The AIR Hurricane Model AIR Atlantic Tropical Cyclone Model V12.0

Transcription

1 The AIR Hurricane Model AIR Atlantic Tropical Cyclone Model V12.0 PRESENTATION TO THE FLORIDA COMMISSION ON HURRICANE LOSS PROJECTION METHODOLOGY

2 Model Identification Name of model and version: Atlantic Tropical Cyclone Model V12.0 Program: CLASIC/2 V12 2

3 General Overview of the Atlantic Tropical Cyclone Model Version 12.0

4 AIR Atlantic Tropical Cyclone Model Components Event Generation Intensity Calculation Exposure Information Damage Calculation Policy Conditions Insured Loss Calculation Validation, Reporting 4

5 Simulated Variables in Hurricane Event Generation Annual Frequency Location Frequency Landfall Angle Catalog Landfall Central Pressure Forward Speed Gradient Wind Reduction Factor Peak Weighting Factor Radius of Maximum winds 5

6 Probability Distributions for Key Model Parameters Annual landfall frequency Negative Binomial distribution Landfall location CDF estimated using historical landfall frequencies Landfall central pressure Combination of Weibull distributions Radius of maximum winds Function of central pressure and latitude Forward speed Lognormal distribution Landfall angle Mixture of Normal distributions Gradient Wind Reduction Factor, Peak Weighting Factor Based on Bivariate Normal distribution 6

7 Windfield Cross Section Storm Path Eye Right Side Weaker Winds R max Stronger Winds Storm Center 7

8 Local Wind Speed Calculation Gradient level 10-minute storm maximum wind Gradient level 10-minute wind at location Over water surface (10- meter) 10-minute wind at location Over water surface (10- meter) 1-minute wind at location Earth relative over water surface (10- meter) 1-minute wind at location Earth relative over actual surface 10- meter 1-minute wind at location Compute Gradient Level Maximum Wind Apply Radial Decay of Gradient Wind at Location Apply GWRF at Location Apply Averaging Time (Gust) Factor Account for Asymmetry in Surface Wind Apply Friction Factor Function of: Central pressure 1 Peripheral pressure 2 Radius of max winds 1,3 Latitude Function of: Max gradient wind Radius of max winds 1,3 Latitude Distance from center Function of: Gradient Wind Reduction Factor 1 Peak Weighting Factor 1 Time Distance from center Function of: Effective roughness length 2 Wind Direction Function of: Forward speed 1 Beta (angle between track and wind) 4 Function of: Effective roughness length 2 Wind Direction 1 Stochastically drawn by storm 2 Functional by location 3 Functional in time 4 Function of other storm parameters 8

9 Typical Vulnerability Function Damage Ratio Roof Covering and Wall Siding Damage Building Envelope and Structural Damage Major Structural Damage Regime II Regime I Regime III v 1 V 2 Wind Speed 9

10 Probability Distribution around the Mean Damage Ratio f ( x D ) Expected Insured Loss = 1 x= 0 f D [ min( x R,P ) DED] ( x)max{ 0, Coins% }dx V L 10

11 Validation of the Atlantic Tropical Cyclone Model Version M Actual Simulated 100 M Losses $ 10 M 1 M M 11

12 The AIR Atlantic Tropical Cyclone Model V

13 Overview of Changes to Atlantic Tropical Cyclone Model Version 12.0 The updated AIR Atlantic Tropical Cyclone Model (Version 12.0) is the most scientifically advanced tool for U.S. hurricane risk assessment and provides a significantly more accurate, realistic and detailed view of the risk through. Use of new hazard and vulnerability data. New meteorology and wind engineering research. More robust simulation of hurricane structure and inland penetration. Increased accuracy in modeling local wind speed and duration Significantly enhanced vulnerability module. Explicit treatment of evolving building code throughout U.S. Comprehensive validation of data sets, both winds and claims. New visualization and analysis tools. Reconciliation of model change at macro and micro scales. 13

14 AIR s Approach to Modeling Hurricane Risk Has Undergone a Steady Stream of Improvements AIR INTRODUCES CAT MODELS TO THE INDUSTRY.... V7.0 MODEL UPDATE V8.0 MODEL UPDATE V9.0 MODEL UPDATE V10.0 MODEL UPDATE V11.0 MODEL UPDATE 1990s HURRICANE ANDREW STORMS OF 2004 STORMS OF 2005 HURRICANE IKE 14

15 Quantifying Risk and Uncertainty: Hazard New Hazard Data and Research Surface roughness New USGS land use land cover data Rmax evolution Wind speed validation Rmax vertical slant Gradient wind Wind directionality Influence of wind waves Catalog parameters High-resolution radar data Availability of robust validation data Recent research and validation data New research and recent dropsonde data Robust wind validation data set (e.g., Texas Tech) Recent research and validation data Updated based on HURDAT database 15

16 Quantifying Risk and Uncertainty: Vulnerability Detailed Claims Analysis, Damage Surveys and Wind Engineering Year built Secondary risk features Commercial engineered Contents coverage Regional unknown damage functions Evolution of building codes and construction practices, claims data, and post-disaster surveys Evolution of building codes and construction practices, detailed claims data, and post-disaster surveys Detailed claims data and post-disaster surveys Detailed claims data and post-disaster surveys Regional inventory distributions 16

17 AIR Scientists and Engineers Have Contributed Published Research to the Scientific Community Hazard Dailey, P. S., G. Ljung, G. Zuba and J. Guin, Probability of Hurricane Intensification and U.S. Hurricane Landfall under Conditions of Elevated Atlantic Sea Surface Temperatures, Hurricanes and Climate Change, eds. James B. Elsner and Thomas H. Jagger, Springer, Dailey, P. S., G. Zuba, G. Ljung, I.M. Dima and J. Guin, On the Relationship Between North Atlantic Sea Surface Temperatures and U.S. Hurricane Landfall Risk, Journal of Applied Meteorology and Climatology 48, 2009, Desflots, M., and I. Dima. Characteristics and climatology of eyewall replacement cycles for Atlantic tropical cyclones from observations. 29th Conference on Hurricanes and Tropical Meteorology, May, Dima, I.M, Dailey, P. S. and G. Zuba, Assessing the Sensitivity of Landfall Risk to Warm Atlantic Conditions, Extended Abstracts, 89th Annual American Meteorological Society Meeting, 4th Symposium on Policy and Socio-Economic Research, Phoenix, Dima, I.M., Dailey, P.S., and T. Doggett. Sensitivity of a parametric hurricane model to different wind profiles. 29th Conference on Hurricanes and Tropical Meteorology, May,

18 AIR Scientists and Engineers Have Contributed Published Research to the Scientific Community Vulnerability Franco, G., R. Green, B. Khazai, A. Smyth and G. Deodatis, A Field Damage Survey of New Orleans Homes in the Aftermath of Hurricane Katrina, Accepted for publication in Natural Hazards Review, American Society of Civil Engineers (ASCE). He, H., Jain, V.K., Leiva G., and Kafali, C. Modeling Relative Spatial and Temporal Hurricane Wind Vulnerability of the Building Stock in the US. 11th Americas Conference on Wind Engineering. San Juan, Puerto Rico. June 22-26, He, H., V. K. Jain, G. Leiva and C Kafali, Modeling Relative Spatial and Temporal Hurricane Wind Vulnerability of the Building Stock in the US, Accepted for publication, Proceedings of the 11th Americas Conference on Wind Engineering, Puerto Rico, American Association for Wind Engineering (AAWE), June Jain, V.K., Guin, J. Modeling Business Interruption Losses From Wind Storms For Insurance Portfolios. 11th Americas Conference on Wind Engineering. San Juan, Puerto Rico. June, Jain, V.K., Guin, J., and He, H., Statistical Analysis of 2004 and 2005 Hurricane Claims Data. 11th Americas Conference on Wind Engineering. San Juan, Puerto Rico. June 22-26,

19 External Peer Review of Atlantic Tropical Cyclone Model Version 12.0 Dr. Kerry Emanuel, MIT Vulnerability Dr. Joe Minor, Independent wind engineering consultant Dr. David Rosowsky, Rensselaer Polytechnic Institute Mr. Jay Crandell, P.E., ARES consulting Mr. Tom Smith, TLSmith Consulting Dr. Marc Levitan, Louisiana State University Dr. Carol Friedman, Louisiana State University Hazard Dr. Peter Black, United States Naval Research Laboratory, Monterey Dr. Robb Contreras, Areté Associates 19

20 External Peer Review of Atlantic Tropical Cyclone Model Version 12.0 (Cont d) John Rollins, FCAS, MAAA, Rollins Analytics Actuarial Narges Pourghasemi, Independent Auditor Computer Science 20

21 Hazard Update Incorporates New Data, New Science, and New Technology on Hurricane Structure and Evolution New research and observations of 4-D storm structure have been integrated into the hurricane model. New land use data from the USGS has been used to develop updated local wind adjustments. Direction of the upstream wind is explicitly modeled. New states added to provide even more complete coverage of inland risk (Illinois, Indiana, and Missouri). Inland filling rates and reintensification have been introduced based on new data and recent experience. 21

22 Vulnerability Update Incorporates New Claims Data and New Engineering Research Incorporation of new data and engineering. Significant increase in detailed company claims data. Wind vulnerability analyses. Data from damage surveys. Explicit modeling of the evolution of building codes and their enforcements across all hurricane states. Refinements in vulnerability relationships. Significant changes to commercial vulnerability and commercial contents. Secondary risk characteristics. Industrial facilities. 22

23 Claims Data Shows Decreasing Wind Vulnerability and Vulnerability Differences Across Different Regions 23

24 Vulnerability Aspects of Commercial Residential High rise buildings are generally well-designed and have a high margin of safety factor. Damage is generally restricted to non-structural components such as cladding and windows. Water can enter through unsealed openings and gaps around windows and doors. Punctured roof can lead to water infiltration. Entry of water can cause extensive contents damage. No Damage after Hurricane Frances to Well Protected Apt Wall Cladding Damage to High Rise Apt 24

25 Updated Losses Are Highly Dependent on the Exposure Mix and Regions at Risk Industry loss changes at the country level are small, however regional and local changes are more significant. Overall, coastal wind speeds are reduced and inland wind speeds are increased. Overall, residential vulnerability is stable and commercial vulnerability is increased. Caution should be exercised before relating industry and/or large-scale changes to a particular book of business. AIR has reconciled changes across all regions, all lines of business, and all building types to specific model updates. 25

26 Version 12.0 Maintains a Consistent Overall View of Risk 26

27 While the Macro View of Risk Is Similar, More Refined Regional and Portfolio Views May Vary Considerably 27

28 While the Macro View of Risk Is Similar, More Refined Regional and Portfolio Views May Vary Considerably 28

29 Summary of Model Changes 2010 Updates to AIR's Atlantic Tropical Cyclone Model Percent Change Event Generation Module -3.67% Windfield Model % Damage Functions % Zip Code Database Update +0.18% Overall Change +4.08% 29

30 Event Generation Module For the 2010 model release, AIR s historical storm set has been updated, incorporating track information from the June 2009 version of HURDAT. The probability distributions used for annual landfall frequency and landfall location in the stochastic catalog have been updated accordingly and a new stochastic catalog has been generated. Landfall location is now continuous. We updated our models for central pressure, rmax, forward speed, and landfall angle. The filling equations for modeling post-landfall intensity were also updated. These updates have resulted in a 3.67% decrease in losses. 30

31 Windfield Model For the 2010 model release, AIR s windfield model has been updated. Land use land cover (LULC) data used to estimate surface roughness, as well as the methodology used to incorporate the influence of wind direction in the roughness calculation, has been updated. This individual update has resulted in a 14.72% decrease in losses. 31

32 Damage Functions For the 2010 model release, methodology to estimate regional and temporal variation in vulnerability has been significantly enhanced for all hurricane states including Florida. Damage functions have been reviewed in light of newly enhanced hazard model, detailed claims data and research reports. Impact of individual risk features has been significantly improved. For renters and condos relationship between building and contents damage function has been updated. This individual update has resulted in 25.91% increase in losses. 32

33 ZIP Code Database Update The ZIP Code database is updated each year. For each new ZIP Code centroid, the following data needs to be re-estimated: distance from coastline, elevation and surface roughness. This is a technical update. This individual update has resulted in minor changes to population-weighted centroids, and its impact on losses is a 0.18% increase. 33

34 Explanation of Resubmitted Pages

35 Explanation of Resubmitted Pages Deficiencies noted by the Commission were addressed. The Professional Team verified that the corrections were made. Clarifications Provided separate responses for Standard G-1, Disclosure 5, A, B and C. Listed ZIP Code databases used by model in Standard G-3, Disclosure 1. Provided more information in Standard M-2, Disclosure 5 with regard to the process for converting the modeled vortex winds to surface winds and justification for the variation in the surface winds conversion factor. Discussed the probability distributions for landfall location and peak weighting factor in Standard M-3, Part A. Numbered table and listed in the Table of Contents for Standard M-4, Disclosure 3. Delineated what part of Attachment F corresponds to Standard V-2, Part B. Addressed (3) claim payment practices, (5) contractual provisions, and (6) relevant underwriting practices underlying those losses in Standard A- 2, Part B. Addressed consideration of damage to local and regional infrastructure in Standard A-9, Disclosure 3. 35

36 Explanation of Resubmitted Pages (Cont.) Deficiencies noted by the Commission were addressed. The Professional Team verified that the corrections were made. Clarifications Updated storm ID numbers provided for Other hurricanes included in Form A-3, Part B. Updated column headings in Forms A-4 and A-5. Provided response for Form S-4, Part B. 36

37 Explanation of Resubmitted Pages (Cont.) AIR resubmitted pages in response to the draft Professional Team Report. Editorial changes Updated reference for Form A1Input09.xls in Form A-1. AIR resubmitted pages in response to the draft Professional Team Report Clarifications Defined acronyms in flowchart in G-1, Disclosure 3. Added references for treatment of roughness lengths in Standard G-1, Disclosure 4. Revised Figures 4-7 in Standard G-1, Disclosure 5, and added new figure for ZIP Code. Clarified location-specific parameters in Standard M-2, Disclosure 3. Clarified how peripheral pressure adjustment is used in Standard M-2, Disclosure 4. Added statement on no assumptions in Standard M-3, Disclosure 1. Added references in Standard M-4, B. Revised figure titles in Standard M-4, Disclosures 1 and 2. Added PWF information to table on in Standard M-4, Disclosure 3. 37

38 Explanation of Resubmitted Pages (Cont.) AIR resubmitted pages in response to the draft Professional Team Report. Clarifications Revised figure in Standard M-5, Disclosure 2. Changed language to be consistent for averaging distance in Standard M-5, Disclosure 3. Revised figure in Form M-1. Changed language to components in Standard V-2, A and V-2, Disclosure 3. Modified statement on mitigation measures in table in Standard V-2, Disclosure 2. Clarified weights in Standard V-2, Disclosures 3 and 4. Revised Form V-1. Provided assumptions in Form V-2, B. Clarified that table applies to the reference structure in Form V-2. Revised maps in Form A-2 to show invalid ZIP Codes as n/a with a footnote to explain n/a. Revised Personal Residential percent of losses in Forms A-4 and A-5. Clarified U.S. hurricanes in Standard S-1, Disclosure 6. 38

39 Explanation of Resubmitted Pages (Cont.) AIR resubmitted pages in response to the draft Professional Team Report. Clarifications Revised figure titles in Standard S-5, Disclosure 1. Updated number in table in Form S-2. Clarified differences in data sets for percent change in loss costs from previous submission and G-1, Disclosure 5 in Form S-5. Updated numbers in Form S-5, Disclosures E, F, and G. 39

40 2009 General Standards

41 G-1 Scope of the Computer Model and Its Implementation The AIR hurricane model projects loss costs for personal lines residential property from hurricane events. There has been no change to the scope of the computer model or its implementation. 41

42 G-2 Qualifications of Modeling Organization Personnel and Consultants AIR employs a large, full-time professional staff in actuarial science, computer science, insurance and reinsurance, mathematics, statistics, meteorology, and other physical sciences, software engineering, and structural engineering. Resumes of new employees were provided to the professional team. 42

43 G-3 Risk Location ZIP Codes used in the model are updated annually with information provided by the United States Postal Service (USPS). The AIR model uses population-weighted ZIP Code centroids. AIR maintains documentation providing step-by-step instructions for processing the centroid related files supplied by AIR s vendor. AIR performs quality control measures to verify the positional accuracy of the vendor-supplied population centroids and ensure their appropriateness. Overlay of the population-weighted centroids with the ZIP Code boundaries Display of the 2008 census block locations and their corresponding population values Independent generation of population weighted centroids for each ZIP Code 43

44 G-4 Independence of Model Components All components of the AIR model are theoretically sound and independently derived. Each component is independently validated. 44

45 G-5 Editorial Compliance The submission was reviewed in its entirety for grammatical correctness, typographical accuracy and completeness by an experienced technical editor and writer. The primary reviewer read and understood the submission requirements as listed in the Report of Activities prior to working on AIR s submission. 45

46 2009 Meteorological Standards

47 M-1 Base Hurricane Storm Set The Base Hurricane Storm Set consists of the latest version of HURDAT supplemented with landfall data from the NOAA Technical Memorandum NWS TPC-5. This version of HURDAT is valid as of June 1, 2009 and spans the years

48 M-2 Hurricane Parameters and Characteristics Methods for depicting all modeled hurricane characteristics are based on information documented in the scientific literature or on research conducted by AIR and accepted by the Commission. 48

49 M-3 Hurricane Probabilities AIR-modeled probability distributions for hurricane strength, eye diameter, forward speed, radii for maximum winds, and radii for hurricane force winds are consistent with observed historical hurricanes in the Atlantic basin and are bounded by observed global extremes as documented in accepted scientific literature available to the Commission. AIR-modeled hurricane probabilities for category 1-5 hurricanes reasonably match the historical record and are consistent with those observed for each geographical area of Florida, Alabama, Georgia and Mississippi. 49

50 M-4 Hurricane Windfield Structure The modeled windfield is consistent with the distribution of observed winds for historical storms affecting Florida. The AIR model uses USGS land use / land cover (LULC) classifications by category and assigns appropriate roughness lengths based upon available scientific literature. 50

51 M-5 Landfall and Over-Land Weakening Methodologies The method used by AIR to model the effects of land friction on wind speeds is based on scientific methods and provides realistic wind speed transitions between adjacent ZIP Codes, counties, and territories. The model s overland weakening rates, or filling rates, compare favorably with the historical records for storms of all intensities. The effects of land friction on wind speeds have been updated from the previously accepted submission. 51

52 M-6 Logical Relationships of Hurricane Characteristics The time variant wind field, including the radial distribution of wind speeds, is consistent with accepted scientific principles and with historical hurricane characteristics. The model wind field has been updated from the previously accepted submission. 52

53 2009 Vulnerability Standards

54 V-1 Derivation of Vulnerability Functions AIR hurricane model vulnerability functions are based on structural engineering research publications, field damage surveys conducted by wind engineering experts, and analyses of detailed loss data from clients. The AIR vulnerability functions and associated uncertainties have been peer reviewed internally and by external experts and are theoretically sound. The AIR hurricane model uses vulnerability functions for several residential construction types, and includes an individual risk analysis module that accounts for a wide range of construction characteristics. For commercial residential construction types, vulnerability varies by height. For single family homes, vulnerability functions do not vary by height. The AIR wind model uses regional modifiers to account for the changes in the building codes and their enforcements, and modifications functions are used to account for mitigation measures. 54

55 V-1 Derivation of Vulnerability Functions (Cont.) AIR engineers have developed separate vulnerability functions for the primary structure, the appurtenant structures, contents and additional living expenses. The model starts calculating losses at 40 mph one-minute average wind speed. Vulnerability functions include damage due to wind speed and pressure, water infiltration, and missile impact. Wind vulnerability functions in the model does not include the explicit damage of flood, storm surge, and wave actions. AIR vulnerability model has been updated since the previously accepted submission. 55

56 V-2 Mitigation Measures Methods for estimating the effects of mitigation measures, as described in Attachment F, U.S. Hurricane Individual Risk Methodology, are theoretically sound, both individually and in combination. AIR s mitigation model has been developed using a structured, knowledgebased expert system that applies structural engineering expertise and building damage observations made in the aftermath of actual hurricanes. The model uses two metrics (rates and weights) for evaluating the impact of a mitigation feature. The building vulnerability component of the AIR model explicitly addresses new construction built in accordance to the new building code, FBC2001. The impact of the mitigation features on building vulnerability listed in Form V- 2 has been updated since the previously accepted submission. 56

57 2009 Actuarial Standards

58 A-1 Modeled Loss Costs and Probable Maximum Loss Levels Modeled loss costs and probable maximum loss levels reflect all insured windrelated damages from storms that reach hurricane strength and produce minimum damaging wind speeds or greater on land in Florida. A by-passer is defined as a hurricane that does not make landfall but comes close enough to land to cause damage. For a storm defined as a by-passer, damage is computed along the entire track of the storm. The model treats damage from wind and surge losses independently. For the purpose of this submission, surge losses were completely excluded from the reported results. 58

59 A-2 Underwriting Assumptions Any adjustments, edits, inclusions or deletions made to client company input data are based upon accepted actuarial, underwriting and statistical procedures. All applicable policy provisions including limits, deductibles, and coinsurance are taken into consideration and modeled appropriately. AIR discusses and documents all assumptions related to validation data with our clients. If data is excluded or adjusted, this is documented in the Project Information & Assumptions Form (PIAF), and in the project file. The composite vulnerability curve, used when the construction type is listed as unknown, is based on a weighted average of the different construction classes. Note that our unknown residential function does not apply weight to the mobile home type. 59

60 A-2 Underwriting Assumptions (Cont.) The model development and validation process assumes that future claims practices will be similar to the past claims practices in use when the losses from historical events were paid. To calculate losses, the model requires replacement value and insured limit by coverage. Damages are calculated based on replacement value, then capped at the policy limit. The model makes no depreciation assumptions. Insurers may make specific assumptions for any depreciation adjustments that reduce replacement value to actual cash value. The model does not include loss adjustment expenses in the losses. 60

61 A-3 Loss Cost Projections and Probable Maximum Loss Levels AIR s hurricane model produces pure loss estimates. Model loss costs do not include risk load, investment income, premium reserves, taxes, assessment or profit margin. The model does not make a prospective provision for economic inflation. Clients in-force exposures, projected exposures, or hypothetical exposures are input to the model. For the purposes of this submission, all modeled loss costs and probable maximum loss levels exclude any provision for direct hurricane storm surge losses. The loss cost for a given ZIP code or county is calculated by dividing the average annual loss for all locations within the area by the corresponding exposures. Probable maximum losses on an annual occurrence basis are calculated by ranking the losses for the largest event in each simulated year in the catalog from highest to lowest, then identifying the loss whose ranking matches the desired exceedance probability level. For example, the 50-year PML is the loss exceeded by only 1/50= 2% of all simulated years. 61

62 A-4 Demand Surge Demand Surge was included in the model s calculation of loss costs and probable maximum loss levels in compliance with Standard A-4. The methods, data, and assumptions used in the estimation of demand surge are actuarially sound. AIR has related the amount of demand surge in a particular event to the amount of total industry-wide insurable losses from the event. The factor is dependent on coverage. For a given event, the demand surge factors by coverage are applied to the corresponding ground-up losses, based on the industry-wide loss for that event. Policy conditions are then applied probabilistically. The sum of these losses by coverage yields the total event loss with demand surge included. 62

63 A-5 User Inputs Assumptions that relate to an insurer s input data are identified on the analysis options form, an output report of CLASIC/2. AIR also sends a Project Information & Assumptions Form (Attachment A of the submission) to clients and requires approval prior to the hurricane analysis. The AIR hurricane model can distinguish among any policy form types. Exposures are distinguished based on vulnerability characteristics, such as construction type and occupancy. There is no single required input form for exposure data. AIR will remap client data to the UNICEDE/px format as necessary. The analysis options appear as header information in all loss exports provided by the software. The PIAF (see Attachment A) relates directly to model input requirements and output to be produced. It includes the model name and version number. Insurer data undergoes a set of structured processing procedures. If data is excluded or adjusted, this is noted in the PIAF. 63

64 A-6 Logical Relationship to Risk The AIR model produces loss costs that are logical in relation to risk. The loss costs are positive and non-zero for all ZIP Codes. Loss costs do not increase as quality of construction, material, workmanship or the presence of mitigation devices or techniques increases, all else being equal, and are consistent with actual insurance data. Loss costs do not increase as the quality of building codes and enforcement increases, all else being equal. Loss costs do decrease as deductibles increase. The relationship of losses for building, appurtenant structures, contents, and additional living expense to the total loss as produced by the model is reasonable and consistent with actual insurance data. Loss cost relationships among coverages, territories, and regions are consistent and reasonable. 64

65 A-7 Deductibles, Policy Limits, and Coinsurance The AIR damageability functions generate a mean damage ratio for a given wind speed. For any estimated mean damage ratio, there is a mixed probability distribution that includes finite probabilities of damage at zero and 100 percent. Thus, the effects of deductibles, coinsurance and other policy conditions can be properly calculated. 1 Expected Insured Loss = f ( x) max{ 0, Coins% [ min( x R V, PL )- DED] }dx D x= 0 The relationship among the modeled deductible loss costs is reasonable. Deductible loss costs are calculated in accordance with the Florida seasonal deductible requirement [F.S (5)(a)]. 65

66 A-8 Contents The methods used in the development of the AIR hurricane model s contents loss costs are actuarially sound. Contents vulnerability is separately modeled (from structure and time element), and a function of both building damage and wind speed. The relationship among modeled structure and contents loss costs is reasonable based on historical relationships in insurance data. 66

67 A-9 Time Element Coverage The AIR hurricane model represents losses to Time Element in an actuarially sound manner, separately from building, contents and appurtenant structures. Loss due to Time Element coverage is based on the mean building damage, the time estimated to make repair or to reconstruct the damaged building and the estimated cost of Time Element per time period. The relationship between modeled Time Element and structure loss costs is reasonable based on historical relationships in insurance data. The model considers Time Element claims that arise from damage to the infrastructure to the extent that such losses are in the validation data used. Time Element loss is a function of mean building damage ratio, which is nonzero beginning at a minimum local wind speed of 40mph. Time Element loss costs are calculated independently for the wind and storm surge perils in the AIR model. No storm surge losses for Time Element coverage are included in the submitted loss costs. The AIR model does not estimate losses from flood damage. 67

68 A-10 Output Ranges Output ranges are logical and deviations are supported. Output ranges reflect declining loss costs with increasing deductibles, reflect lower loss costs for masonry construction versus frame, and reflect lower loss costs for residential risk versus mobile home. Output ranges generally reflect lower loss costs for inland counties versus coastal counties, and lower loss costs for northern counties versus southern counties. Output ranges reflect lower loss costs for contents versus structures, and lower loss costs for additional living expenses versus structures. Output ranges are positive and non-zero for all given risk exposures. During the last year, the following refinements were made to the model: the ZIP Code database was updated, and the stochastic catalog was updated, as the surface windfield model and damage functions. The annual frequency distribution and the probability distribution for landfall location have been updated to reflect HURDAT data as of June 1,

69 A-11 Probable Maximum Loss The AIR hurricane model uses methods, data, and assumptions in the estimation of probable maximum loss levels which are actuarially sound. AIR simulates individual events within individual years. The stochastic hurricane catalog comprises a set number of simulated years in this submission, 50,000. Each year may produce zero, one, or multiple events. Probable maximum losses are calculated on an annual occurrence basis by ranking the largest ground-up loss within each simulated year from highest to lowest, then identifying the event loss whose rank matches the exceedance probability requested. For example, the 50-year PML is the loss exceeded by only 1/50= 2% of all simulated years, or the 1000 th highest year in a 50,000 year catalog. 69

70 2009 Statistical Standards

71 S-1 Modeled Results and Goodness-of-Fit Historical data available in HURDAT have been used to develop the probability distributions for key model variables such as annual hurricane frequency, landfall location, and central pressure. The probability distributions used for individual input variables include Negative Binomial for annual landfall frequency, Weibull for central pressure and Lognormal for forward speed. The adequacy of the fit has been examined using established procedures such as the Kolmogorov-Smirnov and the Shapiro-Wilk tests. Graphical comparisons using Q-Q plots and other procedures were also performed to confirm the agreement between the historical data and the fitted probability distributions. 71

72 S-2 Sensitivity Analysis for Model Output AIR scientists and engineers have done extensive sensitivity testing on all aspects of the hurricane model. This has involved testing alternative probability distributions for key input variables, as well as changing the parameter values of these probability distributions. One-parameter-at-a-time as well as multi-parameter studies have been conducted. Sensitivity of individual model variables on the estimated losses by state, county, and ZIP Code have been tested. Sensitivity of temporal and spatial wind speeds generated by the model has also been investigated. 72

73 S-3 Uncertainty Analysis for Model Output AIR scientists and engineers have performed uncertainty analyses involving model input variables such as central pressure, Rmax, and forward speed. The studies have focused on the temporal and spatial variability in wind speed as well as loss costs attributable to variation in the input variables. One-parameter-at-a-time as well as multi-parameter studies have been conducted. Central pressure and the gradient wind reduction factor, in particular, have been found to be important contributors to the uncertainty in the estimated wind speeds as well as the state, county, and ZIP Code level losses. 73

74 S-4 County Level Aggregation Convergence graphs and inspection of the loss costs for increasing sample sizes indicate the sampling error is negligible for the 50,000-year simulation used to generate the loss costs. AIR uses a constrained Monte Carlo simulation to obtain the average annual loss costs and output ranges. The procedure imposes constraints on the landfall frequency by SS category for each 100-mile coastal segment. The constraints are derived by running the model for 1 million years and scaling the simulated frequencies down to a 50,000-year simulation. 74

75 S-5 Replication of Known Hurricane Losses Losses generated by the model for past hurricane events reasonably replicate actual incurred losses from those events. This is true for both personal residential, commercial residential of various construction types and for mobile homes, as well as for various coverages. County-level comparisons also show reasonable agreement between modeled and incurred losses. 75

76 S-6 Comparison of Projected Hurricane Loss Costs The average annual historical statewide loss cost produced using the 2007 FHCF exposure data and the historical storm set covering the period is $2.579 billion. The average annual statewide loss cost produced by the model using a 50,000-year simulation is $3.301 billion. The difference between these two numbers is statistically reasonable. 76

77 2009 Computer Standards

78 C-1 Documentation A primary document binder containing fully documented sections for each computer standard was made available to the Professional Team. All computer software, data files, and databases are fully documented and such documentation was made available to the Professional team. Documentation is separate from the source code and is provided via in-line detailed comments and external higher level documentation that was made available to the Professional Team. 78

79 C-2 Requirements The CLASIC/2 requirements specification documents describe functional, user interface, data format, security, performance and other requirements of CLASIC/2 for the hurricane peril; it also describes design constraints. Also available to the Professional Team was a document that itemizes changes to the hurricane model and the corresponding support documentation. The requirements specification documents were enhanced to reflect the model refinements. 79

80 C-3 Model Architecture and Component Design A component design document, included in the primary document binder, contains detailed control and data flow diagrams and interface specifications that illustrate the component design of the CLASIC/2 software system and the architecture of the AIR hurricane model, its components and subcomponents. Each data file and database that is used by the model has its schema documented in an external document that is part of the document binder. The component design document was enhanced to illustrate demand surge. The database documentation was enhanced to reflect new tables resulting from the updated ZIP Codes. 80

81 C-4 Implementation AIR maintains a complete set of software engineering practices for coding and documentation guidelines that are followed by the software developers. AIR maintains a procedure for procuring and creating data files and databases. AIR has developed documentation that provides component identification from documentation diagrams down to the code level. AIR has a table of components in the primary document binder that contains each of the Component names, the Number of lines of code, Comments, and Blank lines. AIR has developed documentation that is clearly written and that can by used by new software engineers to gain an understanding of the software being reviewed. AIR has documented the equations and formulas that have been introduced to the AIR hurricane model. All terms, variables, and functions have been defined. 81

82 C-5 Verification AIR software engineers employ a variety of verification procedures to check code correctness. These procedures include code-level debugging, component-level unit testing, verifying newly developed code against a stable reference version, and running diagnostic software tools to detect runtime problems. Unit tests are performed for individual software components, independent of all other components, and are documented. In addition, formal testing procedures are conducted, through all successive phases of development from design, coding, initial testing, and regression testing. AIR utilizes a Verification Utility program which checks the existence, consistency, and correctness of all data files. This program verifies that each data file matches a known version of the data file by performing checksum verification. AIR verifies the correctness of the databases by validating the source counts and ensuring that the changes are affected on the same number of records. Examples of the verification, including counts on the ZIP changed records, county change records, and ZIP centroid updates. 82

83 C-6 Model Maintenance and Revision Since 1987, AIR has implemented a clearly documented policy for model revision with respect to methodology and data. Any enhancement to the model that results in a change in hurricane loss costs also results in a new model version number. AIR s software development group employs source revision and control software for all software product development, including CLASIC/2. Available to the Professional Team was a document that identifies the changes between release versions of CLASIC/2 and the hurricane model. 83

84 C-7 Security AIR has implemented security procedures for access to code, data, and documentation that are in accordance with standard industry practices. AIR employs a number of physical and electronic security measures to protect all code, data and documentation against both internal and external potential sources of damage, and against deliberate and inadvertent, unauthorized changes. AIR s security policy document describes these measures in greater detail. 84