On-line 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 flood inundation forecast. 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 on-line multistep-ahead inundation forecasts over a long lasting forecast period. For comparison, a feedforward time-delay and an on-line feedback configuration of NARX networks (T-NARX and O-NARX) were performed. The results show that (1) T-NARX networks cannot make on-line 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 on-line multistep-ahead forecasts of inundation depths in the study area during typhoon events.