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Multivariate Frequency Analysis of Hydro-Meteorological Variables

A Copula-Based Approach

  • 1st Edition - November 16, 2022
  • Latest edition
  • Author: Fateh Chebana
  • Language: English

Multivariate Frequency Analysis of Hydro-Meteorological Variables: A Copula-Based Approach provides comprehensive and detailed descriptions of the approaches and technique… Read more

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Description

Multivariate Frequency Analysis of Hydro-Meteorological Variables: A Copula-Based Approach provides comprehensive and detailed descriptions of the approaches and techniques used in multivariate frequency analysis (including, but not limited to copula functions), with illustrative examples and real-life case studies provided. The book presents all background material and new developments in one place, presenting the material in a homogeneous and pedagogical way in order to allow students, engineers and researchers to access and efficiently use all information surrounding this topic.

This reference can be used as a guide to apply the available and recent approaches to evaluate hydro-meteorological risks, to design hydraulic structures, in teaching (faculty members), and as a literature review to go to the next steps in research projects (graduate students and postdocs).

Key features

  • Presents methods for analysis of hydro-meteorological risks followed by illustrative examples based on real life data sets
  • Provides definitions throughout on all new topics and key terms
  • Includes case studies and real-life examples covering a variety of situations and showing how this work can be applied in the reader’s own work

Readership

Hydrologists at researcher level and above Meteorologists, Statisticians and Civil-Engineers

Table of contents

1: Introduction

1.1 What is the object of the book?

1.2 Why the multivariate framework in general and in hydro-meteorology?

1.3 Who can benefit from this book?

1.4 What is covered (and not) in this book?

1.5 How to read this book?
References

2: Hydro-Meteorological Frequency Analysis (HFA)

2.1 General aims of hydro- Meteorological frequency analysis

2.2 From univariate to multivariate HFA

2.3 Main steps of a complete multivariate HFA

2.4 Hydro-Meteorological events and their main features
Flood features
Drought features
Rainfall storm features
Sediment features
References

3: Multivariate preliminary analysis

3.1 Context and motivation

3.2 Visualisation

3.3 Cross-Dependence measures

3.4 Outliers

3.5 Location measures

3.6 Scale measures

3.7 Asymmetry

3.8 Kurtosis
References

4: Checking basic assumptions for multivariate HFA

4.1 Introduction and general considerations

4.2 Non-stationarity/trend

4.2.1 Definitions

4.2.2 Multivariate trend tests

4.2.3 Performance evaluation

4.2.4 Discussion

4.2.5 Examples

4.3 Heterogeneity/shift

4.3.1 Definitions

4.3.1 Multivariate shift detection tests

4.3.2 Examples

4.4 Serial dependence

4.4.1 Definitions

4.4.2 Serial independence tests

4.4.3 Examples
References

5: Multivariate modeling

5.1 Introduction

5.2 Description of copula models

5.3 Classes of copula

5.3.1 Archimedean copulas

5.3.2 Extreme-value copulas

5.3.3 Meta-elliptical copulas

5.3.4 Other classes of copulas

5.4. Dependence measures

5.4.1 Overall dependence measures

5.4.2 Tail dependence measures

5.5. Parameter estimation

5.5.1 Inference Functions for Margins Method (IFM)

5.5.2 Maximum Pseudo-likelihood Method (MPL)

5.5.3 Moment-Based Method (MM)

5.5.4 Multi-parameter copula estimation

5.6. Copula selection

5.6.1 Preliminary step

5.6.2 Copula goodness-of-fit testing

5.6.3 Selection criteria for copula

5.6.5 Margin modeling
References

6: Multivariate return period and quantile

6.1 Risk assessment in hydro-meteorology

6.2 Multivariate Return Period and multivariate quantile

6.3 Methods to select combinations

6.4 Illustrations
References

7: Multivariate regional analysis

7.1 Aims and general steps of regional frequency analysis

7.2 Region delineation

7.3 Regional estimation

7.4 Index-flood model

7.5 Example
References

8: Multivariate non-stationary HFA

8.1 General aspects: Non-stationary HFA

8.2 Multivariate non-stationary HFA: literature

8.3 Multivariate non-stationary models

8.4 Example
References

Appendices

1. Depth function

2. Multivariate L-moments

3. Copula simulations

Product details

  • Edition: 1
  • Latest edition
  • Published: November 18, 2022
  • Language: English

About the author

FC

Fateh Chebana

Fateh Chebana’s background is in statistics and since 2005 his interests have been focused on application, adaptation and development of statistical approaches for hydro-meteorological phenomena. Having experience and background in both areas (hydro-meteorological and statistics) allows Chebana to present solid material well theoretically justified, and with applied orientations in terms of problematic, understanding of data, and interpretation of the results as well as indicating their usefulness. Several of his papers and professional activities are closely connected to the topic of the proposed book, in particular two chapters, as a lead author of a community paper about the Legacy of STAHY (international statistical hydrology commission), organised sessions in international conferences, Chair of the STAHY2016 workshop, co-chair of the international CRM–CANSSI 2014 Workshop on New Horizons in Copula Modeling, Invited National Webinar by Canadian Water Resources Association.
Affiliations and expertise
Full Professor, Centre Eau Terre Environnement (ETE), Institut national de la recherche scientifique (INRS), University of Quebec, Canada

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