Stochastic modeling of artificial neural networks for real-time hydrological forecasts based on uncertainties in transfer functions and ANN weights

This study proposes a stochastic artificial neural network (named ANN_GA-SA_MTF), in which the parameters of the multiple transfer functions considered are calibrated by the modified genetic algorithm (GA-SA), to effectively provide the real-time forecasts of hydrological variates and the associated reliabilities under the observation and predictions given (model inputs); also, the resulting forecasts can be adjusted through the real-time forecast-error correction method (RTEC_TS&KF) based on difference between real-time observations and forecasts. The observed 10-days rainfall depths and water levels (i.e., hydrological estimates) from 2008 to 2018 recorded within the Shangping sub-basin in northern Taiwan are adopted as the study data and their stochastic properties are quantified for simulating 1,000 sets of rainfall and water levels at 36 10-days periods as the training datasets. The results from the model verification indicate that the observed 10-days rainfall depths and water levels are obviously located at the prediction interval (i.e., 95% confidence interval), revealing that the proposed ANN_GA-SA_MTF model can capture the temporal behavior of 10-days rainfall depths and water levels within the study area. In spite of the resulting forecasts with an acceptable difference from the observation, their real-time corrections have evident agreement with the observations, namely, the resulting adjusted forecasts with high accuracy.