Role of hydraulic geometry in flood wave propagation

The role of hydraulic geometry in flood wave propagation is investigated by using a diffusion wave model with inertial effects. Power function relationships W = a’ Q^b’ and kS = r’ Q^y’ are used to reproduce the at-a-station variations of water-surface width W and Gauckler-Strickler conductance coefficient kS (the inverse of Manning resistance coefficient) with flow discharge Q. Downstream variations of coefficients a’ and r’ are not considered in this study. The considered hydraulic geometry relationships are incorporated into a diffusion wave model in which the term (1 − Ve^2), Ve being the Vedernikov number, multiplies the Hayami’s diffusivity Q/(2 W S0), S0 being the channel bed slope. This mathematical model is solved numerically by using a matched artificial diffusivity method. Numerical experiments are carried out by evaluating peak attenuation and mean peak celerity of flood waves propagating along channel reaches characterized by coefficients a’ and r’ equal to the average values observed in natural rivers, by all the combinations of exponents b’ and y’ laying in the range 0–0.5, and by values of S0 laying in the range 0.000125–0.032. It is found that: (1) peak attenuation and mean peak celerity display the minimum values for b’ = 0.5 and y’ = 0, (2) for high values of y’, Ve displays values greater than 1 indicating physical instability of flood waves, and (3) around the condition b’ = 0 and y’ = 0, for high values of Q/W and low values of S0, the Peclet number Pe (evaluated over the channel reach length) displays values less than 2 indicating unrealistic hydraulic diffusion (more storage effects than those produced by a reservoir). The region of the plane b’y’ representing relevant flood waves lays therefore between the instability region Ve > 1, where unstable flood waves are physically possible but rarely observed in natural channels and not reproducible with the considered model, and the region of unrealistic diffusion Pe < 2, where numerical solutions are possible but physically questionable. In this region, peak attenuation and mean peak celerity are found to be more sensitive to variations in y’ than in b’. The developed diffusion wave model provides a reliable description of the advection and diffusion processes determining travel times and storage variations at the channel reach scale, with clear implications for reproducing surface flows and their interaction with the subsurface. The obtained results indicate that stream channel geometry plays a critical role in runoff propagation, and thus caution must be exercised in river engineering when altering shape and resistance to flow of channels. In addition, they suggest that the developed model can be usefully combined with field data to understand how kinematic wave celerity and hydraulic diffusivity scale when mountain streams and hillslope rivulets are considered, a challenge for the definition of a new generation of distributed models that are really based on physics at all the spatial and temporal scales characterizing the different processes that occur within the drainage basin