Do we still need the Rational Formula? An alternative empirical procedure for peak discharge estimation in small and ungauged basins

Abstract

1Dipartimento per la innovazione nei sistemi biologici, agroalimentari e forestali (Abstract The Rational Formula is the most applied equation in practical hydrology due to its simplicity and the effective compromise between theory and data availability. Although the Rational Formula has several drawbacks, it is reliable and surprisingly accurate considering the paucity of input information. However, after more than a century, the recent progress in computational ability, theory and large-scale monitoring compel us to try to suggest a more advanced yet still empirical procedure for estimating peak discharge in small and ungauged basins. In this paper, an alternative empirical procedure is described and discussed, and then a discussion as to whether the Rational Formula is still necessary is presented. The presented methodology integrates the three standard steps of the common event-based approach (design hyetograph, rainfall excess and rainfall-runoff transformation) accurately adapted for application with a lack of observed data. The proposed procedure requires the same input information as necessary for application of the Rational Formula (soil properties, intensity-duration-frequency rainfall curves and T c ) and provides both the peak discharge and the design hydrograph shape and, most importantly, reduces the subjectivity of the hydrologist in its application.Avons-nous encore besoin de la formule rationnelle ? Une méthode empirique alternative pour l'estimation du débit de pointe dans les petits bassins et les bassins non jaugés Résumé La formule rationnelle est l'équation la plus appliquée en hydrologie pratique en raison de sa simplicité et d'un bon compromis entre la théorie et la disponibilité des données. Bien que la formule rationnelle soit affectée par plusieurs inconvénients, elle est fiable et étonnamment précise compte-tenu du peu d'information utilisée en entrée. Cependant, après plus d'un siècle, les récents progrès des moyens de calcul, des développements théoriques et du suivi à grande échelle nous amènent à proposer une procédure plus avancée, bien qu'encore empirique, pour estimer le débit de pointe dans les petits bassins et les bassins non jaugés. Dans cet article, nous décrivons et discutons cette méthode empirique alternative, puis nous discutons de la pertinence actuelle de la formule rationnelle. La méthodologie présentée intègre les trois étapes classiques de l'approche événementielle habituelle (hyétogramme de projet, pluie excédentaire et transformation pluie-débit) spécialement adaptées à une application dans le cas d'un manque de données observées. La procédure proposée requiert les mêmes informations d'entrée que la formule rationnelle (propriétés du sol, courbes intensité-durée-fréquence des précipitations et T c ), fournit à le débit de pointe et la forme de l'hydrogramme de projet mais, surtout, réduit la subjectivité de l'hydrologue dans son application.Mots clefs Formule rationnelle ; approche événementielle ; hydrogramme de projet ; WFIUH ; débit de pointe ; bassin non jaug...

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