A hybrid FEDformer-LSTM model for accurate multi-step ahead river streamflow forecasting

Accurate river streamflow forecasting is vital for water resources management, flood control, hydrological and water sciences. Robust prediction models are required due to nonlinearity and complexity of river streamflow process. To address this, different deep learning (DL) methods, including Transformer-based architectures, have been recently developed. This study evaluates the performance of six diverse variants of DL techniques in multi-step ahead forecasting of the daily river streamflows at two hydrometric river stations (10AA001 and 10ED002) located on the Liard River, Canada. The developed models included five baseline models: Frequency Enhanced Decomposed Transformer (FEDformer), Informer, Long Short-Term Memory (LSTM), Transformer, and Inverted Transformer (iTransformer). In addition, a hybrid scheme named FEDformer-LSTM was proposed by integrating the FEDformer and LSTM. The obtained results demonstrated that the proposed FEDformer-LSTM hybrid model not only outperformed the baseline FEDformer but also showed the best performance among all the models developed, confirming its reliable capability for multi-step ahead forecasting of the daily river streamflows at the studied stations. An attempt was finally made to improve the models’ performances through a preprocessing method, namely Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). The findings revealed that the hybrid CEEMDAN-DL frameworks generally achieved better outcomes compared to the relevant baseline DL models. The best river streamflow forecasts were achieved through CEEMDAN-LSTM at both the stations at t + 1 lead time (10AA001 Station: MAE = 6.4435 m3/s, MSE = 251.5336 (m3/s)2, RMSE = 15.8598 m3/s, R2 = 0.9989, NSE = 0.9988, KGE = 0.9911, PBIAS = −0.0637%; 10ED002 Station: MAE = 55.7703 m3/s, MSE = 9249.1674 (m3/s)2, RMSE = 96.1726 m3/s, R2 = 0.9994, NSE = 0.999, KGE = 0.978, PBIAS = 1.7122%). Therefore, the models developed in this study can be proposed as efficient intelligent tools for accurate river streamflow forecasting for optimal water resources management and allocation.