NeQuick Model Research Articles

New technique for calculating the ionospheric phase advance and dual frequency mode of measuring ionospheric TEC

The earlier developed alternative technique for calculating the ionospheric contribution into the full phase of the signal on the transionospheric paths of propagation, based on the perturbation theory in spherical co-ordinates with the spherically symmetric inhomogeneous zero-order approximation for the ionosphere, is further extended in order to apply it to the two-frequency mode of operation of GNSS. When doing this, the method itself is additionally validated and verified in the numerical experiment, where the reconstruction of the slant TEC calculated by the alternative technique for the two-frequency mode of operation is compared to that directly generated by the NeQuick model of the ionosphere.

Independent temporal and spatial variation analysis of ionospheric TEC over Asia-Pacific area based on BDS GEO satellites

GPS has been widely used to monitor ionospheric total electron content (TEC) variations. However, GPS-derived TEC contains ionospheric horizontal gradient information due to the motion of GPS satellites. As a result, the temporal and spatial variation information is mixed. With the advent of the geostationary earth orbit (GEO) of the BeiDou navigation satellite system (BDS), observations from BDS GEO satellites provide a new opportunity for independent research on the temporal and spatial variations of the ionospheric TEC. Furthermore, the GEO satellite also enables continuous and long-term TEC monitoring. Due to its higher orbit, the BDS GEO-derived TEC also contains more plasmaspheric electron content. In this study, the temporal and spatial variation characteristics of the ionospheric TEC derived from the BDS GEO satellites over the Asia-Pacific area are investigated. The achievable TEC theoretical accuracy from the BDS GEO measurements is first deduced. The TEC time series at 26 BDS stations over the Asia-Pacific area is then analyzed. Results acquired from the vertical TEC (VTEC) observations in 2017 indicate obvious periodic variations and spatial variations with a semi-annual anomaly. Through an analysis of the VTEC series over a span of five years, it is revealed that the long-term TEC variations are quite dependent on the solar activity intensity in terms of the F10.7 index. Besides, the BDS GEO-derived VTEC variation trend is consistent with those acquired from the global ionospheric map (GIM) and the NeQuick model. However, significant biases exist at some stations due to uneven accuracy of the two global ionospheric models. The maximum RMS discrepancies reach 4.3 TECU and 9.9 TECU for the GIM and NeQuick, respectively.

On the Analytical Description of the Topside Ionosphere by NeQuick: Modeling the Scale Height Through COSMIC/FORMOSAT-3 Selected Data

The analytical description of the topside ionosphere included in the NeQuick model is studied in detail. First, the modeled scale height behavior is analyzed at infinity and for the lowest part of the topside region; in the latter case, the analysis is done through an expansion in Taylor series near the F2-layer peak. Moreover, the significant influence of the three NeQuick topside parameters in the modeling of the topside profile is investigated in detail and, in particular, it is shown that for the lowest part of the topside the model assumes a linearly increasing trend of the topside scale height. Second, the topside formulation is inverted to derive a fully analytical expression of the topside scale height as a function of the electron density and F2-layer peak parameters. This expression has been applied to a selected and very reliable dataset of Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC)/FORMOSAT-3 radio occultation profiles. Statistical analyses strongly support the hypothesis embedded in NeQuick regarding the linear trend of the topside scale height for the lowest part of the topside.

Neural network based model for global Total Electron Content forecasting

We introduce a novel empirical model to forecast, 24 h in advance, the Total Electron Content (TEC) at global scale. The technique leverages on the Global Ionospheric Map (GIM), provided by the International GNSS Service (IGS), and applies a nonlinear autoregressive neural network with external input (NARX) to selected GIM grid points for the 24 h single-point TEC forecasting, taking into account the actual and forecasted geomagnetic conditions. To extend the forecasting at a global scale, the technique makes use of the NeQuick2 Model fed by an effective sunspot number R12 (R12eff), estimated by minimizing the root mean square error (RMSE) between NARX output and NeQuick2 applied at the same GIM grid points. The novel approach is able to reproduce the features of the ionosphere especially during disturbed periods. The performance of the forecasting approach is extensively tested under different geospatial conditions, against both TEC maps products by UPC (Universitat Politècnica de Catalunya) and independent TEC data from Jason-3 spacecraft. The testing results are very satisfactory in terms of RMSE, as it has been found to range between 3 and 5 TECu. RMSE depend on the latitude sectors, time of the day, geomagnetic conditions, and provide a statistical estimation of the accuracy of the 24-h forecasting technique even over the oceans. The validation of the forecasting during five geomagnetic storms reveals that the model performance is not deteriorated during disturbed periods. This 24-h empirical approach is currently implemented on the Ionosphere Prediction Service (IPS), a prototype platform to support different classes of GNSS users.

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.

Jeomanyetik fırtına süresince NeQuick2 Modelinin Performansı

The aim of this study is to evaluate the performance of NeQuick 2 model during geomagnetic storm process. For this purpose, vertical total electron content (VTEC) values obtained from NeQuick 2 model and GPS (Global Positioning System) receiver were compared for five stations selected from 5 different latitude regions during 05-09 September 2017. Comparison was made by correlation, root mean square error (RMSE) and difference taking methods. The variation of VTEC values obtained by NeQuick 2 and GPS is generally similar, although there are phase shifts and amplitude differences. The maximum correlation was observed in the equator region on the quiet days before the storm (September 5-6), but the correlation coefficient decreased as it moved away from the equator. The maximum correlation coefficient was calculated at the mid-latitude of the southern hemisphere during the initial, main and return phases of the storm. In addition, the lowest correlation was determined at high latitudes of the northern hemisphere. At all stations (except NYAL station on 05, 07, 08 / 09/2017), the maximum value of the calculated difference is smaller than the minimum value. When the GPS VTEC values are higher than the NeQuick 2 model values, the difference is generally low, on the contrary when the NeQuick 2 model values are greater than the GPS VTEC values, the difference is quite large. This shows that the NeQuick 2 model generally overestimates the TEC values

The Calculation and Analysis of the Total Electron Content Over Different Latitudes and Seasons Using the Numerical Trapezoidal and Simpson Methods

It has been shown in ionospheric research that calculation of the total electron content (TEC) is an important factor in global navigation system. In this study, TEC calculation was performed over Baghdad city, Iraq, using a combination of two numerical methods called composite Simpson and composite Trapezoidal methods. TEC was calculated using the line integral of the electron density derived from the International reference ionosphere IRI2012 and NeQuick2 models from 70 to 2000 km above the earth surface. The hour of the day and the day number of the year, R12, were chosen as inputs for the calculation techniques to take into account latitudinal, diurnal and seasonal variation of TEC. The results of latitudinal variation of TEC show anomally called equatorial ionization anomally which presents two crests about the geomagnetic equators. The mean absolute percent errors MAPE for two numerical methods using the electron density profiles shown above were 0.0253, 0.02273 and 0.0213, 0.0124 respectively. The results of seasonal variation of TEC show a larger values for spring and autumn equinoxes other than for summer and winter seasons. The MAPE for autumn equinox has the smallest value than for summer, winter seasons and spring equinox. The MAPE for spring equinox equals to 0.01093 and 0.01015 for Simpson and Trapezoidal methods respectively. For autumn, summer and winter, the MAPE equals to 0.005825 and 0.006629 and 0.04682 and 0.0454, 0.01253 and 0.01231 for Simpson and Trapezoidal methods respectively.

Performance of NeQuick-2, IRI-Plas 2017 and GIM models over Ethiopia during varying solar activity periods

This paper investigates the performance of NeQuick-2, the latest version of International Reference Ionosphere IRI extended to the Plasmasphere (IRI-Plas 2017), and Global Ionospheric Map (GIM) models over four stations deployed in Ethiopia during medium, high, and low solar activity periods. The monthly and seasonal mean diurnal variations of Vertical Total Electron Content (VTEC) derived from NeQuick-2, IRI-Plas 2017 and GIM models were compared with the GPS-VTEC values in terms of Root-Mean-Square Errors (RMSE) and correlation coefficients (r). It was found that the monthly and seasonal mean diurnal VTEC variations agree fairly well with the GPS-VTEC at all stations although with some offsets. For the entire years of the study, the highest monthly mean VTEC variation is observed during equinox months, whereas minimum in the solstice months. The NeQuick-2 model monthly and seasonal mean VTEC output were generally better than IRI-Plas 2017 and GIM models output in most of the stations during medium solar activity year of 2012. For all models, the significant discrepancy (i.e, overestimations or underestimations) is observed during daytimes and seasons of high solar activities. In some cases, the IRI-Plas 2017 model displayed poor performance during medium and low solar activity periods, while it showed a better agreement for some stations (e.g. asos, armi, and bdmt) during high solar activity phase (especially in March equinox and December solstice). The performance of GIM model was good for most of the stations during low-solar activity year of 2016 and during the study years for adis, while it has poor performance during the periods of high solar activity year of 2014. All models correlated well, although GIM model was highly correlated with the GPS-VTEC value (r ≥0.99). The IRI-Plas 2017 model correlated better with the GPS-VTEC than NeQuick-2 model during the study years. Moreover, the performance of IRI-Plas 2017 model was better during high than low and medium periods of solar activity years. The GIM model has better performance for most stations (e.g. adis, asos, and bdmt) over the study region during low-solar activity period.

The ESA Swarm mission to help ionospheric modeling: a new NeQuick topside formulation for mid-latitude regions

The ionospheric topside representation made by the NeQuick model is improved by correcting the H0 parameter used by the model to calculate the topside scale height. The task is accomplished by fitting the NeQuick topside analytical function through two anchor points: the F2-layer absolute electron density maximum; the electron density value as measured by Swarm satellites from December 2013 to September 2018. Specifically, two-dimensional grids of H0 as a function of foF2 and hmF2 are obtained, one by employing data from Swarm A and Swarm C, both flying at about 460 km of altitude, and the other one by employing data from Swarm B, flying at about 520 km of altitude. These two grids are used to calculate corrected values of H0, which allows a more reliable description of the topside region. The new NeQuick formulation is statistically validated by comparing corresponding modeled vertical total electron content values to those derived from COSMIC/FORMOSAT-3 measured Radio Occultation profiles, and those measured by Swarm satellites. The results show that the proposed formulation significantly improves the topside description made by the NeQuick model at mid latitudes, for both high and low solar activities. The International Reference Ionosphere model might benefit of its inclusion.

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.

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 the Plasma Frequency for F2-Region Using Modified Chapman Function and NeQuick2 Model over Different Geographical Locations and Months

Modeling the Plasma Frequency for F2-Region Using Modified Chapman Function and NeQuick2 Model over Different Geographical Locations and Months

Densidad Electronica a 600 Km de Altitud. Comparacion de las Mediciones del Satelite Hinotori y las Predicciones del Modelo Nequick2.

En el presente trabajo se analizó el desempeño del modelo ionosférico NeQuick2 para predecir los valores de densidad de electrones libres (Ne) a 600 Km de altura, en un periodo de alta actividad solar y para las latitudes geomagnéticas -15°, 0° y +15°, las cuales corresponden a la franja de la anomalía ecuatorial.Las predicciones del modelo, fueron comparadas con datos de mediciones de Ne, obtenidas por el satélite japonés Hinotori; que realizó mediciones desde Febrero de 1981 hasta Junio de 1982. Solo se consideraron los registros con valores de F10.7 entre 63 y 193 para seguir recomendaciones de la ITU incluidas en Modelo NeQuick2, lo cual dejo un total de más de 450 mil registros a analizar.Los resultados obtenidos en este trabajo sugieren la necesidad de realizar estudios adicionales que lleven a una mejor representación del perfil de tope de Ne dada por el modelo.

Assessment of NeQuick and IRI-2016 models during different geomagnetic activities in global scale: Comparison with GPS-TEC, dSTEC, Jason-TEC and GIM

The range delay induced by the Earth’s ionosphere is one of main errors affecting the positioning performance of Global Navigation Satellite System (GNSS). It is very significant to analyze the performance of the three-dimensional ionospheric models under different geomagnetic conditions using different methods. With the dual-frequency GPS measurements obtained from 83 globally distributed receivers of the International GNSS Service (IGS), we analyzed the performance of different three-dimensional ionospheric models, i.e. the original NeQuick2, the re-estimated NeQuickC and IRI-2016, under different ionospheric conditions. The absolute GPS-derived total electron contents (TECs), the difference of slant TEC observed in independent ground reference stations (dSTEC), the TEC derived from Jason-2 and the absolute TECs calculated from Global Ionospheric Map (GIM) are selected as reference. The validations against GPS-TEC and GIM-TEC indicate that NeQuickC can mitigate ionospheric delay by 70–76% under different geomagnetic activity levels on a global scale, which is 7–16% higher than that of NeQuick2 model, while IRI-2016 can only correct about 50% of the ionospheric delay. The validations against GPS-dSTEC presented that the NeQuickC model can make a good representation of the subtle variation in the ionospheric TEC. The validations against Jason TEC indicate that the relative error from the NeQuickC model is about 10% smaller than that from other two models over oceanic regions. The results show that the NeQuickC presents the best performance during different ionospheric activities, and the performance of those models during perturbed period is approximately 2–3 times worse than that during the quiet period.

Comparacion entre Valores de Vtec Predichos por el Modelo Nequick2 y los Obtenidos a Partir de Gps sobre Boulder durante muy baja actividad Solar

Una especificación confiable del estado de la ionósfera dada por modelos empíricos es importante para mitigar los efectos que esta zona atmosférica produce sobre las operaciones de los sistemas de posicionamiento y navegación basadas en satélites.Este estudio evalúa la capacidad del modelo NeQuick2 para predecir el contenido electrónico vertical total (VTEC), hasta la altura de los satélites GPS, sobre Boulder (40,00°N, 254,75°E), durante una época de muy baja actividad solar. Para ello se comparan las predicciones del modelo con valores de VTEC obtenidos a partir de señales de satélites GPS, publicados por el National Geophysical Data Center (NGDC) de EEUU.Teniendo en cuenta las incertezas de los valores de GPS VTEC publicados por el NGDC, los resultados muestran que el modelo estudiado, en general, se comporta como un buen predictor del contenido electrónico total en las condiciones solares consideradas.

Erratum to the paper on “Nequick2 Model Behaviour for Global Ionospheric Delay Mitigation During Solar Cycle-24”

Erratum to the paper on “Nequick2 Model Behaviour for Global Ionospheric Delay Mitigation During Solar Cycle-24”

Ionospheric TEC variation over Manama, Bahrain and comparison with NeQuick-2 model

This paper presents the ionospheric total electron content (TEC) variation over Manama city of Bahrain using GNSS observables from International GNSS Services (IGS) station at Manama, Bahrain during the period from January 2016 to December 2017. To understand the behavior of TEC variability, the diurnal, monthly and seasonal vertical TEC (VTEC) variations are studied and subsequently compared with NeQuick-2 model estimations. Diurnal VTEC variation reveals a diurnal peak level of about 14 TECU around 09.00 UT and declines thereafter to reach a level of about 5 TECU around 20.00 UT. However, the comparison study confirms the NeQuick-2 model overestimating the GNSS-VTEC irrespective of time of observation during the day. Monthly behavior of VTEC variation reflects that the NeQuick model is well estimated with GNSS-VTEC during November 2016 and January, February and October months in 2017. The magnitude of variations depicts about 30 to 35 TECU (the highest values) during September 2017 and three continuous months February to April in 2016, while it shows about 10 TECU (the lowest value) during January and December months of 2017, November and December months of 2016. Seasonal VTEC variation shows the underestimation of NeQuick-2 model during the June solstice for the years 2016 and 2017, about 10 TECU. It is notable that NeQuick model shows almost good agreement during the March equinox and December solstice in spite of departure in magnitude difference.

Nequick2 Model Behaviour for Global Ionospheric Delay Mitigation During Solar Cycle-24

Abstract The ionospheric delay is the major current source of potential range delay for single-frequency GNSS users. Different ionospheric delay mitigation methods have been developed to mitigate the ionospheric delay effects for single-frequency users. The NeQuick is a quick-run ionospheric electron density model particularly designed for trans-ionospheric propagation applications developed at the Aeronomy and Radio propagation Laboratory of the Abdus Salam International Centre for Theoretical Physics (ICTP), Italy. NeQuick2 is the latest version of the NeQuick ionosphere electron density model. NeQuick model been used by the European Space Agency (ESA) European Geostationary Navigation Overlay Service (EGNOS) project for assessment analysis and has been adopted for single-frequency positioning applications in the frame work of the European satellite navigation system (Galileo). NeQuick2 model adopted modifications related to the modeling of the F1 layer peak electron density, height and thickness parameter. Also, a new formulation of the shape parameter k has been adopted. This paper presents a global study for the behavior of the modified NeQuick2 model. The zenith ionospheric range delay correction by the model has been assessed using the highly accurate IGS-Global Ionospheric Maps (IGS-GIMs) for two different-latitude stations (Aswan, Egypt) (low-latitude) (24.1o N) and (Helsinki, Finland) (high-latitude) (60.2o N). The study was carried out during current solar cycle-24 over three different months that each of them reflects a different state of solar activity. It can be concluded that NeQuick2 model globally presents overestimation for ionospheric delay for quiet and medium ionospheric activity states respectively, while the model presents underestimation for high activity state of the ionosphere layer.

Evaluation of the IRI-2016 and NeQuick electron content specification by COSMIC GPS radio occultation, ground-based GPS and Jason-2 joint altimeter/GPS observations

We examined performance of two empirical profile-based ionospheric models, namely IRI-2016 and NeQuick-2, in electron content (EC) and total electron content (TEC) representation for different seasons and levels of solar activity. We derived and analyzed EC estimates in several representative altitudinal intervals for the ionosphere and the plasmasphere from the COSMIC GPS radio occultation, ground-based GPS and Jason-2 joint altimeter/GPS observations. It allows us to estimate a quantitative impact of the ionospheric electron density profiles formulation in several altitudinal intervals and to examine the source of the model-data discrepancies of the EC specification from the bottom-side ionosphere towards the GPS orbit altitudes. The most pronounced model-data differences were found at the low latitude region as related to the equatorial ionization anomaly appearance. Both the IRI-2016 and NeQuick-2 models tend to overestimate the daytime ionospheric EC and TEC at low latitudes during all seasons of low solar activity. On the contrary, during high solar activity the model results underestimated the EC/TEC observations at low latitudes. We found that both models underestimated the EC for the topside ionosphere and plasmasphere regions for all levels of solar activity. For low solar activity, the underestimated EC from the topside ionosphere and plasmasphere can compensate the overestimation of the ionospheric EC and, consequently, can slightly decrease the resulted model overestimation of the ground-based TEC. For high solar activity, the underestimated EC from the topside ionosphere and plasmasphere leads to a strengthening of the model underestimation of the ground-based TEC values. We demonstrated that the major source of the model-data discrepancies in the EC/TEC domain comes from the topside ionosphere/plasmasphere system.

Refinement of global ionospheric coefficients for GNSS applications: Methodology and results

We developed the methodology for the optimal estimation of global ionospheric coefficients of the current Global Navigation Satellite Systems (GNSSs), including the eight- and ten-parameter Klobuchar-like as well as NeQuick models. The ionospheric coefficients of those correction models are calculated from two sets of globally distributed tracking stations of the International GNSS Services (IGS). Performance of the re-estimated Klobuchar-like and NeQuick coefficients are validated during 2002–2014 over the continental and oceanic areas, respectively. Over the continental areas, GPS TECs derived from 40 ground GPS receivers are selected as reference. The eight-, ten-parameter Klobuchar-like and NeQuick models can mitigate the ionospheric delay by 65.8, 67.3 and 75.0%, respectively. Over the global oceans, the independent TECs derived from Jason-1&2 altimeters are used as reference. The re-estimated ionospheric correction models can mitigate 56.1–66.7% of the delay errors. Compared to the original GPS Ionospheric Correction Algorithm (ICA), performance of those eight-, ten-parameter Klobuchar-like and NeQuick models has improved 3.4, 5.9 and 13.4% during the whole test period, respectively. The methodology developed here takes the advantage of high-quality ionospheric TECs derived from the global network of GNSS receivers. The re-estimated ionospheric coefficients can be used as precise ionospheric products to monitor and assess GNSS broadcast ionospheric parameters and to improve the performance of various single-frequency GNSS applications.