A MARS-based method for estimating regional 2-D ionospheric VTEC and receiver differential code bias

The geometry-free linear combination of dual-frequency GNSS reference station ground observations are currently used to build the Vertical Total Electron Content (VTEC) model of the ionosphere. As it is known, besides ionospheric delays, there are differential code bias (DCB) of satellite (SDCB) and receiver (RDCB) in the geometry-free observation equation. The SDCB can be obtained using the International GNSS Service (IGS) analysis centers, but the RDCB for regional and local network receivers are not provided. Therefore, estimating the RDCB and VTEC model accurately and simultaneously is a critical factor investigated by researchers. This study uses Multivariate Adaptive Regression Splines (MARS) to estimate the VTEC approximate model and then substitutes this model in the observation equation to form the normal equation. The least squares method is used to solve the RDCB and VTEC model together. The research findings show that this method has good modeling effectiveness and the estimated RDCB has good reliability. The estimated VTEC model applied to GPS single-frequency precise point positioning has better positioning accuracy in comparison to the IGS global ionosphere map (GIM).     

Regional VTEC modeling with multivariate adaptive regression splines

Different algorithms have been proposed for the modeling of the ionosphere. The most frequently used method is based on the spherical harmonic functions achieving successful results for global modeling but not for the local and regional applications due to the bounded spherical harmonic representation. Irregular data distribution and data gaps cause also difficulties in the global modeling of the ionosphere. In this paper we propose an efficient algorithm with Multivariate Adaptive Regression Splines (MARS) to represent a new non-parametric approach for regional spatio-temporal mapping of the ionospheric electron density using ground-based GPS observations. MARS can handle very large data sets of observations and is an adaptive and flexible method, which can be applied to both linear and non-linear problems. The basis functions are directly obtained from the observations and have space partitioning property resulting in an adaptive model. This property helps to avoid numerical problems and computational inefficiency caused by the number of coefficients, which has to be increased to detect the local variations of the ionosphere. Since the fitting procedure is additive it does not require gridding and is able to process large amounts of data with large gaps. Additionally the model complexity can be controlled by the user via limiting the maximal number of coefficients and the order of products of the basis functions. In this study the MARS algorithm is applied to real data sets over Europe for regional ionosphere modeling. The results are compared with the results of Bernese GPS Software over the same region.     

SHAKING: Adjusted spherical harmonics adding KrigING method for near real-time ionospheric modeling with multi-GNSS observations

Precise positioning based on Global Navigation Satellite System (GNSS) technique requires high accuracy ionospheric total electron content (TEC) correction models to account for the ionospheric path delay errors. We present an adjusted Spherical Harmonics Adding KrigING method (SHAKING) approach for regional ionospheric vertical TEC (VTEC) modeling in real time. In the proposed SHAKING method, the VTEC information over the sparse observation data area is extrapolated by the Adjusted Spherical Harmonic (ASH) function, and the boundary distortion in regional VTEC modeling is corrected by the stochastic VTEC estimated using Kriging interpolation. Using real-time GPS, GLONASS and BDS-2/3 data streams of the Crust Movement Observation Network of China (CMONOC), the SHAKING-based regional ionospheric VTEC maps are re-constructed over China and its boundary regions. Compared to GNSS VTECs derived from the independent stations, the quality of SHAKING solution improves by 13–31% and 6–33% with respect to the ASH-only solution during high and low geomagnetic periods, respectively. Compared to the inverse distance weighting (IDW) generated result, significant quality improved of SHAKING-based VTEC maps is also observed, especially over the edge areas with an improvement of 60–80%. Overall, the proposed SHAKING method exhibits notable advantage over the existing regional VTEC modeling techniques, which can be used for regional TEC modeling and associated high-precision positioning applications.     

The spatio-spectral localization approach to modeling VTEC over the western part of the USA using GPS observations

The precise ionosphere modeling is crucial and remains a challenge for GPS positioning and navigation, as well as many other Earth observation systems. In this research, two approaches have been proposed to model the vertical total electron content (VTEC) of the ionosphere using spherical slepian function. For the two-dimensional case, VTEC has been modeled in a sun-fixed reference frame and the three-dimensional approach based on the system of the three-dimensional base functions has been defined as the tensor product of the spherical slepian function for the longitude and latitude in an Earth-fixed reference frame, and the polynomial B-spline function for time. Rather than the spherical harmonics, the spherical slepian functions can be employed to produce the locally and globally orthogonal bases to optimally represent the data in any arbitrary region up to a given degree. The spherical slepian functions have been applied to the real data obtained from the ground-based GPS observation across the western part of the USA.     

Testing the improvement of performance of the IRI model in the estimation of TEC over the mid-latitude American regions

This paper mainly discusses the improvement of performance of the International Reference Ionosphere (IRI) model in estimating the variation of the Vertical Total Electron Content (VTEC) over the mid latitude American regions during the relatively low (2008–2010) and relatively high (2012) solar activity years. This has been conducted employing the VTEC values obtained from the dual frequency ground based Global Positioning System (GPS) receivers located at Mineral Area Community College, MACC (37.85°N, 269.52°W) and Mississippi County Airport, MAIR (36.85°N, 270.64°W), and the latest versions of the IRI online model (IRI 2007, IRI 2012 and IRI 2016). The study mainly focuses to compare the trend of variability of the monthly and seasonal modeled VTEC values (IRI 2007 VTEC, IRI 2012 VTEC and IRI 2016 VTEC) with the corresponding measured VTEC values (GPS VTEC). The overall results show that the IRI VTEC values (almost in all versions of the model) are generally smaller than the GPS VTEC except after about 15:00 UT (09:00 LT) in the December solstice when the Sun shifts to the high solar activity. On the contrary, overestimations of the VTEC values by the model are observed in traversing from the low solar activity (2008) to high solar activity (2012) phase, especially after about 15:00 UT (09::00 LT) with the IRI 2016 version showing the highest. In general, the IRI 2007 and IRI 2012 versions show similar monthly and seasonal underestimations or overestimations showing that the two versions have almost similar performance. The IRI 2016 version is generally better in capturing both the diurnal and arithmetic mean GPS VTEC values with some exceptional months and seasons as compared to those of the IRI 2007 and IRI 2012 versions.     

An analysis on combined GPS/COMPASS data quality and its effect on single point positioning accuracy under different observing conditions

With the rapid development of the COMPASS system, it is currently capable of providing regional navigation services. In order to test its data quality and performance for single point positioning (SPP), experiments have been conducted under different observing conditions including open sky, under trees, nearby a glass wall, nearby a large area of water, under high-voltage lines and under a signal transmitting tower. To assess the COMPASS data quality, the code multipath, cycle slip occurrence rate and data availability were analyzed and compared to GPS data. The datasets obtained from the experiments have also been utilized to perform combined GPS/COMPASS SPP on an epoch-by-epoch basis using unsmoothed single-frequency code observations. The investigation on the regional navigation performance aims at low-accuracy applications and all tests are made in Changsha, China, using the “SOUTH S82-C” GPS/COMPASS receivers. The results show that adding COMPASS observations can significantly improve the positioning accuracy of single-frequency GPS-only SPP in environments with limited satellite visibility. Since the COMPASS system is still in an initial operational stage, all results are obtained based on a fairly limited amount of data.     

Wavelet modelling in support of IRI

The slant total electron content (STEC) of the ionosphere is defined as the integral of the electron density along the ray-path of the signal between the transmitter and the receiver. So-called geometry free GPS measurements provide information on the electron density, which is basically a four-dimensional function depending on spatial position and time. Since ground-based measurements are not very sensitive to the vertical structure within the atmosphere, the ionosphere is often represented by a spherical layer, where all electrons are concentrated. Then the STEC is transformed into the vertical total electron content (VTEC), which is a three-dimensional function depending on longitude, latitude and time.In our approach, we decompose an ionospheric function, i.e. the electron density or the VTEC, into a reference part computed from a given model like the International Reference Ionosphere (IRI) and an unknown correction term expanded in a multi-dimensional series in terms of localizing base functions. The corresponding series coefficients are calculable from GPS measurements applying parameter estimation procedures. Since the GPS receivers are located rather unbalanced, finer structures are modelable just in regions with a sufficient number of observation sites. Due to the localizing feature of B-spline functions we apply a tensor product spline expansion to model the correction term regionally. Furthermore, the multi-resolution representation derived from wavelet analysis allows monitoring the ionosphere at different resolutions levels. We demonstrate the advantages of this procedure by representing a simulated VTEC data set over South America.     

Response of the ionospheric F-region in the Brazilian sector during the super geomagnetic storm in April 2000 observed by GPS

The response of the ionospheric F-region in the equatorial and low latitude regions in the Brazilian sector during the super geomagnetic storm on 06–07 April 2000 has been studied in the present investigation. The geomagnetic storm reached a minimum D_st of −288 nT at 0100 UT on 07 April. In this paper, we present vertical total electron content (VTEC) and phase fluctuations (in TECU/min) from GPS observations obtained at Imperatriz (5.5°S, 47.5°W; IMPZ), Brasília (15.9°S, 47.9°W; BRAZ), Presidente Prudente (22.12°S, 51.4°W; UEPP), and Porto Alegre (30.1°S, 51.1°W; POAL) during the period 05–08 April. Also, several GPS-based TEC maps are presented from the global GPS network, showing widespread and drastic TEC changes during the different phases of the geomagnetic storm. In addition, ion density measurements on-board the satellite Defense Meteorological Satellite Program (DMSP) F15 orbiting at an altitude of 840 km and the first Republic of China satellite (ROCSAT-1) orbiting at an altitude of 600 km are presented. The observations indicate that one of the orbits of the DMSP satellite is fairly close to the 4 GPS stations and both the DMSP F15 ion-density plots and the phase fluctuations from GPS observations show no ionospheric irregularities in the Brazilian sector before 2358 UT on the night of 06–07 April 2000. During the fast decrease of D_st on 06 April, there is a prompt penetration of electric field of magnetospheric origin resulting in decrease of VTEC at IMPZ, an equatorial station and large increase in VTEC at POAL, a low latitude station. This resulted in strong phase fluctuations on the night of 06–07 April, up to POAL. During the daytime on 07 April during the recovery phase, the VTEC observations show positive ionospheric storm at all the GPS stations, from IMPZ to POAL, and the effect increasing from IMPZ to POAL. This is possibly linked to the equatorward directed meridional wind. During the daytime on 08 April (the recovery phase continues), the VTEC observations show very small negative ionospheric storm at IMPZ but the positive ionospheric storm effect is observed from BRAZ to POAL possibly linked to enhancement of the equatorial ionospheric anomaly.     

Using GPS-TEC data to calibrate VTEC computed with the IRI model over Nigeria

This paper presents the development of a Total Electron Content (TEC) map for the Nigerian ionosphere. In this work, TEC measurements obtained from the AFRL-SCINDA GPS (Air Force Research Laboratory-Scintillation Network Decision Aid, Global Positioning System) equipment installed at Nsukka (6.87°N, 7.38°E) are used to adapt the International Reference Ionosphere (IRI) model for the Nigerian Ionosphere. The map is being developed as a computer program (implemented in the MATLAB programming language) that shows spatial and temporal representations of TEC for the Nigerian ionosphere. The method is aimed at showing how the IRI model can be used to estimate VTEC over wide areas by incorporating GPS measurements. This method is validated by using GPS VTEC data collected from a station in Ilorin (8.50°N, 4.55°E).     

Application of neural networks to South African GPS TEC modelling

The propagation of radio signals in the Earth’s atmosphere is dominantly affected by the ionosphere due to its dispersive nature. Global Positioning System (GPS) data provides relevant information that leads to the derivation of total electron content (TEC) which can be considered as the ionosphere’s measure of ionisation. This paper presents part of a feasibility study for the development of a Neural Network (NN) based model for the prediction of South African GPS derived TEC. The South African GPS receiver network is operated and maintained by the Chief Directorate Surveys and Mapping (CDSM) in Cape Town, South Africa. Vertical total electron content (VTEC) was calculated for four GPS receiver stations using the Adjusted Spherical Harmonic (ASHA) model. Factors that influence TEC were then identified and used to derive input parameters for the NN. The well established factors used are seasonal variation, diurnal variation, solar activity and magnetic activity. Comparison of diurnal predicted TEC values from both the NN model and the International Reference Ionosphere (IRI-2001) with GPS TEC revealed that the IRI provides more accurate predictions than the NN model during the spring equinoxes. However, on average the NN model predicts GPS TEC more accurately than the IRI model over the GPS locations considered within South Africa.     

基于三频数据的北斗卫星导航系统DCB参数精度评估方法

差分码偏差（Differential Code Biases,DCB）参数作为导航电文中重要的一项,是影响用户PNT服务的主要误差源之一。北斗卫星导航系统（后文简称“北斗系统”）发射三个频点的导航信号,在导航电文中需要发播卫星的2个TGD（Timing Group Delay）参数。文章首先介绍了北斗系统卫星DCB参数最小二乘解算与形式误差评估;其次根据北斗系统三频特点,提出了不同频点组合计算垂直方向电离层电子总含量（VTEC）互差的DCB精度定量评估方法,并与IGS(International GNSS Service)提供的GPS卫星DCB精度进行比较;最后,详细分析了DCB参数精度对用户等效距离误差（UERE）计算和定位计算的影响,分别采用卫星出场标定DCB参数和经过解算DCB参数进行评估。实测数据分析结果表明,北斗系统卫星DCB参数解算形式误差与IGS解算GPS卫星DCB参数形式误差相当,但受卫星类型和解算测站的几何分布限制,北斗系统卫星DCB参数解算不确定度相比IGS略差,估计精度优于0.5ns,不同频率组合计算VTEC互差绝对值均值优于0.6TECU。相比采用卫星出场标定值,采用系统解算DCB参数后,双频用户三维位置误差改善13.80%～47.42%。     

GPS电离层反演方法研究及其在地震方面的应用

利用地基GPS数据计算了电离层单球壳模型穿刺点上的垂向总电子含量(VTEC), 根据VTEC和卫星及测站接收机的差分码间偏差DCB的不同时变特性采用了复弧法, 将VTEC作为局部变量(每30 min 一组, 可调), DCB作为一天的全局量进行解算. 在解算的过程中, 充分考虑VTEC的空间分布特性, 利用变异函数通过Kriging插值法建立电离层VTEC的二维格网模型, 并给出了卫星和接收机的差分码间偏差DCB. 通过与IGS结果的比较, 发现其结果可靠, 且时空分辨率和稳定性都有较大提高. 同时, 基于简化的三元样条插值基函数对电离层电子密度进行三维展开, 利用乘型代数重建技术MART算法构建了同批数据的四维层析成像结果, 获得了电离层电子密 度的四维分布. 其结果与CHAMP无线电掩星结果非常一致. 利用上面两种算法又分别对2008年5月长江三角洲地区地基GPS数据进行处理, 简要分析了该时段该地区上空电离层总电子含量和电子密度的变化情况及其对汶川地震的响应.      

A regional tropospheric model for airborne GPS applications

A regional tropospheric model can be constructed using surveys from GPS ground networks. Using this model the tropospheric delays of a kinematic station within the region can be interpolated. However, such a model is generally not suitable for an airborne platform high above the ground networks. In this paper, a method of constructing a regional tropospheric model for airborne GPS applications is described. First, the kinematic station in the air is projected onto the ground. Then the tropospheric delays at projected point are interpolated from those of the ground networks. Finally, the tropospheric delays at projected point are extended upward to the airborne platform using pressure and temperature gradients and humidity exponential function. For validation of this method, the data of airborne campaign carried out by BKG in cooperation with GFZ and BGR 2008 in the northern Alps are used. The results show that GPS kinematic positioning precision in height component can be improved using this method.     

Improved predictions of equatorial TEC for real time applications

It is important to use models developed specifically for the equatorial ionospheric estimation for real-time applications, particularly in Satellite Navigation. This work demonstrates a methodology for improved predictions of VTEC in real time using the model developed for the equatorial ionosphere by the authors. This work has been done using TEC data of the low solar activity period of 2005 obtained using dual frequency GPS receivers installed under the GAGAN project of ISRO. For the purpose, the model is first used in conjunction with Kriging technique. Improvement in accuracy is observed when compared with the estimations from the model alone using the measurements as true reference. Further improvement is obtained by Bayesian combination of these estimates with independent Neural Network based predictions. Statistical performance of improvement is provided. An improvement of ∼1 m in confidence level of estimation of VTEC is obtained.     

Low solar activity variability and IRI 2007 predictability of equatorial Africa GPS TEC

Diurnal, seasonal and latitudinal variations of Vertical Total Electron Content (VTEC) over the equatorial region of the African continent and a comparison with IRI-2007 derived TEC (IRI-TEC), using all three options (namely; NeQuick, IRI01-corr and IRI-2001), are presented in this paper. The variability and comparison are presented for 2009, a year of low solar activity, using data from thirteen Global Positioning System (GPS) receivers. VTEC values were grouped into four seasons namely March Equinox (February, March, April), June Solstice (May, June, July), September Equinox (August, September, October), and December Solstice (November, December, January). VTEC generally increases from 06h00 LT and reaches its maximum value at approximately 15h00–17h00 LT during all seasons and at all locations. The NeQuick and IRI01-corr options of the IRI model predict reasonably well the observed diurnal and seasonal variation patterns of VTEC values. However, the IRI-2001 option gave a relatively poor prediction when compared with the other options. The post-midnight and post-sunset deviations between modeled and observed VTEC could arise because NmF2 or the shape of the electron density profile, or both, are not well predicted by the model; hence some improvements are still required in order to obtain improved predictions of TEC over the equatorial region of the Africa sector.     

Tomographic determination of the spatial distribution of water vapor using GPS observations

With the advent of the GPS navigation system, a promising ground based technique has been introduced which makes it possible to estimate the amount of water vapor in the troposphere from operational GPS networks at relatively low additional costs. While the estimation of the integrated amount is currently well established, the determination of the spatial water vapor distribution and its temporal variation are still a major challenge. To account for the vertical resolution, several tomographic approaches were pursued. We developed the software package AWATOS (atmospheric water vapor tomography software) which is based on the assimilation of double differenced GPS observations. Applying a least-squares inversion, the inhomogeneous spatial distribution of water vapor is determined. An extensive investigation has been carried out in Switzerland. GPS measurements are performed by the dense permanent Swiss national GPS network AGNES of the Swiss Federal Office of Topography (swisstopo). A total of 40 equally distributed water vapor profiles have been estimated on an hourly basis. For the purpose of validation, 22 radiosonde profiles were used at the GPS and meteorological station Payerne. Furthermore, data of the numerical weather model aLMo (alpine model in Switzerland, MeteoSwiss) were compared with the tomographic results. An overall good agreement of the three methods with an rms of better than 1.6 g/m³ absolute humidity was achieved. The results show that AGNES can be used as a dedicated network for the purpose of GPS-tomography, using a horizontal resolution of approximately 50 km and height layers of 300–500 m thickness in the lower troposphere.     

Multi-GNSS contributions to differential code biases determination and regional ionospheric modeling in China

Due to the limited number and uneven distribution globally of Beidou Satellite System (BDS) stations, the contributions of BDS to global ionosphere modeling is still not significant. In order to give a more realistic evaluation of the ability for BDS in ionosphere monitoring and multi-GNSS contributions to the performance of Differential Code Biases (DCBs) determination and ionosphere modeling, we select 22 stations from Crustal Movement Observation Network of China (CMONOC) to assess the result of regional ionospheric model and DCBs estimates over China where the visible satellites and monitoring stations for BDS are comparable to those of GPS/GLONASS. Note that all the 22 stations can track the dual- and triple-frequency GPS, GLONASS, and BDS observations. In this study, seven solutions, i.e., GPS-only (G), GLONASS-only (R), BDS-only (C), GPS + BDS (GC), GPS + GLONASS (GR), GLONASS + BDS (RC), GPS + GLONASS + BDS (GRC), are used to test the regional ionosphere modeling over the experimental area. Moreover, the performances of them using single-frequency precise point positioning (SF-PPP) method are presented. The experimental results indicate that BDS has the same ionospheric monitoring capability as GPS and GLONASS. Meanwhile, multi-GNSS observations can significantly improve the accuracy of the regional ionospheric models compared with that of GPS-only or GLONASS-only or BDS-only, especially over the edge of the tested region which the accuracy of the model is improved by reducing the RMS of the maximum differences from 5–15 to 2–3 TECu. For satellite DCBs estimates of different systems, the accuracy of them can be improved significantly after combining different system observations, which is improved by reducing the STD of GPS satellite DCB from 0.243 to 0.213, 0.172, and 0.165 ns after adding R, C, and RC observations respectively, with an increment of about 12.3%, 29.4%, and 32.2%. The STD of GLONASS satellite DCB improved from 0.353 to 0.304, 0.271, and 0.243 ns after adding G, C, and GC observations, respectively. The STD of BDS satellite DCB reduced from 0.265 to 0.237, 0.237 and 0.229 ns with the addition of G, R and GR systems respectively, and increased by 10.6%, 10.4%, and 13.6%. From the experimental positioning result, it can be seen that the regional ionospheric models with multi-GNSS observations are better than that with a single satellite system model.     

Eliminating negative VTEC in global ionosphere maps using inequality-constrained least squares

Currently, ground-based Global Navigation Satellite System (GNSS) stations of the International GNSS Service (IGS) are distributed unevenly around the world. Most of them are located on the mainland, while only a small part of them are scattered on some islands in the oceans. As a consequence, many unreasonable zero values (in fact negative values) appear in Vertical Total Electron Content (VTEC) of European Space Agency (ESA) and Center for Orbit Determination in Europe (CODE) IONEX products, especially in 2008 and 2009 when the solar activities were rather quiet. To improve this situation, we directly implement non-negative physical constraints of ionosphere for global ionosphere maps (GIM) with spherical harmonic functions. Mathematically, we propose an inequality-constrained least squares method by imposing non-negative inequality constraints in the areas where negative VTEC values may occur to reconstruct GIM models. We then apply the new method to process the IGS data in 2008. The results have shown that the new algorithm efficiently eliminates the unwanted behavior of negative VTEC values, which could otherwise often be seen in the current CODE and ESA GIM products in both middle and high latitude areas of the Southern Hemisphere (45°S∼90°S) and the Northern Hemisphere (50°N∼90°N). About 64% of GPS receivers’ DCBs have been significantly improved. Finally, we compare the GIM results between with and without the inequality constraints, which has clearly shown that the GIM result with inequality constraints is significantly better than that without the inequality constraints. The inequality-constrained GIM result is also highly consistent with the final IGS products in terms of root mean squared (RMS) and mean VTEC.     

Short term variations of total electron content (TEC) fitting to a regional GPS network over the Kingdom of Saudi Arabia (KSA)

The ionosphere is a dispersive medium for radio waves with the refractive index which is a function of frequency and total electron content (TEC). TEC has a strong diurnal variation in addition to monthly, seasonal and solar cycle variations and small and large scale irregularities. Dual frequency GPS observations can be utilized to obtain TEC and investigate its spatial and temporal variations. We here studied short term TEC variations over the Kingdom of Saudi Arabia (KSA). A regional GPS network is formed consisting of 16 sites in and around KSA. GPS observations, acquired between 1st and 11th February 2009, were processed on a daily basis by using the Bernese v5.0 software and IGS final products. The geometry-free zero difference smoothed code observables were used to obtain two hour interval snapshots of TEC and their RMS errors at 0.5 × 0.5 degree grid nodes and regional ionosphere models in a spherical harmonics expansion to degree and order six. The equatorial ionized anomaly (EIA) is recovered in the south of 20°N from 08:00 to 12:00 UT. We found that day-by-day TEC variation is more stable than the night time variation.     

Assessment of improvement of the IRI model over Ethiopia for the modeling of the variability of TEC during the period 2013–2016

This paper discusses the monthly and seasonal variation of the total electron content (TEC) and the improvement of performance of the IRI model in estimating TEC over Ethiopia during the solar maximum (2013–2016) phase employing as reference the GPS derived TEC data inferred from four GPS receivers installed in different regions of Ethiopia; Assosa (geog 10.05°N, 34.55°E, Geom. 7.01°N), Ambo (8.97°N, 37.86°E, Geom. 5.42°N), Nazret (8.57°N, 39.29°E, Geom. 4.81°N) and Arba Minch (6.06°N, 37.56°E, Geom. 2.62°N). The results reveal that, in the years 2013–2016, the highest peak GPS-derived diurnal VTEC is observed in the March equinox in 2015 over Arba Minch station. Moreover, both the arithmetic mean GPS-derived and modelled VTEC values, generally, show maximum and minimum values in the equinoctial and June solstice months, respectively in 2014–2015. However, in 2013, the minimum and maximum arithmetic mean GPS-derived values are observed in the March equinox and December solstice, respectively. The results also show that, even though overestimation of the modelled VTEC has been observed on most of the hours, all versions of the model are generally good to estimate both the monthly and seasonal diurnal hourly VTEC values, especially in the early morning hours (00:00–03:00?UT or 03:00–06:00?LT). However, it has also been shown that the IRI 2007 and IRI 2012 versions generally perform best in matching the diurnal GPS derived TEC values as compared to that of the IRI 2016 version. In addition, the IRI 2012 version with IRI2001 option for the topside electron density shows the highest overestimation of the VTEC as compared to the other options. None of the versions of the IRI model are proved to be able to capture the effects of geomagnetic storms.