A fuzzy dynamic flood routing model for natural channels

A fuzzy dynamic flood routing model (FDFRM) for natural channels is presented, wherein the flood wave can be approximated to a monoclinal wave. This study is based on modification of an earlier published work by the same authors, where the nature of the wave was of gravity type. Momentum equation of the dynamic wave model is replaced by a fuzzy rule based model, while retaining the continuity equation in its complete form. Hence, the FDFRM gets rid of the assumptions associated with the momentum equation. Also, it overcomes the necessity of calculating friction slope (S-f) in flood routing and hence the associated uncertainties are eliminated. The fuzzy rule based model is developed on an equation for wave velocity, which is obtained in terms of discontinuities in the gradient of flow parameters. The channel reach is divided into a number of approximately uniform sub-reaches. Training set required for development of the fuzzy rule based model for each sub-reach is obtained from discharge-area relationship at its mean section. For highly heterogeneous sub-reaches, optimized fuzzy rule based models are obtained by means of a neuro-fuzzy algorithm. For demonstration, the FDFRM is applied to flood routing problems in a fictitious channel with single uniform reach, in a fictitious channel with two uniform sub-reaches and also in a natural channel with a number of approximately uniform sub-reaches. It is observed that in cases of the fictitious channels, the FDFRM outputs match well with those of an implicit numerical model (INM), which solves the dynamic wave equations using an implicit numerical scheme. For the natural channel, the FDFRM Outputs are comparable to those of the HEC-RAS model.