A Prediction Method for M(3000)F2 in Mid-latitude Region Based on Statistical Machine Learning

The ionospheric F2 layer 3000 km propagation factor M(3000)F2 is a key parameter supporting frequency selection and system performance evaluation in High Frequency (HF) communication. Accurate M(3000)F2 prediction is critical for reliable communication but remains challenging. The uneven spatial distribution of ionospheric observation instruments and strong temporal variability of the ionosphere limit the performance of conventional prediction methods. To address this issue, a statistical machine learning (SML) model is developed to predict M(3000)F2. Harmonic decomposition is introduced to describe nonlinear and periodic variations of M(3000)F2 at different temporal scales. A stratified validation strategy is also employed to improve model robustness, ensuring that validation samples cover different solar activity levels. The paper analyzes data from nine mid-latitude ionospheric stations, spanning 1996 to 2024. Five solar activity indices are considered, including F10.7, sunspot number, Lyman-α, MgII, and extreme ultraviolet. Their predictive performance is examined both individually and in combination. The results indicate that the optimal model configuration uses Lyman-α, month, and universal time as input variables. Compared with the International Reference Ionosphere (IRI) model, the SML model achieves smaller prediction errors. The mean absolute error and root mean square error are reduced by 0.05 and 0.08, while the coefficient of determination increases by 0.39. These improvements correspond to 38.46%, 42.11%, and 48.15%, respectively. The proposed model maintains stable predictive performance under different solar activity phases, geographical locations, and seasonal conditions, suggesting its applicability to HF communication frequency management and space weather applications.