Analytical solution for channel routing with uniform lateral inflow

Distributed hydrologic models describe both hillslope and channel processes. The presence of a large number of hillslopes requires that flood routing through a channel network be computationally efficient and able to account for hillslope or lateral inflow. This paper presents an analytical solution to the linearized Saint-Venant equation with lateral inflow uniformly distributed along the channel. The solution is given as the sum of two functions. The first function, obtained by several earlier authors, represents the response to the upstream inflow; the second function, derived in this study, represents the contribution from lateral or hillslope inflow. We test the latter on a simple channel, and the results compare well with those of a detailed numerical model for channels with steep to fairly gentle bed slopes. The errors due to linearization are presented, and the effects of channel-bed slope and the reference velocity are discussed. A run time comparison between the numerical and the analytical solutions shows that the latter is more efficient computationally and hence is ideal as an element of a distributed rainfall-runoff model.