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Dominique Fasbender and Taha B. M. J. Ouarda

Abstract

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, regression-based 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.

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Ana I. Requena, Taha B. M. J. Ouarda, and Fateh Chebana

Abstract

Estimation of flood events at ungauged sites is often performed through regional flood frequency analysis (RFFA). RFFA uses the available information at gauged sites to estimate the desired design events at the ungauged site. These regional methods are based on a prior aggregation of the hydrological information at the gauged sites, which implies loss of information. In the present study, a different approach or path for conducting RFFA is presented. First, the daily streamflow series at the ungauged site is regionally estimated from daily information at the gauged sites through a regional flow duration curve approach. Then, a local flood frequency analysis is performed on the extracted maximum peak flow series. The proposed approach, referred to as regional streamflow-based frequency analysis (RSBFA), is applied to a case study in the province of Quebec, Canada. Results indicate that the performance of the RSBFA approach is comparable to traditional methods. However, the proposed method has the advantages of being simple, flexible, and of providing the whole daily streamflow series at the ungauged site, which allows the direct estimation of a large number of other flow characteristics, such as low-flow features. The RSBFA approach also avoids performing a complete at-site flood frequency analysis at each gauged site. The fact that all the regional information is included in the regionally estimated daily streamflow series implies a number of benefits: annual or seasonal, absolute or specific, stationary or nonstationary, and univariate or multivariate flood quantiles corresponding to any return period may then be obtained through the estimated series without reconducting a regional analysis.

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Martin Durocher, Fateh Chebana, and Taha B. M. J. Ouarda

Abstract

This paper presents an approach for regional flood frequency analysis (RFFA) in the presence of nonlinearity and problematic stations, which require adapted methodologies. To this end, the projection pursuit regression (PPR) is proposed. The PPR is a family of regression models that applies smooth functions on intermediate predictors to fit complex patterns. The PPR approach can be seen as a hybrid method between the generalized additive model (GAM) and the artificial neural network (ANN), which combines the advantages of both methods. Indeed, the PPR approach has the structure of a GAM to describe nonlinear relations between hydrological variables and other basin characteristics. On the other hand, PPR can consider interactions between basin characteristics to improve the predictive capabilities in a similar way to ANN, but simpler. The methodology developed in the present study is applied to a case study represented by hydrometric stations from southern Québec, Canada. It is shown that flood quantiles are mostly associated with a dominant intermediate predictor, which provides a parsimonious representation of the nonlinearity in the flood-generating processes. The model performance is compared to eight other methods available in the literature for the same dataset, including GAM and ANN. When using the same basin characteristics, the results indicate that the simpler structure of PPR does not affect the global performance and that PPR is competitive with the best existing methods in RFFA. Particular attention is also given to the performance resulting from the choice of the basin characteristics and the presence of problematic stations.

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Kichul Jung, Taha B. M. J. Ouarda, and Prashanth R. Marpu

Abstract

Regional frequency analysis (RFA) is widely used in the design of hydraulic structures at locations where streamflow records are not available. RFA estimates depend on the precise delineation of homogenous regions for accurate information transfer. This study proposes new physiographical variables based on river network features and tests their potential to improve the accuracy of hydrological feature estimates. Information about river network types is used both in the definition of homogenous regions and in the estimation process. Data from 105 river basins in arid and semiarid regions of the United States were used in our analysis. Artificial neural network ensemble models and canonical correlation analysis were used to produce flood quantile estimates, which were validated through tenfold cross and jackknife validations. We conducted analysis for model performance based on statistical indices, such as the Nash–Sutcliffe efficiency, root-mean-square error, relative root-mean-square error, mean absolute error, and relative mean bias. Among various combinations of variables, a model with 10 variables produced the best performance. Further, 49, 36, and 20 river networks in the 105 basins were classified as dendritic, pinnate, and trellis networks, respectively. The model with river network classification for the homogenous regions appeared to provide a superior performance compared with a model without such classification. The results indicated that including our proposed combination of variables could improve the accuracy of RFA flood estimates with the classification of the network types. This finding has considerable implications for hydraulic structure design.

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Ju-Young Shin, Taesam Lee, and Taha B. M. J. Ouarda

Abstract

Frequency analysis has been widely applied to investigate the behavior and characteristics of hydrometeorological variables. Hydrometeorological variables occasionally show mixture distributions when multiple generating phenomena cause the extreme events to occur. In such cases, a mixture distribution should be applied. Past studies on mixture distributions assumed that they are drawn from the same probability density functions. In fact, many hydrometeorological variables can consist of different types of probability density functions. Research on heterogeneous mixture distributions can lead to improvements in understanding the behavior and characteristics of hydrometeorological variables and in the capacity to model them properly. In the present study heterogeneous mixture distributions are developed to model extreme hydrometeorological events. To fit heterogeneous mixture distributions, the authors present an extension of the metaheuristic maximum likelihood approach. The performance of the parameter estimation method employed was verified through simulation tests. The fits of nonmixture, homogeneous mixture, and heterogeneous mixture distributions were evaluated through the application to a real-world case study of the extreme rainfall events of South Korea. Results indicate that the heterogeneous mixture distribution is a good alternative when sources possessing dissimilar statistical characteristics influence extreme hydrometeorological variables.

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Camille Ternynck, Mohamed Ali Ben Alaya, Fateh Chebana, Sophie Dabo-Niang, and Taha B. M. J. Ouarda

Abstract

Classification of streamflow hydrographs plays an important role in a large number of hydrological and hydraulic studies. For instance, it allows decisions to be made regarding the implementation of hydraulic structures and characterization of different flood types, leading to a better understanding of extreme flow behavior. The employed hydrograph classification methods are generally based on a finite number of hydrograph characteristics and do not include all the available information contained in a discharge time series. In this paper, two statistical techniques from the theory of functional data classification are adapted and applied for the analysis of flood hydrographs. Functional classification directly employs all data of a discharge time series and thus contains all available information on shape, peak, and timing. This potentially allows a better understanding and treatment of floods as well as other hydrological phenomena. The considered functional methodology is applied to streamflow datasets from the province of Quebec, Canada. It is shown that classes obtained using functional approaches have merit and can lead to better representation than those obtained using a multidimensional hierarchical classification method. The considered methodology has the advantage of using all of the information contained in the hydrograph, thus reducing the subjectivity that is inherent in multidimensional analysis of the type and number of characteristics to be used and consequently diminishing the associated uncertainty.

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Bouchra Nasri, Yves Tramblay, Salaheddine El Adlouni, Elke Hertig, and Taha B. M. J. Ouarda

Abstract

The high precipitation variability over North Africa presents a major challenge for the population and the infrastructure in the region. The last decades have seen many flood events caused by extreme precipitation in this area. There is a strong need to identify the most relevant atmospheric predictors to model these extreme events. In the present work, the effect of 14 different predictors calculated from NCEP–NCAR reanalysis, with daily to seasonal time steps, on the maximum annual precipitation (MAP) is evaluated at six coastal stations located in North Africa (Larache, Tangier, Melilla, Algiers, Tunis, and Gabès). The generalized extreme value (GEV) B-spline model was used to detect this influence. This model considers all continuous dependence forms (linear, quadratic, etc.) between the covariates and the variable of interest, thus providing a very flexible framework to evaluate the covariate effects on the GEV model parameters. Results show that no single set of covariates is valid for all stations. Overall, a strong dependence between the NCEP–NCAR predictors and MAP is detected, particularly with predictors describing large-scale circulation (geopotential height) or moisture (humidity). This study can therefore provide insights for developing extreme precipitation downscaling models that are tailored for North African conditions.

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