Numerical approximation of the hydrological time of concentration

The time of concentration, that is the time it takes for a single "drop of water" to move superficially from the most distant point of the watershed to the exit point, is a fundamental parameter of the hydrological analysis. Many studies have been conducted to propose empirical formulas to calculate the time of concentration. One of the best known is the Temez formula based on time series data collected in accounts in Spain with areas of less than 3,000 km. This expression uses the main channel length as a parameter as in many works, for small slopes is approximated by the distance between the geographic coordinates between the starting and ending points, leading for larger catchments and slopes to approaches with a high error. In this work, using a proper discretization of the curve, by using polynomial interpolation methods, we improve the calculation of the length of the main channel and therefore, we provide a more reliable method for calculating the time of concentration using the Temez expression. We illustrate the proposed scheme with different numerical examples comparing the results with those provided by other methods.