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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. [ABSTRACT FROM AUTHOR]

Although traditional physical models have been used to analyse groundwater systems, the emergence of novel machine learning models can improve the accuracy of the predictions. Deep learning has been prominent in environmental and climate change problems. In this paper, we present a framework for utilising deep learning models to predict groundwater levels based on nearby streamflow and rainfall data. We address the missing data problem using a Bayesian linear regression model within the deep learning framework. Our deep learning framework utilises models such as long-short term memory (LSTM) networks and convolutional neural networks (CNN) for multi-step ahead time series prediction. We examine the fluctuations in groundwater levels at various boreholes located near Middle Creek in New South Wales, Australia. We use the National Collaborative Research Infrastructure Strategy (NCRIS) groundwater database and utilise Bayesian linear regression to impute missing data. We investigate the accuracy of the selected models for individual and regional basins and univariate and multivariate strategies. Our results show that the LSTM-based regional model with multivariate strategy using rainfall data provided the best accuracy. • We predict groundwater levels based on stream flow and rainfall data. • Our framework uses Bayesian data imputation and deep learning for multi-step prediction. • We examine the groundwater fluctuations at various boreholes located in Australia. • Results show a fine-tuned regional model with rainfall data yielded the best accuracy. • We find that LSTM models outperformed CNNs using the multivariate approach. [ABSTRACT FROM AUTHOR]

Modelling workflow for BRF-LSTM and BRF-GRU predictive models. [Display omitted] • Deep learning hybrid predictive model (BRF-LSTM) is built for streamflow forecasting. • Climate indices, rainfall and periodicity are factored for accurate predictions. • Adopts feature algorithm (i.e. Boruta) with long short-term memory and gated recurrent unit. • Six gauging sites tested; BRF-LSTM yields > 98% errors in ± 0.015 m, ~1.30% relative error. • The proposed model is useful for hydrological and strategic water resources planning. Long-term forecasting of any hydrologic phenomena is essential for strategic environmental planning, hydrologic and other forms of structural design, agriculture, and water resources management. Climate mode indices, utilising machine learning methods, are frequently considered as predictor variables in order to forecast several different hydrological variables. In this study, a feature selection algorithm based on two different deep learning models, i.e., long short-term memory and a gated recurrent unit, is applied to improve the forecasting capability of streamflow water levels at six gauging stations in the Murray Darling Basin of Australia. This paper therefore aggregates the significant antecedent lag memory of climate mode indices, rainfall, and the monthly factor based on the periodicity as the predictor variables to attain significantly accurate stream water level forecasts. This novel method identifies an improved relationship between the stream water level and climate mode indices through the aggregation of the significant lagged datasets capturing the historical features to predict the future streamflow water level. The boruta feature selection algorithm (BRF) was then applied in a two phase process before and after attaining the significant lagged inputs to screen the optimum predictor variables. The merits of the forecast models were evaluated through different performance evaluation criteria. The results show that the accumulated significant lagged inputs based on climate mode indices, along with the rainfall and periodicity factors are seen to provide improved forecasting of the SWL over the non-BRF deep learning approaches where no prior feature selection was applied. The hybrid LSTM method (i.e., BRF-LSTM model) achieved a unique advantage in terms of SWL forecasting, particularly attaining over 98% of the predictive errors lying within a band of +/-0.015 m with relatively low relative errors (RRMSE ≈1.30% and RMAE ≈ 0.882%), outperforming all of the benchmark models. It is also found that the periodicity factor has a potential influence on the accuracy of the forecast models for the four monitored study stations. This study concludes that the newly developed hybrid deep learning approaches, coupled with the BRF feature selection, provide improved forecasting performance. The hybrid approach developed in this paper can therefore be used to provide a strong provide predictive response algorithm for the hydrological variables that were influenced by the low-frequency variability of the climate model indices in respect to streamflow water level. [ABSTRACT FROM AUTHOR]