Stochastic Modeling of Hydroclimatic Processes Using Vine Copulas

Abstract

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.

The Influence of Spatial Variation on the Design of Foundations of Immersed Tunnels: Advanced Probabilistic Analysis

“…An application of this weight in motion model is used in Torres-Alves et al (2022) in the reliability assessment of an submerged floating tunnel and in Mendoza-Lugo et al (2019) to assess the reliability of bridges. VC can be used as a modelling tool for complex probabilistic dependency and used in many fields of application Aas and Berg, 2009;Min and Czado, 2010;Chollete et al, 2008;Pouliasis et al, 2021;Jäger and Nápoles, 2017). Key in the application is to use a Regular Vine (RV) that represents fairly the data.…”

Reliability Analysis of the Ancient Nezahualcoyotl's Dike: Investigating Failure Due to Overflow Using an Improved Hydrological Model

“…For this study, precipitation and evaporation are the only environmental variables considered. The model proposed by Torres-Alves and Morales-Nápoles (2020), recently used by Pouliasis et al (2021), consists of three stages. In the first stage, a discrete time-state MC is used to generate a long synthetic series of occurrences of wet days (occurrence of precipitation) and dry days (absence of precipitation).…”

“…The Nezahualcoyotl dike has not been operational since 1519 and stopped existing around the late 16th century. It has been somewhat studied from a historical perspective but only recently from an engineering point of view by Torres-Alves and Morales-Nápoles (2020); Pouliasis et al (2021) where the probability of failure due to overflow (P O ) was investigated. Several probabilistic approaches have been used to estimate P O , the most popular including Monte Carlo Simulation methods utilizing Bivariate distributions and copulas to describe hydraulic and hydrological variables (see Pol et al (2023); Rajabzadeh et al (2023) for example).…”

Evolution of flood protection levels and flood vulnerability in Europe since 1950 estimated with vine-copula models

“…Because of their flexibility in representing asymmetries in the joint distribution they have found wide application in different fields. For example, they have been applied in tunnel engineering ('t Hart et al, 2024), reliability analysis of flood defenses (Torres-Alves and Morales-Napoles, 2020; Pouliasis et al, 2021), in ocean engineering (Jäger and Morales-Napoles, 2017;Mares-Nasarre et al, 2024)), hydrology (Tao et al, 2021) among many other fields. Additionally, theoretical developments around vine copulas are still being proposed, as highlighted by Pfeifer and Kovács (2024).…”