The GEV simple scaling model

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Table of contents

I. Introduction 
1. La region des Cevennes : une region au risque hydro-meteorologique eleve
2. Sur l’etude de l’alea pluviometrique
3. Relation Intensite-Duree-Aire-Frequence sous hypothese d’invariance par changement d’echelle
4. Modelisation statistique des extr^emes pluviometriques
5. Donnees pluviometriques utilisees dans cette etude
6. Cadres de developpement des modeles
7. Vue d’ensemble
II. Uncertainty estimation of Intensity-Duration-Frequency relationships : a regional analysis 
1. Introduction
2. Two frameworks of IDF relationships
2.1. Introduction
2.2. Frequentist framework
2.2.1. Model
2.2.2. Inference
2.2.3. Uncertainty computation
2.3. Bayesian framework
2.3.1. Model and priors
2.3.2. Inference
3. Data
4. Evidence of simple scaling
5. Workow
5.1. Frequentist framework
5.2. Bayesian framework
6. Results and discussion
6.1. IDF curves
6.1.1. Estimation and goodness-of-t
6.1.2. Spatial variability of return level across durations
6.1.3. Temporal variability of extreme rainfall
6.2. IDF uncertainty
6.2.1. The example of Montpellier
6.2.2. Regional study
7. Conclusion
III. A regional scale-invariant extreme value model of rainfall Intensity-Duration- Area-Frequency relationships 
1. Introduction
2. Data
3. A exible Gumbel-IDAF model
3.1. Generic IDAF relationships
3.2. Gumbel-IDAF relationships
3.3. Physical meaning of the dierent components of the model
3.4. Model estimation
4. Results
4.1. Empirical validation of the ARF relationships
4.2. Goodness-of-t of the Gumbel-IDAF model
4.3. Characterization of the extreme rainfall regime of the region
4.3.1. Extreme local rainfall features
4.3.2. Extreme areal rainfall structure
4.4. Areal rainfall risk
5. Conclusions
6. Appendix
6.1. Details leading to Eq. (III.4)
6.2. Details leading to Eq. (III.7)
IV. A Bayesian framework for multi-scale assessment of storm severity and related uncertainties 
1. Introduction
2. Data
3. A framework of multi-scale severity modeling
3.1. Extreme value IDAF relationships : frequentist framework
3.2. Extreme value IDAF relationships : Bayesian framework
3.3. Bayesian inference
4. Results
4.1. MCMC monitoring
4.2. Model validation
4.3. Multi-scale severity of the 2011 event
4.4. Generalization to other events
5. Conclusion
6. Appendix
6.1. Adjusted likelihood
6.2. Technical details on the MCMC algorithm
6.2.1. Choice of the priors
6.2.2. DRAM algorithm
V. Rappel des principaux resultats et perspectives 
1. Rappel des principaux resultats
2. Perspectives
2.1. Detection des regions sous echantillonnees (6 mois) et augmentation des donnees (-)
2.2. Non stationnarite de la severite (18 mois)
2.3. Vers une meilleure estimation de l’alea pluviometrique et des incertitudes associees en rel^achant l’hypothese d’independance entre les maxima de dierentes echelles spatio-temporelles (36 mois)
2.4. Alea pluviometrique sur des bassins versants (24 mois)