase. An example of how this factor is applied to an interior equation is shown in Table Also important to note is that a random Weibull variable other than the one applied to the interior equation is used to calculate the electrical damage. The distribution is the same (mean=1 variance=0.2372) but the random variable is just different. This adds the random possibility of utilities damage that would be expected in an actual home, rather than using the same random variable which would produce just a linear relationship between utilities and interior damage defined by ke times the interior damage. So for every site-built home model simulation the mean electrical damage is the maximum value of ke (50% percent) multiplied by each interior damage equation, and distributed about this mean using the same Weibull distribution applied to the interior equations, Figure This figure shows the relationship between electrical and interior damage that result from sheathing damage, unlike Figure 0-24 which is a plot electrical damage as a function of sheathing loss. No data exists to validate the ke values used. In the vulnerability program this variable can easily be changed as required based on the results of further research. Figure 0-26 illustrates how physical damage to a home could result in damage to the electrical system, it can be seen in this picture that failure of the wall caused damage to an electrical outlet and attached conduits, this most likely resulted in electrical failure throughout at least a portion of the home. 61

79 Figure Electrical damage vs. sheathing damage Table Electrical damage as a function of sheathing damage equation y = 1.29*x Elec=ke*Re*y if Elec >= 1.0 Elec = 1.0 if Elec <= Elec = 0 where: x = % sheathing damage y = mean % interior damage as a function of sheathing damage Re = random Weibull variable (mean of the distribution equal to 1) Elec = % electrical damage ke = electric coefficient (0.5) 62

80 Figure Electrical damage vs. interior damage resulting from sheathing damage Figure Electrical damage caused by exterior wall failure 63

81 Plumbing Damage Plumbing damage is predicted in the same way as electrical. The same procedures are applied, however plumbing damage is assumed to occur at a slower rate than electrical damage. Therefore, the coefficient kp is set equal to 0.35 for site-built homes and manufactured homes. Again the same uncertainties discussed for electrical damage apply to the plumbing system. The value of kp can be easily modified based on the results of further research. Little in the way of plumbing damage was documented following the Florida hurricanes of 2004, however one such example can be seen in Figure Figure Plumbing damage resulting from structural failures Mechanical Damage Many things could be considered part of the mechanical system of a home. Some things such as the air conditioning unit of many site-built homes are outside the home, directly exposed to the forces of the wind. Unless we want to construct a Monte Carlo Simulation model to test the probability of damage to an air-conditioning unit, we must predict these damages as a function of the modeled components. Other mechanical elements such as the hot water heater, garage door opener, air handler, etc. are inside of the home so damage may occur at some rate proportional to the interior damage. So like all other utilities a coefficient, km, is defined as a multiple of the interior damage equations. At the present time the value of km is set to be 0.4 for site-built homes and manufactured homes. It is assumed that mechanical damage will occur at a slower rate than electrical damage but slightly quicker than plumbing. Figure 0-29 depicts damage to components of a homes mechanical system resulting from structural failures. 64

82 Figure Wind damaged air condition unit Figure Mechanical damage resulting from structural failures 65

83 Total Building Damage Now that all of the procedures and methods used for predicting damage and repair costs to each component of a home have been defined, calculation of the total repair cost or damage ratio is just a matter of combining all the elements. Again in this model, the total building damage at any given wind speed is expressed as a damage ratio because this ratio can be generally applied to homes of all value. Converting the damage ratio into a repair cost (or insurable loss plus the deductible) is done by simply multiplying it by the insured value of the home. The calculation of the damage ratios for each building type is discussed in the remainder of this section. Site-Built Homes For each Monte Carlo simulation model output, every time the vulnerability program runs it calculates the damage ratio of six different building types. Differences in the replacement ratios or the thresholds applied to each model simulation allow for differences in the vulnerability of the building types (expressed as a replacement cost ratio) given the same amount of physical damage. For example, if the Monte Carlo model simulates 20% roof cover damage the two possibilities that we consider are that this is either a tile or shingle and because the replacement costs (ratios) are different for both tile and shingle roofs two separate damage ratios are computed. The six different building types are as follows: 1. No Sub-region, Tile Roof 2. No Sub-region, Shingle Roof 3. Windborne Debris Region, Tile Roof 4. Windborne Debris Region, Shingle Roof 5. High Velocity Hurricane Zone, Tile Roof 6. High Velocity Hurricane Zone, Shingle Roof The thresholds applied to the physical damage for each of these home types was discussed in Section 0. The calculation of the replacement ratios was described in chapter 3. One general equation is used to calculate the total damage ratio for each model simulation, and the amount of physical damage is adjusted based on the thresholds for each building type. For example if a home in the high velocity zone has 30% roof cover damage it costs the same as replacing 100% so the physical damage is converted to 100% for calculation of the damage ratio. This adjustment is not applied to the calculation of interior and utilities damage, which are based on the actual amount of damage. The general equation is as follows: 66

84 Building Damage Ratio = Σ Adjusted Percent Component Damage * Replacement Ratio of Component A summary of the method used for computing the total building loss for site-built homes is given in the use case in Appendix F.5. Manufactured Homes Because manufactured homes represent a much smaller portion of the building stock in Florida a much simpler modeling method was devised. No attention is paid to the different sub regions or possible variations in construction materials. The same costing model is used for all of the different Monte Carlo Simulation models. Thresholds are applied to all manufactured homes as if they all lie in the high velocity hurricane zone, and as will be shown in chapter 5 this makes little difference in the final results. The same general equation to calculate the damage ratio of site built homes is used for manufactured homes. A summary of the method used for computing the total building loss for manufactured homes is given in the use case in Appendix F.6. Other Coverage s A typical insurance policy covers not only the structure but also the contents, appurtenant structures, and additional living expenses incurred by the residents resulting from hurricane related damage. In this section the prediction of these types of damages will be discussed. Contents Contents includes just about anything in the home (including garage and outbuildings) not attached to the structure and belonging to the policyholder or a member of his family living in the same house, or to resident domestic servants. It also includes property, which is not owned by the policyholder but for which he is responsible, such as rented property. Furniture, furnishings, household goods, electrical appliances, food and drink, clothes, and money up to a specified limit all count as 'contents'. Also included are movable fixtures and fittings, for example, special lighting fittings that would be taken away on removal. Fittings, which would be left in the house, such as built-in furniture, count as part of the 'buildings', although fitted carpets are classed as 'contents'. Certain types of property are excluded. The cover applies principally to contents actually inside the home, although there is some cover under a 'standard' policy for contents temporarily away from the home. 67

85 A typical insurance policy covers contents of a home up to 50% of the insured value of the building. However, from a study of insurance policy files from several different companies it was observed that this value is not always used and the contents covered by a policy may not necessarily be the value of the contents contained within a home. For example, a home with an insured building value of $200,000 may have only $10,000 in contents coverage, or 5% coverage. It is likely that the contents of this home are valued at much greater than $10,000, and is therefore underinsured. In our model, contents damage is estimated and validated based on a value of 50% of the building coverage, or $100,000 for this example. So if an estimate of 30% contents damage was made for this home, this means that there was a $30,000 damage of contents, which is greater than the $10,000 of coverage and therefore would be 100% insured loss. Also, there are many cases where an insurance policy covers contents of a home greater than 50% of the insured building value. For these cases we assume the value of the contents to be the value of coverage given in the policy. Like the interior and utilities, the Monte Carlo simulations to predict potential damages do not model the contents of a home. Contents damage is estimated in the same way as damage to the utility systems. The contents damage is assumed to occur at a rate of kc multiplied by the interior damage equation for each modeled component that causes a breach of the building envelope. The value of kc is estimated from engineering judgment and validated using actual claims data. The value currently being used for both residential and manufactured homes is kc equal to Again, some random distribution must be applied to this relationship to account for uncertainties. However, given the importance of the contents in the overall estimate of insured losses, it was felt that a more sophisticated model was needed for the estimate of the variation of contents damage. In particular, it was felt that the distribution of the contents damage could be linked to the level of overall building damage, based on observations and common sense. To model this a Weibull distribution is still used but the β parameter is assumed to vary linearly between a maximum and minimum value as a function of total building damage ratio damage, instead of assuming a constant value of 2 for all cases as for the interior and utilities predictions.. Again, to maintain the mean values produced by the equations the α parameter of the Weibull distribution is calculated such that the mean of the distribution is equal to one. The maximum and minimum β parameters were selected based on engineering judgment and resulted in a good agreement with the claims data as will be seen later. As with the interior, based on the results of the model the choice of the Weibull parameters is assumed to be reasonable, but a sensitivity study is planned with a view of confirming this assumption or revising the choice. Currently, the maximum β parameter is set at 1.65 and the minimum is set at 0.5, Table 0-11 demonstrates how the Weibull distribution is defined for contents damage predictions. A summary of the contents damage predictions are given in the use case in Appendix F.7. 68

86 Figure 0-30 through Figure 0-32 illustrate contents damages that occurred during the Florida hurricanes of It can be seen from these pictures that the insurable value of contents losses is highly variable and subjective. In these pictures it appears that some of the contents may be salvageable, for others it is uncertain. This uncertainty is accounted for in the model predictions as shown in Figure Table 0-11 Calculation of Weibull distribution for content predictions βmax = 1.65 βmin = 0.5 DR = total building damage ratio (% - maximum = 100%, minimum =0) β = (βmax - βmin)*dr + βmin α = (1/Γ(1+β -1 )) -β Rc = weibrnd(α,β) y = 1.29*x Cont=kc*Rc*y if Cont >= 1.0 Cont = 1.0 if Cont <= Cont = 0 β = Weibull beta parameter α = Weibull alpha parameter (calculated so that the mean of the distribution is equal to 1) Rc = Random Weibull variable (generated by Matlab using the function weibrnd by defining β and α) x = % sheathing damage y = mean % interior damage as a function of sheathing damage Rc = random Weibull variable (mean of the distribution equal to 1) Cont = % contents damage kc = contents coefficient (0.35) 69

87 Figure Contents damage a complete bedroom set lies under the debris Figure Contents damage to a manufactured home 70

88 Figure Contents damage - the whole roof is lost and some furniture may need to be replaced Figure Modeled contents damage vs. structural damage, each point is one model simulation 71

89 Additional Living Expenses Additional Living Expense (ALE) is found in the Farm Fire and Homeowners policies under Loss of Use, Coverage D. Additional Living Expense is coverage for the increase in living expenses that arise when an Insured must live away from the insured location due to a covered loss. Additional Living Expense Coverage covers only expenses actually paid by the Insured. This coverage does not pay all living expenses, only the increase in living expense that results directly from the covered loss, and having to live away from the insured location. If the covered loss does not make the residence unlivable, there will be no Additional Living Expense to claim. Coverage is provided for the shortest time required to repair the covered damage. The value of an ALE claim is obviously dependant on the time that it takes to repair a damaged home, and in some instances even damage to the infrastructure (downed power lines or a damaged bridge to a barrier island could prohibit access). To predict ALE costs first the duration of repairs or rebuilding is estimated as a function of interior damage, Table 0-12 and Figure The duration estimate is based upon interior damage and not total damage for two reasons. The first reason is that logically the extent of interior damage will determine if the home is livable or not, and provide the basis for an ALE claim. There could be significant exterior damage and a substantial structural claim made however, if the interior is undamaged the home may still be livable and there will be no ALE costs. The second reason is that it simplifies the model computations. If the ALE lost costs were based on the total building damage ratio rather the interior damage the ALE costs would vary depending on the structural type, sub region, and construction materials because repair costs also vary depending upon these factors. In contrast, when the ALE prediction is made based on interior damage all damage functions are constant and based entirely on the modeled physical damage, and therefore the same amount of physical damage will on average result in the same ALE costs for all home types. 72

90 Table Estimation of repair times Interior Damage Ratio Estimated Time Home is Unlivable Due to Repairs (days) 0% 0 25% 1 50% 30 75% 90 90% % 300 Figure Time home is unlivable vs. Interior Damage A typical insurance policy covers ALE costs up to 20% of the insured value of the home; for all policies with ALE coverage of less than 20% the predictions and validation are based on this ratio, if coverage is greater than 20%, predictions and validation should be based on the limit of ALE insurance of the policy. On average, 20% of the insured building value is assumed to cover expenses for 365 days or 1 year. So the estimated duration of repairs is divided by 365 to compute the total average percentage of ALE costs. For the ALE predictions some random distribution must also be applied to account for uncertainties in the repair time estimates as well as the variations in additional 73

91 living costs. Since there is almost no data to validate the choice of any distribution type so it is assumed that ALE costs will have a distribution similar to contents damage that varies as a function of the total building damage ratio. Therefore the same linearly varying Weibull distribution that is applied to the contents predictions is also applied to ALE. The modeled ALE predictions plotted vs. building damage is shown in Figure Figure Modeled ALE damage vs. building damage The equation and methods used for manufactured and residential homes are identical. However, it seems logical to reduce the manufactured home ALE predictions because typically a faster repair or replacement time may be expected for these home types. Therefore, a factor Rf was introduced into the manufactured home model. This Rf factor is now set at 0.75 based on engineering judgment, and it multiplies the ALE predictions to adjust the values. A summary of the ALE predictions is given in the use case in Appendix F.8. Appurtenant Structures Appurtenant structures, also called "Other Structures", typically are structures not attached to the dwelling or main residence of your home, but located on the insured property. These types of structures could include: detached garages, guesthouses, pool houses, sheds, gazebos, patio covers, patio decks, swimming pools, spas, etc. 74

92 From insurance claims data there appears to be no obvious relationship between building damage and appurtenant structure claims, Figure One of the primary reasons for this maybe the variability of the structures that are covered by an appurtenant structure policy. In the event of a hurricane, structures such as pools, spas, and patio decks may experience little or no damage at high wind speeds while the main residence on the insured property could be substantially damaged. In contrast, structures such as screened patios, sheds, and gazebos may experience significant damage at relatively low wind speeds that are unlikely to cause damage to the main residence. There are also structures that may be covered under an appurtenant structure policy that will experience wind damage at approximately the same rate as the primary residence these include guest homes, pool homes, and detached garages. Figure 0-37 and Figure 0-38 illustrate some different appurtenant structure types and their vulnerability to wind induced damage. Appurtenant Structure Claims 100% 90% 80% Appurtenant Structure Loss 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Structural Loss Figure Typical plot of appurtenant structure vs. building claims 75

93 Figure Highly susceptible appurtenant structure - the screened patio, and low susceptible - the pool Figure Moderately susceptible appurtenant structure - the pool house, and low susceptible - the pool To model appurtenant structure damage three separate equations are developed as shown in Table 0-13 and Figure Each determines the appurtenant structure damage ratio as a function of wind speed (vulnerability curve). One equation predicts 76

94 damage for structures highly susceptible to wind damage, the second for moderately susceptible, and the third for structures which are effected only slightly by wind. These equations are developed by approximating damage at several different wind speeds for each type of structure and curve fitting an equation. As with equations to predict interior, contents, and ALE damage a Weibull distribution is applied to account for any uncertainties, Figure In this case the β parameter of the Weibull distribution was reduced to 1 which yields an exponential distribution. The very limited insurance data available shows a high concentration of claims with zero losses and a very large scatters of losses elsewhere, this is indicative of an exponential distribution which supports the decision for reducing the β parameter. Wind speed (mph) Table Appurtenant structure damage estimation per wind speed Highly Susceptible to Wind Damage: Screened Patios, Sheds, Gazebos, etc. Moderately Susceptible to Wind Damage: Guest Homes, Pool homes, detached garages etc. Not Susceptible to Wind Damage: Pools, spas, patio decks, etc. 0 0% 0% 0% 40 0% 50 1% 100 1% 0% % % 0% % % 90% 12% 77

95 100% 90% 80% Appurtenant Structure Damage vs. Windspeed y = -3.29E-07x E-04x E-03x R 2 = 9.95E-01 y = -1.43E-07x E-05x E-03x R 2 = 9.78E-01 APS loss ratio 70% 60% 50% 40% 30% 20% 10% 0% Windspeed (mph) 3-second gusts High Moderate Low Poly. (Low) Poly. (High) Poly. (Moderate) y = 4.23E-06x E-04x R 2 = 9.30E-01 Figure Appurtenant structure vulnerability curves Figure APS damage ratio vs. wind speed, exponential distribution Because a typical the insurance portfolio files give no indication of the type of appurtenant structure covered under a particular policy a distribution of the three types 78

96 must be assumed. From the available claims data, it appears that the majority of the appurtenant structures have very little damage even with increasing building damage, and few experience moderate to high damage. Based on this data and engineering judgment a distribution of 90% low, 5% moderate, and 5% high is assumed. This method produces results that provide a good comparison with the claims data, Figure Figure APS damage ratio vs. Building Damage ratio, assuming a random distribution of 5% high, 5% moderate, and 90% low (this figure was developed using a normal distribution, an update is intended) A typical insurance policy covers appurtenant structures up to 10% of the insured building value. The estimates and validation of appurtenant structure damage is based on this value the same way as described in the previous sections for ALE and contents damage. A summary of the ALE predictions is given in the use case in Appendix F.12. Summary In chapter 4 all of the costing procedures used to convert the modeled physical damages to monetary repair costs were defined. The methods used to predict damage to components of the home that are not modeled were also presented. The combination of all of these procedures to compute a total building damage ratio for each structural type was discussed. In addition, the methods developed for predicting damage to the other 79

97 coverage s were presented. The next chapter will provide a complete analysis of the vulnerability model results. 80

98 Chapter 4 Vulnerability Model Results This chapter will discuss the development of the vulnerability matrices and provide an analysis of the results that they contain. Two types of vulnerability matrices will be discussed, first the model matrices and then the weighted matrices. The model matrices are specific to each Monte Carlo model and take into account common different construction materials and building code requirements. These matrices are useful for comparing the vulnerability of homes of different structural types and construction materials. However, they are too specific to apply to the insurance policy files, which lack sufficient information to classify the type of home being considered. For this reason, weighted vulnerability matrices are created based on the results of the previously conducted exposure study. These matrices are developed by weighing each model matrix based on its probability of occurring in each region. This creates general matrices that can be selected and applied to any insurance policy based on known information contained in the policy files. 4.1 Model Vulnerability Matrices Site-Built Homes Building Matrices As was mentioned in Chapter 4, six different building damage ratios are computed for each model simulation, of each Monte Carlo model. For each Monte Carlo model 5000 simulations are performed at 8 different angles and 41 different wind speeds. This is 5000 x 8 x 41 = 1,640,000 simulations per model. From this data we are not so much interested in the damage ratio of each individual model simulation but rather in the statistical distribution of losses or the probability of a certain value loss occurring at a given wind speed. For this reason the data from the 1,640,000 model simulations is transformed into a vulnerability matrix. And because six different damage ratios are computed for each model simulation six separate vulnerability matrices are created for 81

99 each Monte Carlo model, one for each combination of sub region and roof cover material. A partial example of a vulnerability matrix is shown in Table 5-1. The vulnerability matrix for a particular structural type represents the probability of any given damage ratio occurring at a given wind speed. The columns of the matrix represent the different wind speeds from 50 mph to 250 mph in 5 mph increments. These are 3 seconds gust wind speeds at a 10 m height in open terrain. The rows of the matrix correspond to damage ratios of: 0%, 1%, 3%, 5%, etc. in 2% increments up to 20%, and then in 4% increments; 22%, 26%, 30%, 34%, etc., up to 100%. The number of simulations that fall within each range are counted, for example, if 0%<DR<2%: DR=1%, if 2%<DR<4%: DR=3%, etc. After, all the simulations have been ran, each count is divided by the total number of simulations per wind speed to determine the percentage of simulations at any damage state occurring at each speed. These percentages are the conditional probabilities of occurrence of a level of damage, given a certain wind speed. Table Partial example of a vulnerability matrix (columns: wind speed, rows: damage ratio) % % % % % % E % % % % % % % E % % % % E -0 5 The vulnerability program is run through every Monte Carlo model to develop these matrices for every major structural type, region, sub region, and roof cover type. A total of 216 matrices are created, however because the high velocity zone does not exist in central and north Florida 48 of these matrices can be neglected giving a total of 168 structural matrices, a list of all of these is given in Appendix C. From these matrices numerous plots can be generated for comparison and validation purposes. Two important plots derived from the vulnerability matrix are the vulnerability and fragility curves. The vulnerability curve for any structural type is the plot of the mean or average damage ratio vs. wind speed. The fragility curve is depicts the probability of a 82

100 particular damage ratio being exceeded at each wind speed. For the fragility curves 4 damage states are considered: DS1 - minor damage (3% or greater), DS2 - moderate damage (9% or greater), DS3 - severe damage (22% or greater), and DS4 - destruction (46% or greater). These limits were arbitrarily chosen only for the sake of comparison with similar plots provided by the HAZUS model; they could easily be modified for other comparisons as needed. Figure 4-1 is an example of vulnerability and fragility curves. These plots derived from all model vulnerability matrices are given in either Appendix C and on the attached cd. A summary of these procedures is given in the use case in Appendix F.9. Figure Vulnerability and Fragility plots of a model vulnerability matrix It is interesting to see how these vulnerability and fragility curves vary with structural types, building materials, region, and building code requirements. These considerations may form the basis of future mitigation studies. It is also important to note that the vulnerability curve only represents the average loss per wind speed. Processing of claims data from recent hurricanes and surveys of storm damage revealed that there may be an extremely wide distribution of loss values at any given wind speed. This distribution is reflected in the model results as will be discussed in Chapter 6. Clearly, it would not be possible or necessary to make comparisons of all combinations of the different vulnerability model types here. Instead comparisons of only the key differences are presented in Figure 4-2 through Figure 4-6 to show how the modeled vulnerability of homes is affected by each consideration. 83

101 South FL, Concrete Block Homes with tile roofs, Vulnerability Comparisons Gable, no shutters Gable, no shutters, WBDR Gable, no shutters, HVHZ 0.7 Structural Damage Ratio Windspeed (3-second peak gusts mph) Figure Sub region vulnerability comparisons of South FL homes 1.0 South FL, Concrete Block Homes with tile roofs, Vulnerability Comparisons Gable, no shutters Hip, no shutters 0.7 Structural Damage Ratio Windspeed (3-second peak gusts mph) Figure Vulnerability comparison of gable and hip roofs 84

102 South FL, Concrete Block Homes with tile roofs, Vulnerability Comparisons Hip, with shutters Hip, no shutters 0.7 Structural Damage Ratio Windspeed (3-second peak gusts mph) Figure Vulnerability comparison of shuttered and not shuttered homes 1.0 South FL, Concrete Block Homes Vulnerability Comparisons Hip, with shutters, tile roof Hip, with shutters, shingle roof 0.7 Structural Damage Ratio Windspeed (3-second peak gusts mph) Figure Vulnerability comparison of shingle and tile roofs 85

103 South FL, Gable Roof, tile, no shutters Vulnerability Comparisons Concrete Home Wood Home 0.7 Structural Damage Ratio Windspeed (3-second peak gusts mph) Figure Vulnerability comparison of concrete and wood homes South FL, Gable Roof, tile, no shutters Vulnerability Comparisons 1.0 Structural Damage Ratio Story - Wood 1 Story - Wood 2 Story - Concrete/Wood 1 Story - Concrete Windspeed (3-second peak gusts mph) Figure Vulnerability comparison of 1 and 2 story homes 86

104 Figure 4-2 shows that the Florida building code requirements have very little effect on a modeled homes vulnerability. This is because there is not a great difference in the costing considerations made for any of these sub regions, and there is no difference in the modeled physical damage. However, these considerations become important when developing the weighted vulnerability matrices because it can be assumed that in each sub region the building code requirements effect the distribution of shuttered and not shuttered homes, and it can be clearly seen in Figure 4-4 that this makes a substantial difference in the vulnerability of a home. Figure 4-3 shows that as logically would be expected homes with gable roofs have a higher vulnerability than homes with hip roofs. In Figure 4-5 the vulnerability of homes with tile roofs and shingle roofs are compared. Although there is no difference in the physical model that predicts damage to a tile or shingle roof (and, as was presented earlier, neither of these roof types performs significantly better in hurricane force winds), homes with tile roofs have a higher vulnerability than homes with shingle roofs because of the higher repair cost of a tile roof. Figure 4-6 compares the vulnerability of wood and concrete homes, however the results do not turn out exactly as would be expected and therefore require some explanation. Up until wind speeds of about 225 mph the wood homes are more subject to damage than concrete homes, as logic would dictate. However, at about 225 mph there is a crossover point at which concrete homes become more vulnerable than wood homes. Investigation into this issue revealed that this crossover point is coming from the physical Monte Carlo simulation models. The reason for this is that at high wind speeds roof to wall connections of a home readily fail, and when these connections begin to fail the failure mode of the home changes. Instead as acting as a closed structural system with walls that can be idealized as simply supported, they act as cantilevered. Since concrete does not perform nearly as well in tension as wood, brittle failure (or crumbling) of the concrete walls occur at these higher wind speeds, while the cantilever wood walls may perform better. These are issues that may be modified in future improvements to the model. Yet, it should be realized that this discrepancy only occurs at wind speeds in excess of 225 mph and the probability of winds of this velocity occurring anywhere in the state is extremely small. The effect described in the previous paragraph is somewhat enhanced in the two story home models as shown in Figure 4-7. Because the two story homes are at a slightly higher elevation than the 1 story, at higher wind speeds there is less frictional interaction with land which therefore results in greater forces on the structure. This may results in an increased likelihood of physical damage as depicted by the model. In addition, because a greater area of interior may be impacted by some breach of opening the interior damage predictions are compounded. All of these factors contribute to the significantly higher vulnerability prediction for 2-story homes. 87

105 Contents and ALE Matrices Two types of contents and ALE vulnerability matrices can be created with the vulnerability program. The first type (type 1) arranges the model predictions of contents damage and ALE in the exact same form as the building vulnerability matrices, where the cells of the matrix represent the conditional probability of occurrence of a particular state of damage given a 3 seconds gust wind speed. In the second type of matrices (type 2), the cells represent the conditional probability of a particular state of contents or ALE damage given a certain level of structural damage, regardless of wind speed. In these type 2 matrices the columns of the matrix correspond to the different increments of structural damage (same increments as the rows of the building vulnerability matrices, damage ratios of: 0%, 1%, 3%, 5%, etc. in 2% increments up to 20%, and then in 4% increments; 22%, 26%, 30%, 34%, etc., up to 100%) and the rows correspond to the increment (same increments) of contents or ALE damage. Both of these matrix types are used in the complete actuarial loss model. With the type 1 matrices the contents damage and ALE are a function of the wind speed, and with the type 2 matrices these damages are a function of the structural damage. The type 2 matrices are used to distribute the deductible more accurately on a pro-rata basis and are also used in the estimate of the variance of the expected loss, as discussed in Chapter 7 on Model Integration Type 1 As was stated earlier, contents and ALE losses are based entirely on the interior damage (which is derived directly from the modeled physical damage) to a home. The additional considerations or cost factors applied to compute the six separate building vulnerability matrices for each Monte Carlo model have no effect on the contents and ALE losses. Therefore, only one type 1 contents and ALE vulnerability matrix is created for each Monte Carlo model. These matrices are formed the same way as the building vulnerability matrices and the rows and columns represent the same thing for all matrices. Again the vulnerability and fragility curves for contents and ALE are computed from these matrices as shown in Figure 4-8 and Figure

106 Figure Contents vulnerability and fragility curves Figure ALE vulnerability and fragility curves 89

107 Type 2 The type 2 contents and ALE matrices give the conditional probability of a particular state of contents or ALE damage at a given level of structural damage. The damage predictions used to develop the type 1 and type 2 matrices are identical; it is just a matter of rearranging the data to present it in this form. Since there are six different building model types (for each Monte Carlo model, one for each combination of sub region and roof cover material as given in Section 0) there will be a different relationship between contents damage, ALE and building damage. This is because the costs and therefore the structural damage ratios of the six model types are different, although only one prediction of contents damage and ALE is made for all six based on the projected physical interior damage to the home. As a result six different type 2 contents and ALE matrices are created for each Monte Carlo model, taking into account the same factors of sub region and roof materials as the building models. A partial example of a type 2 contents or ALE matrix is given in Table 5-2. Figure 4-10 is a type 2 contents vulnerability curve and Figure 4-11 is a type 2 ALE curve. In these figures the maximum and minimum values of contents and ALE damage are also given to illustrate the range of damages that could be expected. These are obtained from the vulnerability matrices by taking the highest increment of contents or ALE damage with a nonzero probability of occurrence at each level of structural damage. 90

108 Table Partial example of type 2 contents matrix 0% 1% 3% 5% 7% 9% 11% 13% 15% 0% % % % % % % % % % % % % % % % % % Figure Type 2 contents vulnerability curve 91

109 Figure Type 2 ALE vulnerability curve Appurtenant Structure Matrix As was discussed in Chapter 4 the appurtenant structure loss prediction is based only on the estimated vulnerability of three types of structures. These losses are not derived as some function of the building damage because it was concluded that they are not related. Only one appurtenant structure vulnerability matrix is developed and applied to all structural types, because it is not dependant upon building damage. A vulnerability curve can again be calculated from this matrix as shown in Figure

110 Figure Appurtenant structure vulnerability curve Vulnerability for Weak and Medium Models The initial loss estimates from the FPHLPM were consistently lower than would be expected when compared with existing models and claims data. The wind model was first vetted for accuracy and some adjustments were made. It was determined then that the engineering component should be revisited in light of both the preliminary loss prediction results and the recent observed damage from the 2004 hurricane season. This section describes these additional developments of the vulnerability model Rationale for additional models The 2004 hurricane season produced significant damage to residential structures. Several members of the FPHLPM team conducted in-field documentation of this damage, and one very detailed damage assessment study is still being conducted (through May, 2005). Based on these observations it was hypothesized that a defensible means of addressing the low loss predictions would be to adjust the current aggregate damage output from the so-called standard model with those from the base model as defined in the commission standards, and described in Appendix H. The standard model, described in the previous section, was developed as an attempt to replicate the average or typical home in Florida, in each of the 4 regions (North, Central, South, Keys) with 4 models per region (CB-hip, CB-gable, wood-hip, woodgable). However, all of these models employ several of the mitigation measures as default. For example, hurricane straps and 8d nails fastening the roof sheathing. A large 93

111 coefficient of variation was employed to attempt to account for lesser construction. This produces a large spread in the damage results, but the mean values still reflect the stronger construction. Thus the current results are appropriate for the average home in Florida that was built within the era requiring such measures. This is realistic on its face, but in reality the outlier-type structures that are more like the very weak base model are major contributors to losses. For example, in the Punta Gorda region after Charley, most residential homes suffered some but not catastrophic losses. Such homes are currently being reasonably modeled in the FPHLPM. However, a good number of homes in older sections of the town were almost totally destroyed, thus boosting the total losses. These homes, built to earlier eras of code, did not (in general) employ proper strapping of the roof to the walls, or adequate nailing size or spacing for the roof. Such homes are not explicitly accounted for in the current results, but have been modeled as the so-called base case used in the mitigation component. Therefore the engineering team has developed two new additional series of models, a weak series, and a medium series that complement the standard or strong models described in the previous section. The aggregate damage that currently consists of the standard model results will be weighted with results from the weak and medium models. The result will simply reflect a more realistic scenario in which regions impacted by a severe storm will contain homes that resemble the standard model, and others that reflect the weak and medium. It was originally intended that the large coefficient of variation in capacity values would account for such homes, but current results indicate otherwise New Models Residential construction methods have evolved in Florida as experience with severe winds drives the need to reduce vulnerability. To address this, the vulnerability team has developed a standard (strong) model, medium strength model, and a weak model to represent relative quality of construction. The strong model is described in the main previous section. The medium and weak models are described below. Both the weak and medium models were derived from the strong or standard model. The simulations are straightforward using various levels of capacity within the standard model framework. For example, the standard model for south, concrete block, gable roof construction is converted to a weak model by simply lowering the roof-to-wall (r2w) connection capacity to toe-nail strength, lowering the garage capacity, and lowering the sheathing capacity. Simulations have been generated for gable roof, 1 and 2-story wood and 1-story concrete block wall, north, central and south regions. This has been repeated with plywood shutters in place. The medium models are the same as the weak ones except for the clip roof to wall connections. The main characteristics and differences between the 3 models are summarized in Table

112 Table Characteristics of the 3 site built models. Model Garage door Sheathing nailing Roof to wall connections Roof shape Opening protection Weak Weak (30 psf) 6d (100 psf) Toe nails (see aside) Gable only None or plywood (see aside) Medium Weak (30 psf) 6d (100 psf) Clips (see aside) Gable only None or plywood (see aside) Strong (52 psf) Strong 8d (150 psf) Straps (see aside) Gable or hip None or plywood (see aside) Aside: Note 1: Plywood reduces probability of missile impact damage by 50% Note 2: Capacity of toe nails, clips and straps vary for wood vs. masonry walls and gable end vs. long dimensions: Presented as long dimension capacity / gable end capacity all in lbs. Wall type Toe nail Clip strap Wood wall 460 / / / 1260 masonry 700 / / / 640 Once the external damage matrices were generated from the Monte Carlo simulations for the weak and medium models, the vulnerability matrices were derived as explained in the previous section. Some of the resulting weak vulnerability matrices are compared in Figures 5-13 to

113 Wood South Vulnerabilities 100% 90% Damage ratios 80% 70% 60% 50% 40% South Frame HVZ South Wood hvhz (g,shingle, nsh) South Wood hvhz (g,shingle,wsh) South Wood hvhz (g, tile, nsh) South Wood hvhz (g, tile, wsh) South Wood hvhz (g, shingle, 2-story) South Wood hvhz (g, tile, 2-story) 30% 20% 10% 0% sec gust wind speeds 3 Figure 4-13 Weak wood structure vulnerabilities in the South high velocity hurricane zone Timber Structures Central Vulnerabilities 1 Damage ratios Central Frame wbdr Central Wood wbdr (g,shingle, nsh) Central Wood wbdr (g,shingle,wsh) Central Wood wbdr (g, tile, nsh) Central Wood wbdr (g, tile, wsh) Central Wood wbdr (g, shingle, 2-story) Central Wood wbdr (g, tile, 2-story) sec gust wind speeds 3 Figure 4-14 Weak wood structure vulnerabilities in Central wind borne debris region 96

114 Wood North Vulnerabilities 1.00E E-01 Damage ratios 8.00E E E E E-01 North Frame wbdr North Wood wbdr (g,shingle, nsh) North Wood wbdr (g,shingle,wsh) North Wood wbdr (g, tile, nsh) North Wood wbdr (g, tile, wsh) North Wood wbdr (g, shingle, 2-story) North Wood wbdr (g, tile, 2-story) 3.00E E E E sec gust wind speeds 3 Figure 4-15 Weak wood structure vulnerabilities in the North wind borne debris region Masonry South Vulnerabilities 100% South Masonry HVZ 80% South Masonry hvhz (g,shingle, nsh) South Masonry hvhz (g,shingle,wsh) Damage Ratios 60% 40% South Masonry hvhz (g, tile, nsh) South Masonry hvhz (g, tile, wsh) 20% 0% % sec gust wind speeds 3 Figure 4-16 Weak masonry structure vulnerabilities in the South high velocity hurricane zone 97

115 Masonry Central Vulnerabilities Damage Ratios Central Masonry wbd Central Masonry wbdr (g,shingle, nsh) Central Masonry wbdr (g,shingle,wsh) Central Masonry wbdr (g, tile, nsh) Central Masonry wbdr (g, tile, wsh) sec gust wind speeds 3 Figure 4-17 Weak masonry structure vulnerabilities in Central wind borne debris region 98

116 Masonry North Vulnerabilities 100% 90% 80% 70% North Masonry wbdr North Masonry wbdr (g,shingle, nsh) North Masonry wbdr (g,shingle,wsh) North Masonry wbdr (g, tile, nsh) North Masonry wbdr (g, tile, wsh) Damage Ratios 60% 50% 40% 30% 20% 10% 0% sec gust wind speeds 3 Figure 4-18 Weak masonry structure vulnerabilities in North wind borne debris region Manufactured Homes Building Matrices There are four Monte Carlo models for manufactured homes: pre-1994 tied down, pre-1994 not tied down, post-1994 zone 2, and post-1994 zone 3. Variables such as construction materials and building code requirements were not considered for manufactured homes. Therefore, for each Monte Carlo model output, only one vulnerability matrix is created. The vulnerability matrices for manufactured homes are of the same form as for site-built homes. From these matrices, vulnerability and fragility curves can also be computed. These curves for each modeled manufactured home type are shown in Figure 5-19 through Figure

117 1 0.8 Building Vulnerbility, Manufactured Homes Single Wide, Pre-HUD, No Tie-Downs, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Building Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Vulnerability and fragility of pre-1994, not tied-down, manufactured homes Building Vulnerbility, Manufactured Homes Single Wide, Pre-HUD, Tie-Downs, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Building Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Vulnerability and fragility of pre-1994, tied-down, manufactured homes 100

118 1 0.8 Building Vulnerbility, Manufactured Homes Single Wide, Post-HUD II, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Building Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Vulnerability and fragility of post-1994, zone 2, manufactured homes Building Vulnerbility, Manufactured Homes Single Wide, Post-HUD III, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Building Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Vulnerability and fragility of post-1994, zone 3, manufactured homes 101

119 Contents and ALE Matrices Again for manufactured homes the contents and ALE losses are based entirely on the physical damage to the interior projected from the Monte Carlo model simulations, so for each model simulation only one prediction of contents damage and ALE is made. These predictions are again organized in two different types of matrices. The type 1 matrices express the conditional probability of contents damage and ALE for different wind speeds while the type 2 matrices express the conditional probability of contents damage and ALE for different levels of structural damage Type 1 The type 1 contents and ALE vulnerability and fragility curves for each home type are shown in Figure 5-23 through Figure Contents Vulnerbility, Manufactured Homes Single Wide, Pre-HUD, No Tie-Downs, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Contents Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Contents vulnerability and fragility: pre-1994, not tied-down, manufactured 102

120 1 0.8 Contents Vulnerbility, Manufactured Homes Single Wide, Pre-HUD, Tie-Downs, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Contents Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Contents vulnerability and fragility: pre-1994, tied-down, manufactured Contents Vulnerbility, Manufactured Homes Single Wide, Post-HUD II, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Contents Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Contents vulnerability and fragility: post-1994, zone 2, manufactured 103

121 1 0.8 Contents Vulnerbility, Manufactured Homes Single Wide, Post-HUD III, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 Contents Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure Contents vulnerability and fragility: post-1994, zone 3, manufactured ALE Vulnerbility, Manufactured Homes Single Wide, Pre-HUD, No Tie-Downs, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 ALE Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure ALE vulnerability and fragility: pre-1994, not tied-down, manufactured 104

122 1 0.8 ALE Vulnerbility, Manufactured Homes Single Wide, Pre-HUD, Tie-Downs, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 ALE Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure ALE vulnerability and fragility: pre-1994, tied-down, manufactured ALE Vulnerbility, Manufactured Homes Single Wide, Post-HUD II, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 ALE Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure ALE vulnerability and fragility: post-1994, zone 2, manufactured 105

123 1 0.8 ALE Vulnerbility, Manufactured Homes Single Wide, Post-HUD III, Bmax=1.65 Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat. 5 Damage Ratio Windspeed (mph) 3-second peak gusts Probability [Ds>=ds v] Damage State 1 Damage State 2 Damage State 3 Damage State 4 ALE Fragility Cat. 1 Cat. 2 Cat. 3 Cat. 4 Cat Windspeed (mph) 3-second peak gusts Figure ALE vulnerability and fragility: post-1994, zone 3, manufactured It can be seen in many of these contents and ALE plots for manufactured homes that the vulnerability curve flattens out at some point (around 80% for contents and near 60% for ALE). This is because, as discussed earlier, these vulnerability curves only represent the average expected loss at each wind speed. On average even if the structure is a total loss it would be expected that some of the contents remain unharmed, were moved to a safer place prior to the storm, or that the contents of the home are over insured, and that 100% of the additional living expenses allocated by insurance would not be claimed. This is evident when looking at a plot of contents or ALE claims vs. building claims derived from insurance data, the mean value of contents losses or ALE never reaches 100%, even at 100% structural loss. The distribution of losses is possibly more important than just the mean value of the losses in these cases. Validation of these curves with damage surveys and claims data, along with comparisons of the modeled and claims distributions will be presented in Chapter Type 2 Examples of the type 2 contents and ALE vulnerability curves are shown in Figure 5-31 through Figure

124 Figure Type 2 contents vulnerability curve for manufactured homes Figure Type 2 ALE vulnerability curve for manufactured homes 107

125 Appurtenant Structure Matrix The same appurtenant structure matrix used for site-built homes is used for manufactured homes. There is no data to support either increasing or decreasing appurtenant structure losses for manufactured homes. From observations of hurricane damage following the Florida hurricanes of 2004 it appeared that screened porches, lanais, and carports of manufactured homes are extremely susceptible to wind damage, however, these structures may not exactly fit the textbook definition of an appurtenant structure since most are at least partially attached to the structure. 4.2 Weighted Vulnerability Matrices Standard or Strong Site-Built Homes Building Matrices Building vulnerability matrices have been created for every combination of region (South, Central, and North), construction type (masonry or wood), roof type (gable or hip), roof cover (tile or shingle), shutters (with or without), and sub-region (none, windborne debris region, and high velocity zone). As was presented in the previous section there are substantial differences in the vulnerability of each of these home types. However, keep in mind the goal here is to be able to analyze an insurance portfolio and make the best possible insured loss prediction for each policy based upon the information that is provided in the portfolio file. The information provided may vary from company to company. But in general, there is little information available in a portfolio file regarding the structural characteristics and the wind resistance of the insured property. Instead, traditionally, insurance companies have relied on the so-called ISO classification, which is primarily used to define the fire resistance of a home. In addition to the ISO classification, portfolio files will have information on zip code, policy limits, and year built. Currently, the year built is not being utilized to assist in damage predictions. This is because any adjustments to the vulnerability of a home based on the year built at this point would be completely arbitrary. For our purposes we can use the ISO classification to determine if the home is constructed of masonry, timber, or other. The zip code is used to define the region and sub region. And the policy limits are multiplied by the damage ratios to determine the actual dollar losses for each home. These topics will be discussed in more detail in Chapter 7 on model integration. So from the insurance files we can easily determine the region, sub region, and construction type. However this leaves the roof type, roof cover, and shutter options still undefined. But we know from the exposure study the distribution of different roof types, and to some extent roof cover per region. And some estimation of the percentage 108

126 of homes with and without shutters in each sub region can be made. So based on these statistics and estimations we can define a general matrix for each construction type in each region and sub region. Most of the statistics used for this procedure were given in Chapter 3. From the exposure statistics and the different ISO classifications it was decided to distinguish three different structural types: masonry, timber, and other. The ISO classifications that correspond to each of these categories are given in Appendix E. The matrices are weighted based on the statistics presented in Chapter 3, where the masonry homes consist of a weighted average of just the concrete block home types, the timber homes consist of a weighted average of the timber home types including all 2-story types (the data indicates that population of 2-story homes is either wood both stories or concrete first story and wood second story, so to simplify all are considered part of the wood home population), and other consists of a weighted average of all known types. Unknown types are disregarded and assumed to have the same distribution as the known types. Some data was given in the exposure study regarding the roof cover distribution. However there is not enough data to make a conclusive statement about the distribution in each region. From the data that was provided and based on engineering judgment it is assumed that throughout the state 85% of the homes have shingle roof and 15% have tile. These percentages could be adjusted in the future to take into account regional differences. For example, there might be a higher percentage of tile roofs in south east Florida. As was discussed in Chapter 3 homes that have metal or other roof cover types can be considered to have the same vulnerability as tile since the replacement costs are similar. No reliable statistical data was available on the percentage of homes in each region with or without shutters, or more generally opening protection. This is something that could vary greatly between communities, regions, with the age of the home, and with proximity to the coast. It is almost impossible to know how many people have pre-cut plywood or intend to take some other measure for protecting the openings of their homes in the event of a hurricane. Some people may feel that it is not necessary to board up their homes for a category 1 or 2 storm; however if a major hurricane is forecast nearly everyone threatened may take this precaution. Another consideration that may have been overlooked prior to the hurricane season of 2004 is fatigue. Only a week or two after taking down the plywood put up in preparation for Hurricane Frances many people in east central FL did not bother putting it back up for Jeanne. Just to add one more complication, it is not always possible to know the effectiveness of the opening protection used. Some people may put up plywood or sheet metal but if it is not fastened properly it may not serve its intended purpose. Also, tests have shown that thin plywood may be ineffective in stopping the impact of flying debris at extreme wind speeds. Clearly, with all of this said there is no way to exactly pinpoint the percentage of 109

127 homes in a given zip code that will have opening protection in place prior to a storm. For modeling purposes it is probably best to just keep things simple. So it was estimated from experience and judgment that in the high velocity zone of South FL 40% of the homes have opening protection, 25% do in all of the windborne debris regions, and 5% everywhere else (inland regions). The general matrices are simply the sum of the model matrices weighted based on their statistical distribution. So for example, if we know that a home is masonry construction and is in the windborne debris region of central FL, we also know that 66% of the masonry homes in central FL have gable roofs and 34% have hip roofs, around 85% have shingle cover and 15% tile, and 25% have shutters while 75% don t. So weight factors can be computed for each model matrix based on these statistics. For example, the Central FL, gable, tile, no shutters, masonry matrix would have a weight factor of 66% (masonry percent gable) x 15% (percent tile) x 75% (percent without shutters) = 7.4%, this is the percentage of that home type that would be expected in this region. Each model matrix is multiplied by its weight factor, and the results are summed. The final result is a matrix that is a combination of all the model matrices and can be applied to an insurance policy from knowing only the zip code and ISO classification. A total of 30 weighted building matrices are created, but again because the high velocity hurricane zone does not exist in central and north FL 6 of these can be disregarded, giving a total of 24. These matrices are listed in Table 5-4. A summary of the weight process for residential homes is given in the use case in Appendix F

128 Table List of different weighted matrices created Region Construction Type Sub-region 1 South Concrete none 2 South Concrete WBDR 3 South Concrete HVHZ 4 South Wood none 5 South Wood WBDR 6 South Wood HVHZ 7 South Other none 8 South Other WBDR 9 South Other HVHZ 10 Central Concrete none 11 Central Concrete WBDR 12 Central Concrete HVHZ* 13 Central Wood none 14 Central Wood WBDR 15 Central Wood HVHZ* 16 Central Other none 17 Central Other WBDR 18 Central Other HVHZ* 19 North Concrete none 20 North Concrete WBDR 21 North Concrete HVHZ* 22 North Wood none 23 North Wood WBDR 24 North Wood HVHZ* 25 North Other none 26 North Other WBDR 27 North Other HVHZ* 28 Keys Concrete none 29 Keys Wood none 30 Keys Other none * High Velocity Hurricane Zone does not exist in central or north Florida Vulnerability and fragility plots can be produced in the same way as for the model matrices as shown in Figure All of the weighted plots are given in Appendix C. The plots developed from these weighted matrices allow for direct comparisons with available claims data, whereas comparisons with the model matrices are not completely valid because there is not sufficient information in the claims data to classify each 111

129 policy into one of the many models. The validation methods will be discussed in much more detail in Chapter 6. Figure Weighted building vulnerability and fragility curves Contents and ALE Matrices Type 1 The contents and ALE matrices are weighted using the same methods applied to the building matrices. However, because the type 1 model contents and ALE matrices are not dependant upon as many factors the process is a bit simpler. The roof cover type is irrelevant and the only consideration that the sub region adds is the percentage with and without shutters. Examples of the type 1 contents and ALE weighted vulnerability and fragility curves are shown in Figure 4-34 and Figure 4-35 respectively. The same 30 weighted matrices listed in Table 5-4 are created for both contents and ALE. 112

130 Figure Weighted type 1 contents vulnerability and fragility curves Figure Weighted type 1 ALE vulnerability and fragility curves 113

131 Type 2 Since the type 2 contents and ALE matrices vary depending upon the same factors as the building matrices the same exact weight factors can be applied and the same list of weighted matrices given in Table 5-4 is obtained. Figure 4-36 and Figure 4-37 illustrate examples of weighted type 2 contents and ALE matrices. Figure Weighted type 2 contents vulnerability curve 114

132 Figure Weighted type 2 ALE vulnerability curve Appurtenant Structure Matrix Because the appurtenant structure matrix is independent of construction type no weight factors need to be applied to it. Once the matrix is created it can be directly applied to the insurance policies in the portfolio files Weak and Medium Site-Built Homes The vulnerability matrices for the weak and medium models were also averaged as explained in the previous section. The weighs or percentages of distribution of shingle vs. gable, shuttered vs. non shuttered, etc, were assumed to be the same for weak, medium, and strong structures. The average or weighed vulnerabilities are shown with a thick line in each Figures 5-13 to Weak, Medium, and Strong Model Distributions Residential construction methods have evolved in Florida as experience with severe winds drives the need to reduce vulnerability. Consequently, over time, engineers and builders learn more about the interaction between wind and structures, more stringent building codes are enacted, and if properly enforced, result in stronger structures. The weak model, medium strength model, and standard (strong) strength model, developed by the vulnerability team, represent this evolution in time of relative quality of construction in Florida. Each set of models is representative of the prevalent wind 115

133 vulnerability of buildings for a certain historical period in time. It is therefore important to define the cut-off date between the different periods, since the overall aggregate losses in any region are determined as a mixture of homes of various strengths (ages). The initial approach was to consult the building codes of various ages to determine appropriate eras for the weak, medium and strong models. However, it was strongly suggested by several code experts that this approach is not sufficient. The issue of code enforcement has also evolved over time, and it is relatively recent that the State of Florida took an active role in uniform enforcement. Thus a given county may have built to standards that were worse than or exceeded the code in place at the time. Charley Everly of Code Technology Inc. was consulted for guidance. He has been practicing in Florida since 1983, and has a reputation as an expert on code development and enforcement. His view is that the load provisions have been sufficient since the 1970 s, and the issue is not the code, but rather enforcement of the code. His opinion reinforces the above comments regarding enforcement as a function of local builder/community standards. His observations are generalized and summarized below. Southern construction practice recognized the importance of truss to wall connection as early as the 1950 s, when it became common to use clips rather than toe nails. The clips were not as strong as modern straps, but an improvement over nails only. Northern construction suffered from the lack of impact from severe hurricanes over a long period. This sense of safety was compounded by a more localized approach to decision making (old-boy s network). Thus northern construction is expected to be weaker than southern in general. The use of clips became relatively standard state-wide by the mid 1980 s, while they were well used in the south prior to this. The use of rated shingles and resistant garage doors became common after Andrew. Therefore, the classification shown in Table 5-5 was adopted for dividing the regions by age and model. 116

134 Table 5-5 Age classification of the models per region Prior 1970 to 1970 to to present South Keys and ½ weak, ½ medium Medium Medium Standard Central Weak Weak Medium Standard North Weak Weak Medium Standard However, the year-built or year of last upgrade of a structure in a portfolio might not be available, when performing a portfolio analysis to estimate hurricane losses, in a certain region. In that case, it becomes necessary to assume a certain distribution of ages in the region, in order to come up with an average vulnerability between weak, medium, and strong, and estimate the resulting overall damage to a given county (or zip code). That is, a reasonable distribution of weak, medium and strong construction in, for example, Dade County, will be based on the age make-up of the building stock in that county. Although the engineering team did not have detailed information on the building population of every county in Florida, they did have a set of 17 tax appraiser databases. Nine of these databases for Brevard, Hillsborough, Pinellas, Escambia, Leon, Walton, Broward, Palm Beach, and Monroe counties are described in detail in Volume I of the Engineering Report. Eight additional databases that were not available for the original exposure study were acquired as a result of post damage surveys after the 2004 hurricane season, and thus enhance the engineering team ability to properly weigh old and new construction. They correspond to Charlotte, Desoto, Lee, Martin, Orange, Polk, Santa Rosa, and Ste Lucie counties. The databases includes an effective year of construction, and thus provides guidance as to how to weigh the combined weak, medium and strong model results when yearbuilt information is not available in the portfolio file. In each region, the corresponding counties were combined to provide the age statistics. They are listed in Table 5-6. These statistics were used to weigh the average of weak, medium, and strong vulnerabilities in each region. The results are shown in Figures 5-38 to 5-41, for the high velocity hurricane zone in the South, and the wind borne debris region in the North. The different vulnerability curves are shown for the weak, medium, and strong models, superimposed with the age weighted vulnerability curve. 117

135 Table 5-6: Year-built statistics for the different regions. South Average Number of Units Valid EFFYR Date Range Number of Units Percent % % % Prior % Invalid Units % Central Average Number of Units Valid EFFYR Date Range Number of Units Percent % % % 118

136 Prior % Invalid Units % North Number of Units Valid EFFYR Date Range Number of Units Percent % % % Prior % Invalid Units % Keys Number of Units Valid EFFYR Date Range Number of Units Percent % 119

137 % % Prior % Invalid Units % Masonry South Vulnerabilities 100% 90% 80% 70% 60% South Masonry HVZ age weighted South Masonry HVZ strong (post 1994) South Masonry HVZ medium (1970 to 1993) South Masonry HVZ pre-1970 South Masonry HVZ weak Damage Ratios 50% 40% 30% 20% 10% 0% % sec gust wind speeds 3 Figure 4-38 Weighted masonry structure vulnerabilities in the South high velocity hurricane zone 120

138 Wood South Vulnerabilities 100% 90% 80% South Frame HVZ age weighted South Frame HVZ strong (post 1994) South Frame HVZ medium (1970 to 1993) South Frame HVZ pre-1970 South Frame HVZ weak 70% Damage ratios 60% 50% 40% 30% 20% 10% 0% sec gust wind speeds 3 Figure 4-39 Weighted timber structure vulnerabilities in the South high velocity hurricane zone Masonry North Vulnerabilities 100% 90% 80% North Masonry wbdr age weighted North Masonry wbdr strong (post 1994) North Masonry wbdr medium (1984 to 1993) North Masonry wbdr weak (pre 1984) 70% Damage Ratios 60% 50% 40% 30% 20% 10% 0% sec gust wind speeds 3 Figure 4-40 Weighted Masonry structure vulnerabilities in the North wind borne debris region 121

139 Wood North Vulnerabilities 100% 90% 80% 70% North Frame else (age weighted) North Frame wbdr (age weighted) North Frame wbdr strong (post 1994) North Frame wbdr medium (1984 to 1993) North Frame wbdr weak (pre 1984) Damage ratios 60% 50% 40% 30% 20% 10% 0% sec gust wind speeds 3 Figure 4-41 Weighted timber structure vulnerabilities in the North wind borne debris region Manufactured Homes As discussed in Chapter 3, the FHCF provides statistics on the distribution of manufactured home types in the state of Florida. The classification includes statistics for fully tied down pre and post 1994 homes, partially tied down homes, not tied down homes, and unknown types. Also, when analyzing an insurance portfolio file some information is provided that can be used for classifying the home type. This includes the zip code and year built. The zip code can be used to classify the region of HUD wind zone while the year built can be used to determine if the home was constructed before or after If from the portfolio file it is known that a home was constructed prior to 1994 and the zip code tells what region it is in, using the FHCF exposure statistics the probability that the home will either be fully, partially, or not tied down can be determined. So using the FHCF statistics for each region the pre-1994 not tied down and pre fully tied-down matrices are weighted based on their probability of occurring. These statistics are given in Chapter 3. The partially tied down homes are assumed to have the vulnerability that is weighted average of 75% not tied down homes and 25% fully tied down homes. The same weight factors apply to the contents and ALE matrices. There is no need to weight the post 1994 zone 2 and 3 matrices because if the year built 122

140 is after 1994 and the zip code is known it can easily be determined if the zone 2 or zone 3 matrix should be used and these home types are directly modeled. The same weight factors are applied both the type 1 and type 2 contents and ALE matrices. The resulting vulnerability type 1 curves are shown in Figure Manufactured homes vulnerability curves. A summary of the weight process for manufactured homes is given in the use case in Appendix F.11. Manufactured Homes Vulnerabilities 100% 90% 80% 70% Pre-94NoTD Pre-94TD South pre94 Post94 III Post94 II Damage Ratios 60% 50% 40% 30% 20% 10% 0% sec gust wind speeds 3 Figure Manufactured homes vulnerability curves 4.3 Summary The results of the vulnerability model are the vulnerability matrices. The model matrices are developed specifically for one type of home while the weighted matrices are developed to statistically represent an entire population of homes of in a specific area. Type 1 contents and ALE matrices express the probability of these damages as a function of wind speed while the type 2 matrices express the probability of damage as a function of structural damage. Vulnerability and fragility curves can be created for all matrices. The model matrices can be used for future mitigation studies, while the weighted matrices are used for insured loss computations and model validation as discussed in the next chapter. 123

141 Chapter 5 Model Validation Validation of the vulnerability model results presents a very difficult task. The major problem is lack of good reliable data, however the most was made out of what was available. The most solid validation of the model results comes from comparisons with claims data from recent Florida hurricanes, and in particular Hurricane Andrew. Additionally, site surveys from Hurricanes Charley, Frances, and Jeanne provide observational validation and prove that the results and assumptions of the model are within the realm of reality. Complications arise when trying to make comparisons with other model (HAZUS) results, as will be discussed. 5.1 Claims Data Processing At the request of the FDFS, four insurance companies provided insurance claims data for several recent hurricanes. The companies provided two types of files: Sample files with 10% of the exposure selected at random, plus the claims on this 10% exposure, since Hurricane files with premium files for all hurricane claims since 1996, plus all the corresponding claim data since 1996 One of the four companies is a smaller company, and it provided all the exposure and all the claim data, but only for coastal counties. Finally, one of the companies also provided the claim and corresponding premium data for hurricane Andrew. Because of a confidentiality agreement these companies will remain anonymous (they will be referred to as company A, B, C, and D). They represent between 75 and 85% of the insured exposure in the State, and probably around 70% of the claims. Most of the data provided comes only from minor hurricanes and tropical storms that impacted Florida between 1994 and Because of the size of these files the processing of this data was assigned to the computer science team at FIU. First, the files were cleaned up from inconsistencies, duplicate records, outliers, etc. In particular, all policies with building coverage less than $50,000 were eliminated, as 124

142 well as policies with zero contents, appurtenant structure, or ALE coverage. instructions given to the team were then as follows: The 1. Regroup the data in the files according to the structural classification (Appendix F). i.e. all the records corresponding to frames and masonry veneer should be lumped together as "timber"; the records corresponding to Jointed Masonry, Reinforced Masonry, heavy timber joisted masonry, and semi-wind resistive should be lumped together as "masonry". The rest should be classified as "others". 2. For both timber and masonry structures plot contents, appurtenant structure, and additional living expenses loss ratios versus structural loss ratios for each hurricane that we have claims data for, for each insurance company. In all cases compute the structural damage as structural loss plus deductible. The ratios should be computed as structural damage /insured limit. 3. Repeat 2 across all the insurance companies; step 2 asks for the loss ratios from each insurance company to be plotted individually. For this step combine the data for each hurricane from all insurance companies and repeat the same plots requested in step For hurricanes Opal we have actual wind speed data per zip code, which Dr. Powell provided. Plot structural, contents, appurtenant, and additional living expenses versus wind speed for masonry, timber and "others". You will need to aggregate first the losses per zip code in each of the categories (contents, structures, AS, ALE); identify the zip codes with the same wind speeds; aggregate the losses for the zip codes with same wind speeds; divide by the aggregate insured value in the corresponding zip codes, and then plot the loss ratios vs. wind speed. That supposes that we have all the insured value from a particular company in each of the zip codes (regardless of whether or not the property was damaged). 5. Repeat 4 for the aggregate of structures + contents + AS + ALE 6. Plot the claim ratio (ratio of number of claims/total number of policies) versus wind speed. Tasks 2 and 3 above were performed on the hurricane files, while tasks 4 to 6 were performed on the sample files. Therefore, the results for tasks 4 to 6, will be representative of the actual situation only if the sample files were truly randomly sampled (we do not have any means to check that, other than to accept the good faith of the insurance companies), and if the combined insurance companies for which we have data represent the vast majority of the Florida exposure. It is noted that they represent between 75 and 85% of the insured exposure, and probably around 70% of the claims. 125

143 Table 5-1 gives a description of the data provided by each company (note: Ca and Cb are the same company but data was provided by two separate divisions of the company). The table details the number of claims provided by each insurance company resulting from each hurricane. Table 5-1- Summary of processed claims data (number of claims provided) Company A Hurricane Andrew Hurricane Georges Hurricane Opal Tropical Storm Irene Tropical Storm Earl Hurricane Erin Concrete Timber Manufactured Company B Concrete Timber Manufactured Company Ca Concrete Timber Company Cb Concrete Timber Company D Concrete Timber Note: Only building, contents, and appurtenant structure claims were provided by company A (ALE was not provided), all other companies provided data for all four coverage types. In general the processing results yielded very sparse data with mostly only small claims recorded. For example, Figure 5-1 through Figure 5-3 depict contents, ALE, and appurtenant structure losses plotted against structure losses from Hurricane George from company B. Although there is a good amount of data the vast majority of it is at the lower end of building damage (0-30%). At this time this data is not being utilized for any statistical comparisons with the model results, however observational comparisons can be made, and this data is available for future use. The most significant data was provided by company A in particular from Hurricane Andrew. As shown in Figure 5-4 this data covers the complete range of structural and contents losses. Wind speed measurements are also available so validation efforts were primarily concentrated on 126

144 use of this data. Attempts were made to make use of additional data from Hurricane Opal and other storms; however for the most part the amount of processed data available is too small to be statistically significant for validation. Other significant data also includes claims from Hurricane Erin provided by company A. Again this was a smaller storm so the majority of the claims are at the low end of damage, also observed wind speed data was not available until recently. Because of these reasons this data is not currently being utilized, however again it is available for future use. All plots produced that contain a substantial amount of data are given in Appendix G. Company B - Hurricane Georges Contents vs. Structural Loss 100% 90% 80% 70% Contents Loss 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Structural Loss Figure Company B, Hurricane Georges contents losses 127

145 Company B - Hurricane George Appurtenant Loss Ratio vs. Structural Loss Ratio 100% 90% (Appurtenant loss)/(appurtenant Coverage) 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building loss+deductible)/(building Coverage) Figure Company B, Hurricane Georges appurtenant losses Company B - Hurricane Georges ALE Loss Ratio vs. Structural Loss Ratio 100% 90% 80% (ALE loss)/(ale Coverage) 70% 60% 50% 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% 120% (Building loss+deductible)/(building Coverage) Figure Company B, Hurricane Georges additional living expense claims 128

146 Figure Company A, Hurricane Andrew contents losses Hurricane Andrew Hurricane Andrew was a category five hurricane (at the time of landfall it was classified as a category 4 storm however after extensive research in 2002 it was reclassified as a category 5) with widespread catastrophic damage at and near where it made landfall in the southern part of the state in August of This Andrew data provided by company A is one of the primary means by which to validate and calibrate the model. 129

147 Figure 5-5- Satellite image of Hurricane Andrew making landfall (NOAA) Figure The destruction left behind, Naranja Lakes (NOAA) 130

148 Hurricane Andrew was the costliest natural disaster ever in the history of the United States. It therefore makes a perfect event by which to calibrate and validate the results of this model. The insured limits, claim values, ISO classifications, and zip codes of 80,239 insured policies that filed claims following the storm were obtained. It is important to note that the complete insured exposure in the area affected by Andrew was not provided, only the insured policies that filed claims. This is important because when the claims data is compared with the model results there could be a significant number of homes that suffered zero losses, especially at lower wind speeds, that are unaccounted for simply because this data is not available. However, in the zip codes with recorded hurricane wind speeds, in could be argued that most building suffered some kind of damage, albeit minor, and that therefore most of the exposure is accounted for. Of the policies available, 56,732 are within zip codes that we have wind speed data for. Of the 56,732, 55,986 are masonry while 746 are frame construction. An additional 932 manufactured home claims were available in zip codes with known wind speeds. Wind speed data from hurricane Andrew was obtained from two sources: Dr. Mark Powell from the hurricane research division at NOAA, and a master s thesis by Bhinderwala [3]. Actually, Bhinderwala also obtained his wind speed data from Dr. Powell but converted it to gradient wind speeds or flight level wind speeds. Note: in Bhinderwala s thesis these terms are used interchangeably, suggesting they mean the same thing. According to Dr. Powell, the correct term is flight-level wind since it was measured by aircraft and was way to high in altitude to be even close to a computed (free atmosphere) gradient wind (for which you would need a radial profile of the surface pressure). Dr. Powell s data is in the form of 3-second gusts at a 10-meter elevation in open terrain (converted from flight level winds), which is the datum used by the vulnerability model. However, Bhinderwala provided wind speed data for the centroid of 71 different zip codes while Dr. Powell provided it for only 36. It is not known why Bhinderwala has more data than Dr. Powell, though it s thought that the wind speeds in these other zip codes may have been extrapolated from wind speeds in known zip codes. So for Dr. Powell s 36 zip codes his data was used and for the additional 35 (71-36) zip codes Bhinderwala s data was converted back to 3-second gust speeds at a 10-meter elevation in open terrain. This was done by taking the average ratio of the wind speeds provided by Dr. Powell and the wind speeds provided by Bhinderwala in the corresponding zip codes and the multiplying this ratio by the wind speeds given by Bhinderwala in the remaining zip codes, as approved by Dr. Powell. All open terrain wind speed data is given in Table

149 Zip Code Table Hurricane Andrew open terrain wind speeds per zip code 10-m, 3- second Gusts (mph) Zip Code 10-m, 3- second Gusts (mph) Zip Code 10-m, 3- second Gusts (mph) Note that the wind speeds given in Table 5-2 are open terrain wind speeds. However, the terrain where Hurricane Andrew made landfall for the most part can not be considered open, and therefore the open terrain wind speed should not be used for comparison with claims data. Instead these wind speeds should be reduced to account for the roughness of the terrain to more accurately reflect the actual wind speeds acting on the structures which were damaged. To do this a factor of 0.87 is multiplied by the wind speeds listed in Table 5-2. This factor is obtained as described in Appendix F. So knowing the corrected wind speed at each zip code and the zip code in which each claim occurred the wind speeds that resulted in claims of nearly 60,000 insurance 132

150 policies can be determined by simply matching the zip codes. Numerous comparisons of this data with the results of the vulnerability model can be made. The claims data used for these comparisons are the result of processing step 2 described earlier, however adjustments were made to the insured limits of contents as described in the Section 4.5 describing contents loss prediction (based on a value of contents equal to 50% of the structure value). Unfortunately, ALE claims data was only provided for the manufactured home claims of hurricane Andrew. Also, the appurtenant structure data that was provided only for site-built homes seemed suspicious (of nearly 80,000 policies there was only around 200 appurtenant structure claims, which seems extraordinarily low. It may be possible that appurtenant claims were combined with structural claims or these claims were treated differently but any assumptions made would be highly speculative.). The damage ratios of both structures and contents were then plotted against the known wind speeds and a second-degree polynomial trend line was fit to the data. The vulnerability curve calculated by the model was then plotted over the claims data. This process was repeated for masonry, timber, and manufactured homes. These plots are shown in Figure 5-7 through Figure Figure Masonry structural claims from Hurricane Andrew and model results (note: the curve fit starts at 95 mph rather than zero because it is a parabolic curve and a point of inflection occurs prior to 95 mph) 133

151 Figure Masonry contents claims from Hurricane Andrew and model results Figure Masonry contents vs. structural claims, Andrew data and model results 134

152 Figure Timber structural claims from Hurricane Andrew and model results Figure Timber contents claims from Hurricane Andrew and model results 135

153 Figure Manufactured home claims from Hurricane Andrew and model results Figure Manufactured home contents claims from Hurricane Andrew and model results 136

154 Figure Manufactured home ALE claims from Hurricane Andrew and model results Figure Manufactured home ALE claims from Hurricane Andrew and type 2 model results 137

155 A few things should be noted. The original calibration of this model was conducted based on the open terrain wind speeds without using any correction for the roughness of the terrain. With these comparisons very good agreement was achieved between the model results and the claims data. However, because the open terrain wind speeds may not be the actual wind speeds that caused the damage these comparisons could be considered invalid. So rather than have good agreement with a possibly invalid comparison the decision was made to adjust the wind speeds for the roughness of the terrain, which caused a significant shift in the claims trend line. The model will be recalibrated based on these comparisons. As was mentioned earlier the trend line is an average value of only the policies that filed claims following the hurricane. Therefore, the policies that did not file claims are not included in the comparison. If these policies were included it may slightly reduce the value of the trend line especially at lower wind speeds, which maybe good in some cases where compared with the current line we are under predicting losses at low wind speeds. Also to note, there is not enough insurance data to draw any major conclusions regarding the model results of wood or manufactured homes. It appears that the model curve and the trend line for wood homes are slightly off, but if a greater amount of data where available this relationship may look different. The manufactured home loss predictions seem slightly higher than the claims data would indicate however; if more data were available again this may look different. At any rate, if the fit of any these curves are thought to be unsatisfactory improvement can be made by simply adjusting some of the calibration parameters (k values or interior loss equations). Because of the small amount of data provided for wood and manufactured homes an exact fit with the claims data may not be desired. In addition, using a different type of trend line (3- degree polynomial, exponential, logarithmic, moving average, etc.) may improve these comparisons. To provide an even more detailed comparisons of the model results versus the claims data, the probability distribution functions of building and contents damage for each construction type at each wind speed interval were examined, as well as the probability distribution functions of contents and ALE at each building damage interval. Each claim s data point is attributed in the distribution plot to the nearest corresponding wind speed or damage level. For example, if the wind speed for the claim data point was 122 mph, it is added to the 120 mph slot in the histogram, or if the structural damage was 51%, it is added to the 50% slot in the histogram. These plots for masonry homes are shown in Figure 5-32, circles represent the model results while plus signs represent the claims data points. These same plots were also derived for wood and manufactured homes, however because of the lack of data valid comparisons cannot be made. 138

156 Figure Masonry structural damage probability distribution plot, mph Figure Masonry structural damage probability distribution plot, mph 139

157 Figure Masonry structural damage probability distribution plot, mph Figure Masonry structural damage probability distribution plot, mph 140

158 Figure Masonry structural damage probability distribution plot, mph Figure Masonry contents damage probability distribution plot, mph 141

159 Figure Masonry contents damage probability distribution plot, mph Figure Masonry contents damage probability distribution plot, mph 142

160 Figure Masonry contents damage probability distribution plot, mph Figure Masonry contents damage probability distribution plot, 0-5% building loss 143

161 Figure Masonry contents damage probability distribution plot, 7-13% building loss Figure Masonry contents damage probability distribution plot, 15-22% building loss 144

162 Figure Masonry contents damage probability distribution plot, 26-38% building loss Figure Masonry contents damage probability distribution plot, 42-54% building loss 145

163 Figure Masonry contents damage probability distribution plot, 58-70% building loss Figure Masonry contents damage probability distribution plot, 74-86% building loss 146

164 Figure Masonry contents damage probability distribution plot, % building loss Again these distribution plots were thrown off by the roughness correction factor and recalibration to improve the comparisons will be conducted. However, in some cases the distribution still agrees with the claims data fairly well. As stated earlier a much more in depth statistical analysis of this data could be performed to improve the fit of these distributions. At lower wind speeds there is still the question of effect of the policies that did not file claims, and this is thought to be a difference between the model curve and the claims curve at these speeds. However, these plots do indicate that we may not be modeling a wide enough distribution of damage at moderate wind speeds ( mph). Adjustments to the distribution parameters used in the cost estimation model alone cannot compensate for these differences. Some changes must also be made to the Monte Carlo simulation model. This information provides a good tool for analysis of the model results. The data can be used for model calibration and even possibly emergency planning. As data becomes available from more recent storms these same analysis methods can be used. 147

165 5.1.2 Hurricane Opal Figure Hurricane Opal making landfall in the Florida Panhandle (NOAA) Hurricane Opal was a category 3 storm with sustained winds of 125 mph (according to the National Hurricane Center) when it made landfall in the western portion of the Florida panhandle near Pensacola Beach. The damage caused by this storm was nowhere near the devastation seen in south Florida following Hurricane Andrew. However, damage resulting from Opal did total nearly $3 Billion. Unlike Andrew, the majority of the destruction from Opal was attributed to the foot storm surge rather than the wind. 148

166 Figure Storm surge damage caused by Hurricane Opal Some limited claims data was provided for Hurricane Opal. Actual wind speed data for this storm was also obtained from Dr. Mark Powell. This data is given in Table 5-3 and is the peak wind gust at a 10 meter elevation in open terrain. Again to account for the roughness of the terrain when comparing against the claims data a factor of 0.87 is multiplied by the open terrain wind speeds listed in Table 5-3, again choice of this factor is explained in Appendix F. In the zip codes for which wind speed data is available there are a total of 10,813 claims. 8,943 of these claims are timber structures while 1,870 of them are masonry. The same types of plots and analysis performed on the Andrew data were also applied here. Figure 5-35 through Figure 5-37 are plots of the claims data compared with the model vulnerability curves. Figure 5-38 through Figure 5-40 give the distribution of the claims data and the distribution of the modeled damages. 149

167 City Table Hurricane Opal open terrain wind speeds per zip code Zip Code 10-m, 3- second Gusts (mph) City Zip Code 10-m, 3- second Gusts (mph) Fort Walton Beach Milton Destin Pensacola Santa Rosa Beach Milton Fort Walton Beach Panama City Destin Chipley Holt Lynn Haven Baker Pensacola Crestview Pensacola Laurel Hill Pensacola Freeport Pensacola Crestview Panama City Mary Esther Pensacola Shalimar Pensacola Niceville Cantonment Defuniak Springs Milton Panama City Beach Youngstown Valparaiso Pensacola Gulf Breeze Pensacola Gulf Breeze Bay Minette Panama City Port St. Joe Panama City Gulf Shores Panama City Fair Hope Panama City Beach Daphne Orange Beach Saraland

168 Figure Opal wood structure claims data vs. model results Figure Opal wood contents claims vs. model results 151

169 Figure Opal masonry structure claims data vs. model results Figure Wood structural damage probability distribution plot, mph, Opal 152

170 Figure Wood structural damage probability distribution plot, mph, Opal Figure Wood structural damage probability distribution plot, mph, Opal 153

171 It should be obvious from these plots that there is not sufficient data from Hurricane Opal to provide any major validation of the model results. In cases where adequate data does exist fairly good agreement between the claims data and the model results is observed, such as the distribution plots shown in Figure 5-39 and Figure 5-40, however these comparisons were again thrown off by the terrain roughness correction. Opal exhibits a range of damage that would be expected from a moderate to strong hurricane making landfall in Florida. On average only maybe once a century or more does some major catastrophic event like Andrew occur. Therefore it should be more of a concern to validate and calibrate the model with minor to moderate storms such as Opal. As was seen in 2004 the sum of the damages from several moderate hurricanes can easily surpass the grand total from an extreme event like Andrew. 5.2 Damage Surveys In 2004 three hurricanes (Charley, Frances, and Jeanne) made direct landfall in Florida while one other (Ivan) made landfall in coastal Alabama but also had a devastating impact on portions of the Florida Panhandle. There is some discussion going on regarding the classification of these storms. According to the National Hurricane Center (NHC), Charley was a category 4 storm, Frances a strong 2, and Jeanne a category 3. However, actual ground measurements for each of these storms indicate a lower classification: Charley - category 3, Frances - category 1, Ivan - category 1, and Jeanne - category 1. These classifications are based on recorded wind speeds from towers mounted on the path of the storms by engineers from the Florida Coastal Monitoring Program. If anything, these discrepancies show that additional parameters might have to be taken into account in the future to define storm intensity, like for example barometric pressure and storm surge. Damage surveys were conducted following all three of these storms. These surveys provided observational validation for many of the assumptions made in the model and gave good references of the types and severity of damage that can be expected for different category hurricanes and wind speeds. Unfortunately, claims data from these storms may not be available for some time and at the time of these storms resources were not in place to conduct an extensive detailed survey of the interior and contents of damaged homes. Furthermore, many people may find it more than somewhat intrusive to ask questions about and take pictures of their decimated possessions. Yet some people were more than willing to help Hurricane Charley The first and most severe hurricane to strike Florida in the summer of 2004 was Hurricane Charley. As noted above, it was a category 3 (based on recorded wind speeds) or 4 (as classified by the NHC) storm with sustained winds in the range of 110 to

172 mph, and maybe as high as 140 mph, when it made landfall in the southwest portion of the state over northern Captiva Island on August 13. Charley maintained hurricane strength as it raced northeast at 25 mph across the state finally exiting of the Atlantic Coast in the Daytona Beach area. Figure 5-42 was provided by NOAA and illustrates the wind swath of Hurricane Charley. Figure Charley making landfall (NOAA) 155

173 Figure Wind swath of hurricane Charley (NOAA) Damage from this storm was reported all across the state with the most severe being where the eye made landfall near the cities of Punta Gorda and Port Charlotte. The extent of the structural damage to homes and manufactured homes in these cities was surveyed by a team that consisted of around 30 members from UF, FIU, Clemson, and FIT and was conducted under the leadership of the Institute for Business and Home Safety (IBHS). For several days following the storm the team conducted a detailed statistical survey of damage in the impacted areas. Results of this survey can be found on the IBHS website and other information regarding the damage of Charley and other storms can be found at the Florida Tech Wind and Hurricane Impact Research Laboratory website, Manufactured homes in these areas were devastated. Entire mobile home communities were nearly leveled with only a few left standing. It should be noted that manufactured homes constructed after 1994 faired much better than pre 1994 homes. Often the only homes left standing in a manufactured home park were the ones constructed according to the post 1994 code. Damage to site-built homes was variable some were completely untouched while others were destroyed. Typical damage to sitebuilt homes was major loss of roof cover, in some cases sheathing loss and blown in window and doors, and in the most severe cases collapsed walls. No precise measurements of the wind speeds in the areas surveyed are available, however unofficial 156

174 reports of peak gusts in Port Charlotte range between 115 and 150 mph, with similar winds likely in Punta Gorda. The observed damage was indicative of these speeds and agrees with the range and distribution of modeled damage for these same speeds. Some pictures from these areas are shown in Figure 5-43 through Figure Figure Manufactured home park in Port Charlotte following Charley, every manufactured home in sight is destroyed, average damage of pre 1994 homes in the park 75-85% 157

175 Figure Typical manufactured home damage in Port Charlotte: complete interior, and utilities loss, although buried some contents may be salvageable Figure Severe site-built home damage in Punta Gorda, the poor quality of construction is evident in that most other nearby homes suffered far less damage 158

176 Figure In Punta Gorda the average home had a similar extent of roof damage, this most likely caused some interior damage and possibly contents losses Figure More typical roof damage in Punta Gorda 159

177 Looking at the vulnerability curves for manufactured homes between mph an average damage ratio of between 55% and 90% would be expected. This is a very broad range but on average the observed damage tends to be near these values. Figure 5-48 illustrates the model vulnerability curve compared with the average observed losses, if a conservative estimate of the wind speed is taken with a conservative estimate of the damage, or a high estimate of the wind speed is taken with a high estimate of the damage we get points that fall on the model vulnerability curve. The average manufactured home loss in Port Charlotte was most likely near a value of 75% with a peak wind gust of around 130 mph, which is very near the model curve. It should be kept in mind that caution must be used because this type of comparison is highly speculative. In addition, it is not possible to give a precise assessment of the repair costs of every home inspected expressed as a percentage of its insured value, since the financial information was not available. A more meaningful comparison will be made when insurance claims data becomes available some time in the future. 1.0 Pre-1994 Manufactured Home Vulnerability, South FL Model Curve Observed Points Building Damage Ratio Wind speed 3-sec peak gusts (mph) Figure Model manufactured home vulnerability curve and observed points For site-built homes at these wind speeds we would expect average damage to range between 3 and 25%. This appears to be the case with most homes needing the roof cover replaced; some with sheathing loss and most likely interior damage. If it is assumed that the average home in Port Charlotte needs only the roof cover replaced (around 7% 160

178 damage) and the wind speeds were around 130 mph we again get a point that falls on the model vulnerability curve as shown in Figure Site-Built Home Vulnerability (other), South FL Model Curve Observed Points Building Damage Ratio Wind speed 3-sec peak gusts (mph) Figure Site-built home modeled vulnerability and observed damage (the other home matrix is used because it encompasses all structural types) In some cases an attempt was made to define the percentage of interior damage resulting from exterior damage (sheathing, window, door loss, etc.) however, again this is very speculative and cannot be done on a large scale. Figures depicting these damages were shown in Chapter 4. Again the observations tend to agree with the results and assumptions of the model. Figure 5-50 was shown previously in Chapter 4 however it will be used again to demonstrate. It can be seen in this figure that the home experienced 15-20% sheathing damage, corresponding interior damage between 20-25%, and contents damage around 10-15%. It should be clear this is not a highly scientific method, and the actual insured losses may vary substantially based on the discretion of the insurance adjuster. However, it can be seen in Figure 5-51 that the interior damage of this home falls well within the range of modeled damages and is in fact very close to the average predicted value. 161

179 Figure Sheathing damage and resulting interior and contents damage Figure The model average at 15% sheathing damage results in about 20% interior damage, and this case falls well within the modeled range Several other similar cases could be presented for each interior damage equation with similar results. 162

180 5.2.2 Hurricane Frances Hurricane Frances was the second storm of the 2004 season. This storm was forecast to be a strong category 4 or even 5 a few days prior to landfall however interaction with the Bahaman Island chain and some dry air caused weakening down to category 1 (based on recorded wind speeds) or 2 (based on the NHC classification) strength at landfall near Stuart, FL, on September 5, The most notable attributes of this hurricane were its size and duration. On the east coast areas from the upper Key s all the way to near Jacksonville in the north experienced wind gusts of tropical storm force or higher. A map of the wind swath again provided by NOAA is shown in Figure The slow movement of this storm made for an agonizingly long labor-day weekend for residents who either evacuated or decided to ride the storm out. The storm sat stationary off the coast for hours on end until it finally began a slow drift inland and across the state. Figure Frances making landfall (NOAA) 163

181 Figure Wind swath of hurricane Frances (NOAA) This very slow movement caused a relentless battering of wind and rain, fatiguing structures and enhancing the damage that would otherwise be expected from a quicker moving storm of similar strength. However, other than a few isolated locations damage was fairly light yet very widespread. Damage was surveyed in areas from Cocoa Beach to Stuart in eastern FL. Although damage from Frances was not nearly as severe as from Charley the same extensive survey conducted in Punta Gorda and Port Charlotte was also conducted in the impacted areas. Great efforts were made to monitor the strength and resulting damage from the storm, as part of the Florida Coastal Monitoring Program. Towers were set up to record wind speeds all along the coast in locations where the storm was forecast to make landfall. Sensors to record the wind induced pressure were deployed on the roofs of several homes. Following the storm, members of the same team that surveyed Charley, photographed and recorded damage throughout the area. Areas of Fort Pierce appeared to be hardest hit with severe damage to many homes in some areas. Figure 5-54 through Figure 5-62 depict typical damages from hurricane Frances seen in various locations. 164

182 Figure Roof Cover damage to Indian Harbor Beach Home, typical in the area probably about 1 in 8 (or more) homes needed a new roof following the storm Figure Manufactured home damage in Indian Harbor Beach, recorded peak wind gust 78 mph approximately 1 mile north 165

183 Figure Manufactured home in Indian Harbor Beach, this home experienced greater damage than any other in the park, it was the only one not shielded by nearby structures Figure Fort Pierce, garage door damage caused internal pressurization resulting in loss of roof sheathing 166

184 Figure Site-built home damage in one of the hardest hit areas of Fort Pierce, beachside near the inlet state park, wind gusts in the area measured up to 108 mph Figure Collapsed roof in Fort Pierce 167

185 Figure More site-built home damage in Fort Pierce, the overhang prior to the storm extended 5 feet beyond the front wall, severe interior damage also occurred Figure Manufactured home damage in Fort Pierce, on U.S. 1 near Indrio Rd. 168

186 Figure Severe manufactured home damage in Fort Pierce These figures from Fort Pierce illustrate some of the most extreme cases of damage seen during Hurricane Frances. Many homes experienced little to no damage. Residents in the neighborhood where the pictures in Figure 5-57 through Figure 5-60 were taken said that this damage could have been the result of a tornado, which seems to make sense because damage only a few streets over was much lighter. A 10 meters 3 second peak wind gust in Fort Pierce was measured at 108 mph by a Florida Coastal Monitoring System Research Tower (FCMSRT). On average, at this wind speed the modeled vulnerability of site-built homes is fairly low around 2%; however there is a slight probability of much more substantial damage. In general, the observed damage agrees with the model predicted damage at 110 mph, however in some locations the vulnerability model results would indicate wind gusts closer to the range of 130 mph. It can be seen in Figure 5-57 through Figure 5-60 that severe damage occurred to many homes, the homes on two entire blocks resembled the homes depicted in these figures. Obviously these damages are greatly in excess of the modeled average damage of 2%, however as was mentioned earlier this was only an isolated area. This again reiterates the difficulties of making comparisons based on observations alone without any claims data to derive a statistical average. And if the severe damage seen was the result of a tornado rather than straight line winds it would not be correct to include these observed damages in an average at 110 mph, because most likely wind speeds were greatly in excess of this. At any rate, if it is assumed that the wind speed on these blocks was in fact near 110 mph, the average damage taken over 169

187 the entire area is probably near 15% as shown in Figure 5-63 (the point at 80 mph is based on observations in Indian Harbor Beach as discussed in proceeding paragraphs). Many manufactured homes in Fort Pierce directly exposed to the wind experienced significant damage. Some were completely destroyed however it was not the mass destruction that was seen in Port Charlotte following Hurricane Charley. The average damage ratio in the worst locations was probably between 25% and 35%, which agrees with the model predictions at likely wind speeds in excess of 100 mph, Figure Site-Built Home Vulnerability (other), South FL Model Curve Observed Points Building Damage Ratio Wind speed 3-sec peak gusts (mph) Figure Site-built model vulnerability curve compared with observations from Frances 170

188 Pre-1994 Manufactured Home Vulnerability, South FL Model Curve Observed Points Building Damage Ratio Wind speed 3-sec peak gusts (mph) Figure Manufactured home vulnerability curves compared with observations from Frances Damage in central and southern Brevard county in the communities of Satellite, Indian Harbor, Indialantic, and Melbourne Beach was fairly light, some homes lost a portion of the roof cover, lots of fallen trees and debris, screened patios and weaker structures suffered heavier damage, a small percentage of homes lost roof sheathing or had more severe structural damage, but many homes were unharmed. The peak measured wind gust in Indian Harbor Beach was 78 mph, also measured by a FCMSRT at 10 meters in a park that could be considered suburban terrain. This wind speed is conducive to the extent of damage that was observed, as can be seen in the vulnerability curve in Figure 5-63 on average only very minor damage is predicted. At locations near the coast, higher levels of damage up to possibly 10-15% were observed, that would seem to correspond to higher wind speed in the range of 85 to 90 mph. That is consistent with the fact that the wind speeds on the coast will be closer to open terrain values than where the wind speed measurement was taken (Gleason Park approximately ¾ of a mile from the beach), however if this is not the case it may indicate that minor adjustments should be made to the model to reflect the wider distribution of damages observed. There are very few manufactured homes in the surveyed beachside areas of Brevard County; only two very small parks in Indian Harbor Beach/Indialantic off Eau Gallie Causeway were toured. Damage in these parks was mostly very light, with only a few 171

189 homes more severely damaged. The peak wind gust of 78 mph was measured about 1 mile from these locations, so these homes probably also experienced winds within this range. The observed damage is consistent with what is modeled at these speeds, on average around 2-3%, as shown in Figure 5-64, with a small probability of more severe losses. Manufactured homes in areas inland such as Barefoot Bay (Southern Brevard County near Palm Bay) were also surveyed by other members of the team with similar types of damage reported. The more severe damage seen at manufactured home parks in Fort Pierce was discussed earlier Hurricane Jeanne Jeanne was the last in the series of storms that hit or threatened FL in This was also a category 1 storm at landfall, according to wind speeds measured by ground anemometers of the FCMPT (however, eye wall winds were not captured) but classified as a category 3 by the NHC, and it took a path across the state nearly identical to Hurricane Frances only 3 weeks prior. This storm was not quite as large as Frances and not as slow moving but stronger, with recorded sustained 1 minute winds between 85 and 90 mph. A map of the wind swath again provided by NOAA is shown in Figure Figure Hurricane Jeanne approaching the Florida East Coast (NOAA) 172

190 Figure Wind swath of hurricane Jeanne (NOAA) Damage from Hurricane Jeanne in many locations was very similar to what was seen from Hurricane Frances. In many cases damage to structures that was initially caused by Frances was compounded by Jeanne. Fatigue of structures from the winds of two hurricanes within three weeks most likely played a roll in the most severe cases of damage in areas such as Vero Beach and Fort Pierce. On a positive note, in some areas most of the weak trees and components of the home (shingles, screened porches, fences, etc.) were already cleaned up by Frances so when Jeanne hit little or no further damage was seen. Without knowledge of the area it would be very difficult to tell what damage was caused by Jeanne and what was caused by Frances. Similar efforts as were taken for Frances to monitor the winds and survey the damage were taken for Jeanne. Towers and pressure sensors were again deployed at various locations near where landfall was forecast. Following the storm members of the team surveyed areas from Stuart to Cocoa Beach. These surveys consisted primarily of cataloging and photographing various observations of damage in the impacted areas, as was done with Frances. 173

191 Figure story Fort Pierce Home, both garage doors damaged, extensive roof and interior damage Figure Vero Beach home, severe roof damage 174

192 Figure Vero Beach, severe roof and interior damage Figure Wabaso 2 story home, severe wall, roof, and interior damage 175

193 Figure More typical extent of damage seen in Vero (also more representative of the modeled home types) Figure Vero, destroyed manufactured home 176

194 Figure 5-67 through Figure 5-72 illustrates some of the worst cases of damage in the hardest hit areas from Hurricane Jeanne. A 3 second peak wind gusts in Vero Beach was measured to be 122 mph by another FCMSRT at 10 meters, while 2-minute average sustained winds at this location reached 78 mph. Observed damage in this and nearby areas is indicative of these wind speeds. We could make comparisons of the observed damage with the model vulnerability curves and find agreement, as before. We can also compare the observed damage with the modeled distribution of damage at the measured wind speed. In general it can be said that nearly every home in areas of Fort Pierce and Vero (where 3 second gust wind speeds reached 120 mph) saw some damage from Hurricane Jeanne, this could be as minor as one or two shingles and the majority may not result in any insurance claims. This is in agreement with the model results that show that 70% of the homes had less than 2% damage, Figure With most insurance deductibles being 2% very few of these will result in insured losses. A much smaller percentage of homes in the surveyed area had more substantial damage. May be 15% needed new roofs, and the most heavily damaged structures had probably between 30 and 40% damage, which tends to agree with the modeled distribution. As before, this is very speculative and a more meaning comparison cannot be made without insurance claims data. However, these observations also may indicate that a wider distribution of damage should be modeled at these low to moderate wind speeds. Figure Probability distribution for other structure at 120 mph (the other structure distribution is used because it encompasses all structural types) 177

195 It is very difficult to draw any hard conclusions from just observations alone. Often the completely random path of destruction only leads to even more confusion. Yet, many lessons were learned from these storms. The quality of construction is an enormous factor in the vulnerability of a home. Flaws and poor quality construction become very evident at a gust of 120 mph. While a well built home is left practically unharmed, the residents of a poorly built one may be looking for a new place to live. The 1994 HUD requirements significantly improved the performance of manufactured homes. As was seen following Hurricane Charley these were often the only undamaged homes in parks of hundreds. In addition, there are many insights that can be gained from these observations that could be used to make future improvements to this model. One could be to model falling tree damage. During the 2004 hurricanes in inland locations such as Kissimmee and Orlando falling trees were one of the leading causes of structural damage, Figure Another could be to model storm surge damage. Many beachfront homes were completely destroyed from the effects of storm surge, Figure 5-75, but statistically these homes only constitute a small percentage of the Florida residential building stock therefore these considerations may not be justified. Also, as was mentioned earlier, observations of damage (and claims data) indicate that a wider distribution of losses should be modeled at lower to moderate wind speeds. Figure Falling tree damage 178

196 Figure Effects of storm surge in Satellite Beach 5.3 Other Model Results Because most other models of this type are proprietary there is no access to their results to provide validation or comparisons. There are some papers mentioned in the literature review which present vulnerability curves obtained from regression analysis of claims data that may be used in some way for validation. The HAZUS model also provides vulnerability curves for many different structural types however complications arise when making comparisons to our model results Other Model/Regression Comparisons Insurance loss data provided in the master s thesis by Bhinderwala [3] is extensively referenced as a comparison for other vulnerability curves. Figure 5-78 is a comparison between the total loss ratio of individual claims (provided in Bhinderwala s Appendix A) with its exponential trend line and the Florida Public model results for other homes in South FL. Very good agreement between the two curves is observed. However, when making comparisons with the data aggregated per zip code (Appendix D) in Bhinderwala s thesis a much different relationship is observed. According to the thesis, both sets of data came from different insurers; however this may not explain these inconsistencies. 179

197 Bhinderwala Data vs. Florida Public Model Total Loss Ratio (Building + Contents + ALE + APS) vs. Windspeed Bhinderwala 70 Florida Public Model Loss Ratio (%) Expon. (Bhinderwala) Windspeed 10 m 3-sec gust (mph) Figure Total loss comparison Bhinderwala (company 1 data) vs. Florida Public model 100 Bhindewala vs. Florida Public Model Total loss Comparisons - Aggregated Data Bhinderwala Florida Public Model 70 Expon. (Bhinderwala) Damage Ratio (%) Windspeed 10-m 3-sec peak gust (mph) Figure Comparison with Bhinderwala data (company 2) aggregated data by zip code 180

198 Attempts may also be made to compare the Florida Public model results with the analytical expressions developed by Huang [17]. However, the wind speed term used in this equation is in the form of effective mean wind speed (average 10 minute sustained), while the Florida Public model uses 3-sec peak gusts. Some conversion could be made of either his or our wind speeds, yet there is not an extremely accurate means of doing this and it can be seen from simple observation of a plot of this equation that good agreement between the curves will not be achieved. The Florida Public model produces more smoothly sloped loss predictions while Huang s curve shows a near vertical increase in losses between wind speeds of 35 and 40 m/s (78 to 90 mph) HAZUS Comparisons The only other public vulnerability model that is available for comparison is the HAZUS model. However, even here comparison is difficult because in most cases ours and their modeled home types are not identical. Also, the HAZUS vulnerability curves are heavily dependant upon the roughness of the terrain, while the vulnerability curve of the Florida Public model is independent of the roughness of the terrain and is a representation of the actual wind speed acting on the structure. Since the datum used to plot the HAZUS curves is the open terrain wind speeds our vulnerability curves correspond to a Zo of 0.03 (for open terrain) used by HAZUS. It can be seen in Figure 5-78 that the HAZUS model drastically over predicts our vulnerability curve for this model type. Comparisons with other model types look very similar. 181

199 Vulnerability Curve Wood Home, Gable Roof, No-Shutters, 8d, Strapped 100% 90% Hazus-Zo=0.03m Loss Ratio (%) 80% 70% 60% 50% 40% Public Model-North Hazus-Zo=1.00m Public Model-South Public Model-Central 30% 20% 10% 0% Windspeed 3 sec-gusts (mph) Figure Comparison of Florida Public model results with HAZUS All of these comparisons tend to agree that the Florida Public Hurricane Loss projection model is currently under predicting losses. Recalibration of the model based on these considerations is intended. 5.4 Summary In this chapter the methods and results of the model validation were presented. The model was validated and calibrated primarily based on insurance loss data from Hurricane Andrew. Some other validation was also provided by Hurricane Opal. Observations of damage from Florida Hurricanes of 2004 provided a good reference for the types of damage that are expected with hurricanes of different strengths. 182

200 Chapter 6 Model Integration Up to this point all of the results of the vulnerability model have been obtained and validated. Now, these results must be integrated together with the meteorological model into the complete actuarial model that will compute the insured losses. There are two type of analyses that can be performed by the complete insurance loss projection model. One is a scenario based procedure where the losses for a historical or hypothetical hurricane can be computed for a given insurance portfolio. The other is the computation of the average annual expected loss for the entire state, based on the probability of occurrence of to different peak wind speeds. The same weighted vulnerability matrices are used for both procedures, and as explained in previous chapters, the weighted vulnerability matrices were developed in a way such that all relevant available information in the policy files is used. In this chapter, the complete model procedures will be explained. The requirements of the Florida Commission on Hurricane Loss Projection Methodology will also be addressed. 6.1 Program Design In the insurance portfolio files the zip code for each home is given. From this the region and sub region of the home can be determined. The list of zip codes that correspond to each region and sub region are given in Appendix D. Also provided in the policy files are the ISO classifications, which are used to define the structural types (masonry, wood, or other). Because the classifications used by each insurance company might vary, some preprocessing is needed to relate each individual company s classifications to one of the three model types (masonry, timber, or other). The general ISO classifications and the classifications for some insurance companies are given in Appendix E. The name of the companies used as examples are not revealed because this information is confidential. The first step in the actuarial model is to select the appropriate vulnerability matrix for to be used for each policy. A flow chart illustrating the selection process is shown in Figure 6-1. The file is read, the zip code defines the region and sub region and the 183

201 construction classification defines the structural type. For each region, sub region and structural type there is one building, contents, and ALE matrix that is selected and used for predicting the expected losses. If the policy is for a manufactured home different selection criteria apply. The zip code is still considered to define the region or HUD wind zone, but in addition the year built is also used to define pre or post 1994 construction. Separate building, contents, and ALE matrices are defined for each region for pre 1994 manufactured homes, and for each wind zone for post 1994 manufactured homes. A flowchart to illustrate the matrix selection process for manufactured homes is shown in Figure

202 Portfolio File Zip Code (Determine region & eliminate all matrixes which do not apply) North Central South Keys Sub-Region (Detrmine based on zip code & eliminate all matrixes which do not apply) Neither (least stringent replacement requirenments apply) Windborne Debris Region (more stringent replacement requirenments apply to windows) High Velocity Hurricane Zone (most stringent replacement requirenments apply to windows and roof) Structural Type (Determine from portfolio file info, eliminate matrixes which do not apply, if unknown use other matrix) Select Applicable Weighted Vulnerability Matrix Figure Matrix selection process for site-built homes 185

203 Select a company Ci Loop 3 Ci = Ci+1 Select a policy Pi,j Loop 2 Pi,j = Pi, j+1 [get information of Construction type, Zip code, ISO classification available? a Use weighted matrices Xn, XC n Is it concrete Is it timber Loop 1 Wi = Wi+1 INPUT Vulnerability Matrices for Structure (S), Content (C), Appurtenant (AP) and ALE (for a given construction type, region based on a given mix of construction features). Assume the number of damage ratio intervals is N *Get damage ratio vectors (i.e., the middle point values for N intervals) XS, XC, XAP, XALE ** For a wind speed Wi, get the vectors of the probability of damage Use weighted concrete matrices Xn, XCn Vi available? DMS = Vi * XS C = LMC * XC AP = LMAP * XAP ALE = LMALE * XALE Use weighted timber matrices Xn, XC n Policy is replacemen t Cost? Vi = 1.25 * LMS Use weighted Misc. matrices Xn, XC n Vi = LMS DM S = Σ(PDS* XS) / N DM C = Σ(PDC* XC) / N DM AP = Σ(PDAP* XAP) / N DMS <= DS C <= DC AP <= DAP ALE <= DALE DMS - DS = 0 C - DC = 0 AP - DAP = 0 ALE - DALE = 0 SumDM DM = S DM + C DM + AP DM + ALE DS = DC = DM S *D/SumDM DM C *D/SumDM DM LS = DMS - DS LC = C - DC LAP = AP - DAP LALE = ALE - DALE b Figure Insurance algorithm flowchart part 1 186

204 b SumLS = SumLS + LS * PD S SumLC = SumLC + LC * PD C Output SumLS, SumLAPP, SumLALE INPUT Probability of wind speed PW i for given wind speed in the given zip code SumEL = SumEL + (SumLs + SumLC + SumLAPP + SumLALE ) * PW i Finish wind speed? Loop 1 Output SumEL SumAEL = SumAEL + SumEL Finish policy? Loop 2 Output SumAEL Finish company? Loop 3 Stop REMARKS: SumL is expected loss of the property for a given wind speed, SumEL is across all wind speeds and SumAEL aggregates all expected losses for one company. Save information (zip code, county, region, construction type, limit of 4 losses, property value, company) for SumLS, SumLAPP, SumLALE & SumEL. For SumLS, SumLAPP, SumLALE, save wind speed too and for SumEL, save (Vi/sum of Vi) where sum of Vi is for each construction type (Masonry, Timber, Mobile home) and is calculated offline. Figure Insurance algorithm flowchart part 2 187

205 Portfolio File Manufactured Homes Year Built Zip Code Pre 1994 Post 1994 North Central South Keys Wind Zone II Wind Zone III Figure Matrix selection process for manufactured homes Once the appropriate matrix is selected for the policy, the insured loss is computed by applying the deductibles and limits at each damage level, and computing the mean loss at any given wind speed defined at the zip code centroid. In the case of a scenario analysis the peak wind speed come from the modeling of the event in the wind model. In the case of a non scenario analysis, the expected loss is computed by integrating the losses over all the wind speeds, based on the probability of occurrence of the wind speeds. The algorithms for both cases are represented in the flow charts of Figure 6-2 and Figure 6-3. It can be seen that the approach adopted in the actuarial algorithm is a traditional one, in which the mean loss is computed for each policy, and no matter how many times the model is run for the same policy, it will always yield the same mean loss. Another approach would be to randomly distribute the loss to any given policy based on the distribution of probabilities for the damage at any particular wind speed. That would mean that every time that the model is run, a different loss would be computed for the same policy, and the mean loss of the portfolio would result from adding the losses of the particular policies. For a sufficiently large portfolio, the mean would be always statistically the same, and should coincide with the mean loss from the first approach. The advantage of the second approach is that it would mimic more accurately what happens in the real world, and therefore comparisons, validations, and calibrations against actual claim data might be more meaningful. The disadvantage is that if the 188

206 procedure would be applied to a small portfolio of a hundred or so policies for example, different runs of the model might yield different mean losses for the entire portfolio. Further information regarding the actuarial model should be available soon from the actuarial team under the guidance of Dr. Shahid Hamid. Further information regarding the computer platform should also be available soon from the computer science team under the guidance of Dr. Shu-Ching Chen. 6.2 Florida Commission Requirements This report fulfills the majority of the documentation requirements set forth by the Florida Commission on Hurricane Loss Projection Methodology. Sections of the vulnerability standards and also the actuarial standards apply to the work completed here. Section V-1 deals with the derivation of vulnerability functions and may apply to the functions developed to predict interior, contents, utilities, additional living expense, and appurtenant structure losses. Each standard which applies will be addressed individually. A. Development of the vulnerability functions is to be based on a combination of the following: (1) historical data, (2) tests, (3) structural calculations, (4) expert opinion, or (5) site inspections. The development of all equations presented here is based on a component approach that combines engineering modeling and simulations with engineering judgment. The external damage of buildings is based on structural calculations and Monte Carlo simulations, while the internal and contents damage is extrapolated form the external damage based upon expert opinion, and confirmed using historical claims data and site inspections of areas impacted by recent hurricanes. B. The method of derivation of vulnerability functions shall be theoretically sound. The method used in the derivation is based on extrapolating the results of Monte Carlo simulations, through simple equations based on engineering judgment and expert opinions. Uncertainties at each stage are accounted for by distributing the damage according to different Weibull distributions. C. Any modification factors/functions to the vulnerability functions or structural characteristics and their corresponding effects shall be clearly defined and be theoretically sound. 189

207 This requirement applies more to the generation of the damage matrices using the Monte Carlo simulation model rather than the functions derived here. The Monte Carlo models take into account many variations in structural characteristics and the result clearly filters through the cost estimation model. There are different costing considerations applied to each structural type and these are clearly defined in Chapter 3 and Appendix A. These adjustments come directly from resources developed exclusively for defining repair costs to structures and therefore can be considered to be theoretically sound. D. Construction type and construction characteristics shall be used in the derivation and application of vulnerability functions. A detailed exposure study was carried on to define the most significant construction types and characteristics in the Florida building stock. E. In the derivation and application of vulnerability functions, assumptions concerning building code revisions and building code enforcement shall be reasonable and theoretically sound. Building code considerations are discussed in detail in Chapter 4. All Florida Building Code requirements that apply to the repair of existing homes are taken into consideration when computing the repair costs of a structure. The enforcement of these codes is considered by applying a higher weight factor to the shuttered home matrices in regions in which opening protection is required when computing the weighted vulnerability matrices. F. Vulnerability functions shall be separately derived for building structures, mobile homes, appurtenant structures, contents and additional living expense. They are as explained in Chapter 4. G. The minimum wind speed that generates damage shall be reasonable. The minimum wind speed at which some damage is observed is 50 mph for appurtenant structures. Site-built and manufactured homes have a very small probability of some very minor damage at 55 mph; this probability becomes more significant at 60 mph and increases from there. 190

208 Sections A-6 is the standard for contents loss modeling and A-7 is the standard for additional living expense loss modeling. The requirements will again be addressed individually. A-7 Contents A. The methods used in the development of contents losses shall be actuarially sound. The contents losses are estimated as a function of the physical damage to the structure. Actuarial considerations are then applied to these predictions. B. The relationship between modeled building and contents loss costs shall be reasonable, based on the relationship between historical building and contents losses. Differences in the relationship of building and contents loss costs from those previously found acceptable shall be reasonable. This relationship is presented in chapter 6. Good agreement between historical losses and modeled losses is achieved. A-8 Additional Living Expenses (ALE) A. The methods used in the development of Additional Living Expense (ALE) loss costs shall be actuarially sound. The ALE losses are modeled as a function of the physical damage to the structure based upon an estimation of repair time. Actuarial considerations are then applied to these predictions. B. ALE loss cost derivations shall consider the estimated time required to repair or replace the property. The ALE loss prediction is based entirely upon the time required to repair a modeled extent of physical damage. C. The relationship between modeled building and ALE loss costs shall be reasonable, based on the relationship between historical building and ALE losses. Differences in the relationship of building and ALE loss costs from those previously found acceptable shall be reasonable. This relationship is presented in chapter 6. Only a small amount of historical data is available and it is for manufactured homes. However, good agreement is achieved with the available data. Basically all of the documentation requirements of the commission for this portion of the model have been fulfilled, leaving only the simulated storm events and required forms to be completed, at the time of this writing. The necessary vulnerability model 191

209 components (vulnerability matrices) from the engineering team are in place to complete this task, however this requires running the complete insurance loss model for which all modules (wind model, actuarial model, computer model) must be finalized. This is nearing a state of completion and should be done by the end of January Summary In this chapter the methods by which the vulnerability matrices are integrated into the actuarial model were presented. Also the means by which the Florida Commission on Hurricane Loss Projection Methodology requirements are met or will be met were discussed. 192

210 Chapter 7 Conclusions and Recommendations This report presented the modeling methods, results obtained, and validation of the Public Hurricane Loss Projection vulnerability model. In this final chapter future development and recommendations for improvements will be discussed. 7.1 Current Research The vulnerability model is currently being adapted for mitigation studies. This involves developing new simulation models and modifying the relationships between external and internal damage to reflect improved resistance of a structure to hurricane related damage when specific mitigation measures are in place. The vulnerability of the enhanced models will be compared to the vulnerability of the unmitigated models and a cost benefit analysis will be performed. Although this may seem simple it should prove rather challenging because there is almost little data available to model some of the mitigation measures. 7.2 Conclusions This project was a very interesting challenge. The overall goal, aside from developing the model for insurance loss projection, is to explain the nature of hurricane related damage. This is an extraordinary task in many ways. It would be a very simple thing to just curve fit equations to insurance loss data, do some statistical analysis to define a likely distribution of claims, and then call it a loss projection model. But instead, the component based approach used in this project, although more complicated, is more general and it forces the modeler to rationalize every aspect of the prediction model. All facets of the complete model and its components down to the smallest detail have some impact on the final estimate of losses. Minor adjustments to some tiny aspect (such as the k factors used in the interior loss equations) can cause a significant shift in the loss 193

211 predictions and many times in unintended ways. This requires a back and forth process until some equilibrium is reached. At any rate, I hope the ideas, methods, and results presented here will be useful in the future of this or similar projects, and in future hurricane research. And if you made it this far, hope you enjoyed reading. 7.3 Recommendations Many recommendations for future areas of research have been presented throughout the body of this report. The major problem experienced during the period in which this work was completed was lack of information. Many modeling assumptions must be made simply because there is absolutely no way of obtaining the information required to proceed with development. In addition, validation is very difficult because insufficient data was provided for different hurricane events from different insurance companies. In any case, because different insurance companies may have different procedures for awarding claims and the range of damages will be different for every storm the validation and calibration of the model shouldn t be entirely based on the analysis of claims from one insurance company from one hurricane. However, since this is all that is available there was little other choice. In time claims data from the Florida hurricanes of 2004 may be available. This data should help to provide better validation and calibration of the model. By simply formatting the available data all the programs used here for analyzing claims data just need to be rerun to develop the same plots for other storms. If this model were being developed for a specific insurance company it would be recommended that data collection methods be improved so that more useful information is provided in the policy files. Information such as with or without shutters, roof type, appurtenant structure type or types, age of roof, any other mitigation measures, etc would be useful to define the vulnerability of a particular home. Some of this information is provided by some companies, but most is not. A standardization of this data for every insurance company would help with a project of this type. Also, more detailed claims data would be the biggest recommendation. A statistical analysis could easily be performed to greatly improve the interior loss equations and other assumptions if an itemized list of the components damaged and the amount specifically paid to repair each was obtained for every home that filed a claim. However, this may be a massive amount of data to try to keep track of. 194

212 References [1] ASCE 7-98 Standard, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, New York, NY. [2] NAHB Research Center, Assessment of Damage to Single-Family Homes Caused by Hurricanes Andrew and Iniki, Prepared for U.S. Department of Housing and Urban Development, Office of Policy Development and Research, [3] S. Bhinderwala, Insurance Loss Analysis of Single Family Dwellings Damaged in Hurricane Andrew, Master s Thesis, Clemson University, Clemson, SC, Department of Civil Engineering, [4] J-P. Pinelli, L. Zhang, C. Subramanian, A. Cope, K. Gurley, S. Gulati, S. Hamid, Classification of structural models for wind damage predictions in Florida, Proceedings of the 11 th International Conference on Wind Engineering, Lubbock, TX, June, 2003, [5] L. Zhang, Public Hurricane Loss Projection Model: Exposure and Vulnerability Components, Master s Thesis, Florida Institute of Technology, Melbourne, FL, Department of Civil Engineering, [6] Florida Commission on Hurricane Loss Projection Methodology: Report of Activities as of November 1, 2003 [7] Multi-hazard Loss Estimation Methodology Hurricane Model HAZUS MH Technical Manual, Federal Emergency Management Agency, [8] B. Sill, R. Kozlowski, Analysis of storm damage factors for low-rise structures, J. Perform. Constr. Fac., ASCE 11 (4) (1997) [9] Florida Building Code, Tallahassee, FL, [10] 2004 National Renovation & Insurance Repair Estimator, J. Russell, Craftsman Book Company, Carlsbad, CA [11] CEIA Cost 2002, R. Langedyk, V. Ticola, Construction Estimating Institute, Sarasota, FL [12] Florida Commision on Hurricane Loss Projection Methodology, Report of Activities as of November 1,

213 [13] Dr. Shu-Ching Chen (FIU), Dr. Mei-Ling Shyu (UM), "Public Hurricane Risk and Loss Model," March 12th, 2004 [14] Shahid S. Hamid, Ph.D., "FIU Public Hurricane Loss Projection Model," May 2003 [15] S. Cocke, L.M. Axe, M. Powell, "Progress of the FSU Storm Track, Wind and Roughness Model," October 16th, 2003 [16] P.R Sparks, S.D. Schiff, Wind damage to the envelopes of houses and consequent insurance losses, J. of Wind Eng. And Industrial Aerodynamics, 53 (1994) [17] Huang Z. Stochastic models for hurricane hazard analysis. PhD Dissertation. Department of Civil Engineering, Clemson University, Clemson, SC, 1999 [18] Huang Z., D.V. Rosowsky, P.R. Sparks, Long-term risk assessment and expected damage to residential structures, Reliability Engineering and System Safety, 74 (2001) [19] Cope A., Predicting the vulnerability of typical residential buildings to hurricane damage, Department of Civil Engineering, University of Florida, Gainesville, FL, 2004 [20] 2002 Florida Hurricane Catastrophe Fund Industry Data Technical Guide [21] Walpole, Myers, Myers, Probability and Statistics for Engineers and Scientists, Sixth edition, Prentice Hall, Upper Saddle River, New Jersey [22] A.C. Khanduri, G.C. Morrow, Vulnerability of buildings to windstorms and insurance loss estimation, J. of Wind Eng. And Industrial Aerodynamics, 91 (2003)

214 Appendix A Replacement Ratios This appendix provides the replacement ratios for each home type used for computing the total structural replacement ratios. 197

215 Construction Type Appendix Table 1 - Replacement Ratios - Concrete, South, Hip Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Region South South South South South South Roof Type Hip Hip Hip Hip Hip Hip Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 4% 4% 4% 4% Cover 13% 13% 13% 5% 5% 5% Trusses 10% 10% 10% 9% 8% 8% Exterior Walls 24% 23% 23% 26% 25% 25% Windows (with or w/o shutters) 5% 7% 7% 5% 8% 8% Entrance Door and Sliding Back Door 1% 1% 1% 1% 1% 1% Garage 1% 1% 1% 1% 1% 1% Gable Ends 0% 0% 0% 0% 0% 0% Interior 32% 31% 31% 35% 34% 34% Mechanical 6% 6% 6% 7% 7% 7% Electrical 8% 8% 8% 9% 9% 9% Plumbing 10% 9% 9% 10% 10% 10% Wall Sheathing 0% 0% 0% 0% 0% 0% Total 114% 113% 113% 113% 113% 113% 198

216 Construction Type Appendix Table 2 - Replacement Ratios - Concrete, South, Gable Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Region South South South South South South Roof Type Gable Gable Gable Gable Gable Gable Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 4% 4% 4% 4% Cover 13% 13% 13% 6% 5% 5% Trusses 9% 9% 9% 7% 7% 7% Exterior Walls 24% 23% 23% 26% 25% 25% Windows (with or w/o shutters) 5% 7% 7% 5% 8% 8% Entrance Door and Sliding Back Door 1% 1% 1% 1% 1% 1% Garage 1% 1% 1% 1% 1% 1% Gable Ends 1% 1% 1% 1% 1% 1% Interior 32% 31% 31% 35% 34% 34% Mechanical 6% 6% 6% 7% 7% 7% Electrical 8% 8% 8% 9% 9% 9% Plumbing 10% 9% 9% 11% 10% 10% Wall Sheathing 0% 0% 0% 0% 0% 0% Total 114% 114% 114% 113% 113% 113% 199

217 Appendix Table 3 - Replacement Ratios - Wood, South, Hip Construction Type Wood Wood Wood Wood Wood Wood Region South South South South South South Roof Type Hip Hip Hip Hip Hip Hip Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 4% 5% 4% 4% Cover 14% 14% 14% 6% 6% 6% Trusses 10% 10% 10% 9% 9% 9% Exterior Walls 13% 13% 13% 15% 14% 14% Windows (with or w/o shutters) 5% 8% 8% 6% 9% 9% Entrance Door and Sliding Back Door 1% 1% 1% 1% 1% 1% Garage 1% 1% 1% 1% 1% 1% Gable Ends 0% 0% 0% 0% 0% 0% Interior 33% 32% 32% 36% 35% 35% Mechanical 6% 6% 6% 7% 7% 7% Electrical 8% 8% 8% 9% 9% 9% Plumbing 10% 10% 10% 11% 11% 11% Wall Sheathing 4% 3% 3% 4% 4% 4% Total 110% 110% 110% 109% 109% 109% 200

218 Appendix Table 4 - Replacement Ratios - Wood, South, Gable Construction Type Wood Wood Wood Wood Wood Wood Region South South South South South South Roof Type Gable Gable Gable Gable Gable Gable Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 4% 5% 4% 4% Cover 14% 14% 14% 6% 6% 6% Trusses 9% 9% 9% 8% 7% 7% Exterior Walls 13% 13% 13% 15% 14% 14% Windows (with or w/o shutters) 5% 8% 8% 6% 9% 9% Entrance Door and Sliding Back Door 1% 1% 1% 1% 1% 1% Garage 1% 1% 1% 1% 1% 1% Gable Ends 1% 1% 1% 1% 1% 1% Interior 33% 32% 32% 36% 35% 35% Mechanical 6% 6% 6% 7% 7% 7% Electrical 8% 8% 8% 9% 9% 9% Plumbing 10% 10% 10% 11% 11% 11% Wall Sheathing 4% 3% 3% 4% 4% 4% Total 110% 110% 110% 110% 109% 109% 201

219 Construction Type Appendix Table 5 - Replacement Ratios - Concrete, Central, Hip Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Region Central Central Central Central Central Central Roof Type Hip Hip Hip Hip Hip Hip Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 4% 4% 0% Cover 13% 13% 0% 5% 5% 0% Trusses 10% 10% 0% 9% 8% 0% Exterior Walls 24% 23% 0% 26% 25% 0% Windows (with or w/o shutters) 5% 7% 0% 5% 8% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 1% 1% 0% Gable Ends 0% 0% 0% 0% 0% 0% Interior 32% 31% 0% 35% 34% 0% Mechanical 6% 6% 0% 7% 7% 0% Electrical 8% 8% 0% 9% 9% 0% Plumbing 10% 9% 0% 10% 10% 0% Wall Sheathing 0% 0% 0% 0% 0% 0% Total 114% 113% 0% 113% 113% 0% 202

220 Appendix Table 6 - Replacement Ratios - Wood, Central, Hip Construction Type Wood Wood Wood Wood Wood Wood Region Central Central Central Central Central Central Roof Type Hip Hip Hip Hip Hip Hip Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 5% 4% 0% Cover 14% 14% 0% 6% 6% 0% Trusses 11% 10% 0% 9% 9% 0% Exterior Walls 13% 13% 0% 15% 14% 0% Windows (with or w/o shutters) 6% 8% 0% 6% 9% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 2% 1% 0% Gable Ends 0% 0% 0% 0% 0% 0% Interior 32% 31% 0% 35% 34% 0% Mechanical 6% 6% 0% 7% 7% 0% Electrical 8% 8% 0% 9% 9% 0% Plumbing 10% 9% 0% 11% 10% 0% Wall Sheathing 4% 3% 0% 4% 4% 0% Total 110% 110% 0% 109% 109% 0% 203

221 Construction Type Appendix Table 7 - Replacement Ratios - Concrete, Central, Gable Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Region Central Central Central Central Central Central Roof Type Gable Gable Gable Gable Gable Gable Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 4% 4% 0% Cover 13% 13% 0% 6% 5% 0% Trusses 9% 9% 0% 7% 7% 0% Exterior Walls 24% 23% 0% 26% 25% 0% Windows (with or w/o shutters) 5% 7% 0% 5% 8% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 1% 1% 0% Gable Ends 1% 1% 0% 1% 1% 0% Interior 32% 31% 0% 35% 34% 0% Mechanical 6% 6% 0% 7% 7% 0% Electrical 8% 8% 0% 9% 9% 0% Plumbing 10% 9% 0% 11% 10% 0% Wall Sheathing 0% 0% 0% 0% 0% 0% Total 114% 114% 0% 113% 113% 0% 204

222 Appendix Table 8 - Replacement Ratios - Wood, Central, Gable Construction Type Wood Wood Wood Wood Wood Wood Region Central Central Central Central Central Central Roof Type Gable Gable Gable Gable Gable Gable Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 5% 4% 0% Cover 14% 14% 0% 6% 6% 0% Trusses 9% 9% 0% 8% 8% 0% Exterior Walls 13% 13% 0% 15% 14% 0% Windows (with or w/o shutters) 6% 8% 0% 6% 9% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 2% 1% 0% Gable Ends 1% 1% 0% 1% 1% 0% Interior 32% 31% 0% 36% 35% 0% Mechanical 6% 6% 0% 7% 7% 0% Electrical 8% 8% 0% 9% 9% 0% Plumbing 10% 9% 0% 11% 10% 0% Wall Sheathing 4% 3% 0% 4% 4% 0% Total 110% 110% 0% 109% 109% 0% 205

223 Construction Type Appendix Table 9 - Replacement Ratios - Concrete, North, Hip Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Region North North North North North North Roof Type Hip Hip Hip Hip Hip Hip Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 4% 4% 0% Cover 14% 13% 0% 6% 5% 0% Trusses 10% 10% 0% 9% 9% 0% Exterior Walls 24% 23% 0% 26% 25% 0% Windows (with or w/o shutters) 6% 9% 0% 7% 9% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 2% 2% 0% Gable Ends 0% 0% 0% 0% 0% 0% Interior 30% 30% 0% 33% 32% 0% Mechanical 6% 6% 0% 6% 6% 0% Electrical 8% 7% 0% 8% 8% 0% Plumbing 9% 9% 0% 10% 10% 0% Wall Sheathing 0% 0% 0% 0% 0% 0% Total 113% 113% 0% 113% 112% 0% 206

224 Construction Type Appendix Table 10 - Replacement Ratios - Concrete, North, Gable Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Concrete Block Region North North North North North North Roof Type Gable Gable Gable Gable Gable Gable Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 4% 4% 0% Cover 14% 13% 0% 6% 5% 0% Trusses 9% 9% 0% 7% 7% 0% Exterior Walls 24% 23% 0% 26% 25% 0% Windows (with or w/o shutters) 6% 9% 0% 7% 9% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 2% 2% 0% Gable Ends 1% 1% 0% 1% 1% 0% Interior 31% 30% 0% 34% 33% 0% Mechanical 6% 6% 0% 6% 6% 0% Electrical 8% 7% 0% 8% 8% 0% Plumbing 9% 9% 0% 10% 10% 0% Wall Sheathing 0% 0% 0% 0% 0% 0% Total 113% 113% 0% 113% 113% 0% 207

225 Appendix Table 11 - Replacement Ratios-Wood, North, Hip Construction Type Wood Wood Wood Wood Wood Wood Region North North North North North North Roof Type Hip Hip Hip Hip Hip Hip Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 5% 4% 0% Cover 14% 14% 0% 6% 6% 0% Trusses 11% 10% 0% 9% 9% 0% Exterior Walls 13% 13% 0% 15% 14% 0% Windows (with or w/o shutters) 6% 8% 0% 6% 9% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 2% 1% 0% Gable Ends 0% 0% 0% 0% 0% 0% Interior 32% 31% 0% 35% 34% 0% Mechanical 6% 6% 0% 7% 7% 0% Electrical 8% 8% 0% 9% 9% 0% Plumbing 10% 9% 0% 11% 10% 0% Wall Sheathing 4% 3% 0% 4% 4% 0% Total 110% 110% 0% 109% 109% 0% 208

226 Appendix Table 12 - Replacement Ratios-Wood, North, Gable Construction Type Wood Wood Wood Wood Wood Wood Region North North North North North North Roof Type Gable Gable Gable Gable Gable Gable Tile or Shingle Tile Tile Tile Shingle Shingle Shingle Sub region Neither WBDR HVHZ Neither WBDR HVHZ Sheathing 4% 4% 0% 5% 4% 0% Cover 14% 14% 0% 6% 6% 0% Trusses 9% 9% 0% 8% 8% 0% Exterior Walls 13% 13% 0% 15% 14% 0% Windows (with or w/o shutters) 6% 8% 0% 6% 9% 0% Entrance Door and Sliding Back Door 1% 1% 0% 1% 1% 0% Garage 1% 1% 0% 2% 1% 0% Gable Ends 1% 1% 0% 1% 1% 0% Interior 32% 31% 0% 36% 35% 0% Mechanical 6% 6% 0% 7% 7% 0% Electrical 8% 8% 0% 9% 9% 0% Plumbing 10% 9% 0% 11% 10% 0% Wall Sheathing 4% 3% 0% 4% 4% 0% Total 110% 110% 0% 109% 109% 0% 209

227 210

228 Appendix B Programs Included in this appendix is a list and description of all programs used to create the results presented in the body of the thesis. These programs can be found on the attached cd in the folder called programs. Note that the programs listed here are the main programs used, many other programs have been created to serve some minor purpose. Some of these have been included on the attached cd as well so that they may be of some use in the future. B.1 Site-Built 1. ContUtilities_Validation_Prog_ m a. Description - Creates plots of contents, utilities, interior, and ALE damage vs. total building damage b. Input - Monte Carlo Output files c. Output - Figure files 2. Vulnerability_Prog_ m a. Description - Creates type 1 and type 2 vulnerability matrices b. Input - Monte Carlo Output files c. Output - Type 1 vulnerability matrices in a folder called Vulnerability_(RUNDATE), and type 2 vulnerability matrices within the Vulnerability_(RUNDATE) folder in another folder called Vulnerability_Type2 3. Vulnerability_Fragility_Plot_Prog_111904_type1.m a. Description - Creates the vulnerability and fragility plots from the vulnerability matrices b. Input - Type 1 vulnerability matrices c. Output - Vulnerability and fragility plots in a folder called VulnFrag and the points of the vulnerability curves in a folder called VulnPoints 4. Matrix_Weight_Prog_112004_final.m a. Description - Weights the vulnerability matrices based on exposure statistics b. Input - Type 1 or Type 2 vulnerability matrices 211

229 c. Output - Weighted vulnerability matrices in a folder called Weighted 5. Final_VM_Plot_Prog_ m a. Description - Creates the weighted vulnerability and fragility curves from the weighted type 1 vulnerability matrices b. Input - Weighted type 1 vulnerability matrices c. Output - Weighted vulnerability and fragility plots in a folder called VulnFrag and the points of the vulnerability curves in a folder called VulnPoints 6. histogram_prog_type1_ m a. Description - Creates the comparison probability distribution plots from preformatted claims data and the weighted vulnerability matrices b. Input - Preformatted claims data and weighted type 1 vulnerability matrices c. Output - Probability distribution plots in a folder called Histograms 7. MaxMin_Prog_80904.m a. Description - Plots the weighted type 1 matrices vs. claims data showing the modeled maximum and minimum values and average vulnerability curve, b. Input - Weighted type 1 vulnerability matrices and preformatted claims data c. Output - Figures in a folder called MaxMin 8. Vulnerability_Fragility_Plot_Prog_111904_type2.m a. Description - Plots the model type 2 vulnerability and fragility curves b. Input - Model type 2 vulnerability matrices c. Output - Figures in a folder called VulnFrag 9. Weighted_Plot_Prog_type2_ m a. Description - Plots the vulnerability and fragility curves of the weighted type 2 matrices b. Input - Weighted type 2 matrices c. Output - Figures in a folder called VulnFrag 10. histogram_prog_manuf_ m a. Description - Plots probability distribution functions of losses from preformatted claims data and type 2 vulnerability matrices (will also work on manufactured homes) b. Input - Preformatted claims data and weighted type 2 vulnerability matrices c. Output - Figures in a folder called Histograms 11. MaxMin_Prog_Combined_ m & (111804) 212

230 a. Description - Plots the weighted type 2 matrices vs. claims data showing the modeled maximum and minimum values, the program uses a trend line while the program computes an average from the data b. Input - Weighted type 2 vulnerability matrices an preformatted claims data c. Output - Figures in a folder called MaxMin 12. APS_Prog_weibull.m a. Description - creates the appurtenant structure vulnerability matrix based on the theories described in the text b. Input - none c. Output - appurtenant structure vulnerability matrix B.2 Manufactured 13. Manufac_Homes_Prog_ m a. Description - Creates manufactured home vulnerability matrices b. Input - Monte Carlo output files c. Output - Type 1 vulnerability matrices in a folder called Vulnerability_(RUNDATE) and type 2 vulnerability matrices in a folder called Vulnerability_Type2 within the other folder 14. Vulnerability_Fragility_Plot_manuf_Prog_type1_ m a. Description - Plots the type 1 manufactured home vulnerability and fragility curves b. Input - Model type 1 manufactured home vulnerability matrices c. Output - Figures in a folder called VulnFrag 15. Matrix_Weight_Prog_Manuf_ m a. Description - Weights the model vulnerability matrices using Exposure statistics b. Input - Model type 1 or type 2 vulnerability matrices c. Output - Weighted vulnerability matrices in a folder called weighted 16. Weighted_manuf_plot_Prog_type1_ m a. Description - plots the weighted type 1 manufactured home vulnerability and fragility curves b. Input - Weighted type 1 vulnerability matrices c. Output - Figures in a folder called Plots 17. histogram_prog_manuf_type1_ m a. Description - Plots the probability distribution functions of the model results and compares with preformatted claims data 213

231 b. Input - Weighted type 1 manufactured home vulnerability matrices and preformatted claims data c. Output - figures in a folder called Histograms 18. MaxMin_Prog_Manuf_type1_ m a. Description - Compares the modeled average, maximum, and minimum values with preformatted claims data b. Input - Weighted type 1 vulnerability matrices and formatted claims data c. Output - Figures in a folder called MaxMin 19. Vulnerability_Fragility_Plot_manuf_Prog_ m a. Description - Plots type 2 manufactured home vulnerability and fragility curves b. Input - Type 2 manufactured home vulnerability matrices c. Output - Figures in a folder called VulnFrag 20. Weighted_manuf_plot_Prog_type2_ m a. Description - Plots the weighted type 2 vulnerability and fragility curves for manufactured homes b. Input - Weighted type 2 manufactured home vulnerability matrices c. Output - Figures in a folder called plots 21. MaxMin_Prog_Manuf_ m a. Description - Compares the modeled maximum minimum and average values with claims data b. Input - Preformatted claims data and weighted type 2 vulnerability matrices c. Output - Figures in a folder called MaxMin 22. histogram_prog_manuf_ m a. Description - Compares the modeled probability distribution functions with the probability distribution functions of the claims data b. Input - Preformatted claims data and weighted type 2 vulnerability matrices c. Output - Figures in a folder called Histograms 214

232 Appendix C Results Included in this appendix is list of all the model vulnerability and fragility curves created. All manufactured home curves were given in Chapter 5. Because it would take a great deal of space to plot all of these curves, and the majority are very similar, only a few that are representative of most others have been included, the remainder can be found on the attached cd in the folder called Results. Also note that there are separate contents and ALE curves are created for each of these model types, these are also found on the attached cd. 215

233 C.1 Vulnerability/Fragility Curves Figure Region Construction Roof Type Roof Cover Shutters Stories FBC Region 1* South Concrete Hip Tile No 1 none 2* South Concrete Hip Tile No 1 WBDR 3* South Concrete Hip Tile No 1 HVHZ 4* South Concrete Hip Shingle No 1 none 5 South Concrete Hip Shingle No 1 WBDR 6 South Concrete Hip Shingle No 1 HVHZ 7* South Concrete Hip Tile Yes 1 none 8 South Concrete Hip Tile Yes 1 WBDR 9 South Concrete Hip Tile Yes 1 HVHZ 10 South Concrete Hip Shingle Yes 1 none 11 South Concrete Hip Shingle Yes 1 WBDR 12 South Concrete Hip Shingle Yes 1 HVHZ 13* South Concrete Hip Tile No 2 none 14 South Concrete Hip Tile No 2 WBDR 15 South Concrete Hip Tile No 2 HVHZ 16 South Concrete Hip Shingle No 2 none 17 South Concrete Hip Shingle No 2 WBDR 18 South Concrete Hip Shingle No 2 HVHZ 19 South Concrete Gable Tile No 1 none 20 South Concrete Gable Tile No 1 WBDR 21 South Concrete Gable Tile No 1 HVHZ 22* South Concrete Gable Shingle No 1 none 23 South Concrete Gable Shingle No 1 WBDR 24 South Concrete Gable Shingle No 1 HVHZ 25 South Concrete Gable Tile Yes 1 none 26 South Concrete Gable Tile Yes 1 WBDR 27 South Concrete Gable Tile Yes 1 HVHZ 28 South Concrete Gable Shingle Yes 1 none 29 South Concrete Gable Shingle Yes 1 WBDR 30 South Concrete Gable Shingle Yes 1 HVHZ 31 South Concrete Gable Tile No 2 none 32 South Concrete Gable Tile No 2 WBDR 33 South Concrete Gable Tile No 2 HVHZ 34 South Concrete Gable Shingle No 2 none 35 South Concrete Gable Shingle No 2 WBDR 36 South Concrete Gable Shingle No 2 HVHZ 216

234 37* South Wood Hip Tile No 1 none 38 South Wood Hip Tile No 1 WBDR 39 South Wood Hip Tile No 1 HVHZ 40 South Wood Hip Shingle No 1 none 41 South Wood Hip Shingle No 1 WBDR 42 South Wood Hip Shingle No 1 HVHZ 43 South Wood Hip Tile Yes 1 none 44 South Wood Hip Tile Yes 1 WBDR 45 South Wood Hip Tile Yes 1 HVHZ 46 South Wood Hip Shingle Yes 1 none 47 South Wood Hip Shingle Yes 1 WBDR 48 South Wood Hip Shingle Yes 1 HVHZ 49 South Wood Hip Tile No 2 none 50 South Wood Hip Tile No 2 WBDR 51 South Wood Hip Tile No 2 HVHZ 52 South Wood Hip Shingle No 2 none 53 South Wood Hip Shingle No 2 WBDR 54 South Wood Hip Shingle No 2 HVHZ 55 South Wood Gable Tile No 1 none 56 South Wood Gable Tile No 1 WBDR 57 South Wood Gable Tile No 1 HVHZ 58 South Wood Gable Shingle No 1 none 59 South Wood Gable Shingle No 1 WBDR 60 South Wood Gable Shingle No 1 HVHZ 61 South Wood Gable Tile Yes 1 none 62 South Wood Gable Tile Yes 1 WBDR 63 South Wood Gable Tile Yes 1 HVHZ 64 South Wood Gable Shingle Yes 1 none 65 South Wood Gable Shingle Yes 1 WBDR 66 South Wood Gable Shingle Yes 1 HVHZ 67 South Wood Gable Tile No 2 none 68 South Wood Gable Tile No 2 WBDR 69 South Wood Gable Tile No 2 HVHZ 70 South Wood Gable Shingle No 2 none 71 South Wood Gable Shingle No 2 WBDR 72 South Wood Gable Shingle No 2 HVHZ 73 Central Concrete Hip Tile No 1 none 74 Central Concrete Hip Tile No 1 WBDR 75 Central Concrete Hip Tile No 1 HVHZ 76 Central Concrete Hip Shingle No 1 none 217

235 77 Central Concrete Hip Shingle No 1 WBDR 78 Central Concrete Hip Shingle No 1 HVHZ 79 Central Concrete Hip Tile Yes 1 none 80 Central Concrete Hip Tile Yes 1 WBDR 81 Central Concrete Hip Tile Yes 1 HVHZ 82 Central Concrete Hip Shingle Yes 1 none 83 Central Concrete Hip Shingle Yes 1 WBDR 84 Central Concrete Hip Shingle Yes 1 HVHZ 85 Central Concrete Hip Tile No 2 none 86 Central Concrete Hip Tile No 2 WBDR 87 Central Concrete Hip Tile No 2 HVHZ 88 Central Concrete Hip Shingle No 2 none 89 Central Concrete Hip Shingle No 2 WBDR 90 Central Concrete Hip Shingle No 2 HVHZ 91 Central Concrete Gable Tile No 1 none 92 Central Concrete Gable Tile No 1 WBDR 93 Central Concrete Gable Tile No 1 HVHZ 94 Central Concrete Gable Shingle No 1 none 95 Central Concrete Gable Shingle No 1 WBDR 96 Central Concrete Gable Shingle No 1 HVHZ 97 Central Concrete Gable Tile Yes 1 none 98 Central Concrete Gable Tile Yes 1 WBDR 99 Central Concrete Gable Tile Yes 1 HVHZ 100 Central Concrete Gable Shingle Yes 1 none 101 Central Concrete Gable Shingle Yes 1 WBDR 102 Central Concrete Gable Shingle Yes 1 HVHZ 103 Central Concrete Gable Tile No 2 none 104 Central Concrete Gable Tile No 2 WBDR 105 Central Concrete Gable Tile No 2 HVHZ 106 Central Concrete Gable Shingle No 2 none 107 Central Concrete Gable Shingle No 2 WBDR 108 Central Concrete Gable Shingle No 2 HVHZ 109 Central Wood Hip Tile No 1 none 110 Central Wood Hip Tile No 1 WBDR 111 Central Wood Hip Tile No 1 HVHZ 112 Central Wood Hip Shingle No 1 none 113 Central Wood Hip Shingle No 1 WBDR 114 Central Wood Hip Shingle No 1 HVHZ 115 Central Wood Hip Tile Yes 1 none 116 Central Wood Hip Tile Yes 1 WBDR 218

236 117 Central Wood Hip Tile Yes 1 HVHZ 118 Central Wood Hip Shingle Yes 1 none 119 Central Wood Hip Shingle Yes 1 WBDR 120 Central Wood Hip Shingle Yes 1 HVHZ 121 Central Wood Hip Tile No 2 none 122 Central Wood Hip Tile No 2 WBDR 123 Central Wood Hip Tile No 2 HVHZ 124 Central Wood Hip Shingle No 2 none 125 Central Wood Hip Shingle No 2 WBDR 126 Central Wood Hip Shingle No 2 HVHZ 127 Central Wood Gable Tile No 1 none 128 Central Wood Gable Tile No 1 WBDR 129 Central Wood Gable Tile No 1 HVHZ 130 Central Wood Gable Shingle No 1 none 131 Central Wood Gable Shingle No 1 WBDR 132 Central Wood Gable Shingle No 1 HVHZ 133 Central Wood Gable Tile Yes 1 none 134 Central Wood Gable Tile Yes 1 WBDR 135 Central Wood Gable Tile Yes 1 HVHZ 136 Central Wood Gable Shingle Yes 1 none 137 Central Wood Gable Shingle Yes 1 WBDR 138 Central Wood Gable Shingle Yes 1 HVHZ 139 Central Wood Gable Tile No 2 none 140 Central Wood Gable Tile No 2 WBDR 141 Central Wood Gable Tile No 2 HVHZ 142 Central Wood Gable Shingle No 2 none 143 Central Wood Gable Shingle No 2 WBDR 144 Central Wood Gable Shingle No 2 HVHZ 145 North Concrete Hip Tile No 1 none 146 North Concrete Hip Tile No 1 WBDR 147 North Concrete Hip Tile No 1 HVHZ 148 North Concrete Hip Shingle No 1 none 149 North Concrete Hip Shingle No 1 WBDR 150 North Concrete Hip Shingle No 1 HVHZ 151 North Concrete Hip Tile Yes 1 none 152 North Concrete Hip Tile Yes 1 WBDR 153 North Concrete Hip Tile Yes 1 HVHZ 154 North Concrete Hip Shingle Yes 1 none 155 North Concrete Hip Shingle Yes 1 WBDR 156 North Concrete Hip Shingle Yes 1 HVHZ 219

237 157 North Concrete Hip Tile No 2 none 158 North Concrete Hip Tile No 2 WBDR 159 North Concrete Hip Tile No 2 HVHZ 160 North Concrete Hip Shingle No 2 none 161 North Concrete Hip Shingle No 2 WBDR 162 North Concrete Hip Shingle No 2 HVHZ 163 North Concrete Gable Tile No 1 none 164 North Concrete Gable Tile No 1 WBDR 165 North Concrete Gable Tile No 1 HVHZ 166 North Concrete Gable Shingle No 1 none 167 North Concrete Gable Shingle No 1 WBDR 168 North Concrete Gable Shingle No 1 HVHZ 169 North Concrete Gable Tile Yes 1 none 170 North Concrete Gable Tile Yes 1 WBDR 171 North Concrete Gable Tile Yes 1 HVHZ 172 North Concrete Gable Shingle Yes 1 none 173 North Concrete Gable Shingle Yes 1 WBDR 174 North Concrete Gable Shingle Yes 1 HVHZ 175 North Concrete Gable Tile No 2 none 176 North Concrete Gable Tile No 2 WBDR 177 North Concrete Gable Tile No 2 HVHZ 178 North Concrete Gable Shingle No 2 none 179 North Concrete Gable Shingle No 2 WBDR 180 North Concrete Gable Shingle No 2 HVHZ 181 North Wood Hip Tile No 1 none 182 North Wood Hip Tile No 1 WBDR 183 North Wood Hip Tile No 1 HVHZ 184 North Wood Hip Shingle No 1 none 185 North Wood Hip Shingle No 1 WBDR 186 North Wood Hip Shingle No 1 HVHZ 187 North Wood Hip Tile Yes 1 none 188 North Wood Hip Tile Yes 1 WBDR 189 North Wood Hip Tile Yes 1 HVHZ 190 North Wood Hip Shingle Yes 1 none 191 North Wood Hip Shingle Yes 1 WBDR 192 North Wood Hip Shingle Yes 1 HVHZ 193 North Wood Hip Tile No 2 none 194 North Wood Hip Tile No 2 WBDR 195 North Wood Hip Tile No 2 HVHZ 196 North Wood Hip Shingle No 2 none 220

238 197 North Wood Hip Shingle No 2 WBDR 198 North Wood Hip Shingle No 2 HVHZ 199 North Wood Gable Tile No 1 none 200 North Wood Gable Tile No 1 WBDR 201 North Wood Gable Tile No 1 HVHZ 202 North Wood Gable Shingle No 1 none 203 North Wood Gable Shingle No 1 WBDR 204 North Wood Gable Shingle No 1 HVHZ 205 North Wood Gable Tile Yes 1 none 206 North Wood Gable Tile Yes 1 WBDR 207 North Wood Gable Tile Yes 1 HVHZ 208 North Wood Gable Shingle Yes 1 none 209 North Wood Gable Shingle Yes 1 WBDR 210 North Wood Gable Shingle Yes 1 HVHZ 211 North Wood Gable Tile No 2 none 212 North Wood Gable Tile No 2 WBDR 213 North Wood Gable Tile No 2 HVHZ 214 North Wood Gable Shingle No 2 none 215 North Wood Gable Shingle No 2 WBDR 216 North Wood Gable Shingle No 2 HVHZ * Indicates plots that have been included 221

239 222

240 223

241 224

242 225

243 Appendix D Zip Code Classifications In this appendix all of the criteria used to classify the region of each zip code are presented. 226

244 FHCF ZIP Code Rating Region County Code County Name HUD Wind Zone Region High Velocity Hurricane Zone Windborne Debris Region Clay 2 North No No St. Johns 2 North No No Clay 2 North No No Putnam 2 North No No Suwannee 2 North No No Nassau 2 North No No Nassau 2 North No No Lafayette 2 North No No Columbia 2 North No No Columbia 2 North No No Union 2 North No No Clay 2 North No No St. Johns 2 North No No Nassau 2 North No Yes Nassau 2 North No No Columbia 2 North No No Baker 2 North No No Nassau 2 North No No Bradford 2 North No No Clay 2 North No No Bradford 2 North No No Nassau 2 North No No Clay 2 North No No Hamilton 2 North No No Hamilton 2 North No No Union 2 North No No Columbia 2 North No No Columbia 2 North No No Bradford 2 North No No Madison 2 North No No Suwannee 2 North No No Columbia 2 North No No Suwannee 2 North No No Baker 2 North No No Suwannee 2 North No No Clay 2 North No No Lafayette 2 North No No Clay 2 North No No Clay 2 North No No Suwannee 2 North No No Baker 2 North No No 227

245 Clay 2 North No No Clay 2 North No No St. Johns 2 North No No St. Johns 2 North No Yes Union 2 North No No St. Johns 2 North No Yes St. Johns 2 North No No St. Johns 2 North No Yes Baker 2 North No No Bradford 2 North No No St. Johns 2 North No No Suwannee 2 North No No St. Johns 2 North No Yes Hamilton 2 North No No Nassau 2 North No Yes Duval 2 North No No Lake 2 Central No No Volusia 2 Central No No Flagler 2 Central No No Marion 2 Central No No Putnam 2 North No No Marion 2 Central No No Volusia 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Putnam 2 North No No Volusia 2 Central No No Marion 2 Central No No Marion 2 Central No No 228

246 Flagler 2 Central No Yes Flagler 2 Central No Yes Flagler 2 Central No Yes Putnam 2 North No No Putnam 2 North No No Putnam 2 North No No Volusia 2 Central No Yes Flagler 2 Central No Yes St. Johns 2 North No No Putnam 2 North No No Putnam 2 North No No Putnam 2 North No No Flagler 2 Central No Yes Putnam 2 North No No Lake 2 Central No No Lake 2 Central No No Clay 2 North No No Sumter 2 Central No No Flagler 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No Yes Putnam 2 North No No Putnam 2 North No No Marion 2 Central No No Volusia 2 Central No No Putnam 2 North No No Marion 2 Central No No Marion 2 Central No No Putnam 2 North No No Putnam 2 North No No Putnam 2 North No No Volusia 2 Central No No Marion 2 Central No No Putnam 2 North No No Marion 2 Central No No Volusia 2 Central No No Duval 2 North No No Duval 2 North No No 229

247 Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No Yes Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No Yes Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No Yes Duval 2 North No Yes Duval 2 North No Yes Duval 2 North No Yes Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No Yes Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No No Duval 2 North No Yes Duval 2 North No No Duval 2 North No Yes 230

248 Duval 2 North No No Duval 2 North No No Duval 2 North No Yes Duval 2 North No No Duval 2 North No No St. Johns 2 North No No St. Johns 2 North No No Duval 2 North No Yes Duval 2 North No No Duval 2 North No No Duval 2 North No Yes Duval 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Franklin 3 North No Yes Liberty 2 North No No Franklin 3 North No Yes Franklin 3 North No Yes Gadsden 2 North No No Wakulla 2 North No No Wakulla 2 North No No Franklin 3 North No Yes Franklin 3 North No Yes Gadsden 2 North No No Madison 2 North No No Gadsden 2 North No No Gadsden 2 North No No 231

249 Liberty 2 North No No Liberty 2 North No No Jefferson 2 North No No Jefferson 2 North No No Madison 2 North No No Madison 2 North No No Gadsden 2 North No No Jefferson 2 North No No Jefferson 2 North No No Wakulla 2 North No No Taylor 2 North No No Taylor 2 North No No Madison 2 North No No Gadsden 2 North No No Gadsden 2 North No No Gadsden 2 North No No Wakulla 2 North No No Taylor 2 North No No Taylor 2 North No No Wakulla 2 North No No Taylor 2 North No Yes Liberty 2 North No No Jefferson 2 North No No Leon 2 North No No Leon 2 North No No Leon 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Bay 2 North No No Jackson 2 North No No Calhoun 2 North No No Walton 2 North No No 232

250 Jackson 2 North No No Calhoun 2 North No No Holmes 2 North No No Jackson 2 North No No Washington 2 North No No Washington 2 North No No Calhoun 2 North No No Jackson 2 North No No Jackson 2 North No No Walton 2 North No No Walton 2 North No No Walton 2 North No No Washington 2 North No Yes Bay 2 North No No Walton 2 North No Yes Jackson 2 North No No Jackson 2 North No No Jackson 2 North No No Bay 2 North No No Jackson 2 North No No Jackson 2 North No No Jackson 2 North No No Jackson 2 North No No Calhoun 2 North No Yes Holmes 2 North No No Walton 2 North No No Walton 2 North No No Gulf 3 North No Yes Gulf 3 North No Yes Walton 2 North No Yes Jackson 2 North No No Walton 2 North No No Washington 2 North No No Washington 2 North No No Holmes 2 North No No Gulf 3 North No Yes Bay 2 North No No Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes 233

251 Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Santa Rosa 2 North No Yes Okaloosa 2 North No No Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Okaloosa 2 North No No Okaloosa 2 North No Yes Walton 2 North No No Okaloosa 2 North No No Okaloosa 2 North No Yes Okaloosa 2 North No Yes Okaloosa 2 North No Yes Okaloosa 2 North No Yes Okaloosa 2 North No Yes Okaloosa 2 North No Yes Okaloosa 2 North No Yes Walton 2 North No No Escambia 2 North No Yes Escambia 2 North No Yes Santa Rosa 2 North No Yes Santa Rosa 2 North No Yes Santa Rosa 2 North No Yes Okaloosa 2 North No Yes Santa Rosa 2 North No No Santa Rosa 2 North No Yes Okaloosa 2 North No No Escambia 2 North No Yes Okaloosa 2 North No Yes Santa Rosa 2 North No No 234

252 Santa Rosa 2 North No Yes Santa Rosa 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Okaloosa 2 North No Yes Okaloosa 2 North No Yes Okaloosa 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Santa Rosa 2 North No Yes Okaloosa 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Escambia 2 North No Yes Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Marion 2 Central No No Alachua 2 North No No Gilchrist 2 North No No 235

253 Levy 2 North No No Bradford 2 North No No Levy 2 North No Yes Levy 2 North No Yes Alachua 2 North No No Dixie 2 North No No Alachua 2 North No No Alachua 2 North No No Marion 2 Central No No Alachua 2 North No No Levy 2 North No No Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Levy 2 North No No Dixie 2 North No Yes Alachua 2 North No No Alachua 2 North No No Alachua 2 North No No Clay 2 North No No Alachua 2 North No No Alachua 2 North No No Marion 2 Central No No Marion 2 Central No No Putnam 2 North No No Alachua 2 North No No Levy 2 North No No Alachua 2 North No No Dixie 2 North No No Marion 2 Central No No Levy 2 North No No Marion 2 Central No No Dixie 2 North No No Gilchrist 2 North No No Alachua 2 North No No Levy 2 North No No Union 2 North No No Seminole 2 Central No Yes Lake 2 Central No No Orange 2 Central No No Orange 2 Central No No Volusia 2 Central No No Seminole 2 Central No Yes 236

254 Seminole 2 Central No Yes Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Volusia 2 Central No No Seminole 2 Central No Yes Seminole 2 Central No Yes Seminole 2 Central No Yes Seminole 2 Central No Yes Seminole 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Lake 2 Central No No Lake 2 Central No No Volusia 2 Central No No Seminole 2 Central No Yes Seminole 2 Central No Yes Seminole 2 Central No Yes Lake 2 Central No No Lake 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Volusia 2 Central No No Seminole 2 Central No Seminole 2 Central No Yes Seminole 2 Central No Yes Seminole 2 Central No Yes Orange 2 Central No No Seminole 2 Central No Yes Volusia 2 Central No No Brevard 2 Central No Yes Lake 2 Central No No Lake 2 Central No No Volusia 2 Central No Yes Seminole 2 Central No Yes Volusia 2 Central No No Volusia 2 Central No No Seminole 2 Central No Yes Seminole 2 Central No Yes 237

255 Lake 2 Central No No Orange 2 Central No No Seminole 2 Central No Yes Seminole 2 Central No Yes Seminole 2 Central No Yes Volusia 2 Central No No Brevard 2 Central No Yes Lake 2 Central No No Orange 2 Central No No Lake 2 Central No No Seminole 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Lake 2 Central No No Orange 2 Central No No Orange 2 Central No No Seminole 2 Central No Yes Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Seminole 2 Central No Yes Brevard 2 Central No Yes Orange 2 Central No No Seminole 2 Central No Yes Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Brevard 2 Central No Yes Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No 238

256 Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No Orange 2 Central No No 239

257 Orange 2 Central No No Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No No Brevard 2 Central No No Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Indian River 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No Yes Brevard 2 Central No No Brevard 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Brevard 2 Central No Yes Indian River 2 Central No Yes 240

258 Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Indian River 2 Central No Yes Brevard 2 Central No Yes Indian River 2 Central No Yes Monroe 3 Keys No Yes Miami-Dade 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes 241

259 Miami-Dade 3 South Yes Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Miami-Dade 3 South Yes Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Monroe 3 Keys No Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Monroe 3 Keys No Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Miami-Dade 3 South Yes Yes 242

260 Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes 243

261 Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes 244

262 Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Miami-Dade 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes 245

263 Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes 246

264 Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Hendry 3 Central No No Broward 3 South Yes Yes Broward 3 South Yes Yes Broward 3 South Yes Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Martin 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Glades 2 Central No No 247

265 Palm Beach 3 South No Yes Martin 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Palm Beach 3 South No Yes Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Sumter 2 Central No No Sumter 2 Central No No Sumter 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Pasco 2 Central No No Sumter 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No 248

266 Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No Yes Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Pasco 2 Central No No Hillsborough 2 Central No No Pasco 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Sumter 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Pasco 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Sumter 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No 249

267 Hillsborough 2 Central No No Hillsborough 2 Central No Yes Hillsborough 2 Central No Yes Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No Yes Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No Yes Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No 250

268 Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Hillsborough 2 Central No No Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes 251

269 Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Highlands 2 Central No No Highlands 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Hardee 2 Central No No 252

270 Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Osceola 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Highlands 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Highlands 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Highlands 2 Central No No Polk 2 Central No No Hardee 2 Central No No Polk 2 Central No No Polk 2 Central No No Highlands 2 Central No No Highlands 2 Central No No Highlands 2 Central No No Hardee 2 Central No No Highlands 2 Central No No Highlands 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No 253

271 Polk 2 Central No No Hardee 2 Central No No Polk 2 Central No No Polk 2 Central No No Polk 2 Central No No Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No No Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No No Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No No Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Charlotte 3 Central No Yes Lee 3 Central No Yes Hendry 3 Central No No Lee 3 Central No Yes Lee 3 Central No Yes Hendry 3 Central No No Lee 3 Central No No Charlotte 3 Central No Yes Glades 2 Central No No Lee 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No Yes 254

272 Charlotte 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Highlands 2 Central No No Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No No Lee 3 Central No No Hendry 3 Central No No Charlotte 3 Central No Yes Charlotte 3 Central No Yes Charlotte 3 Central No No Charlotte 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Lee 3 Central No Yes Collier 3 Central No Yes 255

273 Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Miami-Dade 3 South Yes Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Collier 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No No Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Sarasota 3 Central No Yes Charlotte 3 Central No Yes Manatee 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes 256

274 Sarasota 3 Central No Yes Sarasota 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No No Manatee 3 Central No Yes Manatee 3 Central No Yes DeSoto 2 North No No DeSoto 2 North No No DeSoto 2 North No No DeSoto 2 North No No DeSoto 2 North No No Manatee 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Manatee 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Sarasota 3 Central No Yes Marion 2 Central No No Marion 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No 257

275 Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Levy 2 North No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Citrus 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Sumter 2 Central No No Citrus 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Marion 2 Central No No Levy 2 North No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No 258

276 Pasco 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Hernando 2 Central No No Pasco 2 Central No No Pasco 2 Central No Yes Pasco 2 Central No Yes Pasco 2 Central No No Pasco 2 Central No Yes Pasco 2 Central No No Pinellas 3 Central No Yes Hernando 2 Central No No Pasco 2 Central No Yes Pasco 2 Central No Yes Pasco 2 Central No No Pasco 2 Central No No Pasco 2 Central No No Pinellas 3 Central No Yes Pasco 2 Central No No Pasco 2 Central No No Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pasco 2 Central No Yes Pasco 2 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Pinellas 3 Central No Yes Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No Orange 2 Central No No Lake 2 Central No No Lake 2 Central No No Osceola 2 Central No No 259

277 Orange 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No Osceola 2 Central No No Polk 2 Central No No Orange 2 Central No No Orange 2 Central No No Lake 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Osceola 2 Central No No Orange 2 Central No No Orange 2 Central No No Sumter 2 Central No No Orange 2 Central No No Orange 2 Central No No Lake 2 Central No No Lake 2 Central No No Lake 2 Central No No St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes Martin 3 South No Yes Martin 3 South No Yes 260

278 Martin 3 South No Yes Okeechobee 2 Central No Yes Okeechobee 2 Central No Yes Okeechobee 2 Central No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes St. Lucie 2 South No Yes Martin 3 South No Yes Martin 3 South No Yes Martin 3 South No Yes Martin 3 South No Yes Martin 3 South No Yes Martin 3 South No Yes Martin 3 South No Yes 261

279 Appendix E ISO Structural Types 262

280 Construction Type Frame Joisted Masonry Non- Combustible Masonry Non- Combustible Modified Fire Resistive Fire Resistive Heavy Timber Joisted Masonry Superior Non- Combustible Superior Masonry Non- Combustible Masonry Veneer Unknown Description Buildings where the exterior walls are wood or other combustible materials, including construction where the combustible materials are combined with other materials such as brick veneer, stone veneer, wood iron-clad and stucco on wood Buildings where the exterior walls are constructed of masonry materials such as adobe, brick, concrete, gypsum block, hollow concrete block, stone, tile or similar materials and where the floor and roof are combustible. Buildings where the exterior walls and the floors and roof are constructed of, and supported by, metal, asbestos, gypsum or other non-combustible materials. (Other than constructions defined by the description for Code 8. Buildings where the exterior walls are constructed of masonry materials as described in Code 2 with the floors and roof of metal or other non-combustible materials. (Other than constructions defined by the description for Code 9. Buildings where the exterior walls and the floors and roof are constructed of masonry or fire resistive materials with a fire rating of one hour or more but less than two hours Buildings where the exterior walls and floors and roof are constructed of masonry or fire resistive materials having a fire resistance rating of not less than two hours Joisted Masonry construction where the following additional conditions exist: Roof Deck has a minimum thickness of 2 inches with roof supports having a minimum dimension of 6 inches, or roof assembly is documented to have a UL wind uplift classification of 90 or equivalent Non-combustible construction where the following additional conditions exist: Floors and roof constructed of 2 inches of masonry on steel supports, or documented to be constructed of 22 gauge metal or heavier on steel supports, or documented to have a wind uplift classification of 90 or equivalent. Masonry non-combustible construction where the following additional conditions exist: Floors and roof constructed of 2 inches of masonry on steel supports, or documented to be constructed of 22 gauge metal or heavier on steel supports, or documented to have a wind uplift classification of 90 or equivalent. Buildings with exterior walls of combustible construction veneered with brick, masonry, or stone. Unknown commercial or residential construction 263

281 Mobile Home - Fully Tied Down, manufactured before 7/13/94 Mobile Home - Fully Tied Down, manufactured on or after 7/13/94 Mobile Home Partially Tied Down Mobile Home - Not Tied Down Mobile Home - Unknown Mobile/Manufactured Housing which has anchors and tie-downs as required by Section , Florida Statutes. Mobile/Manufactured Housing which has anchors and tie-downs as required by Section , Florida Statutes. Mobile/Manufactured Housing which is exempt from Section , Florida Statutes, and has anchors and tie-downs. These units shall meet the Department of Highway Safety and Motor Vehicles minimum standards for the manufacture or installation of anchors, tie-downs, over-the-roof ties, or other reliable methods of securing when over-the-roof ties are not suitable due to factors such as unreasonable cost, design, or potential damage to the unit. These devices, when properly installed, shall cause the unit to resist overturning or sliding from the force of wind. Known that the mobile home is not tied down. Unknown if the mobile home is tied down, or nature of the tie-downs is unknown. 264

282 Code ISO Construction Classification Construction Type 1 Frame Timber 2 Jointed Masonry and Reinforced Masonry Masonry 3 Non-Combustible Other 4 Masonry Non-Combustible Other 5 Modified Fire Resistive Other 6 Fire Resistive Other 7 Heavy Timber Jointed Masonry Masonry 8 Superior Non-Combustible Other 9 Superior Masonry Non-Combustible Other 10 Masonry Veneer Timber 11 Unknown Other 12 Mobile Home-Fully tied down, Manufactured before 7/13/94 Mobile Home 13 Mobile Home-Fully tied down, Manufactured on or after 7/13/94 Mobile Home 14 Mobile Home- Partially tied down Mobile Home 15 Mobile Home- Not tied down Mobile Home 16 Mobile Home unknown Mobile Home Code Construction Classification Construction Type 1 BRICK STONE OR MASONRY Masonry 2 BRICK STONE OR MASONRY VENEER Timber 3 CONCRETE BLOCK OR TILE Masonry 4 FIRE RESISTIVE OR FIRE PROOF Other 5 FOUNDATION / CHASSIS TIE-DOWN Mobile Home 6 FOUNDATION / FULL TIE-DOWN Mobile Home 7 FOUNDATION / NO TIE-DOWN Mobile Home 8 FRAME - MODULAR/PREFAB CONSRUCTION Other 9 FRAME NOT OTHERWISE CLASSIFIED Timber 10 FRAME W/ ALUMINUM OR PLASTIC SIDING Timber 11 FRAME W/ ASBESTOS OR STUCCO SIDING Timber 12 NO FOUNDATION / CHASSIS TIE-DOWN Mobile Home 13 NO FOUNDATION / FULL TIE-DOWN Mobile Home 14 NO FOUNDATION / NO TIE-DOWN Mobile Home 265

283 Code Construction Classification Construction Type 1 UNKNOWN Other 2 ALUMIN. SIDING Other 3 FIRE RESISTIVE Other 4 FRAME Timber 5 MASONRY Masonry 6 MASONRY VENEER Timber Code Classification Construction Classification Construction Type 1 FRM Frame Timber 2 MAS Masonry Masonry 3 MIX Mixed Other 4 RM Reinforced Masonry Masonry 5 SWR Semi-Wind resistive Other 6 WR Wind resistive Other 7 Other 266

284 Appendix F Use Cases The use cases presented in this appendix were created to fulfill the Florida Commission on Hurricane Loss Projection Methodology documentation requirements. They provide a summary of the methods described in the body of the thesis along with programming details. 267

285 F.1 Subassembly Replacement Ratio for Residential Homes Use Case Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.1.1 Summary All homes are comprised of several typical subassemblies. These include: roof sheathing and cover, trusses (connections), exterior walls, windows, doors, garage, gable ends (if gable roof), interior, mechanical, electrical, plumbing, wall sheathing (for wood homes), and the foundation. The cost of each of these subassemblies constructed in a new home is determined using unit costs obtained from the 2004 National Renovation & Insurance repair Estimator. The square footages and unit information (number of windows, doors, etc.) is based upon the home types modeled by the Monte Carlo simulations. The cost of constructing a new home is determined by summing the costs of constructing each subassembly. To determine the subassembly replacement ratio for any particular assembly, the removal costs are added to the new construction cost and divided by the cost of constructing a complete new home. The subassembly replacement ratio represents the cost of replacing a particular assembly divided by the cost of constructing a new home. F.1.2 References 2004 National Renovation & Insurance repair Estimator CEIA Cost 2002 F.1.3 Implementation Input Costing Data Modeled home information Steps a) Define the building and living areas, and the information for each home type: %% For Concrete Homes %% List Roof Area for homes in each Region (ft^2) % For South Florida Region(1,1)=3072; % For Central Florida Region(1,2)=3072; 268

286 % For North Florida Region(1,3)=2520; %% List Building Areas for homes in each region % For South Region(2,1)=2640; % For Central Region(2,2)=2640; % For North Region(2,3)=2128; %% List Living Area for homes in each region for i=1:3; Region(3,i)=Region(2,i)-400; b) Define unit costs for new construction of each subassembly: % Cost of foundation ($/ft^2) foundation=2.99; % Costs of roof and wall sheathing ($/ft^2) sheathing=1.42; remove_sheathing=0.37; % Cost of roof cover ($/ft^2) shingle=1.96; remove_shingle=0.29; tile=5.03; remove_tile=0.99; c) Multiply unit information by the new construction unit cost: 3072 (ft^2) x 1.96 ($/ft^2) = $6,021 - the cost of constructing a shingle roof d) Sum the new construction unit costs to determine the new home construction cost: Appendix Table 13 - New construction costs Sheathing $ 4,362 Cover $ 6,021 Trusses $ 9,155 Exterior Walls $ 26,136 Windows (with or w/o shutters) $ 6,525 Entrance Door and Sliding Back Door $ 1,404 Garage $ 1,484 Gable Ends $ - Interior $ 35,168 Mechanical $ 8,086 Electrical $ 8,333 Plumbing $ 10,461 Foundation $ 9,185 Wall Sheathing $ - Total $ 126,320 e) Determine replacement costs for each subassembly, the cost of new construction plus removal costs: 269

287 3072 (ft^2) x (1.96 ($/ft^2) ($/ft^2)) = $6,912 - the cost of replacing a shingle roof f) Divided the replacement cost of each subassembly by the new home construction cost $6,912 / $126,320 = 5.5% replacement ratio for shingle roof g) Repeat this process for each home type modeled and considering typical variations in construction materials (shingle or tile roof, windows with or without shutters): Appendix Table 14 - Replacement ratios Construction Type Concrete Block Concrete Block Concrete Block Concrete Block Region South South South South Roof Type Hip Hip Hip Hip Tile or Shingle Tile Tile Tile Shingle Subregion Neither WBDR HVHZ Neither Sheathing 4% 4% 4% 4% Cover 13% 13% 13% 5% Trusses 10% 10% 10% 9% Exterior Walls 24% 23% 23% 26% Windows (with or w/o shutters) 5% 7% 7% 5% Entrance Door and Sliding Back Door 1% 1% 1% 1% Garage 1% 1% 1% 1% Gable Ends 0% 0% 0% 0% Interior 32% 31% 31% 35% Mechanical 6% 6% 6% 7% Electrical 8% 8% 8% 9% Plumbing 10% 9% 9% 10% Wall Sheathing 0% 0% 0% 0% Total 114% 113% 113% 113% h) Save the replacement ratio data in a matrix named after the region save south 'south' save north 'north' save central 'central' Note: When this information is recalled the command: S = eval(filename); is used, filename is an input required at the beginning of the program to identify the region for which the vulnerability is being calculated. 270

288 F.2 Subassembly Replacement Ratio for Manufactured Homes Use Case Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.2.1 Summary The procedure for calculating the replacement ratios for manufactured homes is identical to the process used for residential homes; see Subassembly Replacement Ratio for Residential Homes Use Case. The only differences are in the square footages of the homes and in some of the unit costs of the components. F.2.2 References 2004 National Renovation & Insurance repair Estimator F.2.3 Implementation Input Costing Data Modeled home information Programming Steps i) Define the building areas, and the lengths of each home type: %% Bldg and Roof Area for each manuf home type % For Single Wides Area(1,1)=13*56; % For Double Wides Area(1,2)=26*56; %% Bldg and Roof lengths % For Single Wides Area(2,1)=2*(13+56); % For Double Wides Area(2,2)=2*(26+56); j) Define unit costs for new construction of each subassembly: % Cost of foundation ($) foundation_1=589.00; foundation_2=785.00; % Costs of roof and wall sheathing ($/ft^2) sheathing=1.42; 271

289 remove_sheathing=0.37; vinyl=0.86; remove_vinyl=0.32; % Cost of roof cover ($/ft^2) cover=1.96; remove_cover=0.29; % Cost of new trusses and connections ($), assume 14' 24" o.c. gable_truss= ; remove_truss=119.56; % Cost of new exterior walls ($/lf), assume 2"x6" wall=25.90; remove_wall=1.32; % Cost of new windows ($/each) windows=115.00; remove_windows=9.83; shutters=35.00; remove_shutters=2.30; % Cost of new front entrance and back sliding doors ($) doors= ; remove_doors=75.0; % Cost of new interior ($/ft^2) interior=15.70; remove_interior=4.05; % Cost of new mechanical ($/ft^2) mechanical=3.61; remove_mechanical=0.20; % Cost of electrical ($/ft^2) electrical=3.72; remove_electrical=1.25; % Cost of plumbing ($/ft^2) plumbing=4.67; remove_plumbing=1.25; k) Multiply unit information by the new construction unit cost: 728 (ft^2) x 1.96 ($/ft^2) = $1,427 - the cost of roof cover l) Sum the new construction unit costs to determine the new home construction cost: 272

290 Appendix Table 15 - New Manufactured home costs Single Wide Double Wide Windows $ 920 $ 1,150 Doors $ 630 $ 630 Roof Sheathing $ 1,034 $ 2,068 Roof Cover $ 1,427 $ 2,854 Wall Sheathing and Siding $ 1,660 $ 3,320 Trusses $ 1,383 $ 2,766 Interior $ 11,430 $ 22,859 Mechanical $ 2,628 $ 5,256 Electrical $ 2,708 $ 5,416 Plumbing $ 3,400 $ 6,800 Foundation $ 589 $ 785 Wall Framing $ 3,574 $ 4,248 Total $ 31,382 $ 58,151 m) Determine replacement costs for each subassembly, the cost of new construction plus removal costs: 728 (ft^2) x ( ) ($/ft^2) = $1,638 - the cost of roof cover n) Divided the replacement cost of each subassembly by the new home construction cost $1,638/$31,382 = 5.2% o) Repeat this process for each home type modeled (single and double wide): Appendix Table 16 - Manufactured Home replacement ratios Single Wide Double Wide Windows 3% 2% Doors 2% 1% Roof Sheathing 4% 4% Roof Cover 5% 6% Wall Sheathing and Siding 7% 7% Trusses 5% 5% Interior 46% 49% Mechanical 9% 10% Electrical 12% 12% Plumbing 14% 15% Total 106% 112% 273

291 F.3 Interior Damage for Residential and Manufactured Homes Use Case Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.3.1 Summary The most significant portion of a homes value is made up by the interior. Appendix Table 14, lists the replacement ratios for a typical home, it can be seen that the single largest ratio is the interior. As explained in the subassembly replacement ratio document, the percentages in Appendix Table 14 add up to more than 100% because they represent the cost of replacing a subassembly divided by the cost of constructing a new home of this type, additional costs are incurred when replacing a damaged component is required. The interior of a home is comprised of the kitchen, carpets/flooring, interior walls, ceiling, painting, interior doors, and insulation. The percentage that each of these components contributes to the total value is listed in Appendix Table 18. Currently, the Monte Carlo simulations only model damage to the exterior components of a home, leaving the majority of the value unaccounted for. Obviously, to accurately predict losses experienced in the event of a hurricane, damage to the interior of a home must be estimated as well. To do this, equations that relate damage of modeled components to interior losses are developed. 274

292 Appendix Table 17 - Replacement ratios for a typical home Construction Type Concrete Block Region South Roof Type Hip Tile or Shingle Tile Subregion Neither Sheathing 4% Cover 13% Trusses 10% Exterior Walls 24% Windows (with or w/o shutters) 5% Entrance Door and Sliding Back Door 1% Garage 1% Gable Ends 0% Interior 32% Mechanical 6% Electrical 8% Plumbing 10% Wall Sheathing 0% Total 114% Appendix Table 18 - Value of interior components in a typical home Interior Component % of Value Kitchen 15% Carpets/Flooring 15% Interior Walls 34% Ceiling 30% Painting 3% Interior Doors 2% Insulation 1% Total 100% The equations that relate modeled losses and interior damage are derived from engineering judgment, based on the physics of the problem. For each modeled exterior component, at several different percentages of damage, the likely corresponding losses of each interior component are estimated. The total interior loss is computed by multiplying the estimated percent damage of each interior component by its percentage of the total value. The interior losses are plotted vs. the percentage of the component damage and a curve is fit to the data points. This process is shown in Appendix Table

293 Appendix Table 19 - Derivation of sheathing interior damage equation Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 10% 15% % Sheathing Loss Carpets/Flooring 75% 15% 11% 25% Interior Walls 15% 34% 5% Ceiling 50% 30% 15% Painting 20% 3% 1% Interior Doors 30% 2% 1% Insulation 100% 1% 1% Total 100% 35% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 25% 15% % Sheathing Loss Carpets/Flooring 100% 15% 15% 50% Interior Walls 35% 34% 12% Ceiling 75% 30% 23% Painting 100% 3% 3% Interior Doors 50% 2% 1% Insulation 100% 1% 1% Total 100% 58% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 100% 15% % Sheathing Loss Carpets/Flooring 100% 15% 15% 75% Interior Walls 100% 34% 34% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 100% Envelope Breach Interior Component % Damaged % of Value % of Interior Value Lost Sheathing Kitchen 100% 15% % Sheathing Loss Carpets/Flooring 100% 15% 15% 100% Interior Walls 100% 34% 34% Ceiling 100% 30% 30% Painting 100% 3% 3% Interior Doors 100% 2% 2% Insulation 100% 1% 1% Total 100% 100% 100% Sheathing 90% 80% 70% y = x % Interior Loss 60% 50% 40% 30% 20% 10% 0% 0% 20% 40% 60% 80% 100% % Component Loss Appendix Figure 1 - Interior damage equation for sheathing loss 276

294 Clearly, there is much uncertainty involved with predicting these damages. To account for this a random variable generated from a Weibull distribution with a mean=1 and variance= is multiplied by the equation. Since the mean of the distribution is equal to one, the product of this results in interior damage with a mean defined by the equation and having a distribution defined by the parameters of the Weibull distribution. The distribution was estimated based on engineering judgment. Appendix Figure 2- Interior damage as a function of sheathing damage, no random distribution (mean values) Appendix Figure 3- Interior damage as a function of sheathing damage using Weibull distribution, mean=1 variance=

295 This process is repeated for each modeled component that results in a breach of envelope that may allow rain to penetrate the interior of the home. These components include exterior doors, roof cover, roof sheathing, walls, gable ends, and windows. The total loss to the interior is the maximum value given by any of these equations. The maximum value is used so that interior damage is not accounted for twice. All the interior equations used by the program, before the Weibull distribution is applied are listed below: Appendix Table 20 - Interior damage equations Modeled Component Roof sheathing: Roof cover: Walls or wall sheathing: Windows: Doors: Gable Ends: y=% interior damage x=% component damage Interior Equation y=1.29*x y=0.62*x^2-0.2*x y=7.91*x^3-8.70*x^ *x y=0.39*x^ *x^2 y=0.26*x y=0.38*x^ *x For manufactured homes minor sliding is assumed to result on average in 5% interior damage and major sliding, 30%. The same Weibull distribution is applied to these values. Also, overturning on average is assumed to cause 75% interior damage with the same distribution. F.3.2 References 2004 National Renovation & Insurance repair Estimator HAZUS Wind Loss Estimation Methodology F.3.3 Implementation Input Monte Carlo Simulation Data Programming Steps p) Convert the Monte Carlo simulation data into percentages of each component lost: % Convert Monte Carlo Damage Values into percentages DP=[D(:,1)/100, D(:,2)/100, D(:,3)/100, D(:,4)/4, D(:,5)/15, D(:,6)/2, D(:,7), D(:,9)/15, D(:,10)/100, D(:,12)/100]; 278

296 DP(a,1)=%sheathing loss DP(a,2)=%cover loss DP(a,3)=%connection loss DP(a,4)=%wall loss DP(a,5)=%window loss (total) DP(a,6)=%doors loss DP(a,7)=%garage loss DP(a,8)=%windows loss (due to impact) DP(a,9)=%gable end loss DP(a,10)=%wall sheathing loss q) Compute Weibull variables: %%%%% Calculate Weibull Distribution Parameters per wind speed B(1,ii)=2; A(1,ii)=(1/gamma(1+B(1,ii)^-1))^-B(1,ii); %% Compute Random Weibull Variables R(a,ii)=weibrnd(A(1,ii),B(1,ii)); r) Calculate Interior Loss as a function of % damage to each modeled component (breach of envelope): note: to facilitate changes to these equations the coefficients are listed first %% Coefficients %% For Sheathing a1=0; b1=0; c1=1.29; %% For Cover a2=.62; b2=-.02; c2=0; %% For Walls a3=7.91; b3=-8.70; c3=4.21; %% For Windows a4=.39; b4=.31; c4=0; %% For Doors a5=0; b5=.26; c5=0; %% For Gable Ends a6=.38; b6=.23; c6=0; %%%%%%%%%%%%%%%%%%%%%%%% if datenum==3; %% for 2 story homes increase interior damage by k2 k2=1.1; 279

297 else k2=1.0; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Function of Sheathing eq1(a,1)=(a1*(dp(a,1))^3+b1*dp(a,1)^2+c1*dp(a,1))*k2; Int(a,1)=(R(a,ii)*eq1(a,1)); if Int(a,1)>=1.0; Int(a,1)=1.0; end if Int(a,1)<=0.001; Int(a,1)=0; end % Function of Cover eq2(a,1)=(a2*dp(a,2)^2+b2*dp(a,2)+c2)*k2; Int(a,2)=(R(a,ii)*eq2(a,1)); if Int(a,2)>=1.0; Int(a,2)=1.0; end if Int(a,2)<=0.001; Int(a,2)=0; end %%%%%%%%%%%%%%%%%%%%%%%%%% % Function of Walls eq3(a,1)=(a3*dp(a,4)^3+b3*dp(a,4)^2+c3*dp(a,4))*k2; Int(a,3)=(R(a,ii)*eq3(a,1)); if Int(a,3)>=1.0; Int(a,3)=1.0; end if Int(a,3)<=0.001; Int(a,3)=0; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Function of Windows eq4(a,1)=(a4*dp(a,5)^2+b4*dp(a,5)+c4)*k2; Int(a,4)=(R(a,ii)*eq4(a,1)); if Int(a,4)>=1.0; Int(a,4)=1.0; end if Int(a,4)<=0.001; Int(a,4)=0; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Function of Doors eq5(a,1)=(a5*dp(a,6)^2+b5*dp(a,6)+c5)*k2; Int(a,5)=(R(a,ii)*eq5(a,1)); 280

298 if Int(a,5)>=1.0; Int(a,5)=1.0; end if Int(a,5)<=0.001; Int(a,5)=0; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Function of Gabel Ends eq6(a,1)=(a6*dp(a,9)^2+b6*dp(a,9)+c6)*k2; Int(a,6)=(R(a,ii)*eq6(a,1)); if Int(a,6)>=1.0; Int(a,6)=1.0; end if Int(a,6)<=0.001; Int(a,6)=0; end s) Determine the maximum interior loss calculated from these equations: % Compute Total Interior Damage IntTotal(a,1)=max([Int(a,1) Int(a,2) Int(a,3) Int(a,4) Int(a,5) Int(a,6)]); 281

299 F.4 Utilities Damage Use Case for Residential and Manufactured Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.4.1 Summary Similar to the interior, the utilities (plumbing, electrical, and mechanical systems) make up a significant portion of a homes cost and yet are not modeled by the Monte Carlo simulations to predict potential losses. Damage to the utilities of a home is assumed to occur at a rate slower than damage to the interior. So to predict damage to each of the utility systems the equation used to predict interior losses is multiplied by some factor k, estimated by engineering judgment. Again, the value used for computing total losses is the maximum value obtained from all equations. The k values being used by the model for residential homes are: ke(for electrical)= 0.5, kp(for plumbing)= 0.35, and km(for mechanical)=0.4. For manufactured homes, because of possibly lower quality construction, it is assumed that utility damage will occur at a slightly faster rate and therefore the k values are increased accordingly. Again, like the interior equations the same Weibull distribution is applied to account for uncertainties. Appendix Figure 4- Electrical damage vs. sheathing damage 282

300 F.4.2 Implementation Input Monte Carlo Simulation Data Programming Steps t) Convert the Monte Carlo simulation data into percentages of each component lost: % Convert Monte Carlo Damage Values into percentages DP=[D(:,1)/100, D(:,2)/100, D(:,3)/100, D(:,4)/4, D(:,5)/15, D(:,6)/2, D(:,7), D(:,9)/15, D(:,10)/100, D(:,12)/100]; DP(a,1)=%sheathing loss DP(a,2)=%cover loss DP(a,3)=%connection loss DP(a,4)=%wall loss DP(a,5)=%window loss (total) DP(a,6)=%doors loss DP(a,7)=%garage loss DP(a,8)=%windows loss (due to impact) DP(a,9)=%gable end loss DP(a,10)=%wall sheathing loss u) Calculate Interior Loss as a function of % damage to each modeled component (breach of envelope): See interior use case % Function of Sheathing eq1(a,1)=(a1*(dp(a,1))^3+b1*dp(a,1)^2+c1*dp(a,1))*k2; Int(a,1)=(R(a,ii)*eq1(a,1)); if Int(a,1)>=1.0; Int(a,1)=1.0; end if Int(a,1)<=0.001; Int(a,1)=0; end v) Multiply the previously defined interior equations by the k factor to determine the percentage of utilities damage resulting from damage to each modeled component: %% Apply Electrical Equations % Function of Sheathing Elec(a,1)=ke*(Re(a,ii)*eq1(a,1)); if Elec(a,1)>=1.0; Elec(a,1)=1.0; end if Elec(a,1)<=0.001; Elec(a,1)=0; end 283

301 w) Determine the maximum utility loss calculated from these equations: % Compute Total Electrical Damage ElecTotal(a,1)=max([Elec(a,1) Elec(a,2) Elec(a,3) Elec(a,4) Elec(a,5) Elec(a,6)]); x) Repeat the process for mechanical and plumbing systems. 284

302 F.5 Building Damage Use Case for Residential Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.5.1 Summary The percentage of damage to each building component modeled by the Monte Carlo Simulation and the estimated percentage of interior and utilities damage are multiplied by their corresponding replacement ratios, for each structural type considered, and the result is summed to determine the building damage ratio for each model simulation. The building damage ratio is the repair costs of a structure expressed as a percentage of the building value. Once the building damage ratio is computed for each model simulation the results are saved in a vulnerability matrix. The vulnerability matrix is the probability of a particular state of damage occurring at a given wind speed. For each building type modeled by the Monte Carlo Simulation six vulnerability matrixes are created. The modeled building types include all combinations of: masonry and wood homes, in South, Central, and North Florida, with or without storm shutters, with a gable or hip roof. The cost estimation model then considers each of these types with either shingle or tile roof, in a windborne debris region, high velocity hurricane zone (Miami-Dade and Broward counties), or not in a sub-region. Obviously, the cost of replacing a shingle roof is less than a tile roof, and in the wbdr and hvhz the Florida building code requires more stringent requirements for the replacement of windows and roofing. The differences in the replacement ratios are explained in the Subassembly Replacement Ratio for Residential Homes Use Case. In the windborne debris region and high velocity zone the cost of shutters is included in the replacement cost of the windows since they are required by the FBC. Also, in these regions if 50% or greater of the windows are damaged all must be replaced. An additional requirement is placed on roofing in the high velocity zone, if 25% or greater of the roof cover or roof sheathing is damaged all must be replaced. In the other sub-regions this threshold is 35%. F.5.2 References 2004 National Renovation & Insurance repair Estimator Florida Building Code F.5.3 Implementation Input Monte Carlo Simulation Data Programming Steps 285

303 y) Calculate replacement ratio data for each home type - see Subassembly Replacement Ratio for Residential Homes Use Case z) Estimate interior damage - see Interior Damage for Residential Homes Use Case aa) Estimate utilities damage see Utilities Damage Use Case for Residential and Manufactured Homes bb) Apply thresholds based on Florida Building Code Requirements %% Adjust Damage Percentages/Apply Thresholds % Windows % In Windborne Debris region or High Velocity Hurricane Zone if DP(a,5)>=0.5; WindAdj(a,1)=1.0; else WindAdj(a,1)=DP(a,5); end % Not in Windborne Debris Region or meets age requirements WindAdj(a,2)=DP(a,5); % Roof Cover % In High Velocity Hurricane Zone if DP(a,2)>=.25; CoverAdj(a,1)=1.0; else CoverAdj(a,1)=DP(a,2); end % Not in High Velocity Hurricane Zone or meets age requirements if DP(a,2)>=.35; CoverAdj(a,2)=1.0; else CoverAdj(a,2)=DP(a,2); end % Roof Sheathing % In High Velocity Hurricane Zone if DP(a,1)>=.25; SheathAdj(a,1)=1.0; else SheathAdj(a,1)=DP(a,1); end % Not in High Velocity Hurricane Zone or meets age requirements if DP(a,1)>=.35; SheathAdj(a,2)=1.0; else SheathAdj(a,2)=DP(a,1); End cc) For each home type, multiply the adjusted percentage damage of each subassembly by its corresponding replacement ratio and sum the results 286

304 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Convert Physical Damage into Monetary Damage for b=1:24; for n=1:8; if b==3*n; c=1; else c=2; end if b==3*n-2; d=2; else d=1; end BuildingDamage(a,b)=SheathAdj(a,c)*S(1,b)+CoverAdj(a,c)*S(2,b)+DP(a,3)*S(3,b)+DP(a,4)* S(4,b)+WindAdj(a,d)*S(5,b)+DP(a,6)*S(6,b)+DP(a,7)*S(7,b)+DP(a,9)*S(8,b)+DP(a,10)*S(13,b)+ IntTotal(a,1)*S(9,b)+MechTotal(a,1)*S(10,b)+ElecTotal(a,1)*S(11,b)+PlumTotal(a,1)*S(12,b) end end dd) Depending on the modeled home type select the vulnerability matrices to create ee) %% Building Vulnerability Matrixes %% Check Home Type concrete or wood if type==1; x=1; else x=7; end %% Check if gable or hip roof if roof_type=='h'; x=x; else x=x+12; end % VM, tile, neither if BuildingDamage(a,x)==0.0; Compute the vulnerability matrices for tile and shingle in each sub-region 287

305 F.6 Building Damage Use Case for Manufactured Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.6.1 Summary The total building damage ratio of a modeled manufactured home is computed the same way as for residential homes, see Building Damage Use Case for Residential Homes. However, to simplify the process the regions are not divided into sub-regions and only the typical materials are considered (no separation of tile and shingle roof). In the same way as for residential homes, thresholds are applied to window, cover, and sheathing loss. The estimated interior, utilities, and adjusted component losses are multiplied by the corresponding replacement ratios to determine the total building damage ratio. The building damage ratio is the repair costs of a structure expressed as a percentage of the building value. F.6.2 References 2004 National Renovation & Insurance repair Estimator Florida Building Code F.6.3 Implementation Input Monte Carlo Simulation Data Programming Steps ff) Calculate replacement ratio data for each home type - see Subassembly Replacement Ratio for Manufactured Homes Use Case gg) Estimate interior damage - see Interior Damage for Manufactured Homes Use Case hh) Estimate utilities damage see Utilities Damage Use Case for Residential and Manufactured Homes ii) Apply thresholds based on Florida Building Code Requirements %% Adjust Damage Percentages/Apply Thresholds % Windows 288

306 % If Greater than 50% damaged replace all if DP(a,1)>=0.5; WindAdj(a,1)=1.0; else WindAdj(a,1)=DP(a,1); end % Roof Cover % If greater than 25% damaged replace all if DP(a,5)>=.25; CoverAdj(a,1)=1.0; else CoverAdj(a,1)=DP(a,5); end jj) % Roof Sheathing % If greater than 35% damaged replace all if DP(a,4)>=.35; SheathAdj(a,1)=1.0; else SheathAdj(a,1)=DP(a,4); end For each home type, multiply the adjusted percentage damage of each subassembly by its corresponding replacement ratio and sum the results %% For Single-post use column 1 of S matrix, single-pre column 2, %% double-post column 3, double-pre column 4 if type=='1' & PrePost==0; ll=1; elseif type=='1' & PrePost==1; ll=2; elseif type=='2' & PrePost==0; ll=3; else ll=4; end BuildingDamage(a,1)=WindAdj(a,1)*S(1,ll)+DP(a,3)*S(2,ll)+SheathAdj(a,1)*S(3,ll)+CoverAdj( a,1)*s(4,ll)+dp(a,6)*s(5,ll)+dp(a,7)*s(6,ll)+inttotal(a,1)*s(7,ll)+mechtotal(a,1)*s(8,ll)+electot al(a,1)*s(9,ll)+plumtotal(a,1)*s(10,ll); kk) Save the results in a Vulnerability Matrix 289

307 F.7 Contents Damage Use Case for Residential and Manufactured Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.7.1 Definition Contents includes just about anything in the home (including garage and outbuildings) belonging to the policyholder or a member of his family living in the same house, or to resident domestic servants. It also includes property, which is not owned by the policyholder but for which he is responsible, such as rented property. Furniture, furnishings, household goods, electrical appliances, food and drink, clothes, and money up to a specified limit all count as 'contents'. Also included are movable fixtures and fittings, for example, special lighting fittings which would be taken away on removal. Fittings, which would be left in the house, such as built-in furniture, count as part of the 'buildings', although fitted carpets are classed as 'contents'. Certain types of property are excluded. The cover applies principally to contents actually inside the home, although there is some cover under a 'standard' policy for contents temporarily away from the home. Some policies also include theft of household contents from the garden or immediate vicinity of the home. F.7.2 Summary A typical insurance policy covers contents of a home up to 50% of the insured value of the building. However, from a study of insurance policy files from several different companies it was observed that this value is not always used and the contents covered by a policy may not necessarily be the value of the contents contained within a home. For example, a home with an insured building value of $200,000 may have only $10,000 in contents coverage, or 5% coverage. It is likely that the contents of this home are valued at much greater than $10,000, so contents losses are estimated and validated based on a value of 50% of the building coverage, or $100,000 for this example. So if an estimate of 30% contents loss was made for this home, this means that there was a $30,000 loss of contents, which is greater than the $10,000 of coverage and therefore would be 100% loss. Also, there are many cases where an insurance policy covers contents of a home greater than 50% of the insured building value. For these cases we assume the value of the contents to be the value of coverage given in the policy. Like the interior and utilities, the Monte Carlo simulations to predict potential losses do not model the contents of a home. Contents losses are estimated in the same way as damage to the utility systems. The contents losses are assumed to occur at a rate of kc multiplied by the interior loss equation for each modeled component that causes a breach of the building envelope. The value of kc is estimated from engineering judgment and validated using actual claims data. The value currently being used for residential homes kc=0.35, and for manufactured homes kc=

308 Again, some random distribution must be applied to this relationship to account for uncertainties. However, given the importance of the contents in the overall estimate of insured losses, it was felt that a more sophisticated model was needed for the estimate of the variation of contents damage. In particular, it was felt that the distribution of the contents damage could be linked to the level of overall building damage, based on observations and common sense. To model this a Weibull distribution is still used but the β parameter is assumed to vary linearly between a maximum and minimum value as a function of total building damage ratio damage, instead of assuming a constant value of 2 for all cases as for the interior and utilities predictions.. Again, to maintain the mean values produced by the equations the α parameter of the Weibull distribution is calculated such that the mean of the distribution is equal to one. The maximum and minimum β parameters were selected based on engineering judgment and resulted in a good agreement with the claims data as will be seen later. A more rigorous calculation of these parameters could be an area for future improvement of the model. Currently, the maximum β parameter is set at 1.65 and the minimum is set at 0.5,Appendix Table 13 demonstrates how the Weibull distribution is defined for contents damage predictions. Appendix Table 21 - Calculation of Weibull distribution for content predictions Βmax = 1.65 Bmin = 0.5 DR = total building damage ratio (% - maximum = 100%, minimum =0) B = (Bmax - Bmin)*DR + Bmin A = (1/gamma(1+B^-1))^-B Rc = weibrnd(a,b) y = 1.29*x Cont=kc*Rc*y if Cont >= 1.0 Cont = 1.0 if Cont <= Cont = 0 B = Weibull beta parameter A = Weibull alpha parameter (calculated so that the mean of the distribution is equal to 1) Rc = Random Weibull variable (generated by Matlab using the function weibrnd by defining B and A) x = % sheathing damage y = mean % interior damage as a function of sheathing damage Rc = random Weibull variable (mean of the distribution equal to 1) Cont = % contents damage kc = contents coefficient (0.35) 291

309 F.7.3 Implementation Input Monte Carlo Simulation Data Use case for Contents Loss prediction Programming Steps ll) Convert the Monte Carlo simulation data into percentages of each component lost: % Convert Monte Carlo Damage Values into percentages DP=[D(:,1)/100, D(:,2)/100, D(:,3)/100, D(:,4)/4, D(:,5)/15, D(:,6)/2, D(:,7), D(:,9)/15, D(:,10)/100, D(:,12)/100]; DP(a,1)=%sheathing loss DP(a,2)=%cover loss DP(a,3)=%connection loss DP(a,4)=%wall loss DP(a,5)=%window loss (total) DP(a,6)=%doors loss DP(a,7)=%garage loss DP(a,8)=%windows loss (due to impact) DP(a,9)=%gable end loss DP(a,10)=%wall sheathing loss mm) Calculate Interior Loss as a function of % damage to each modeled component (breach of envelope): see interior use case % Function of Sheathing eq1(a,1)=(a1*(dp(a,1))^3+b1*dp(a,1)^2+c1*dp(a,1)); std1(a,1)=cov*eq1(a,1); Int(a,1)=(z(1,1)*std1(a,1)+eq1(a,1)); if Int(a,1)>=1.0; Int(a,1)=1.0; end if Int(a,1)<=0; Int(a,1)=0; end nn) Compute utilities damages: see utilities use case oo) Compute total building damage: see building damage use case pp) Compute parameters of the Weibull distribution based on the total building loss: 292

310 if BuildingDamage(a,x)>1; BDR(a,1)=1; else BDR(a,1)=BuildingDamage(a,x); end B2(a,1)=(Bmax-Bmin)*BDR(a,1)+Bmin; A2(a,1)=(1/gamma(1+B2(a,1)^-1))^-B2(a,1); Ra(a,1)=weibrnd(A2(a,1),B2(a,1)); Rc(a,1)=weibrnd(A2(a,1),B2(a,1)); qq) Multiply the previously defined interior equations by the k factor to determine the percentage of contents damage resulting from damage to each modeled component: rr) ss) % Function of Cover Cont(a,2)=kc*(Rc(a,1)*eq2(a,1)); if Cont(a,2)>=1.0; Cont(a,2)=1.0; end if Cont(a,2)<=0.001; Cont(a,2)=0; end Determine the maximum contents loss calculated from these equations: % Compute Total Contents Damage ContTotal(a,1)=max([Cont(a,1) Cont(a,2) Cont(a,3) Cont(a,4) Cont(a,5) Cont(a,6)]); Convert losses into a damage matrix determine the percentage of simulations falling within a given range of losses at each wind speed: Appendix Table 22 - Partial example of contents matrix 293

311 % % E E % % E % % E E % E E E % E-05 15% E E-05 17% E-05 19% % % E % % % % E % % E tt) From the vulnerability matrix calculate the vulnerability curve to determine the average loss ratio at each wind speed: 80 mph *0% *1% = % - average loss ratio at 80 mph 294

312 F.8 Additional Living Expenses for Residential and Manufactured Homes Use Case Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.8.1 Definition Additional Living Expense (ALE): This is found in the Farm Fire and Homeowners policies under Loss of Use, Coverage D. Additional Living Expense is coverage for the increase in living expenses that arise when an Insured must live away from the insured location due to a covered loss. Additional Living Expense Coverage covers only expenses actually paid by the Insured. This coverage does not pay all living expenses, only the increase in living expense that results directly from the covered loss, and having to live away from the insured location. If the covered loss does not make the residence unlivable, there will be no Additional Living Expense to claim. Coverage is provided for the shortest time required to repair the covered damage. F.8.2 Summary Additional living expenses are dependant on the time that a home is unlivable due to repairs. To predict ALE losses the time a home is unlivable based on the duration of repairs or rebuilding is estimated as a function of interior loss, Appendix Figure 5. For the ALE predictions some random distribution must also be applied to account for uncertainties in the repair time estimates as well as the variations in additional living costs. Since there is almost no data to validate the choice of any distribution type it is assumed that ALE costs will have a distribution that varies as a function of the total building damage ratio, as observations of claims data indicate. So based on engineering judgment the same linearly varying Weibull distribution applied to contents is applied to ALE. A typical insurance policy covers ALE losses up to 20% of the insured value of the home; all estimates and validation are based on this ratio. On average this is estimated to cover expenses for 365 days or 1 year. So to determine the percentage of ALE losses, the days that a home is unlivable due to repairs are divided by 365. The equation and methods used for manufactured and residential homes are identical. 295

313 Appendix Figure 5 - Time home is unlivable vs. Interior Damage Appendix Figure 6 - Modeled ALE damage vs. building damage F.8.3 Implementation Input Monte Carlo Simulation Data Programming Steps 296

314 uu) Predict total interior loss for each model simulation - as detailed in the Interior Damage for Residential Homes Use Case and the Interior Damage for Manufactured Homes Use Case. vv) Compute total building damage: see building damage use case ww) Compute parameters of the Weibull distribution based on the total building loss: if BuildingDamage(a,x)>1; BDR(a,1)=1; else BDR(a,1)=BuildingDamage(a,x); end B2(a,1)=(Bmax-Bmin)*BDR(a,1)+Bmin; A2(a,1)=(1/gamma(1+B2(a,1)^-1))^-B2(a,1); Ra(a,1)=weibrnd(A2(a,1),B2(a,1)); Rc(a,1)=weibrnd(A2(a,1),B2(a,1)); xx) Apply ALE equation to total interior loss: Dayseq(a,1)=1426.3*IntTotal(a,1)^ *IntTotal(a,1)^ *IntTotal(a,1)^ *IntTotal(a,1)+.1922; Days(a,1)=round(Days(a,1)); if Days(a,1)<=0; Days(a,1)=0; end yy) Determine the percentage of the ALE value paid divide days by 365: zz) ALE(a,1)=Days(a,1)/365; Apply Weibull Distribution ALE(a,1)=(Ra(a,1)*DaysR(a,1)); if ALE(a,1)<=0.001; ALE(a,1)=0; elseif ALE(a,1)>=1.0; ALE(a,1)=1.0; else ALE(a,1)=ALE(a,1); end aaa) Convert losses into a damage matrix determine the percentage of simulations falling within a given range of losses at each wind speed: 297

315 Appendix Table 23 - Partial example of an ALE vulnerability matrix % % E E % % E % % E E % E E E % E-05 15% E E-05 17% E-05 19% % % E % % % % E % % E bbb) From the vulnerability matrix calculate the vulnerability curve to determine the average loss ratio at each wind speed: 80 mph *0% *1% = % - average loss ratio at 80 mph ccc) Validate Results by comparing with actual claims data 298

316 F.9 Vulnerability and Fragility Use Case for Residential and Manufactured Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.9.1 Summary The vulnerability matrix for a particular structural type represents the probability of any given damage ratio occurring at a given wind speed. The rows of the matrix correspond to damage ratios of: 0%, 1%, 3%, 5%, etc. in 2% increments up to 20%, and then in 4% increments; 22%, 26%, 30%, 34%, etc., up to 100%. To derive the vulnerability matrix the building damage ratio, see Building Damage Use Case for Residential Homes and Building Damage Use Case for Manufactured Homes, is computed for each model simulation. The number of simulations that fall within a certain range are counted, if 0%<DR<2%: DR=1%, if 2%<DR<4%: DR=3%, etc. After, all the simulations have been ran, the entire matrix is divided by the total number of simulations per wind speed to determine the probability of any damage state occurring at each speed. To compute the vulnerability curve for any structural type the average damage ratio is calculated from the vulnerability matrix at each wind speed and plotted. The fragility curve is determined by calculating the probability of a particular damage ratio being exceeded at each wind speed. For the fragility curves 4 damage states are considered: DS1 minor damage (3% or greater), DS2 moderate damage (9% or greater), DS3 severe damage (22% or greater), and DS4 destruction (46% or greater). F.9.2 Implementation Input Monte Carlo Simulation Data Programming Steps ddd) Calculate the building damage ratio for each model simulation see Building Damage Use Case for Residential Homes and Building Damage Use Case for Manufactured Homes eee) Count the number of simulations falling within each range of building damage Vuln_Bldg_A=zeros(32,num); if BuildingDamage(a,x)==0.0; Vuln_Bldg_A(1,ii)=Vuln_Bldg_A(1,ii)+1; 299

317 end if BuildingDamage(a,x)<=0.02 & BuildingDamage(a,x)>0.0; Vuln_Bldg_A(2,ii)=Vuln_Bldg_A(2,ii)+1; end if BuildingDamage(a,x)<=0.04 & BuildingDamage(a,x)>0.02; Vuln_Bldg_A(3,ii)=Vuln_Bldg_A(3,ii)+1; end if BuildingDamage(a,x)<=0.06 & BuildingDamage(a,x)>0.04; Vuln_Bldg_A(4,ii)=Vuln_Bldg_A(4,ii)+1; end if BuildingDamage(a,x)<=0.08 & BuildingDamage(a,x)>0.06; Vuln_Bldg_A(5,ii)=Vuln_Bldg_A(5,ii)+1; end if BuildingDamage(a,x)<=0.1 & BuildingDamage(a,x)>0.08; Vuln_Bldg_A(6,ii)=Vuln_Bldg_A(6,ii)+1; end if BuildingDamage(a,x)<=0.12 & BuildingDamage(a,x)>0.1; Vuln_Bldg_A(7,ii)=Vuln_Bldg_A(7,ii)+1; end if BuildingDamage(a,x)<=0.14 & BuildingDamage(a,x)>0.12; Vuln_Bldg_A(8,ii)=Vuln_Bldg_A(8,ii)+1; end if BuildingDamage(a,x)<=0.16 & BuildingDamage(a,x)>0.14; Vuln_Bldg_A(9,ii)=Vuln_Bldg_A(9,ii)+1; end if BuildingDamage(a,x)<=0.18 & BuildingDamage(a,x)>0.16; Vuln_Bldg_A(10,ii)=Vuln_Bldg_A(10,ii)+1; end if BuildingDamage(a,x)<=0.2 & BuildingDamage(a,x)>0.18; Vuln_Bldg_A(11,ii)=Vuln_Bldg_A(11,ii)+1; end if BuildingDamage(a,x)<=0.24 & BuildingDamage(a,x)>0.2; Vuln_Bldg_A(12,ii)=Vuln_Bldg_A(12,ii)+1; end if BuildingDamage(a,x)<=0.28 & BuildingDamage(a,x)>0.24; Vuln_Bldg_A(13,ii)=Vuln_Bldg_A(13,ii)+1; end if BuildingDamage(a,x)<=0.32 & BuildingDamage(a,x)>0.28; Vuln_Bldg_A(14,ii)=Vuln_Bldg_A(14,ii)+1; end if BuildingDamage(a,x)<=0.36 & BuildingDamage(a,x)>0.32; Vuln_Bldg_A(15,ii)=Vuln_Bldg_A(15,ii)+1; end if BuildingDamage(a,x)<=0.4 & BuildingDamage(a,x)>0.36; Vuln_Bldg_A(16,ii)=Vuln_Bldg_A(16,ii)+1; end if BuildingDamage(a,x)<=0.44 & BuildingDamage(a,x)>0.4; Vuln_Bldg_A(17,ii)=Vuln_Bldg_A(17,ii)+1; end if BuildingDamage(a,x)<=0.48 & BuildingDamage(a,x)>0.44; Vuln_Bldg_A(18,ii)=Vuln_Bldg_A(18,ii)+1; end if BuildingDamage(a,x)<=0.52 & BuildingDamage(a,x)>0.48; Vuln_Bldg_A(19,ii)=Vuln_Bldg_A(19,ii)+1; end if BuildingDamage(a,x)<=0.56 & BuildingDamage(a,x)>0.52; Vuln_Bldg_A(20,ii)=Vuln_Bldg_A(20,ii)+1; 300

318 fff) end if BuildingDamage(a,x)<=0.60 & BuildingDamage(a,x)>0.56; Vuln_Bldg_A(21,ii)=Vuln_Bldg_A(21,ii)+1; end if BuildingDamage(a,x)<=0.64 & BuildingDamage(a,x)>0.6; Vuln_Bldg_A(22,ii)=Vuln_Bldg_A(22,ii)+1; end if BuildingDamage(a,x)<=0.68 & BuildingDamage(a,x)>0.64; Vuln_Bldg_A(23,ii)=Vuln_Bldg_A(23,ii)+1; end if BuildingDamage(a,x)<=0.72 & BuildingDamage(a,x)>0.68; Vuln_Bldg_A(24,ii)=Vuln_Bldg_A(24,ii)+1; end if BuildingDamage(a,x)<=0.76 & BuildingDamage(a,x)>0.72; Vuln_Bldg_A(25,ii)=Vuln_Bldg_A(25,ii)+1; end if BuildingDamage(a,x)<=0.8 & BuildingDamage(a,x)>0.76; Vuln_Bldg_A(26,ii)=Vuln_Bldg_A(26,ii)+1; end if BuildingDamage(a,x)<=0.84 & BuildingDamage(a,x)>0.8; Vuln_Bldg_A(27,ii)=Vuln_Bldg_A(27,ii)+1; end if BuildingDamage(a,x)<=0.88 & BuildingDamage(a,x)>0.84; Vuln_Bldg_A(28,ii)=Vuln_Bldg_A(28,ii)+1; end if BuildingDamage(a,x)<=0.92 & BuildingDamage(a,x)>0.88; Vuln_Bldg_A(29,ii)=Vuln_Bldg_A(29,ii)+1; end if BuildingDamage(a,x)<=0.96 & BuildingDamage(a,x)>0.92; Vuln_Bldg_A(30,ii)=Vuln_Bldg_A(30,ii)+1; end if BuildingDamage(a,x)<1.0 & BuildingDamage(a,x)>0.96; Vuln_Bldg_A(31,ii)=Vuln_Bldg_A(31,ii)+1; end if BuildingDamage(a,x)>=1.0; Vuln_Bldg_A(32,ii)=Vuln_Bldg_A(32,ii)+1; end Divide the matrix by the total number of simulations per wind speed to determine the percentage of simulations with each damage ratio Vuln_Bldg_A=Vuln_Bldg_A/(8*nnn); ggg) Name and Save the Vulnerability matrix R=strcat('VM','_','bldg','_',filename,'_',constr,'_',roof_type,'_',shut,'_','tile','_','na','_',COV); save(r,'vuln_bldg_a'); hhh) Compute the vulnerability curve from the vulnerability matrix multiply the percentage of simulations at each damage ratio by the damage ratio, and sum the results repeat for each wind speed for i = 1:num; z1(i)=0.01*x1(2,i)+0.03*x1(3,i)+0.05*x1(4,i)+0.07*x1(5,i)+0.09*x1(6,i)+0.11*x1(7,i)+0.13*x1(8,i) +0.15*x1(9,i)+0.17*x1(10,i)+0.19*x1(11,i)+0.22*x1(12,i)+0.26*x1(13,i)+0.30*x1(14,i)+0.34*x1(15,i 301

319 )+0.38*x1(16,i)+0.42*x1(17,i)+0.46*x1(18,i)+0.5*x1(19,i)+0.54*x1(20,i)+0.58*x1(21,i)+0.62*x1(2 2,i)+0.66*x1(23,i)+0.70*x1(24,i)+0.74*x1(25,i)+0.78*x1(26,i)+0.82*x1(27,i)+0.86*x1(28,i)+0.9* x1(29,i)+0.94*x1(30,i)+.98*x1(31,i)+1*x1(32,i); iii) Compute the Fragility Curve sum the percentage of simulations above the value of the given damage state at each wind speed %%%%%%%%%% Fragility %Damage state 1; Minor Damage-3% or greater for i = 1:num; z1a(i)=x1(3,i)+x1(4,i)+x1(5,i)+x1(6,i)+x1(7,i)+x1(8,i)+x1(9,i)+x1(10,i)+x1(11,i)+x1(12,i)+x1(13,i)+x 1(14,i)+x1(15,i)+x1(16,i)+x1(17,i)+x1(18,i)+x1(19,i)+x1(20,i)+x1(21,i)+x1(22,i)+x1(23,i)+x1(24,i)+ x1(25,i)+x1(26,i)+x1(27,i)+x1(28,i)+x1(29,i)+x1(30,i)+x1(31,i)+x1(32,i); %Damage state 2; Moderate Damage-9% or greater for i = 1:num; z1b(i)=x1(6,i)+x1(7,i)+x1(8,i)+x1(9,i)+x1(10,i)+x1(11,i)+x1(12,i)+x1(13,i)+x1(14,i)+x1(15,i)+x1(16,i )+x1(17,i)+x1(18,i)+x1(19,i)+x1(20,i)+x1(21,i)+x1(22,i)+x1(23,i)+x1(24,i)+x1(25,i)+x1(26,i)+x1(27,i)+x1(28,i)+x1(29,i)+x1(30,i)+x1(31,i)+x1(32,i); jjj) Plot the Curves vs. wind speed Appendix Figure 7 - Vulnerability and fragility curves 302

320 F.10 Matrix Weight Program Use Case for Residential Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.10.1 Summary As described in the Building Damage Use Case for Residential Homes separate building vulnerability matrixes are created for all combinations of region (South, Central, and North), construction type (masonry or wood), roof type (gable or hip), roof cover (tile or shingle), shutters (with or without), and sub-region (none, windborne debris region, and high velocity zone). A total of 144 vulnerability matrixes are created. Statistical information about the distribution of home types throughout Florida was obtained from Public Hurricane Loss Prediction Model: Exposure and Vulnerability Components by Liang Zhang. Using these statistics the 216 matrixes are weighted and combined to produce a Masonry, Timber, and Other matrix for each region and sub-region (South, WBDR, masonry or North, none, wood etc.). The use of these weighted matrices greatly simplifies the loss projection model. 303

321 Portfolio File Zip Code (Determine region & eliminate all matrixes which do not apply) North Central South Keys Sub-Region (Detrmine based on zip code & eliminate all matrixes which do not apply) Neither (least stringent replacement requirenments apply) Windborne Debris Region (more stringent replacement requirenments apply to windows) High Velocity Hurricane Zone (most stringent replacement requirenments apply to windows and roof) Structural Type (Determine from portfolio file info, eliminate matrixes which do not apply, if unknown use other matrix) Select Applicable Weighted Vulnerability Matrix Appendix Figure 8 - Weighted Matrix selection process Because of this process the vulnerability of any home in an insurance policy file can be defined knowing only the zip code and ISO classification. The matrix selection process is shown in Appendix Figure 8. It is important to note that the year built provided in the insurance policy file is not used in matrix selection or to define the vulnerability. This is because any adjustments made to the vulnerability of a home based on the year built at this point would be completely arbitrary. There is no statistical data or conclusive evidence that proves an older home may be more susceptible to hurricane damage than a new home, or vice versa. A well-built older home may in fact be much stronger than poorly constructed new home. Two factors that we do considerer that are related to the age of the home are the damage thresholds applied to the windborne debris region and high velocity hurricane zone. The Florida building code states that in Miami-Dade and Broward counties if a home experiences greater than 25% roof damage the entire roof must be made to comply with the wind load requirements of the code which was been in place since So this replacement threshold will apply to every home with a roof constructed prior to The problem is that based on only the year built it is not really possible to determine the age of the roof, some extrapolation could be made based on a replacement cycle of maybe 15 to 20 years. But again this is very arbitrary, not reliable, and in the end makes very little difference in the average vulnerability of a home. For the windborne 304

322 debris regions if damaged the windows of a home must be replaced with shutters if the not already in place. This code has been in force since 2002, so it would be possible to say that all homes built after 2002 would already have shutters in place and wouldn t have to comply with this requirement. However, probably greater than 95% of the homes in any portfolio file were built prior to 2002 and again this factor makes very little difference in the final result. So because of its minor effects and to simplify the processing of the portfolio files the year of construction is ignored. Because the statistical data indicates almost all two-story home types are at least partially constructed of wood these homes are weighted as part of the wood homes matrix. F.10.2 References Public Hurricane Loss Prediction Model: Exposure and Vulnerability Components F.10.3 Implementation Input Vulnerability Matrixes Statistical information Programming Steps kkk) Input Statistical data for each region %% For South Florida Type1=.46; % 1 story, concrete, gable Type2=.23; % 1 story, concrete, hip Type3=.04; % 1 story, wood, gable Type4=.02; % 1 story, wood, hip Type5=.08; % 2 stories, 1st concrete, 2nd wood, gable Type6=.04; % 2 stories, 1st concrete, 2nd wood, hip Type7=.01; % 2 stories, wood, gable Type8=.01; % 2 stories, wood, hip per_tile=.15; per_shingle=.85; lll) Since there are some unknown structural types adjust the statistics based on the known data Total=Type1+Type2+Type3+Type4+Type5+Type6+Type7+Type8; %% Adjust Percentages Adj_Type1=Type1/Total; Adj_Type2=Type2/Total; Adj_Type3=Type3/Total; Adj_Type4=Type4/Total; Adj_Type5=Type5/Total; 305

323 Adj_Type6=Type6/Total; Adj_Type7=Type7/Total; Adj_Type8=Type8/Total; mmm) Compute weight factors for each home type %% Determine Probability of 1 story Concrete Block or Wood Home, and 2 %% story per_cb=adj_type1+adj_type2; per_fr=adj_type3+adj_type4; per_2st=adj_type5+adj_type6+adj_type7+adj_type8; %% Determine probability of hip or gable roof for Concrete homes cb_per_gable=(adj_type1)/per_cb; cb_per_hip=1-cb_per_gable; %% Determine probability of hip or gable roof for Wood homes fr_per_gable=(adj_type3)/per_fr; fr_per_hip=1-fr_per_gable; nnn) Multiply the vulnerability matrices for not shuttered homes by their corresponding weight factors, for both known and unknown construction types %%% Weight South Florida Vulnerability Matrixes for roof type %% For Concrete Homes with Hip Roofs eval(['load ','VM_bldg_south_concrblk_h_nsh_tile_na_',Bmax]); X1=Vuln_Bldg_A*cb_per_hip*per_tile; X25=Vuln_Bldg_A*per_hip*per_tile*per_cb; eval(['load ','VM_bldg_south_concrblk_h_nsh_tile_WBD_',Bmax]); X2=Vuln_Bldg_B*cb_per_hip*per_tile; X26=Vuln_Bldg_B*per_hip*per_tile*per_cb; ooo) Sum all weighted matrices of the same construction type for not shuttered homes in the same sub-region %% Sum all weighted matrixes of Not Shuttered Concrete homes in the Same subregion VM1=X1+X4+X7+X10; % Not in a Subregion VM2=X2+X5+X8+X11; % Windborne Debris Region VM3=X3+X6+X9+X12; % High Zelocity Zone %% Sum all weighted matrixes of Not Shuttered Wood homes in the Same subregion VM4=X13+X16+X19+X22; % Not in a Subregion VM5=X14+X17+X20+X23; % Windborne Debris Region VM6=X15+X18+X21+X24; % High Zelocity Zone %% Sum all weighted matrixes of Not Shuttered Unknown home types in the Same subregion VM7=X25+X28+X31+X34+X37+X40+X43+X46; % Not in a Subregion VM8=X26+X29+X32+X35+X38+X41+X44+X47; % Windborne Debris Region VM9=X27+X30+X33+X36+X39+X42+X45+X48; % High Zelocity Zone ppp) Apply the same weight factors the shuttered vulnerability matrices %%%%%%%%%%% For Shuttered Homes %%% Weight South Florida Vulnerability Matrixes for roof type 306

324 %% For Concrete Homes with Hip Roofs eval(['load ','VM_bldg_south_concrblk_h_wsh_tile_na_',COV]); X1b=Vuln_Bldg_A*cb_per_hip*per_tile; X25b=Vuln_Bldg_A*per_hip*per_tile*per_cb; eval(['load ','VM_bldg_south_concrblk_h_wsh_tile_WBD_',COV]); X2b=Vuln_Bldg_B*cb_per_hip*per_tile; X26b=Vuln_Bldg_B*per_hip*per_tile*per_cb; qqq) Sum all weighted matrices of the same construction type for shuttered homes in the same sub-region %% Sum all weighted matrixes of Shuttered Concrete homes in the Same subregion VM10=X1b+X4b+X7b+X10b; % Not in a Subregion VM11=X2b+X5b+X8b+X11b; % Windborne Debris Region VM12=X3b+X6b+X9b+X12b; % High Zelocity Zone rrr) Estimate the percentage of homes in each sub-region with and without shutters per_shut_na=.05; %% Percentage of shuttered homes not in subregion per_shut_wbdr=.25; %% Percentage of shuttered homes in windborne region per_shut_hvhz=.40; %% Percentage of shuttered homes in High Velocity zone per_nshut_na=1-per_shut_na; %% Percentage of not shuttered homes per_nshut_wbdr=1-per_shut_wbdr; per_nshut_hvhz=1-per_shut_hvhz; sss) Weight and sum the previously weighted matrices based on the probability of the home having shutters VM_south_concrblk=VM1*per_nshut_na+VM10*per_shut_na; VM_south_concrblk_wbdr=VM2*per_nshut_wbdr+VM11*per_shut_wbdr; VM_south_concrblk_hvhz=VM3*per_nshut_hvhz+VM12*per_shut_hvhz; VM_south_wood=VM4*per_nshut_na+VM13*per_shut_na; VM_south_wood_wbdr=VM5*per_nshut_wbdr+VM14*per_shut_wbdr; VM_south_wood_hvhz=VM6*per_nshut_hvhz+VM15*per_shut_hvhz; VM_south_other=VM7*per_nshut_na+VM16*per_shut_na; VM_south_other_wbdr=VM8*per_nshut_wbdr+VM17*per_shut_wbdr; VM_south_other_hvhz=VM9*per_nshut_hvhz+VM18*per_shut_hvhz; ttt) Name and Save the Matrices %% Rename Vulnerability Matrixes R=strcat('VM_south_concrblk'); S=strcat('VM_south_concrblk_wbdr'); T=strcat('VM_south_concrblk_hvhz'); U=strcat('VM_south_wood'); V=strcat('VM_south_wood_wbdr'); W=strcat('VM_south_wood_hvhz'); X=strcat('VM_south_other'); 307

325 Y=strcat('VM_south_other_wbdr'); Z=strcat('VM_south_other_hvhz'); %% Save Vulnerability matrixes as.mat files save(r,'vm_south_concrblk'); save(s,'vm_south_concrblk_wbdr'); save(t,'vm_south_concrblk_hvhz'); save(u,'vm_south_wood'); save(v,'vm_south_wood_wbdr'); save(w,'vm_south_wood_hvhz'); save(x,'vm_south_other'); save(y,'vm_south_other_wbdr'); save(z,'vm_south_other_hvhz'); uuu) Repeat the process for each region note: for the Key s the South Florida High Velocity Zone vulnerability matrices are used, but weighted using the statistical distribution of building types in the Keys it is assumed that homes with metal roofs cost approximately the same as shingle and in this region the distribution of metal roofs replace shingle, therefore the tile and shingle weight factors are modified to reflect this distribution 308

326 F.11 Matrix Weight Program Use Case for Manufactured Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.11.1 Summary There are 4 Monte Carlo simulation models for manufactured homes: Pre 1994 Tied Down, Pre 1994 not Tied Down, Post 1994 zone 2, and post 1994 zone 3. The Florida Hurricane Catastrophe Fund (FHCF) database provides exposure statistics detailing the distribution of different manufactured home types in each zip code of Florida. Because of limited data in some zip codes this data was aggregated for each region. The data includes the exposure of Fully Tied Down Pre and Post 1994 homes, partially tied down homes, not tied down homes, and unknown types. A plot of the statistics from south Fl is shown in figure 1. South Florida Manufactured Home Building Exposure 0.0% 0.9% 2.6% 14.6% Full TD <94 Full TD >94 Partial TD No TD Unknown 81.8% Appendix Figure 9 - Manufactured home distribution Also, when analyzing an insurance portfolio file some information is provided that can be used for classifying the home type. This includes the zip code and year built. The zip code can be used to classify the region of HUD wind zone while the year built can be used to determine if the home was constructed before or after So essentially only three types of matrices need to be created for analyzing the portfolio files: pre 1994, post 1994 zone 2, and post 1994 zone 3. The pre 1994 matrices are just weighted averages of the Pre 1994 Tied Down, Pre 1994 not Tied Down matrices based on the regional statistics obtained from the FHCF. The post 309

327 1994 zone 2, and post 1994 zone 3 are simply the matrices created from the Monte Carlo models no weighting is required. The matrix selection process is shown in figure 2. Portfolio File Manufactured Homes Year Built Zip Code Pre 1994 Post 1994 North Central South Keys Wind Zone II Wind Zone III Appendix Figure 10 - Manufactured home matrix selection flowchart F.11.2 References Florida Hurricane Catastrophe Fund Exposure Database F.11.3 Implementation Input Vulnerability Matrixes Statistical information Programming Steps vvv) Input Statistical data for each region %% For South Florida Type1=.818; % Pre-94 TD Type2=.146; % Post-94 TD Type3=.00; % No TD Type4=.009; % Partial TD Type5=.026; % Unknown www) Since there are some unknown structural types adjust the statistics based on the known pre 1994 data 310

328 xxx) % Weight the Pre 94 home matrixes to account for Partial and no tie downs Total_pre94=Type1+Type3+Type4; %% Adjust Percentages Adj_Type1=Type1/Total_pre94; Adj_Type3=Type3/Total_pre94; Adj_Type4=Type4/Total_pre94; Weight each matrix based on its statistical distribution (Assume the partially tied down distribution to have vulnerability equal to 75% of the no tied down and 25% of the full tie down) %%% Weight South Florida Vulnerability Matrixes %% For pre 94 not Tied Down eval(['load ','VM_manuf_1p_noTD_COV',COV]); eval(['load ','VM_ale_manuf_1p_noTD_COV',COV]); eval(['load ','VM_cont_manuf_1p_noTD_COV',COV]); X1=vuln_bldg_manuf*Adj_Type3; X1a=vuln_ale_manuf*Adj_Type3; X1c=vuln_cont_manuf*Adj_Type3; %% For Partially Tied Down weight not tied down and tied down matrixes Xp1=vuln_bldg_manuf*.75; Xp1a=vuln_ale_manuf*.75; Xp1c=vuln_cont_manuf*.75; %% For pre 94 Tied Down eval(['load ','VM_manuf_1p_TD_COV',COV]); eval(['load ','VM_ale_manuf_1p_TD_COV',COV]); eval(['load ','VM_cont_manuf_1p_TD_COV',COV]); X2=vuln_bldg_manuf*Adj_Type1; X2a=vuln_ale_manuf*Adj_Type1; X2c=vuln_cont_manuf*Adj_Type1; %% For Partially Tied Down weight not tied down and tied down matrixes Xp2=vuln_bldg_manuf*.25; Xp2a=vuln_ale_manuf*.25; Xp2c=vuln_cont_manuf*.25; %% Partially tied down Xp=(Xp1+Xp2)*Adj_Type4; Xpa=(Xp1a+Xp2a)*Adj_Type4; Xpc=(Xp1c+Xp2c)*Adj_Type4; %% For post 94 Tied Down zone 2 eval(['load ','VM_manuf_1HUD_II_COV',COV]); eval(['load ','VM_ale_manuf_1HUD_II_COV',COV]); eval(['load ','VM_cont_manuf_1HUD_II_COV',COV]); X3=vuln_bldg_manuf; X3a=vuln_ale_manuf; X3c=vuln_cont_manuf; %% For post 94 Tied Down zone 3 eval(['load ','VM_manuf_1HUD_III_COV',COV]); eval(['load ','VM_ale_manuf_1HUD_III_COV',COV]); eval(['load ','VM_cont_manuf_1HUD_III_COV',COV]); 311

329 X4=vuln_bldg_manuf; X4a=vuln_ale_manuf; X4c=vuln_cont_manuf; yyy) Sum all the pre 1994 weighted matrices to compute a general pre 1994 matrix for each region. zzz) %% Sum all weighted matrixes for South FL VM_manuf_bldg_south_pre94=X1+X2+Xp; % Building Vulnerability pre 94 VM_manuf_ale_south_pre94=X1a+X2a+Xpa; % ALE Vulnerability pre 94 VM_manuf_cont_south_pre94=X1c+X2c+Xpc; % Contents Vulnerability pre 94 VM_manuf_bldg_zone2_post94=X3; % Building Vulnerability post 94 zone 2 VM_manuf_ale_zone2_post94=X3a; % ALE Vulnerability post 94 zone 2 VM_manuf_cont_zone2_post94=X3c; % Contents Vulnerability post 94 zone 2 VM_manuf_bldg_zone3_post94=X4; % Building Vulnerability post 94 zone 3 VM_manuf_ale_zone3_post94=X4a; % ALE Vulnerability post 94 zone 3 VM_manuf_cont_zone3_post94=X4c; % Contents Vulnerability post 94 zone 3 Repeat based on the statistics of each region 312

330 F.12 Appurtenant Structure Use Case for Residential and Manufactured Homes Josh Murphree, Jean-Paul Pinelli, Chelakara Subramanian 12/08/2004 F.12.1 Definition Appurtenant Structures: Also called "Other Structures", typically are structures not attached to the dwelling or main residence of your home, but located on the insured property. These types of structures could include: detached garages, guesthouses, pool houses, sheds, gazebos, patio covers, patio decks, swimming pools, spas, etc. F.12.2 Summary From insurance claims processing results there appears to be no obvious relationship between building damage and appurtenant structure claims, Appendix Figure 11. One of the primary reasons for this maybe the variability of the structures that are covered by an appurtenant structure policy. In the event of a hurricane, structures such as pools, spas, and patio decks may experience little or no damage at high wind speeds while the main residence on the insured property could be completely destroyed. In contrast, structures such as screened patios, sheds, and gazebos may experience significant damage at relatively low wind speeds that are unlikely to cause damage to the main residence. There are also structures that may be covered under an appurtenant structure policy that will experience wind damage at approximately the same rate as the primary residence these include guest homes, pool homes, and detached garages. Citizen - All Storms, Masonry Appurt vs. Bldg. Loss Ratio % 90.00% Appurtenate Loss Ratio (%) 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% % Building Loss Ratio (%) Appendix Figure 11 - Claims data processing results, only Citizen data shown, data from other companies is similar 313

331 To model appurtenant structure losses three separate equations are developed, Appendix Figure 12, each determines the appurtenant structure insured loss ratio as a function of wind speed (vulnerability curve). One equation predicts losses for structures highly susceptible to wind damage, the second for moderately susceptible, and the third for structures which are effected only slightly by wind. These equations are developed by approximating losses at several different wind speeds for each type of structure and curve fitting an equation. As with equations to predict interior, contents, and ALE losses a Weibull distribution is applied to account for uncertainties. In this case the alpha and beta parameters are equal to one which yields an exponential distribution. 100% 90% 80% Appurtenant Structure Damage vs. Windspeed y = -3.29E-07x E-04x E-03x R 2 = 9.95E-01 y = -1.43E-07x E-05x E-03x R 2 = 9.78E-01 APS loss ratio 70% 60% 50% 40% 30% 20% 10% 0% Windspeed (mph) 3-second gusts High Moderate Low Poly. (Low) Poly. (High) Poly. (Moderate) y = 4.23E-06x E-04x R 2 = 9.30E-01 Appendix Figure 12 - APS damage ratio vs. wind speed Because the insurance portfolio files give no indication of the type of appurtenant structure covered under a particular policy a distribution of the three types must be assumed. From the available claims data, it appears that the majority of the appurtenant structures have very little damage even with increasing building damage, and few experience moderate to high damage. Based on this data and engineering judgment a distribution of 90% low, 5% moderate, and 5% high is assumed. 314

332 Appendix Figure 13 - APS damage ratio vs. Building Damage ratio, assuming a random distribution of 5% high, 5% moderate, and 90% low A typical insurance policy covers appurtenant structures up to 10% of the insured building value. The estimates of appurtenant structure loss are based on this value. To clarify this an example is given below. Example 1. The Ratio of the Building Limit of Insurance and APS Limit of Insurance is not always consistent for all the policies in the portfolio files. Below is an example of coverage that could be expected. Building Limit of insurance APS Limit of insurance Ratio of BldgLOI/ApsLOI % % % It is assumed that the value of appurtenant structures in a typical home is 10% of the insured building value. Policies that have coverage of less than 10% are assumed to be under insured, while for policies with greater than 10% coverage it is assumed that the value of the appurtenant structures are greater than 10%. So when an estimate of the percentage of appurtenant structure loss is made it is based on an appurtenant structure value of 10% of the insured building value for homes with less than or equal to 10% coverage, and for structures with greater than 10% coverage the estimate of losses is based on the insured appurtenant structure value given in the policy file. To clarify an example is shown below. 315

333 Building Limit of insurance APS Limit of insurance Adjusted APS Limit of insurance Estimated % Damage Damage ($) % % % 5000 The Damage ($) is the estimated percent damage multiplied by the adjusted APS limit of insurance. Then to compute the actual percentage of loss the divide the Damage ($) by the actual APS limit of insurance given in the policy file. APS Limit of insurance Damage ($) APS Loss Ratio (%) % % % F.12.3 Implementation H. Input Number of simulations Standard Deviation Assumed Distribution of structural types I. Use case for Appurtenant Structure Vulnerability aaaa) Based on the assumed distribution of structural types calculate the number of simulations to run for each type, at each wind speed: nnn=40000; % number of simulations per wind speed high=0.05; % percent highly susceptible mod=0.05; % moderately low=0.90; % low lnum=round(low*nnn) = simulations mnum=round(mod*nnn) = 2000 simulations hnum=round(high*nnn) = 2000 simulations bbbb) Calculate the appurtenant structure loss for each type, for the required number of simulations ws(a,1)=winds(1,ii); %% Compute Random Weibul Variables z(a,ii)=weibrnd(a(1,ii),b(1,ii)); %% Structures Highly Suceptable to Wind APSeq1(a,1)=(-3.29*10^-7)*ws(a,1)^3+(1.14*10^-4)*ws(a,1)^2-(3.96*10^-3)*ws(a,1); APSloss(a,1)=z(a,1)*APSeq1(a,1); if APSloss(a,1)<=0.001; 316

334 APSloss(a,1)=0; end if APSloss(a,1)>=1.0; APSloss(a,1)=1.0; end end for b=(hnum+1):(hnum+mnum); ws(b,1)=winds(1,ii); %% Compute Random Weibul Variables z(b,ii)=weibrnd(a(1,ii),b(1,ii)); %% Structures Moderately Suceptable to Wind APSeq2(b,1)=(-1.43*10^-7)*ws(b,1)^3+(6.83*10^-5)*ws(b,1)^2-(4.47*10^-3)*ws(b,1); APSloss(b,1)=z(b,1)*APSeq2(b,1); if APSloss(b,1)<=0.001; APSloss(b,1)=0; end if APSloss(b,1)>=1.0; APSloss(b,1)=1.0; end end for c=(hnum+mnum+1):nnn; ws(c,1)=winds(1,ii); %% Compute Random Weibul Variables z(c,ii)=weibrnd(a(1,ii),b(1,ii)); %% Structures Not Suceptable to Wind APSeq3(c,1)=(4.23*10^-6)*ws(c,1)^2-(6.03*10^-4)*ws(c,1); APSloss(c,1)=z(c,1)*APSeq3(c,1); if APSloss(c,1)<=0.001; APSloss(c,1)=0; end if APSloss(c,1)>=1.0; APSloss(c,1)=1.0; end end cccc) Convert losses into a damage matrix determine the percentage of simulations falling within a given range of losses at each wind speed: 317

335 Appendix Table 24 -Partial example of appurtenant structure vulnerability matrix % % % % % % E % % % % % % % E % % % % E -0 5 dddd) From the vulnerability matrix calculate the vulnerability curve to determine the average loss ratio at each wind speed: 50 mph *0% *1% *3% = 0.06% - average loss ratio at 50 mph Appendix Figure 14 - Vulnerability curve based on the assumed distribution of appurtenant structure types 318

336 319

337 Appendix G Claims Data Included in this appendix are plots of all relevant claims data obtained from the four insurance companies mentioned in chapter 6, as processed by the computer science team at FIU. There are many files so in some instances only a few representative cases have been included. G.1 Company A G.1.1 Masonry Contents 320

338 Company A- Hurricane Erin Contents vs. Structural (Masonry) 80.00% 70.00% (Contents Loss)/( Contents Coverage) 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% % (Building Loss+Deductible)/(Building Coverage) 100% Company A - Tropical Strom Irene Contents vs. Structural (Masonry) (Contents Loss)/( Contents Coverage) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building Loss+Deductible)/(Building Coverage) 321

339 Company A- Hurricane Andrew Contentsvs. Structural (Masonry) 100% (Contents Loss)/( Contents Coverage) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building Loss+Deductible)/(Building Coverage) Appurtenant Structures From the appurtenant structure data from company A for every storm there are almost no claims. The figure below is from the Hurricane Andrew data, all others look the same. Obviously, nothing is gained from this figure so similar plots from other storms are not included here. 322

340 Company A - Hurricane Andrew Appurtenant vs. Structural (Masonry) 120% (Appurtenant loss)/(appurtenant Coverage) 100% 80% 60% 40% 20% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building loss+deductible)/(building Coverage) G.1.2 Wood Contents 323

341 Company A - Hurricane Opal Conents vs. Structural (Timber) 100% (Contents Loss)/( Contents Coverage) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% (Building Loss+Deductible)/(Building Coverage) 25% Company A- Hurricane Georges Contents vs. Structural (Timber) (Contents Loss)/( Contents Coverage) 20% 15% 10% 5% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building Loss+Deductible)/(Building Coverage) 324

342 Company A - Hurricane Erin Contents vs. Structural (Timber) 100% 90% (Contents Loss)/( Contents Coverage) 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building Loss+Deductible)/(Building Coverage) 100% Company A - Tropical Storm Irene Contents vs. Structural (Timber) 90% (Contents Loss)/( Contents Coverage) 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building Loss+Deductible)/(Building Coverage) 325

343 100% Company A - Hurricane Andrew Contents vs. Structural (Timber) 90% (Contents Loss)/( Contents Coverage) 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building Loss+Deductible)/(Building Coverage) G.2 Company B G.2.1 Masonry Contents 326

344 100.00% Company B - Irene Contents vs. Structural (Masonry) (Contents Loss)/( Contents Coverage) 90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% % (Building loss+deductible)/(building Coverage) 100% Company B - Georges Contents vs. Structural (Masonry) (Contents Loss)/( Contents Coverage) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building loss+deductible)/(building Coverage) 327

345 100% Company B - Erin Contents vs. Structural (Masonry) (Contents Loss)/( Contents Coverage) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building loss+deductible)/(building Coverage) ALE Company B - Irene (Masonry) ALE Loss Ratio vs. Structural Loss Ratio 120% (ALE loss)/(ale Coverage) 100% 80% 60% 40% 20% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% (Building loss+deductible)/(building Coverage) 328

346 Company B- Georges ALE vs. Structural (Masonry) % 90.00% (ALE loss)/(ale Coverage) 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 0% 20% 40% 60% 80% 100% 120% (Building loss+deductible)/(building Coverage) Appurtenant (Appurtenant loss)/(appurtenant Coverage) 100% 90% 80% 70% 60% 50% 40% 30% 20% Company B - Georges Appurtenant vs. Structural (Masonry) 10% 0% 0% 20% 40% 60% 80% 100% (Building loss+deductible)/(building Coverage) G.2.2 Wood Contents 329

347 Company B - Hurricane Georges Contents vs. Structural Loss (Timber) 100% 90% 80% 70% Contents Loss 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Structural Loss 100% Company B - Erin Contents vs. Structural (Timber) (Contents Loss)/( Contents Coverage) 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building loss+deductible)/(building Coverage) ALE 330

348 Company B - Opal ALE vs. Structural (Timber) 50.00% 45.00% (ALE loss)/(ale Coverage) 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% (Building loss+deductible)/(building Coverage) Appurtenant 331

349 Company B - Hurricane George Appurtenant vs. Structural (Timber) 100% 90% (Appurtenant loss)/(appurtenant Coverage) 80% 70% 60% 50% 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% (Building loss+deductible)/(building Coverage) 14% Company B - Irene Appurtenant vs. Structura (Timber) 12% (Appurtenant loss)/(appurtenant Coverage) 10% 8% 6% 4% 2% 0% 0% 5% 10% 15% 20% 25% 30% 35% 40% (Building loss+deductible)/(building Coverage) G.3 Company Ca No significant data was provided by Company Ca that warrants being plotted here. G.4 Company Cb No significant data was provided by Company Cb that warrants being plotted here. 332

350 G.5 Company D No significant data was provided by Company D that warrants being plotted here. 333

351 334

352 Appendix H Mitigation Summary In form V-2, we investigate the difference in mean damage for different wind speeds, at five different zip code locations, between a base structure defined by the commission in Form V-1, and the same base structure modified with different mitigation measures listed in form V 2. The purpose is to evaluate the effectiveness of different mitigation measures. Definitions and Required Procedures Base and mitigated models are defined here as dictated by the Florida Commission on Hurricane Loss Prediction Methodology (Commission Report, November, 2004). The procedure for completing form V-2 is then provided. Base case models Table 1 is the definition of the base models (wood frame & masonry site built, and manufactured home) as provided by the commission (from the Commission on Hurricane Loss Projection Methodology standards November 2004, page 90). The intent is to provide a baseline weak structure against to which to compare various combinations of mitigation measures. This represents a weaker model than is modeled by the vulnerability team s standard model, and hence represents a more vulnerable structure than would be typical of Florida exposure. Table 1: Definition of base case as defined by the Florida Commission on Hurricane Loss Projection Methodology in the standards published in November, 2004 (page 90). Base Frame Structure: One story Unbraced gable end roof Base Masonry Structure: One story Unbraced gable end roof 335

353 Normal shingles (55mph) ½ plywood deck 6d nails, deck to roof members Toe nail truss to wall anchor Wood framed exterior walls 5/8 diameter anchors at 48 centers for wall/floor/foundation connections No shutters Standard glass windows No door covers No skylight covers Constructed in 1980 Normal shingles (55mph) ½ plywood deck 6d nails, deck to roof members Toe nail truss to wall anchor Masonry exterior walls No vertical wall reinforcing No shutters Standard glass windows No door covers No skylight covers Constructed in 1980 Base Mobile Home Structure: Tie downs Single unit Mitigated models The mitigated model represents a specific combination of mitigation measures, defined in Table 2 (from the Commission on Hurricane Loss Projection Methodology standards November 2004, page 92). Note that this mitigated structure does not include several common mitigation measures (e.g. wind rated shingles, door covers). However, the modeling of such measures is required, and is accounted for when completing form V-2 (next section). Table 2: Definition of mitigated case as defined by the Florida Commission on Hurricane Loss Projection Methodology in the standards published in November, 2004 (page 92). Mitigated Frame Structure: One story Unbraced gable end roof Rated shingles (110mph) ½ plywood deck 8d nails, deck to roof members Mitigated Masonry Structure: One story Unbraced gable end roof Rated shingles (110mph) ½ plywood deck 8d nails, deck to roof members 336

354 Truss straps at roof Wood framed exterior walls 5/8 diameter anchors at 48 centers for wall/floor/foundation connections Shutters Standard glass windows No door covers No skylight covers Constructed in 1980 Truss straps at roof Masonry exterior walls No vertical wall reinforcing Shutters Standard glass windows No door covers No skylight covers Constructed in 1980 Form V-2 base case, mitigated case, and individual mitigation measures Table 3 presents a blank form V-2 from page 94 of the Commission standards. When completed, this form contains a comparison of the defined base case, defined mitigated case, and many individual mitigation measures that are applied singly to the base case. Procedure for completing form V-2 The required procedure is to first produce model results for the base structure (Table 1), and the mitigated structure (Table 2). These results are placed in the bottom section of form V-2 (Table 3). Note that the mitigated case (Table 2) does not include many of the individual mitigation measures listed in Table 3. Individual mitigations measures are then added singly to the base masonry and frame models. Only one mitigation measure is applied to the base model to fill any given cell in Table 3 (except for the mitigated structure case as discussed above). The next section of this report will discuss the details of the modeling of the base and mitigation measures. 337

355 Table 3: Form V-2, Mitigation Measures - Range of Changed in Damage INDIVIDUAL MITIGATION MEASURES CHANGES IN DAMAGE (MITIGATION MEASURES) FRAME STRUCTURE MASONRY STRUCTURE LOW % HIG H % WIND SPEED LOW % HIG H % WIND SPEED ROOF UNBRACED GABLE ENDS BRACED GABLE ENDS HIP ROOF NORMAL SHINGLES (55 MPH) RATED SHINGLES (110 MPH) MEMBRANE OF NAILING 6d DECK 8d TOE NAILS CLIPS STRAPS ROOF-TO- WALL- NAILS TIES OR CLIPS STRAPS 5/8 φ

356 CENTERS WINDOW, DOOR, WALL- LARGER ANCHORS OR CLOSER SPACING STRAPS NO VERTICAL REINFORCING VERTICAL REINFORCING NONE PLYWOOD SHUTTER STEEL S ENGINEERE D STD GLASS WINDOW LAMINATED S IMPACT GLASS NO DOOR OR SKYLIGHT COVERS DOOR AND SKYLIGHT COVERS BASE STRUCTURE 339

357 MITIGATED STRUCTURE Modeling the base case and mitigation measures This section will provide details of the modeling developed to satisfy the Commission required form V-2 (Table 3). Initially the probabilistic structural vulnerability models for site built and manufactured homes were developed prior to the mitigation requirements were in place. These models were then modified to account for the base and mitigation measures. The modifications generally took the form of additional choices for the capacity of various components. In some cases load path and failure mode assumptions were altered as well. The methodology for modeling each of the items (rows) in Table 3 (form V-2) is provided below. Roof strength UNBRACED GABLE ENDS The standard model does not account for bracing in the gable walls. These walls become more vulnerable to failure when roof to wall (r2w) connections fail. If more than ¼ of the total r2w connections fail, the load is changed to a cantilevered condition (increased load). BRACED GABLE ENDS Braced gable ends tie the end trusses to the internal roof trusses using 2x4 members, thereby providing increased stability under loading on the gable end walls. This is modeled by increasing the number of roof to wall connections that need to fail before load increases. ¾ of all r2w connections must fail. Physically this represents the connection of the outside truss to the inner trusses taking additional loading, keeping the load condition simply supported. HIP ROOF This is modeled as one of our standard models. Hip roof uplift loading differs from that used on the gable roof shape, and the r2w connections on the short ends of the hip roof building are more numerous than for gable ends. Roof Covering 340

358 NORMAL SHINGLES (55 MPH) The uplift capacity for normal shingles is 51 psf. The 1970 s era Southern Building Code Congress International (SBCCI) required that cladding materials withstand an external positive or negative pressure of 25 psf. Assuming that 90% of the older roof coverings in Florida would meet or exceed this requirement, a coefficient of variation of 0.4 is assigned to account for a wide variety of quality and adding effects. A Gaussian distribution then gives a mean capacity of 51 mph. RATED SHINGLES (110 MPH) The uplift capacity for rated shingles is 70 psf. The Dade County 110 Mph requirement corresponds to 51 psf uplift in open exposure. 95% of rated shingles are assumed to pass this requirement with a coefficient of variation of 0.15, giving a mean capacity of 70 psf. The increase to 95% and reduction in COV is due to the Dade County standard being applied to more recently manufactured products. MEMBRANE For that particular case, the relationship between roof cover and interior damage is modified based on the assumption that the membrane will prevent or greatly reduce the intrusion of water in the home, in the event of a roof cover loss. The new relationship between roof cover loss (x) and interior damage (y) is y = 0.074x This reduction in interior damage results in reduced utility and contents damages if the primary source of interior damage is loss of roof cover. NAILING OF DECK 6d 6d nails were used to attach sheathing for the base case. A reduction factor of 0.84 was applied to the 8d testing (below) based on experimental evaluation of relative nail strength. NAILING OF DECK 8d The standard model uses 8d nails in determining the capacity of roof sheathing. Based on a series of in-situ testing conducted by Clemson University on a group of structures in South Carolina over a range of ages and roof types (planked and plywood). The average uplift capacity of 150 psf was applied as the mean with a large COV of 0.4 to account for a large variability. Roof to Wall strength 341

359 Capacity of the roof to wall (r2w) connection that attaches the roof trusses to the top plate (wood frame) or tie beam (concrete block). Capacity values are based on literature from and conversations with Simpson Strong-Tie representatives. TOE NAILS Trusses nailed to the top plate at a 45 degree angle. Low capacity results in a high probability of connection failure. CLIPS Clips are metal devices that are nailed to the truss and top plate to provide a continuous load path. The capacity value is taken from Simpson Strong Tie manufacturer information, using a factor of safety of 3 (as provided by manufacturer). Wood wall capacity is ~ 650 lbs. mean, masonry is ~ 1100 lbs. (both multiplied by 3 for factor of safety). COV is 0.2 STRAPS Straps are metal devices that are nailed to the truss and top plate to provide a continuous load path. Straps wrap over the top of the truss, providing additional capacity compared to clips. The capacity value is taken from Simpson Strong Tie manufacturer information, using a factor of safety of 3 (as provided by manufacturer). Wood wall capacity is ~ 1250 lbs. mean, masonry is ~ 1400 lbs. (both multiplied by 3 for factor of safety). COV is 0.2 Wall to Floor strength Capacity of the wall to floor connection that attaches the vertical studs to the sill plate (wood frame only). The connection of the sill plate to the foundation is considered in the wall to foundation section next. The total uplift capacity at the connection between the studs and sill plate comes from the nails or clips or straps connecting the studs to the sill, and also the nails that connect the wall sheathing to both the sill and studs. NAILS Toe nailed stud to sill plate connection. Uplift capacity is ~ 350 lbs plus the sheathing nails. Resistance capacities are obtained from the 1997 National Design Specification for Wood Construction (NDS). TIES OR CLIPS Replacing the nails from stud to sill with clips, the uplift capacity becomes 550 lbs. (multiplied by a factor of safety of 3) according to Simpson Strong Tie. Assigned COV is

360 STRAPS Replacing the nails from stud to sill with straps, the uplift capacity becomes 647 lbs. (multiplied by a factor of safety of 3) according to Simpson Strong Tie. Assigned COV is 0.20 Wall to Foundation strength 5/8 48 CENTERS LARGER ANCHORS OR CLOSER SPACING STRAPS The anchoring of the sill plate to the foundation has not been found in damage investigation to be a critical failure in terms of insured loss. Roof cover loss, wall failure, and other contributors to loss far outweigh the impact of a sill to foundation failure. That is, by the time sill to foundation becomes an issue, the structure is typically almost totally destroyed. Therefore the standard model developed by the vulnerability team does not consider sill to foundation as a failure mode. The different mitigation options are all suitable to prevent this mode as a first-pass damage, and thus this mitigation is ignored. NO VERTICAL REINFORCING VERTICAL REINFORCING Separate values for bending stress and tensile capacity are used to determine concrete block wall failure in combined uplift and bending. The presence of reinforcing steel increases both the tensile capacity and bending capacity. Opening protection Windows are evaluated for failure due to both pressure loading and missile impact. The application of shutters improves resistance to both pressure and missile impact. NO SHUTTERS The ability of unprotected windows to resist pressure loads is dependent on the size and thickness of the glass panes. Assuming that most typical windows are ¼ inch thick, the strength chart for annealed glass provided in ASTM E1300, Standard Practice for Determining Load Resistance of Glass in Buildings, is used to determine the strength of typically sized windows. The factor of safety built into the design values is known to be

361 (correspondence with Dr. Jim McDonald), thus failure capacities are obtained as below. A COV of 0.2 is assigned. Table 4. Mean failure pressures for typical unprotected windows Description Size (ft x ft) Mean Failure Capacity (psf) Small 3.5 x Medium 3.5 x Tall 3.5 x Picture 6.5 x PLYWOOD SHUTTERS STEEL SHUTTERS ENGINEERED SHUTTERS Plywood, steel and engineered shutters increase pressure and impact capacity. The increase in pressure capacity actually represents a reduction in pressure load due to the presence of the shutter. Given the wide variety of shutter types, installation procedures, and workmanship, Simple factors were used to represent a logical increase in capacity. Table 5 presents the factors used to alter pressure and impact resistance relative to the unshuttered window using standard glass. Pressure factor is a multiplier by the pressure capacity provided above in Table 4. Impact factor is multiplied by the probability of debris damage. Thus pressure factor > 1 and impact factor < 1 represent increased capacity. Table 5: Improved pressure and impact capacity for various shutter types Shutter type Pressure factor Impact factor Plywood Steel Engineered Window & Door strength STANDARD GLASS 344

362 above. The description of standard glass and its pressure capacity is described in Table 4 LAMINATED WINDOWS IMPACT GLASS WINDOWS The use of laminated or impact resistant glass increases the window s resistance to pressure and impact loads. Given the large variety of products, simple factors were used to increase capacity based on standard glass. Table 6 presents the factors used to alter pressure and impact resistance relative to the standard glass window. Pressure factor is a multiplier by the pressure capacity provided above in Table 4. Impact factor is multiplied by the probability of debris damage. Thus pressure factor > 1 and impact factor < 1 represent increased capacity. Note that the reduced vulnerability of a window due to both the use of shutters and improved glass is cumulative. Table 6: Improved pressure and impact capacity for various window glass types Glass type Pressure factor Impact factor Laminated Impact resistant NO DOOR OR SKYLIGHT COVERS DOOR AND SKYLIGHT COVERS Skylights are not modeled. Door covering is modeled by increasing pressure capacity by a factor of Mitigated Structure 345

363 In each case, the Monte Carlo simulation program is rerun with the corresponding modified parameters to generate new damage matrices for the different wind speeds and wind orientations. Vulnerability matrices and curves The procedure for the generation of the base case and mitigated cases vulnerability matrices and curves is identical to the one described in the use case Vulnerability & Fragility Use Case and Matrix Weight Program Use Case for Residential and Manufactured Homes. The resulting vulnerability curves are shown in Figure 1 for masonry structures and in Figure 2 for wood frame structures. Masonry Vulnerabilities 100% 90% Damage Ratios 80% 70% 60% 50% 40% 30% 20% 10% Base Masonry Hip masonry reinforced R2Wclips R2Wstraps ShuttersPlywood Membrane GableBraced ShuttersSteel ShuttersEng ImpactResistantGlass DoorCovered AllMitigated 8dDeckNails Shingles LaminatedGlass 0% % 3 sec gust wind speeds Figure 1: Masonry structures vulnerabilities for different mitigation measures 346

364 Frame Vulnerabilities 100% 90% Damage ratios 80% 70% 60% 50% 40% 30% 20% 10% Base Frame Hip Frame S2Sclips R2Wclips R2Wstraps ShuttersPlywood Membrane GableBraced ShuttersSteel ShuttersEng ImpactResistantGlass DoorCovered AllMitigated LaminatedGlass 8dDeckNails Shingles S2Sstraps 0% % 3 sec gust wind speeds Figure 1: Frame structures vulnerabilities for different mitigation measures 347