System identification and subsequent discharge estimation based on level data alone—Gradually varied flow condition

• Discharge estimation can be accomplished in a channel having stage observations alone.
• Roughness coefficient can also be determined through discharge estimation process.
• Discharge estimation in GVF condition can be treated as an optimization problem.
• Implementation of GA to handle a nearly flat objective function which has numerous local optima.
• Modified genetic algorithm can reliably determine the appropriate pair of roughness coefficient and flow discharge.

Discharge estimation via depth/stage measurement alone in a channel reach with unknown roughness coefficient seems to be important, since it can replace the rating curve development process with all its impediments in practice. Many attempts have been made in this regard especially in the last decade which led to the development of methodologies based on hydraulic or hydrologic routing approaches. Although flow regime is considered to be transient in the literature associated to this subject, it seems that the flow under steady state condition is ignored. In this study the system identification (roughness coefficient determination) and subsequent discharge estimation is carried out for the steady state gradually varied flow condition in two cases: the first case is a wide rectangular channel with constant primarily unknown Chezy's roughness coefficient and the second one is a nonprismatic trapezoidal channel with constant primarily unknown Manning's roughness coefficient. In this regard, it was assumed that there exists a number of depth/stage observations along the reach and it was attempted to find an appropriate pair of roughness coefficient and discharge which produces a longitudinal steady state gradually varied flow profile similar to the one observed. It is shown that the problem can be treated as an optimization problem in which the sum of the squared deviations of calculated flow profile depths from the observed one is considered as the objective function. In order to choose an appropriate optimum search technique, the objective function contour map is drawn which demonstrates that the objective function surface is flat and highly near optimum in a wide range of roughness coefficient and discharge pairs. Hence, the derivative-based optimization approaches were rejected. Since the genetic algorithm is a derivative free adaptive exploratory optimum search technique parallel processing capability on a set of candidates, this method is utilized in this study to solve the corresponding optimization problem. The standard genetic algorithm is modified in order to prevent getting trapped in local optima. This modification guarantees the achievement of the global optimum solution. This GA-based optimization technique for system identification and subsequent discharge estimation in channel with depth/stage observations alone in steady state gradually varied flow condition leads to the desired performance through which the objective pair of roughness coefficient and discharge can be obtained in both wide rectangular and nonprismatic trapezoidal geometric conditions.