A history of the concept of time of concentration

Abstract

The concept of time of concentration in the analysis of catchment responses dates back over 150 years to the introduction of the rational method. Since then it has been used in a variety of ways in the formulation of both unit hydrograph and distributed catchment models. It is normally discussed in terms of the velocity of flow of a water particle from the furthest part of a catchment to the outlet. This is also the basis for the definition in the International Glossary of Hydrology. While conceptually simple, this definition is, however, wrong when applied to catchment responses where, in terms of how surface and subsurface flows produce hydrographs, it is more correct to discuss and teach the concept based on celerities and time to equilibrium. While this has been recognized since the 1960s, some recent papers and texts remain confused over the definition and use of the time of concentration concept. The paper sets out the history of its use and clarifies its relationship with time to equilibrium but suggests that both terms are not really useful in explaining hydrological responses. An Appendix is included that quantifies the differences between the definitions of response times for subsurface and surface flows under simple assumptions that might be useful in teaching.