Genetic Algorithm-Based Discharge Estimation at Sites Receiving Lateral Inflows

The genetic algorithm (GA) technique is applied to obtain optimal parameter values of the standard rating curve model (RCM) for predicting, in real time, event-based flow discharge hydrographs at sites receiving significant lateral inflows. The standard RCM uses the information of discharge and effective cross-sectional flow area at an upstream station and effective cross-sectional flow area wave travel time later at a downstream station to predict the flow rate at this last site. The GA technique obtains the optimal parameter values of the model, here defined as the GA-RCM model, by minimizing the mean absolute error objective function. The GA-RCM model was tested to predict hydrographs at three different stations, located on the Upper Tiber River in central Italy. The wave travel times characterizing the three selected river branches are, on the average, 4, 8, and $12\mathrm{h}$ . For each river reach, seven events were employed, four for the model parameters’ calibration and three for model testing. The GA approach, employing 100 chromosomes in the initial gene pool, 75% crossover rate, 5% mutation rate, and 10,000 iterations, made the GA-RCM model successfully simulate the hydrographs observed at each downstream section closely capturing the trend, time to peak, and peak rates with, on the average, less than 5% error. The model performance was also tested against the standard RCM model, which uses, on the contrary to the GA-RCM model, different values for the model parameters and wave travel time for each event, thus, making the application of the standard RCM for real time discharge monitoring inhibited. The comparative results revealed that the RCM model improved its performance by using the GA technique in estimating parameters. The sensitivity analysis results revealed that at most two events would be sufficient for the GA-RCM model to obtain the optimal values of the model parameters. A lower peak hydrograph can also be employed in the calibration to predict a higher peak hydrograph. Similarly, a shorter travel time hydrograph can be used in GA to obtain optimal model parameters that can be used to simulate floods characterized by longer travel time. For its characteristics, the GA-RCM model is suitable for the monitoring of discharge in real time, at river sites where only water levels are observed.