In this paper, a statistical inference of Southeastern Canada extreme daily precipitation amounts is proposed using a classical nonstationary peaks-over-threshold model. Indeed, the generalized ...Pareto distribution (GPD) is fitted to excess time series derived from annual averages of independent precipitation amount events above a fixed threshold, the 99th percentile. Only the scale parameter of the fitted distribution is allowed to vary as a function of a covariate. This variability is modeled using B-spline function. Nonlinear correlation and cross-wavelet analysis allowed identifying two dominant climate indices as covariates in the study area, Arctic Oscillation (AO) and Pacific North American (PNA). The nonstationary frequency analysis showed that there is an east-west behavior of the AO index effects on extreme daily precipitation amounts in the study area. Indeed, the higher quantiles of these events are conditional to the AO positive phase in Atlantic Canada, while those in the more southeastern part of Canada, especially in Southern Quebec and Ontario, are negatively related to AO. The negative phase of PNA also gives the best significant correlation in these regions. Moreover, a regression analysis between AO (PNA) index and conditional quantiles provided slope values for the positive phase of the index on the one hand and the negative phase and on the other hand. This statistic allows computing a slope ratio which permits to sustain the nonlinear relation assumption between climate indices and precipitation and the development of the nonstationary GPD model for Southeastern Canada extremes precipitation modeling.
ABSTRACT
Quantile estimates are generally interpreted in association with the return period concept in practical engineering. To do so with the peaks‐over‐threshold (POT) approach, combined ...Poisson‐generalized Pareto distributions (referred to as PD‐GPD model) must be considered. In this article, we evaluate the incorporation of non‐stationarity in the generalized Pareto distribution (GPD) and the Poisson distribution (PD) using, respectively, the smoothing‐based B‐spline functions and the logarithmic link function. Two models are proposed, a stationary PD combined to a non‐stationary GPD (referred to as PD0‐GPD1) and a combined non‐stationary PD and GPD (referred to as PD1‐GPD1). The teleconnections between hydro‐climatological variables and a number of large‐scale climate patterns allow using these climate indices as covariates in the development of non‐stationary extreme value models. The case study is made with daily precipitation amount time series from southeastern Canada and two climatic covariates, the Arctic Oscillation (AO) and the Pacific North American (PNA) indices. A comparison of PD0‐GPD1 and PD1‐GPD1 models showed that the incorporation of non‐stationarity in both POT models instead of solely in the GPD has an effect on the estimated quantiles. The use of the B‐spline function as link function between the GPD parameters and the considered climatic covariates provided flexible non‐stationary PD‐GPD models. Indeed, linear and nonlinear conditional quantiles are observed at various stations in the case study, opening an interesting perspective for further research on the physical mechanism behind these simple and complex interactions.
Using statistical tools like the cross‐wavelet analysis illustrated in the figure, common features of variability are found between precipitation extreme events and the Artic Oscillation index at the Upper Stewiacke station located in Nova Scotia (Canada). Using this index as covariate, we developed non‐stationary Poisson‐generalized Pareto models, which allow observing conditional quantiles with concave form. The proposed models are more flexible than classical extreme value non‐stationary models which often used prior assumption of linear dependence.
Climate impact studies often require a reduction of the ensembles of opportunity from the Coupled Model Intercomparison Project when the simulations are used to drive impact models. An impact model’s ...nature limits the number of feasible realizations based on complexity and computational requirements or capacities. For the purpose of driving a hydrological model and an ocean model in the BaySys research program, two hierarchical, differently sized simulation ensembles were produced to represent climate evolution for the region of the Hudson Bay Drainage Basin. We compare a 19-member ensemble to a 5-member subset to demonstrate comparability of the driving climate used to produce model results. Ten extreme climate indicators and their changes are compared for the full study region and seven sub regions, on an annual and seasonal basis and for two future climate horizons. Results indicate stronger warming in the North and for cold temperatures and an East-West gradient in precipitation with larger absolute increases to the East and South of the Hudson Bay. Generally, the smaller ensemble is sufficient to adequately reproduce the mean and spread in the indicators found for the larger ensemble. The analysis of extreme climate indicators ensures that the tails of the distribution of temperature and precipitation are addressed. We conclude that joint analysis at the interface of the hydrological and ocean model domains are not limited by the application of differently sized climate simulation ensembles as driving input for the two different modeling exercises of the BaySys project environmental studies, yet acknowledging that impact model output may be dependent on other factors.
L’analyse fréquentielle (AF) est un outil statistique très utilisé en hydrologie pour la prédiction des quantiles d’évènements extrêmes. L’objectif général de la présente thèse était de proposer de ...nouvelles approches d’AF des extrêmes basées sur la méthode des dépassements de seuil ou peaks-over-threshold (POT) en anglais.En effet, avec la problématique des changements climatiques (CC), les indices climatiques sont fréquemment utilisés comme covariables dans le développement de modèles d’AF non-stationnaire du fait de la présence de tendances, dépendances, cycles ou ruptures dans les séries d’observations hydroclimatiques. Le premier objectif spécifique de cette thèse visait à analyser les téléconnexions entre les oscillations climatiques à grande échelle et les processus hydrologiques locaux/régionaux, afin de développer des modèles POT avec covariables. Les précipitations étant par essence très variables dans le temps et dans l’espace, la relation de dépendance entre plusieurs indices climatiques et des séries temporelles décrivant l’intensité et la fréquence des évènements extrêmes de la précipitation totale journalière, a été examinée à l’échelle du Sud-Est du Canada. Deux méthodes d’évaluation complémentaires, à savoir l’analyse de corrélation des rangs par le calcul du tau de Kendall ainsi que l’analyse par ondelettes, ont été employées pour confirmer statistiquement les interactions existantes. Cette analyse préliminaire a permis d’identifier deux indices climatiques ayant une influence significative sur l’intensité et la fréquence des précipitations extrêmes à l’échelle de la zone d’étude choisie : l’indice de l’oscillation arctique (AO pour Arctic Oscillation) et l’indice du Pacifique-Amérique du Nord (PNA pour Pacific North American). Des modèles de Pareto Généralisée (GPD pour Generalized Pareto Distribution) non-stationnaires ont été alors développés en faisant varier le paramètre d’échelle de la GPD en fonction de l’indice AO ou PNA au moyen de l’utilisation de fonctions semi-paramétriques, les fonctions B-splines. Celles-ci permettent de capturer aussi bien les relations simples (c’est à dire linéaires) que complexes (c’est à dire non-linéaires).Les quantiles de la précipitation extrême ont été estimés à partir du modèle de la GPD stationnaire (où tous les paramètres sont constants) et de différents modèles GPD-B-splines qui ont été développés en faisant varier deux paramètres déterminants de la fonction B-spline: le degré (d) du polynôme et le nombre de noeuds internes (k). Les modèles GPD non-stationnaires ont montré une meilleure performance que le modèle GPD stationnaire à la lumière des valeurs minimales du critère d’information d’Akaïke observées surtout avec le modèle GPD-B-spline (k=2 et d=1).La structure physique des indices climatiques comportant une phase négative et une phase positive, les modèles GPD-B-splines se sont montrés flexibles. En effet, des réponses linéaires et non-linéaires des précipitations extrêmes aux indices AO et PNA ont pu être détectées au Sud-Est du Canada. D’où des possibilités de régionalisation de ces modèles locaux pour fournir un outil robuste de prédiction des quantiles.Toutefois, l’interprétation pratique des quantiles est généralement associée à la notion de période de retour. Pour cette raison, il y un intérêt à incorporer l’information sur le taux moyen annuel des dépassements de seuil dans la modélisation des dépassements de seuil. Pour ce faire, l’étude de la surdispersion dans l’occurrence annuelle de ces évènements est suggérée au préalable pour valider ou non l’hypothèse que la fréquence des dépassements de seuil est distribuée suivant un processus de Poisson.
In Burkina Faso, water resources are limited and their availability is irregular given the spatial and temporal variability of climatic factors in addition to the complexity of the hydrological ...network and the high population densities. Indeed, these resources are subject to many pressures and, being able to organize its management would provide equal opportunities of socio-economic development in the four major watersheds of Burkina Faso. Therefore, this study is focused on the watershed of the Nakanbé River, which is one of the main areas of concentration in terms of human dynamics but also economic and political representativeness. For this, the Nakanbé River watershed as experienced an accelerated degradation of its environment since the 1970s. Consequently, it became necessary and urgent to address the management of its water resources and propose sustainable solutions. This study initially consists to an analysis of climate data to understand and assess the dynamics trends in the historical evolution of parameters such rainfall, temperature and potential evapotranspiration. To do so, statistical analysis with simple comparison analysis, Mann-Kendall trend test and Sen's method of slopes estimation have been used. On the other hand, a survey with the local residents helped to assess their perceptions of the local climate evolution with the induced effects, and the local dynamic of the water resources management. As results, the Mann-Kendall test detected at a significance level of α = 0.05, a downward yearly trends of rainfall and an higher yearly trends of temperature at Ouahigouya and Ouagadougou synoptic stations. In addition, the local population perceptions reflect a decline and irregular rainfall, an increase in heat and a reduction of cold months. Adaptation actions are then taken at national level arising from the new policy of water resources integrated management. Then, this research shall be an additional tool to assess the vulnerability of the Nakanbé River watershed to climate variability for sustainable management of its water resources. Key Words : Burkina Faso; Nakanbé River; Water; Climate Variability-Change; Perception
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