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

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 Tc) and provides both the peak discharge and the design hydrograph shape and, most importantly, reduces the subjectivity of the hydrologist in its application.Editor D. Koutsoyiannis