Online multistep-ahead inundation depth forecasts by recurrent NARX networks

Various types of artificial neural networks (ANNs) have been successfully applied in hydrological fields, but relatively scant on multistep-ahead flood inundation forecasting, which is very difficult to achieve, especially when dealing with forecasts without regular observed data. This study proposes a recurrent configuration of nonlinear autoregressive with exogenous inputs (NARX) network, called R-NARX, to forecast multistep-ahead inundation depths in an inundation area. The proposed R-NARX is constructed based on the recurrent neural network (RNN), which is commonly used for modeling nonlinear dynamical systems. The models were trained and tested based on a large number of inundation data generated by a well validated two-dimensional simulation model at thirteen inundation-prone sites in Yilan County, Taiwan. We demonstrate that the R-NARX model can effectively inhibit error growth and accumulation when being applied to online multistep-ahead inundation forecasts over a long lasting forecast period. For comparison, a feedforward time-delay and an online feedback configuration of NARX networks (T-NARX and O-NARX) were performed. The results show that (1) T-NARX networks cannot make online forecasts due to unavailable inputs in the constructed networks even though they provide the best performances for reference only; and (2) R-NARX networks consistently outperform O-NARX networks and can be adequately applied to online multistep-ahead forecasts of inundation depths in the study area during typhoon events.