A history of the concept of time of concentration

Keith J Beven

doi:10.5194/hess-24-2655-2020

Abstract

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.

Highlights

The concept of the time of concentration of a catchment dates back to at least Mulvany (1851, reproduced in Loague, 2010) as the basis for estimating an appropriate timescale for rainfall duration in the rational method for estimating peak flows
Time of concentration was defined by the International Glossary of Hydrology (WMO, 1974; Johannsson, 1984) as the period of time required for storm runoff to flow from the most remote part of a drainage basin to the outlet
Wong (2003, 2009) treats the time of concentration as being equivalent to the time to equilibrium. This is how the time of concentration has often been used in practice when applied to the analysis and prediction of hydrographs, even if many explanations of the concept are still presented in terms of velocities rather than celerities

Summary

Introduction

The concept of the time of concentration of a catchment dates back to at least Mulvany (1851, reproduced in Loague, 2010) as the basis for estimating an appropriate timescale for rainfall duration in the rational method for estimating peak flows. Beven: A history of the concept of time of concentration but the relevant surface, subsurface, and channel flow celerities or wave velocities It seems that this might first have been suggested by Laurenson (1964), but has since been applied by many others He represents the effect by using nonlinear storage elements in the time–area discretization of the catchment area It is the celerities or wave velocities that govern the hydrograph response to an input, for both surface and subsurface flows. Wong (2003, 2009) treats the time of concentration as being equivalent to the time to equilibrium In effect, this is how the time of concentration has often been used in practice when applied to the analysis and prediction of hydrographs, even if many explanations of the concept are still presented in terms of velocities rather than celerities. This is a result of the historical development of the concept which the following text will explore in more detail

Early concepts of time of concentration

Reconnecting to catchment topography – the GIUH

Mathematical celerities and natural hillslopes

Teaching the concept of time of concentration in future