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Lee T.,Gyeongsang National University | Modarres R.,INRS ETE | Ouarda T.B.M.J.,INRS ETE | Ouarda T.B.M.J.,Masdar Institute of Science and Technology
Hydrological Processes | Year: 2013

In recent decades, copula functions have been applied in bivariate drought duration and severity frequency analysis. Among several potential copulas, Clayton has been mostly used in drought analysis. In this research, we studied the influence of the tail shape of various copula functions (i.e. Gumbel, Frank, Clayton and Gaussian) on drought bivariate frequency analysis. The appropriateness of Clayton copula for the characterization of drought characteristics is also investigated. Drought data are extracted from standardized precipitation index time series for four stations in Canada (La Tuque and Grande Prairie) and Iran (Anzali and Zahedan). Both duration and severity data sets are positively skewed. Different marginal distributions were first fitted to drought duration and severity data. The gamma and exponential distributions were selected for drought duration and severity, respectively, according to the positive skewness and Kolmogorov-Smirnov test. The results of copula modelling show that the Clayton copula function is not an appropriate choice for the used data sets in the current study and does not give more drought risk information than an independent model for which the duration and severity dependence is not significant. The reason is that the dependence of two variables in the upper tail of Clayton copula is very weak and similar to the independent case, whereas the observed data in the transformed domain of cumulative density function show high association in the upper tail. Instead, the Frank and Gumbel copula functions show better performance than Clayton function for drought bivariate frequency analysis. © 2012 John Wiley & Sons, Ltd.

Lee T.,Gyeongsang National University | Ouarda T.B.M.J.,INRS ETE | Ouarda T.B.M.J.,Masdar Institute of Science and Technology
Journal of Geophysical Research: Atmospheres | Year: 2011

Long-term nonstationary oscillations (NSOs) are commonly observed in climatological data series such as global surface temperature anomalies (GSTA) and low-frequency climate oscillation indices. In this work, we present a stochastic model that captures NSOs within a given variable. The model employs a data-adaptive decomposition method named empirical mode decomposition (EMD). Irregular oscillatory processes in a given variable can be extracted into a finite number of intrinsic mode functions with the EMD approach. A unique data-adaptive algorithm is proposed in the present paper in order to study the future evolution of the NSO components extracted from EMD. To evaluate the model performance, the model is tested with the synthetic data set from Rössler attractor and with GSTA data. The results of the attractor show that the proposed approach provides a good characterization of the NSOs. For GSTA data, the last 30 observations are truncated and compared to the generated data. Then the model is used to predict the evolution of GSTA data over the next 50 years. The results of the case study confirm the power of the EMD approach and the proposed NSO resampling (NSOR) method as well as their potential for the study of climate variables. Copyright 2011 by the American Geophysical Union.

Lee T.,INRS ETE | Salas J.D.,Colorado State University | Prairie J.,University of Colorado at Boulder
Water Resources Research | Year: 2010

Stochastic streamflow generation is generally utilized for planning and management of water resources systems. For this purpose, a number of parametric and nonparametric models have been suggested in literature. Among them, temporal and spatial disaggregation approaches play an important role particularly to make sure that historical variance-covariance properties are preserved at various temporal and spatial scales. In this paper, we review the underlying features of existing nonparametric disaggregation methods, identify some of their pros and cons, and propose a disaggregation algorithm that is capable of surmounting some of the shortcomings of the current models. The proposed models hinge on k-nearest neighbor resampling, the accurate adjusting procedure, and a genetic algorithm. The models have been tested and compared to an existing nonparametric disaggregation approach using data of the Colorado River system. It has been shown that the model is capable of (1) reproducing the season-to-season correlations including the correlation between the last season of the previous year and the first season of the current year, (2) minimizing or avoiding the generation of flow patterns across the year that are literally the same as those of the historical records, and (3) minimizing or avoiding the generation of negative flows. In addition, it is applicable to intermittent river regimes. Copyright 2010 by the American Geophysical Union.

Modarres R.,INRS ETE | Sarhadi A.,Isfahan University of Technology
Global and Planetary Change | Year: 2011

Iran is a large country with diverse geophysical and climatic conditions which are influenced by both large atmospheric circulation patterns and local effects. The density of rainfall station network of Iran is not enough for rainfall estimation at ungauged regions.Therefore, rainfall regionalization should be used to extend rainfall data to regions where rainfall data are not available. The aim of this study is to use cluster analysis and L-moment methods together to quantify regional rainfall patterns of Iran using annual rainfall of 137 stations for the period of 1952-2003. The cluster analysis follows "Ward's method" and shows eight regions of rainfall in Iran. The homogeneity test of L-moments shows that most of these regions are homogeneous. Using the goodness-of-fit test, Z Dist, the regional frequency distribution functions for each group are then selected. The 3-parameter Log Normal (LN3), Generalized Extreme Value (GEV) and generalize logistic (GLOG) distributions are selected for the first, second and the remaining 6 regions of rainfall over Iran, respectively. However, because of different rainfall generating mechanisms in Iran such as elevation, sea neighborhood and large atmospheric circulation systems, no parent distribution could be found for the entire country. © 2010 Elsevier B.V.

Modarres R.,INRS ETE | Ouarda T.B.M.J.,INRS ETE | Ouarda T.B.M.J.,Masdar Institute of Science and Technology
Hydrological Processes | Year: 2013

The existence of time-dependent variance or conditional variance, commonly called heteroscedasticity, in hydrologic time series has not been thoroughly investigated. This paper deals with modelling the heteroscedasticity in the residuals of the seasonal autoregressive integrated moving average (SARIMA) model using a generalized autoregressive conditional heteroscedasticity (GARCH) model. The model is applied to two monthly rainfall time series from humid and arid regions. The effect of Box-Cox transformation and seasonal differencing on the remaining seasonal heteroscedasticity in the residuals of the SARIMA model is also investigated. It is shown that the seasonal heteroscedasticity in the residuals of the SARIMA model can be removed using Box-Cox transformation along with seasonal differencing for the humid region rainfall. On the other hand, transformation and seasonal differencing could not remove heteroscedasticity from the residuals of the SARIMA model fitted to rainfall data in the arid region. Therefore, the GARCH modelling approach is necessary to capture the heteroscedasticity remaining in the residuals of a SARIMA model. However, the evaluation criteria do not necessarily show that the GARCH model improves the performance of the SARIMA model. © 2012 John Wiley & Sons, Ltd.

Fasbender D.,INRS ETE | Ouarda T.B.M.J.,INRS ETE
Journal of Climate | Year: 2010

Atmosphere-ocean general circulation models (AOGCMs) are useful for assessing the state of the climate at large scales. Unfortunately, they are not tractable for the finer-scale applications (e.g., hydrometeorological variables). Downscaling methods allow the transfer of large-scale information to finer scales and they are thus relevant for the assessment of finer-scale variables. Among a wide range of downscaling methods, regressionbased approaches are commonly used for downscaling AOGCM data because of their low computational requirements. However, downscaled variables are generally reproduced at gauged weather stations only. Results at the gauged stations can then be interpolated a posteriori at ungauged locations with kriging or other methods. In this paper, a spatial Bayesian model is proposed for the downscaling of coarse-scale atmospheric data (i.e., either reanalysis or AOGCM) to minimum and maximum daily temperatures. This approach uses a Bayesian framework for mixing a prior distribution reflecting the monthly spatial dependence of the temperatures with the daily fluctuations induced by the atmospheric predictors. Local characteristics (i.e., altitude and latitude) are also taken into account in the mean of the prior distribution by using a geographical regression model. The posterior distribution thus reflects both monthly local patterns because of the prior and daily larger-scale fluctuations. Finally, the Bayesian approach also allows for the accounting of estimated parameter uncertainty, making it more stable to poor parameter fitting. The method is applied to the southern part of the province of Quebec, Canada. Results show that the downscaled distributions of the temperatures at gauged sites are in sufficient agreement with the validation dataset compared to a classical regression-based method. The proposed model has also the advantage of directly producing temperature maps. © 2010 American Meteorological Society.

Modarres R.,INRS ETE
Water Resources Management | Year: 2010

The spatial variation of the statistical characteristics of the extreme dry events, such as the annual maximum dry spell length (AMDSL), is a key practice for regional drought analysis and mitigation management. For arid and semi arid regions, where the data set is short and insufficient, the regionalization methods are applied to transfer at-site data to a region. The spatial variation and regional frequency distribution of annual maximum dry spell length for Isfahan Province, located in the semi arid region of Iran, was investigated using a daily database compiled from 31 rain gauges and both L-moment and multivariate analysis. The use of L-moment method showed a homogeneous region over entire province with generalized logistic distribution (GLOG) as the regional frequency distribution. However, the cluster analysis performed two regions in west and east of the province where L-moment method demonstrated the homogeneity of the regions and GLOG and Pearson Type III (PIII) distributions as regional frequency distributions for each region, respectively. The principal component analysis was applied on at-site statistics of AMDSL and found the L-coefficient of skewness (LCs) and maximum AMDSL the main variables describing the spatial variation of AMDSL over the Isfahan Province. The comparison of two homogeneous regions also proved the difference between two regions. Therefore, this study indicates the advantage of the use of multivariate methods with L-moment method for hydrologic regionalization and spatial variation of drought statistical characteristics. © Springer Science+Business Media B.V. 2009.

This paper presents an implementation of the convolutional perfectly matched layer for the velocity-stress formulation of poroviscoelastic equations in anisotropic media, with high-order time and space formulations. After its introduction by Bérenger in 1994 for Maxwell's equation, the perfectly matched layer (PML) quickly became the standard approach to absorb outgoing waves on a numerical mesh. Subsequent developments include generalization and formulation in terms of a convolutional operator and auxiliary differential equations that improve efficiency and allow for the implementation of high-order time integration schemes. In this work, a fourth-order Runge-Kutta scheme is employed. Also, with the convolutional formulation, the wavefields need not be split as in the original formalism. Such unsplit PMLs allow for the implementation with a pseudospectral operator as presented in this paper. Although efforts have been deployed for the optimization of PML parameters, such an approach is not always tractable, especially for seismic wave propagation because different types of waves interact with the medium. Hence, the performance of the implementation is evaluated through a series of numerical experiments. Tests are performed for waves impinging on the PML interface both at normal and grazing incidence, for both isotropic and anisotropic media. The results highlight the advantage of the convolutional formulation for waves at grazing incidence and show that anisotropic media require a larger number of absorbing layers to achieve performances comparable to those obtained in isotropic media. © 2011 Elsevier Ltd.

Chebana F.,INRS ETE | Dabo-Niang S.,Charles de Gaulle University - Lille 3 | Ouarda T.B.M.J.,INRS ETE | Ouarda T.B.M.J.,Masdar Institute of Science and Technology
Water Resources Research | Year: 2012

The prevention of flood risks and the effective planning and management of water resources require river flows to be continuously measured and analyzed at a number of stations. For a given station, a hydrograph can be obtained as a graphical representation of the temporal variation of flow over a period of time. The information provided by the hydrograph is essential to determine the severity of extreme events and their frequencies. A flood hydrograph is commonly characterized by its peak, volume, and duration. Traditional hydrological frequency analysis (FA) approaches focused separately on each of these features in a univariate context. Recent multivariate approaches considered these features jointly in order to take into account their dependence structure. However, all these approaches are based on the analysis of a number of characteristics and do not make use of the full information content of the hydrograph. The objective of the present work is to propose a new framework for FA using the hydrographs as curves: functional data. In this context, the whole hydrograph is considered as one infinite-dimensional observation. This context allows us to provide more effective and efficient estimates of the risk associated with extreme events. The proposed approach contributes to addressing the problem of lack of data commonly encountered in hydrology by fully employing all the information contained in the hydrographs. A number of functional data analysis tools are introduced and adapted to flood FA with a focus on exploratory analysis as a first stage toward a complete functional flood FA. These methods, including data visualization, location and scale measures, principal component analysis, and outlier detection, are illustrated in a real-world flood analysis case study from the province of Quebec, Canada. © 2012 by the American Geophysical Union.

Malo M.,INRS ETE | Bedard K.,INRS ETE
Energy Procedia | Year: 2012

The assessment of the CO2 storage potential in the Province of Québec, Canada, evaluates the four Paleozoic sedimentary basins present in the south of the province. The St. Lawrence Lowlands sub-basin represents by far the most prospective basin for CO2 storage. It contains excellent reservoir-seal pairs and several large CO2 emitters are present. The Anticosti sub-basin and the Magdalen basins are geologically prospective for CO2 storage, but infrastructure and accessibility are poor due to their offshore setting and large CO2 emitters are located far away. The prospectivity of the Appalachian and Gaspé Belt basins for CO 2 storage is evaluated as very low, except for the northeastern part of the Gaspé Peninsula which offers more potential. © 2012 The Authors. Published by Elsevier Ltd.

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