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Presently, the high and increasing number of worldwide permanent Global Navigation Satellite System (GNSS) receivers providing the raw measurements in real-time (RT) and openly from a large fleet of GNSS transmitters, has opened the door to an accurate real-time determination of the distribution of the ionospheric electron content, either at global scale. The motivations are diverse for such a scientific and technological challenging target, for instance: (1) to facilitate the fast carrier phase ambiguity resolution of roving users and corresponding fast decimeter-error level navigation at large distances (hundreds of kilometers) from supporting permanent GNSS receivers (see Hernández-Pajares et al. 2000, Juan et al. 2012, Olivares-Pulido et al. 2021); and (2) the possibility of generating in real-time realistic global maps of ionospheric storm state and Vertical Total Electron Content (VTEC) gradients like it can be done with a latency of 1 day (Liu et al. 2021a, 2022 respectively) based on UQRG GIMs, one of the best behaving ones in the International GNSS Service (IGS), see Roma-Dollase et al. (2018). This might be feasible thanks the recent advances in individual and collaborative real-time global VTEC mapping (see Yang et al. 2021 and Liu et al. 2021b, respectively) and in global VTEC forecasting (Monte-Moreno et al. 2022). These potential new RT products might be useful as ionospheric storm semaphores and quantifiers for example for contributing to the integrity of single-frequency GNSS based navigation in civil aviation. One possible evolution in this field might include the consistent 4D combination of the already existing RT GNSS measurements with the potential RT additional geodetic measurements sensitive to the ionospheric delay, like Doppler measurements (DORIS), and like dual-frequency vertical delay measurements over the oceans provided by altimeters, such as JASON-3 among others (Hernández-Pajares et al. 2021). This would significantly extend the coverage and accuracy at global scale, improving as well the vertical resolution. References Hernández‐Pajares, M., Juan, J. M., Sanz, J., & Colombo, O. L. (2000). Application of ionospheric tomography to real‐time GPS carrier‐phase ambiguities resolution, at scales of 400–1000 km and with high geomagnetic activity. Geophysical Research Letters, 27(13), 2009-2012. Juan, J. M., Hernández-Pajares, M., Sanz, J., Ramos-Bosch, P., Aragon-Angel, A., Orus, R., ... & Tossaint, M. (2012). Enhanced precise point positioning for GNSS users. IEEE transactions on geoscience and remote sensing, 50(10), 4213-4222. Liu, Q., Hernández‐Pajares, M., Lyu, H., Nishioka, M., Yang, H., Monte‐Moreno, E., ... & Orús‐Pérez, R. (2021a). Ionospheric storm scale index based on high time resolution UPC‐IonSAT global ionospheric maps (IsUG). Space Weather, 19(11), e2021SW002853. Liu, Q., Hernández-Pajares, M., Yang, H., Monte-Moreno, E., Roma-Dollase, D., García-Rigo, A., ... & Ghoddousi-Fard, R. (2021b). The cooperative IGS RT-GIMs: A reliable estimation of the global ionospheric electron content distribution in real time. Earth System Science Data, 13(9), 4567-4582. Liu, Q., Hernández‐Pajares, M., Yang, H., Monte‐Moreno, E., García‐Rigo, A., Lyu, H., ... & Orús‐Pérez, R. (2022). A New Way of Estimating the Spatial and Temporal Components of the Vertical Total Electron Content Gradient Based on UPC‐IonSAT Global Ionosphere Maps. Space Weather, 20(2), e2021SW002926. Monte-Moreno, E., Yang, H., & Hernández-Pajares, M. (2022). Forecast of the Global TEC by Nearest neighbour technique. Remote Sensing, 14(6), 1361. Olivares-Pulido, G., Hernández-Pajares, M., Lyu, H., Gu, S., García-Rigo, A., Graffigna, V., ... & Orús-Pérez, R. (2021). Ionospheric tomographic common clock model of undifferenced uncombined GNSS measurements. Journal of Geodesy, 95(11), 1-13. Roma-Dollase, D., Hernández-Pajares, M., Krankowski, A., Kotulak, K., Ghoddousi-Fard, R., Yuan, Y., ... & Gómez-Cama, J. M. (2018). Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle. Journal of Geodesy, 92(6), 691-706. Yang, H., Monte-Moreno, E., Hernández-Pajares, M., & Roma-Dollase, D. (2021). Real-time interpolation of global ionospheric maps by means of sparse representation. Journal of Geodesy, 95(6), 1-20.

The Real-Time Working Group (RTWG) of the International GNSS Service (IGS) is dedicated to providing high-quality data, high-accuracy products for Global Navigation Satellite System (GNSS) positioning, navigation, timing, and Earth observations. As one part of real-time products, the IGS combined Real-Time Global Ionosphere Map (RT-GIM) has been generated by the real-time weighting of the RT-GIMs from IGS real-time ionosphere centers including the Chinese Academy of Sciences (CAS), Centre National d’Etudes Spatiales (CNES), Universitat Politècnica de Catalunya (UPC), and Wuhan University (WHU). The performance of global Vertical Total Electron Content (VTEC) representation in all of the RT-GIMs has been assessed by VTEC from Jason3-altimeter during one month over oceans and dSTEC-GPS technique with 2-day observations over continental regions. According to the Jason3-VTEC and dSTEC-GPS assessment, the real-time weighting technique is sensitive to the accuracy of RT-GIMs. Compared with the performance of post-processed rapid Global Ionosphere Maps (GIMs) and IGS combined final GIM (igsg) during the testing period, the accuracy of UPC RT-GIM (after the transition of interpolation technique) and IGS combined RT-GIM (IRTG) is equivalent to the rapid GIMs and reaches around 2.7 and 3.0 TECU (TEC Unit, 1016 el/m2) over oceans and continental regions, respectively. The accuracy of CAS RT-GIM and CNES RT-GIM is slightly worse than the rapid GIMs, while WHU RT-GIM requires a further upgrade to obtain similar performance. In addition, the strong response to the recent geomagnetic storms has been found in the Global Electron Content (GEC) of IGS RT-GIMs (especially UPC RT-GIM and IGS combined RT-GIM). The IGS RT-GIMs turn out to be reliable sources of real-time global VTEC information and have great potential for real-time applications including range error correction for transionospheric radio signals (such as GNSS positioning, search and rescue, air traffic, radar altimetry, and radioastronomy), the monitoring of space weather (such as geomagnetic and ionospheric storms, ionospheric disturbance) and detection of natural hazards on a global scale (such as hurricanes/typhoons, ionospheric anomalies associated with earthquakes). All the IGS combined RT-GIMs generated and analyzed during the testing period are available at http://doi.org/10.5281/zenodo.4651445 (Liu et al., 2021b).

In this paper, we propose a method for the generation of real-time global ionospheric map (RT-GIM) of vertical total electron content (VTEC) from GNSS measurements. The need for interpolation arises from the fact that the ionospheric pierce point (IPP) measurements from satellites to stations are not distributed uniformly over the ionosphere, leaving unfilled gaps at oceans or poles. The method we propose is based on using a high-quality historical database of post-processed GIMs that comprises more than two solar cycles, calculates the GIM by weighted superposition on a subset of the database with the compatible solar condition. The linear combination of GIMs in the database was obtained by minimizing a ℓ distance between VTEC measurements at the IPPs and the VTECs from the database, adding a ℓ penalization on the weights to assure a sparse solution. The process uses a Sun-fixed geomagnetic reference frame. This method uses the atomic decomposition/least absolute shrinkage and selection operator (LASSO), which will be denoted as atomic decomposition interpolator of GIMs (ADIGIM). As the computation is done in milliseconds, the interpolation is performed in real time. In this work, two products were developed, denoted as UADG and UARG, the UADG in real time and UARG with a latency of 24 h to benefit from the availability of a greater number of stations. The altimeter JASON3 VTEC measurements were used as reference. The quality of interpolated RT-GIMs from day 258 of 2019 to 155 of the year 2020 is compared with other RT/non-RT GIM products such as those from International GNSS Service (IGS), Centre National d’Etudes Spatiales (CNES), Chinese Academy of Sciences (CAS), Polytechnic University of Catalonia (UPC) and others. The RT ADIGIM performance proved to be better, nearly as good as the rapid or final GIMs computed retrospectively with delays of hours to days. Besides, the non-RT ADIGIM quality is as good or better than most GIM products. The oceanic regions have been included in the assessment which showed that ADIGIM interpolation gives the best estimation (referred to JASON3). The developed method, UADG, will constitute the next-generation UPC RT-GIM, and also UARG will improve the current product UQRG (the current UPC rapid GIM product computed retrospectively) due to its complementary information., This work has been partially supported by the Project PID2019-107579RB-I00 (MICINN). Also was partially supported by the 2017 SGR-0851 Grant of the Generalitat de Catalunya and by the EU Project 101007599 - PITHIA-NRF.

In the original publication of the articles, “Methodology and consistency of slant and vertical assessments for ionospheric electron content models” and “Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle”, a common typo affecting the text only (not the computations) has been recently noticed. It compromised the definition of the scaling factor from Global Navigation Satellite Systems ionospheric delay to electron content is clarified in this erratum.

Benefiting from global multi-frequency and multi-constellation GNSS measurements provided by the experimental International GNSS real-time service (IGS RTS), a predicting-plus-modeling approach employed by Chinese Academy of Sciences (CAS) for the routine generation of real-time global ionospheric maps (RT-GIM) is first reported. Along with RT-GIMs generated by Universitat Politècnica de Catalunya (UPC), the quality of CAS and UPC RT-GIMs in IONEX format is assessed during a low soar activity period from September 2017 to December 2019. The differential slant total electron contents (dSTEC) derived from 50 GPS stations of the IGS and Jason-3 vertical TECs (VTEC) over the ocean are used as references. In comparison with different reference TECs, CAS and UPC RT-GIMs are approximately 1.7–4.9% and 8.6–12.5% worse than the respective post-processed GIMs CASG and UQRG, respectively. Using RTCM ionospheric data streams from CAS, Centre National d’Etudes Spatiales (CNES) and UPC, the first experimental IGS combined RT-GIM is generated and validated in actual real-time conditions. Compared to Jason-3 VTEC measurements available during the period of common availability, from October 2018 to April 2019, RT-GIM discrepancies present similar relative RMS errors, which are 33, 36, 36 and 38% for CNES, combined one, UPC and CAS, respectively. Aside from a better understanding of the influence of working in the original IONEX versus RTCM ionospheric formats, the update to a new experimental adaptation of RT strategy is highlighted by UPC, and the computation of multi-layer RT-GIM is emphasized by CAS in view of the inadequacy of single-layer ionospheric assumption in the presence of large latitudinal gradients., The authors acknowledge the IGS and other agencies for providing real-time GNSS data and products. This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDA17010202), the National Natural Science Foundation of China (41674043, 41704038), the National Key Research Program of China (2017YFGH002206), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00190-017-1088-9. 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.

Recommendations of the International Reference Ionosphere (IRI) Workshop 2017 in Taoyuan City, Taiwan and International GNSS Service (IGS) Workshop 2018 in Wuhan, China included establishment of an ionosphere mapping service that would fuse measurements from two independent sensor networks: IGS permanent GNSS receivers providing the vertical total electron content (VTEC) measurements and ionosondes of the Global Ionosphere Radio Observatory (GIRO) that compute the bottomside vertical profiles of the ionospheric plasma density. Using available GAMBIT software at GIRO, we introduced new VTEC products to its data roster: previously unavailable global average (climate) maps of VTEC and slab thickness based on climatological capabilities of IRI. Incorporation of the VTEC and τ maps into the GAMBIT Explorer environment provided data analysts with nearly 10-year history of the reference average VTEC records and opened access to the GAMBIT toolkit for evaluation and validation of the τ computations. This result is the first step towards establishing an infrastructure and the data workflow to provide GAMBIT users with the low latency and consistent quality and usability of the ionospheric weather-climate specifications. Combination of IGS-provided VTEC and GIRO-provided peak density of F2 layer NmF2 allows ground-based evaluation of the equivalent slab thickness τ, a derived property of the near-Earth plasma that characterizes the skewness of its vertical profile up to the GNSS spacecraft altitudes.

This is a post-peer-review, pre-copyedit version of an article published in Gps solutions. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10291-018-0767-1 The number of existing global positioning system (GPS) single-frequency receivers continues growing. More than 90% of GPS receivers are implemented as low-cost single-frequency chipsets embedded in smartphones. This provides new opportunities, in particular for ionospheric sounding. In this context, we present the new sidereal days ionospheric graphic (SIg) combination of single-frequency GNSS measurements. SIg is able to monitor, for each given GNSS transmitter–receiver pair, the vertical total electron content (VTEC) relative to the previous observation with the same or almost the same line-of-sight (LOS) vector. In such arrangements the SIg multipath error mostly cancels, thus increasing the accuracy of the ¿VTEC significantly. This happens for the GPS constellation after one sidereal day (about 23 h 56 m) and for Galileo after 10 sidereal days approximately. Moreover, we show that the required calibration of the corresponding carrier phase ambiguity can be accurately performed by means of VTEC global ionospheric maps (GIMs). The results appear almost as accurate as those based on the dual-frequency technique, i.e., about 1 TECU or better, and with much more precision and resolution than the GIM values in the ionospheric region sounded by each given single-frequency receiver. The performance is demonstrated using actual data from 9 permanent GPS receivers during a total solar eclipse on August 21, 2017 over North America, where the corresponding ionospheric footprint is clearly detected in agreement with the total solar eclipse predictions. The advantages of extending SIg to lower carrier frequencies and the feasibility of applying it to other global navigation satellite system (GNSS) systems are also studied. This is shown in terms of a fully consistent VTEC depletion signature of the same eclipse phenomena, obtained with Galileo-only data in North America at mid and low latitude. Finally the SIg feasibility, including the cycle slip detection, is shown as well with actual mass-market single frequency GPS receivers at mid and high latitude.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00190-017-1032-z A summary of the main concepts on global ionospheric map(s) [hereinafter GIM(s)] of vertical total electron content (VTEC), with special emphasis on their assessment, is presented in this paper. It is based on the experience accumulated during almost two decades of collaborative work in the context of the international global navigation satellite systems (GNSS) service (IGS) ionosphere working group. A representative comparison of the two main assessments of ionospheric electron content models (VTEC-altimeter and difference of Slant TEC, based on independent global positioning system data GPS, dSTEC-GPS) is performed. It is based on 26 GPS receivers worldwide distributed and mostly placed on islands, from the last quarter of 2010 to the end of 2016. The consistency between dSTEC-GPS and VTEC-altimeter assessments for one of the most accurate IGS GIMs (the tomographic-kriging GIM ‘UQRG’ computed by UPC) is shown. Typical error RMS values of 2 TECU for VTEC-altimeter and 0.5 TECU for dSTEC-GPS assessments are found. And, as expected by following a simple random model, there is a significant correlation between both RMS and specially relative errors, mainly evident when large enough number of observations per pass is considered. The authors expect that this manuscript will be useful for new analysis contributor centres and in general for the scientific and technical community interested in simple and truly external ways of validating electron content models of the ionosphere.