## The hurricane vulnerability index

In order to rank the susceptibility of coastal areas to hurricane damage we calculate a Hurricane Vulnerability Index (HVI) which is a composite of the elements that contribute to hurricane damage. Three elements contribute to the degree to which communities experience hurricane damage: (1) the level of exposure, (2) physical susceptibility to the hurricane, and (3) the hurricane's frequency and intensity. Each element is comprised of several indicators that represent characteristics of risk. The seven indicators that we employ are: population, number of housing units, house value, probability of hurricane strike, building code effectiveness, building age, and vulnerability to sea-level rise.1 The rationale for choosing these indicators was discussed in the previous section.

We use multiattribute utility theory to formulate the HVI (Keeney and Raiffa 1976). We standardize the indicators using a range from 1 to 10 because the indicators are measured in different units (dollars and percentage, e.g.). The value 1 is equal to the minimum risk and 10 is the maximum risk. The formula used to standardize the indicators is:

where Rij and xij are the scaled and unscaled value of risk indicator i for county j; and mini and maxi are the minimum and maximum values for the ith indicator, respectively. The HVI is calculated with the following equation:

where E and S are the exposure and susceptibility to the hurricane, and H is likelihood of the hazard. We use a multiplicative model because risk is a product of exposure, susceptibility, and hazard. We weight the scaled values in order to adjust for the relative importance of the indicators. We use Saaty's (1980) analytic hierarchy process, which creates a pair wise comparison of the indicators, to guide in the selection of the appropriate weights. The three elements are calculated with the following equations:

where R E1, R E2, and R E3 are population, housing units, and housing value; R S1, R S2, and RS3 are building code effectiveness, average building age, and vulnerability to sea-level rise ; R H1 is hurricane probability; and w is the appropriate weight for each indicator