An improved dynamics framework for accurate multi-step ahead daily streamflow prediction with spatial–temporal and global information

Accurate and reliable multi-step ahead streamflow forecasting is important for water resource management and flood prevention. To alleviate the temporal lag in multi-step prediction and improve peak prediction capability, this research develops a multi-head self-attention-spatiotemporal skip-connection model (MHSA-STSM), which is based on nonlinear dynamic systems and deep learning approaches. MHSA-STSM comprises a temporal module constructed from a convolutional neural network (CNN), a spatiotemporal module fashioned from a multi-head self-attention mechanism, along with a skip connection that links directly to the original input; these modules enable MHSA-STSM to effectively amalgamate temporal, spatiotemporal, and global information within the data. By learning the mapping between the original attractors and the delay attractors, MHSA-STSM can extract spatiotemporal features from the original attractors, thereby enabling the prediction of future values for the target variable. MHSA-STSM is applied to make a multi-step forecast of daily streamflow in rivers in the states of Maine, USA. For a five-step forecast, the highest R value of MHSA-STSM is 0.960, which is 1.05%–11.10% higher than CNN, multi-head self-attention mechanism-Long Short-Term Memory (MHSA-LSTM) and STSM; the lowest R value of 0.792 is at the USGS1047000 station, which shows a 91.4% improvement over the average of CNN, MHSA-LSTM and STSM; the RMSE and MAPE values of MHSA-STSM are 10.76%–102.50% and 19.26%–305.51% lower than those of three comparative models; the NSE of MHSA-STSM is significantly greater than that of the other models, and is as high as 0.920 at USGS 01013500 station. Moreover, sensitivity experiments on the prediction step length are performed for the model. It is found that MHSA-STSM performed excellently in five-step, seven-step, and ten-step predictions and can effectively alleviate the time lag issue. The R value ranges from 0.960 to 0.938, with NSE from 0.920 to 0.836. As the step length increases from 5 to 10, the R value decreases by only 2.3%, and the NSE decreases by 9.1%, demonstrating high stability, while the performance of other models significantly declines. Therefore, MHSA-STSM can effectively capture the spatiotemporal information embedded in high-dimensional data and make accurate multi-step predictions of daily streamflow.