Modélisation de la structure de dépendance hauteur—durée d'événements pluvieux par la copule de Gumbel

Résumé

L'objet de cet article est la mise en évidence de la structure de dépendance de deux variables hydrologiques: la hauteur (ou volume) de pluie et sa durée. La dépendance est prospectée par chi plot et Kendall (K) plot, et mesurée grâce à deux coefficients de corrélation de rang: le τ de Kendall et le ρ de Spearman. La distribution conjointe du couple hauteur de pluie—durée est construite à l'aide de la copule de Gumbel. Les durées sont ajustées par la loi GEV et les hauteurs de pluie par la loi de Burr XII étendue à trois paramètres. Pour l'adéquation des lois marginales, le test d'Anderson-Darling a été utilisé. L'identification de la copule parmi trois modèles courants (Gumbel, Frank et Clayton) est réalisée par: (a) la comparaison entre les versions empiriques des fonctions K, J, M, L et R et leurs versions théoriques, et (b) le test du χ² bidimensionnel. Cette approche par les copules a permis la reconstitution par simulation de l'échantillon hauteur de pluie—durée d'événements pluvieux à la station du lac collinaire Saddine 1 (35°48′06″N; 9°04′09″E).     

Regional models of flow-duration curves of perennial and intermittent streams and their use for calibrating the parameters of a rainfall–runoff model

Abstract

One of the main challenges faced by hydrologists and water engineers is the estimation of variables needed for water resources planning and management in ungauged river basins. To this end, techniques for transposing information, such as hydrological regional analyses, are widely employed. A method is presented for regionalizing flow-duration curves (FDCs) in perennial, intermittent and ephemeral rivers, based on the extended Burr XII probability distribution. This distribution shows great flexibility to fit data, with accurate reproduction of flow extremes. The performance analysis showed that, in general, the regional models are able to synthesize FDCs in ungauged basins, with a few possible drawbacks in the application of the method to intermittent and ephemeral rivers. In addition to the regional models, we summarize the experience of using synthetic FDCs for the indirect calibration of the Rio Grande rainfall–runoff model parameters in ungauged basins.

Editor D. Koutsoyiannis

Citation Costa, V., Fernandes, W., and Naghettini, M., 2013. Regional models of flow-duration curves of perennial and intermittent streams and their use for calibrating the parameters of a rainfall–runoff model. Hydrological Sciences Journal, 59 (2), 262–277.     

Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis / Modèles d’extrêmes utilisant le système Burr XII étendu à trois paramètres et application à l’analyse fréquentielle des crues

Abstract

Abstract A new theoretically-based distribution in frequency analysis is proposed. The extended three-parameter Burr XII distribution includes the generalized Pareto distribution, which is used to model the exceedences over threshold; log-logistic distribution, which is also advocated in flood frequency analysis; and Weibull distribution, which is a part of the generalized extreme value distribution used to model annual maxima as special cases. The extended Burr distribution is flexible to approximate extreme value distribution. Note that both the generalized Pareto and generalized extreme value distributions are limiting results in modelling the exceedences over threshold and block extremes, respectively. From a modelling perspective, generalization might be necessary in order to obtain a better fit. The extended three-parameter Burr XII distribution is therefore a meaningful candidate distribution in the frequency analysis. Maximum likelihood estimation for this distribution is investigated in the paper. The use of the extended three-parameter Burr XII distribution is demonstrated using data from China.     

A new method for modelling flow duration curves and predicting streamflow regimes under altered land-use conditions / Une nouvelle méthode de modélisation des courbes de débits classés et de prévision des régimes d'écoulement sous conditions modifiées d'occupation du sol

Abstract

The impact of changes in land-use/cover on streamflow at short time scales is evaluated by examining the changes in the flow duration curve (FDC) before and after land-use/cover change. The FDC characterizes the relationship between the magnitude and frequency and hence provides the complete range of streamflow over time. Two issues need to be considered in predicting the FDC due to land-use changes: (a) the appropriate parametric form of the FDC that enables application of the same expression of FDCs before and after the changes; and (b) the ability of parameters to capture and characterize the effect of land-use changes. In this paper, we propose a model which is a four-parameter double power form as a function of the FDC, where the two hydrological parameters represent the mean annual flow ([Qbar]) and the cease-to-flow point (τ expressed as a percentage), while the other two parameters (α and β) determine the shape of the FDC. The properties of this function are investigated in order to assign parameters to cope with the land-use changes. The model is used for several typical catchments in Australia for demonstration.