For a long time, the equivalent ionospheric slab thickness τ has remained in the shadow of ionospheric main parameters: the maximum density, NmF2 (or the critical frequency, foF2), and the total electron content. Empirical global models have been developed for these two parameters. Recently, several global models of τ have appeared concurrently. This paper compares τ of the Neustrelitz equivalent slab thickness model (NSTM), with τ(IRI-Plas) of the IRI-Plas model, and τ(Appr) of the approximation model, constructed along the 30° E meridian using data from several ionosondes. The choice of the model of the best conformity with observational data was made, which was used to study the effects of space weather during several magnetic storms in March 2012. The effects included: (1) a transition from negative disturbances at high latitudes to positive ones at low latitudes, (2) the super-fountain effect, which had been revealed and explained in previous papers, (3) a deepening of the main ionospheric trough. The efficiency of using τ(Appr) and τ(IRI-Plas) models for studying the effects of space weather has been confirmed. The advantage of the τ(Appr) model is its closeness to real data. The advantage of the τ(IRI-Plas) model is the ability to determine foF2 without ionosondes. The efficiency of the NSTM model is insufficient for a role of a global τ model due to the accuracy decreasing with the increasing latitude.
Machine learning can play a significant role in bringing new insights in GNSS remote sensing for ionosphere monitoring and modeling to service. In this paper, a set of multilayer architectures of neural networks is proposed and considered, including both neural networks based on LSTM and GRU, and temporal convolutional networks. The set of methods included 10 architectures: TCN, modified LSTM-/GRU-based deep networks, including bidirectional ones, and BiTCN. The comparison of TEC forecasting accuracy is performed between individual architectures, as well as their bidirectional modifications, by means of MAE, MAPE, and RMSE estimates. The F10.7, 10 Kp, Np, Vsw, and Dst indices are used as predictors. The results are presented for the reference station Juliusruh, three stations along the meridian 30°E (Murmansk, Moscow, and Nicosia), and three years of different levels of solar activity (2015, 2020, and 2022). The MAE and RMSE values depend on the station latitude, following the solar activity. The conventional LSTM and GRU networks with the proposed modifications and the TCN provide results at the same level of accuracy. The use of bidirectional neural networks significantly improves forecast accuracy for all the architectures and all stations. The best results are provided by the BiTCN architecture, with MAE values less than 0.3 TECU, RMSE less than 0.6 TECU, and MAPE less than 5%.
The equivalent slab thickness τ of the ionosphere links two of its parameters: the critical frequency foF2 and the total electron content TEC and, as a consequence, allows the determination of foF2 using TEC. Interest in the parameter τ has recently increased, as evidenced by a publication in Space Science Reviews 2022, 218:37, 1-65, which provides a historical overview of τ research, presents features of τ behavior in different regions of the globe under different solar activity conditions, and indicates directions for further research. This led to the following objectives for this paper: (1) estimating the correlation coefficient between foF2 and TEC, (2) testing a unique global model τ(NSTM) - the Neustrelitz equivalent Slab Thickness Model, (3) estimating the relation between τ and the Dst index. Using data from 78 stations divided into several longitude zones, it is shown for April 2022: (1) a high correlation between foF2 and TEC on a global scale is confirmed, but there is a large dependence on data quality, (2) each longitude zone has stations for which τ(NSTM) gives good agreement with experimental values and can be used in applications, (3) the correlation coefficient ρ(τ-Dst) is found to depend on longitude, which may have a physical nature.
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