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Modarres R.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.M.J.,Masdar Institute of Science and Technology
Hydrological Sciences Journal | Year: 2013

Time series modelling approaches are useful tools for simulating and forecasting hydrological variables and their change through time. Although linear time series models are common in hydrology, the nonlinear time series model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, has rarely been used in hydrology and water resources engineering. The GARCH model considers the conditional variance remaining in the residuals of the linear time series models, such as an ARMA or an ARIMA model. In the present study, the advantages of a GARCH model against a linear ARIMA model are investigated using three classes of the GARCH approach, namely Power GARCH, Threshold GARCH and Exponential GARCH models. A daily streamflow time series of the Matapedia River, Quebec, Canada, is selected for this study. It is shown that the ARIMA (13,1,4) model is adequate for modelling streamflow time series of Matapedia River, but the Engle test shows the existence of heteroscedasticity in the residuals of the ARIMA model. Therefore, an ARIMA (13,1,4)-GARCH (3,1) error model is fitted to the data. The residuals of this model are examined for the existence of heteroscedasticity. The Engle test indicates that the GARCH model has considerably reduced the heteroscedasticity of the residuals. However, the Exponential GARCH model seems to completely remove the heteroscedasticity from the residuals. The multi-criteria evaluation for model performance also proves that the Exponential GARCH model is the best model among ARIMA and GARCH models. Therefore, the application of a GARCH model is strongly suggested for hydrological time series modelling as the conditional variance of the residuals of the linear models can be removed and the efficiency of the model will be improved. © 2013 Copyright 2013 IAHS Press.


Lee T.,Gyeongsang National University | Ouarda T.B.M.J.,Masdar Institute of Science and Technology | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Jeong C.,Induk University
Journal of Hydrology | Year: 2012

A multivariate stochastic generation model for daily weather variables is proposed that extends the multivariate . k-nearest neighbor resampling approach (MKNN). Major drawbacks of the MKNN approach include repetitive historical multivariate patterns, underestimating variance and serial correlation, and reshuffling of historical data. These drawbacks cause under-generation of events that are extreme in their frequency and magnitude. In this study, these drawbacks are addressed by applying a stochastic optimization technique (i.e., a genetic algorithm (GA)) and a perturbation using a gamma kernel density estimate (GKDE). The competitive selection operator in the GA was used to better preserve the historical variance and serial correlation as well as to produce unprecedented multivariate patterns. By employing the GKDE, the resampled precipitation data are perturbed, and thus new precipitation values are generated. To preserve the distribution of the annual maximum events fitted to a general extreme value (GEV), the GKDE bandwidth was selected by employing the statistics of the historical annual maximum. The proposed method was applied to generate six daily weather variables (maximum temperature, minimum temperature, dew point temperature, solar radiation, wind speed, and precipitation) of the summer season (June-September) for a station in Seoul, South Korea. The presented results indicate that the suggested weather generator is an appropriate alternative for generating daily weather variables while reproducing the historical extreme distribution. © 2012 Elsevier B.V.


Modarres R.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.M.J.,Masdar Institute of Science and Technology | Vanasse A.,Université de Sherbrooke | And 2 more authors.
Bone | Year: 2012

The investigation of the association of the climate variables with hip fracture incidences is important in social health issues. This study examined and modeled the seasonal variation of monthly population based hip fracture rate (HFr) time series. The seasonal ARIMA time series modeling approach is used to model monthly HFr incidences time series of female and male patients of the ages 40-74 and 75. + of Montreal, Québec province, Canada, in the period of 1993-2004. The correlation coefficients between meteorological variables such as temperature, snow depth, rainfall depth and day length and HFr are significant. The nonparametric Mann-Kendall test for trend assessment and the nonparametric Levene's test and Wilcoxon's test for checking the difference of HFr before and after change point are also used. The seasonality in HFr indicated sharp difference between winter and summer time. The trend assessment showed decreasing trends in HFr of female and male groups. The nonparametric test also indicated a significant change of the mean HFr. A seasonal ARIMA model was applied for HFr time series without trend and a time trend ARIMA model (TT-ARIMA) was developed and fitted to HFr time series with a significant trend. The multi criteria evaluation showed the adequacy of SARIMA and TT-ARIMA models for modeling seasonal hip fracture time series with and without significant trend. In the time series analysis of HFr of the Montreal region, the effects of the seasonal variation of climate variables on hip fracture are clear. The Seasonal ARIMA model is useful for modeling HFr time series without trend. However, for time series with significant trend, the TT-ARIMA model should be applied for modeling HFr time eries. © 2011 Elsevier Inc.


Khalil B.,Helwan University | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.M.J.,Masdar Institute of Science and Technology | St-Hilaire A.,Canada Research Chair on the Estimation of Hydrometeorological Variables
Water Resources Management | Year: 2012

The extension of records at monthly, weekly or daily time steps at a short-record gauge from another continuously measured gauge is termed "record extension". Ordinary least squares regression (OLS) of the flows, or any hydrological or water quality variable, is a traditional and still common record-extension technique. However, its purpose is to generate optimal estimates of each daily (or monthly) record, rather than the population characteristics, for which the OLS tends to underestimate the variance. The line of organic correlation (LOC) was developed to correct this bias. On the other hand, the Kendall-Theil robust line (KTRL) method has been proposed as an analogue of OLS, its advantage being its robustness in the presence of extreme values. In this study, four record-extension techniques are described, and their properties are explored. These techniques are OLS, LOC, KTRL and a new technique (KTRL2), which includes the advantage of LOC in reducing the bias in estimating the variance and the advantage of KTRL in being robust in the presence of extreme values. A Monte-Carlo study is conducted to examine these four techniques for bias, standard error of moment estimates and full range of percentiles. An empirical examination is made of the preservation of historic water quality concentration characteristics using records from the Nile Delta water quality monitoring network in Egypt. The Monte-Carlo study showed that the OLS and KTRL techniques are shown to have serious deficiencies as record-extension techniques, while the LOC and KTRL2 techniques show results that are nearly similar. Using real water quality records, the KTRL2 is shown to lead to better results than the other techniques. © 2012 Springer Science+Business Media B.V.


Lee T.,Gyeongsang National University | Ouarda T.B.M.J.,Masdar Institute of Science and Technology | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological variables
International Journal of Climatology | Year: 2012

One of the important issues in climate change detection is the selection of climate models for the background noise. The background noise is generally chosen in a somewhat subjective manner. In the current study, we propose an approach of detecting climate change signal in order to mitigate the effects of background noise and to improve climate change detection ability. At first, the high-frequency components of three climate datasets (climate signal, observation, background noise) induced from the random noise process are extracted from empirical mode decomposition (EMD) analysis. Then, statistical detection techniques are applied to the datasets from which the high-frequency random components are excluded. The proposed approach is tested with synthetically generated data and with a real-world case study represented by global surface temperature anomaly (GSTA) data. The case study reveals that each component of the observed GSTA data from EMD contains the information related to external and internal forcings such as solar activity and oceanic circulation. Among these components, the statistically significant low-frequency components are employed in climate change detection. Compared to one of the existing approaches, some improvements in the slope coefficient estimates and the signal-to-noise ratio (SNR) are observed in the synthetic application of the proposed model. The application to the GSTA data shows higher SNR in the proposed approach than in the existing approach. © 2011 Royal Meteorological Society.


Chebana F.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological Variables
Environmetrics | Year: 2011

Several hydrological phenomena are described by two or more correlated characteristics. These dependent characteristics should be considered jointly to be more representative of the multivariate nature of the phenomenon. Consequently, probabilities of occurrence cannot be estimated on the basis of univariate frequency analysis (FA). The quantile, representing the value of the variable(s) corresponding to a given risk, is one of the most important notions in FA. The estimation of multivariate quantiles has not been specifically treated in the hydrological FA literature. In the present paper, we present a new and general framework for local FA based on a multivariate quantile version. The multivariate quantile offers several combinations of the variable values that lead to the same risk. A simulation study is carried out to evaluate the performance of the proposed estimation procedure and a case study is conducted. Results show that the bivariate estimation procedure has an analogous behaviour to the univariate one with respect to the risk and the sample size. However, the dependence structure between variables is ignored in the univariate case. The univariate estimates are obtained as special combinations by the multivariate procedure and with equivalent accuracy. Copyright © 2009 John Wiley & Sons, Ltd.


Nezhad M.K.,Hydro - Quebec | Chokmani K.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Barbet M.,Hydro - Quebec | Bruneau P.,Hydro - Quebec
Hydrological Processes | Year: 2010

In this article, an approach using residual kriging (RK) in physiographical space is proposed for regional flood frequency analysis. The physiographical space is constructed using physiographical/climatic characteristics of gauging basins by means of canonical correlation analysis (CCA). This approach is a modified version of the original method, based on ordinary kriging (OK). It is intended to handle effectively any possible spatial trends within the hydrological variables over the physiographical space. In this approach, the trend is first quantified and removed from the hydrological variable by a quadratic spatial regression. OK is therefore applied to the regression residual values. The final estimated value of a specific quantile at an ungauged station is the sum of the spatial regression estimate and the kriged residual. To evaluate the performance of the proposed method, a cross-validation procedure is applied. Results of the proposed method indicate that RK in CCA physiographical space leads to more efficient estimates of regional flood quantiles when compared to the original approach and to a straightforward regression-based estimator. © 2010 John Wiley & Sons, Ltd.


Lee T.,Gyeongsang National University | Ouarda T.B.M.J.,Masdar Institute of Science and Technology | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological variables
Journal of Hydrology | Year: 2011

Among the various stochastic models used in hydrology and meteorology, the k-nearest neighbor resampling (KNNR) has been one of the most common alternatives to supplement the short historical records. In the KNNR model one needs to select the model order (d) and the number of nearest neighbors (k). Traditionally, the prescriptive selection (k=n 1/2 where n is the record length) has been used for k and no practical solutions were provided to choose d. Another applicable approach is generalized cross-validation (GCV). However, it has been reported in the literature that GCV is not practical for the selection of d and k in the KNNR model. In the current study we propose an approach to select d and k based on the Akaike information criterion (AIC). The proposed approach was validated on a number of simulated datasets and applied to the case study of the Colorado River system. The results indicate that the proposed AIC-based approach represents a robust model for the selection of d and k. In the simulation study, the model led particularly to the selection of the same model orders as the real orders of the simulated datasets. It also gave acceptable k values in the case study. © 2011 Elsevier B.V.


Chebana F.,Canada Research Chair on the Estimation of Hydrometeorological Variables | Ouarda T.B.,Canada Research Chair on the Estimation of Hydrometeorological Variables
Environmetrics | Year: 2011

Extreme value theory (EVT) is commonly applied in several fields, such as finance, hydrology and environmental modeling. It is extensively developed in the univariate setting. A number of studies have focused on the extension of EVT to the multivariate context. However, most of these studies are based on a direct extension of univariate extremes. In the present paper, we present a procedure to identify the extremes in a multivariate sample. The present procedure is based on the statistical notion of depth function combined with the orientation of the observations. The extreme identification itself is important and it can also serve as basis for the modeling and the asymptotic studies. The proposed procedure is also employed to detect peaks-over-thresholds in the multivariate setting. This method is general and includes several special cases. Furthermore, it is flexible and can be applied to several situations depending on the degree of extreme event risk. The procedure is mainly motivated by application considerations. A simulation study is carried out to evaluate the performance of the procedure. An application, based on air quality data, is presented to show the various elements of the procedure. The procedure is also shown to be useful in other statistical areas. © 2011 John Wiley & Sons, Ltd.


Khalil B.,Helwan University | Ouarda T.B.M.J.,Masdar Institute of Science and Technology | Ouarda T.B.M.J.,Canada Research Chair on the Estimation of Hydrometeorological Variables | St-Hilaire A.,Canada Research Chair on the Estimation of Hydrometeorological Variables
Journal of Hydrology | Year: 2011

Three models are developed for the estimation of water quality mean values at ungauged sites. The first model is based on artificial neural networks (ANN), the second model is based on ensemble ANN (EANN) and the third model is based on canonical correlation analysis (CCA) and EANN. The ANN and EANN models are developed to establish the functional relationship between water quality mean values and basin attributes. In the CCA-based EANN model, CCA is used to form a canonical attributes space using data from gauged sites. Then, an EANN is applied to identify the functional relationships between water quality mean values and the attributes in the CCA space. Four water quality variables are selected as output of these models. Variable selection is based on principal component analysis. The water quality variables which showed the highest loading factors in the first four components are selected. The three models are applied to 50 subcatchments in the Nile Delta, Egypt. A jackknife validation procedure is used to evaluate the performance of the three models. The results show that the EANN model provides better generalization ability than the ANN. However, the CCA-based EANN model performed better than the other two models in terms of prediction accuracy. © 2011 Elsevier B.V.

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