Volume-Conservative Nonlinear Flood Routing

The nonlinear Muskingum and diffusion wave methods for flood routing are deduced from a conservative modified-advection equation as an approximation of the one-dimensional Saint-Venant equations. The modified-advection equation has the kinematic wave speed and attenuation parameter as functions of discharge, which can be derived for the particular averaged geometry for the cross section and hydraulic properties of the reach. The nonlinear Muskingum and diffusion wave methods also include any uniformly distributed time-dependent lateral inflow along the river and are valid for any Froude number. The methods are discussed in relation to corresponding methods derived recently for Muskingum routing and for diffusion wave routing. Numerical experiments on a synthetic river including extensive flood plains show that the proposed nonlinear Muskingum method is highly accurate compared with a full solution of the Saint-Venant equations. The deterioration of accuracy with decreasing bed gradient is highlighted for cases with and without lateral inflow.