Ionospheric Total Electron Content Model Research Articles

Constructing a Regional Ionospheric TEC Model in China with Empirical Orthogonal Function and Dense GNSS Observation

Using Global Navigation Satellite Systems (GNSS) observation data for developing a high-precision ionospheric Total Electron Content (TEC) model is one of the essential subjects in ionospheric physics research and the application of satellite navigation correction. In this study, we integrate the Empirical Orthogonal Function (EOF) method with the TEC data provided by the Center for Orbit Determination in Europe (CODE), and observed by the dense GNSS receivers operated by the Crustal Movement Observation Network of China (CMONOC) to construct a regional ionospheric TEC model over China. The EOF analysis of CODE TEC in China from 1998 to 2010 shows that the first-order EOF component accounts for 90.3813% of the total variation of the ionospheric TEC in China. Meanwhile, the average value of CODE TEC is consistent with the spatial and temporal distribution characteristics of the first-order EOF base function, which mainly reflects the latitude and diurnal variations of TEC in China. The first-order coefficient after EOF decomposition shows an obvious 11-year period and semi-annual variations. The maximum amplitude of semi-annual variation mainly appears in March and October, which is closely associated with the variation in geographical longitude, the semi-annual change of the low-latitude electric field, and the ionospheric fountain effect. The second-order coefficient has an evident annual variation, the minimum amplitude mainly occurs in March, August, and September, and the amplitude values in the high solar activity years are more significant than those in the low solar activity years. The third-order coefficient mainly shows the characteristics of annual variation, and the fourth-order coefficient shows the noticeable semi-annual and annual variations. The third and fourth-order coefficients are both modulated by the solar activity index F10.7. The ionospheric TEC model in China, driven by CMONOC real-time GNSS observation data, can better reflect the latitude, local time and seasonal variation characteristics of ionospheric TEC over China. In particular, it can clearly show the spring and autumn asymmetry of ionospheric TEC in the low latitudes. The root mean square error of the absolute error between the model and the actual observation is mainly distributed around 2.45 TECU (1 TECU = 1016 electrons/m2). The values of the TEC model constructed in this study are closer to the actual observed values than those of the CODE TEC in China.

An Ionospheric Total Electron Content Model with a Storm Option over Japan Based on a Multi-Layer Perceptron Neural Network

Ionospheric delay has a severe effect on reducing the accuracy of positioning and navigation of single-frequency receivers. Therefore, it is necessary to construct a precise regional ionospheric model for real-time Global Navigation Satellite System (GNSS) applications. The total electron contents (TECs) of 839 GNSS stations affiliated with the GPS Earth Observation Network were used to build a Japanese ionospheric model (JIM) based on a multi-layer perceptron neural network. During quiet space conditions, the correlation coefficient between the targets and the predictions of the JIM was about 0.98, and the root-mean square error (RMSE) of TEC residuals was ~1.5TECU, while under severe space events, the correlation coefficient increased to 0.99, and the corresponding RMSE dropped to 0.96 TECU. Moreover, the JIM model successfully reconstructed the two-dimensional (time vs latitude) TEC maps, and the TEC maps had evident hourly and seasonal variations. Most of TEC residuals accumulated between universal time 01–06 with an averaged magnitude of 1-2TECU. Furthermore, the JIM model had a perfect prediction performance under various kinds of complex space environments. In the quiet days, the prediction accuracy of the JIM was nearly equal to the global ionosphere map (GIM), and in some moments, the JIM was more competitive than the GIM. In the disturbed days, the RMSEs of TEC residuals were proportional to the solar wind speed and were inversely proportional to the geomagnetic Dst value. The maximum RMSE of the JIM was lower than 2TECU, while the corresponding RMSEs for the IRI and TIE-GCM exceeded 5TECU.

An Investigation of Ionospheric TEC Prediction Maps Over China Using Bidirectional Long Short‐Term Memory Method

AbstractThe ionospheric total electron content (TEC) is an important ionospheric parameter, and it is widely utilized in research such as space weather prediction and precise positioning. However, it is still challenging to develop an ionospheric TEC prediction model with high accuracy. In this study, a new ionospheric TEC model over China was developed using the bidirectional long short‐term memory (bi‐LSTM) method and observations from 257 ground‐based global navigation satellite system (GNSS) stations in the Crustal Movement Observation Network of China from January 2018 to December 2021. The root mean square errors of the bi‐LSTM‐based model’s 1 and 2 hr ahead predictions on the test data set (from June 2021 to December 2021) are 1.12 and 1.68 TECU, respectively, which are 75/50/32% and 72/48/22% smaller than those of the IRI‐2016, artificial neural network and LSTM‐based models, correspondingly. The bi‐LSTM‐based model shows the best performance, which is most likely due to the fact that the sequence information in both forward and backward directions is taken into consideration in the new model. In addition, the diurnal variation, seasonal variation of the ionospheric TEC, and variations under geomagnetic storm conditions are successfully captured by the bi‐LSTM‐based model. Moreover, the TEC maps resulting from the bi‐LSTM model agree well with those obtained from the final ionospheric product from the Chinese Academy of Sciences. Hence, the new model can be a good choice for the investigation of the spatiotemporal variation trend in the ionosphere and GNSS navigation.

Correction to: GIMLi: Global Ionospheric total electron content model based on machine learning

In the original article published, the references Wang et al. 2016a and Wang et al. 2016b are incorrect.

GIMLi: Global Ionospheric total electron content model based on machine learning

EXtreme Gradient Boosting over Decision Trees (XGBoost or XGBDT) is a powerful tool to model a wide range of processes. We propose a new approach to create a global total electron content model, using machine-learning-based techniques, in particular, gradient boosting. The model is based on the Global Ionospheric Maps computed by Universitat Politecnica de Catalunya with a tomographic-kriging combined technique (UQRG). To reduce the problem complexity, we used empirical orthogonal functions (EOFs). The created model involves the first 16 spatial EOFs. For training and validation we used the 1998–2016 data sets, and the 2017 data as a test data set. To drive the model, we used the following features: (1) geomagnetic activity indexes (Kp, Ap, AE, AU, AL) and solar activity indexes (R, F10.7); (2) derivative values from these indexes such as the mean value and standard deviations within the last 12 h, last 11 days, and last 40 days; (3) day of the year (DOY); (4) averaged EOFs for given Kp and UT, and those for a given DOY and UT. The validation data set revealed the following hyperparameters for XGBoost learning: number of trees is 100, tree depth is 6, and learning rate is 0.1. Comparisons with the NeQuick2, Klobuchar, and GEMTEC models show that machine learning achieves higher accuracy for the 2017 test data set. The global averaged root-mean-square errors and mean absolute percentage errors were about 2.5 TECU and 19% for the nonlinear GIMLi-XGBDT model, about 4 TECU and 30–40% for NeQuick2, GEMTEC, and the linear model GIMLi-LM, and about 5.2 TECU and 73% for the Klobuchar model. A 4-fully-connected-layer artificial neural network provided a higher error (3.28 TECU and 27.7%) as compared to GIMLi-XGBDT. For all models mentioned, the error peaked in the equatorial anomaly region. The solar activity increase does not affect the error of the nonlinear GIMLi-XGBDT model. However, an increase in geomagnetic activity strongly affects that model.

Least‐squares collocation modelling of regional ionospheric TEC for accelerating real‐time single‐frequency PPP convergence

Modelling of the regional ionospheric total electron content (TEC) is an important means for mitigating the ionospheric delay errors in the single-frequency (SF) precise point positioning (PPP). Mostly, the existing regional ionospheric models (RIM) only takes the trend term of the ionospheric TEC variations into account and neglect their random variable part. As a result, the TEC's irregular variations cannot be well modelled. In this study, a regional ionospheric TEC model based on the least-squares collocation (LSC) approach is proposed to account for both the trend and random parts. The predicted TEC from the LSC RIM is then employed in the real-time (RT) SF PPP for speeding up convergence. Datasets collected in two different latitude regions are utilised to establish the LSC RIM with a comparison to the conventional polynomial model and the global ionosphere map (GIM)-predicted products. The results show that the LSC model can remove ionospheric delay errors of at least 92%, which is larger than the polynomial model and GIM products. Further, the GPS RT SF PPP after introducing the predicted TEC from the LSC RIM can significantly reduce the convergence time by at least 48%, 58%, and 5% in the east, north, and up directions.

Empirical Orthogonal Function analysis and modeling of ionospheric TEC over South Korean region

This paper presents the ionospheric Total Electron Content (TEC) variations over the low-middle latitude South Korean region using dual frequency Global Navigation Satellite System (GNSS) observations from 14 permanent stations with the data spanning approximately eight years (January 2010 to December 2017). Although, significant work has been conducted in the Korean territory on high-precision positioning, surveying, natural disaster mitigation, and reference frame and datum definition; however, there is substantial scope for modeling of the low-middle latitude ionosphere over the region, which would provide further navigational and communicational benefits. Therefore, in this study, we investigated spatial and temporal TEC variations in GNSS observables through Empirical Orthogonal Function (EOF) modeling and substantiate our findings against existing empirical International Reference Ionosphere (IRI-2016) and NeQuick-2 models. In addition, observation and modeling studies conducted during a geomagnetic storm period (3–9 September, 2017), when the vertical TEC (VTEC) value was almost double that of its regular level, confirm the superior performance of the EOF model in the percentage deviation and correlation plots. To ascertain the performance of the EOF model, the geomagnetic coordinates and PCN index were considered in this study along with other solar and geomagnetic indices (F10.7, Ap and Dst). Analysis of results emphasizes the superior performance of the EOF model compared to other regional and global models with respect to its accuracy and quality relating to quick convergence of decomposition modes and discrimination of temporal as well as spatial components.

TEC Regional Modeling and prediction using ANN method and single frequency receiver over IRAN

In order to study in the field of the dynamics and continuous variations in the ionosphere, the ionospheric measurement tools such as ionosondes, incoherent scatter radars, satellites, and Global Positioning System (GPS) networks should be used. Total Electron Content (TEC) is a key parameter in the investigation and identification of ionosphere layer. From observations of dual frequency GPS receivers, the ionospheric TEC can be extracted. Global Ionospheric Maps (GIM) are auxiliary Maps for a study on ionosphere layer in around the world. It is necessary to produce the regional TEC map for precise studying of the ionospheric TEC. Bernese software is used to extract TEC by dual frequency GPS receivers. Regional modeling of ionospheric TEC by Artificial Neural Network (ANN) is a significant domain for prediction TEC at both single and double frequency GPS receivers. Five locations in Iran during the period of 2006-2010 were identified and used in the development of an input space and ANN architecture for the TEC modeling. The input space included the day number (seasonal variation), hour (diurnal variation), sunspot number (a measure of the solar activity) and magnetic index (a measure of magnetic activity). Based on the results, the ANN have capability and flexibility to model and to predict TEC. TEC predicted by ANN A (NN TEC) and TEC obtained from the IRI2007 version of the International Reference Ionosphere (IRI TEC) are compared during equinoxes and solstices. Results show that ANN predicts GPS TEC more accurately than the IRI over Iran. The IRI-2007 model is not a suitable method to produce TEC over IRAN.

A real-time ionospheric model based on GNSS Precise Point Positioning

This paper proposes a method of real-time monitoring and modeling the ionospheric Total Electron Content (TEC) by Precise Point Positioning (PPP). Firstly, the ionospheric TEC and receiver’s Differential Code Biases (DCB) are estimated with the undifferenced raw observation in real-time, then the ionospheric TEC model is established based on the Single Layer Model (SLM) assumption and the recovered ionospheric TEC. In this study, phase observations with high precision are directly used instead of phase smoothed code observations. In addition, the DCB estimation is separated from the establishment of the ionospheric model which will limit the impacts of the SLM assumption impacts. The ionospheric model is established at every epoch for real time application. The method is validated with three different GNSS networks on a local, regional, and global basis. The results show that the method is feasible and effective, the real-time ionosphere and DCB results are very consistent with the IGS final products, with a bias of 1–2 TECU and 0.4ns respectively.

Carrier-Phase Differential Global Positioning System Navigation Filter for High-Altitude Spacecraft

A new navigation Kalman filter has been developed which uses carrier-phase differential Global Positioning System techniques in a framework that includes integer ambiguities to estimate the relative states of high-altitude, formation-flying spacecraft. This model-based approach to relative navigation allows spacecraft formations to use carrier-phase techniques above the Global Positioning System constellation. The filter uses dynamics models for the spacecraft orbits, receiver clocks, ionospheric total electron content, and Global Positioning System satellite residual position and clock errors. The process noise driving the orbital dynamics is separated into a common-mode part and lower intensity differential-mode part to better model how disturbances influence formations. The ionospheric total electron content model contains information that allows the filter to decide when to use the dual-frequency measurements to correct for the ionosphere and when to use them to aid in integer ambiguity resolution. The filter tracks undifferenced carrier-phase ambiguities, but still resolves the double-differenced integer ambiguities for use in the relative navigation solution. Monte Carlo simulations are used to evaluate the filter's performance. In geostationary scenarios, the filter's mean relative position error magnitude is 1.2 cm, and its maximum error magnitude is 6 cm. In high-Earth-orbit scenarios at an apogee distance of 18 Earth radii, the filter's mean error magnitude is 11 cm, and its maximum error magnitude is 54 cm. The correct integer ambiguities are resolved in one or two 30 s measurement steps in most cases.

Development of a regional GPS-based ionospheric TEC model for South Africa

Advances in South African space physics research and related disciplines require better spatial and time resolution ionospheric information than was previously possible with the existing ionosonde network. A GPS-based, variable degree adjusted spherical harmonic (ASHA) model was developed for near real-time regional ionospheric total electron content (TEC) mapping over South Africa. Slant TEC values along oblique GPS signal paths are quantified from a network of GPS receivers and converted to vertical TEC by means of the single layer mapping function. The ASHA model coefficients and GPS differential biases are estimated from vertical TEC at the ionospheric pierce points and used to interpolate TEC at any location within the region of interest. Diurnal TEC variations with one minute time resolution and time-varying 2D regional TEC maps are constructed. In order to validate the ASHA method, simulations with an IRI ionosphere were performed, while the ASHA results from actual data were compared with two independent GPS-based methodologies and measured ionosonde data.

Regional ionosphere map over Japanese Islands

Based on the high time and spatial resolution total electron content (TEC) data, which is estimated from the phase and code observables obtained by using GPS (Global Positioning System) Earth Observation Network (GEONET), the TEC distribution and its time variation over Japanese Islands are scaled into 0.5° × 0.5° grid data for each 10 minutes. The TEC daily map time series are arranged in an array to show the TEC evolution. Based on the spherical harmonics expansion of global ionospheric TEC model (GIM), which is estimated from global GPS observation, the TEC maps are expanded firstly through as high as 60 degrees and orders for a spherical harmonic function as a regional ionosphere map (RIM). The evolution history of medium scale traveling ionospheric disturbances (MSTIDs), i.e. polarward intense TEC enhancement and pre-noon rapid irregular fluctuations near the geomagnetic equator, are identified and confirmed in a quiet geomagnetic period.