Grey neural networks for river stage forecasting with uncertainty

In this paper a new approach to set up a river stage forecasting model based on neural networks in which uncertainty is directly taken into account is presented. The approach is based on the use of an artificial neural network whose parameters are represented by grey numbers. The output of the proposed forecasting model is an interval (not a crisp value) which thus directly quantifies the imprecision/uncertainty or the vagueness of the forecasted value. The proposed approach is applied to a real case study and its results are compared with those provided by a Bayesian neural network-based forecasting model. The comparison of the results reveals that the bands obtained by the envelope of the intervals representing the outputs of the grey neural network generally have a slightly narrower width compared to the uncertainty bands produced by the Bayesian neural network, the percentage of observed values actually contained within the bands being the same or similar. Finally, it is shown that crisp forecasts can also be derived from the grey neural network forecasting model by considering properly selected crisp values extracted from the grey forecasts; the accuracy of these forecasts is equivalent, and in some cases even better than that of the crisp forecasts provided by the Bayesian neural network