Dynamics of River Flood Waves below Hydropower Dams and Their Relation to Natural Floods

Abstract

The dynamic behavior of flood waves on rivers is essential to flood prediction. Natural flood waves are complex due to tributary inputs, rainfall variations, and overbank flows, so this study examines hydropower dam releases, which are simpler to analyze because channel effects are isolated. Successive arrival times and heights of peaks along 9 rivers with multiple stream gauges downstream of hydroelectric dams show that flow peaks typically become exponentially lower and wider with distance. The propagation velocity of peaks increases with water depth and channel slope but decreases with downstream distance and greater channel tortuosity. A rich hierarchy of velocities was found. Hydropower pulses progress at or in slight excess of the theoretical celerity, which is faster than the propagation rate of average natural floods, which in turn exceeds the mean velocity of water in the channel, yet the water moves faster than the peaks of record floods. The progressive changes to the height, shape, and velocity of hydropower flow peaks are simulated by the first analytical solution to the convolution integral for a rectangular source pulse that is based on diffusion-advection theory. Available data support some widely held expectations while refuting others. An expanded definition of “water mining” is proposed.

Keywords

• hydroelectric dam pulses
• flood waves
• natural floods
• water mining
• convolution integrals