Exploring Multivariate Return Periods: Enhancing Accuracy in Hydrological Analysis for Flood Prediction&#160;
Authors: Urrea Méndez Diego Armando , V. Gómez Dina , Del Jesus Peñil Manuel 
Published: March 2024

The assessment of multivariate return periods determines how frequently different variables co-occur within a specific region. Recent studies have used two- and three-dimensional copulas for this assessment. G. Salvadori et al., (2011) introduced an approach based on Archimedean copulas and the Kendall measure. Gr&#228;ler et al., (2013) calculated the trivariate return period using Vine copulas and Kendall distribution functions, incorporating annual maximum peak discharge, volume, and duration. Tosunoglu et al., (2020) applied three-dimensional Archimedean, Elliptical, and Vine copulas to study flood characteristics. These methodologies enhance the accuracy of extreme events risk measurement, emphasizing the importance of understanding tail dependence and the appropriate selection of copulas.In multivariate analysis of compound extreme events, addressing the dependence structure in the tails of the variables of interest becomes essential. If the selected copula fails to accurately capture this extreme dependence, the estimation of extreme values may be significantly affected by uncertainty (Hangshing &amp; Dabral, 2018). Therefore, conducting a comprehensive assessment of the copula model fit to the data is crucial, with a particular focus on tail dependence (Serinaldi, 2015). This process guides the choice of the most suitable copula family to model these compound extreme events.We propose a two-part methodology: (I) In this phase, we focus on comparing various multivariate models that address the entirety of uncertainty. This involves analyzing different models and copula structures. The main objective is to evaluate how goodness of fit and tail dependence impact the calculation of design events, where, in some cases, underestimation may occur.(II) In a subsequent stage, we formulate a more robust approach that encompasses the study, evaluation, and implementation of various statistical and machine learning techniques. The focus is on using the results obtained in the previous stage to develop flood models. These models enable us to compare multivariate approaches in terms of their performance in flood prediction and other associated impacts.The study results highlight the importance of diversifying approaches in the hydrological analysis of precipitation-conditioned design events. It was found that the use of a multivariate approach provides more accurate estimations of precipitation compared to the univariate method. The careful choice of the multivariate model is crucial, as Gaussian models underestimate extreme events, while extreme vine copula models yield more tightly fitted results. This advancement benefits engineering by reducing uncertainty in design processes and providing a more precise approximation of climate impacts, with the potential to enhance territorial management.ReferencesSalvadori, C. De Michele, &amp; F. Durante., 2011. On the return period and design in a multivariate framework. Hydrol. Earth Syst. Sci., 15(11), 3293&#8211;3305.Gr&#228;ler, B., Berg, M. J. van den, Vandenberghe, S., Petroselli, A., Grimaldi, S., De Baets, B. &amp; Verhoest, N. E. C., 2013. Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. Hydrol. Earth Syst. Sci., 17(4), 1281&#8211;1296.Hangshing, L. &amp; Dabral, P. P., 2018. Multivariate Frequency Analysis of Meteorological Drought Using Copula. Water Resour Manage, 32(5), 1741&#8211;1758.Serinaldi, F., 2015. Dismissing return periods! Stoch Environ Res Risk Assess, 29(4), 1179&#8211;1189.