Groundwater level forecasting in Northern Bangladesh using nonlinear autoregressive exogenous (NARX) and extreme learning machine (ELM) neural networks

Groundwater resources (GWR) are vital to agricultural crop production, everyday life, and economic development. As a result, accurate groundwater level (GWL) prediction would aid in the long-term management of GWR. A comparative analysis was performed to test the predictive capabilities of models based on non-linear autoregressive with exogenous inputs (NARX) and extreme learning machine (ELM). Long-term predictions were performed using GWL and rainfall time series measured in two sites, Bogra and Dinajpur, in Bangladesh’s northwest region from 1981 to 2017. The delay between precipitation and GWL was assessed through the cross-correlation function, computing an input delay equal to 2 months for both sites. Furthermore, the auto-correlation of the GWL was also performed to evaluate the optimal feedback delay, showing the seasonality of GWL fluctuations with a peak at 12 months for both sites. However, the sensitivity to changes in the feedback delay was also assessed, comparing the predictions produced for a feedback delay equivalent to 12 months with those computed for delays ranging from 1 to 11 months. Outputs of the two proposed models were evaluated using different metrics: the root mean square error (RMSE), mean absolute error (MAE), relative absolute error (RAE), and correlation coefficient (CC). The results revealed that NARX models outperformed ELM models. NARX models were able to provide accurate long-term predictions, with R2 equal to 0.918 and 0.947 for Bogra and Dinajpur sites, respectively, with a forecasting horizon τ = 12 months. ELM models also provided good forecasts for Dinajpur, but less accurate for Bogra, with R2 respectively equal to 0.825 and 0.675 with τ = 12 months. This research would provide a practical and efficient approach to GWL prediction that could aid policymakers in implementing long-term GWR management.