Multivariate Probability Analysis of Compound Flooding Dynamics.
Authors: Gomez Rave Dina Vanessa , Urrea Méndez Diego Armando , Del Jesus Peñil Manuel 
Published: February 2023

Coastal cities are increasingly prone to compound flooding events. Particularly in estuaries, interactions between both freshwater fluxes (rainfall or discharge) and coastal water levels (tide, surge, waves, or combinations thereof) can strongly modulate flood hazard. These separate but physically connected processes can often occur simultaneously (but not necessarily in extreme conditions), resulting in compound events that may eventually have significant economic, environmental and social impacts. Conventional risk assessment mainly considers univariate-flooding drivers and does not include multivariate approaches; nevertheless, ignoring compound analysis may lead to a significant misestimation of flood risk.In this respect, the complex interactions between coastal flooding drivers imply multidimensionality, nonlinearity and nonstationarity issues, and consequently, more relevant uncertainties. Copula-based frameworks are flexible alternatives to overcome limitations of traditional univariate approaches, and can incorporate the joint boundary conditions in riverine and coastal interactions in a statistically sound way (Harrison et al., 2021; Bevacqua et al., 2019; Couasnon et al., 2018, Moftakhari et al., 2017).&#160; However, incorporations are often limited to the bivariate joint case. Trivariate (or higher dimensional) joint distribution are scarce, due to the convoluted and computationally expensive composition (Latif & Sinonovic, 2022). Notably, a need for robust and efficient approaches that help to characterize the nature of compound hazard remains (Moftakhari et al., 2021).This study aims to improve copula-based methodologies that can adequately estimate the compound flood probability in estuarine regions, considering more than two variables, including more sources of uncertainty into the stochastic dependence analysis, raising the degree of accuracy to risk inference. This work develops a vine copula framework for the analysis of estuarine compound flooding risk, considering interactions and dependency structures between several oceanographic, hydrological, and meteorological processes and variables (rainfall, river discharge, waves, and storm tides). We show the potential of the framework in Santo&#241;a, a strategic estuarine ecosystem in Northern Spain. In order to yield proper design events, we focus here on estimating the multivariate joint and conditional joint return periods statistics, using the best-fitted model in the assessment of the extreme regime, based on Archimedean and Elliptical copula families. We also present the complexities of determining the ensemble of compound events corresponding to a given return period and compare these ensembles to the results of univariate extreme value analysis, to remark the importance of multivariate characterization of extremes.ReferencesBevacqua, E., Maraun, D., Vousdoukas, M. I., Voukouvalas, E., Vrac, M., Mentaschi, L., & Widmann, M. (2019). Higher probability of compound flooding from precipitation and storm surge in Europe under anthropogenic climate change. Science advances, 5(9), eaaw5531.Couasnon, A., Sebastian, A., & Morales-N&#225;poles, O. (2018). A copula-based Bayesian network for modeling compound flood hazard from riverine and coastal interactions at the catchment scale: An application to the Houston Ship Channel, Texas. Water, 10(9), 1190.