Stacking ensemble learning models for daily runoff prediction using 1D and 2D CNNs

In recent years, applications of convolutional neural networks (CNNs) to runoff prediction have received some attention due to their excellent feature extraction capabilities. However, existing studies are still limited since merely either 1D or 2D CNNs are developed to predict runoff. In this study, a stacking ensemble learning model for daily runoff prediction based on different types of 1D and 2D CNNs is proposed and applied to the Quinebaug River Basin, Connecticut, USA. The structure of the CNN models is developed with reference to the classic LeNet5 network. Especially, the predictors are reconstructed into 1D vectors and 2D matrices with 10-, 20-and 30-day time steps. Totally 18 member models are constructed through selecting 3 representative 1D and 2D CNN models with 3 time steps. The simple average method (SAM) is used to integrate different CNN member models. The results show that the performance of the same-type SAM based on either 1D or 2D CNNs improves because it can counteract the effects of both positive and negative predicted values by the member models to some extent. Furthermore, the mixed-type SAM models based on both 1D and 2D CNN member models can further improve the prediction accuracy. The optimal model SAM15 consists of two 1D CNNs and four 2D CNNs. Compared with the optimal CNN member models, SAM15 reduces the validation RMSE by about 13% and improves the vali-dation R and NSE by about 3% and 7%, respectively. This study highlights that the proposed stacking ensemble learning model can improve the daily runoff prediction accuracy through integration of the nonlinear fitting ability of 1D and 2D CNN member models.