An explainable multiscale LSTM model with wavelet transform and layer-wise relevance propagation for daily streamflow forecasting

Developing an accurate and reliable daily streamflow forecasting model is important for facilitating the efficient resource planning and management of hydrological systems. In this study, an explainable multiscale long shortterm memory (XM-LSTM) model is proposed for effective daily streamflow forecasting by integrating the a` trous wavelet transform (ATWT) for decomposing data, the Boruta algorithm for identifying model inputs, and the layer-wise relevance propagation (LRP) for explaining the prediction results. The proposed XM-LSTM is tested by performing multi-step-ahead forecasting of daily streamflow at four stations in the middle and lower reaches of the Yangtze River basin and compared with the X-LSTM. The X-LSTM is formed by coupling the long short-term memory (LSTM) with the LRP. For comparison, the inputs of these two models are identified by the Boruta selection algorithm. The results show that all models exhibit good ability to forecast daily streamflow, however, the prediction performance decreases as the lead time increases. The XM-LSTM provides a better forecasting performance than the X-LSTM, suggesting the ability of the ATWT to improve the LSTM for daily streamflow forecasting. Moreover, the correlation scores analysis by the LRP shows that the ATWT can extract useful information that influences the daily streamflow from the raw predictors, and the water level has the most significant contribution to streamflow prediction. Accordingly, the XM-LSTM model can be viewed as a potentially useful approach for increasing the accuracy and explainability of streamflow forecasting.