State space neural networks for short term rainfall-runoff forecasting

Rainfall-runoff processes are dynamic systems that are better described by a dynamic model. In this paper, a specific dynamic neural network, called state space neural network (SSNN), is modified to perform short term rainfall-runoff forecasts. The lead time is extended to 3 h. To improve the link between the weights of the network and physical concepts that most neural networks lack for, a method of the unit hydrograph representation is proposed to reproduce the unit hydrographs based on the weights of the network. Hence, a transition of rainfall-runoff systems can be observed via the changes of the unit hydrograph hour by hour. Furthermore, a new learning method developed from the interchange of the roles of the network states and the weight matrix is applied to train the SSNN and helps the network to evolve into a time-variant model while forecasting the rainfall-runoff process. A study case has been implemented in Taiwanʹs Wu-Tu watershed, where the runoff path-lines are short and steep. Forty-seven events from 1966 to 1997 are forecasted via the SSNN, and the results are validated via four criteria. The convergence of the new learning algorithm is shown during the model training process. Performance of the SSNN for short term rainfall-runoff forecasting reveals that the specific dynamic recurrent neural network is appropriate for hydrological forecasts.