Innovative polygonal coastal index concept and probabilistic vulnerability predictions

The classical coastal vulnerability index (CVI) has five mutually exclusive integer scores: 1, 2, 3, 4, and 5. This paper proposes to plot the given US-ranked CVI input variables in polygonal graphical formats bounded by single straight lines for the maximum and minimum data sets for two, and three segments for each input variable, with extreme values ​​and between maximum and minimum data set’s variation space is illustrated with logical rules of direct or inverse proportionality, leading to mathematical formulations. This innovative method is called the polygonal coastal index (IPCI), and the diagrams illustrate the relationship between each input variable and output scores. A numerical implementation of the IPCI concept is provided for an empirical data set selected from the variation space of each variable. The most important part of the IPCI calculation is the final output score estimate in the form of probabilistic theoretical cumulative distribution functions (CDFs). These functions enable risk and reliability assessment of vulnerability at various levels not achievable by any existing CVI procedure in the literature. It is possible without difficulty to extend and further develop the use of the IPCI procedure by taking into account as many input variables as possible.