Grey neural networks for estimating the uncertainty band of a real time forecasting model

A procedure for estimating the uncertainty band of a real time forecasting model using grey artificial neural networks is here presented. Given the output (e.g. water levels or discharges) of the selected hydrological forecasting model, the corresponding uncertainty band is estimated through a neural network model whose parameters, namely, the weights and biases, are represented by grey numbers. To this end, the grey parameters of the neural network are estimated using a calibration procedure that imposes a constraint whereby the envelope of the corresponding intervals representing the outputs (grey levels or discharges, calculated at different points in time) must include a prefixed percentage of observed values. The application of the procedure to real hydrologic data shows its effectiveness in estimating the uncertainty associated to the forecast. The grey neural network enables us to define a band that describes the range of variability of the forecasted value; an analysis of the results reveals that these bands generally have a slightly narrower width compared to the bands obtained using other standard techniques, the percentage of observed values expected within the bands being the same or similar.