Bernard Bobée

Daily reservoir inflow forecasting using artificial neural networks with stopped training approach

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 enhances generalization performance. The methodology is assessed using multivariate hydrological time series from Chute-du-Diable hydrosystem in northern Quebec (Canada). The performance of the model is compared to benchmarks from a statistical model and an operational conceptual model. Since the ultimate goal concerns the real-time forecast accuracy, overall the results show that the proposed method is effective for improving prediction accuracy. Moreover it offers an alternative when dynamic adaptive forecasting is desired.

Towards operational guidelines for over-threshold modeling

Abstract 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 stationarity of the process, and also presents an application.

Artificial neural network modeling of water table depth fluctuations

Three types of functionally different artificial neural network (ANN) models are calibrated using a relatively short length of groundwater level records and related hydrometeorological data to simulate water table fluctuations in the Gondo aquifer, Burkina Faso. Input delay neural network (IDNN) with static memory structure and globally recurrent neural network (RNN) with inherent dynamical memory are proposed for monthly water table fluctuations modeling. The simulation performance of the IDNN and the RNN models is compared with results obtained from two variants of radial basis function (RBF) networks, namely, a generalized RBF model (GRBF) and a probabilistic neural network (PNN). Overall, simulation results suggest that the RNN is the most efficient of the ANN models tested for a calibration period as short as 7 years. The results of the IDNN and the PNN are almost equivalent despite their basically different learning procedures. The GRBF performs very poorly as compared to the other models. Furthermore, the study shows that RNN may offer a robust framework for improving water supply planning in semiarid areas where aquifer information is not available. This study has significant implications for groundwater management in areas with inadequate groundwater monitoring network.

The Gumbel mixed model for flood frequency analysis

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.

Regional flood frequency estimation with canonical correlation analysis

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 review of bivariate gamma distributions for hydrological application

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 Pearsons 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.

Bayesian change-point analysis in hydrometeorological time series. Part 1. The normal model revisited

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, a change in variability is investigated. In hydrology, to our knowledge, this problem has not been studied from a Bayesian perspective. Even if this model is quite simple, no analytic solutions for parameter inference are available, and recourse to approximations is needed. It is shown that the Gibbs sampler is particularly suitable for change-point analysis, and this Markovian updating scheme is used. Finally, a case study involving annual energy inflows of two large hydropower systems managed by Hydro-Quebec is presented in which informative prior distributions are specified from regional information.

Recent advances in flood frequency analysis

Research on flood frequency analysis has taken place with varying intensity over the last couple of decades. The eighties proved to be important years with many significant contributions, reviewed for instance by Greis [1983], Potter [1987], Kirby and Moss [1987], Cunnane [1987], NRC [1988], WMO [1989], and Bobee and Ashkar [1991]. Due to its large economical and environmental impact, flood frequency analysis remains a subject of great importance and interest, and the research on improved methods for obtaining reliable flood estimates has continued into the nineties, although with different emphasis. In the seventies and eighties much effort was spent on developing efficient at-site flood frequency procedures. New distributions and estimation methods were introduced in the hydrologic journals, some of them developed specifically for flood frequency analysis. It seems that this tendency has decelerated somewhat in the beginning of the nineties. Researchers are increasingly realizing that the lack of sufficiently long data series imposes an upper limit on the degree of sophistication that can reasonably be justified in at-site flood frequency analysis. It has been emphasized by many that instead of developing new methodologies for flood frequency analysis, effort should be spent on comparing existing ones and on looking for other sources of information [Potter, 1987; Bobee et al, 1993a]. Regionalization is probably the most viable avenue for improving flood estimates, and fortunately this seems to be the direction that the research in flood frequency analysis has taken in the nineties.

Bayesian change-point analysis in hydrometeorological time series. Part 2. Comparison of change-point models and forecasting

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 change hypothesis and various possible situations that may occur. The approach is based on Bayesian model selection and is illustrated using univariate normal models. Four univariate normal models are considered: the no change hypothesis, a single change in the mean level only, a single change in the variance only, and a simultaneous change in both the mean and the variance. First, inference analysis of posterior distributions via Gibbs sampling for a given change-point model is recalled. This scientific reporting framework is then generalized to the problem of selecting among different configurations of a single change and the no change hypothesis. The important operational issue of forecasting a future observation, often neglected in the literature on change-point analysis, is also treated in the previous model selection perspective. To illustrate the approach, a case study involving annual energy inflows for eight large hydropower systems situated in Quebec is detailed.

A Review of Statistical Water Temperature Models

The use of statistical models to simulate or to predict stream water temperature is becoming an increasingly important tool in water resources and aquatic habitat management. This article provides an overview of the existing statistical water temperature models. Different models have been developed and used to analyze water temperature-environmental variables relationship. These are grouped into two major categories: deterministic and statistical/stochastic models. Generally, deterministic models require numerous input data (e.g., depth, amount of shading, wind velocity). Hence, they are more appropriate for analyzing different impact scenarios due to anthropogenic effects (e.g., presence of reservoirs, thermal pollution and deforestation). In contrast to the deterministic models, the main advantage of the statistical models is their relative simplicity and relative minimal data requirement. Parametric models such as linear and non-linear regression are popular methods often used for shorter time scales (e.g., daily, weekly). Ridge regression presents an advantage when the independent variables are highly correlated. The periodic models present advantages in dealing with seasonality that often exists in periodic time series. Non-parametric models (e.g., k-nearest neighbours, artificial neural networks) are better suited for analysis of nonlinear relationships between water temperature and environmental variables. Finally, advantages and disadvantages of existing models and studies are discussed.