ON THE EFFECTS OF DOWNSTREAM BOUNDARY-CONDITIONS ON DIFFUSIVE FLOOD ROUTING

The advection-diffusion (AD) equation is widely used to represent floo d wave propagation in waterways. Laplace transform methods are employe d to obtain the exact solution of a nonhomogeneous AD equation with sp atially varied initial condition and time dependent Dirichlet boundary conditions. Numerical inversion of the Laplace transform is employed to solve the AD equation with Neumann and Robin boundary conditions sp ecified at the downstream end of a finite reach of channel. The Neuman n boundary condition is specified by the assumption that water level r emains constant at the downstream boundary, that is, by a mass conserv ation version. This is a special case of the general condition that is obtained by plugging a steady rating curve into the continuity equati on. Backwater effects are assessed by analyzing response functions of flood wave movement in a semi-infinite channel and of a finite channel with the general condition prescribed as the downstream boundary cond ition. The Robin boundary condition, however, is derived on the basis of momentum conservation through the stage-discharge relationship. To investigate backwater effects a simple parameterized inflow hydrograph , based on Hermite polynomials, is introduced. The inflow flood hydrog raph is completely determined, given three parameters: the time to pea k t(p), the base time t(b), and the peak discharge Q(p). Comparisons b etween backwater effects associated with the Neumann and the Robin bou ndary conditions are made.