Forecasting of ROTI index in polar regions using BWO-VMD-LSTM hybrid model

The Rate of TEC Index (ROTI), a crucial indicator of fluctuations in the ionospheric Total Electron Content (TEC), has long served as an effective proxy for characterizing ionospheric activity. However, ROTI sequences exhibit significant nonstationary and nonlinear characteristics, which intensify during substorms, making high-accuracy prediction challenging for traditional models. To address these complications, we propose a hybrid forecasting model, named BWO-VMD-LSTM, that integrates the Beluga Whale Optimization (BWO) algorithm, Variational Mode Decomposition (VMD), and Long Short-Term Memory (LSTM) networks. Our methodology first employs BWO to adaptively optimize the key parameters of VMD, achieving an optimal decomposition configuration. The optimized VMD then decomposes the original non-stationary ROTI sequence into several relatively stable Intrinsic Mode Functions (IMFs). Subsequently, an LSTM model is constructed to independently forecast each IMF. Finally, the predictions of all components are reconstructed to produce the final ROTI forecast. Experimental results demonstrate that our model outperforms baseline models under various geomagnetic conditions (including quiet, normal, and substorm periods), showing significant improvements in key metrics such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE), thereby exhibiting superior prediction accuracy and stability. This study presents an effective and robust tool for high-precision ROTI forecasting, with promising potential for enhancing space weather monitoring and scintillation warning services.