Multivariate Frequency Analysis of Hydro-Meteorological Variables

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