Use of hysteresis for defining the nature of flood wave propagation in natural channels

The hysteresis (eta) of the non-dimensional site-specific rating curve is used to describe the occurrence of a kinematic wave (KW), a diffusion wave (DW) or a dynamic wave (DYW) in the downstream valleys of the Teton dam, USA, and the Machhu dam II, India. Criteria are developed for the occurrence of these waves. The study reveals that the hysteresis is the energy loss occurring at a particular site and is related to the speed of travel, wave number, phase difference and attenuation characteristics of the flood wave. The role of eta is shown to be of vital importance in: (i) choosing a suitable downstream boundary for improving the results; and (ii) identifying the wave zones where approximate models can substitute the complete DYW model.