Multi-phase hybrid bidirectional deep learning model integrated with Markov chain Monte Carlo bivariate copulas function for streamflow prediction

In recent years, deep learning (DL) approaches have been proven effective in addressing high nonlinear relationships within complex systems. Although various scientific studies have primarily focused on optimizing model architecture and enhancing its computational efficiency through hybridization, they have neglected the crucial aspect of selecting appropriate predictor variables (PV) and their influence on the model’s predictions. In this paper, a new multi-phase stochastic DL model is designed with a feature selection framework for monthly streamflow prediction. The multi-phase hybrid MCMC–BC–BiLSTM–BiGRU model is based on bidirectional long short-term memory (BiLSTM) and bidirectional gated recurrent unit (BiGRU) integrated with Markov Chain Monte Carlo (MCMC) based bivariate copulas (BC). First, Ant Colony Optimization (ACO) algorithm was employed for screening optimal PV, and then significant antecedent streamflow was coupled with it to generate optimized input combinations. In addition, 25 different MCMC–BC models were adopted for each input combination to determine the dependency of previous month's streamflow on current and future streamflow. Finally, best-fitted MCMC–BC model was integrated with hybrid BILSTM–BiGRU model to predict streamflow at nine different catchments in the Victoria region of the Upper Murray Basin (UMB), Australia. The experimental results show that the multi-phase hybrid MCMC–BC–BiLSTM–BiGRU model showed remarkable performance in comparison to its benchmark counterparts with respect to different robust statistical error metrics. Therefore, this study demonstrates that stochastic DL techniques can be effectively employed as a promising alternative predictive tool for upstream discharge predictions with high consistency and accuracy, specifically when a statistically significant relationship with the antecedent streamflow exists.