SMGformer: integrating STL and multi-head self-attention in deep learning model for multi-step runoff forecasting.

Accurate runoff forecasting is of great significance for water resource allocation flood control and disaster reduction. However, due to the inherent strong randomness of runoff sequences, this task faces significant challenges. To address this challenge, this study proposes a new SMGformer runoff forecast model. The model integrates Seasonal and Trend decomposition using Loess (STL), Informer's Encoder layer, Bidirectional Gated Recurrent Unit (BiGRU), and Multi-head self-attention (MHSA). Firstly, in response to the nonlinear and non-stationary characteristics of the runoff sequence, the STL decomposition is used to extract the runoff sequence's trend, period, and residual terms, and a multi-feature set based on 'sequence-sequence' is constructed as the input of the model, providing a foundation for subsequent models to capture the evolution of runoff. The key features of the input set are then captured using the Informer's Encoder layer. Next, the BiGRU layer is used to learn the temporal information of these features. To further optimize the output of the BiGRU layer, the MHSA mechanism is introduced to emphasize the impact of important information. Finally, accurate runoff forecasting is achieved by transforming the output of the MHSA layer through the Fully connected layer. To verify the effectiveness of the proposed model, monthly runoff data from two hydrological stations in China are selected, and eight models are constructed to compare the performance of the proposed model. The results show that compared with the Informer model, the 1th step MAE of the SMGformer model decreases by 42.2% and 36.6%, respectively; RMSE decreases by 37.9% and 43.6% respectively; NSE increases from 0.936 to 0.975 and from 0.487 to 0.837, respectively. In addition, the KGE of the SMGformer model at the 3th step are 0.960 and 0.805, both of which can maintain above 0.8. Therefore, the model can accurately capture key information in the monthly runoff sequence and extend the effective forecast period of the model.

Improving forecasting accuracy of medium and long-term runoff using artificial neural network based on EEMD decomposition.

Hydrological time series forecasting is one of the most important applications in modern hydrology, especially for the effective reservoir management. In this research, an artificial neural network (ANN) model coupled with the ensemble empirical mode decomposition (EEMD) is presented for forecasting medium and long-term runoff time series. First, the original runoff time series is decomposed into a finite and often small number of intrinsic mode functions (IMFs) and a residual series using EEMD technique for attaining deeper insight into the data characteristics. Then all IMF components and residue are predicted, respectively, through appropriate ANN models. Finally, the forecasted results of the modeled IMFs and residual series are summed to formulate an ensemble forecast for the original annual runoff series. Two annual reservoir runoff time series from Biuliuhe and Mopanshan in China, are investigated using the developed model based on four performance evaluation measures (RMSE, MAPE, R and NSEC). The results obtained in this work indicate that EEMD can effectively enhance forecasting accuracy and the proposed EEMD-ANN model can attain significant improvement over ANN approach in medium and long-term runoff time series forecasting.