Constructing prediction interval for artificial neural network rainfall runoff models based on ensemble simulations

This paper presents a method of constructing prediction interval for artificial neural network (ANN) rainfall runoff models during calibration with a consideration of generating ensemble predictions. A two stage optimization procedure is envisaged in this study for construction of prediction interval for the ANN output. In Stage 1, ANN model is trained with genetic algorithm (GA) to obtain optimal set of weights and biases vector. In Stage 2, possible variability of ANN parameters (obtained in Stage 1) is optimized so as to create an ensemble of models with the consideration of minimum residual variance for the ensemble mean, while ensuring a maximum of the measured data to fall within the estimated prediction interval. The width of the prediction interval is also minimized simultaneously. The method is demonstrated using a real world case study of rainfall runoff data for an Indian basin. The method was able to produce ensembles with a prediction interval (average width) of 26.49m³/s with 97.17% of the total observed data points lying within the interval in validation. One specific advantage of the method is that when ensemble mean value is considered as a forecast, the peak flows are predicted with improved accuracy by this method compared to traditional single point forecasted ANNs.