Uncertainty in Flood Wave Routing in a Lateral-Inflow-Dominated Stream

Abstract

Flood wave routing is a common problem in water resources engineering, for example, when a hydrograph enters a stream channel and passes downstream to an observation station. In the past, the problem has been approached by making the best possible estimate of the inflow hydrograph. The channel properties such as geometry and roughness are also estimated, along with any lateral inflow. The best estimates are used with a flood wave routing model to predict the hydrograph at the downstream observation station. Making a prediction by this procedure is full of challenges. It is impossible to exactly know the precise form of the hydrograph that will enter the channel. It is also difficult to select the channel properties from the range of values that may be appropriate. Lateral inflow is notoriously difficult to quantify. Making predictions under these circumstances is full of uncertainties. One approach to analyzing uncertainties is to use Monte Carlo modeling to make quantitative estimates of the uncertainty in flood wave routing results. The best estimates used for boundary conditions and model parameters are replaced by probability estimates. The ensemble of results from the Monte Carlo framework can be analyzed to develop probabilistic estimates of the routed hydrograph at the outlet of the channel reach. While this is a powerful approach, it also requires extensive probability data for the boundary conditions and channel properties. Such input data are rare in the published literature and do not appear to exist at all for lateral-inflow-dominated streams. This study examines the flood wave routing problem in a probabilistic framework using the kinematic wave model. It develops a complete data set for a lateral-inflow-dominated stream that includes a probabilistic description of the inflow hydrograph and lateral inflow. It also includes probability density functions for the parameters used in the kinematic wave model. The resulting data set appears to be the first developed for a lateral-inflow-dominated stream, though data sets do exist for streams without significant lateral inflows. Beyond the development of a new data set, this study seeks to evaluate the relative contributions of uncertainty in boundary conditions and channel parameters to the total uncertainty in the routed flood wave. Results for the lateral-inflow-dominated case developed here are compared to a similar example where lateral inflow is not significant. The results found here suggest that in both cases it is the uncertainty in boundary conditions that is most significant and dominates the total uncertainty in the routed flood wave.