Bernard Bobée

• National Institute of Scientific Research

Hydrological frequency analysis is the most widely used method to estimate risk for extreme values. The most used statistical distributions to fit extreme value data in hydrology can be regrouped in three classes: class C of regularly varying distributions, class D of sub exponential and class E, Exponential depending on their tail behavior. The Ha...

In flood frequency analysis (FFA), the adequate choice of distribution to fit data is a major problem. The three-parameter lognormal (LN3) distribution has an intermediate tail behavior between the distributions of the Class C (regularly varying distributions) and those of the Class D (subexponential distributions). HYFRAN software performs a compl...

This paper proposes a methodology for the regional analysis of drought flows. This approach lies on the combination of two procedures. (i) The simple scale invariance method for regional series of drought flows, based on the analysis of the relation moments-surfaces or the relation quantiles-surfaces, explains the spatial variability of drought pro...

It is often necessary to estimate extreme events at sites where little or no hydrometric data are available. In such cases, one may use a regional estimation procedure, utilizing data available from other sites in the same hydrologic region. In general, a regional flood frequency procedure consists of two steps: determination of hydrologically homo...

The natural inflow at a site is a key variable for optimal management of water resources, particularly for hydroelectric production. For sites with dams and hydroelectric powerplants, this variable cannot be measured directly, and the water balance equation is used to determine the quantity of water a site receives on its surface during a certain p...

Log-linear models are frequently used in hydrology, especially for the regional estimation of flood volumes based on the physiographic data of a set of basins. A log-linear model describes a linear relationship between the log of a dependant variable and independent variables which are functions of parameters, of which the value remains to be deter...

Most bivariate models assume the same type of marginal distribution, with two parameters, for two variables (gamma, type I extreme values, and so forth). The disadvantage of these models is that it is often difficult to make adjustments for observed flows. This study shows the application flexibility of a program that calculates the joint probabili...

The daily net basin supply of the large reservoirs of Hydro-Québec is currently computed by the water balance equation that relies, in particular, on gauge measurements. The number of gauge and their location heavily depend on simplified hypotheses that generate many errors in the computation. Also, for various technical reasons, the daily net basi...

Resume : L’analyse de frequence de certaines variables hydrologiques comme les volumes de crue, les apports naturels maximums, les precipitations maximums et les equivalents en eau est importante pour les compagnies hydroelectriques qui ont a gerer efficacement et de maniere securitaire leurs ressources hydriques. Dans cet article nous presentons u...

Mots clés : réseau de neurones artificiels, prévision hydrologique, modèle stochastique, perceptrons multicouches. Abstract: Artificial neural networks (ANN) are a novel approximation method for complex systems especially useful when the well-known statistical methods are not efficient. The multilayer perceptrons have been mainly used for hydrologi...

In this study, a new methodological approach is proposed to analyze the spatial variability of the water quality of a set of lakes. The Quebec region under study is located in the southeast part of the Canadian Shield between the Ottawa River and the Saguenay River. The proposed methodology is based on the combined use of correspondence analysis an...

Statistical criteria used to evaluate the best distribution fit give large weights to the center of distributions. This is, however, not consistent with the objective of frequency analysis which is to estimate the quantiles with large return periods. In this study, the usefulness of a recently proposed decision support system ͑DSS͒, which defines t...

The Halphen family of distributions is a flexible and complete system to fit sets of observations independent and identically distributed. Recently, it is shown that this family of distributions represents a potential alternative to the generalized extreme value distributions to model extreme hydrological events. The existence of jointly sufficient...

The Halphen system the generalized extreme-value (GEV) distributions are recommended for the estimation of the hydrological extreme events. The GEV system is widely used, whereas the Halphen distributions are less known by hydrologists. The objective of this study is to compare these two systems on the basis of various criteria. A simulation study...

The estimation of flood flows is of major importance for the design and management of hydraulic structures. Two main classes of laws are used in hydrology frequency analysis: the class D of sub-exponential distributions and the class C of regularly varying distributions with a heavier tail. No criteria were available for the choice between these tw...

The purpose of an hydrometric network is to obtain data giving answers to problems raised by the use of water. The methodology suggested in this paper is essentially based on the regional identification of the actual and potential uses of water, on the estimate of the intensity of their use and on the determination of the hydrological characteristi...

Within the framework of the World Meteorological Organizations'(WMO) standardization activities, the "Guide to Hydrological Practices" was first published in 1965. The intent is to provide information on current practices,procedures and instrumentation.The Guide has become a popular reference document for hydrologists and engineers worldwide.The pr...

Halphen laws have been proposed as a complete system of distributions with sufficient statistics that lead to estimation with minimum variance. The Halphen system provides a flexibility to fit a large variety of data sets from natural events. In this paper we present the method of moments (MM) to estimate the Halphen type B and IB distribution para...

Résumé L’estimation adéquate des événements hydrologiques extrêmes (événements de conception) est primordiale en raison des risques importants associés à une connaissance insuffisante de ces événements. Dans les sites où l’on dispose de peu ou même d’aucune information hydrologique, on a recours aux méthodologies d’estimation régionale pour l’estim...

Water temperature is an important abiotic variable in aquatic habitat studies and may be one of the factors limiting the potential fish habitat (e.g. salmonids) in a stream. Stream water temperatures are modelled using statistical approaches with air temperature and streamflow as exogenous variables in the Nivelle River, southern France. Two differ...

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 t...

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 Pánuco River Basins located in Mexico. Four approaches are used in this study for the delineation of homogeneous regions: The first one is the hierar...

Peat bog harvesting is an important industry in many countries, including Canada. To harvest peat, bogs are drained and drainage water is evacuated towards neighboring rivers, estuaries or coastal waters. High suspended sediment concentrations (SSC) were found in the drainage water at one particular site during the 2001-2002 spring seasons in New B...

In this paper we present algorithms based on the acceptance-rejection (A-R), and Markov chain Monte Carlo methods to draw samples from Halphen distributions. Quantiles computed with these generating techniques are compared to those given by the method of importance sampling. Results show that our choice of the instrumental distribution considered i...

A review of nonparametric tests for trend leads to the conclusion that Mann-Whitney, Spearman, and Kendall tests are the best choice for trend detection in water quality time series. Recently these tests have been adapted to account for dependence and seasonality in such series (Lettenmaier, 1976; Hirsch, et al., 1972; Hirsch and Slack, 1984). For...

The Pearson type 3 (P3) and log Pearson type 3 (LP3) distributions are very frequently used in flood frequency analysis. Existing methods for constructing confidence intervals for quantiles (Xp) of these two distributions are very crude. Most of these methods are based on the idea of adjusting confidence intervals for quantiles Yp of the normal dis...

Specific conductivity, pH, dissolved oxygen, carbon, phosphorous, and nitrogen species were measured at 36 stations in the Richibucto River drainage basin, including the estuary, in New Brunswick, Canada, over the six-year period 1996 through 2001. Each station was sampled between 1 and 26 times (mean = 7.5, standard deviation = 6.0) during the ice...

ABSTRACT Physico-chemical data from 234 lakes were collected during the spring and summer of 1980 by the Quebec Ministry of the Environment, the Quebec Ministry of Recreation, Hunting and Fishing and the Canadian Wildlife Service. A statistical method, based on the joint use of factorial correspondence analysis and cluster analysis, was applied to...

This work presents an adaptation of some regional estimation approaches to southern climates and an application of regional frequency analysis to the Balsas River Basin located in Mexico. Three approaches are used in this study for the delineation of homogeneous regions: the first one is the cluster analysis approach which leads to fixed hydrologic...

Flood-duration-frequency modelling is an extension of standard flood frequency analysis that takes into account the multi-duration aspect of flood hydrographs. The key assumption of this approach is that the parameters describing the flood frequency distribution for any flood duration do not change over time. In reality, however, as a consequence o...

The objective of the present study is to develop efficient estimation methods for the use of the GEV distribution for quantile estimation in the presence of nonstationarity. Parameter estimation in the nonstationary GEV model is generally done with the maximum likelihood estimation method (ML). In this work, we develop the generalized maximum likel...

Water temperature is an important physical variable in aquatic ecosystems. It can affect both chemical and biological processes such as dissolved oxygen concentration and both the metabolism and growth of aquatic organisms. For water resource management, stream water temperature models that can accurately reproduce the essential statistical charact...

Successful applications of stochastic models for simulating and predicting daily stream temperature have been reported in the literature. These stochastic models have been generally tested on small rivers and have used only air temperature as an exogenous variable. This study investigates the stochastic modelling of daily mean stream water temperat...

Summer-season (May–September) daily maximum temperature (T max) and daily minimum temperature (T min) observations and three types of heat spells obtained from these temperature observations at seven weather stations located in southern Quebec (Canada) for the 60-year period from 1941 to 2000 are studied to assess temporal changes in their characte...

A new L-moment estimation method for the parameters of three-parameter distributions is presented. Traditional L-moment estimators of a statistical distribution’s parameters are based on the solution of the system of equations obtained by equating sample and distribution L-moments. For three-parameter distributions, the third equation equates the s...

Because of their impact on hydraulic structure design as well as on floodplain management, flood quantiles must be estimated with the highest precision given available information. If the site of interest has been monitored for a sufficiently long period (more than 30-40 years), at-site frequency analysis can be used to estimate flood quantiles wit...

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 us...

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 ass...

Acting as natural filters, peatlands are important wetland ecosystems in many northern countries, including Canada. To harvest peat, the vegetation must be removed and the harvested area ditched to drain and dry the peat. Drainage ditches are often designed to route water to settling ponds prior to releasing runoff into nearby water bodies. The pre...

Habitat models serve three main purposes: First, to predict species occurrences on the basis of abiotic and biotic variables, second to improve the understanding of species-habitat relationships and third, to quantify habitat requirements. The use of statistical models to predict the likely occurrence or distribution of species based on relevant va...

One of the most important parameters for spring runoff forecasting is the snow water equivalent on the watershed, often estimated by kriging using in situ measurements, and in some cases by remote sensing. It is known that kriging techniques provide little information on uncertainty, aside from the kriging variance. In this paper, two approaches us...

One major challenge with the modelization of complex problems using Markov chain Monte Carlo (MCMC) methods is the determination of the length of the chain in order to reach convergence. This paper is devoted to parametric empirical methods testing the stationarity. We compare the methods of Gelman and Rubin, Yu and Mykland, Raftery and Lewis, Gewe...

Résumé La littérature scientifique de la dernière décennie contient un grand nombre de travaux qui détaillent le développement des méthodes de « désagrégation » (downscaling) de l’échelle globale à l’échelle hydrologique pour tenter d’estimer les impacts du changement global sur la disponibilité et la distribution des ressources en eau. Cet article...

During the last decade, a large volume of literature has been published on the development of "downscaling" methods from the global to the hydrological scale in order to estimate the impact of global climate change on the availability and distribution of water resources. The present paper proposes a comprehensive review and a synthesis of climatic...

Fitting statistical laws from a short time series does not give any guarantee of reliability on extreme flood estimation. Historical investigation through documentary sources can enlarge the record period. This paper presents a case study on the Ardèche river, based on collaboration between historians, archivists, hydraulic engineers and hydrologis...

Heatwaves can have adverse affects on public health and can considerably impact social and economic activities. Climate-change scenarios have shown that the temperature regime will likely be modified significantly over the course of the next 50 years and more. The frequency of occurrence and amplitude of heatwaves may be impacted by changes in the...

A major issue in real-time management of water resources is the need for accurate and reliable hydrologic forecasts at least 24 or 48 h ahead. An experiment on improving the accuracy of a conceptual hydrologic model used for daily reservoir inflow forecasting, by resorting to model combination, is presented. A robust weighted-average method is used...

A complete regional analysis of daily precipitations is carried out in the southern half of the province of Quebec, Canada. The first step of the regional estimation procedure consists of delineating the homogeneous regions within the area of study and testing for homogeneity within each region. The delineation of homogeneous regions is based on us...

The identification of flood seasonality is a procedure with many practical applications in hydrology and water resources management. Several statistical methods for capturing flood seasonality have emerged during the last decade. So far, however, little attention has been paid to the uncertainty involved in the use of these methods, as well as to t...

Il est d'usage en pratique de tirer des conclusions globales sur la non-stationnarité de séries hydrologiques en analysant indépendamment les ruptures en moyennes et/ou en variance de chacune des séries appartenant à une même région (voir notamment Perreault et al. (1999)). Selon nous, ce type de procédure devrait être revue. D'une part, les relati...

The catastrophic floods recently occurring in Europe warn of the critical need forhydrologic data on floods over long-time scales. Palaeoflood techniques provideinformation on hydrologic variability and extreme floods over long-time intervals(100 to 10,000 yr) and may be used in combination with historical flood data (last1,000 yr) and the gauge re...

This paper proposes an approach for analyzing rainfall variability over West Africa during the 1950 90 period. Three grid boxes, corresponding to three selected areas over West Africa, have been constructed. For each candidate area the set of annual grid maps are stored in 3D matrices, reflecting time and geographical position, called here space ti...

The determination of seasons of high and low probability of flood occurrence is a task with many practical applications in contemporary hydrology and water resources management. Flood seasons are generally identified subjectively by visually assessing the temporal distribution of flood occurrences and, then at a regional scale, verified by comparin...

The increasing demand on water resources requires better management of the water deficit situation, may it be unusual droughts or yearly recurring low flows. We propose to use alternating non-homogeneous point processes to model the occurrences and durations of water deficits and surplus. The advantage of this approach is that it is a relatively si...

Résumé Une méthodologie d'analyse régionale complète des précipitations journalières a été mise en oeuvre pour la moitié sud du Québec (Canada). La première étape d'une procédure d'estimation régionale consiste à définir les régions homogènes de la zone d'étude et à valider cette homogénéité pour chaque région ainsi définie. Les rapports de L-momen...

This article presents the modeling of multivariate extreme values using copulas. Our approach allows us to model the dependence structure independently of the marginal distributions, which is not possible with standard classical methods. The methodology has been applied on two different problems in hydrology. The first application is concerned with...

In recent years in North America, a number of government agencies and industries have begun to reinvest in meteorological networks. This investment must be based on sound scientific advice. Increased meteorological station network density can be beneficial for a number of purposes, including flood forecasting. This study aimed at investigating the...

Most often, flood frequency analysis describes a flood event only by its peak. However, the true flood severity is also defined by its volume and duration. This paper presents an approach allowing flood events to be considered in a more complete way: the flood-duration–frequency (QdF) approach. In a similar manner to the rainfall intensity–duration...

Design flood estimates at ungauged sites or at gauged sites with short records can be obtained through regional estimation techniques. It is important to accurately estimate the values of these design floods to avoid over- and under-estimation of hydraulic structures. Various methods have been employed for the regional analysis of extreme hydrologi...

L'estimation de l'intensité de précipitations extrêmes est un sujet de recherche en pleine expansion. Nous présentons ici une synthèse des travaux de recherche sur l'analyse régionale des précipitations. Les principales étapes de l'analyse régionale revues sont les méthodes d'établissement de régions homogènes, la sélection de fonctions de distribu...

Artificial neural networks are alternatives to stochastic models even if the optimization of their architectures remains a tricky problem. Two different approaches in long-term forecasting of potential energy inflows using a feedforward neural network (FNN) and a recurrent neural network (RNN) are proposed. The problem of overfitting, particularly...

A recent trend in regional frequency analysis is to consider floating regions where only basins that are sufficiently similar to the design site are considered for information transfer. Similarity is measured in some suitable metric of catchment characteristics. This paper discusses the analogy between this idea and nonparametric regression. Some o...

The shape of a flood hydrograph is a random event. This study develops a method for describing statistical properties of the shape of a flood hydrograph. Two shape variables, namely, shape mean (S-m) and shape variance (S-v), are defined to express the randomness of a flood hydrograph. The two-parameter beta probability density function (pdf) is ad...

The aim of this research paper is to develop a statistical model that provides a more complete description of a basin's flood regime. The approach adopted in this paper is based on the flood-duration–frequency (QdF) analysis which takes into account the temporal variability of floods. This approach is analogous to the intensity-duration–frequency (...

La détermination du débit de crue d'une période de retour donnée nécessite l'estimation de la distribution des crues annuelles. L'utilisation des distributions non paramétriques - comme alternative aux lois statistiques - est examinée dans cet ouvrage. Le principal défi dans l'estimation par la méthode des noyaux réside dans le calcul du paramètre...

Although such an hypothesis is rarely stated explicitly, the assumption that stochastic time series are stationary plays a crucial role in water resources management. Under the assumption that tomorrow will statistically behave like yesterday, stochastic models are fitted to hydrometeorological variables such as river flow, precipitation and temper...

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. Th...

An experiment on predicting multivariate water resource time series, specifically the prediction of hydropower reservoir inflow using temporal neural networks, is presented. This paper focuses on dynamic neural networks to address the temporal relationships of the hydrological series. Three types of temporal neural network architectures with differ...

The key problem in nonparametric frequency analysis of flood and droughts is the estimation of the bandwidth parameter which defines the degree of smoothing. Most of the proposed bandwidth estimators have been based on the density function rather than the cumulative distribution function or the quantile that are the primary interest in frequency an...

A canonical correlation method for determining the homogeneous regions used for estimating flood characteristics of ungauged basins is described. The method emphasizes graphical and quantitative analysis of relationships between the basin and flood variables before the data of the gauged basins are used for estimating the flood variables of the ung...

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...

The issue of selecting appropriate model input parameters is addressed using a peak and low flow criterion (PLC). The optimal artificial neural network (ANN) models selected using the PLC significantly outperform those identified with the classical root-mean-square error (RMSE) or the conventional Nash–Sutcliffe coefficient (NSC) statistics. The co...

Three types of functionally different artificial neural network (ANN) models are calibrated using a relatively short length of groundwater level records and related hydrometeorlogical data to simulate water table fluctuations in the Gondo aquifer, Burkina Faso. Input delay neural network (IDNN) with static memory structure and globally recurrent ne...

SUMMARY The design and management of hydraulic structures require a good know- ledge of the characteristics of extrême hydrologie events such as floods and droughts, that may occur at the site of interest. Occurrences of such events may be modelled as temporal point processes. This modelling approach allows the dérivation of various performance ind...

Nous nous intéressons dans ce travail de recherche à la modélisation d'une série d'événements par la théorie des processus ponctuels temporels. Un processus ponctuel est défini comme étant un processus stochastique pour lequel chaque réalisation constitue une collection de points. Un grand nombre d'ouvrages traitent particulièrement de ces processu...

In probability theory, the Bayes’ rule of inference plays a central role as corroborated by the ever-increasing number of applications in various fields. The rule allows to revise a prior probability distribution when new information becomes available; the posterior probability distribution takes the form of a conditional distribution. Although sev...

It is often necessary to estimate extreme events at sites where little or no hydrometric data are available. In such cases, one may use a regional estimation procedure, utilizing data available from other stations in the same hydrologic region. In general, a regional flood frequency procedure consists of two steps, delineation of hydrologically hom...

This paper evaluates the potential of using low-frequency climatic mode indices to forecast regional annual runoÄ in northern Quebec and the Labrador region. The impact of climatic trends in the forecast accuracy is investigated using a recurrent neural networks (RNN) approach, time-series of inflow to eight large hydropower systems in Quebec and L...

Although hydrological time series for different sites in a given region are usually correlated and that climate changes should have a regional impact on water resources, very little has appeared in the literature about multivariate change-point analysis. This paper generalizes the univariate Bayesian approach for the detection of a single shift in...

The Thirteenth Entretiens Jacques Cartier held in Montréal (October 3-5, 2000) are one of annual international meetings aimed at cultural and scientific exchanges between the Province of Quebec and the Rhône-Alpes region of France, but also between the rest of Europe et North América. The proceedings of the session 1 " Climate variability : seasona...

This paper provides a methodology to test existence, type, and strength of changes in the distribution of a sequence of hydrometeorological random variables. Unlike most published work on change-point analysis, which consider a single structure of change occurring with certainty, it allows for the consideration in the inference process of the no ch...

A Bayesian method is presented for the analysis of two types of sudden change at an unknown time-point in a sequence of energy inflows modeled by independent normal random variables. First, the case of a single shift in the mean level is revisited to show how such a problem can be straightforwardly addressed through the Bayesian framework. Second,...

In this paper, an early stopped training approach (STA) is introduced to train multi-layer feed-forward neural networks (FNN) for real-time reservoir inflow forecasting. The proposed method takes advantage of both Levenberg–Marquardt Backpropagation (LMBP) and cross-validation technique to avoid underfitting or overfitting on FNN training and enhan...