Total Electron Content Estimation Research Articles

Exploring ionospheric dynamics: a comprehensive analysis of GNSS TEC estimations during the solar phases using linear function model

Abstract The modeling and forecasting of Total Electron Content (TEC) play a major role in influencing signals from satellite-based navigation systems and impact the performance of diverse satellite-dependent technologies. The intensity of solar ionizing radiation and the state of geomagnetic field activity influence the Global Navigation Satellite System (GNSS)-TEC. This paper uses a Linear TEC Function (LTF) climatology model to understand ionospheric behavior under solar and geomagnetic activities that cause variations in the electron distribution of the ionosphere medium. The LTF model integrates representations of solar EUV photon (MgII) and geomagnetic (SYMH) activities, incorporating solar-modulated oscillations (periodic variations) at four seasonal cycles and a linear trend. The LTF model examined the time series of GPS-TEC at a location (geographic 34.95° N, 134.05° E) with a time resolution of 1 h, from 1997 to 2016, covering solar cycles 23 and 24. The Root Mean Square Deviation (RMSD) and correlation coefficient between the GNSS-TEC and model TEC (LTF) was 5.30 TECU and 95 %. The results indicate that solar components, as well as annual and semi-annual variations, have a significant impact on the daily average TEC. Solar activity appears to be the predominant determining factor of TEC during the solar phases of cycles 23 and 24. In contrast, periodic influences primarily outline TEC during periods characterized by minimal solar activity. The geomagnetic component presents an increased influence, particularly during storm periods. The model demonstrates superior performance in Total TEC modeling compared to other state-of-the-art approaches.

Analysis of differential code biases for GPS receivers over the Indian region

Abstract The GPS Aided Geo Augmented Navigation (GAGAN) system provides the navigational services for single-frequency GNSS user via broadcasting the differential corrections with GEO stationary satellites. The significant differential correction contribution comes from ionospheric time delays and is necessary to be determined precisely. Dual-frequency GPS receivers measure the ionospheric time delays using GPS code and carrier phase measurements. The determination of absolute ionospheric Total Electron Content (TEC) requires the calibration of GPS satellites and receiver hardware biases due to different frequency-dependent signals (L1 and L2) due to environmental changes (Temperature and Humidity). In this paper, A receiver-based Differential Code Biases (DCB) algorithm is implemented to derive a joint estimation of TEC and RDCB parameters using the weighted Least Square (WLS) method. The daily averaged DCBs data for 26 GPS receivers are obtained for 3 years (2014–2016) from 26 GPS reeivers over Indian region. The receiver DCB algorithmis validated with the Fitted Receiver Biases (FRB) method. The correlation (R) between VTEC and RDCB is conducted to investigate the RDCB stability. The results would be useful for the accurate determination of ionospheric differential corrections to GAGAN users.

Efficient and accurate TEC modeling and prediction approach with random forest and Bi-LSTM for large-scale region

The total electron content (TEC) is a crucial parameter for ionosphere monitoring, and the development of accurate TEC estimation and prediction models is significant for high-precision positioning. However, establishing a high-precision ionospheric model that can effectively improve prediction accuracy remains a challenging task. We propose a method that combines random forest with a Bi-LSTM neural network to establish a high-precision ionospheric prediction model. The random forest algorithm is used for regression analysis and to estimate the variable importance of input parameters. We use observation data from the Crustal Movement Observation Network of China and International GNSS Services while estimating the relative importance of 14 input variables at different latitudes. The results demonstrate that our proposed model achieves more efficient and accurate predictions, with a correlation coefficient of 0.96, indicating significant improvement in accuracy compared to traditional RNN and LSTM models. Overall, the Bi-LSTM forecast model based on random forest can effectively capture the temporal and spatial variation characteristics of ionospheric TEC in China. This enables the model to provide accurate ionospheric information for positioning users, thereby improving the precision of positioning applications.

Parametric Dependence of Topside Ionospheric Empirical Scale Height and Electron Density Profiles in NeQuick2 Model Over the Equatorial and Low Latitudes and Its Consequences on the Estimation of TEC

AbstractConstructing realistic vertical electron density profiles is a crucial step in accurately estimating the ionospheric total electron content (TEC) in empirical models. Inadequate representation of electron density profiles leads to under‐ or over‐estimation of TEC in model outputs. One of the widely used ionospheric empirical model, the NeQuick2 exhibits large uncertainties over equatorial and low latitudes, particularly in the topside ionosphere. The NeQuick2 model employs semi Epstein type of polynomials to characterize the topside ionospheric structure, wherein, the scale height (H) is the key parameter. NeQuick2 model estimates H value using empirical formulations, which contain three major parameters namely, Ho—the scale height at the F‐layer peak, g—height gradient in H, and r—which controls the increase in H at higher altitudes. In this study, a systematic analysis has been carried out with particular focus on the equatorial and low latitudes to explore the variability of topside scale height and electron density profiles on the above three empirical parameters using COSMIC observations over Trivandrum and Ahmedabad, in India. Model uncertainties in estimating Ho and their impacts on the estimation of TEC are investigated. Data assimilation analysis has been carried out to obtain a quantitative understanding on the effect of deviations in topside scale height on the uncertainties in accurate estimation of TEC over equatorial and low latitudes. This study reveals the impact of scale height uncertainties on errors in modeled TEC and demonstrates the need for improvement in empirical formulations for improving accuracies in ionospheric modeling over equatorial and low latitude sectors.

ThingSpeak an IOT Application and Analytics System for GNSS with MATLAB Analysis

The ionosphere is an essential component of the Global Navigation Satellite System (GNSS) that can affect the accuracy and dependability of GNSS location. MATLAB provides comprehensive tools for the analysis of ionospheric data and its impact on GNSS positioning. To examine the ionospheric data utilized in GNSS positioning, we advise utilizing MATLAB in this application. The analysis is based on a determination of the Total Electron Content (TEC) of the ionosphere in order to account for the ionospheric delay in the GNSS signals. The system consists of a GNSS receiver module connected to a microcontroller with Wi-Fi capabilities, which transmits data to Matlab. The data is processed in Matlab before being used there. Then, in order to account for the ionospheric delay in the GNSS signals, the TEC of the ionosphere is calculated using Matlab. The recommended system provides a scalable and flexible environment for GNSS-based ionospheric data analysis. The system is practical for a range of applications, including surveying, geodesy, and navigation, and it may be readily adapted to fulfill specific customer requirements.For Matlab analysis, the approach has a number of advantages. In order to measure the TEC of the ionosphere precisely, it first provides cutting-edge signal processing technologies. Additionally, it makes it possible to display ionospheric data in a number of different ways, such as maps, graphs, and time-series plots. This can be applied to the data to identify patterns and trends. The proposed MATLAB-based system offers a scalable, flexible, and cutting-edge platform for the estimation of the ionosphere's TEC and the correction of the ionospheric delay in the GNSS signals.

Method for Assemblage of an Open Access Data Set for Research in Geomagnetic Effects on GPS/GNSS Ionospheric Delay in Sub-equatorial Regions

Space weather, geomagnetic, and ionospheric effects are major sources of Global Navigation Satellite System’s (GNSS) Positioning, Navigation, and Timing (PNT) service degradation. Researchers studying the problem often face an obstacle in missing large data sets comprising ionospheric effects variables and space weather ones for their studies. Here a formal assemblage method is proposed for data set assemblage for GNSS ionospheric effects assessment that utilises experimental sets of space weather/geomagnetic observations, and raw GNSS pseudorange observations polluted with uncorrected ionospheric delay effects to estimate Total Electron Content (TEC) as a target variable outlining the ionospheric effects on GNSS. The five Observations Quality Principles (OQP) are proposed for the observations to be used in statistical learning model development to comply to. The proposed assemblage method is demonstrated in a particular case study of an assembled data set for Darwin, NT, Australia, in sub-equatorial zone, using a tailored software developed in the R environment for scientific computing, and a freely available TEC estimation software. The assembled massive data obtained in the demonstration of the proposed method is provided in the open-access manner in support of the international scientific community.

Epoch-Wise Estimation and Analysis of GNSS Receiver DCB under High and Low Solar Activity Conditions

Differential code bias (DCB) is one of the main errors involved in ionospheric total electron content (TEC) retrieval using a global navigation satellite system (GNSS). It is typically assumed to be constant over time. However, this assumption is not always valid because receiver DCBs have long been known to exhibit apparent intraday variations. In this paper, a combined method is introduced to estimate the epoch-wise receiver DCB, which is divided into two parts: the receiver DCB at the initial epoch and its change with respect to the initial value. In the study, this method was proved feasible by subsequent experiments and was applied to analyze the possible reason for the intraday receiver DCB characteristics of 200 International GNSS Service (IGS) stations in 2014 (high solar activity) and 2017 (low solar activity). The results show that the proportion of intraday receiver DCB stability less than 1 ns increased from 72.5% in 2014 to 87% in 2017, mainly owing to the replacement of the receiver hardware in stations. Meanwhile, the intraday receiver DCB estimates in summer generally exhibited more instability than those in other seasons. Although more than 90% of the stations maintained an intraday receiver DCB stability within 2 ns, substantial variations with a peak-to-peak range of 5.78 ns were detected for certain stations, yielding an impact of almost 13.84 TECU on the TEC estimates. Moreover, the intraday variability of the receiver DCBs is related to the receiver environment temperature. Their correlation coefficient (greater than 0.5 in our analyzed case) increases with the temperature. By contrast, the receiver firmware version does not exert a great impact on the intraday variation characteristics of the receiver DCB in this case.

Comparison of the Performance of the Regression Models in GPS-Total Electron Content Prediction

The ionosphere is an important layer that provides radio communication in the upper atmosphere. The ionosphere is located between 50 km and 1000 km above the atmosphere. Electron density, which is the most important parameter of the ionosphere, changes depending on location, time, seasons, altitude, solar, geomagnetic and seismic activity. A significant measurable amount of electron density is Total Electron Content (TEC), which is used to probe the structure of the ionosphere and upper atmosphere. The Global Positioning System (GPS), which has a low cost and widespread receiver network is prominent used in TEC estimation. The IONOLAB-TEC data estimated from GPS is used in this study. Prediction of TEC is important phenomenon to operate and to plan the Earth-space and satellite-to-satellite communication systems, to generate the earthquake precursor signals using TEC and to detect of anomalies in the ionosphere. In this study, IONOLAB-TEC data obtained from GPS is estimated using regression models. Among the tested algorithms, it is observed that the Exponential Gaussian Process Regression and Interactions Linear Regression algorithms are very successful and high-performance models for TEC estimation.

Mapping of the Ionospheric Total Electron Content over the East African Low–Latitude Region

Ionospheric behaviour is often monitored using total electron content (TEC) measurements from Global Navigation Satellite System (GNSS) receivers. However, the GNSS receivers are sparse over the East African low-latitude region, resulting in spatio-temporal gaps. In an attempt to address this challenge, the possibility of constructing East African ionospheric maps using Kriging method was investigated in this study. Prior to constructing the maps, the behaviour of the low-latitude ionosphere over this region was characterised using TEC data for 2014 and 2018 during quiet and disturbed conditions. The results show that the highest values of TEC exist between 10:00 UT and 13:00 UT and the minimum values exist at around 03:00 UT. The seasonal trend of TEC reveals that the highest values of TEC occur during March equinox and the lowest during June solstice. The post-sunset TEC often show enhancements between 18:00 UT and 21:00 UT. The enhancements were more pronounced in 2014 than in 2018, especially during the equinoctial months for stations at the crest of the equatorial ionisation anomaly region. These enhancements occurred about an hour earlier at MAL2 than at ADIS during March and September, 2014. The spatial variation of TEC over the East African region was analysed by fitting different semivariogram models. The results reveal that the best semivariogram that describes the spatial variation of TEC over the East African low-latitude region is the Gaussian model. Further analysis shows that the spatial variation of TEC is larger in the meridional direction than in the zonal direction. The Gaussian semivariogram model was then used to construct the TEC maps over the region. The TEC maps were validated using TEC derived from GNSS receivers. The results show very high positive correlation with correlation coefficients between 0.9360 and 0.9970. This suggests that the TEC maps generated by the Kriging interpolation method can be used as good estimates of the GPS-derived TEC at the unmeasured grid points over the region. Therefore, the maps can be used to fill the gaps that exist in the TEC data over the region.

ІОНОСФЕРНІ ЗБУРЕННЯ У БЛИЖНІЙ ЗОНІ, ВИКЛИКАНІ ЕКСПЛОЗИВНИМ ВИВЕРЖЕННЯМ ВУЛКАНА ТОНГА 15 СІЧНЯ 2022 р.

Subject and Purpose. The thermal energy of the Tonga volcano reached 3.9 . 1018 J, its power amounted to 9.1 . 1013 W. The energy and power of the blast waves approached (6.7...7.5) . 1013 J and 1011 W, respectively. Ionospheric effects caused by the explosive eruption of the Tonga volcano on January 15, 2022 have received due attention. It was established that the ionospheric disturbances spread over global distances, with the greatest disturbances occurring in the near zone. The aim of the present paper is to describe aperiodic and quasi-periodic disturbances started by the Tonga volcano explosion and occurring in the near ionospheric zone. Methods and Methodology. To detect ionospheric disturbances generated by the volcanic eruption, temporal variations of the total electron content (TEC) in a vertical column in the ionosphere were analyzed. The total error of the TEC estimation did not exceed 0.1 TECU. Results. The quantitative characteristics of ionospheric disturbances caused by the explosive eruption of the Tonga volcano have been obtained. It was proved that the appearance of the ionospheric "hole" was caused directly by the volcanic explosion. With dis- tance away from the volcano, the TEC deficit in absolute values decreased from ~10 to ~2.5 TECU. As that was happening, the time taken to form the ionospheric "hole" increased from ~20 to ~100 min. Three groups of disturbances were observed. One group picks out disturbances having an N-shaped profile and caused by a blast wave with a speed exceeding ~1 000 m/s. Another group includes disturbances with a propagation speed within ~340...620 m/s, which is characteristic of atmospheric gravity waves at ionospheric heights. The last group is specified by the disturbance propagation speed within ~110 to 320 m/s. The disturbances of the kind can be generated by tsunamis, Lamb waves and atmospheric gravity waves. The wave disturbance periods varied within ~ 5 to 20 min, the disturbance amplitudes were within 0.5...1.0 TECU. Conclusions. It has been proven that aperiodic and quasi-periodic ionospheric disturbances in the near zone were caused directly by the explosion of the Tonga volcano.

Short-term Adaptive Forecast Model for TEC over equatorial low latitude region

In today's world, satellite navigation is one of the most widely used navigational aids, which is why accurate positioning is of critical importance. The ionosphere's Total Electron Content (TEC) is a significant contributor to the positional error in signal traveling between a satellite and the earth and reduces the system's positional accuracy. The ionosphere adds an excess delay to the radio wave traversing through it, resulting in position estimation error. Since the delay is a function of the ionospheric parameter TEC, estimation of TEC can help in correcting the errors. The challenge in estimating TEC in the equatorial region is that it exhibits a non-deterministic or unpredictable characteristic due to the complex electrodynamics resulting from Equatorial Ionospheric Anomaly (EIA). In addition, space weather phenomena like geomagnetic storms further disturb the ionosphere causing irregular short-term disturbances. This study explores the inherent VTEC pattern during geomagnetic storm conditions, especially during the high solar activity period, and proposes a short-term adaptive segmented regression model to forecast VTEC. The study is undertaken over six years of high solar activity period in the 24th solar cycle. The forecast model uses both linear and polynomial autoregression coefficients of recent past data. The model's performance is evaluated for extreme conditions, including the high solar activity and geomagnetic storms, which are the most challenging scenario for TEC prediction. The accuracy of the predicted output is calculated in terms of RMSE and correlation coefficient. The results were also compared with IRI 2016 model. The proposed short-term prediction model thus aims to help fill the precision required by long-term forecast models by considering near real-time nonlinear dynamics in the ionosphere.

Ionospheric Assimilation of GNSS TEC into IRI Model Using a Local Ensemble Kalman Filter

Ionospheric total electron content (TEC) is important data for ionospheric morphology, and also an important parameter for ionospheric correction in Global Navigation Satellite System (GNSS) precise positioning, navigation, and radio science. In this study, we present a data assimilation model for regional ionosphere based on a local ensemble Kalman filter (LEnKF) with the International Reference Ionosphere 2016 (IRI-2016) model as the background, to assimilate ionospheric TEC observations from GNSS. To demonstrate the results, the TEC estimates from the Crustal Movement Observation Network of China (CMONOC), which is about 260 stations in China, are applied as observation. The assessments are performed against the TEC estimates from BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and against the final products from the Center for Orbit Determination in Europe (CODE). The assimilation results are in good agreement with BDS GEO TEC and the CODE TEC on a quiet or disturbed day. The correlation coefficient after assimilation is increased by about 17% compared with that before assimilation, and the RMSE after assimilation is decreased by about 42% compared with that before assimilation. Furthermore, the assimilated method is also evaluated in the single-frequency precise point positioning (PPP). The experimental results indicate that the PPP/Assimilated method can improve the GNSS positioning accuracy more effectively in comparison to the PPP/CODE. These results reveal that the LEnKF method can be considered as a useful tool for ionospheric assimilation.

Using Support Vector Machine (SVM) with GPS Ionospheric TEC Estimations to Potentially Predict Earthquake Events

There are significant controversies surrounding the detection of precursors that may precede earthquakes. Natural hazard signatures associated with strong earthquakes can appear in the lithosphere, troposphere, and ionosphere, where current remote sensing technologies have become valuable tools for detecting and measuring early warning signals of stress build-up deep in the Earth’s crust (presumably associated with earthquake events). Here, we propose implementing a machine learning support vector machine (SVM) technique, applied with GPS ionospheric total electron content (TEC) pre-processed time series estimations, to evaluate potential precursors caused by earthquakes and manifested as disturbances in the TEC data. After filtering and screening our data for solar or geomagnetic influences at different time scales, our results indicate that for large earthquakes (>Mw 6), true negative predictions can be achieved with 85.7% accuracy, and true positive predictions with an accuracy of 80%. We tested our method with different skill scores, such as accuracy (0.83), precision (0.85), recall (0.8), the Heidke skill score (0.66), and true skill statistics (0.66).

Arctic TEC Mapping Using Integrated LEO-Based GNSS-R and Ground-Based GNSS Observations: A Simulation Study

Ionospheric total electron content (TEC) maps with high spatial and temporal resolutions are essential for depicting the state of the ionosphere and for performing ionospheric delay corrections associated with satellite navigation applications. Low Earth orbit (LEO) CubeSat-based global navigation satellite system (GNSS) reflectometry (GNSS-R) measurements provide a promising opportunity for retrieval of ionospheric TEC over sea ice and calm waters, which offers a potential new data source to fill the gaps of ground-based GNSS networks. However, the GNSS-R slant TEC (sTEC) estimations include contributions from the incident and reflection ray paths, whose ionospheric piercing points (IPPs) can be separated by hundreds of kilometers. This article presents an algorithm that integrates sTEC measurements from the GNSS-R CubeSats and available ground-based GNSS receivers to derive Arctic vertical TEC (vTEC) maps. A simulation study using the model ionosphere constructed from the NeQuick-2 is conducted to assess the performance of the algorithm. Varying levels of temporal resolutions and solar activities, and the number of CubeSats and the number of maximum simultaneously tracked reflection signals by a CubeSat are implemented in the simulation. The results show that the inclusion of coherent GNSS-R measurements improves the accuracy of the vTEC maps under all levels of solar activities. The RMSE improvement percentage is most obvious when the update interval is the shortest. Increasing the number of CubeSats further improves the accuracy. However, no significant improvement in vTEC map accuracy is observed when the number of maximum simultaneously tracked GNSS-R satellites is higher than 4. Quantitative measures and analyses of the algorithm performances are presented in this article.

Analysis and Empirical Modeling of Ionospheric Horizontal Gradients in the TEC Mapping Onboard LEO Satellites

The ionospheric mapping function (IMF) is fundamental in retrieving total electron content (TEC) from observations on board low earth orbiting (LEO) satellites, as well as the receiver differential code bias (DCB) estimation. Most IMFs apply the assumption that the electron density field is spherical symmetric, only dependent on the elevation angle of signal ray path without considering the azimuthal diversity. However, the ionospheric horizontal asymmetry may introduce large mapping errors in slant to vertical TEC conversion or vice versa especially at low elevation angles. This study investigates the variations of the horizontal gradients in the topside ionosphere and plasmasphere, and proposes a formalism for parametrizing the time, location, elevation and azimuth angle dependent horizontal gradients based on the Global Core Plasma Model (GCPM). Several parameters are estimated to represent the north-to-south, east-to-west asymmetric patterns of slant TEC and the horizontal mapping factor with varying elevation angle. Results show the empirical model of the horizontal gradients are well constructed and contribute positively to reducing the mapping error of vertical TEC. The root-mean-square error (RMS) at all elevation angles are decreased to 0.5 TECU and 1.0 TECU under low and high solar activity conditions respectively. This approach is potential to be used in the absolute GNSS/LEO TEC and DCB estimation and topside ionosphere/plasmasphere exploration.

Analysis of Earth’s Ionosphere Effects on Englacial Layering Detectability in Spaceborne Radar Sounders Data

Several studies are in progress for proposing an Earth orbiting radar sounder (EORS) mission. Some of them consider as baseline system architecture a recently proposed distributed radar sounding array in formation flight with enhanced capabilities of clutter suppression. Besides clutter, the detectability of subsurface targets may also be affected by the propagation of the radar signal through Earth’s ionosphere. These effects include frequency-dependent phase dispersion and scintillations. In this letter, we present a subsurface detection performance assessment of an EORS with distributed architecture focusing on the ionospheric effects. The novel contributions of this work are: (i) simulation of the coherent radar response of a representative polar ice target (englacial layering) in the distributed radar sounding case; (ii) inclusion of spatially-dependent ionospheric scintillation effects on the distributed beam pattern; (iii) inclusion of phase dispersion effects for different values of total electron content (TEC), and (iv) analysis of the subsurface detection performance. Detectability analysis is performed after applying a state-of-the-art technique for compensating ionospheric phase-dispersion effects. The results show that the englacial layering is detectable by compensating the dispersion effects in the range between 1 and 21 TECU in the ionosphere. The layering is also detectable at higher values of TEC by improving the accuracy of TEC estimation. Moreover, even without compensation, the worst-case ionospheric phase scintillations of 25° produces a negligible effect on the detectability.

Galileo E5 AltBOC Signals: Application for Single-Frequency Total Electron Content Estimations

Global navigation satellite system signals are known to be an efficient tool to monitor the Earth ionosphere. We suggest Galileo E5 AltBOC phase and pseudorange observables—a single-frequency combination—to estimate the ionospheric total electron content (TEC). We performed a one-month campaign in September 2020 to compare the noise level for different TEC estimations based on single-frequency and dual-frequency data. Unlike GPS, GLONASS, or Galileo E5a and E5b single-frequency TEC estimations (involving signals with binary and quadrature phase-shift keying, such as BPSK and QPSK, or binary offset carrier (BOC) modulation), an extra wideband Galileo E5 AltBOC signal provided the smallest noise level, comparable to that of dual-frequency GPS. For elevation higher than 60 degrees, the 100 s root-mean-square (RMS) of TEC, an estimated TEC noise proxy, was as follows for different signals: ~0.05 TECU for Galileo E5 AltBOC, 0.09 TECU for GPS L5, ~0.1TECU for Galileo E5a/E5b BPSK, and 0.85 TECU for Galileo E1 CBOC. Dual-frequency phase combinations provided RMS values of 0.03 TECU for Galileo E1/E5, 0.03 and 0.07 TECU for GPS L1/L2 and L1/L5. At low elevations, E5 AltBOC provided at least twice less single-frequency TEC noise as compared with data obtained from E5a or E5b. The short dataset of our study could limit the obtained estimates; however, we expect that the AltBOC single-frequency TEC will still surpass the BPSK analogue in noise parameters when the solar cycle evolves and geomagnetic activity increases. Therefore, AltBOC signals could advance geoscience.

Double-thin-shell approach to deriving total electron content from GNSS signals and implications for ionospheric dynamics near the magnetic equator

A new technique was developed to estimate the ionospheric total electron content (TEC) from Global Navigation Satellite System (GNSS) satellite signals. The vertically distributed electron density was parameterized by two thin-shell layers (double-shell approach). The spatiotemporal variation of TEC (strictly speaking, partial electron content) associated with each shell was approximated by the functional fitting of spherical surface harmonics. The major improvements over the conventional single-shell approach were as follows: (1) the precise estimation of TEC was achieved; (2) the estimated TEC was less dependent on the choice of shell heights; and (3) the equatorial anomaly was captured more correctly. Furthermore, higher and lower shells exhibited a different pattern of local time vs latitude variation, providing information on the ionosphere–thermosphere dynamics.

Statistical analysis of ionospheric total electron content (TEC): long-term estimation of extreme TEC in Japan

Ionospheric total electron content (TEC) is one of the key parameters for users of radio-based systems, such as the Global Navigation Satellite System, high-frequency communication systems, and space-based remote sensing systems, since total ionospheric delay is proportional to TEC through the propagation path. It is important to know extreme TEC values in readiness for hazardous ionospheric conditions. The purpose of this study is to estimate extreme TEC values with occurrences of once per year, 10 years, and hundred years in Japan. In order to estimate the extreme values of TEC, a cumulative distribution function of daily TEC is derived using 22 years of TEC data from 1997 to 2018. The extreme values corresponding to once per year and 10 years are 90 and 110 TECU, respectively, in Tokyo, Japan. On the other hand, the 22-year data set is not sufficient to estimate the once-per-100-year value. Thus, we use the 62-year data set of manually scaled ionosonde data for the critical frequency of the F-layer (foF2) at Kokubunji in Tokyo. First, we study the relationship between TEC and foF2 for 22 years and investigate the slab thickness. Then the result is applied to the statistical distribution of foF2 data for 62 years. In this study, two methods are applied to estimate the extreme TEC value. In the first method, the distribution of slab thickness is artificially inflated to estimate extreme TEC values. In the second method, extreme slab thicknesses are applied to estimate extreme TEC values. The result shows that the once-per-100-year TEC is about 150–190 TECU at Tokyo. The value is also estimated to be 180–230 TECU in Kagoshima and 120–150 TECU in Hokkaido, in the southern and northern parts of Japan, respectively.

TEC derived from local GPS network in Pakistan and comparison with IRI-2016 and IRI-PLAS 2017

The existing global network of continuously operating stand-alone GNSS reference stations provides an opportunity to estimate total electron content (TEC) from raw Global Positioning System (GPS) measurements. The TEC driven from a local GPS network in Pakistan was compared to two international models: IRI-2016 and IRI-PLAS 2017. The performance was analyzed statistically based on residual analysis, RMSE and correlation. It is observed that the TEC estimated by all three methods follows the same diurnal trend where it maximizes around noon ( $$12:00 {-} 14:00 LT$$ ) and reduces in the afternoon ( $$15:00 {-} 17:00 LT$$ ). Both empirical models provide a better estimation of nighttime TEC as compared to daytime TEC and exhibit maximum deviation in the month of April with the lowest deviation in December. The IRI-2016 underestimates TEC by $$5 - 10 TECU,$$ whereas the IRI-PLAS 2017 overestimates TEC by $$10 - 22 TECU$$ . However, the IRI-2016 conforms better to GPS-TEC ( $$\overline{\gamma } = 0.9710$$ ) as compared to IRI-PLAS 2017 ( $$\overline{\gamma } = 0.8337$$ ). The study shows that local GNSS stations in collaboration with TEC estimated from global models may be used in development of an efficient local TEC model over Pakistan which will not only assist in local ionosphere studies but also aid in improving the positioning accuracy.