Total Electron Content Model Research Articles

Comparison of TEC prediction methods in mid-latitudes with GIM maps

There are many long-term and short-term prediction methods of Total Electron Content (TEC) that need to be tested for each specific region. Recently, much attention has been paid to testing TEC models in high-, low-latitude and equatorial regions. This paper compares the TEC prediction methods in the mid-latitude zone according to the data of the Juliusruh, Rostov, Manzhouli stations in 2008 and 2015. For a long-term prediction, the IRI-Plas and NeQuick models are compared with the Global Ionospheric Maps (GIM) presented by the Jet Propulsion Laboratory (JPL) and the Technical University of Catalonia (UPC). For a short-term prediction, the Standard Persistence Model (SPM) method, a 27 day median model, and the proposed short-term prediction method are compared for one day ahead. It is shown that for all stations the IRI-Plas model provides better compliance with GIM maps than the NeQuick model irrespective of a solar activity level. An average absolute error lays in the range of 3–3.5 TECU, relative root square mean (RMS) error in the range of 22–27% in 2015 and 1.7–2 TECU, 20–25% in 2008. For the NeQuick model, these estimates were 6.7–8.2 TECU and 42–45% in 2015 and 2.2–3.6 TECU, 30–37% in 2008. For the short-term forecast, the best results were obtained by the SPM method with an average absolute error in the range of 1.95–2.15 TECU in 2015 and 0.59–0.98 TECU in 2008, a relative RMS error in the range of 17–21% in 2015, 11.5–15% in 2008. For the proposed short-term prediction method, these errors were 2.04–2.2 TECU and 12–14% in 2015 and 0.7–1.0 TECU, 7–11% in 2008. Using medians, the errors were 3.1–3.4 TECU and 17–21% in 2015 and 1.0–1.3 TECU, 10–15% in 2008. The dependence of results on the Dst-index was obtained.

Performance evaluation of neural network TEC forecasting models over equatorial low-latitude Indian GNSS station

Global Positioning System (GPS) services could be improved through prediction of ionospheric delays for satellite-based radio signals. With respect to latitude, longitude, local time, season, solar cycle and geomagnetic activity the Total Electron Content (TEC) have significant variations in both time and space. These temporal and spatial TEC variations driven by interplanetary space weather conditions such as solar and geomagnetic activities can degrade the communication and navigation links of GPS. Hence, in this paper, performance of TEC forecasting models based on Neural Networks (NN) have been evaluated to forecast (1-h ahead) ionospheric TEC over equatorial low latitude Bengaluru (12.97∘N,77.59∘E), Global Navigation Satellite System (GNSS) station, India. The VTEC data is collected for 2009–2016 (8 years) during current 24th solar cycle. The input space for the NN models comprise the solar Extreme UV flux, F10.7 proxy, a geomagnetic planetary A index (AP) index, sunspot number (SSN), disturbance storm time (DST) index, solar wind speed (Vsw), solar wind proton density (Np), Interplanetary Magnetic Field (IMF Bz). The performance of NN based TEC forecast models and International Reference Ionosphere, IRI-2016 global TEC model has evaluated during testing period, 2016. The NN based model driven by all the inputs, which is a NN unified model (NNunq) has shown better accuracy with Mean Absolute Error (MAE) of 3.15 TECU, Mean Square Deviation (MSD) of 16.8 and Mean Absolute Percentage Error (MAPE) of 19.8% and is 1–25% more accurate than the other NN based TEC forecast models (NN1, NN2 and NN3) and IRI-2016 model. NNunq model has less Root Mean Square Error (RMSE) value 3.8 TECU and highest goodness-of-fit (R2) with 0.85. The experimental results imply that NNunq/NN1 model forecasts ionospheric TEC accurately across equatorial low-latitude GNSS station and IRI-2016 model performance is necessarily improved as its forecast accuracy is limited to 69–70%.

Application of Singular Spectrum Analysis Using Artificial Neural Networks in TEC Predictions for Ionospheric Space Weather

The prediction of the ionospheric state has become increasingly important as more and more terrestrial and space-based radiocommunication systems rely on the ionospheric space weather. This article presents a new ionospheric prediction model, named the singular spectrum analysis-artificial neural network (SSA-ANN) model. SSA is used as a preprocessing tool for the ionosphere total electron content (TEC) prediction based on the ANN approach. The hourly global positioning system (GPS)-TEC observations from the period of 2009–2017 at the Bangalore (13.02° N and 77.57° E) station are taken into account for analysis. The quick convergence of the SSA decomposition makes it possible to use the first four SSA modes to represent 99.57% of the total variance of the GPS-TEC dataset. The root mean square error between the observations and the SSA-ANN model TEC value is 1.40 TECU for the period of 2009–2017, and the correlation coefficient is 0.99. The performance of SSA-ANN is evaluated using autoregressive moving average (ARMA) and International Reference Ionosphere-16 (IRI-16) models in three different cases of solar phase periods, namely the ascending solar phase (ASP), high solar phase (HSP), and descending solar phase (DSP), and in different seasons. The SSA-ANN model predicts the absence of winter anomaly during the ASP period (2012), but the ARMA model and IRI models failed to predict the absence of the anomaly. The proposed SSA-NN model resulted in higher prediction accuracy and reduced training and testing times, which would be useful for the development of an ionospheric predicting system.

Ionospheric Interhemispheric Asymmetry Induced by Planetary Wave Under Solar Minimum Condition

AbstractThe westward quasi‐6‐day planetary wave with zonal wave number 1 (Q6DW) is important in the Earth's atmospheric coupling. The International Global Navigation Satellite System Service total electron content (TEC) maps show that the Q6DW‐related ionospheric perturbations exhibit clear interhemispheric asymmetry, which do not always agree with the interhemispheric asymmetry feature of the background TEC. The National Center for Atmospheric Research Thermosphere‐Ionosphere‐Mesosphere Electrodynamic General Circulation Model is then used to investigate the reasons for planetary wave‐induced interhemispheric asymmetry by imposing Q6DW forcing at the model lower boundary at vernal equinox under solar minimum condition. The interhemispheric asymmetry features of the ionospheric responses to Q6DW are well captured by our model simulations. For example, the southern branch of the Q6DW perturbation in F region is ~26% larger than that in the Northern Hemisphere at 30°E, while the background Model TEC is~4.7% stronger in the Northern Hemisphere. We found that the vertical plasma transportation induced by Q6DW perturbations in the neutral wind fields in F region show the same asymmetric features with TEC, which leads to corresponding ionospheric perturbations by changing the local recombination effect. Our further simulations show that the vertical plasma drifts induced by Q6DW through E × B process can also cause interhemispheric asymmetry in Model TEC. It is also found that the zonal component of Q6DW perturbations contributes more to the asymmetry than the meridional component through both neutral wind direct transportation effects and E region wind dynamo effects. Moreover, the ionospheric asymmetry of the Q6DW‐related oscillations also exhibit clear longitudinal variabilities.

Remote sensing ionospheric variations due to total solar eclipse, using GNSS observations

For years great interest has been taken in the effects of physical phenomena on ionosphere structure. A total solar eclipse was visible in North America on August 21st, 2017. This event offered a great opportunity for remote sensing the ionospheric behavior under the eclipse condition. In this study we investigated the effects of total solar eclipse on variations of Total Electron Content (TEC), and consequently deviations on regional models of Vertical TEC (VTEC), as well as variations in ionospheric scintillation occurrence. Although variations of TEC due to total solar eclipse are studied thoroughly by many authors, but the effect of solar eclipse on ionospheric scintillation has never been considered before. Our study is based on measurements from a high-rate GPS network over North America on the day of eclipse, a day before and after its occurrence, on the other hand, GPS measurements from ground-based stations on similar days were used to model TEC on the day of event, and also one day before and after it. The results of this study demonstrate that solar eclipse reduced scintillation occurrence at the totality region up to 28 percent and TEC values showed a decrease of maximum 7 TECU. Considering TEC models, our study showed apparent variations in the regional models, which confirms previous studies on ionospheric responses to eclipse as well as theoretical assumptions.

Linear time-series modeling of the GNSS based TEC variations over Southwest Japan during 2011–2018 and comparison against ARMA and GIM models

A significant amount of research has been conducted in Southwest (SW) Japan on climate modeling, disaster management, earthquake prediction, precise positioning, datum definition, and reference frames. However, there is substantial scope for numerical modeling and forecasting of ionospheric Total Electron Content (TEC) variations over the region, which would be beneficial for further communication and navigation purposes. Therefore, in this study we examined spatio-temporal ionospheric TEC variations using long-term Global Navigation Satellite System (GNSS) measurements from 01 January, 2011 to 31 December, 2018 through a modified Linear Time-series Model (LTM) and substantiated our findings by comparing them with those of the existing empirical Global Ionospheric Map (GIM) and Auto-Regressive Moving Average (ARMA) methods. We analyzed TEC variations at 10 permanent stations covering three districts of SW Japan, which mainly include the Kyushu district and parts of the Chugoku and Shikoku districts. To determine the performance of the LTM, the geomagnetic (Northern Polar Cap (PCN) and Disturbance (Dst)) indices were included, together with the additional solar and planetary geomagnetic disturbance indices (F10.7 and Ap). Our comparison results show that the Root Mean Square Error (RMSE) values in terms of TEC units (TECUs) between the observed and the TEC predicted by the LTM vary from 1.57 to 1.66, which are better than those between the observed and the TEC predicted by the ARMA (1.84–1.93) and the GIM (9.67–9.84) TEC models. An analysis of the results emphasizes the superior performance of the LTM over the other models in terms of its discriminability of temporal, as well as spatial, components.

Modeling of GPS-TEC using QR-decomposition over the low latitude sector during disturbed geomagnetic conditions

Given the continuous operation of satellite-based navigation applications, modeling of Total Electron Content (TEC) during magnetic disturbed periods is a significant challenge. The Global Positioning System (GPS)-TEC observations of the Bangalore station (13.02°N, 77.57°E) has been considered and covers the period (2009–2016) of the solar cycle 24. The study emphases on the analysis of TEC variations in eight geomagnetic storms of different intensity: (−223 nT < Dst < −80 nT). The QR decomposition is computed using the Gram-Schmidt (GS) process and is based on observational data from low latitude sectors. For interpolation, the QR model was evaluated on storms that occurred during different periods of solar activity (2009–2016), while for extrapolation the assessment was conducted for the intense storm of March 17, 2015 (St. Patrick's Day storm: Dst −223 nT) in different latitudes, covering the Asian sector between 10°N and 26°N. The R1 and Q1 modes patterns are consistent with changes in the solar proxy index (F10.7) and with regular daily variations and the correlation coefficient is 0.80 and 0.99. The post-residue between the QR model TEC and the GPS- TEC values is ±3 TECU. The QR model captured the TEC responses in consecutive storm cases (18–24, February 2014).The spatial variation of the TEC deviations increases as it moves towards the Equatorial Ionization Anomaly (EIA) crest from the magnetic equator and decreases beyond the crest. The proposed work could be useful for the further study of the Global Navigation Satellite System (GNSS) performance during geomagnetic magnetic disturbed periods.

Evaluation of the SSN and F10.7 indices as a cause for performance variation of the IRI 2016 and IRI-Plas 2017 models

This paper mainly focuses on the evaluation of efficiency of the Sunspot Number (SSN) and the 10.7 cm Solar Radio Flux (F10.7) indices as a cause for the variation of the performance of the latest versions of the International Reference Ionosphere model (IRI 2016 with NeQuick, IRI01-corr and IRI2001 options for the topside electron density) and the IRI Extended to the Plasmasphere (IRI-Plas 2017) for the modeling of the Total Electron Content (TEC). The Global Positioning System (GPS)-derived TEC data obtained from the dual frequency GPS receivers located at Observation Rock, OBSR (geog 46.90°N, 238.18°W, Geom. 52.46°N) and Husband, HUSB (44.12°N, 238.15°W, Geom. 49.73°N) in the West Pacific region during the recent solar maximum (2012-2014) years have been considered for the validation of the performance of the models. The results show that both the GPS-derived TEC (GPS VTEC) and modelled (IRI 2016 and IRI-Plas 2017 VTEC) seasonal diurnal values tend to peak at 00:00 UT (16:00 LT) and 20:00 (12:00 LT) with the highest being observed mostly at 20:00 (12:00 LT); while, their minima are mostly observed at about 13:00 UT (05:00 LT). In addition, in utilizing the SSN, the best performance is generally observed in the June solstice months, especially by the IRI-Plas 2017 model. However, for the equinoctial and December solstice months, the best performance is generally observed by the IRI 2016 model with NeQuick and IRI01 options. It has also been shown that the root-mean-square deviations between the GPS-derived and modelled VTEC diurnal variation in using the F10.7 index are generally less than those of the SSN option in all months, revealing that both the IRI 2016 and IRI-Plas 2017 models generally show better performance using F10.7 index than the SSN. Hence, the F10.7 option is recommended for better TEC modeling employing the IRI 2016 and IRI-Plas 2017 models during the recent solar maximum years over the West Pacific region. In addition, both models cannot effectively estimate the geomagnetic storm time TEC variation.

Possibilities of the usage of the total electron content in a low-latitude zone

Last years, the small quantity of ionosondes at low latitudes could not give a sufficient picture of behavior of the ionosphere in these areas. Now, reception of experimental data, their analysis and detection of total electron content (TEC) variations at low latitudes are an actual problem. When moving from describing the state of the ionosphere using vertical sounding parameters to describing using TEC, it is important to identify similarities and differences in their behavior in order to assess the possibilities of using TEC. This paper carries out research on four ways of TEC usage in low-latitude zone: (1) research of climatological peculiarities of the TEC behavior, (2) validation of up-to-date TEC models, (3) foF2 calculation according to observational TEC, and (4) peculiarities of TEC behavior during geomagnetic disturbances. Results for station Hainan show the following. 1. In addition to previous investigation it is shown, that the empirical global and local models of TEC provide the values close to observational ones, however climatological features of TEC behavior described by various models may still differ from each other and from the experimental data showing in this case TEC maxima of diurnal variation in the afternoons, seasonal variations in March and October, some slight winter anomaly. 2. In contrast to previous investigation it is shown that the closest to the experimental values of TEC are provided by the IRI-Plas model, while this model overestimates values, and the model NeQuick underestimates values compared to the observational ones. 3. For the first time, the ionospheric equivalent slab thickness τ, which plays the role of the coefficient of proportionality between TEC and NmF2, was compared for the IRI, IRI-Plas, NeQuick models with the experimental median τ(med) and it was shown, that the usage of observational TEC data and τ(med) for calculation of critical frequencies foF2 allows improving correspondence with experimental data by 1.2–2 times compared to the models. 4. Comparison of foF2 and TEC behavior has a particular importance during disturbances. Using the example of 15 strong magnetic storms (Dst < −50 nT), it was shown that, despite its global nature, the details of the TEC response strongly depend on the region. So, the peculiarities of δTEC in comparison with the mid-latitude region are the predominance of the positive phase, and a smaller value of response. The synchronism of variations δTEC and δfoF2 was very high, although there are cases of mismatch. Using the median τ(med) allows determining foF2 during disturbances and filling data gaps.

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.

Modeling and analysis of ionosphere TEC over China and adjacent areas based on EOF method

On the basis of the empirical orthogonal function (EOF) decomposition technique, the spatiotemporal characteristics of the ionospheric total electron content (TEC) from 2007 to 2016 over China and adjacent areas (15°–55°N, 70°–145°E) were studied. The spatial patterns and temporal variations of the TEC were separated by EOF decomposition and can be represented well by the base functions and associated coefficients, respectively. The time variation features of different scales can also be obtained by continually decomposing the coefficients that reflect the temporal variations. Results show that this method is extremely beneficial to the comprehensive analysis of the overall spatiotemporal variations in the ionospheric TEC. The base functions of EOF reflect that the TEC in China and adjacent areas experiences annual and semiannual changes with the latitudinal and longitudinal changes, as well as equatorial anomaly phenomenon. The coefficients of these spatial patterns have evident regularity with the changes in solar activity, season, and local time (LT). After the spatial patterns and the diurnal variations with LT were extracted through a two-layer EOF decomposition, the remaining time variation features were modeled using seasonal variations, solar activity, and geomagnetic activity. Finally, an empirical TEC model was established by incorporating the modeled coefficients and the original EOF base functions. The EOF-based TEC model can demonstrate the temporal and spatial variation characteristics of TEC, and the EOF-based model can obtain significantly smaller modeling errors and achieve better performance in terms of TEC modeling than the International Reference Ionosphere model IRI-2016.

A New Global Total Electron Content Empirical Model

Research on total electron content (TEC) empirical models is one of the important topics in the field of space weather services. Global TEC empirical models based on Global Ionospheric Maps (GIMs) TEC data released by the International GNSS Service (IGS) have developed rapidly in recent years. However, the accuracy of such global empirical models has a crucial restriction arising from the non-uniform accuracy of IGS TEC data in the global scope. Specifically, IGS TEC data accuracy is higher on land and lower over the ocean due to the lack of stations in the latter. Using uneven precision GIMs TEC data as a whole for model fitting is unreasonable. Aiming at the limitation of global ionospheric TEC modelling, this paper proposes a new global ionospheric TEC empirical model named the TECM-GRID model. The model consists of 5183 sections, corresponding to 5183 grid points (longitude 5°, latitude 2.5°) of GIM. Two kinds of single point empirical TEC models, SSM-T1 and SSM-T2, are used for TECM-GRID. According to the locations of grid points, the SSM-T2 model is selected as the sub-model in the Mid-Latitude Summer Night Anomaly (MSNA) region, and SSM-T1 is selected as the sub-model in other regions. The fitting ability of the TECM-GRID model for modelling data was tested in accordance with root mean square (RMS) and relative RMS values. Then, the TECM-GRID model was validated and compared with the NTCM-GL model and Center for Orbit Determination in Europe (CODE) GIMs at time points other than modelling time. Results show that TECM-GRID can effectively describe the Equatorial Ionization Anomaly (EIA) and the MSNA phenomena of the ionosphere, which puts it in good agreement with CODE GIMs and means that it has better prediction ability than the NTCM-GL model.

Solving a navigation problem with the total electron content model GEMTEC

This article explores the possibility of improving the accuracy of positioning in single-frequency satellite radio navigation equipment through the use of an empirical model of the total electronic content GEMTEC. The effectiveness of this model is compared with that of the Klobuchar model, which is recommended for the GPS interface control document. We conducted testing at our observation points, using data from the international network of IGS stations in the GPS system. The use of the international network allowed us to select a long period of time for the testing from 2001 to 2017. As a result, it was shown that the GEMTEC model significantly reduces the average positioning errors as compared to the Klobuchar model. We also demonstrate the possibility of introducing the GEMTEC model and its full-featured use in single-frequency home-class receivers, for example, in the Russian receiver MNP-M7.

Fast ionospheric correction using Galileo Az coefficients and the NTCM model

Europe's Global Navigation Satellite System (GNSS) Galileo broadcasts three parameters for ionospheric correction as part of satellite navigation messages. They are called effective ionization coefficients and are used to drive the NeQuickG model in single frequency Galileo operations. The NeQuickG is a three-dimensional electron density model based on several Epstein layers whose anchor points, such as ionospheric peak densities and heights, are derived using the spatial and temporal interpolation of numerous global maps. This makes the NeQuickG computationally more expensive when compared with the GPS equivalent, the Klobuchar model. We propose here an alternative ionospheric correction approach for single frequency Galileo users. In the proposed approach, the broadcast coefficients are used to drive another ionospheric model called the Neustrelitz Total Electron Content Model (NTCM) instead of the NeQuickG. The proposed NTCM is driven by Galileo broadcast parameters and the investigation shows that it performs better than the NeQuickG when compared with the reference vertical total electron content (VTEC) data. It is found that the root mean squares (RMS) and standard deviations (STD) of residuals are approx. 1.6 and 1.2 TECU (1 TECU?=?1016 electrons/m2) less for the NTCM than the NeQuickG. A comparison with the slant TEC reference data shows that the STD, mean and RMS residuals are approx. 9.5, 0.6, 10.0 TECU for the NeQuickG whereas for the NTCM, they are 9.3, 2.5, 10.1 TECU respectively. A comparison with Jason-2 altimeter datasets reveals that the NTCM performs better than the NeQuickG with RMS/STD deviations of approx. 7.5/7.4 and 8.2/7.9 TECU respectively. The investigation shows that the Galileo broadcast messages can be effectively used for driving the NTCM.

Highlights about the performances of storm-time TEC modelling techniques for low/equatorial and mid-latitude locations

A statistical evaluation of storm-time total electron content (TEC) modelling techniques over various latitudes of the African sector and surrounding areas is presented. The source of observational TEC data used in this study is the Global Navigation Satellite Systems (GNSS), specifically the Global Positioning Systems (GPS) receiver networks. For each selected receiver station, three different storm-time models based on empirical orthogonal functions (EOF) analysis, non-linear regression analysis (NLRA) and Artificial neural networks (ANN), were implemented. Storm-time GPS TEC data used for both development and validation of the models was selected based on the storm criterion of Dst⩽-50 nT or Kp⩾4 to take into account both coronal mass ejections (CMEs) and co-rotating interaction regions (CIRs) driven storms, respectively. To make an independent test of the models, storm periods considered for validation were excluded from datasets used during the implementation of the models and results are compared with observations, monthly median values, and International Reference Ionosphere (IRI-2016) predictions. Considering GPS TEC as reference, a statistical analysis performed over six storm periods reserved for validation revealed that ANN model is about 10%, 26%, and 58% more accurate than EOF, NLRA, and IRI models, respectively. It was further found that, EOF model performs 15%, and 44% better than NLRA, and IRI models, respectively, while NLRA is 25% better than IRI. On the other hand, results are also discussed referring to the background ionosphere represented by monthly median TEC (MM TEC) and statistics are provided. Moreover, strengths and weaknesses of each model are highlighted.

On the advantage of stochastic methods in the modeling of ionospheric total electron content: Southeast Asia case study

This article describes an implementation of precise point positioning (PPP) and the least-squares collocation (LSC) method in the modeling of total electron content (TEC) in Southeast Asia, which is characterized by relatively homogeneous Global Navigation Satellite Systems (GNSS) data from International GNSS Service (IGS) stations and the occurrence of the highest TEC anomalies. A homogeneous coverage of the data in this region provides an opportunity for the testing of different spatial modeling methods applied to TEC data. The spherical harmonic expansion (SHE) and spherical splines (SS) have been the most popular mathematical tools for the interpolation of TEC in the ionosphere over the last decades. The developed stochastic model (PPPLSC) is compared with the well-known stochastic global UQRG model, which is interpolated by the ordinary kriging (OK) and CODG global TEC model based on spherical harmonics (SH), and also the IGSG model, which is a combination of several models developed by the IGS Ionosphere Associate Analysis Centers. These four models derived from different approaches are assessed together using self-consistency analysis based on a geometry-free combination of carrier-phase observations, and also using external validation employing dual-frequency altimeter TEC from three low-Earth-orbit satellites.The study implements the LSC modeling technique, which is quite new for TEC and is a valuable step towards increasing the accuracy and resolution of ionosphere models. LSC, similarly to OK, is a stochastic parametric technique, applying the covariance based on data properties. Therefore LSC restores the fullest possible signal in the interpolated model in terms of spatial resolution. Leave-one-out (LOO) validation of the covariance parameters assures optimal interpolation results in the least-squares sense. The covariance matrices of LSC parametrized by LOO validation enable estimation with reliable internal precision for the model. The self-consistency analysis of TEC models with the use of carrier-phase observations proves a better consistency of stochastic models in relation to TEC models based on SHE. The set of statistical values of external comparisons with three altimetry-derived trajectories of TEC observations additionally confirms the advantage of stochastic PPPLSC and UQRG models. The validation results all together indicate a better quality of stochastic models in relation to those based on the summation of spherical functions. The factor that is suspected to decrease the accuracy of the latter models is the loss of the higher frequency signal due to the spectral limitation coming from the low order of SHE applied in IGSG and CODG.

Modeling of GPS total electron content over the African low-latitude region using empirical orthogonal functions

Abstract. In this paper, an empirical total electron content (TEC) model and trends in the TEC over the African low-latitude region are presented. GPS-derived TEC data from Malindi, Kenya (geographic coordinates 40.194∘ E, 2.996∘ S), and global ionospheric maps (GIMs) were used. We employed an empirical orthogonal function (EOF) analysis method together with least-squares regression to model the TEC. The EOF-based TEC model was validated through comparisons with GIMs, the GPS-derived TEC and the TEC derived from the International Reference Ionosphere 2016 (IRI-2016) model for selected quiet and storm conditions. The single-station EOF-based TEC model over Malindi satisfactorily reproduced the known diurnal, semiannual and annual variations in the TEC. Comparison of the EOF-based TEC model results with the TEC derived from the IRI-2016 model showed that the EOF-based model predicted the TEC over Malindi with fewer errors than the IRI-2016. For the selected storms, the EOF-based TEC model simulated the storm time TEC response over Malindi better than the IRI-2016. In the case of the regional model, the EOF-based TEC model was able to reproduce the TEC characteristics in the equatorial ionization anomaly region. The EOF-based TEC model was then used as a background for estimating TEC trends. A latitudinal dependence in the trends was observed over the African low-latitude region.

Analysis of Total Electron Content (TEC) Near Real Time Using Dual Frequency GPS Data (Study Case: Surabaya)

Ionosphere is part of the atmospheric layer located between 50 to 1000 km above the earth's surface which consists of electrons that can influence the propagation of electromagnetic waves in the form of additional time in signal propagation, this depends on Total Electron Content (TEC) in the ionosphere and frequency GPS signal. In high positioning precision with GPS, the effect of the ionosphere must be estimated so that ionospheric correction can be determined to eliminate the influence of the ionosphere on GPS observation. Determination of ionospheric correction can be done by calculating the TEC value using dual frequency GPS data from reference stations or models. In making the TEC model, a polynomial function is used for certain hours. The processing results show that the maximum TEC value occurs at noon at 2:00 p.m. WIB for February 13, 2018 with a value of 35,510 TECU and the minimum TEC value occurs in the morning at 05.00 WIB for February 7, 2018 with a value of 2,138 TECU. The TEC model spatially shows the red color in the area of Surabaya and its surroundings for the highest TEC values during the day around 13.00 WIB to 16.00 WIB.

Improvement of the Ionospheric Radio Occultation Retrievals by Means of Accurate Global Ionospheric Maps

AbstractThe Abel inversion method is the classic approach to retrieve electron density profiles from radio occultation measurements, assuming that the electron density is only dependent upon height. In the early 2000s, the total electron content (TEC)‐aided inversion method was introduced, where horizontal gradients in the electron density distribution are taken into account by using information from an external model of total electron content (TEC). We show how the quality of the chosen external ionospheric model influences the radio occultation retrievals. Using a two‐layer TEC model, the 68% percentiles of the global error distributions of retrieved critical frequency and bottomside ionospheric electron content for 2014 improve more than 30%, with regard to the classic Abel inversion results. In a well‐sounded region like Europe, this improvement raises to about 40–45%, while 10% improvement is achieved using two‐layer maps with regard to the retrievals using single‐layer TEC maps. We point out that using the TEC to describe the horizontal gradient incurs an implicit mismodeling that, until now, has not been taken into account. A new technique is presented that, thanks to TEC modeling by means of two layers, can assess the impacts of such mismodeling. From this technique, a method to select the most accurate radio occultation retrievals is applied to demonstrate that the resulting errors in the retrieved critical frequencies for the European region are smaller than 7% in nearly 82% of the cases, very similar to the relative difference between measurements of two nearby ionosondes.