Vine copulas have become the standard tool for modelling complex probabilistic dependence. It has been shown that the number of regular vines grows extremely quickly with the number of nodes. Chimera is the first attempt to map the vast space of regular vines. Software for operating with regular vines is available for R, matlab and Python. However, no dataset containing all regular vines is available. Our atlas of regular vines, Chimera, comprises all 24 4 × 4 matrices representing regular vines on 4 nodes, 480 5 × 5 matrices representing regular vines on 5 nodes, 23,040 6 × 6 matrices representing regular vines on 6 nodes, 2,580,480 7 × 7 matrices representing regular vines on 7 nodes and 660,602,880 8 × 8 matrices representing regular vines on 8 nodes. Regular vines in Chimera are classified according to their tree-equivalence class. We fit all regular vines to synthetic data to demonstrate the potential of Chimera. Chimera provides thus a tool for researchers to navigate this vast space in an orderly fashion.

A submerged floating tunnel (SFT) is a structure that has been proposed as an innovative solution for waterway crossings around the world. However, to this day, no SFT has been constructed yet. One of the main reasons is that there is an insufficient insight into the structural reliability of the SFT. Here, a method to assess the expected structural response of an SFT under traffic loads and a reliability assessment of the results is presented. To do this, traffic models and structural response and reliability are coupled. The methodology presented herein proposes an innovative way to combine copula-based models and structural models to obtain more a more realistic structural response of the SFT. The focus will be on one failure mechanism, leakage caused by bending failure of the SFT in the longitudinal direction. The method utilizes a copula-based model to characterize the traffic loads and simulate traffic loads on the SFT (axle weight, inter-axle distance, and inter-vehicle distance). Next, a structural model is used to assess the structural response and derive stresses. Using a probabilistic analysis, the design of the cross-section can be adapted so that it meets the requirements for leakage caused by bending moments. For the case study is demonstrated that for a buoyancy weight ratio (BWR) of 1.1 an optimal design can be achieved based on a probabilistic method. This methodology could be extended to other failure modes of an SFT or to other structures.

In past decades, the construction of a submerged floating tunnel (SFT) has been presented as an innovative solution for water crossings. One of the main challenges surrounding the design of this type of structure is the lack of data since no SFT has been constructed yet, except for a prototype in Qingdao Lake in China (Mazzolani, Faggiano, & Martire 2010). Additionally, there are uncertainties related to the environmental variables relevant for the construction and operation of a SFT. Wave and current data will be considered for this study. These variables are usually taken as deterministic for design of marine and hydraulic structures and its values represent extreme events. In this paper, a joint probability distribution analysis is proposed to characterize the variables and their dependence. This task was carried out using a copula-based model. In this way, the design conditions for the SFT can be modeled more realistically. The results are several synthetic time series of hourly values and extreme values of all the variables involved.

The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto-and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.