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Although hydrological processes are generally nonlinear, linear time series models are commonly adopted in the field of water sciences. Nonlinear approaches such as threshold time series and conditional heteroscedasticity models are still seldom used. In this study, first, two- and three-regime Self-Exciting Threshold Autoregressive (SETAR) models are used to model the mean behavior of daily streamflows. The residual time series computed from the difference between observations and lag-one time-ahead best-estimates of the fitted models are also obtained. Second, the conditional variance behavior of the residual series obtained from the two- and three-regime SETAR models is modeled using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The GARCH model is hence used to capture the time-varying variance behavior of residuals as a nonlinear phenomenon and thus it removes the existence of autoregressive conditional heteroscedasticity so-called ARCH effect. Finally, the performance of SETAR models and their combination with the GARCH model are evaluated. Six deseasonalized daily streamflow series from upstream watershed rivers of Zarrineh Rood dam, in the southern part of Lake Urmia in Iran, are used to illustrate and test the procedure. The McLeod-Li test, a formal test for demonstrating the ARCH effect, indicates that the ARCH effect exists in all residual series, which means that the residuals of streamflow time series are nonstationary in terms of the variance. Results indicate that the hybrid SETAR-GARCH models performed better than the models without GARCH component. Results demonstrate also that the use of nonlinear SETAR and GARCH improves streamflow modeling efficiency by capturing the heteroscedasticity in the residuals of nonlinear threshold time series.

Hydrologic regionalization consists of regrouping stations and catchments in pools based on a similarity measure. Regionalization is commonly used to extract a robust signal that can be used to describe the hydrology of the region, or extrapolated to a location without measured information. Obviously, the similarity measure used affects the type of hydrological behavior one would expect from stations within a region. Most regionalization methods assume a stable and/or linear relationship between parameters of interests while it is well known that the physical processes driving the behavior of hydrometeorological variables are inherently non-linear and non-stationary. In this paper, we propose a similarity measure that is based on the location of changepoints in hydrological time series. The proposed method has the unique advantage over other hydrological region delineation methods to detect regions where hydrological member stations are non-linearly correlated, and where the strength of the relation varies with time. It therefore has the potential to uncover similarities that would not have been detected by existing regionalization techniques. The proposed method is applied to the Tensift watershed located in Morocco, North Africa. The coherence of the detected regions is checked using wavelet coherence.

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 a...

Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, it is possible that the assumption of stationarity, which is prerequisite for traditional frequency analysis and hence, the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extremes based on B-Spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates with linear and non-linear dependence. A Markov Chain Monte Carlo (MCMC) algorithm was used to estimate quantiles and their posterior distributions. A coefficient of determination and Bayesian information criterion (BIC) for quantile regression are used in order to select the best model, i.e. for each quantile, we choose the degree and number of knots of the adequate B-spline quantile regression model. The method is applied to annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in the variable of interest and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for an annual maximum and minimum discharge with high annual non-exceedance probabilities.

The delineation of hydrologically homogeneous regions is an important issue in regional hydrological frequency analysis. In the present study, an application of the Growing Neural Gas (GNG) network for hydrological data clustering is presented. The GNG is an incremental and unsupervised neural network, which is able to adapt its structure during the training procedure without using a prior knowledge of the size and shape of the network. In the GNG algorithm, the Minimum Description Length (MDL) measure as the cluster validity index is utilized for determining the optimal number of clusters (sub-regions). The capability of the proposed algorithm is illustrated by regionalizing drought severities for 40 synoptic weather stations in Iran. To fulfill this aim, first a clustering method is applied to form the sub-regions and then a heterogeneity measure is used to test the degree of heterogeneity of the delineated sub-regions. According to the MDL measure and considering two different indices namely CS and Davies–Bouldin (DB) in the GNG network, the entire study area is subdivided in two sub-regions located in the eastern and western sides of Iran. In order to evaluate the performance of the GNG algorithm, a number of other commonly used clustering methods, like K-means, fuzzy C-means, self-organizing map and Ward method are utilized in this study. The results of the heterogeneity measure based on the L-moments approach reveal that only the GNG algorithm successfully yields homogeneous sub-regions in comparison to the other methods.

Hydrological frequency analysis (HFA) is commonly used for the assessment of the risk associated to hydrological events. HFA is generally based on the assumptions of homogeneity, independence and stationarity of the hydrological data. Hydrological events are often described through a number of dependent characteristics, such as peak, volume and duration for floods. Unfortunately, in this multivariate setting, the verification of the above assumptions is often neglected. When a shift occurs in a data series, it can affect the stationarity and the homogeneity of the data. The objective of this paper is to study tests for shift detection in multivariate hydrological data. The considered shift tests are mainly based on the notion of depth function, except for one test that is considered for comparison purposes. A simulation study is performed to evaluate and compare the power of all these tests with hydrological constraints. A flood analysis application is also carried out to show the practical aspects of the considered tests. The power of the considered tests is influenced by a number of factors, including the sample size, the shift amplitude, the magnitude of the series and the location of the shift in the series.

It is necessary to properly simulate groundwater levels in order to ensure an adequate management of scarce water resources. However, simulating groundwater levels accurately is one of the challenging issues in hydrology because of its complex system. In the current study, Gene Expression Programming (GEP) and M5 model tree (M5) are combined with Ensemble Empirical Mode Decomposition (EEMD) and Complementary Ensemble Empirical Mode Decomposition (CEEMD) methods for pre-processing input data to produce hybrid models for groundwater simulation. The performance of hybrid models is compared with the outputs of sole GEP and M5 and their counterparts combined with Wavelet transform (WT). The results indicate that pre-processing can improve the performance of the simple models and WT as well as CEEMD are better than EEMD to produce hybrid models. By employing pre-processing techniques, the improvement of R2 for GEP and M5, regarding Multiple Linear Regression (MLR) as a benchmark, is 13.11%, 6.65% and 8.20% for EEMD-GEP, CEEMD-GEP and CEEMD-M5 respectively, while it is –3.28% for EEMD-M5 for the first data set. For the second data set, the improvement of EEMD-GEP = 103.23%, CEEMD-GEP = 125.81% and CEEMD-M5 = 77.42%, and for the third data set, EEMD-GEP = 76%, CEEMD-GEP = 80% and CEEMD-M5 = 54%. In the second and third data set, the performance of EEMD-M5 decreases again. According to the results, hybrid GEP shows the best performance for groundwater water simulation, while M5 combined with EEMD is not recommended for the simulation due to its weak performance.

Flood quantile estimation at sites with little or no data is important for the adequate planning and management of water resources. Regional Hydrological Frequency Analysis (RFA) deals with the estimation of hydrological variables at ungauged sites. Random Forest (RF) is an ensemble learning technique which uses multiple Classification and Regression Trees (CART) for classification, regression, and other tasks. The RF technique is gaining popularity in a number of fields because of its powerful non-linear and non-parametric nature. In the present study, we investigate the use of Random Forest Regression (RFR) in the estimation step of RFA based on a case study represented by data collected from 151 hydrometric stations from the province of Quebec, Canada. RFR is applied to the whole data set and to homogeneous regions of stations delineated by canonical correlation analysis (CCA). Using the Out-of-bag error rate feature of RF, the optimal number of trees for the dataset is calculated. The results of the application of the CCA based RFR model (CCA-RFR) are compared to results obtained with a number of other linear and non-linear RFA models. CCA-RFR leads to the best performance in terms of root mean squared error. The use of CCA to delineate neighborhoods improves considerably the performance of RFR. RFR is found to be simple to apply and more efficient than more complex models such as Artificial Neural Network-based models.

To study hydrological events, such as floods and droughts, frequency analysis (FA) techniques are commonly employed. FA relies on some assumptions, especially, the stationarity of the data series. However, the stationarity assumption is not always fulfilled for a variety of reasons such as climate change and human activities. Thus, it is essential to check the stationarity or we should develop models that take into account the non-stationarity in a new risk assessment framework. On the other hand, a majority of hydrological phenomena are described by a number of correlated characteristics. To model the dependence structure between these hydrological variables, copulas are the most employed tool. Generally in the literature, the multivariate model is assumed to be the same over time even though multivariate stationarity is required. Considering the non-stationarity in the dependence structure is important because when the copula parameter changes, the multivariate quantile curve changes accordingly. Different scenarios can be considered when choosing a multivariate non-stationary model since several variables and a dependence structure are involved. The objective of the present study is to construct a model that integrates simultaneously multivariate and non-stationarity aspects along with hypothesis testing. For the copula part, we consider versions called Dynamic copulas and series of association measures are obtained through rolling windows of the corresponding series. Adapted versions of the AIC criterion are employed to select the final model (margins and copula). The procedure is applied to a flood volume and peak dataset from Iran. The obtained model constitutes of a lognormal distribution for the margins with linear trend in the peak series, stationary for the volume series and a quadratic trend in the logistic Gumbel copula parameter for the dependence structure.

The present study investigates the use of the spatial copula approach for predicting flood quantiles at ungauged basins. Spatial copulas are the formalization of traditional geostatistics by copulas. In regional flood frequency analysis (RFFA), the regression of flood quantiles is often carried out at the logarithmic scale. Consequently, traditional interpolation methods introduce a bias and provide suboptimal predictions. In this study, the copula framework is examined for offering proper corrections in this framework. Moreover, copula techniques separate the regional distribution of flood quantiles from spatial dependence. This provides a full probabilistic model that represents a more flexible framework where proper combinations of regional distribution and dependence can be adapted to various situations that are encountered in RFFA. The adequacy of the investigated methodology is evaluated on a real world case study involving hydrometric stations from southern Quebec, Canada. Results show that the spatial copula framework is able to deal with the problem of bias, is robust to the presence of problematic stations and may improve the quality of quantile predictions while reducing the level of complexity of the models used in RFFA.

Summary Several studies have shown that improvements in the regional prediction of low-flow characteristics can be obtained through the inclusion of a parameter characterising catchment baseflow recession. Usually, a linear reservoir model is assumed to define recession characteristics used as predictors in regional models. We propose in this study to adopt instead a non-linear model. Predictors derived from the linear model and the non-linear model are used separately in low-flow regional models along with other predictors representing physiographical and meteorological characteristics. These models are applied to selected gaged catchments. Results show that better performances are obtained with the parameter from the non-linear model. One drawback of using recession parameters for regional estimation is that a streamflow record is required at the site of interest. However, recession parameters can be estimated with short streamflow records. In this study, to simulate the performances obtained at partially gaged catchments, the recession parameters are estimated with very short streamflow records at target sites. Results indicate that, with a streamflow record as short as one year, a model with a recession parameter from the non-linear model leads to better performances than a model with only physiographical and meteorological characteristics.

Summary The aim of regional frequency analysis (RFA) is to estimate extreme hydrological events at sites where little or no hydrological data are available. The delineation of sub-regions and the regional estimation within these sub-regions are the two main steps of RFA. As currently practiced, the delineation step is unrobust and subjective. To overcome these limitations, the present paper aims to propose a new robust approach for delineating homogeneous sub-regions. The proposed approach is objective and based on the concept of depth function. A data set from three geographical regions in the North-West of Italy is used to apply and compare the proposed approach with a traditional one. Results indicate that the proposed Depth-based approach leads to more homogeneous sub-regions in terms of H heterogeneity measure, and leading to more efficient quantile estimations in terms of relative bias and relative root mean square error, than those obtained by the traditional approach.

Summary Generally, hydrological event such as floods, storms and droughts can be described as a multivariate event with mutually dependent characteristics. In the literature, two types of studies are performed focusing either on the evolution of one variable or more but separately, or on the joint distribution of two or more variables on a fixed window period. The main aspect in multivariate analysis is the dependence between the studied variables. It is important to study the evolution of this dependence over a long period especially in studies dealing with climate change (CC). The aim of the present study is to evaluate and analyze the dependence evolution between hydrological variables with an emphasis on the following flood characteristics, peak ( Q ), volume ( V ) and duration ( D ). This analysis includes confidence interval determination, stationarity analysis and change-point detection over a moving window series of three dependence measures. Two watersheds are considered along with observed and simulated flow data, obtained from two hydrological models. Results show that the dependence between the main flood characteristics over time is not constant and not monotonic. The corresponding behavior is sensitive to the choice of hydrological model, to climate scenarios and to the global climate model being used. The dependence of ( Q , V ) decreases when that of ( V , D ) increases. Moreover, the two considered hydrological models generally overestimate the dependence of ( Q , V ) and underestimate the dependence of ( V , D ) and ( Q , D ). All simulated dependence series are stationary over the whole period and present several break-points corresponding to short trends. This study allows also to check the ability of hydrological models, and if necessary, to recalibrate them to correctly simulate the dependence historically and in the future.

Summary The traditional hydrologic time series approaches are used for modeling, simulating and forecasting conditional mean of hydrologic variables but neglect their time varying variance or the second order moment. This paper introduces the multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) modeling approach to show how the variance–covariance relationship between hydrologic variables varies in time. These approaches are also useful to estimate the dynamic conditional correlation between hydrologic variables. To illustrate the novelty and usefulness of MGARCH models in hydrology, two major types of MGARCH models, the bivariate diagonal VECH and constant conditional correlation (CCC) models are applied to show the variance–covariance structure and cdynamic correlation in a rainfall–runoff process. The bivariate diagonal VECH-GARCH(1,1) and CCC-GARCH(1,1) models indicated both short-run and long-run persistency in the conditional variance–covariance matrix of the rainfall–runoff process. The conditional variance of rainfall appears to have a stronger persistency, especially long-run persistency, than the conditional variance of streamflow which shows a short-lived drastic increasing pattern and a stronger short-run persistency. The conditional covariance and conditional correlation coefficients have different features for each bivariate rainfall–runoff process with different degrees of stationarity and dynamic nonlinearity. The spatial and temporal pattern of variance–covariance features may reflect the signature of different physical and hydrological variables such as drainage area, topography, soil moisture and ground water fluctuations on the strength, stationarity and nonlinearity of the conditional variance–covariance for a rainfall–runoff process.

Hydrological frequency analysis (HFA) relies on a number of assumptions on the data series, especially independence, homogeneity and stationarity. In the univariate setting, these assumptions are generally checked before the modeling step. During the last decade, multivariate HFA approaches have gained popularity since most hydrological events can be described through a number of dependent characteristics, e.g. peak, volume and duration for floods. However, checking the above assumptions remains neglected in the multivariate HFA literature whereas the focus is directly on the modeling. For a reliable analysis and accurate results, these assumptions should also be checked prior to modeling in the multivariate setting. The present paper attempts to start bridging this gap in the multivariate HFA by highlighting the importance of the testing step and focusing on the review and application of nonparametric tests for monotonic trends. The presented multivariate trend tests are usually developed and employed to treat water quality data. In the present work, two types of multivariate applications are performed, multi-variable for flood attributes and multi-site for different locations. The results indicate that, in both types of applications, the univariate and multivariate tests led to the detection of different trend signals. It is hence recommended to jointly apply univariate and multivariate trend tests in order to capture all existing trend components and guide the user towards the appropriate models.

summary This study attempts to compare the performance of two statistical downscaling frameworks in downscaling hydrological indices (descriptive statistics) characterizing the low flow regimes of three rivers in Eastern Canada – Moisie, Romaine and Ouelle. The statistical models selected are Relevance Vector Machine (RVM), an implementation of Sparse Bayesian Learning, and the Automated Statistical Downscaling tool (ASD), an implementation of Multiple Linear Regression. Inputs to both frameworks involve climate variables significantly (a = 0.05) correlated with the indices. These variables were processed using Canonical Correlation Analysis and the resulting canonical variates scores were used as input to RVM to estimate the selected low flow indices. In ASD, the significantly correlated climate variables were subjected to backward stepwise predictor selection and the selected predictors were subsequently used to estimate the selected low flow indices using Multiple Linear Regression. With respect to the correlation between climate variables and the selected low flow indices, it was observed that all indices are influenced, primarily, by wind components (Vertical, Zonal and Meridonal) and humidity variables (Specific and Relative Humidity). The downscaling performance of the framework involving RVM was found to be better than ASD in terms of Relative Root Mean Square Error, Relative Mean Absolute Bias and Coefficient of Determination. In all cases, the former resulted in less variability of the performance indices between calibration and validation sets, implying better generalization ability than for the latter. 2013 Elsevier B.V. All rights reserved.

Summary 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.

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.

This study investigates the temporal evolution of annual and seasonal low-flow regimes of 144 Czech river basins for the 1961-2005 period. Summer and winter low-flow seasons are identified and delimited. The gauging stations are classified into two categories, mountain and lowland, according to their low-flow regime. The standard and modified versions of the Mann-Kendall trend test were used in the study to detect trends in several low-flow variables. These include 7-day annual, summer and winter low flows, number of days with discharge under two low-flow thresholds and deficit volumes delimited with the same two low-flow thresholds. At majority of stations, trends in low-flow variables are not significant. Among significant trends, decreasing summer low flows, increasing winter low flows and increasing drought durations as well as deficit volumes are observed. Such combination of trends is typical for the north-eastern part of the Czech Republic and if it continues in the future this area might become drought-prone. It was found that proportions of positive and negative trends between mountain and lowland stations are similar. Thus the low-flow evolution is irrespective of the basins altitudes and climates. Dates of low flows were evaluated to study the evolution of the timing of summer and winter low flows. Non-significant trends prevail for the timing of seasonal low flows, but at a number of stations the dates of summer minima shift towards earlier dates. This can be explained by an earlier onset of the spring flood caused by warmer winters.

Summary The onset date of positive water temperature in the annual thermal cycle of North-American streams is modeled using parametric (regression) and non-parametric (artificial neural networks) approaches. Physiographic, land cover and weather-related variables are used to predict the date of positive temperature onset for 191 station-years at 48 locations in Canada and in Northern US. Preliminary correlation analysis is performed in order to test the relationships between the physiographic/land cover/weather variables and the date of positive temperature onset. Moreover, several different subsets of variables are tested as inputs to each model type. Artificial neural networks can predict the date of positive temperature onset for a given station-year, given its longitude, lake coverage of its drainage basin, and two January–February daily temperature indices, with a split-sample validation root mean square error (RMSE) ∼8.8 days. Ordinary least square (OLS) regression models allow to predict the onset date with RMSE ∼9.5 days, given the station’s latitude, longitude, lake coverage and one January–February daily temperature index. OLS regression models adjusted on canonical variates combining 13 physiographic/land cover and weather variables achieve prediction performance ∼9.1 days. The precipitation does not impact much on the onset date prediction for all tested models.

Summary Despite several decades of operation and the increasing importance of water quality monitoring (WQM) networks, authorities still rely on subjective or semi-subjective decision processes to identify the optimal combination of water quality variables to measure. For this purpose, a statistical approach is developed for assessment and selection of the optimal combination of water quality variables. The proposed approach overcomes deficiencies in the conventional correlation–regression approach used to assess and eventually reduce the number of water quality variables in WQM networks. For the reduction of water quality variables, criteria developed from record-augmentation procedures are integrated with correlation analysis and cluster analysis to identify highly associated water quality variables. This step is followed by the application of an information performance index to systematically identify the optimal combination of variables to be continuously measured and those to be discontinued. The linear regression and maintenance of variance (MOVE) record-extension techniques are employed to reconstitute information about discontinued variables. The proposed approach is applied for rationalization of the water quality variables in the Nile Delta surface WQM network in Egypt. Results indicate that the proposed approach represents a useful decision support tool for the optimized selection of water quality variables. The MOVE record-extension technique is shown to result in better performance than regression for the estimation of discontinued variables.

Artificial neural network ensemble (ANN ensemble) prediction is a technique in which the outputs of a set of separately trained ANNs are combined to form one unified prediction. ANN ensemble models are developed in this paper to improve the results of single artificial neural network (single ANN) for the estimation of the ice thickness in a number of selected Canadian lakes during the early winter ice growth period. An effective ensemble consists of a set of ANNs that may not be highly performing when they are used separately, but have their prediction errors greatly reduced once combined. This paper evaluates the effectiveness of a number of ensemble techniques including randomization, bagging and boosting for creating members of an ensemble, then averaging and stacking techniques for combining ensemble members. The experiments show that, in the context of estimation of lake ice thickness, boosting is much better than randomization, and sometimes better than bagging. Stacking was found to be more competitive than averaging. Overall, ANN ensemble models for the estimation of ice thickness proved to be more accurate than single ANN models, especially when boosting is used for combining ensemble members and when stacking is used to combine the outputs from individual members. ANN ensembles achieve the best generalization performance when the ensemble size is increased to around 20.

The number of stations monitoring daily suspended sediment concentration (SSC) has been decreasing since the 1980s in North America while suspended sediment is considered as a key variable for water quality. The objective of this study is to test the feasibility of regionalising extreme SSC, i.e. estimating SSC extremes values for ungauged basins. Annual maximum SSC for 72 rivers in Canada and USA were modelled with probability distributions in order to estimate quantiles corresponding to different return periods. Regionalisation techniques, originally developed for flood prediction in ungauged basins, were tested using the climatic, topographic, land cover and soils attributes of the watersheds. Two approaches were compared, using either physiographic characteristics or seasonality of extreme SSC to delineate the regions. Multiple regression models to estimate SSC quantiles as a function of watershed characteristics were built in each region, and compared to a global model including all sites. Regional estimates of SSC quantiles were compared with the local values. Results show that regional estimation of extreme SSC is more efficient than a global regression model including all sites. Groups/regions of stations have been identified, using either the watershed characteristics or the seasonality of occurrence for extreme SSC values providing a method to better describe the extreme events of SSC. The most important variables for predicting extreme SSC are the percentage of clay in the soils, precipitation intensity and forest cover.

This study investigates trends in the timing and magnitude of seasonal maximum flood events across Canada. A new methodology for analyzing trends in the timing of flood events is developed that takes into account the directional character and multi-modality of flood occurrences. The methodology transforms the directional series of flood occurrences into new series by defining a new location of the origin. A test of flood seasonality (multi-modality) is then applied to identify dominant flood seasons. Floods from the dominant seasons are analyzed separately by a seasonal trend analysis. The Mann-Kendall test in conjunction with the method of pre-whitening is used in the trend analysis. Over 160 streamflow records from one common observation period are analyzed in watersheds with relatively pristine and stable land-use conditions. The results show weak signals of climate variability and/or change present in the timing of floods in Canada during the last three decades. Most of the significant trends in the timing of spring snowmelt floods are negative trends (earlier flood occurrence) found in the southern part of Canada. There are no significant trends identified in the timing of fall rainfall floods. However, the significance of the fall, rainfall-dominated flood season has been increasing in several analyzed watersheds. This may indicate increasing intensity of rainfall events during the recent years. Trends in the magnitude of floods are more pronounced than the trends in the timing of floods. Almost one fifth of all the analyzed stations show significant trends in the magnitude of snowmelt floods. Most of the significant trends are negative trends, suggesting decreasing magnitudes of snowmelt floods in Canada over the last three decades. Significant negative trends are found particularly in southern Ontario, northern Saskatchewan, Alberta and British Columbia. There are no significant trends in the magnitude of rainfall floods found in the analyzed streamflow records. The results support the outcomes of previous streamflow trend studies conducted in Canada.

Summary In order to investigate trends in time series of hydrological variables, observational records are generally assumed to be independent (IND) or having short-term persistence (STP), as opposed to long-term persistence (LTP). This study systematically investigates the effect of these assumptions for estimating significance of trends using simulated time series of known STP- and LTP-like serial structures and using observational records of annual, winter and summer 30-day low flows occurring in pristine rivers basins of Canada. For the analyses, the Mann–Kendall (MK) test and two modified versions of this test and a block bootstrap resampling based test is used to estimate significance of temporal trends under the assumptions of IND and STP. A semiparametric and a parametric procedure based on the fractional autoregressive integrated moving average modeling approach and a MK scaling test are used to estimate significance of temporal trends under the assumption of LTP. The results of the study suggest that for the majority of the time series of low flows analyzed, the assumption of IND or STP cannot be ruled out. On the contrary, the fluctuating behavior of trends revealed in selected time series of low flows, with longer records, using moving window technique favor the LTP hypothesis. However, only a modest evidence for the presence of LTP in low flow time series using estimates of the Hurst exponent could be revealed, perhaps because of small sample uncertainties. In general, the results of trend investigation suggest that the estimates of trend significance are highly sensitive to IND, STP and LTP assumptions, e.g. adopting IND assumption instead of LTP for a given set of hydrological time series exhibiting LTP, could result in incorrect estimation of trend significance. Also, substituting IND assumption for STP would result in incorrect estimates of trend significance. Therefore, for reliable trend investigation, satisfactory identification of STP- or LTP-like behavior in hydrological time series, which seldom exceed 100 years, is important and challenging and must be given adequate attention in all trend investigation studies.

A data-driven model is designed using artificial neural networks (ANN) to predict the average onset for the annual water temperature cycle of North-American streams. The data base is composed of daily water temperature time series recorded at 48 hydrometric stations in Quebec (Canada) and northern US, as well as the geographic and physiographic variables extracted from the 48 associated drainage basins. The impact of individual and combined drainage area characteristics on the stream annual temperature cycle starting date is investigated by testing different combinations of input variables. The best model allows to predict the average temperature onset for a site, given its geographical coordinates and vegetation and lake coverage characteristics, with a root mean square error (RMSE) of 5.6 days. The best ANN model was compared favourably with parametric approaches.

Identification of temporal changes in hydrological regimes of river basins is an important topic in contemporary hydrology because of the potential impacts of climate change on river flow regimes. For this purpose, generally parametric and nonparametric techniques have been employed; the latter have been widely used mainly because of a fewer number of assumptions involved in their implementation. The results of these techniques when applied at local/point scales are affected by the presence of serial correlation in time series of hydrological variables and interpretation of the collective results is sensitive to cross correlation present in a hydrological network. Though challenging, often these issues have received little attention in a majority of studies on trends. This study reviews the usefulness of some selected methods for the identification of hydrological trends in the presence/absence of short-term serial and cross correlations. To facilitate easy comprehension and clear demonstration of the ability of various reviewed methods for detecting trends in time series of hydrological variables and interpreting their collective results, a complete case study of annual mean daily flows of Canadian river basins, included in the reference hydrometric basin network, is presented and discussed. Such a comparative evaluation of various methods has never been attempted earlier. Both the reviewed literature and detailed results of the case study demonstrate that failure to incorporate the effects of serial and cross correlations in the trend investigation study could result in erroneous conclusions. Hence, the old practice of identifying hydrological trends without the consideration of serial and cross correlations should be avoided and these characteristics should be given adequate attention in all studies on temporal trends.

Healthy river conditions through optimal thermal regime controls water quality as well as the availability and distribution of fish habitat. A multivariate and geostatistical approach was developed to estimate maximum stream temperatures at a large basin scale. The methodology relies on the construction of a physiographical space using characteristics of gauging stations by testing two multivariate methods: principal components analysis (PCA) and canonical correlation analysis (CCA). Within the physiographical space, a geostatistical technique called ordinary kriging was then used to interpolate stream temperatures. Data from 12 temperature monitoring stations during July 1996 and July 1997 were used to estimate monthly maximum temperature. Results from the proposed approach were evaluated by comparing kriging performance obtained using both multivariate methods. Cross-validation technique has been performed on both approaches and satisfactory results were obtained. Kriging in the CCA physiographical space leads to better results because this approach seems more adapted to link physiographical information with specific water temperature. In addition, CCA requires less physiographical information than PCA (i.e. 10 metrics for PCA vs 8 metrics for CCA) to provide more satisfactory results (up to 15% decrease in RMSEr). In physiographical space, the gauging stations were found to cluster, potentially providing information to improve the accuracy of interpolation in that space. An example is provided to illustrate how to estimate one of the stream temperature properties at ungauged stations using the PCA algorithm. The relevance of the results regarding the quality of fish habitats of the Moisie river is discussed.

The study of the tail behaviour of extreme event distributions is important in several fields such as hydrology, finance, and telecommunications. Based on two classifications and five graphical criteria, this paper presents a practical procedure to select the class of distributions that provides the best fit to a dataset, especially for the right tail (large extreme events). Some numerical illustrations show that, almost all graphical tools allow discriminating between the regularly varying class and the sub-exponential class of distributions and lead to coherent conclusions.

The purpose of this study is to test and compare artificial neural network (ANN) and regression models for estimating river streamflow affected by ice conditions. Three regression models are investigated including: multiple regression, stepwise regression and ridge regression. A case study conducted on the Fraser River in British Columbia (Canada) is presented in which various combinations of hydrological and meteorological explanatory variables were used. Discharge estimates obtained by statistical modeling were also compared to the official estimates made by Water Survey of Canada (WSC) hydrometric technologists. The case study shows that ANN models are relatively more successful than regression models for winter streamflow estimation purposes. However, due to data scarcity, it was difficult to make a definitive assessment. Stepwise regression was found to be the most effective of the three regressive approaches investigated. Statistical modeling is a viable approach for winter streamflow data estimation, but data completeness and reliability is a major limitation.

In this paper, the methodology of using adaptive neuro-fuzzy inference systems (ANFIS) for flood quantile estimation at ungauged sites is presented. The proposed approach has the system identification and interpretability of fuzzy models and the learning capability of artificial neural networks (ANNs). The structure of the ANFIS is identified using the subtractive clustering algorithm. A hybrid learning algorithm consisting of back-propagation and least-squares estimation is used for system training. The ANFIS approach provides an integrated mechanism for identifying the hydrological regions, generating knowledge from the data, providing flood estimates and self-tuning to achieve the optimal performance. The proposed approach is applied to 151 catchments in the province of Quebec, Canada, and is compared to the ANN approach, the nonlinear regression (NLR) approach and the nonlinear regression with regionalization approach (NLR-R). A jackknife procedure is used for the evaluation of the performances of the three approaches. Results indicate that the ANFIS approach has a much better generalization capability than the NLR and NLR-R approaches and is comparable to the ANN approach.

This paper presents an adaptation of some regional estimation approaches to tropical climates and a comparison of their performance on the basis of their application to data from the Balsas, Lerma and Panuco River Basins located in Mexico. Four approaches are used in this study for the delineation of homogeneous regions: The first one is the hierarchical cluster analysis approach which leads to fixed hydrologic regions. The second one is the canonical correlation analysis (CCA) which allows the determination of hydrologic neighborhoods that are specific to the site of interest. The third one is a revised version of the canonical correlation analysis approach that is free of parameter optimization and which can be automated easily. Finally, the fourth one is the technique of canonical kriging which consists in interpolating hydrological variables over the canonical physiographical space. The methods based on the canonical correlation analysis approach provide also the basis for identifying the explanatory variables to be used during the step of regional estimation. Regional estimation is carried out based on a multiple regression approach. A data set of 29 stations from several Mexican River Basins in and around the Balsas region is used to show the advantages and weaknesses of each method and to demonstrate their usefulness in the context of regional flood quantile estimation. This study allows also to test the robustness of these methods through their application to a real world case study with a relatively limited number of stations. While all methods performed quite adequately, results indicate clearly the advantages of the neighborhood type of approach and the superiority of the canonical correlation analysis based methods. Results demonstrate that CCA-based methods lead to best performances overall. While hierarchical clustering seems generally to lead to less biased quantile estimates, the lowest root mean square error values are almost consistently obtained for the CCA-based methods. Results seem also to point out that all methods are quite sensitive to the quality and quantity of data available. The method of canonical kriging does not seem to be more sensitive to the database quality than the other two CCA-based methods.

Summary Flood frequency data for different durations of floods are required in many practical hydrologic applications. The estimation of flood frequency as an integrated function of return period and flood duration can be accomplished by flood-duration-frequency modeling. This study introduces a new approach to regional flood-duration-frequency modeling that is based on statistical properties of combined flood–rainfall events. The approach integrates flood-duration-frequency (QDF) and rainfall depth-duration-frequency (DDF) models into one regional flood–rainfall duration-frequency model (QDDF). The proposed model has only one local parameter, which accounts for site-specific physiographic characteristics. Regional parameters of the model are determined from statistical properties of regional rainfall depth-duration-frequency curves. The main advantage of the proposed approach is that it relies on rainfall data, which are spatially and temporally more abundant than streamflow data, and usually also available in hydrologically ungaged areas. The regional QDDF model was applied to a set of small catchments from a hydro-climatologically homogeneous region in south-western Ontario, Canada. The performance of the model was compared to the performance of the conventional regional converging QDF model by means of a jack-knife procedure. The results showed that the proposed approach significantly outperformed the converging QDF model, leading to quantile estimates with three-times lower average BIAS and RMSE. The proposed QDDF model seems to be a promising alternative for the regional QDF modeling of floods in the study area.

Regional flood frequency analysis (FFA) is commonly used to estimate flood risk at a particular site where little or no information is available on peak flows. This approach requires the assumption of flood stationarity. In this paper, we present a method to perform regional FFA at ungauged sites when the assumption of stationarity is not valid. Non-stationary at-site models are used to estimate flood risk at gauged sites. This information can then be used along with meteorological and drainage basin characteristics to define a hydrologic neighborhood of the ungauged site by means of canonical correlation analysis (CCA). A multiple regression model is then developed within the hydrologic neighborhood. Feasibility of regional FFA at ungauged sites is illustrated with a group of river flow gauging stations located in southeastern Canada and northeastern United States and which show a signal of non-stationarity. Results indicate that the development of a multiple regression model using 2–4 explanatory variables (including basin drainage area) leads to efficient estimation of the non-stationary regional flood quantiles Q5(t) and Q100(t) for the end of the historic observation period (relative root mean square error (RMSEr) of 38.2% and 60.8%, respectively). The use of CCA for the definition of a hydrologic neighborhood did not lead to better results. This is explained by the fact that the total number of sites (29) is small and, consequently, the size of the hydrologic neighborhoods is too low to develop efficient regression models within each of them. Comparison with the stationary results show that ignoring a trend in the hydrologic regime of an ungauged site can lead to serious under- or overestimation of the quantile estimates for that site.

The immobilization of water in the form of deposited ice on the reservoir’s embankments during winter operations has received little attention in hydrological literature. In Nordic countries like Canada, this phenomenon is likely to have significant negative impacts on reservoir operation. In a previous work (Seidou, O., Ouarda, T.B.M.J., Bilodeau, L., Hessami, M., St-Hilaire, A., Bruneau, P., 2006. Modeling ice growth on Canadian lakes using artificial neural metworks. Water Resources Research 42. doi: doi:10.1029/2005WR004622); the authors developed a global artificial neural network model to predict ice thickness growth in unmonitored Canadian lakes and reservoirs. This model is used in this paper to compute a time series of ice thickness on the Gouin reservoir (Saint-Maurice River, Quebec, Canada) and the Outardes 4 reservoir (Aux Outardes River, Quebec, Canada). This and the relationship between surface water area and water level were then used to evaluate the volume of ice left on the banks of the two reservoirs during winter operation, as its water level is progressively lowered in order to release water for hydroelectric production at downstream power dams. Results show that the ratio of frozen water left on the banks to the active storage varies from 2% to 8% at the Gouin reservoir, and from 0.41% to 1.15% at the Outardes 4 reservoir depending on the water usage policy and the geometry of the reservoir.

Frequency analysis is a technique of fitting a probability distribution to a series of observations for defining the probabilities of future occurrences of some events of interest, e.g., an estimate of a flood magnitude corresponding to a chosen risk of failure. The use of this technique has played an important role in engineering practice. The assumptions of independence and stationarity are necessary conditions to proceed with such analyses. However, in the context of climate change, it is possible that these assumptions would no longer hold and the results of conventional frequency analysis would become doubtful. Under such circumstances, it is important that recourse be made to other suitable approaches which incorporate non-independence and non-stationarity of hydro-meteorological extremes. In paper, a brief review of the current approaches to these issues is presented. Approaches that remove the effect of serial dependence to obtain independent observations are presented and the ones that involve kernel or wavelet-based probability density estimation are only discussed for frequency analysis of dependent observations. For frequency analysis of non-stationary observations, the reviewed approaches include the extremal, r-largest, peaks-over-threshold, time-varying moments, pooled flood frequency analysis, local likelihood and quantile regression. Synthesis of the reviewed approaches is presented, issues related to establishing non-stationary behavior are discussed and future challenges in frequency analysis of hydro-meteorological extremes are discussed as well. Extensions to some of the reviewed approaches and new avenues of research have been identified for further development and improvement. It is also concluded that, to be most useful, non-stationarity considerations be incorporated into new risk assessment frameworks.

During the last 10 years a growing number of regional flood frequency estimation studies have used flood seasonality descriptors for delineating hydrologically homogeneous regions. Seasonality of floods reflects a complex catchment’s hydrologic response to flood producing processes. Due to the high accuracy and robustness of flood date data, the use of flood seasonality indices became an attractive alternative to traditional regionalization approaches for the delineation of homogeneous regions, a key step in any regionalization study. This paper presents a data-based comparison of three flood seasonality regionalization methods. The methods are applied to a set of catchments in the province of Quebec (Canada). A jack-knife procedure is used to assess the performance of the methods in regional quantile estimation. The results are compared to those obtained from a traditional regionalization approach based on catchment physiographic similarities, and to the results from a scenario where information available in all catchments is used in the analysis. The seasonality method based on the peaks-over-threshold approach was concluded to lead to best results.

Flood-duration-frequency (QdF) analysis is becoming a popular tool for estimating the severity of flood events as an integrated function of return period and flood duration. QdF models are often applied in regional flood studies, leading to regional QdF relations derived for hydrologically homogeneous regions. Regional QdF models can be used to estimate flood quantiles for a given return period and flood duration at any ungaged site of a homogeneous region. By combining the information on sampling variability from hydrologically similar neighboring sites, the regional approach to QdF modeling also decreases the estimation uncertainty at gaged sites of the region. Regional QdF models have been developed for stable environmental conditions. Nevertheless, recent studies on stationarity of hydrologic records conducted in different parts of the world have identified significant changes in the statistical parameters of the analyzed records. Changing environmental conditions call for new flood estimation methods that can take into account the nonstationary character of hydrologic records and that can deal with time-dependent parameters of flood frequency distributions. This study defines the key concepts of a nonstationary approach to regional QdF modeling. The proposed approach uses regional trend analysis to identify time-dependent parameters of the model, and to estimate and predict flood quantiles for the present and near future time horizons. The model can be flexibly applied to various scenarios of nonstationarity at both local and regional scales. The approach is illustrated on a set of data from a hydrologically homogeneous region in Quebec, Canada. A split-sample experiment is used to compare the performance of the proposed model with the traditional stationary regional QdF model. The case study results demonstrate that ignoring statistically significant nonstationarity of hydrologic records can seriously bias flood quantiles estimated for the near future.

Despite its potential advantages, canonical correlation analysis (CCA) has been little used in the fields of hydrology and water resources. In a regional flood frequency analysis, canonical correlations can be used to investigate the correlation structure between the two sets of variables represented by watershed characteristics and flood peaks. This paper presents a clear theoretical framework for the use of canonical correlations in regional flood frequency analysis. Some additional results are also presented for the case of gauged target-basins. The approach described in this paper allows one to carry out the determination of homogeneous hydrologic neighborhoods and identifies the variables to use during the step of regional estimation. A data set of 106 stations from the province of Ontario (Canada) is used to demonstrate the advantages of this method and investigate various aspects in relation with its robustness. Results indicate that the method is robust to such factors as the number of stations and the type of parametric distribution being used. Step-by-step algorithms for the delineation of hydrologic neighborhoods in the cases of gauged and ungauged basins are also presented.

A univariate gamma distribution is one of the most commonly adopted statistical distributions in hydrological frequency analysis. A bivariate gamma distribution constructed from specified gamma marginals may be useful for representing joint probabilistic properties of multivariate hydrological events such as floods and storms. This article presents a review of various bivariate gamma distribution models that are constructed from gamma marginals. Advantages and limitations of each of these models are pointed out. Applicability of a few bigamma distributions whose gamma marginal distributions have different scale and shape parameters is investigated. The dependence of these models is directly or indirectly measured via the Pearson's product-moment correlation coefficient. The scale and shape parameters of the models are estimated from their marginal distributions by the method of moments. Results indicate that these bigamma distribution models will be useful for describing the joint probability distribution of two correlated random variables with gamma marginals.

Many hydrological engineering planning, design, and management problems require a detailed knowledge of flood event characteristics, such as flood peak, volume and duration. Flood frequency analysis often focuses on flood peak values, and hence, provides a limited assessment of flood events. This paper proposes the use of the Gumbel mixed model, the bivariate extreme value distribution model with Gumbel marginals, to analyze the joint probability distribution of correlated flood peaks and volumes, and the joint probability distribution of correlated flood volumes and durations. Based on the marginal distributions of these random variables, the joint distributions, the conditional probability functions, and the associated return periods are derived. The model is tested and validated using observed flood data from the Ashuapmushuan river basin in the province of Quebec, Canada. Results indicate that the model is suitable for representing the joint distributions of flood peaks and volumes, as well as flood volumes and durations.

Annual maximum flood (AMF) sampling remains the most popular approach to flood frequency analysis. An alternative, the " peaks over threshold " (POT) approach, deals with the selection of over-threshold values. However, the POT approach remains under-employed mainly because of the complexities associated with its use. Among the difficulties are the choice of threshold and the selection of criteria for retaining flood peaks. The literature remains sparse and incoherent concerning the various elements and complexities of the POT model. The purpose of the present paper is to shed some light on some of the recurrent and most important questions with regard to the practice of POT modeling, and to make a first step in establishing a set of coherent practice-oriented guidelines for the use of the POT model. This paper reviews tests and methods useful for modeling the process of over-threshold values, the choice of the threshold level, the verification of the independence of the values and the stationnarity of the process, and also presents an application., L'analyse fréquentielle des crues repose généralement sur l'extraction des valeurs maximales annuelles. Une alternative consiste à retenir toutes les valeurs dépassant un certain seuil. Cette approche reste sous-employée du fait notamment de difficultés liées au choix du seuil d'extraction et à la définition de critères permettant de respecter l'indépendance des valeurs. L'objet de cet article est de proposer, au travers d'une revue bibliographique, une série de recommandations opérationnelles pour l'emploi de cette approche. Il s'agit de tests et de méthodes pour modéliser le processus d'occurrence des crues, choisir le seuil d'extraction, vérifier l'indépendance et la stationnarité des valeurs. Une application pratique illustre ces différentes recommandations.

The two-parameter generalized Pareto distribution (GPD) has been recommended for the frequency analysis of environmental extreme events. In the present paper, we concentrate on one form of the GPD (which we will call GPDB) which can be useful in the frequency analysis of two types of hydrological variables: (1) when the shape parameter α is positive, the distribution (denoted by GPDB-2) can be used to study phenomena such as flood flows, which are bounded from below but have a long right tail; (2) when α is negative, the resulting distribution (GPDB-3) could be used to study variables such as low flows which are bounded from both sides but with a left tail. Six versions of the generalized method of moments (GMM) for fitting GPDB are investigated. The flexibility of the GMM provides the user with the possibility of choosing a version of the method (i.e. the moment pair that is used in fitting the distribution) which assigns larger weight to the larger elements of the sample, or another version which gives more weight to the smaller elements, depending on the problem at hand. A general formula for the asymptotic variance of the T-year event XT obtained by combining any two moments of GPDB is presented and applied. It is shown that the adequate choice of the order of these two moments to fit the distribution can lead, in some cases, to a considerable reduction in the variance of the estimator of XT, in comparison with estimation by the traditional method of moments (which uses moments of order one and two). The performance indices that are used to compare the different versions of the GMM are based on root mean square error, bias, and variance—both asymptotic and observed (based on simulation)—of GPDB quantiles and parameters. It is shown that moments of order (0),−1) and (2,−1) lead to the best results when the shape parameter a is positive (GPDB − 2), and the traditional method of moments can be considered as most efficient for negative values of α (GPDB −3). The GMM with moments of order 0 and one is shown to be rather consistent and moderately satisfactory for both GPDB-2 and GPDB-3.

Floods are the most common natural disaster in the world and are becoming a more and more important problem with large economic losses and social disruption. Technical measures for mitigating flood impacts are included within three basic categories: predictive, preventive and corrective measures. Prevention techniques are broadly used by most of the world's flood agencies using both probabilistic and deterministic methods. In both cases, the estimation of rare, large magnitude floods is problematic due to the short gauging station records and their limited spatial distribution. Hydrologists and engineers have developed different techniques to cope with the lack of flood data by using precipitation data, regional flood information and by calculating the so called “probable maximum flood”. New developing methods on discharge estimation of past floods using geomorphological indicatiors (palaeofloods) and documentary evidence allows the lengthening of instrumental records by hundreds to thousands of years. The scientific and applied interest of these studies is evident since the estimation of return periods used for design purposes and risk planning can be supported by actual data, rather than reliance on statistical extrapolation of instrumental flood series that often record only relatively modest events.