A Simulation–Optimization Technique to Estimate Discharge in Open Channels Based on Water Level Data Alone: Gradually Varied Flow Condition

Discharge estimation in open-channel hydraulics is required for a variety of purposes including design of hydraulic structures, reservoir routing, water pricing and payment. This estimation procedure lasts for almost two centuries. Nowadays, research interest in discharge estimation methods based on the water level data alone has grown due to the drawbacks of direct velocity measurement. Recent trend in this field is switched from physical measurement to numerical by linking a gradually varied flow equation solver with either structured or random search optimization algorithm to obtain channel roughness and associated discharge. In this paper, in reference to the existing research gaps, the authors intend to evaluate the performance and accuracy of the above proposal for both M1 and M2 water surface profiles in both hypothetical and real-world settings. In this regard, a number of water surface profiles with various discharges, slopes and bed roughness were synthetically generated and/or measured on a very fine stream-wise grid in a laboratory flume for both M1 and M2 profiles. This enabled us to assess and investigate the impact of hydraulic conditions, simulation and optimization parameters on discharge estimation. The results show that, while synthetic water depth data on M1 and M2 can be effectively utilized to compute channel discharge, the discharge estimation based on laboratory data has a high accuracy for M2 profiles compared with M1 profiles. As the roughness coefficient and consequently the error in water level data measurements increases, the accuracy of the proposed method decreases. In addition, the aforementioned method has better results in steep waterways where the subcritical flow regime acquires high Froude number. Moreover, the results show that the values of initial guess and upper bounds of n and Q are not important in M2 water surface profiles. However, for M1, using initial guesses and upper bounds approximately near to the actual known’s n and Q gives better results. In addition, by increasing the distance between nodes and consequently decreasing the number of required water level data, the accuracy of discharge estimation decreases. In conclusion, both private and government sectors in water industry can benefit from water level monitoring to estimate discharge for various applications in real-world settings.