Hazard Assessment under Multivariate Distributional Change-Points: Guidelines and a Flood Case Study

Gianfausto Salvadori,Fabrizio Durante,Mauro Bernardi,Carlo De Michele

doi:10.3390/w10060751

Gianfausto Salvadori, Fabrizio Durante + Show 2 more

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https://doi.org/10.3390/w10060751

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Abstract

One of the ultimate goals of hydrological studies is to assess whether or not the dynamics of the variables of interest are changing. For this purpose, specific statistics are usually adopted: e.g., overall indices, averages, variances, correlations, root-mean-square differences, monthly/annual averages, seasonal patterns, maximum and minimum values, quantiles, trends, etc. In this work, a distributional multivariate approach to the problem is outlined, also accounting for the fact that the variables of interest are often dependent. Here, the Copula Theory, the Failure Probabilities, and suitable non-parametric statistical Change-Point tests are used in order to provide an assessment of the hazard. A hydrological case study is utilized to illustrate the issue and the methodology (viz., assessment of a dam spillway), considering the bivariate dynamics of annual maximum flood peak and volume observed at the Ceppo Morelli dam (located in the Piedmont region, Northern Italy) over a 50-year period. In particular, several problems—often present in hydrological analyses—are debated: namely, (i) the uncertainties due to the presence of heavy tailed random variables, and (ii) the hydrological meaning/interpretation of the results of statistical tests. Furthermore, the suitability of the procedures proposed to fulfill the goals of the study (viz., detecting and interpreting non-stationarity) is discussed. Overall, the main recommendation is that statistical (multivariate) investigations may represent a necessary step, though they may not be sufficient to assess hydrological (environmental) hazards.

Highlights

IntroductionIn the current hydrological practice, water engineering works, including dams, levees, detention basins, and sewers, are designed under the hypothesis of stationarity of the random variables at play.This assumption entails the time invariance of the probability distribution of the variables (strong stationarity), which implies that the family of distribution and its parameters are fixed and constant, or the time invariance of the statistical moments (weak stationarity)—see [1,2].In hydrological literature, the stationarity assumption has mainly been investigated under a univariate framework [3]
In the current hydrological practice, water engineering works, including dams, levees, detention basins, and sewers, are designed under the hypothesis of stationarity of the random variables at play.This assumption entails the time invariance of the probability distribution of the variables, which implies that the family of distribution and its parameters are fixed and constant, or the time invariance of the statistical moments—see [1,2].In hydrological literature, the stationarity assumption has mainly been investigated under a univariate framework [3]
We focus the attention on the possible consequences of violating the stationarity assumptions from a hazard assessment perspective

Summary

Introduction

In the current hydrological practice, water engineering works, including dams, levees, detention basins, and sewers, are designed under the hypothesis of stationarity of the random variables at play.This assumption entails the time invariance of the probability distribution of the variables (strong stationarity), which implies that the family of distribution and its parameters are fixed and constant, or the time invariance of the statistical moments (weak stationarity)—see [1,2].In hydrological literature, the stationarity assumption has mainly been investigated under a univariate framework [3]. In the current hydrological practice, water engineering works, including dams, levees, detention basins, and sewers, are designed under the hypothesis of stationarity of the random variables at play. This assumption entails the time invariance of the probability distribution of the variables (strong stationarity), which implies that the family of distribution and its parameters are fixed and constant, or the time invariance of the statistical moments (weak stationarity)—see [1,2]. The stationarity assumption has mainly been investigated under a univariate framework [3] This is the case of streamflow, traditionally considered as the design variable. Possible departures from stationarity are judged to slightly affect the results [3]

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