Multivariate Frequency Analysis of Hydro-Meteorological Variables: A Copula-Based Approach

Front Cover
Multivariate Frequency Analysis of Hydro-Meteorological Variables
Copyright Page
Contents
Acknowledgments
1 Introduction
	1.1 Context
	1.2 Purpose and aims
	1.3 Readership
	1.4 Structure and content
	1.5 How to read this book?
	1.6 Final points
	References
2 Multivariate hydrological frequency analysis, overview
	2.1 General aims of hydrological frequency analysis
	2.2 From univariate to multivariate hydrological frequency analysis
		2.2.1 Main steps of a complete multivariate hydrological frequency analysis
			2.2.1.1 Exploratory analysis
			2.2.1.2 Testing basic assumptions
			2.2.1.3 Modeling and parameter estimation
			2.2.1.4 Multivariate quantile and return period
	2.3 Hydrological events and their main features
		2.3.1 Flood features
		2.3.2 Illustrative example
		2.3.3 Drought features
		2.3.4 Rainfall storm features
		2.3.5 Sediment features
	References
3 Multivariate preliminary analysis
	3.1 Context and motivation
	3.2 Visualization
	3.3 Cross-dependence measures
	3.4 Outliers
		3.4.1 Outlyingness
		3.4.2 Threshold
	3.5 Location measures
		3.5.1 Sample mean
		3.5.2 Component-wise median
		3.5.3 Depth-based median
		3.5.4 Spatial median
		3.5.5 α depth-trimmed mean
	3.6 Scale measures
		3.6.1 α-trimmed sample dispersion matrix
		3.6.2 Scalar form of scale
	3.7 Asymmetry
		3.7.1 Spherical symmetry
		3.7.2 Elliptical symmetry
		3.7.3 Antipodal symmetry
		3.7.4 Angular symmetry
	3.8 Kurtosis
		3.8.1 Lorenz curve of Mahalanobis distance
		3.8.2 Shrinkage plot
		3.8.3 Fan plot
		3.8.4 Quantile-based measure
	References
4 Checking basic assumptions for multivariate hydrological frequency analysis
	4.1 Introduction and general considerations
	4.2 Stationarity
		4.2.1 Multivariate trend tests
			4.2.1.1 Mann–Kendall type tests
			4.2.1.2 The covariance inversion test
			4.2.1.3 The covariance sum test
			4.2.1.4 The covariance eigenvalue test
			4.2.1.5 Spearman’s rho type tests
		4.2.2 Performance evaluation
		4.2.3 Further discussion
			4.2.3.1 Example
	4.3 Homogeneity
		4.3.1 Multivariate shift detection tests
			4.3.1.1 The Cramér test
			4.3.1.2 The M-test
			4.3.1.3 The T-test
			4.3.1.4 The Wilcoxon test
			4.3.1.5 The quality index test
			4.3.1.6 The Zhang test
		4.3.2 Comparisons and other approaches
		4.3.3 Example
	4.4 Serial independence
		4.4.1 Serial empirical copula test
		4.4.2 Illustrative example
	4.5 Complete illustrative example
	References
5 Modeling in multivariate hydrological frequency analysis with copula
	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 Copula parameter estimation
		5.5.1 Inference functions for margins method
		5.5.2 Maximum Pseudo-likelihood method
		5.5.3 Moment-based method
		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
		5.6.4 Margin modeling
	References
6 Multivariate return period and quantile
	6.1 Risk assessment in hydrology
	6.2 Multivariate return periods and multivariate quantile: generalities
		6.2.1 Definitions and presentation
		6.2.2 Illustrative example 1
	6.3 Methods to select combinations
		6.3.1 Most likely design realization approach
		6.3.2 Structure-based approach
		6.3.3 Kendall return period approach
		6.3.4 Conditional distribution approach
		6.3.5 Regression-based approach
		6.3.6 Multivariate quantile curve, proper part approach
		6.3.7 Alpha-region approach
		6.3.8 Ilustrative example 2
	References
7 Multivariate nonstationary frequency analysis
	7.1 Nonstationary hydrological frequency analysis
	7.2 Multivariate nonstationary hydrological frequency analysis literature
	7.3 Multivariate nonstationary models
		7.3.1 Modeling description
		7.3.2 Covariate-varying copulas
		7.3.3 Covariate-varying margins
		7.3.4 Nonstationary model selection
		7.3.5 Bayesian multivariate nonstationary model
		7.3.6 Modeling procedure steps
			Step 1: descriptive study
			Step 2: testing trends
			Step 3: joint distribution selection
				3a: selection of nonstationary margins
				3b: selection of nonstationary copula
			Step 4: nonstationary multivariate quantile and return period
		7.3.7 Data series length and moving window series
	7.4 Illustrative example
	References
8 Multivariate regional frequency analysis
	8.1 Regional hydrological frequency analysis
	8.2 Multivariate regional frequency analysis
	8.3 Delineation
		8.3.1 Multivariate discordancy
		8.3.2 Multivariate homogeneity
	8.4 Multivariate estimation (index-flood model)
	8.5 Discussion
	References
Appendix A Ties in the copula-based framework and in hydrology
	References
Appendix B Statistical depth functions
	References
Appendix C Multivariate L-moments
	References
Appendix D p-Value computation
	Reference
Index
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