On the effects of downstream boundary conditions on diffusive flood routing

Wei Hao Chung, Alvaro A. Aldama, James A. Smith

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The advection-diffusion (AD) equation is widely used to represent flood wave propagation in waterways. Laplace transform methods are employed to obtain the exact solution of a nonhomogeneous AD equation with spatially 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 specified at the downstream end of a finite reach of channel. The Neumann boundary condition is specified by the assumption that water level remains constant at the downstream boundary, that is, by a mass conservation version. This is a special case of the general condition that is obtained by plugging a steady rating curve into the continuity equation. 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 condition. 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 hydrograph is completely determined, given three parameters: the time to peak tp, the base time tb, and the peak discharge Qp. Comparisons between backwater effects associated with the Neumann and the Robin boundary conditions are made.

Original languageEnglish (US)
Pages (from-to)259-275
Number of pages17
JournalAdvances in Water Resources
Issue number5
StatePublished - 1993

All Science Journal Classification (ASJC) codes

  • Water Science and Technology


  • advection-diffusion equation
  • backwater effects
  • flood routing
  • open-channel flow
  • rating curve


Dive into the research topics of 'On the effects of downstream boundary conditions on diffusive flood routing'. Together they form a unique fingerprint.

Cite this