Timing the time of concentration: shedding light on a paradox

From the origins of hydrology, the time of concentration, t(c), has conventionally been tackled as a constant quantity. However, theoretical proof and empirical evidence imply that t(c) exhibits significant variability against rainfall, making its definition and estimation a hydrological paradox. Adopting the assumptions of the Rational method and the kinematic approach, an effective procedure in a GIS environment for estimating the travel time across a catchment's longest flow path is provided. By application in 30 Mediterranean basins, it is illustrated that t(c) is a negative power function of excess rainfall intensity. Regional formulas are established to infer its multiplier (unit time of concentration) and exponent from abstract geomorphological information, which are validated against observed data and theoretical literature outcomes. Besides offering a fast and easy solution to the paradox, we highlight the necessity of implementing the varying t(c) concept within hydrological modelling, signalling a major shift from current engineering practices.