Comparative analysis of joint distribution models for tropical cyclone atmospheric parameters in probabilistic coastal hazard analysis

In probabilistic coastal hazard assessments based on the Joint Probability Method, historical storm data is used to build distribution models of tropical cyclone atmospheric parameters (i.e., central pressure deficit, forward velocity, radius of maximum wind, and heading direction). Recent models have used a range of assumptions regarding the dependence structure between these random variables. This research investigates the performance of a series of joint distribution models based on assumptions of parameter independence, partial-dependence (i.e., dependence between only central pressure deficit and radius of maximum wind), and full dependence (i.e., dependence between each pair of tropical cyclone atmospheric parameters). Full dependence models consider a range of copula models, such as the Gaussian copula and vine copulas that combine linear-circular copulas with Gaussian or Frank copulas. The consideration of linear-circular copulas allows for the characterization of correlation between linear variables (e.g., central pressure deficit) and circular variables (e.g., heading direction). The sensitivity of the results to different joint distribution models is assessed by comparing hazard curves at representative locations in New Orleans, LA (USA). The stability of hazard curves generated using a Gaussian copula considering variation in the selection of the zero-degree convention is also assessed. The tail dependence between large central pressure deficit and large radius of maximum wind associated with various copula models are also compared using estimated conditional probability. It is found that the linear-circular Frank vine copula model improve the stability of hazard curves and maximize tail dependence between large central pressure deficit and large radius of maximum wind. However, the meta-Gaussian copula model exhibits performance within this study region that was generally consistent with the tested vine copulas and have the advantage of being easier to implement.