Modelling intersite dependence for regional frequency analysis of extreme marine events

The duration of observation at a site of interest is generally too low to reliably estimate marine extremes. Regional frequency analysis (RFA), by exploiting the similarity between sites, can help to reduce uncertainties inherent to local analyses. Extreme observations in a homogeneous region are especially assumed to follow a common regional distribution, up to a local index. The regional pooling method, by gathering observations from different sites into a regional sample, can be employed to estimate the regional distribution. However, such a procedure may be highly affected by intersite dependence in the regional sample. This paper derives a theoretical model of intersite dependence, dedicated to the regional pooling method in a "peaks over threshold" framework. This model expresses the tendency of sites to display a similar behavior during a storm generating extreme observations, by describing both the storm propagation in the region and the storm intensity. The proposed model allows the assessment of i) the regional effective duration of the regional sample and ii) different regional hazards, e.g., return periods of storms. An application to the estimation of extreme significant wave heights from the numerical sea-state database ANEMOC-2 is provided, where different patterns of regional dependence are highlighted

Application of regional frequency analysis to the estimation of extreme storm surges

International audienceTraditionally, extreme value theory is applied to single-site series of surge observations in order to estimate the probability of occurrence of extreme events at that particular site. However, single-site analyses give uncertain estimation of extreme quantiles, mainly because of the limited duration of observation periods. In order to reduce this uncertainty, regional frequency analysis (RFA) approaches suggest collecting information not only from a single-site series but also from all (statistically) similar available series of observation. The use of RFA is widely increasing in geosciences, but few applications have been attempted yet for surge estimation. The aim of this study is to examine the applicability of RFA to extreme storm surges. The surge data observed at 18 French harbors, located on the Atlantic coast from the Spanish to Belgian borders, were collected. The series span a period of 30 years, on average, with the longest series going back to the 19th century. Stationary and independent samples of extreme surges (peaks over a given threshold) are extracted and their (statistical) homogeneity has been tested via heterogeneity and discordancy measures based on L moments. Homogeneous regions have been identified and, in order to merge information on frequency of occurrence of surges from all the sites, a surge index pooling method is defined. Finally, a regional frequency distribution has been estimated. The hypothesis and the applicability of RFA application are discussed, with some ideas for future developments in the research direction

The flood probability distribution tail: how heavy is it?

International audienceThis paper empirically investigates the asymptotic behaviour of the flood probability distribution and more precisely the possible occurrence of heavy tail distributions, generally predicted by multiplicative cascades. Since heavy tails considerably increase the frequency of extremes, they have many practical and societal consequences. A French database of 173 daily discharge time series is analyzed. These series correspond to various climatic and hydrological conditions, drainage areas ranging from 10 to 10(5) km(2), and are from 22 to 95 years long. The peaks-over-threshold method has been used with a set of semi-parametric estimators (Hill and Generalized Hill estimators), and parametric estimators (maximum likelihood and L-moments). We discuss the respective interest of the estimators and compare their respective estimates of the shape parameter of the probability distribution of the peaks. We emphasize the influence of the selected number of the highest observations that are used in the estimation procedure and in this respect the particular interest of the semi-parametric estimators. Nevertheless, the various estimators agree on the prevalence of heavy tails and we point out some links between their presence and hydrological and climatic conditions

Methodologie de caracterisation et d’estimation des aleas climatiques extremes

Le dimensionnement des ouvrages de protection des sites de production nécessite la détermination d’aléas hydro-météorologiques rares mais susceptibles d’intervenir au cours de leur durée d’exploitation. L’estimation des probabilités d’occurrence de valeurs extrêmes ou de niveaux associés à des probabilités très rares est un sujet transverse à EDF et un effort de capitalisation et de mutualisation des pratiques des différents métiers a été entrepris depuis quelques années. La caractérisation est basée au maximum sur l’application de la théorie statistique des valeurs extrêmes, avec des extensions dans les cas où elle n’est pas applicable directement. Un état des lieux synthétique est ici proposé. Cet état des lieux éclairera la proposition d’EDF de considérer, dans le contexte post Fukushima, de nouveaux aléas dits « hors-dimensionnement ». Ces aléas sont des aléas encore plus rares que les aléas de dimensionnement, dont la prise en compte vise à améliorer la robustesse des sites vis-à-vis des agressions externes et notamment de l’inondation

Méthodologie de caractérisation et d’estimation des aléas climatiques extrêmes

Le dimensionnement des ouvrages de protection des sites de production nécessite la détermination d’aléas hydro-météorologiques rares mais susceptibles d’intervenir au cours de leur durée d’exploitation. L’estimation des probabilités d’occurrence de valeurs extrêmes ou de niveaux associés à des probabilités très rares est un sujet transverse à EDF et un effort de capitalisation et de mutualisation des pratiques des différents métiers a été entrepris depuis quelques années. La caractérisation est basée au maximum sur l’application de la théorie statistique des valeurs extrêmes, avec des extensions dans les cas où elle n’est pas applicable directement. Un état des lieux synthétique est ici proposé. Cet état des lieux éclairera la proposition d’EDF de considérer, dans le contexte post Fukushima, de nouveaux aléas dits “horsdimensionnement”. Ces aléas sont des aléas encore plus rares que les aléas de dimensionnement, dont la prise en compte vise à améliorer la robustesse des sites vis-à-vis des agressions externes et notamment de l’inondation

Regional frequency analysis of extreme storm surges using the extremogram approach

International audienceTo withstand coastal flooding, protection of coastal facilities and structures must be designed with the most accurate estimate of extreme storm surge return levels (SSRLs). However, because of the paucity of data, local statistical analyses often lead to poor frequency estimations. Regional Frequency Analysis (RFA) reduces the uncertainties associated with these estimations, by extending the dataset from local (only available data at the target site) to regional (data at all the neighbouring sites including the target site) and by assuming, at the scale of a region, a similar extremal behaviour. In this work, Empirical Spatial Extremogram (ESE) approach is used. It is a graph representing all the coefficients of extremal dependence between a given target site and all the other sites in the whole region. It allows quantifying the pairwise closeness between sites based on the extremal dependence. The ESE approach, which should help being more confident about the physical homogeneity of the region of interest, is applied on a database of extreme skew storm surges (SSSs) and used to perform a RFA

Qualité de l'eau de la Durance à St Chamas - Les apports en nutriments et en matières en suspension de la centrale hydro-électrique à l'étang de Berre

L'Etang de Berre est un écosystème eutrophe qui reçoit de l'eau douce et des nutriments par deux rivières et par la Durance via la centrale hydro-électrique de Saint Chamas (SC). En intégrant les variations horaires, les échantillons journaliers nous ont permis de calculer un bilan annuel représentatif des apports en nutriments : SC apporte 1085 tonnes de N total (93 % est équi-réparti entre les formes nitrates et azote organique dissous) et 30 tonnes de P total (80 % est sous forme particulaire) sur la période Octobre 2008 à Novembre 2009. La fréquence d'échantillonnage requise pour obtenir le flux annuel en N total avec une erreur de 25 % est mensuelle. Pour le flux annuel de P total, l'erreur minimale est obtenue à partir de l'échantillonnage le plus fréquent testé (i.e. hebdomadaire) mais varie entre -30 % et +60 %. Si on compile toutes les études, on observe que les apports en nutriments à la lagune ont diminué ces 2 dernières décennies. En 2006, SC représente 50 % et 14 % des apports allochtones en N total et P total respectivement. Les sources diffuses et atmosphériques et la labilité des fractions organique dissoute et particulaire restent à préciser

Roughness and Discharge Uncertainty in 1D Water Level Calculations

In this study, we investigate the effect of two key uncertainty sources in one-dimensional (1D) water level calculations: the roughness coefficient and the upstream discharge. The work shows how these two uncertainties, separately and together, propagate through the hydraulic model and result in the uncertainty of water levels. The analysis is conducted for the case of uniformflow in rectangular channels and for steady gradually varied flow in real rivers. In the first case, the exact probability density functions (PDFs) of water levels are obtained analytically through the derived distribution method, while in the second case, the output PDFs are heuristically obtained via Monte Carlo simulations. The results show that (1) the water level PDFs have a lower coefficient of variation than the input PDFs due to the mathematical nature of the relationship between input and output; (2) the propagation of symmetric input distributions through the uniform and steady flow equations determines asymmetric output distributions, due to model nonlinearities. In particular, discharge uncertainty leads to left skewed water level PDFs while roughness uncertainty is responsible for output distributions with heavier right tails. Therefore, in the case of roughness uncertainty, the adoption of symmetrical PDFs would lead to underestimation of high quantiles; (3) water level calculations are more sensitive to uncertainty in the Strickler coefficient rather than in upstream discharge, when the two variables are characterised by the same level of uncertainty, and (4) roughness and discharge uncertainties have a significant effect on the predicted water levels, and they should not be neglected in the practical applications, such as flood forecasting, floodplain mapping and design of flood protection solutions