Hydrological peaks evaluation at chitral and tarbela stations, Pakistan, using combined Bayesian regularized neural network and signal difference average based variational mode decomposition method: a case study

Pakistan, being an agricultural country, highly depends on its natural water resources which originate from the upper regions of Hindu Kush-Karakoram-Himalaya Mountains and nourish one of the world's largest Indus Basin irrigation systems. This paper presents streamflow modelling and forecasting using signal difference average (SDA) based variational mode decomposition (VMD) combined with machine learning (ML) methods at Chitral and Tarbela stations on the Indus River network. For this purpose, VMD based random forest (VMD-RF), gradient boosting machine (VMD-GBM) and Bayesian regularized neural network (VMD-BRNN) have been chosen. Moreover, traditional time series flow models, that is seasonal autoregressive integrated moving average (SARIMA) and classical decomposition approach with particle swarm optimization-based support vector regression (PSO-SVR), are considered as benchmark models for comparison. The results show that overall, VMD-BRNN performed best, followed by VMD-GBM and VMD-RF, whereas SARIMA and PSO-SVR ranked last. Overall, SARIMA and PSO-SVR are failing to capture most of the peaks even during the training period whereas hybridization of VMD and ML methods has shown increased robustness of the models. The results show that the influential role of the high dimensional components and robustness on the river flow may be explored by most optimum SDA based VMD signals hybrid with BRNN method.