Comparison of the annual minimum flow and the deficit below threshold approaches: case study for the province of New Brunswick, Canada

Abstract

A low-flow frequency analysis using the annual minimum flow (AMF) and the deficit below threshold (DBT) approaches was carried out for 30 hydrometric stations across the province of New Brunswick. The AMF method considers only the annual minimum events, and the DBT method considers all low flows below a certain threshold (or truncation level). In the present study, the DBT method characterizes low flow in terms of deficit intensity, which is becoming increasingly important in both water and aquatic resources management. The annual minimum series were fitted using the three-parameter Weibull distribution (AMF-WEI3), and the intensity data series were fitted using the two-parameter Weibull distribution (DBT-WEI2) and the generalized Pareto distribution (DBT-GP). All parameter estimates were obtained using the maximum likelihood method. The AMF-WEI3 and DBT-GP approaches provided a good fit to at-site data in terms of annual minimum flow and deficit intensity, respectively. However, the present study showed that the DBT-WEI2 approach underestimated the right tail of low-flow intensity. The Anderson-Darling statistic was also calculated for the data series and can provide insight into which distribution may adequately model the low-flow characteristics. A regionalization study was also performed using the AMF-WEI3 and DBT-GP methods.Résumé : Une analyse fréquentielle en période de faible écoulement utilisant les méthodes de l'écoulement annuel minimal (« AMF ») et l'analyse de séries de dépassement incomplète (« DBT -deficit below threshold ») a été réalisée dans 30 stations hydrométriques dans la province de Nouveau-Brunswick. La méthode AMF ne considère que les événements annuels minimums alors que la méthode DBT tient compte de tous les écoulements sous un certain seuil (ou niveau de coupure). Dans cette étude, la méthode DBT caractérise le faible écoulement en termes d'intensité de déficit, qui devient de plus en plus important en gestion de l'eau et des ressources aquatiques. Les séries minimales annuelles ont été ajustées en utilisant une distribution de Weibull à trois paramètres (AMF-WEI3); les séries de données d'intensité ont été ajustées en utilisant la distribution de Weibull à deux paramètres (AMF-WEI2) et la distribution de Pareto généralisée (DBT-GP). Toutes les estimations de paramètres ont été obtenues en utilisant la méthode de vraisemblance maximale. Les approches AMF-WEI3 et DBT-GP ont fourni un bon ajustement aux données sur le site en termes respectifs d'écoulement minimum annuel et d'intensité de déficit. Toutefois, la présente étude montre que l'approche DBT-WEI2 sous estime la queue droite de l'intensité de l'écoulement faible. La statistique Anderson-Darling a également été calculée pour les séries de données et elle peut fournir un aperçu selon lequel la distribution peut adéquatement modéliser les caractéristiques de faible écoule-ment. Une étude de régionalisation a également été réalisée en utilisant les méthodes AMF-WEI3 et DBT-GP.Mots-clés : faible écoulement, analyse fréquentielle, éc...

Utilization of Time-Based Meteorological Droughts to Investigate Occurrence of Streamflow Droughts

“…A comprehensive review of the low flow characteristics and methodologies has been given by Smakhtin (2001). In a recent study, Benyaha et al (2009) analyzed the low-flow frequency behavior, using the annual minimum flow and the deficit below threshold.…”

Comparison of Probability Distribution Function in Determining Minimum Annual and Monthly Streamflow

“…Na construção de intervalos de confiança a partir dos estimadores de MV, observa-se uma significativa precisão em estimativas de vazões, em relação a outros métodos como, por exemplo, aos gerados com base no teorema central do limite, cuja construção é bastante trabalhosa e menos confiável para distribuições assintóticas [9], [15], [22], [23].…”

“…O teste de Anderson-Darling (AD) apresenta-se como uma boa alternativa a estudos de vazões mínimas [9], [14], pois busca atribuir maior significância aos extremos das distribuições, nos quais as maiores (ou menores) observações podem alterar a qualidade do ajuste. O teste, tal como o de KS, baseia-se na diferença entre as funções de probabilidades acumuladas empírica e teórica.…”

On the distributions of seasonal river flows: Lognormal or power law?

“…Distributional analysis of river flow time series is a basic task in hydrology [e.g., Smakhtin , 2001; Morrison and Smith , 2002; Laio , 2004; Carreau et al , 2009; De Domenico and Latora , 2011; Sharwar et al , 2011]. For example, under the assumption that statistical features of the flow of a river remain fairly constant, when one wants to estimate the probability of drought and develop suitable means to mitigate the effects of drought, one needs to best summarize known knowledge to determine a threshold value and calculate the probability that the river discharge data do not exceed the chosen threshold value [e.g., Smakhtin , 2001; Kroll and Vogel , 2002; Benyahya et al , 2009]. On the other hand, if one wishes to estimate the probability of floods and assess various kinds of risks associated with them, then one needs to determine another threshold value and calculate the probability that the river discharge data exceed the chosen threshold [e.g., Fernández and Salas , 1999; Fernandes et al , 2010; Um et al , 2010].…”