Machine learning based approach for modeling and forecasting of GPS–TEC during diverse solar phase periods

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.

The Total Electron Content (TEC) depletion near the equatorial ionization anomaly crest region in the Indian ionospheric sector has been analyzed during the year March 2005 to February 2006, and May 2016 to August 2017, low solar activity periods of 23 rd and 24 th solar cycle respectively.TEC data from March 2005 to February 2006 is recorded by GPS Ionospheric Scintillation and TEC Monitor (GISTM) GSV4004A and data from May 2016 to August 2017 is obtained from a multifrequency multi-constellation Global Navigation Satellite System (GNSS) receiver installed at Bhopal (23.2 N, 77.4 E & MLAT 14.8 N).TEC depletions have long been recognized as one of the most prominent concerns of space weather as they produce intense scintillation in trans-ionospheric satellite radio signals.All the TEC depletion in the present study occurred in pre-midnight hours and they are more frequent in equinox months during both solar cycles.Among all the events, the severe depletion in TEC was observed on magnetically disturbed day i.e. on 25 October 2016 which may be due to the occurrence of plasma bubble.From ~2 to ~43 TECU and ~5 to ~20 TECU depletions has been detected for the satellite passes along the line of sight of the signal for low solar activity period of 24 th and 23 rd solar cycle respectively.TEC depletions also show good correspondence with the occurrence of scintillation patches.Rate of change of TEC Index (ROTI) measurements are used to predict the presence of scintillation causing irregularities and its values show the strength of irregularity.Losses of lock were also detected during the encounter of the irregularity when the depletion in TEC is greater than 5 TECU.Results are discussed in terms of possible source mechanism responsible for the occurrence of plasma density depletion.

Prediction of global positioning system total electron content using Neural Networks over South Africa

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.

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

The ionosphere widely affects Global Navigation Satellite Systems (GNSS) applications, inducing among others a delay in GNSS measurements. This delay is closely linked to the Total Electron Content (TEC) of the ionosphere, a major parameter which can hence be monitored using GNSS. To this extent, phase measurements are taken as a basis for their lower noise level. Levelling strategies have then to be defined for the phase measurements are obtained with an initial unknown number of cycles called ambiguity. The most common technique, referred to as carrier-to-code levelling, consists in using the differences between code and phase measurements and their average on a continuous set of epochs. This option, chosen at the Royal Meteorological Institute (RMI) of Belgium to compute TEC for Belgian GPS stations, requires code hardware delays estimation. Another has been proposed which takes benefit from Global Ionospheric Maps (GIMs) to compute a reference TEC used for ambiguity resolution. In order to understand the consequences of using one method or the other, we compare slant TEC data obtained from both techniques for a mid-latitude station (Brussels) during a high solar activity period (2002). We observed large differences (6.8 TECu on average) showing features apparently related to ionospheric and geomagnetic activity. We attribute these observations to a combination of effects originating in code delays estimation, multipath and noise as well as GIMs errors. We try to differentiate between these effects by focusing on several days and satellites. We concentrate for example on days presenting large TEC differences and geomagnetic disturbances simultaneously (or not) or on satellites displaying recurrent patterns on consecutive days. Finally we highlight the impact of the choice of GIMs involved in sTEC calibration. To this extent, we analyse vertical TEC statistics showing a general underestimation from RMI data. The highest bias (5.8 TECu) is obtained for the UPC GIMs used in the second levelling technique.

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 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.

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.

<p>The development of space-geodetic observation techniques has brought out a wide range of applications such as positioning and navigation, where the Global Navigation Satellite System (GNSS) is the main tools to provide surveying measurements in these applications. Though GNSS signals enable the calculation of receiver's position, some errors restrict their accuracy. Among these errors, the ionospheric delay is considered as an important error source in the Standard Point Positioning (SPP) applications. Empirical ionospheric models such as Klobuchar, International Reference Ionosphere (IRI), and NeQuick are often applied for computing the Total Electron Content (TEC) within ionosphere and its equivalent delays. However the simulation and forecasting skills of these models are limited due to the simplified model structures and model sensitivity to the calibration period. In this study, we present a novel sequential Calibration approach based on the Ensemble Kalman Filter (C-EnKF) to improve the performance of TEC estimations for SPP applications. To demonstrate the results, the IRI model is used as our basis and the TEC estimates from 56 IGS stations in Europe are applied as observation. The C-EnKF is applied to calibrate some selected model parameter so that IRI can be tuned over Europe. The numerical assessments are performed against the TEC estimates from dual frequency GNSS measurements and against the final IONEX products (that are available with 11 days delays). Based on the forecasting results (during September 2017), we show that the accuracy of TEC estimates from the C-EnKF is improved in the range of 3.7-64.87% compared to IRI. <strong>Keywords: </strong>Ionosphere, Sequential Calibration, Ensemble Kalman Filter (EnKF), IRI, Total Electron Content (TEC), Standard Point Positioning (SPP), GNSS</p>

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.

This work evaluates the performance of two standard models for specifying Earth's ionospheric parameters, the International Reference Ionosphere (IRI) and the NeQuick model.The performance of these models has been validated for Antarctica (ANT) (High latitude; Geographic: 70.46 S, 11.13 E; Geomagnetic: 62.45 S), Trivandrum (TRV) (Equatorial, Geographic: 8.524 N, 76.936 E; Geomagnetic:0.3N) and Delhi (DEL) (Low latitude, Geographic: 28.637 N, 77.174 E; Geomagnetic:22.4N).For this, the Total Electron Content (TEC) values estimated from these models for the locations are compared with the TEC values derived from the Global Ionospheric Scintillation and TEC Monitoring (GISTM) Systems present at the respective locations for the year 2008 which was at the descending phase of Solar Cycle 23.The results show that the equatorial TEC exhibits semi-annual, annual, and seasonal variations with maximum values appearing during equinoctial months and minimum during solstitial months.The low latitude TEC also exhibits similar variations but at times delayed.Generally, the TEC values produced by the IRI and NeQuick 2 models agree with the observed TEC for TRV and DEL but the models significantly underestimate the TEC at ANT at all times.For Diurnal variation, both the models show a good correlation during the noon time for the equatorial and low latitude stations but not for the high latitude station.For post-sunset and post-midnight periods, quite a disagreement is seen between the models and observed TEC for all three stations.So, it can be said that both IRI and NeQuick 2 models can predict TEC with good correlation in most cases for the Equatorial and Low Latitude stations but are incapable for high latitude regions.

The Global Positioning System (GPS) applications are highly vulnerable to the ionospheric space weather effects. Modelling and forecasting the ionospheric effects such as time delays for GPS signals are important for real time alerts of space weather effects on GPS services. In the present work, the performance of Neural Networks (NN) model is compared with International Reference Ionosphere (IRI) models. The ionospheric Total Electron Content (TEC) observations have been collected during 2015 year, descending phase of 24th solar cycle, over three Indian low latitude GPS stations namely, Bengaluru (Geographic coordinates: 13.02°N and 77.57°E), near to geomagnetic equator, Guntur (Geographic coordinates: 16.37°N and 80.37°E), which is at Equatorial Ionization Anomaly (EIA) and Lucknow (Geographic coordinates: 26.83°N and 80.92°E), which is beyond EIA region. The performance of NN model in predicting the ionospheric TEC values is compared with IRI (IRI-2012 and IRI-2016) models during test period, October–December 2015 over three Indian low latitude regions. It is observed that IRI models (IRI-2012 and IRI-2016) have shown more the temporal differences with GPS-VTEC during sunrise hours compared to sunset hours over three low latitude regions. The performance of IRI-2016 model has apparently better than IRI-2012 model. However, it is observed that IRI-2016 model has large discrepancies over Bengaluru and Guntur station due to high VTEC fluctuations at equatorial and low latitudes. The NN models are well predicted the measured diurnal mean VTEC variations with the less errors, ±5 TECU but the differences of IRI models are ±15 TECU over all the three stations. Later, GPS-data for 10 years, 2009–2018, is collected over Bengaluru station during 24th solar cycle. The performance of NN model is validated during 2016, 2017 and 2018 years over Bengaluru GPS station. The error measurements and experimental results reported that the measured GPS-VTEC values are well predicted by NN model compared to IRI-2016 model over equatorial and low latitude GPS stations.

Evaluation of the improvement of IRI-2016 over IRI-2012 at the India low-latitude region during the ascending phase of cycle 24