Auto-Regressive Neural-Network Models for Long Lead-Time Forecasting of Daily Flow

Accurate reservoir-inflow forecasting is especially important for optimizing operation of multi-propose reservoirs that provide hydropower generation, flood control, and water for domestic use and irrigation. There are no previous reports of successful daily flow prediction using a 1-year lead-time. This paper reports successful daily stream flow predictions for that extended lead-time. It presents the first NARX (Nonlinear Auto Regressive model with eXogenous inputs)-type recurrent neural network (NARX-RNN) model used to forecast daily reservoir inflow for a long lead-time. It is the first use of dynamic memory to extend the forecast lead-time beyond the previously reported 1-week lead-times. For new nonlinear NARX-RNN models, we present and test 1600 alternative structures, differing in transfer functions (2), and numbers of inputs (2 to 5), neurons per hidden layer (1 to 20), input delays and output delays. For predicting inflow to the reservoir of the multi-purpose Dez Dam, we contrast accuracies of forecasts from the new models, and from a conventional auto-regressive linear ARIMA model. Based upon normalized root-mean-square error \( \mathrm{RMSE}/{\overline{Q}}_{obs} \) the best NARX-RNN has log-sigmoid transfer functions, three inputs, one hidden layers, four neurons in the hidden layer, two input delays, and 10 output delays. That NARX-RNN structure yields \( \mathrm{RMSE}/{\overline{Q}}_{obs} \) values of 0.616 in training and 0.678 in forecasting. The proposed model’s forecasting \( \mathrm{RMSE}/{\overline{Q}}_{obs} \) is 20% lower than that of the ARIMA model.