Global Ionospheric Total Electron Content Research Articles

Prediction of global ionospheric TEC using attention based bidirectional long short-term memory and gated recurrent unit

An accurate prediction of ionospheric total electron content (TEC) at the primary stage is essential for applications related to global navigation satellite systems (GNSS) under varying weather conditions. The previous TEC prediction schemes contribute for each time step that increases the prediction time. The eye contact phenomenon establishes a metaphorical connection which intends to capture and emphasize the attention worthy elements in a sequence. This research introduces a deep learning approach which is a combination of attention-based bidirectional long short-term memory and gated recurrent unit (Bi-LSTM GRU) to predict TEC in the ionosphere. Bidirectional LSTM is the better option for achieving durability when combined with a gated recurrent unit (GRU) to predict TEC in the ionosphere. The proposed approach is evaluated with the existing LSTM approach for root mean square error (RMSE) during training and validation. The RMSE while predicting the global ionospheric delay using the existing LSTM for 20 epochs is seen to be 0.004, whereas the existing approach achieves a training error of 0.003.

Operational Forecasting of Global Ionospheric TEC Maps 1-, 2-, and 3-Day in Advance by ConvLSTM Model

In this paper, we propose a global ionospheric total electron content (TEC) maps (GIM) prediction model based on deep learning methods that is both straightforward and practical, meeting the requirements of various applications. The proposed model utilizes an encoder-decoder structure with a Convolution Long Short-Term Memory (ConvLSTM) network and has a spatial resolution of 5° longitude and 2.5° latitude, with a time resolution of 1 h. We utilized the Center for Orbit Determination in Europe (CODE) GIM dataset for 18 years from 2002 to 2019, without requiring any other external input parameters, to train the ConvLSTM models for forecasting GIM 1, 2, and 3 days in advance. Using the CODE GIM data from 1 January 2020 to 31 December 2023 as the test dataset, the performance evaluation results show that the average root mean square errors (RMSE) for 1, 2 and 3 days of forecasts are 2.81 TECU, 3.16 TECU, and 3.41 TECU, respectively. These results show improved performance compared to the IRI-Plas model and CODE’s 1-day forecast product c1pg, and comparable to CODE’s 2-day forecast c2pg. The model’s predictions get worse as the intensity of the storm increases, and the prediction error of the model increases with the lead time.

Different data-driven prediction of global ionospheric TEC using deep learning methods

Ionospheric Total Electron Content (TEC) is a crucial parameter for monitoring the ionosphere and space weather disasters. Its accurate prediction is vital for precise applications of Interferometric Synthetic Aperture Radar (InSAR) and Global Navigation Satellite System (GNSS). This study proposes a novel method for ionospheric TEC prediction that considers multiple TEC-related factors. We present the random forest method and the Autoformer deep learning with multilayer perceptron (Autoformer-MLP) to predict the global TEC by incorporating the geomagnetic and solar activity parameters. Two schemes with different ionospheric data, i.e., spherical harmonic coefficients (SHC) and vertical TEC (VTEC), are performed by Autoformer-MLP. Ionospheric products from 2009 to 2019 (Cycle 24), obtained from the Center for Orbit Determination in Europe (CODE), are collected to test and evaluate the proposed method. Experimental results demonstrate that the root mean square errors (RMSEs) of predicted global ionospheric maps (GIMs) using the SHC scheme are 3.79 and 1.39 TECU in 2015 and 2019, respectively, and those are 3.55 and 1.28 TECU for the VTEC scheme. Moreover, the RMSEs of the prediction results are 0.5 and 0.2 TECU lower than that of CODE's 1-day predicted global ionospheric map (GIM) product (C1PG) during high and low solar activity years, respectively. These analyses indicate that the proposed random forest and Autoformer-MLP deep learning methods exhibit high accuracy and stability for data-driven prediction of global ionospheric TEC in various scenarios.

Prediction of Global Ionospheric Total Electron Content (TEC) Based on SAM‐ConvLSTM Model

AbstractThis paper first applies a prediction model based on self‐attention memory ConvLSTM (SAM‐ConvLSTM) to predict the global ionospheric total electron content (TEC) maps with up to 1 day of lead time. We choose the global ionospheric TEC maps released by the Center for Orbit Determination in Europe (CODE) as the training data set covering the period from 1999 to 2022. Besides that, we put several space environment data as additional multivariate‐features into the framework of the prediction model to enhance its forecasting ability. In order to confirm the efficiency of the proposed model, the other two prediction models based on convolutional long short‐term memory (LSTM) are used for comparison. The three models are trained and evaluated on the same data set. Results show that the proposed SAM‐ConvLSTM prediction model performs more accurately than the other two models, and more stably under space weather events. In order to assess the generalization capabilities of the proposed model amidst severe space weather occurrences, we selected the period of 22–25 April 2023, characterized by a potent geomagnetic storm, for experimental validation. Subsequently, we employed the 1‐day predicted global TEC products from the Center for Operational Products and Services (COPG) and the SAM‐ConvLSTM model to evaluate their respective forecasting prowess. The results show that the SAM‐ConvLSTM prediction model achieves lower prediction error. In one word, the ionospheric TEC prediction model proposed in this paper can establish the ionosphere TEC of spatio‐temporal data association for a long time, and realize high precision of prediction performance.

Analysis of Ionospheric Anomalies before the Tonga Volcanic Eruption on 15 January 2022

In this paper, GNSS stations’ observational data, global ionospheric maps (GIM) and the electron density of FORMOSAT-7/COSMIC-2 occultation are used to study ionospheric anomalies before the submarine volcanic eruption of Hunga Tonga–Hunga Ha’apai on 15 January 2022. (i) We detect the negative total electron content (TEC) anomalies by three GNSS stations on 5 January before the volcanic eruption after excluding the influence of solar and geomagnetic disturbances and lower atmospheric forcing. The GIMs also detect the negative anomaly in the global ionospheric TEC only near the epicenter of the eruption on 5 January, with a maximum outlier exceeding 6 TECU. (ii) From 1 to 3 January (local time), the equatorial ionization anomaly (EIA) peak shifts significantly towards the Antarctic from afternoon to night. The equatorial ionization anomaly double peak decreases from 4 January, and the EIA double peak disappears and merges into a single peak on 7 January. Meanwhile, the diurnal maxima of TEC at TONG station decrease by nearly 10 TECU and only one diurnal maximum occurred on 4 January (i.e., 5 January of UT), but the significant ionospheric diurnal double-maxima (DDM) are observed on other dates. (iii) We find a maximum value exceeding NmF2 at an altitude of 100~130 km above the volcanic eruption on 5 January (i.e., a sporadic E layer), with an electron density of 7.5 × 105 el/cm3.

Regional ionospheric TEC modeling during geomagnetic storm in August 2021- data fusion using multi-instrument observations

Regional ionospheric Total Electron Content (TEC) models are most significant to investigate the variability of ionosphere during all-weather conditions. Since the ground-based TEC measurements are not available in oceanic and polar regions, space-based observations are incorporated to increase the positional accuracy and reliability of Global Ionospheric TEC Maps (GIMs). Therefore, data fusion techniques are necessary to enhance the prediction capability of regional ionospheric models by considering multi-source data. In view of this, an attempt is made to investigate Equatorial Ionization Anomaly (EIA) structures in low-latitudinal Indian region using multi-instrument data. Data observations from background model CODEGIM, available International GNSS Service (IGS) stations in India, GNSS receivers at KLEF and Tripura stations, FORMOSAT/COSMIC radio occultation and SWARM during geomagnetic storm period August 26–28, 2021 are used for the study. Spherical Harmonics Function (SHF) of order 4 is employed along with Weighted Least Squares analysis (WLS), where separate weight constraint is computed for each data source. TEC maps of spatial resolution 5° x 5° and temporal resolution of 1 h are generated to illustrate the dynamic behavior of ionosphere. The standard deviation for 3 days is obtained as 0.42, 0.61 and 1.43 TECU respectively. TEC depletions and enhancements are observed on August 27 and 28, with mean values of 12.74 and 15.27 TECU respectively, demonstrating negative and positive storm effects.

Predicting global ionospheric TEC maps using Gaussian process regression

The integration of machine learning technology into ionospheric prediction has emerged as a burgeoning field of research. However, several challenges still exist, such as the disregard of delays in real-world data acquisition, variations in accuracy due to different input data and methods. In this study, we present an ionospheric Gaussian process regression (GPR) model with multiple input parameters to forecast global ionospheric total electron content (TEC). We assess two solutions based on GPR model that leverage different ionospheric data, namely the vertical TEC (VTEC) and spherical harmonic coefficients (SHC) prediction solutions. Our findings demonstrate that both GPR models exhibit strong accuracy and stability. Specifically, for 1-day-ahead-predicted global ionospheric maps (GIMs) in 2015 year and 2019 year, the root mean square error (RMSE) of the SHC prediction solution is 4.343 TECU and 1.702 TECU, respectively, while the VTEC prediction solution has RMSE values of 4.321 TECU and 1.673 TECU. Moreover, in high and low solar activity, over 29% and 68% of the absolute residuals are within 1.0 TECU, respectively. Furthermore, we compare the GPR model with conventional methods (such as Adaptive Autoregressive Model (AAR)) and observe that the RMSE of the GPR model is lower than that of the AAR model for GIMs predicted under different solar and geomagnetic activities, with a difference ranging from 0.2 to 0.4 TECU. In addition, the GPR model can provide prediction intervals for the predicted values. These intervals are typically represented using the mean and standard deviation, where the mean represents the predicted value and the standard deviation represents the uncertainty associated with the prediction. Prediction intervals can assist users in understanding the uncertainty of the model's predictions.

Near real-time global ionospheric total electron content modeling and nowcasting based on GNSS observations

For the purposes of routinely providing reliable and low-latency Global Ionosphere Maps (GIMs), a method of estimating hourly updated near real-time GIM with a time latency of about 1–2 h based on a 24-h data sliding window of Global Navigation Satellite System (GNSS) near real-time observations and real-time data streams was presented. On the basis of the implementation of near real-time GIM estimation, an hourly updated GIM nowcasting method was further proposed to improve the accurate of short-term total electron content (TEC) prediction. We estimated the Shanghai Astronomical Observatory near real-time GIM (SHUG) and nowcasting GIM (SHPG) in the solar relatively active year (2014) and quiet year (2021), and employed GIMs provided by the International GNSS Service, the Global Positioning System (GPS) differential slant TECs (dSTECs) extracted from global independent GNSS stations, and the vertical TECs (VTECs) inverted from satellite altimetry as the references to validate the estimated results. The GPS dSTECs evaluation results show that SHUG behaves fairly consistent with the rapid GIMs, with a discrepancy of less than 1 TEC unit (TECu) overall. The standard deviations (STDs) of SHUG with respect to Jason-2/-3 VTECs are no more than 10% over the majority of rapid GIMs due to the instability of observations. The performance of 1-h nowcasting SHPG is significantlybetter than the Center for Orbit Determination in Europe (CODE) 1-day predicted GIM (C1PG). GPS dSTEC validation results indicate that 1-h nowcasting SHPG is 1 to 2 TECu more reliable than C1PG in eventful ionospheric electron activity regions, and it outperforms the C1PG by 10% overall versus Jason-2/-3 VTECs. The hourly updated SHUG and SHPG have relatively high reliability and low time latency, and thus can provide excellent service for (near) real-time users and offer more accurate TEC background information than daily predicted GIM for real-time GIM estimation.

Global Ionospheric TEC Forecasting for Geomagnetic Storm Time Using a Deep Learning‐Based Multi‐Model Ensemble Method

AbstractIn recent years, deep learning has been extensively used for ionospheric total electron content (TEC) prediction, and many models can yield promising prediction results, particularly under quiet conditions. Owing to the ionosphere's intricate and dramatic changes during geomagnetic storms, the high‐reliable prediction of the storm‐time ionospheric TEC remains a challenging problem. In this study, we developed a new deep learning‐based multi‐model ensemble method (DLMEM) to forecast geomagnetic storm‐time ionospheric TEC that combines the Random Forest (RF) model, the Extreme Gradient Boosting (XGBoost) algorithm, and the Gated Recurrent Unit (GRU) network with the attention mechanism. Seven features in 170 geomagnetic storm events, including the three components Bx, By and Bz of interplanetary magnetic field (IMF), the Kp and Dst indices of geomagnetic activity data, the F10.7 index of solar activity data and global TEC data, were used for modeling. The test set results showed that the DLMEM model can reduce the root mean square errors (RMSE) by an average of 43.6% in comparison to our previously presented model Ion‐LSTM, especially during the recovery period of geomagnetic storms. Furthermore, compared to Ion‐LSTM, the RMSE values of the low‐, middle‐ and high‐latitude single‐station forecast TEC can be greatly decreased by 33%, 53% and 59%, respectively. It was shown that the new model allows for more precise short‐term global ionospheric forecasting during geomagnetic storms, enabling real‐time monitoring of ionospheric changes.

Global TEC Map Fusion Through a Hybrid Deep Learning Model: RFGAN

AbstractTimely, reliable and comprehensive global observation information is essential for space weather research. However, limited observation technology hinders the consecutive global coverage of observation data. For the integrity and continuity of the global observation data, deep learning can obtain a global Ionospheric total electron content (TEC) map by fusing multi‐source TEC maps. Different from the previous methods, in the study, a deep learning hybrid model (RFGAN) based on Dual‐Discriminator Conditional Generative Adversarial Network (DDcGAN) and Free‐Form Image Inpainting with Gated Convolution (Deepfill v2) is proposed to fuse the Massachusetts Institute of Technology (MIT)—TEC, International Global Navigation Satellite System TEC (IGS‐TEC) and altimetry satellite TEC. Throughout the RFGAN structure, we use an autoencoder model with gated convolution to inpaint the missing parts of MIT‐TEC and altimetry satellite TEC. Meanwhile, DDcGAN fuses the inpainted MIT‐TEC (MIT'‐TEC) and IGS‐TEC to get a global TEC map with high accuracy. To a certain extent, we inpainted the ocean area of MIT‐TEC through RFGAN. At the same time, RFGAN keeps the consistency of RFGAN‐TEC and MIT‐TEC in the continent area. Our proposed deep learning hybrid model can be easily extended and widely applied to other fields of space science, especially in addressing observational data loss and multi‐source data fusion.

Global Ionospheric Total Electron Content Completion with a GAN-Based Deep Learning Framework

The ionosphere serves as a critical medium for radio signal propagation in outer space. A good morphology of the global TEC distribution is very useful for both ionospheric studies and their relative applications. In this work, a deep learning framework was constructed for better spatial estimation in ionospheric TEC. Both the DCGAN and WGAN-GP were considered, and their performances were evaluated with spatial completion for a regional TEC. The performances were evaluated using the correlation coefficient, RMSE, and MAE. Moreover, the IAAC rapid products were used to make comparisons. The results show that both the DCGAN and WGAN-GP outperformed the IAAC CORG rapid products. The spatial TEC estimation clearly goes well with the solar activity trend. The RMSE differences had a maximum of 0.5035 TECu between the results of 2009 and 2014 for the DCGAN and a maximum of 0.9096 TECu between the results of 2009 and 2014 for the WGAN-GP. Similarly, the MAE differences had a maximum of 0.2606 TECu between the results of 2009 and 2014 for DCGAN and a maximum of 0.3683 TECu between the results of 2009 and 2014 for WGAN-GP. The performances of the CORG, DCGAN, and WGAN-GP were also verified for two selected strong geomagnetic storms in 2014 and 2017. The maximum RMSEs were 1.8354 TECu and 2.2437 TECu for the DCGAN and WGAN-GP in the geomagnetic storm on 18 February 2014, respectively, and the maximum RMSEs were 1.3282 TECu and 1.4814 TECu in the geomagnetic storm on 7 September 2017. The GAN-based framework can extract the detailed features of spatial TEC daily morphologies and the responses during geomagnetic storms.

ML Prediction of Global Ionospheric TEC Maps

AbstractThis paper applies the convolutional long short‐term memory (convLSTM)‐based machine learning models to forecast global ionospheric total electron content (TEC) maps with up to 24 hr of lead time at a 1‐hr interval. Four convLSTM‐based models were investigated, and the one that implements the L1 loss function and the residual prediction strategy demonstrates the best performance. The convLSTM models are trained and evaluated using Center for Orbit Determination in Europe (CODE) global TEC maps over a period of nearly seven years from 19 October 2014 to 21 July 2021. Results show that the best convLSTM model outperforms the 1‐day predicted global TEC products released by CODE analysis center (c1pg) and persistence models under various levels of solar and geomagnetic activities, except for a lead time beyond 8 hr during the storm time where the c1pg has slightly better performance. The convLSTM forecasting performance degrades as the lead time increases.

ED‐ConvLSTM: A Novel Global Ionospheric Total Electron Content Medium‐Term Forecast Model

AbstractIn this paper, we proposed an innovative encoder‐decoder structure with a convolution long short‐term memory (ED‐ConvLSTM) network to forecast global total electron content (TEC) based on the International GNSS Service (IGS) TEC maps from 2005 to 2018 with 1‐hr time cadence. The ED‐ConvLSTM model is used to forecast TEC maps 1–7 days in advance through iterations. To investigate the model's performance, we compared the model with International Reference Ionosphere (IRI2016) model in 2014 and 2018, and compared the model with 1‐day Beijing University of Aeronautics and Astronautics (BUAA) model in 2018. The results show that our 7‐day ED‐ConvLSTM model (ED‐ConvLSTM model that forecasts 7 days in advance) outperforms IRI2016 in 2014 and 2018, and our 5‐day ED‐ConvLSTM model (ED‐ConvLSTM model that forecasts 5 days in advance) outperforms 1‐day BUAA model. Furthermore, the root mean square error (RMSE) from the 1‐day ED‐ConvLSTM model with respect to the IGS TEC maps decreases by 51.5% and 43%, respectively, in 2014 and 2018 compared with that from IRI2016 model. The RMSE from the 1‐day ED‐ConvLSTM model is 20.3% lower than that from the 1‐day BUAA model in 2018. In addition, our model has the highest RMSE in the Equatorial Ionospheric Anomaly (EIA) region, but can roughly predict the features and locations of EIA. However, the model fails to forecast localized TEC enhancement and the sudden ionospheric response to the geomagnetic storms. Overall, the model shows competitive performance in medium‐term global TEC maps prediction during geomagnetic quiet periods.

Correlation Analysis of Global Ionospheric Total Electron Content Maps in March 2015

Correlation Analysis of Global Ionospheric Total Electron Content Maps in March 2015

Deep Learning for Global Ionospheric TEC Forecasting: Different Approaches and Validation

AbstractThe application of deep learning technology to ionospheric prediction has become a new research hotspot. However, there are still some gaps, such as the prediction effect with different input solar and geomagnetic activity parameters, and the forecast accuracy with different prediction methods as well as the validation of long period data results, to be filled. We developed an ionospheric long short‐term memory network (Ion‐LSTM) with multiple input parameters to predict the global ionospheric total electron content (TEC). Two solutions with different ionospheric data based on Ion‐LSTM were assessed, namely spherical harmonic coefficients (SHC) and vertical TEC (VTEC) prediction solution. The results show two solutions, both perform well in accuracy and stability. The input of the geomagnetic activity index improves the prediction effect of the model in the storm period. For the 1‐ and 2‐day‐predicted global ionospheric maps (GIMs) from 2015 to 2020, the root mean square error (RMSE) of SHC prediction solution is 1.69 TECU and 1.84 TECU while that of the VTEC prediction solution is 1.70 TECU and 1.84 TECU, respectively. Over 70% of the absolute residuals are within 3 TECU in high solar activity and over 96% in low solar activity. Further, by comparing the predicted results between Ion‐LSTM and conventional methods (e.g., Center for Orbit Determination in Europe (CODE) predicted GIMs), the evaluation results show that the RMSE of Ion‐LSTM is 0.7 TECU lower than that of CODE predicted GIMs under different solar and geomagnetic activities. Additionally, the accuracy of the Ion‐LSTM prediction results decreases slightly as the input time span increases.

A Spatiotemporal Network Model for Global Ionospheric TEC Forecasting

In the Global Navigation Satellite System, ionospheric delay is a significant source of error. The magnitude of the ionosphere total electron content (TEC) directly impacts the magnitude of the ionospheric delay. Correcting the ionospheric delay and improving the accuracy of satellite navigation positioning can both benefit from the accurate modeling and forecasting of ionospheric TEC. The majority of current ionospheric TEC forecasting research only considers the temporal or spatial dimensions, ignoring the ionospheric TEC’s spatial and temporal autocorrelation. Therefore, we constructed a spatiotemporal network model with two modules: (i) global spatiotemporal characteristics extraction via forwarding spatiotemporal characteristics transfer and (ii) regional spatiotemporal characteristics correction via reverse spatiotemporal characteristics transfer. This model can realize the complementarity of TEC global spatiotemporal characteristics and regional spatiotemporal characteristics. It also ensures that the global spatiotemporal characteristics of the global ionospheric TEC are transferred to each other in both temporal and spatial domains at the same time. The spatiotemporal network model thus achieves a spatiotemporal prediction of global ionospheric TEC. The Huber loss function is also used to suppress the gross error and noise in the ionospheric TEC data to improve the forecasting accuracy of global ionospheric TEC. We compare the results of the spatiotemporal network model with the Center for Orbit Determination in Europe (CODE), the convolutional Long Short-Term Memory (convLSTM) model and the Predictive Recurrent Neural Network (PredRNN) model for one-day forecasts of global ionospheric TEC under different conditions of time and solar activity, respectively. With internal data validation, the average root mean square error (RMSE) of our proposed algorithm increased by 21.19, 15.75, and 9.67%, respectively, during the maximum solar activity period. During the minimum solar activity period, the RMSE improved by 38.69, 38.02, and 13.54%, respectively. This algorithm can effectively be applied to ionospheric delay error correction and can improve the accuracy of satellite navigation and positioning.

Prediction of Global Ionospheric TEC Based on Deep Learning

AbstractThe accurate prediction of ionospheric Total Electron Content (TEC) is important for global navigation satellite systems (GNSS), satellite communications and other space communications applications. In this study, a prediction model of global IGS‐TEC maps are established based on testing several different long short‐term memory (LSTM) network (LSTM)‐based algorithms to explore a direction that can effectively alleviate the increasing error with prediction time. We find that a Multi‐step auxiliary algorithm based prediction model performs best. It can effectively predict the global ionospheric IGS‐TEC in the next 6 days (the mean absolute deviation (MAD) and root mean square error (RMSE) are 2.485 and 3.511 TECU, respectively) compared to the IRI (the MAD and RMSE are 4.248 and 5.593 TECU). The analyses of four geomagnetic storm events are completely separate from the time range of the training set, so as to further validate the performance of the model. The International Reference Ionosphere model is used as a reference for the performance of our predictive model, and a rotated persistence is estimated by time‐shift algorithm of IGS‐TEC. The result suggests that the Multi‐step auxiliary prediction model has a good generalization performance and can have a relatively good stability and low error during a geomagnetic storm and quiet time.

An Approach for Predicting Global Ionospheric TEC Using Machine Learning

Accurate corrections for ionospheric total electron content (TEC) and early warning information are crucial for global navigation satellite system (GNSS) applications under the influence of space weather. In this study, we propose to use a new machine learning model—the Prophet model, to predict the global ionospheric TEC by establishing a short-term ionospheric prediction model. We use 15th-order spherical harmonic coefficients provided by the Center for Orbit Determination in Europe (CODE) as the training data set. Historical spherical harmonic coefficient data from 7 days, 15 days, and 30 days are used as the training set to model and predict 256 spherical harmonic coefficients. We use the predicted coefficients to generate a global ionospheric TEC forecast map based on the spherical harmonic function model and select a year with low solar activity (63.4 < F10.7 < 81.8) and a year with the high solar activity (79.5 < F10.7 < 255.0) to carry out a sliding 2-day forecast experiment. Meanwhile, we verify the model performance by comparing the forecasting results with the CODE forecast product (COPG) and final product (CODG). The results show that we obtain the best predictions by using 15 days of historical data as the training set. Compared with the results of CODE’S 1-Day (C1PG) and CODE’S 2-Day (C2PG). The number of days with RMSE better than COPG on the first and second day of the low-solar-activity year is 151 and 158 days, respectively. This statistic for high-solar-activity year is 183 days and 135 days.

Statistical analysis of large and extreme global ionospheric total electron content

Ionospheric disturbances, due to photoionization and energetic particle precipitation, occurring both on a regular recurring basis, and heightened due to space weather, impact global positioning, navigation, and timing services provided by Global Navigation Satellite Systems (GNSS). The development of operational services to mitigate the risks to users requires knowledge of how space weather impacts critical systems, and the frequency and magnitude of ionospheric disturbances including extreme events. Analysis of the largest values of total electron content (TEC) is important for the assessment of space weather hazards for systems sensitive to ionospheric effects on radio wave propagation and for the development of risk mitigation strategies. In this study, twenty years of global TEC maps are analyzed to determine the global distribution of the daily maximum TEC. Maximum TEC is shown to reach magnitudes of about 200 TECU in extreme cases, with the largest TEC normally observed at equatorial latitudes. A generalized extreme value distribution has been applied to the daily global maximum TEC and for the high (60°–90°; −90° to −60°), mid (30°–60°; −60° to −30°), and low-latitude (0°–30°; −30°–0°) regions in geographic latitudes to determine the 1-in-44 year (4 solar cycles) and 1-in-100 year maximum TEC with a 95% confidence interval. Additionally, the return period for TEC thresholds defined for safe operation by the International Civil Aviation Organization are discussed. Extreme values provide criteria for the development of operational systems and vulnerability assessment of critical systems dependant on GNSS.

Near Real-Time Global Ionospheric Modeling Based on an Adaptive Kalman Filter State Error Covariance Matrix Determination Method

Aiming at the urgent demands on (near) real-time ionosphere products, we study the near real-time (NRT) modeling of the global ionospheric total electron content (TEC) by IGS hourly data and introduce the Kalman filter (KF) to solve the model parameters. The main objective of this article is to propose an adaptive method for determining the KF process noise covariance matrix. This method can reflect the change regularity of spherical harmonic (SH) between epochs and consider the impact of the current ionosphere level on SH. It can adaptively adjust the KF process noise covariance matrix of each epoch to improve the accuracy of NRT global ionosphere maps (GIMs). We analyze the effects of different initial values of the state vector and its covariance matrix on the SH coefficients and propose a method to avoid repeated filter initialization. The results show that for different initial values, the filter can reach the state of convergence within 6 h, but a high-precision initial value can significantly accelerate the KF convergence speed. Compared with Global Navigation Satellite System (GNSS) differential slant TEC (dSTEC) observables, the rms of our NRT products xrtg during quiet and magnetic storms are 1.47 and 1.56 TECU, respectively, larger than the postprocessed GIMs, but significantly smaller than those of real-time GIMs. Compared with Jason VTEC, the results also show that the accuracy of xrtg is even better than European Space Agency (ESA) final products during the magnetic storm.