Performance of different TEC models to provide GPS ionospheric corrections

Research on longitudinal discrepancies in local ionospheric variability, especially in equatorial and low-latitude regions, is a focal point of interest for the space weather modeling community. The ionosphere over these regions is influenced by complex electrodynamics, wind, and temperature dynamics that can seriously impact dynamic technological systems such as satellite tracking and positioning, satellite radio communication, and navigation control systems. Here, we researched the longitudinal variability in the ionospheric total electron content (TEC) by analyzing observed global positioning system (GPS)-derived TEC values along with those extracted from the most reliable global ionospheric maps (GIMs) and the International Reference Ionosphere (IRI-2016) model at selected stations in the vicinity of the magnetic equator along the American, African, and Asian longitude sectors. The period of study covered the descending (2016–2017) and deep solar minimum (2018–2019) years in the 24th solar cycle. Apart from the decreasing trend of the TEC from the descending to deep solar minimum period irrespective of season and longitude sector, the results showed a relatively higher magnitude of TEC in the African longitude than the other two longitude sectors. Despite evident overestimation and underestimations of TEC in both models, GIM predictions generally looked better in terms of observed variation patterns, especially in the African longitude. The study also highlights the seasonal and semiannual effects of longitudinal variations in TEC, manifesting in local time offsets and some peculiar anomalies, which seemed to be different from previously reported results, especially during the solar minimum years at the three longitude sectors. The insignificant effects of longitudinal variations on the equinoctial asymmetry are attributed to the diverse electron density distribution and ionospheric morphology at the three longitude sectors that will prompt further investigations in the future. The outcomes from this study may augment the past efforts of scientists to understand the seasonal effects of the longitudinal variations in TEC, thereby complementing the improvements of ionospheric representations in global ionosphere models and maps.

Mapping high spatial resolution ionospheric total electron content by integrating Time Series InSAR with International Reference Ionosphere model

Automated daily process for global ionospheric total electron content maps and satellite ocean altimeter ionospheric calibration based on Global Positioning System data

Temporal extrapolation of TEC using WNN during 2007–2018 and comparison against GIM, IRI2016 and Kriging

The international reference ionosphere (IRI) models have been widely used for correcting the ionospheric scintillations at different altitude levels. An evaluation on the performance of VTEC correction from IRI models (version 2007, 2012 and 2016) over Sukkur, Pakistan (27.71º N, 68.85º E) is presented in this work. Total Electron Content (TEC) from IRI models and GPS in 2019 over Sukkur region are compared. The main aim of this comparative analysis is to improve the VTEC in low latitude Sukkur, Pakistan. Moreover, this study will also help us to identify the credible IRI model for the correction of Global Positioning System (GPS) signal in low latitude region in future. The development of more accurate TEC finds useful applications in enhancing the extent to which ionospheric influences on radio signals are corrected. VTEC from GPS and IRI models are collected between May 1, 2019 and May 3, 2019. Additionally, Dst and Kp data are also compared in this work to estimate the geomagnetic storm variations. This study shows a good correlation of 0.83 between VTEC of GPS and IRI 2016. Furthermore, a correlation of 0.82 and 0.78 is also recorded for IRI 2012 and IRI 2007 respectively, with VTEC of GPS. The IRI TEC predictions and GPS-TEC measurements for the studied days reveal the potential of IRI model as a good candidate over Pakistan.

Obtaining ionospheric Total Electron Content (TEC) with high spatial and temporal resolution is crucial for satellite navigation and space weather monitoring. Global Ionospheric Maps (GIMs) are key sources of TEC data. However, the temporal resolution of GIMs from ionosphere associate analysis centers does not satisfy the requirements for space weather monitoring. To address this issue, the Massachusetts Institute of Technology (MIT) Haystack Observatory has provided high‐time‐resolution TEC maps since 1998, using data from ∼5,000 Global Navigation Satellite System (GNSS) tracking stations. However, our research reveals a significant systematic bias in MIT's TEC maps. Unlike the biases between GIMs, it exhibits an unexpected pattern of variation and is also present in comparisons with radio occultation TEC. Further analysis indicates that the systematic bias in MIT TEC decreases with increasing geomagnetic latitude and is correlated with solar activity. In low‐latitude regions, the bias can reach up to 30 TECU, while in high‐latitude regions, it can drop to nearly 0 TECU. During diurnal and seasonal variations, the systematic bias in MIT TEC follows TEC patterns but appears unaffected by small‐scale ionospheric structures. Finally, we analyze the factors potentially contributing to the systematic bias and find that Differential Code Biases (DCBs) provided by MIT exhibits errors of a magnitude comparable to the TEC bias, with a strong correlation between the two. Through further investigation, we confirm that the systematic bias in MIT TEC primarily stems from its DCB estimation strategy and choice of mapping function, and this bias persists both before and after MIT updated its DCB estimation approach.

Dual-frequency global navigation satellite systems (GNSS) observations provide most of the input data for development of global ionosphere map (GIM) of vertical total electron content (VTEC). The international GNSS service (IGS) develops different ionosphere products. The IGS tracking network stations are not homogeneously distributed around the world. The large gaps of this network in Middle East, e.g., Iran plateau, reduce the accuracy of the IGS GIMs over this region. Empirical ionosphere models, such as international reference ionosphere (IRI), also provide coarse forecasts of the VTEC values. This paper presents a new regional VTEC model based on the IRI 2007 and global positioning system (GPS) observations from Iranian Permanent GPS Network. The model consists of a given reference part from IRI model and an unknown correction term. Compactly supported base functions are more appropriate than spherical harmonics in regional ionosphere modeling. Therefore, an unknown correction term was expanded in terms of B-spline functions. The obtained results are validated through comparison with the observed VTEC derived from GPS observations.

Validation of CAS’s final global ionospheric maps during different geomagnetic activities from 2015 to 2017

Global ionospheric mapping (GIM) is a new and emerging technique for determining global ionospheric TEC (total electron content) based on measurements from a worldwide network of Global Positioning System (GPS) receivers. In this study, GIM accuracy in specifying TEC is investigated by comparison with direct ionospheric measurements from the TOPEX altimeter. A climatological model (Bent model) is also used to compare with the TOPEX altimeter data. We find that the GIM technique has much better agreement with TOPEX in TEC measurements, compared with the predictions of the climatological model. The difference between GIM and TOPEX in TEC measurements is very small (less than 1.5 TEC units (TECU)) within a 1500‐km range from a reference GPS station. The RMS gradually increases with increasing distance from the station, while the Bent model shows a constant large RMS, unrelated to any station location. Within a 1000‐km distance of a GPS site (elevation angle > 25°), GIM has a good correlation (R > 0.93) to TOPEX with respect to TEC measurements. The slope of the linear fitting line to the data set from two TOPEX cycles is 44.5° (near the ideal 45°). In the northern hemispheric regions, ionospheric specification by GIM appears to be accurate to within 3‐10 TECU up to 2000+ km away from nearest GPS station (corresponding to ∼1° elevation angle cutoff). Beyond 2000 km, GIM accuracy, on average, is reduced to the Bent model levels. In the equatorial region, the Bent model predictions are systematically lower (∼5.0 TECU) than TOPEX values and often show a saturation at large TEC values. During ionospheric disturbed periods, GIM sometimes shows differences from TOPEX values due to transient variations of the ionosphere. Such problems may be improved by the continuous addition of new GPS stations in data‐sparse regions. Thus, over a GPS station's measurement realm (up to 2000 km in radius), GIM can produce generally accurate TEC values. Through a spatial and temporal extrapolation of GPS‐derived TEC measurements, the GIM technique provides a powerful tool for monitoring global ionospheric features in near real time.

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.

Aside from the ionospheric total electron content (TEC) information, root-mean-square (RMS) maps are also provided as the standard deviations of the corresponding TEC errors in global ionospheric maps (GIMs). As the RMS maps are commonly used as the accuracy indicator of GIMs to optimize the stochastic model of precise point positioning algorithms, it is of crucial importance to investigate the reliability of RMS maps involved in GIMs of different Ionospheric Associated Analysis Centers (IAACs) of the International GNSS Service (IGS), i.e., the integrity of GIMs. We indirectly analyzed the reliability of RMS maps by comparing the actual error of the differential STEC (dSTEC) with the RMS of the dSTEC derived from the RMS maps. With this method, the integrity of seven rapid IGS GIMs (UQRG, CORG, JPRG, WHRG, EHRG, EMRG, and IGRG) and six final GIMs (UPCG, CODG, JPLG, WHUG, ESAG and IGSG) was examined under the maximum and minimum solar activity conditions as well as the geomagnetic storm period. The results reveal that the reliability of the RMS maps is significantly different for the GIMs from different IAACs. Among these GIMs, the values in the RMS maps of UQRG are large, which can be used as ionospheric protection level, while the RMS values in EHRG and ESAG are significantly lower than the realistic RMS. The rapid and final GIMs from CODE, JPL and WHU provide quite reasonable RMS maps. The bounding performance of RMS maps can be influenced by the location of the stations, while the influence of solar activity and the geomagnetic storm is not obvious.

The present work analyzes results coming from global maps of ionospheric total electron content (TEC) obtained from observations and from different empirical models like the International Reference Ionosphere (IRI), the model family developed at Trieste and Graz (NeQuick, COSTprof, and NeUoG‐plas), and the GPS operational model (formulation by J. A. Klobuchar). Since they still appear in the context of assessment studies we have also included “old” models like the Bent model. The attention is focused on situations which occurred in the present period of high solar activity, pointing out features like the equatorial anomaly and polar regions, which are crucial test regions for ionospheric TEC models. Experimental estimates of slant TEC from International GPS Service (IGS) stations have been compared particularly with the predictions of the NeQuick and GPS models. A very simple picture of the ionosphere like the one given by the GPS operational model appears to be insufficient to reproduce the global complex behavior of the ionosphere, as it is needed for assessment studies or for modern operational real‐time corrections of transionospheric propagation errors. The IRI estimates of TEC still present serious problems, essentially owing to the topside under high solar activity conditions, and the model cannot be integrated to heights above 2000 km. With processing resources suitable for real‐time operation, it seems that the NeQuick model can give a more widely reliable picture of the TEC estimated from GPS measurements. Computing times for this model are considerably smaller than for more complex models like NeUoG‐plas.

Investigation of the variability of total electron content (TEC) is one of the most important parameters of the observation and monitoring of space weather, which is the main cause of signal disturbance in space-based communication, positioning, and navigation systems. TEC is defined as the total number of electrons on a ray path. The Global Positioning System (GPS) provides a cost-effective solution for the estimation of TEC. Due to various physical and operational disturbances, TEC may have temporal and spatial domain gaps. Global ionospheric maps (GIMs) provide worldwide TEC with 1- to 2-h temporal resolution and $2.5^{\circ}\, \times 5^{\circ}$ spatial resolution in latitude and longitude, respectively. The GIM-TEC with the highest possible accuracy can be obtained 10 days after the recording of the signals. Therefore, a high-resolution and accurate interpolation of TEC is necessary to image and monitor the regional distribution of TEC in near-real time. In this study, a novel spatiotemporal interpolation algorithm with automatic gridding is developed for 2-D TEC imaging by data fusion of GPS-TEC and GIM-TEC. The algorithm automatically implements optimum spatial resolution and desired temporal resolution with universal kriging with linear trend for midlatitude regions and ordinary kriging for other regions. The theoretical semivariogram function is estimated from GPS network data using a Matern family, whose parameters are determined with a particle swarm optimization algorithm. The developed algorithm is applied to the Turkish National Permanent GPS Network (TNPGN-Active), a dense midlatitude GPS network. For the first time in the literature, high spatial resolution TEC maps are obtained between May 2009 and May 2012 with a 2.5-min temporal update period. These TEC maps will be used to investigate the spatiotemporal variability of the ionosphere over the diurnal and annual trend structure, including seasonal anomalies and geomagnetic and seismic disturbances over ionosphere.

Global ionosphere models may not be accurate enough in regions where there are insufficient observations. Therefore, there is strong interest in regional ionosphere modeling using observations from dual-frequency Global Navigation Satellite System (GNSS) receivers in such regions. This paper presents a data assimilation method for hourly total electron content (TEC) modeling along with estimation of the receivers’ differential code biases (DCBs). For this purpose, first, initial values for slant TEC (STEC) and the receivers’ DCBs are estimated utilizing global ionosphere maps (GIMs). Second, STEC is expanded to a linear combination of spherical radial basis functions with time-dependent coefficients to reduce the number of unknowns, and a constrained least-squares adjustment is applied to resolve the corrected STEC and DCB values in the study area using observations from dual-frequency GNSS receivers. Third, the resolved STEC at ionospheric pierce points (IPPs) are converted to vertical TEC (VTEC) using a mapping function and assimilated into the background provided by spatial and temporal interpolation of GIM. Retrieved VTECs are weighted according to the satellites’ elevation angles, and an objective function is defined to determine the background’s covariance matrix. In this study, the Iranian permanent Global Positioning System (GPS) network is used to construct the regional hourly VTEC model and calculate hourly DCB variations. The proposed method is validated in two ways. First, some of the VTEC values are excluded from the dataset for use as test data and compared with modeling results. The root mean square (RMS) of the constructed regional assimilative model on test data is significantly better than GIM. Second, the RINEX file of Tehran station, whose observations did not play a role in modeling, is corrected using the regional model. The single-frequency positioning results with corrected observations show much better accuracy than GIMs.

A statistical comparison of IRI TEC prediction with GPS TEC measurement over Varanasi, India