Comparaison des méthodes d’estimation des paramètres du modèle GEV non stationnaire

L’analyse fréquentielle des événements extrêmes est un des outils privilégiés pour l’estimation des débits de crue et de leurs périodes de retour. En analyse fréquentielle, les observations doivent être indépendantes et identiquement distribuées (iid). Ces hypothèses ne sont pas souvent respectées et les paramètres de la loi à ajuster sont fonction du temps ou de covariables. Le modèle GEV non stationnaire permet de tenir compte de cette dépendance. L’objectif du présent travail est de comparer la méthode du maximum de vraisemblance pour l’estimation des quantiles à la méthode du maximum de vraisemblance généralisée (GML) et à une généralisation de la méthode des L‑moments dans le cas non stationnaire. Trois modèles sont considérés : le modèle stationnaire (GEV0), le cas où le paramètre de position est une fonction linéaire de la covariable (GEV1) et le cas d’une dépendance quadratique (GEV2). Un cas d’étude des précipitations à une station de la Californie montre le potentiel des modèles non stationnaires.In frequency analysis, data must generally be independent and identically distributed (i.i.d), which implies that they must meet the statistical criteria of independence, stationarity and homogeneity. In reality, the probability distribution of extreme events can change with time, indicating the existence of non-stationarity. The objective of the present study was to develop efficient estimation methods for the use of the GEV distribution for quantile estimation in the presence of non-stationarity. Parameter estimation in the non-stationary GEV model is generally done with the Maximum Likelihood Estimation method. In this work, we suggest two other estimation methods: the Generalized Maximum Likelihood Estimation (GML) and the generalization of the L-moment method for the non-stationary case. A simulation study was carried out to compare the performances of these three estimation methods in the case of the stationary GEV model (GEV0), the non-stationary case with a linear dependence (GEV1), and the non-stationary case with a quadratic dependence on covariates (GEV2). The non-stationary GEV model was also applied to a case study from the State of California to illustrate its potential

Méthodes de désagrégation appliquées aux Modèles du Climat Global Atmosphère-Océan (MCGAO)

La littérature scientifique de la dernière décennie contient un grand nombre de travaux qui détaillent le développement des méthodes de « désagrégation » (downscaling) de l’échelle globale à l’échelle hydrologique pour tenter d’estimer les impacts du changement global sur la disponibilité et la distribution des ressources en eau. Cet article présente une revue et une synthèse des méthodologies de « désagrégation climatique » présentées dans la littérature afin de simuler les réponses régionales au changement global du climat. L’accent est mis sur les avancées récentes et sur les problèmes reliés à l’application pratique des modèles dans les études d’impact. L’article présente également une discussion des avantages et limites des différentes approches, ainsi que quelques suggestions pour l’étude future des impacts du changement global sur les ressources en eau.During the last decade, a large volume of literature has been published on the development of “downscaling” methods from the global to the hydrological scale in order to estimate the impact of global climate change on the availability and distribution of water resources. The present paper proposes a comprehensive review and a synthesis of climatic downscaling methodologies presented in the literature in order to simulate the regional response to global climate change. The paper focuses mainly on recent advances in the field, and on the practical problems that may arise from the application of the various models in impact studies. The paper presents also a discussion of the advantages and limitations of the various methods. The paper concluded with some suggestions for future work dealing with the impacts of global change on water resources

Synthèse des développements récents en analyse régionale des extrêmes hydrologiques

L’estimation adéquate des événements hydrologiques extrêmes (événements de conception) est primordiale en raison des risques importants associés à une connaissance insuffisante de ces événements. Dans les sites où l’on dispose de peu ou même d’aucune information hydrologique, on a recours aux méthodologies d’estimation régionale pour l’estimation des extrêmes hydrologiques. De nombreuses méthodologies ont été développées durant les dernières années pour améliorer l’estimation régionale de la distribution des extrêmes hydrologiques. Cet article présente une synthèse exhaustive des derniers développements en matière d’analyse hydrologique régionale. Une discussion dégage les directions principales de ces développements récents, met en évidence les défis majeurs en matière d’analyse régionale pour les années futures et évoque des pistes prometteuses de travaux de recherche afin de répondre à ces nouveaux défis.Adequate estimation of extreme hydrological variables is essential for the rational design and operation of a variety of hydraulic structures, due to the significant risk that is associated with these activities. Local frequency analysis is commonly used for the estimation of extreme hydrological events at sites where an adequate amount of data is available. However, data are usually only collected at a relatively limited number of sites. In practice, it frequently happens that little or no streamflow data is available at a site of interest (where a dam is to be constructed for example). In such cases, hydrologists can utilize a regional flood frequency procedure, relying on data available from other basins with a similar hydrologic regime.Various methods have been developed over the last few years for the regional analysis of extreme hydrological events. These regionalization approaches aim to estimate different characteristics of the extreme hydrological phenomena of interest, make different assumptions and hypotheses concerning these hydrological phenomena, rely on various types of data, and often fall under completely different theories. The present paper aims to review and classify recent developments in regional frequency analysis of extreme hydrological variables.The specific objectives of the paper are to: i) review the main recent developments in regional hydrologic modeling that have been proposed during the last few years; ii) classify these developments into different groups according to the theoretical background of the method, its specific objectives, and the characteristics of hydrological extreme phenomena it is intended to deal with; iii) propose a comprehensive discussion of these methods, and point out the hypotheses, limitations, data requirements, and potential of each one; iv) identify the new challenges facing engineers in terms of regional frequency analysis of hydrological extremes; and v) propose potential promising directions for future research work which aim to meet these new challenges.Recent developments reviewed in the present paper include improvements in classical approaches for regional delineation and for information transfer, methods combining the delineation and estimation steps, seasonality-based methods, multivariate models for regional frequency analysis, the QdF approach, non stationary models, and approaches for the combination of local and regional data. The paper provides also a discussion of the various hydrological variables treated with regional estimation methodologies, comparative studies of these methodologies, and practical tools that were developed for regional frequency analysis. It is hoped that this document will contribute towards closing the gap between theory and practice, by narrowing the wide body of literature that is available, and by providing comprehensive propositions for regional frequency analysis approaches that meet the new challenges facing hydrologic engineers

Utilisation des réseaux de neurones et de la régularisation bayésienne en modélisation de la température de l’eau en rivière

Dans ce travail, nous avons élaboré un modèle de prédiction des variations de la température d’un cours d’eau en fonction de variables climatiques, telles que la température de l’air ambiant, le débit d’eau et la quantité de précipitation reçue par le cours d’eau. Les réseaux de neurones statiques ont été utilisés pour approximer la relation entre ces différentes variables avec une erreur moyenne de 0,7 °C. Par ailleurs, nous proposons un modèle de prédiction de l’évolution de la température de l’eau à court et moyen termes pour les jours (j + i, i = 1,2,..). Deux méthodes ont été appliquées : la première, de type itérative, utilise la valeur estimée du jour j pour prédire la valeur de la température de l’eau au jour j + 1; la seconde méthode, beaucoup plus simple à mettre en oeuvre, consiste à estimer la température de tous les jours considérés en une seule fois.L’optimisation de la fonction de coût par l’algorithme de Levenberg-Marquardt, disponible dans l’outil « réseaux de neurones » de MATLAB a permis d’améliorer nettement la performance des modèles. Des résultats très satisfaisants sont alors obtenus en testant la validité du modèle par la validation croisée avec des erreurs moyennes de prédiction à sept jours de 1,5 °C.Understanding and predicting water temperatures is essential in order to help prevent or forecast high temperature problems. To attain this objective, we define in this work a model that predicts temperature variations in a small stream according to climatic variables, such as air temperature, water flow and quantity of rainfall in the river catchment. Static neural networks were used as a technique for evaluation of the relations among the various variables, with a mean error of 0.7°C.In addition, we developed a forecasting model able to estimate the short-term and mid-term variations of water temperature, i.e., to forecast the temperature of days (j+i , i=1,2…) from climatic parameters of day j. Two methods were used: the first one is iterative and uses the estimated value of day j to estimate the value of the water temperature for day j+1. The second method is much simpler, involving an estimate of the temperature of all days at once. The Levenberg-Marquardt algorithm implemented in the Matlab neural network toolbox allowed a marked improvement in the performance of the model. Very satisfactory results were then obtained by testing the validity by cross validation technique with a mean error of 1.5°C for long term prediction of 7 days

Directed transport in a classical lattice with a high-frequency driving

We analyze the dynamics of a classical particle in a spatially periodic potential under the influence of a periodic in time uniform force. It was shown in [S.Flach, O.Yevtushenko, Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000)] that despite zero average force, directed transport is possible in the system. Asymptotic description of this phenomenon for the case of slow driving was developed in [X. Leoncini, A. Neishtadt, A. Vasiliev, Phys. Rev. E 79, 026213 (2009)]. Here we consider the case of fast driving using canonical perturbation theory. An asymptotic formula is derived for the average drift velocity as a function of the system parameters and the driving law. We show that directed transport arises in an effective Hamiltonian that does not possess chaotic dynamics, thereby clarifying the relation between chaos and transport in the system. Sufficient conditions for transport are derived.Comment: 5 page

Streamflow forecasting using functional regression

Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To this end, this paper introduces the functional linear models and adapts it to hydrological forecasting. More precisely, functional linear models are regression models based on curves instead of single values. They allow to consider the whole process instead of a limited number of time points or features. We apply these models to analyse the flow volume and the whole streamflow curve during a given period by using precipitations curves. The functional model is shown to lead to encouraging results. The potential of functional linear models to detect special features that would have been hard to see otherwise is pointed out. The functional model is also compared to the artificial neural network approach and the advantages and disadvantages of both models are discussed. Finally, future research directions involving the functional model in hydrology are presented

Une évaluation de la robustesse de la méthode du krigeage canonique pour l’analyse régionale des débits

Dans le présent article, on se propose d’évaluer la généralité et la robustesse du krigeage canonique, une méthode d’estimation régionale du débit, en l’appliquant pour l’estimation du débit moyen interannuel en régime hydrologique tropical et dans des conditions imparfaites de qualité et de disponibilité de données. Pour ce faire, la méthode du krigeage canonique a été appliquée au cas de Haïti dont le réseau de stations hydrométriques est très limité. Le krigeage canonique a été comparé à la régression linéaire, une méthode simple d’estimation régionale. Selon les critères de performance définis, le krigeage canonique paraît légèrement plus performant que la régression. Il produit des estimations moins biaisées (un biais relatif moyen de ‑ 13 % contre ‑ 20 % pour la régression) et des erreurs relatives légèrement moins importantes (54,4 % contre 59,6 %). Toutefois, le krigeage canonique a été moins performant pour l’estimation du débit des plus grands bassins versants, bien que ses performances globales demeurent acceptables. Par ailleurs, vu les conditions très défavorables dans lesquelles la méthode a été appliquée, il n’a pas été possible de relier la baisse dans les performances du krigeage canonique à une déficience dans la généralité de l’approche et/ou dans sa robustesse.The objective of this study was to test the general application and the robustness of canonical kriging, a new approach regional hydrological estimation. The evaluation of the robustness was carried out for the estimation of mean annual streamflow over the continental territory of Haiti, under a tropical climate and under non-optimal conditions of data quality and availability. The performances of canonical kriging were studied using cross validation. The results were compared to those of the linear regression between the mean annual streamflow and the watershed area applied for the same conditions. In general, canonical kriging yields slightly higher performances. It produces less biased estimates (mean relative bias of ‑ 13% against ‑ 20% for regression) with slightly less significant relative errors (54.4% against 59.6% for regression). However, the linear regression produced better estimates for the largest basins although the global performances of canonical krigeage remained acceptable. In addition, considering the very unfavourable conditions in which the method was applied, it was not possible to connect the decrease in the performances of canonical krigeage to a lack in the general application of the approach and/or its robustness

Historical and Projected Surface Temperature over India during the 20th and 21st century.

Surface Temperature (ST) over India has increased by ~0.055 K/decade during 1860-2005 and follows the global warming trend. Here, the natural and external forcings (e.g., natural and anthropogenic) responsible for ST variability are studied from Coupled Model Inter-comparison phase 5 (CMIP5) models during the 20th century and projections during the 21st century along with seasonal variability. Greenhouse Gases (GHG) and Land Use (LU) are the major factors that gave rise to warming during the 20th century. Anthropogenic Aerosols (AA) have slowed down the warming rate. The CMIP5 projection over India shows a sharp increase in ST under Representative Concentration Pathways (RCP) 8.5 where it reaches a maximum of 5 K by the end of the 21st century. Under RCP2.6 emission scenarios, ST increases up to the year 2050 and decreases afterwards. The seasonal variability of ST during the 21st century shows significant increase during summer. Analysis of rare heat and cold events for 2080-2099 relative to a base period of 1986-2006 under RCP8.5 scenarios reveals that both are likely to increase substantially. However, by controlling the regional AA and LU change in India, a reduction in further warming over India region might be achieved

Estimation of local extreme suspended sediment concentrations in California Rivers

International audienceThe total amount of suspended sediment load carried by a stream during a year is usually transported during one or several extreme events related to high river flow and intense rainfall, leading to very high suspended sediment concentrations (SSCs). In this study quantiles of SSC derived from annual maximums and the 99th percentile of SSC series are considered to be estimated locally in a site-specific approach using regional information. Analyses of relationships between physiographic characteristics and the selected indicators were undertaken using the localities of 5-km radius draining of each sampling site. Multiple regression models were built to test the regional estimation for these indicators of suspended sediment transport. To assess the accuracy of the estimates, a Jack-Knife re-sampling procedure was used to compute the relative bias and root mean square error of the models. Results show that for the 19 stations considered in California, the extreme SSCs can be estimated with 40–60% uncertainty, depending on the presence of flow regulation in the basin. This modelling approach is likely to prove functional in other Mediterranean climate watersheds since they appear useful in California, where geologic, climatic, physiographic, and land-use conditions are highly variable

Evaluation of a Depth-Based Multivariate k

A nonparametric simulation model (k-nearest neighbor resampling, KNNR) for water quality analysis involving geographic information is suggested to overcome the drawbacks of parametric models. Geographic information is, however, not appropriately handled in the KNNR nonparametric model. In the current study, we introduce a novel statistical notion, called a “depth function,” in the classical KNNR model to appropriately manipulate geographic information in simulating stormwater quality. An application is presented for a case study of the total suspended solids throughout the entire United States. The stormwater total suspended solids concentration data indicated that the proposed model significantly improves the simulation performance compared with the existing KNNR model