Trivariate Probabilistic Assessments of the Compound Flooding Events Using the 3-D Fully Nested Archimedean (FNA) Copula in the Semiparametric Distribution Setting

Severe flooding in coastal areas can result from the joint probability of oceanographic, hydrological, and meteorological factors, resulting in compound flooding (CF) events. Recently, copula functions have been used to enable a much more flexible environment in joint modelling. Incorporating a higher dimensional copula framework via symmetric 3-D Archimedean or elliptical copulas has statistical limits, and the preservation of all lower-level dependencies would be impossible. The heterogeneous dependency in CF events can be effectively modelled via a fully nested Archimedean (FNA) copula. Incorporating FNA under parametric settings is insufficiently flexible since it is restricted by the prior distributional assumption of the function type for both marginal density and copulas in parametric fittings. If the marginal density is of a specific parametric distribution, it could be problematic if underlying assumptions are violated. This study introduces a 3-D FNA copula simulation in a semiparametric setting by introducing nonparametric marginal distributions conjoined with parametric copula density. The derived semiparametric FNA copula is applied in the trivariate model in compounding the joint impact of rainfall, storm surge, and river discharge based on 46 years of observations on the west coast of Canada. The performance of the derived model has also been compared with the FNA copula constructed with parametric marginal density. It is concluded that the performance of FNA with nonparametric marginals outperforms the FNA copula built under parametric settings. The derived model is employed in multivariate analysis of flood risks in trivariate primary joint and conditional joint return periods. The trivariate hydrologic risk is analyzed using failure probability (FP) statistics. The investigation reveals that trivariate events produce a higher FP than bivariate (or univariate) events; thus, neglecting trivariate joint analysis results in FP being underestimated. Moreover, it indicates that trivariate hydrologic risk values increase with an increase in the service time of hydraulic facilities.