Development of discharge-stage curves affected by hysteresis using time varying models, model trees and neural networks

Flow data forms the base on which much of the edifice of water management is raised. However, flow measurements are expensive and difficult to conduct. Therefore, the more accessible stage measurements are employed in combination with stage-discharge relationships. Setting up such relationships is often infeasible using traditional regression techniques. Two case studies are examined that show hystereses using various approaches, namely (1) single rating curves, (2) rating curves with dynamic correction, (3) artificial neural networks (ANN) and (4) M5′ model trees. All methods outperform the traditional rating curve. The presented approach that uses a dynamically corrected rating curve delivers accurate results and allows for physical interpretation. The ANNs mimic the calibration data precisely, but suffer from overfitting when a small amount of data is applied for training. The rarely used M5′ model tree's architecture is easier to interpret than that of neural networks and delivers more accurate results.