A Machine Learning-Based Method for Modeling TEC Regional Temporal-Spatial Map

Abstract

In order to achieve the high-accuracy prediction of the total electron content (TEC) of the regional ionosphere for supporting the application of satellite navigation, positioning, measurement, and controlling, we proposed a modeling method based on machine learning (ML) and use this method to establish an empirical prediction model of TEC for parts of Europe. The model has three main characteristics: (1) The principal component analysis (PCA) is used to separate TEC’s temporal and spatial variation characteristics and to establish its corresponding map, (2) the solar activity parameters of the 12-month mean flux of the solar radio waves at 10.7 cm (F10.712) and the 12-month mean sunspot number (R12) are introduced into the temporal map as independent variables to reflect the temporal variation characteristics of TEC, and (3) The modified Kriging spatial interpolation method is used to achieve the spatial reconstruction of TEC. Finally, the regression learning method is used to determine the coefficients and harmonic numbers of the model by using the root mean square error (RMSE) and its relative value (RRMSE) as the evaluation standard. Specially, the modeling process is easy to understand, and the determined model parameters are interpretable. The statistical results show that the monthly mean values of TEC predicted by the proposed model in this paper are highly consistent with the observed values curve of TEC, and the RRMSE of the predicted results is 12.76%. Furthermore, comparing the proposed model with the IRI model, it can be found that the prediction accuracy of TEC by the proposed model is much higher than that of the IRI model either with CCIR or URSI coefficients, and the improvement is 38.63% and 35.79%, respectively.

A High Accuracy Spatial Reconstruction Method Based on Surface Theory for Regional Ionospheric TEC Prediction

“…Finally, the actual observed values of the training stations were used to predict the TEC of the validation station according to the weight coefficients determined before. Through cross‐validation of modeling stations, RRMSE was used as the evaluation standard to determine the optimal SF (Y. R. Liu et al., 2022). Therefore, SF is chosen as 1.15 in this paper.…”

Forecast of Ionospheric TEC Maps Using ConvGRU Deep Learning Over China

“…In recent years, more and more researches have used the deep learning method, which can reflect TEC variations well and has a better fitting effect on nonlinear data, to establish a TEC prediction model [9] - [23]. For global TEC forecasting, Lee et al [11] proposed a TEC forecast model based on generative adversarial network, and its forecast accuracy was higher than the 1-day forecast product released by CODE Center.…”

“…Sivakrishna et al [19] applied bidirectional LSTM algorithm to predict TEC data over Indian region, and illustrated that the potential of bi-LSTM in time series processing is enhanced by having both forward and backward connections. Liu et al [23] presented a machine learning method based on principal component analysis and leastsquare regression to predict TEC over Europe. The above studies have shown that the LSTM model perform well in forecasting ionospheric TEC.…”

A Hybrid Deep Learning‐Based Forecasting Model for the Peak Height of Ionospheric F2 Layer

“…The critical parameters of the F2 layer can be estimated using ionosondes (Yao et al., 2010). These parameters are widely used in satellite, navigation, and high‐frequency communication (e.g., Atac et al., 2009; Kouris et al., 2004; Y. R. Liu et al., 2022b; Moses et al., 2020; Panda et al., 2015; Wang et al., 2022, 2023). The peak height of the ionospheric F2 layer (hmF2) is an essential parameter in the ionospheric F2 layer, which is determined by the height of the ionospheric electron density peak.…”