Review of Time-of-Concentration Equations and a New Proposal in Italy

The time of concentration is a fundamental parameter used for hydrological analysis in professional and scientific communities. The availability of equations for its estimation leads to significant variability and uncertainty. In this work, the most commonly used 24 equations were selected among the empirically based models to compare their estimates and to quantify the accuracy in predicting the time of concentration observed from 46 river basins in northern Italy. The practical definition for direct time of concentration estimation used in this work computes it as the time from the end of effective rainfall to the end of direct runoff on the recession limb of the total hydrograph. The results show a large discrepancy between the observed values and those estimated with the selected equations: the best performances are achieved by Bransby-Williams, Giandotti, Soil Conservation Service, Témez, and Ferro equations. The catchment classification into classes of basins with homogeneous climatological and physiographic characteristics shows that none of the analyzed equations significantly improves the predictions. Finally, a new equation is proposed for the area of the Upper Po River Basin that can significantly decrease the time-of-concentration estimation error.