Ionosphere Associate Analysis Centers Research Articles

Investigating the Performance of IGS Real-Time Global Ionospheric Maps under Different Solar Conditions

In recent years, real-time global ionospheric map (RT-GIM) products have been actively developed by the international global navigation satellite system (GNSS) service (IGS) and its ionosphere associate analysis centers (IAACs) along with the increase of RT-GNSS multi-frequency and multi-constellation observations. In this study, the accuracy and consistency of three RT-GIM products from the Chinese Academy of Sciences (CAS), Wuhan University (WHU), and IGS are evaluated and analyzed utilizing three validation methods, namely, comparison with JASON-3 vertical total electron content (VTEC), the difference of slant total electron content (dSTEC), and IGS combined final GIM (IGSG) data. The test period was from 1 January 2019 to 31 December 2022, including the different solar activities. First, the comparison with JASON-3 data illustrates that the quality of the three RT-GIM products over oceans is in great consistency with that of the IGSG during different levels of solar activity and the daily mean bias (MEAN) values in low and high solar activities are approximately 5 and 10 TECU, respectively. The root mean square (RMS) values under low and high solar activities can be up to 7 and 12 TECU. Furthermore, the dSTEC validation results present that the MEAN values of RT-GIM products from different IAACs at high- and mid-latitude stations are about 0.5 TECU, which is smaller than those at low-latitude stations at about 1 TECU over continental regions. The standard deviation (STD) and RMS values for various RT-GIM products are within 3 and 4 TECU at low latitudes, respectively. In terms of the comparison with IGSG, the result shows that IGS combined RT-GIM (IRTG) presents better consistency than CAS RT-GIM (CRTG) and WHU RT-GIM (WRTG) in 2021 and 2022, with average annual STD and RMS values of 2.56 and 2.78 TECU, respectively. The daily biases of the RT-GIM products relative to IGSG can reach 4 TECU in high solar activities and the daily STD and RMS values are mainly within the 5 to 6 TECU range, respectively.

Performance and Consistency of Final Global Ionospheric Maps from Different IGS Analysis Centers

Ionospheric delay is one of the most problematic errors in satellite-based positioning data processing. The Global Ionospheric Map (GIM), which is publicly available daily in various analysis centers, is thus vitally important for positioning users. There are variations in the accuracy and consistency of GIMs issued by Ionosphere Associate Analysis Centers (IAACs) due to the differences in ionospheric modeling methods and selected tracking stations. In this study on the International GNSS Service’s (IGS) final GIM, the ionospheric total electron content (TEC) (from 243 global navigation satellite system (GNSS) monitoring stations around the world) and the ionospheric TEC (from the Jason-3 altimeter satellite) are selected as reference. By using these three references, we evaluate the performance and consistency of final GIM products from seven IGS IAACs, including the Chinese Academy of Sciences (CAS), the Center for Orbit Determination in Europe (CODE), Natural Resources Canada (EMR), the European Space Agency (ESA), the Jet Propulsion Laboratory (JPL), Universitat Politècnica de Catalunya (UPC), and Wuhan University (WHU) in the mid-solar activity year (2022) and the low-solar activity year (2020). Firstly, the comparison with the IGS final GIM shows that the consistency of each GIMs is basically the same, with the mean value ranging from −0.3 TECu (total electron content unit) to 1.4 TECu. Secondly, the validation with Jason-3 altimeter satellite shows that the accuracy of several GIMs is almost the same, except for the JPL with the worst accuracy and an overall mean deviation (BIAS) between 2 and 6 TECu. Thirdly, the comparison with VTEC extracted from GNSS monitor stations shows that the CAS has the best accuracy in different latitude bands with a root mean square (RMS) of about 2.2–4.7 TECu. In addition, it is found that the accuracy in areas with more stations for ionospheric modelling is better than those with less stations in different latitude bands; meanwhile, the accuracy is closely related to the modeling methods of different GIMs.

A Novel Approach for Establishing the Global Ionospheric Model With High Spatiotemporal Resolution

The global ionospheric model is the most effective way to study the structure and variation of the global ionosphere. However, the current global ionosphere maps (GIMs) have the defect of low spatiotemporal resolution and cannot reflect the short-term nonlinear changes and small-scale structures of the vertical total electron content (VTEC). This article proposes a new method for establishing a global ionospheric model with high spatiotemporal resolution. The spherical harmonic (SH) expansions are used to model the VTEC observations, and the Kalman filter is used to estimate the model’s coefficients with high accuracy. The method calculates SH coefficients every 5 min, increasing the spatial resolution to 7.2°. Precise determination methods for the state noise covariance matrix and the observation noise covariance matrix in the Kalman filter are also proposed. The model with a high spatiotemporal resolution was established using the observations of 300 global navigation satellite system (GNSS) tracking stations worldwide. The results show that the model with high spatiotemporal resolution can more finely reflect the nonlinear changes of VTEC in a short period and the small-scale structure of the ionosphere. The accuracy of the high-resolution model is validated using high-precision differential slant total electron content (dSTEC) observations from three sets of tracking stations and compared with the final product of three international GNSS service ionosphere associate analysis centers (IGS IAACs). The results show that the accuracy of the high spatiotemporal resolution model in this article is better than the products of IGS IAACs. The research in this article provides a new idea for establishing GIMs with higher spatiotemporal resolution and accuracy.

Evaluation and validation of various rapid GNSS global ionospheric maps over one solar cycle

Compared with the final global ionospheric maps (GIMs) product on a weekly basis, rapid GIMs products on a daily basis have significant improvement in the availability, and are an important ionospheric information source for timely studies of global, regional, or local space weather events and corresponding other applications. Therefore, it is essential to analyze and validate the performance of different rapid products. In this contribution, we evaluate the accuracy and consistency of nine rapid GIMs released by different international GNSS service (IGS) ionosphere associate analysis centers (IAACs) from various aspects in detail, including IGS final GIMs, JASON-2/-3 ionospheric data, the difference of slant total electron content (dSTEC) data over one solar cycle from January 2009 to December 2020. In comparison with the IGS final GIMs, the variation trend of the standard deviation (STD) is consistent with the solar activities, and accompanied by seasonal and annual periodic variations. The mean bias (MEAN) between IGS and individual IAAC is approximately −2 to 2 TECU, and the STD is approximately 0.7 to 4.0 TECU. Over oceanic regions, the MEAN values of the different rapid GIMs with regard to JASON-2 are about 2 to 3 TECU and that of JASON-3 are about 4 to 5 TECU, except for JPRG. The STD performance of the various GIMs relative to the JASON-2 and JASON-3 vertical total electron content (VTEC) is both within 3 TECU. Over continental regions, the validation with the dSTEC data shows that the STD values of the external and internal verification range from 0 to 4.5 TECU and from 0 to 3 TECU, respectively, and the STD performance of the UQRG is the best.

Accuracy of Global Ionosphere Maps in Relation to Their Time Interval

Global ionosphere maps (GIMs) representing ionospheric total electron content (TEC) are applicable in many scientific and engineering applications. However, the GIMs provided by seven Ionosphere Associated Analysis Centers (IAACs) are generated with different temporal resolutions and using different modeling techniques. In this study, we focused on the influence of map time interval on the empirical accuracy of these ionospheric products. We investigated performance of the high-resolution GIMs during high (2014) and low (2018) solar activity periods as well as under geomagnetic storms (19 February 2014 and 17 March 2015). In each of the analyzed periods, GIMs were also assessed over different geomagnetic latitudes. For the evaluation, we used direct comparison of GIM-derived slant TEC (STEC) with dual-frequency GNSS observations obtained from 18 globally distributed stations. In order to perform a comprehensive study, we also evaluated GIMs with respect to altimetry-derived vertical TEC (VTEC) obtained from the Jason-2 and Jason-3 satellites. The study confirmed the influence of GIMs time interval on the provided TEC accuracy, which was particularly evident during high solar activity, geomagnetic storms, and also at low latitudes. The results show that 120-min interval contributes significantly to the accuracy degradation, whereas 60-min one is sufficient to maintain TEC accuracy.

Validation of GNSS-derived global ionosphere maps for different solar activity levels: case studies for years 2014 and 2018

Ionosphere Associate Analysis Centers (IAACs) of the International GNSS Service (IGS) independently produce global ionosphere maps (GIMs) of the total electron content (TEC). The GIMs are based on different modeling techniques, resulting in different TEC levels and accuracies. In this study, we evaluated the accuracy and consistency of the IAAC GIMs during high (2014) and low (2018) solar activity periods of the 24th solar cycle. In our study, we applied two different evaluation methods. First, we carried out a comparison of the GIM-derived slant TEC (STEC) with carrier phase geometry-free combination of GNSS signals obtained from 25 globally distributed stations. Second, vertical TEC (VTEC) from GIMs was compared to altimetry-derived VTEC obtained from the Jason-2 and Jason-3 satellites and complemented for plasmaspheric TEC. The analyzed GIMs obtained STEC RMS values reaching from 1.98 to 3.00 TECU and from 0.96 to 1.29 TECU during 2014 and 2018, respectively. The comparison to altimetry data resulted in VTEC STD values that varied from 3.61 to 5.97 TECU and from 1.92 to 2.78 TECU during 2014 and 2018, respectively. The results show that among the IAACs, the Center for Orbit Determination in Europe global maps performed best in low and high solar activity periods. However, the highest accuracy was obtained by a non-IGS product—UQRG GIMs provided by Universitat Politècnica de Catalunya. It was also shown that the best results were obtained using a modified single layer model mapping function and that the map time interval has a relatively small influence on the resulting map accuracy.

High-Resolution Ionosphere Corrections for Single-Frequency Positioning

The ionosphere is one of the main error sources in positioning and navigation; thus, information about the ionosphere is mandatory for precise modern Global Navigation Satellite System (GNSS) applications. The International GNSS Service (IGS) and its Ionosphere Associated Analysis Centers (IAAC) routinely provide ionospheric information in terms of global ionosphere maps (final GIM). Typically, these products are modeled using series expansion in terms of spherical harmonics (SHs) with a maximum degree of n=15 and are based on post processed observations from Global Navigation Satellite Systems (GNSS), as well as final satellite orbits. However, precise applications such as autonomous driving or precision agriculture require real-time (RT) information about the ionospheric electron content with high spectral and spatial resolution. Ionospheric RT-GIMs are disseminated via Ntrip protocol using the SSR VTEC message of the RTCM. This message can be streamed in RT, but it is limited for the dissemination of coefficients of SHs of lower degrees only. It allows the dissemination of SH coefficients up to a degree of n=16. This suits to most the SH models of the IAACs, but higher spectral degrees or models in terms of B-spline basis functions, voxels, splines and many more cannot be considered. In addition to the SHs, several alternative approaches, e.g., B-splines or Voxels, have proven to be appropriate basis functions for modeling the ionosphere with an enhanced resolution. Providing them using the SSR VTEC message requires a transfer to SHs. In this context, the following questions are discussed based on data of a B-spline model with high spectral resolution; (1) How can the B-spline model be transformed to SHs in order to fit to the RTCM requirements and (2) what is the loss of detail when the B-spline model is converted to SHs of degree of n=16? Furthermore, we discuss (3) what is the maximum necessary SH degree n to convert the given B-spline model and (4) how can the transformation be performed to make it applicable for real-time applications? For a final assessment, we perform both, the dSTEC analysis and a single-frequency positioning in kinematic mode, using the transformed GIMs for correcting the ionospheric delay. The assessment shows that the converted GIMs with degrees n≥30 coincide with the original B-spline model and improve the positioning accuracy significantly.

Performance evaluation of GIMs released by different IGS ionosphere associate analysis centers in ionospheric constrained single-frequency precise point positioning

Single-frequency precise point positioning (PPP) is widely used with the advantage of cost-efficient, while its further development and application are limited by the difficulty of ionospheric delay correction and the long-time convergence, especially for real-time positioning. And the development of high-accuracy ionospheric models plays an important role for the correction of ionospheric delay in single-frequency PPP. In this paper, the final and rapid global ionospheric map (GIM) products released by Chinese Academy of Science (CAS), Center for Orbit Determination in Europe (CODE), European Space Agency (ESA), Jet Propulsion Laboratory (JPL), Universitat Politècnica de Catalunya (UPC), Wuhan University (WHU) and International GNSS Service (IGS) were used as external constraints in static, simulation kinematic and kinematic single-frequency PPP respectively. The performance and practicality of each product were analyzed by using IGS station observation data (September 2017 and January 2018, with different ionospheric activity levels) and a kinematic experiment. The results indicate that GIM products may improve convergence time in most areas of middle and high latitudes of the globe. However, the improvement of convergence time of some regions in low latitudes or near the equator with dense and uniform distributed IGS stations show even better performance than the regions in middle and high latitudes. Comparing with standard PPP (S-PPP), the convergence time of static PPP is reduced about 14–42% and 13–29% with GIM final and rapid products respectively. In simulation kinematic PPP, the convergence time improves 10–43% and 12–25% for final and rapid products respectively. In the kinematic positioning, the addition of external ionospheric constraints may speed up the convergence in the early stage of positioning and improve the accuracy to a certain extent. Among all GIM products, the final products show better performance than that of the rapid products obviously. The GIM products from CAS and CODE and UQRG from UPC express the best performance are recommended to process ionospheric delay in the high-accuracy positioning.

Near real-time modeling of global ionospheric vertical total electron content using hourly IGS data

The International GNSS Service (IGS) has been providing reliable Global Ionospheric Maps (GIMs) since 1998. The Ionosphere Associate Analysis Centers (IAACs) model the global ionospheric Total Electron Content (TEC) and generate the daily GIM products within the context of the IGS. However, the rapid and final daily GIM products have a latency of at least one day and one week or so, respectively. This limits the value of GIM products in real-time GNSS applications. We propose and develop an approach for near real-time modeling of global ionospheric TEC by using the hourly IGS data. We perform an experiment in a real operating environment to generate near real-time GIM (named BUHG) products for more than two years. Final daily GIM products, Precise Point Positioning (PPP) based VTEC resources, and JASON-3 Vertical TEC (VTEC) measurements are collected for testing the performance of BUHG. The results show that the performance of BUHG is very close to that of the daily GIM products. Also, there is good agreement between BUHG and PPP-derived VTEC as well as with JASON-3 VTEC. It is possible that BUHG would be further improved with an increase in available hourly GNSS data.

Global and Regional High-Resolution VTEC Modelling Using a Two-Step B-Spline Approach

The ionosphere is one of the largest error sources in GNSS (Global Navigation Satellite Systems) applications and can cause up to several meters of error in positioning. Especially for single-frequency users, who cannot correct the ionospheric delay, the information about the state of the ionosphere is mandatory. Dual- and multi-frequency GNSS users, on the other hand, can correct the ionospheric effect on their observations by linear combination. However, real-time applications such as autonomous driving or precision farming, require external high accuracy corrections for fast convergence. Mostly, this external information is given in terms of grids or coefficients of the vertical total electron content (VTEC). Globally distributed GNSS stations of different networks, such as the network of the International GNSS Services (IGS), provide a large number of multi-frequency observations which can be used to determine the state of the ionosphere. These data are used to generate Global Ionosphere Maps (GIM). Due to the inhomogeneous global distribution of GNSS real-time stations and especially due to the large data gaps over oceanic areas, the global VTEC models are usually limited in their spatial and spectral resolution. Most of the GIMs are mathematically based on globally defined radial basis functions, i.e., spherical harmonics (SH), with a maximum degree of 15 and provided with a spatial resolution of 2.5 ° × 5 ° in latitude and longitude, respectively. Regional GNSS networks, however, offer dense clusters of observations, which can be used to generate regional VTEC solutions with a higher spectral resolution. In this study, we introduce a two-step model (TSM) comprising a global model as the first step and a regional model as the second step. We apply polynomial and trigonometric B-spline functions to represent the global VTEC. Polynomial B-splines are used for modelling the finer structures of VTEC within selected regions, i.e., the densification areas. The TSM provides both, a global and a regional VTEC map at the same time. In order to study the performance, we apply the developed approach to hourly data of the global IGS network as well as the EUREF network of the European region for St. Patrick storm in March 2015. For the assessment of the generated maps, we use the dSTEC analysis and compare both maps with different global and regional products from the IGS Ionosphere Associated Analysis Centers, e.g., the global product from CODE (Berne, Switzerland) and from UPC (Barcelona, Spain), as well as the regional maps from ROB (Brussels, Belgium). The assessment shows a significant improvement of the regional VTEC representation in the form of the generated TSM maps. Among all other products used for comparison, the developed regional one is of the highest accuracy within the selected time span. Since the numerical tests are performed using hourly data with a latency of one to two hours, the presented procedure is seen as an intermediate step for the generation of high precision regional real-time corrections for modern applications.

Global ionospheric maps forecasting based on an adaptive autoregressive modeling of grid point VTEC values

In the context of the International GNSS Service (IGS), the Ionosphere Associate Analysis Centers (IAACs) generate daily global ionospheric maps (GIMs). Time delays of at least one day for the daily GIMs product limit its value in real-time GNSS applications requiring high precision. Short-time forecasting of GIMs would be a good way to provide a basic background model for single-frequency GNSS users. We propose an improved algorithm for GIMs forecasting based on an adaptive autoregressive (AR) modeling of grid point vertical total electron content (VTEC) values (TVPG). We compare final daily GIMs (BUAG) with precise point positioning (PPP) derived VTEC values (PPPG) and JASON-2 VTEC values (J2TEC) to evaluate the performance of the TVPG and the GIMs based on the prediction of spherical harmonics coefficients (SHPG). The results of the comparison indicate that the TVPG have no obvious overestimate or underestimate with respect to BUAG. While, SHPG overestimates VTEC values in northern latitudes, and underestimates VTEC values in southern latitudes, by more than 2 TECU in some latitudes. Also, according to a comparison with PPPG and J2TEC, the TVPG is essentially better than the SHPG in middle and high latitudes at both low and high solar activity. However, it is worthy of further study to improve the performance of forecast GIMs in low latitudes.

Modelling Global Ionosphere Based on Multi-Frequency, Multi-Constellation GNSS Observations and IRI Model

With the emergence of BeiDou and Galileo as well as the modernization of GPS and GLONASS, more available satellites and signals enhance the capability of Global Navigation Satellite Systems (GNSS) to monitor the ionosphere. However, currently the International GNSS Service (IGS) Ionosphere Associate Analysis Centers (IAACs) just use GPS and GLONASS dual-frequency observations in ionosphere estimation. To better determine the global ionosphere, we used multi-frequency, multi-constellation GNSS observations and a priori International Reference Ionosphere (IRI) to model the ionosphere. The newly estimated ionosphere was represented by a spherical harmonic expansion function with degree and order of 15 in a solar-geomagnetic frame. By collecting more than 300 stations with a global distribution, we processed and analysed two years of data. The estimated ionospheric results were compared with those of IAACs, and the averaged Root Mean Squares (RMS) of Total Electron Content (TEC) differences for different solutions did not exceed 3 TEC Unit (TECU). Through validation by satellite altimetry, it was suggested that the newly established ionosphere had a higher precision than the IGS products. Moreover, compared with IGS ionospheric products, the newly established ionosphere showed a more accurate response to the ionosphere disturbances during the geomagnetic storms.

Estimating satellite and receiver differential code bias using a relative Global Positioning System network

Abstract. Precise total electron content (TEC) is required to produce accurate spatial and temporal resolution of global ionosphere maps (GIMs). Receivers and satellite differential code biases (DCBs) are one of the main error sources in estimating precise TEC from Global Positioning System (GPS) data. Recently, researchers have been interested in developing models and algorithms to compute DCBs of receivers and satellites close to those computed from the Ionosphere Associated Analysis Centers (IAACs). Here we introduce a MATLAB code called Multi Station DCB Estimation (MSDCBE) to calculate satellite and receiver DCBs from GPS data. MSDCBE based on a spherical harmonic function and a geometry-free combination of GPS carrier-phase, pseudo-range code observations, and weighted least squares was applied to solve observation equations and to improve estimation of DCB values. There are many factors affecting the estimated values of DCBs. The first one is the observation weighting function which depends on the satellite elevation angle. The second factor is concerned with estimating DCBs using a single GPS station using the Zero Difference DCB Estimation (ZDDCBE) code or using the GPS network used by the MSDCBE code. The third factor is the number of GPS receivers in the network. Results from MSDCBE were evaluated and compared with data from IAACs and other codes like M_DCB and ZDDCBE. The results of weighted (MSDCBE) least squares show an improvement for estimated DCBs, where mean differences from the Center for Orbit Determination in Europe (CODE) (University of Bern, Switzerland) are less than 0.746 ns. DCBs estimated from the GPS network show better agreement with IAAC than DCBs estimated from precise point positioning (PPP), where the mean differences are less than 0.1477 and 1.1866 ns, respectively. The mean differences of computed DCBs improved by increasing the number of GPS stations in the network.

Accuracy and consistency of different global ionospheric maps released by IGS ionosphere associate analysis centers

Due to the differences of ionospheric modeling methods and selected tracking stations, the accuracy and consistency of Global Ionospheric Maps (GIMs) released by Ionosphere Associate Analysis Centers (IAACs) are different. In this study, we evaluate and analyze in detail the accuracy and consistency of GIMs final products provided by six IAACs from three different aspects. Firstly, the comparison of these GIMs shows that the mean bias (MEAN) is related to the modeling methods of various IAACs. The variation trend of the standard deviation (STD) is consistent with the solar activities, and accompanied by certain seasonal and annual periodic variations. The MEAN between IGS and each center is about −1.3 to 1.0 TECU, and the STD is about 1.4–2.5 TECU. Secondly, the validation with GPS TEC shows that the STD of CODE is the smallest at various latitudes, and the STD is about 0.7–4.5 TECU. Thirdly, The validation with the Jason2 VTEC shows that the STD between Jason2 and IAACs is about 4.4–5.2 TECU. In addition, the STD between Jason2 and six GIMs in the areas with more tracking stations is better than that of the regions with fewer tracking stations in different latitude regions. Regardless of whether the tracking stations are more or less, the MEAN and STD in high solar activity are larger than in low solar activity.

High-resolution vertical total electron content maps based on multi-scale B-spline representations

Abstract. For more than 2 decades the IGS (International GNSS Service) ionosphere associated analysis centers (IAACs) have provided global maps of the vertical total electron content (VTEC). In general, the representation of a 2-D or 3-D function can be performed by means of a series expansion or by using a discretization technique. While in the latter case, pixels or voxels are usually chosen for a spherical function such as VTEC, for a series expansion spherical harmonics (SH) are primarily used as basis functions. The selection of the best suited approach for ionosphere modeling means a trade-off between the distribution of available data and their possibility of representing ionospheric variations with high resolution and high accuracy. Most of the IAACs generate global ionosphere maps (GIMs) based on SH expansions up to the spectral degree n=15 and provide them with a spatial resolution of 2.5∘×5∘ with respect to the latitudinal and longitudinal directions, respectively, and a temporal sampling interval of 2 h. In recent years, it has frequently been claimed that the spatial resolution of the VTEC GIMs has to be increased to a spatial resolution of 1∘×1∘ and to a temporal sampling interval of about 15 min. Enhancing the grid resolution means an interpolation of VTEC values for intermediate points but with no further information about variations in the signal. n=15 in the SH case, for instance, corresponds to a spatial sampling of 12∘×12∘. Consequently, increasing the grid resolution concurrently requires an extension of the spectral content, i.e., to choose a higher SH degree value than 15. Unlike most of the IAACs, the VTEC modeling approach at Deutsches Geodätisches Forschungsinstitut der Technischen Universität München (DGFI-TUM) is based on localizing basis functions, namely tensor products of polynomial and trigonometric B-splines. In this way, not only can data gaps be handled appropriately and sparse normal equation systems be established for the parameter estimation procedure, a multi-scale representation (MSR) can also be set up to determine GIMs of different spectral content directly, by applying the so-called pyramid algorithm, and to perform highly effective data compression techniques. The estimation of the MSR model parameters is finally performed by a Kalman filter driven by near real-time (NRT) GNSS data. Within this paper, we realize the MSR and create multi-scale products based on B-spline scaling, wavelet coefficients and VTEC grid values. We compare these products with different final and rapid products from the IAACs, e.g., the SH model from CODE (Berne) and the voxel solution from UPC (Barcelona). In contrast to the abovementioned products, DGFI-TUM's products are based solely on NRT GNSS observations and ultra-rapid orbits. Nevertheless, we can conclude that the DGFI-TUM's high-resolution product (“othg”) outperforms all products used within the selected time span of investigation, namely September 2017.

On the advantage of stochastic methods in the modeling of ionospheric total electron content: Southeast Asia case study

This article describes an implementation of precise point positioning (PPP) and the least-squares collocation (LSC) method in the modeling of total electron content (TEC) in Southeast Asia, which is characterized by relatively homogeneous Global Navigation Satellite Systems (GNSS) data from International GNSS Service (IGS) stations and the occurrence of the highest TEC anomalies. A homogeneous coverage of the data in this region provides an opportunity for the testing of different spatial modeling methods applied to TEC data. The spherical harmonic expansion (SHE) and spherical splines (SS) have been the most popular mathematical tools for the interpolation of TEC in the ionosphere over the last decades. The developed stochastic model (PPPLSC) is compared with the well-known stochastic global UQRG model, which is interpolated by the ordinary kriging (OK) and CODG global TEC model based on spherical harmonics (SH), and also the IGSG model, which is a combination of several models developed by the IGS Ionosphere Associate Analysis Centers. These four models derived from different approaches are assessed together using self-consistency analysis based on a geometry-free combination of carrier-phase observations, and also using external validation employing dual-frequency altimeter TEC from three low-Earth-orbit satellites.The study implements the LSC modeling technique, which is quite new for TEC and is a valuable step towards increasing the accuracy and resolution of ionosphere models. LSC, similarly to OK, is a stochastic parametric technique, applying the covariance based on data properties. Therefore LSC restores the fullest possible signal in the interpolated model in terms of spatial resolution. Leave-one-out (LOO) validation of the covariance parameters assures optimal interpolation results in the least-squares sense. The covariance matrices of LSC parametrized by LOO validation enable estimation with reliable internal precision for the model. The self-consistency analysis of TEC models with the use of carrier-phase observations proves a better consistency of stochastic models in relation to TEC models based on SHE. The set of statistical values of external comparisons with three altimetry-derived trajectories of TEC observations additionally confirms the advantage of stochastic PPPLSC and UQRG models. The validation results all together indicate a better quality of stochastic models in relation to those based on the summation of spherical functions. The factor that is suspected to decrease the accuracy of the latter models is the loss of the higher frequency signal due to the spectral limitation coming from the low order of SHE applied in IGSG and CODG.

Global Ionosphere Mapping and Differential Code Bias Estimation during Low and High Solar Activity Periods with GIMAS Software

Ionosphere research using the Global Navigation Satellite Systems (GNSS) techniques is a hot topic, with their unprecedented high temporal and spatial sampling rate. We introduced a new GNSS Ionosphere Monitoring and Analysis Software (GIMAS) in order to model the global ionosphere vertical total electron content (VTEC) maps and to estimate the GPS and GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS) satellite and receiver differential code biases (DCBs). The GIMAS-based Global Ionosphere Map (GIM) products during low (day of year from 202 to 231, in 2008) and high (day of year from 050 to 079, in 2014) solar activity periods were investigated and assessed. The results showed that the biases of the GIMAS-based VTEC maps relative to the International GNSS Service (IGS) Ionosphere Associate Analysis Centers (IAACs) VTEC maps ranged from −3.0 to 1.0 TECU (TEC unit) (1 TECU = 1 × 1016 electrons/m2). The standard deviations (STDs) ranged from 0.7 to 1.9 TECU in 2008, and from 2.0 to 8.0 TECU in 2014. The STDs at a low latitude were significantly larger than those at middle and high latitudes, as a result of the ionospheric latitudinal gradients. When compared with the Jason-2 VTEC measurements, the GIMAS-based VTEC maps showed a negative systematic bias of about −1.8 TECU in 2008, and a positive systematic bias of about +2.2 TECU in 2014. The STDs were about 2.0 TECU in 2008, and ranged from 2.2 to 8.5 TECU in 2014. Furthermore, the aforementioned characteristics were strongly related to the conditions of the ionosphere variation and the geographic latitude. The GPS and GLONASS satellite and receiver P1-P2 DCBs were compared with the IAACs DCBs. The root mean squares (RMSs) were 0.16–0.20 ns in 2008 and 0.13–0.25 ns in 2014 for the GPS satellites and 0.26–0.31 ns in 2014 for the GLONASS satellites. The RMSs of receiver DCBs were 0.21–0.42 ns in 2008 and 0.33–1.47 ns in 2014 for GPS and 0.67–0.96 ns in 2014 for GLONASS. The monthly stability of the GPS satellite DCBs was about 0.04 ns (0.07 ns) in 2008 (2014) and that for the GLONASS satellite DCBs was about 0.09 ns in 2014. The receiver DCBs were less stable than the satellite DCBs, with a mean value of about 0.16 ns (0.47 ns) in 2008 (2014) for GPS, and 0.48 ns in 2014 for GLONASS. It can be demonstrated that the GIMAS software had a high accuracy and reliability for the global ionosphere monitoring and analysis.

Improved Modeling of Global Ionospheric Total Electron Content Using Prior Information

The Ionosphere Working Group of the International GNSS Service (IGS) has been a reliable source of global ionospheric maps (GIMs) since 1998. Modeling of the global ionospheric total electron content (TEC) is performed daily by several Ionosphere Associate Analysis Centers (IAACs). Four IAACs (CODE, ESA, CAS and WHU) use the spherical harmonic (SH) expansion as their primary method for modeling GIMs. The IAACs generally solve a normal equation to obtain the SH coefficients and Differential Code Biases (DCBs) of satellites and receivers by traditional least-squares estimation (LSE) without any prior knowledge. In this contribution, an improved method is proposed and developed for global ionospheric modeling based on utilizing prior knowledge. Prior values of SH coefficients and DCBs of satellites and receivers, as well as the variance factor and covariance matrix, could be obtained from the ionospheric modeling on the previous day. The parameters can subsequently be updated through GNSS measurements to achieve higher accuracy. Comparisons are carried out between WHU products based either on priori information or original LSE and IGS final products, other IAAC products, and JASON data for the year 2014. The results indicate that there is improved consistency between WHU GIMs and IGS final GIMs, other IAAC products, and JASON data, particularly in comparison with ESA and UPC products, with the probabilities of achieving better consistency with these products exceeding 95%. Moreover, WHU-produced DCBs of satellites also have slightly improved consistency with IGS final GIMs and IAAC products.

Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle

In the context of the International GNSS Service (IGS), several IGS Ionosphere Associated Analysis Centers have developed different techniques to provide global ionospheric maps (GIMs) of vertical total electron content (VTEC) since 1998. In this paper we present a comparison of the performances of all the GIMs created in the frame of IGS. Indeed we compare the classical ones (for the ionospheric analysis centers CODE, ESA/ESOC, JPL and UPC) with the new ones (NRCAN, CAS, WHU). To assess the quality of them in fair and completely independent ways, two assessment methods are used: a direct comparison to altimeter data (VTEC-altimeter) and to the difference of slant total electron content (STEC) observed in independent ground reference stations (dSTEC-GPS). The main conclusion of this study, performed during one solar cycle, is the consistency of the results between so many different GIM techniques and implementations.

Project Loon based augmentation for global ionospheric modeling over Southern Hemisphere

Global ionospheric products of vertical total electron content (VTEC) derived from GNSS measurements may have low accuracy over oceans and southern latitudes where there are not rich observations. Project Loon provides a great opportunity to enhance the measurements over those areas. In this contribution, a simulation of Project Loon based augmentation for global ionospheric modeling is performed by using the international reference ionosphere (IRI) which could simulate VTEC measurements for the balloons. The performance of the enhanced method based on simulation of Project Loon is investigated by comparing with VTEC maps from Ionosphere Associate Analysis Centers (IAACs) as well as IGS final GIMs. The comparison indicates that there is a better consistency between the VTEC maps by the enhanced method and IGS final GIMs. Also, obvious improvements of RMS maps in GIMs for the middle latitudes and southern latitudes are enabled by the augmentation of Project Loon. Additionally, JASON data are used to validate the specific improvement of the VTEC maps. The results show that the performance of VTEC maps is improved slightly, especially in southern latitudes. It is possible that the VTEC maps could be improved significantly by using real GPS measurements from balloons of Project Loon in the near future.