Flood Propagation Forecasting Based on Non-linear Diffusive Wave Equation

Document Type : Research Article



Existence of a quick and accurate flood routing model is of great importance for river training as well
as flood forecasting and warning systems in order to prevent or mitigate flood casualties and damages.
Diffusive wave is one of the channel routing methods in which acceleration terms have been neglected
in momentum equation. Among different types of diffusive wave models, Cappelaere equation,
considering its unique features, was applied in present research. This model is an advection-diffusion
equation, including non-linear parameters, with main advantage of no need for topographic and
hydraulic characteristics of the river. In this paper, Leapfrog-Dufort Frankel finite difference
numerical scheme was used for discretization and numerical solution of the Cappelaere equation
which increases computational speed of flood routing. Furthermore, a novel method of estimating
celerity(C) and diffusivity (D) parameters was proposed which is superior to previous methods. In this
method, C and D parameters can be calibrated just by observed hydrographs in a reach and are
applicable for future flood forecasting in the same reach. By this method, absolute independency of
parameter estimation in diffusive wave routing method from river geometry, manning roughness and
bed slope is obtained. To validate the model and the proposed method of parameter estimation, the
routed hydrographs were compared with the dynamic Saint-Venant equations in a synthetic prismatic
channel. Furthermore, the model was calibrated in a 80 km reach, Yasavol-Gharegooni, of Ghezel-
Ozan river and results were tested against the observed hydrographs. Using the model, duration of
routing in the channel and river were found to be 15.7 and 59 seconds respectively. Maximum error in
peak discharge in the channel and river does not exceed 0.04% and 0.24% respectively. Concerning
time to peak, the maximum error in the channel and river were 0.87% and 1.57% respectively. Results
in the channel and the river showed that the proposed model is not only accurate in predicting peak
discharge and time of peak, but also is successful in Conserving mass of flood.