Data description paper 23 Sep 2021
Data description paper  23 Sep 2021
The cooperative IGS RTGIMs: a reliable estimation of the global ionospheric electron content distribution in real time
 ^{1}Department of Mathematics, Universitat Politècnica de Catalunya (UPCIonSAT), Barcelona, Spain
 ^{2}Institut d'Estudis Espacials de Catalunya (IEEC), Barcelona, Spain
 ^{3}School of Electronic Information and Engineering, Yangtze Normal University, 408100 Chongqing, China
 ^{4}Department of Signal Theory and Communications, TALP, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
 ^{5}Aerospace Information Research Institute (AIR), Chinese Academy of Sciences (CAS), Beijing, China
 ^{6}Centre National d'Etudes Spatiales, Toulouse, France
 ^{7}GNSS Research Center, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, China
 ^{8}Collaborative Innovation Center of Earth and Space Science, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, China
 ^{9}German Aerospace Center (DLR), German Space Operations Center (GSOC), 82234 Weßling, Germany
 ^{10}European Space Operations Center, European Space Agency, Darmstadt, Germany
 ^{11}Geo++ GmbH, Steinriede 8, 30827 Garbsen, Germany
 ^{12}BKG, Federal Agency for Cartography and Geodesy, Frankfurt, Germany
 ^{13}Space RadioDiagnostics Research Centre, University of Warmia and Mazury in Olsztyn, 10719 Olsztyn, Poland
 ^{14}Astronomical Institute, the University of Bern, Sidlerstrasse 5, Bern 3012, Switzerland
 ^{15}Federal Office of Topography (swisstopo), Wabern, Switzerland
 ^{16}Navigation Support Office, Telespazio Germany GmbH c/o European Space Agency/European Space Operations Centre, RobertBoschStraße 5, 64293 Darmstadt, Germany
 ^{17}Near Earth Tracking Systems Group (335S), NASA – Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, M/S 138317, Pasadena, CA 91109, USA
 ^{18}Canadian Geodetic Survey, Natural Resources Canada, Ottawa, Canada
 ^{1}Department of Mathematics, Universitat Politècnica de Catalunya (UPCIonSAT), Barcelona, Spain
 ^{2}Institut d'Estudis Espacials de Catalunya (IEEC), Barcelona, Spain
 ^{3}School of Electronic Information and Engineering, Yangtze Normal University, 408100 Chongqing, China
 ^{4}Department of Signal Theory and Communications, TALP, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
 ^{5}Aerospace Information Research Institute (AIR), Chinese Academy of Sciences (CAS), Beijing, China
 ^{6}Centre National d'Etudes Spatiales, Toulouse, France
 ^{7}GNSS Research Center, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, China
 ^{8}Collaborative Innovation Center of Earth and Space Science, Wuhan University, No. 129 Luoyu Road, Wuhan 430079, China
 ^{9}German Aerospace Center (DLR), German Space Operations Center (GSOC), 82234 Weßling, Germany
 ^{10}European Space Operations Center, European Space Agency, Darmstadt, Germany
 ^{11}Geo++ GmbH, Steinriede 8, 30827 Garbsen, Germany
 ^{12}BKG, Federal Agency for Cartography and Geodesy, Frankfurt, Germany
 ^{13}Space RadioDiagnostics Research Centre, University of Warmia and Mazury in Olsztyn, 10719 Olsztyn, Poland
 ^{14}Astronomical Institute, the University of Bern, Sidlerstrasse 5, Bern 3012, Switzerland
 ^{15}Federal Office of Topography (swisstopo), Wabern, Switzerland
 ^{16}Navigation Support Office, Telespazio Germany GmbH c/o European Space Agency/European Space Operations Centre, RobertBoschStraße 5, 64293 Darmstadt, Germany
 ^{17}Near Earth Tracking Systems Group (335S), NASA – Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, M/S 138317, Pasadena, CA 91109, USA
 ^{18}Canadian Geodetic Survey, Natural Resources Canada, Ottawa, Canada
Correspondence: Manuel HernándezPajares (manuel.hernandez@upc.edu)
Hide author detailsCorrespondence: Manuel HernándezPajares (manuel.hernandez@upc.edu)
The RealTime Working Group (RTWG) of the International GNSS Service (IGS) is dedicated to providing highquality data and highaccuracy products for Global Navigation Satellite System (GNSS) positioning, navigation, timing and Earth observations. As one part of realtime products, the IGS combined RealTime Global Ionosphere Map (RTGIM) has been generated by the realtime weighting of the RTGIMs from IGS realtime 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 RTGIMs has been assessed by VTEC from Jason3 altimeter for 3 months over oceans and dSTECGPS technique with 2 d observations over continental regions. According to the Jason3 VTEC and dSTECGPS assessment, the realtime weighting technique is sensitive to the accuracy of RTGIMs. Compared with the performance of postprocessed rapid global ionosphere maps (GIMs) and IGS combined final GIM (igsg) during the testing period, the accuracy of UPC RTGIM (after the improvement of the interpolation technique) and IGS combined RTGIM (IRTG) is equivalent to the rapid GIMs and reaches around 2.7 and 3.0 TECU (TEC unit, 10^{16} el m^{−2}) over oceans and continental regions, respectively. The accuracy of CAS RTGIM and CNES RTGIM is slightly worse than the rapid GIMs, while WHU RTGIM requires a further upgrade to obtain similar performance. In addition, a strong response to the recent geomagnetic storms has been found in the global electron content (GEC) of IGS RTGIMs (especially UPC RTGIM and IGS combined RTGIM). The IGS RTGIMs turn out to be reliable sources of realtime global VTEC information and have great potential for realtime applications including range error correction for transionospheric radio signals, the monitoring of space weather, and detection of natural hazards on a global scale. All the IGS combined RTGIMs generated and analyzed during the testing period are available at https://doi.org/10.5281/zenodo.5042622 (Liu et al., 2021b).
The global ionosphere maps (GIMs), containing vertical total electron content (VTEC) information at given grid points (typically with a spatial resolution of 2.5^{∘} in latitude and 5^{∘} in longitude), have been widely used in both scientific and technological communities (HernándezPajares et al., 2009). Due to the high quality and global distribution of VTEC estimation, GIM has been applied to investigating the behavior of the ionosphere, such as the climatology of mean total electron content (TEC), potential ionospheric anomalies before earthquakes, semiannual variations in TEC in the ionosphere, the VTEC structure of the polar ionosphere under different cases and W index for ionospheric disturbance warning (e.g., Liu et al., 2009, 2006; Zhao et al., 2007; Jiang et al., 2019; HernándezPajares et al., 2020; Gulyaeva and Stanislawska, 2008; Gulyaeva et al., 2013). In addition, the high accuracy of GIM enables precise range corrections for transionospheric radio signals including radar altimetry, radio telescopes and Global Navigation Satellite System (GNSS) positioning (e.g., Komjathy and Born, 1999; Fernandes et al., 2014; SotomayorBeltran et al., 2013; Le and Tiberius, 2007; Zhang et al., 2013a; Lou et al., 2016; Chen et al., 2020). The Center for Orbit Determination in Europe (CODE), European Space Agency (ESA), Jet Propulsion Laboratory (JPL), Canadian Geodetic Survey of Natural Resources Canada (NRCan) and Universitat Politècnica de Catalunya (UPC) agreed on the computation of individual GIMs in IONosphere map EXchange (IONEX) format and created the Ionosphere Working Group (IonoWG) of the International GNSS Service (IGS) in 1998 (Schaer et al., 1996, 1998; Feltens and Schaer, 1998; Feltens, 2007; Mannucci et al., 1998; HernándezPajares et al., 1998, 1999). In the IGS 2015 workshop, the Chinese Academy of Sciences (CAS) and Wuhan University (WHU) became new Ionospheric Associate Analysis Centers (IAACs) (Li et al., 2015; GhoddousiFard, 2014; Zhang et al., 2013b). Currently, there are three types of postprocessed IGS GIMs at different latencies: final, rapid and predicted GIMs. With the contribution from different IAACs, the final and rapid GIMs are assessed and combined by corresponding weights and uploaded to File Transfer Protocol (FTP) or Hypertext Transfer Protocol (HTTP) servers with the latency of 1–2 weeks and 1–2 d, respectively. The 1 and 2 d predicted GIMs can provide valuable VTEC information in advance for ionospheric activities and corrections. However, the accuracy of predicted GIMs is limited due to the nonlinear variation in ionosphere and the lack of realtime ionospheric observations (HernándezPajares et al., 2009; GarcíaRigo et al., 2011; Li et al., 2018).
In order to satisfy the growing demand for realtime GNSS positioning and applications, the RealTime Working Group (RTWG) of IGS was established in 2001 and officially started to provide realtime service (RTS) in 2013 (Caissy et al., 2012; Elsobeiey and AlHarbi, 2016). Aside from multiGNSS realtime data streams, the IGSRTS also generates RTGNSS product streams, including satellite orbits, clocks, code/phase biases and GIM. These highquality IGSRTS products enable precise GNSS positioning, navigation, timing (PNT), ionosphere monitoring and hazard detection. In the Radio Technical Commission for Maritime Services (RTCM) Special Committee (SC104), the State Space Representation (SSR) correction data format is defined as the standard message (RTCMSSR) for realtime GNSS applications. In support of flexible multiGNSS applications within current multiconstellation and multifrequency environments, a new format (IGSSSR) is developed. The dissemination of IGS RealTime Global Ionosphere Maps (RTGIMs) adopts spherical harmonic expansion to save the bandwidth in both RTCMSSR and IGSSSR formats (RTCMSC, 2014; IGS, 2020).
The accuracy of RTGIMs is typically worse than postprocessed GIMs due to the short span of ionospheric observations, sparse distribution of stations, higher noises in carriertocode leveling, or difficulty in carrier ambiguity estimation in realtime processing mode. While RTGIMs perform slightly worse than postprocessed GIMs, it is found that RTGIMs are helpful to reduce the convergence time of dualfrequency precise point positioning (PPP), and they strengthen the solution (Li et al., 2013). With the corrections of RTGIMs, the accuracy of singlefrequency PPP reaches decimeter and meter level in horizontal and vertical directions (Ren et al., 2019), while the instantaneous (singleepoch) realtime kinematic (RTK) positioning over medium and long baselines is able to obtain a higher success rate of the ambiguity fixing and reliability for rover stations at a level of a few centimeters (Tomaszewski et al., 2020). In addition, the feasibility of ionospheric storm monitoring based on RTGIMs is tested (García Rigo et al., 2017). A first fusion of IGSGIMs and ionosonde data from the Global Ionosphere Radio Observatory (GIRO) paves the way for the improvement of realtime International Reference Ionosphere (Froń et al., 2020). Currently, the routine RTGIMs are available from CAS, Centre National d'Etudes Spatiales (CNES), German Aerospace Center in Neustrelitz (DLRNZ), JPL, UPC, WHU and IONOLAB (Li et al., 2020; Laurichesse and Blot, 2015; Jakowski et al., 2011; Hoque et al., 2019; Komjathy et al., 2012; Roma Dollase et al., 2015; Sezen et al., 2013). Individual RTGIMs from different IGS centers can be gathered from IGSRTS by means of Network Transportation of RTCM by Internet Protocol (NTRIP) (Weber et al., 2007). With the contribution of IGS RTGIMs from CAS, CNES and UPC, a first IGS realtime combination of GIMs was generated in 2018 (RomaDollase et al., 2018a).
Recently, one of the IGS RTGIMs (UPCIonSAT) has completely changed the realtime interpolation strategy, with a significant improvement. In addition, the number of contributing centers has been increased from three to four, thanks to the participation of Wuhan University. A new version of IGS combined RTGIM (IRTG) has been developed to improve the performance and also adapt to the newly updated IGSSSR format. In addition, the developed software has been further parallelized to decrease the latency of IRTG computation to a few minutes (Tange, 2011). This paper summarizes the computation methods of IGS RTGIMs from different ionosphere centers and the generation of IRTG. In addition, the performance of different RTGIMs and the realtime weighting technique is shown and discussed. The conclusions and future improvements are given in the final section.
2.1 Realtime GNSS data processing
In order to generate RTGIMs, the realtime GNSS observations from worldwide stations are received and transformed into slant TEC (STEC). It should be noted that extraction of STEC in an unbiased way can be obtained by fitting an ionospheric model to the observations. With the global distributed STEC, different strategies are chosen for the computation of RTGIMs.
Currently, two methods are commonly used for the calculation of realtime STEC. The first method is the socalled carriertocode leveling (CCL) as shown in Eq. (3) (Ciraolo et al., 2007; Zhang et al., 2019). The geometryfree (GF) combination of pseudorange and carrier phase observations is formed to extract STEC and differential code bias (DCB) in an unbiased way by fitting an ionospheric model (for example, spherical harmonic model). Due to the typically shorter phasearc length in realtime mode, the impact of multipath and thermal noise is higher than in postprocessing mode (Li et al., 2020).
Here P_{1,t} and P_{2,t} are the pseudorange observations of epoch t at first and second frequencies, respectively. α_{GF} can be approximated as $\mathrm{40.3}(\frac{\mathrm{1}}{{f}_{\mathrm{2}}^{\mathrm{2}}}\frac{\mathrm{1}}{{f}_{\mathrm{1}}^{\mathrm{2}}})$. f_{1} and f_{2} are the first and second frequencies of observation. STEC_{t} is the STEC of epoch t. r is receiver and s is satellite. c is the speed of light in vacuum. D_{r} and D^{s} are the receiver differential code biases (DCBs) and satellite DCB. ϵ_{M} and ϵ_{T} are the code multipath error and thermal noise error. L_{1,t} and L_{2,t} are the carrier phase observations including the priori corrections (such as windup term) of epoch t at first and second frequencies. B_{GF} equals B_{1}−B_{2}, while B_{1} and B_{2} are the carrier phase ambiguities including the corresponding phase bias at first and second frequencies, respectively. k is the length of smoothing arc from beginning epoch to epoch t, and ${\stackrel{\mathrm{\u0303}}{P}}_{\text{GF},t}$ represents the smoothed P_{GF} of epoch t, which is significantly affected by the pseudorange multipath in realtime mode than in postprocessing.
The second method is the GF combination of phaseonly observations, and the B_{GF} is estimated together with the realtime TEC model (for example, described in terms of tomographic voxelbased basis functions) in Eq. (2) (HernándezPajares et al., 1997, 1999). Although the STEC from the second method is accurate and free of code multipath and thermal noise in postprocessing, the convergence time can affect the accuracy of the STEC, most likely in the isolated receivers. In addition, the computation methods of RTGIMs from different IGS realtime ionosphere centers were compared in detail at the next subsection and summarized in Table 1. Some ionosphere centers (CAS, CNES, WHU) directly estimate and disseminate spherical harmonic coefficients in a sunfixed reference frame as Eq. (4) (RTCMSC, 2014; Li et al., 2020), while UPC generates the RTGIM in IONEX format and transforms RTGIM into spherical harmonic coefficients for the dissemination.
Here z is the satellite zenith angle, and M_{z} is the mapping function between STEC_{t} and VTEC_{t}. H_{ion} is the height of the ionospheric singlelayer assumption, and R_{E} is the radius of the earth. VTEC_{t} is the VTEC of epoch t. N_{SH} is the max degree of spherical harmonic expansion, and M_{SH} is the max order of spherical harmonic expansion. n and m are corresponding indices. P_{n,m} is the normalized associated Legendre functions. C_{n,m} and S_{n,m} are sine and cosine spherical harmonic coefficients. φ_{I} and λ_{I} are the geocentric latitude and longitude of ionospheric pierce point (IPP). λ_{S,t} is the mean sun fixed and phaseshifted longitude of IPP of epoch t (typically shifted by 2 h to approximate TEC maximum at 14:00 LT). t is the current epoch. t_{0} is a common reference of shifted hours, taken as 0 h in the present broadcasting of RTGIM for WHU and 2 h for CAS, CNES and UPC.
2.2 The computation of RTGIMs by different IGS realtime ionosphere centers
The strategies for generating RTGIMs differ between IGS realtime ionospheric analysis centers (ACs). In this subsection, a brief introduction on the generation of RTGIMs from individual ACs and the strategy comparison between different ACs are given.
2.2.1 Chinese Academy of Sciences
The postprocessed GIM of CAS has been computed and uploaded to IGS since 2015 (Li et al., 2015). A predictingplusmodeling approach is used by CAS for the computation of RTGIM (Li et al., 2020). CAS RTGIM is generated with multiGNSS, GPS and GLONASS L1 + L2, BeiDou B1 + B2, and Galileo E1 + E5a realtime data streams, provided by the IGS and regional GNSS tracking network stations. The realtime DCBs are estimated as part of the local ionospheric VTEC modeling using a generalized trigonometric series (GTS) function as Eq. (5). Then 3 d aligned biases are incorporated to increase the robustness of realtime DCBs (Wang et al., 2020).
Here r is receiver and s is satellite. φ_{d} and λ_{d} are the difference between IPP and station in latitude and longitude, respectively. i,j and l represent the degrees in the polynomial model and Fourier series expansion. ${E}_{i,j},{C}_{l}$ and S_{l} are unknown parameters.
The realtime STEC is computed by subtracting estimated DCB in Eq. (5) from ${\stackrel{\mathrm{\u0303}}{P}}_{\text{GF},t}$ in Eq. (3), and then the STEC is converted into VTEC by means of a mapping function. The realtime VTEC from 130 global stations is directly modeled in a solargeographic reference frame as Eq. (4). To mitigate the impacts of the unstable realtime data streams, e.g., the sudden interruption of the data streams, CASpredicted TEC information is also included for RTGIM computation. The broadcasted CAS RTGIM is computed by the weighted combination of realtime VTEC spherical harmonic coefficients and predicted ionospheric information (Li et al., 2020).
2.2.2 Centre National d'Etudes Spatiales
In the framework of the RTS of the IGS, CNES has computed global VTEC in real time thanks to the CNES PPPWIZARD project since 2014. The realtime VTEC is extracted by pseudorange and carrier phase GF combination as Eq. (3) with the help of a mapping function. The singlelayer assumption in the mapping function adopts an altitude of 450 km above the Earth.
CNES also uses a spherical harmonic model for global VTEC representation, and the equation is the same as Eq. (4). Spherical harmonic coefficients are computed by means of a Kalman filter and simultaneous STEC from 100 stations of the realtime IGS network. CNES started to broadcast RTGIM at the end of 2014 and changed spherical harmonic degrees from 6 to 12 in May of 2017 (Laurichesse and Blot, 2015).
2.2.3 Universitat Politècnica de Catalunya
UPC has been providing daily GIMs in IONEX format to IGS since 1998 (HernándezPajares et al., 1998, 1999; Orús et al., 2005). In order to meet the demand of realtime GIM, the second author of this paper (from UPCIonSAT) developed the RealTime TOMographic IONosphere model software (RTTOMION) and started to generate the UPC RTGIM on 6 February 2011. The phaseonly GF combination as Eq. (2) is used for obtaining realtime STEC from around 260 stations, and a 4D voxelbased tomographic ionosphere model is adopted for global electron content modeling. The ionosphere is divided into two layers in the tomographic model, and the electron density of each voxel is estimated together with the ambiguity term B_{GF} by means of a Kalman filter in the sunfixed reference frame. The estimated electron density is condensed at a fixed effective height (450 km) for the generation of a singlelayer VTEC map, and then the VTEC interpolation method is adopted in a sunfixed geomagnetic reference frame for filling the data gap on a global scale.
From 2011 to 2019, the kriging technique is selected by UPC for realtime VTEC interpolation. And the spherical harmonic model has been adopted by UPC since 8 September 2019. Recently, a new interpolation technique, denoted atomic decomposition interpolator of GIMs (ADIGIM), was developed. Since the global ionospheric electron content mainly depends on the diurnal, seasonal and solar variation, ADIGIM is computed by the weighted combination of goodquality historical GIMs (e.g., UQRG) with similar ionosphere conditions. The database of historical GIMs covers the last two solar cycles since 1998. The method for obtaining the weights of the linear combination of past maps is based on Eq. (6), which was first introduced in the problem of face recognition (Wright et al., 2008, 2010). While the face recognition is affected by the occlusions (such as glasses) in the face image, the reconstruction of GIM has problems in the regions that are not covered by GNSS stations. The problems have to be taken into account when selecting the past maps for combination and should not introduce a bias. As shown in Eq. (6), the problem is solved by introducing ℓ_{2} norm and ℓ_{1} norm. The property of the atomic decomposition and the least absolute shrinkage and selection operator (LASSO) is that it can select a small set of past maps which are the most similar to the realtimemeasured VTEC at IPPs. The ADIGIM technique minimizes the difference between observed VTEC measurement and weighted VTEC from historical UQRG in similar ionosphere conditions. The underlying assumption is that the VTEC distribution over the areas not covered by the IPPs can be represented by the elements of the historical library of UQRG (Yang et al., 2021). The UPC RTGIM with the new technique is denoted as UADG and generated by Eq. (6). Due to the improvement provided by the UADG, the broadcasted UPCGIM was changed from USRG to UADG on 4 January 2021. In addition, the USRG and UADG are generated in realtime mode and saved in IONEX format at HTTP as shown in Table 1.
Here VTEC_{I,t} is the observed VTEC at IPP of epoch t. It is assumed that VTEC_{I,t} can be approximated by ${D}_{g,\mathrm{I},t}$ and α_{t}, while ${D}_{g,\mathrm{I},t}$ is the VTEC extracted at IPP from historical databases of GIM g (for UPC, the UQRG is used), and α_{t} is the unknown weight vector of each historical GIM at epoch t. ${\stackrel{\mathrm{\u0303}}{\mathit{\alpha}}}_{t}$ is the estimated weight vector of each selected UQRG at epoch t. The estimated weight vector ${\stackrel{\mathrm{\u0303}}{\mathit{\alpha}}}_{t}$ is obtained by the LASSO regression method with loss function norm ℓ_{2} and regularization norm ℓ_{1}. ℓ_{2} is the norm for minimizing the Euclidean distance between observed VTEC measurements and historical UQRG databases at epoch t. ℓ_{1} is the regularization norm for penalizing the approximation coefficients to limit the number of UQRG involved in the estimation, and ρ controls the sparsity of solution. G_{t} is the generated UPC RTGIM of epoch t and is the weighted combination of historical UQRG. For mathematical convenience, each 2D GIM is reformed as a 1D vector (i.e., the columns are stacked along the meridian in order to create a vector of all the grid points of the map). This is justified because the measure of similarity is done over cells of $\mathrm{2.5}{}^{\circ}\times \mathrm{5.0}$^{∘} in the maps, and therefore the underlying ℝ^{2} (coordinate space of dimension 2) structure is not relevant for computing Euclidean distances in ℓ_{2} norm. D_{t} is the selected historical UQRG database with similar ionosphere conditions at epoch t.
2.2.4 Wuhan University
The daily rapid and final GIM products have been generated with new WHU software named GNSS Ionosphere Monitoring and Analysis Software (GIMAS) since 21 June 2018 (Zhang and Zhao, 2018). At the end of the year 2020, WHU also published a first RTGIM product.
WHU uses the spherical harmonic expansion model, and the formula is identical to Eq. (4). Currently, only the GPS realtime data streams from about 120 globally distributed IGS stations are used. The doublefrequency code and carrier phase observations with a cutoff angle of 10^{∘} are used to gather precise geometryfree ionospheric data with the CCL method as Eq. (3) and ionospheric mapping function with the layer height of 450 km. In order to avoid the influence of satellite and receiver DCB on ionospheric parameter estimation, WHU directly uses the previous estimated DCB from the WHU rapid GIM product. According to previous experience, the realtime data are not enough to model the ionosphere precisely on a global scale with the spherical harmonic expansion technique. Considering the lack and the uneven distribution of the GPSderived ionospheric data, 2 d predicted GIM as external ionospheric information is also incorporated. It is important to balance the weight between the realtime data and the background information. Both the RTGIM quality and the root mean square (rms) map are influenced by the weight (Zhang and Zhao, 2019).
In the year 2021, WHU is going to focus on how to further improve the accuracy of RTGIM and update the computation method. The precise WHU RTGIMs with multiGNSS data and the application of WHU RTGIM in the GNSS positioning as well as space physics domain are expected as next steps.
2.3 The combination of IGS RTGIMs
Thanks to the contribution of the initial IGS realtime ionosphere centers (CAS, CNES and UPC) and globally distributed realtime GNSS stations, the first experimental IRTG was generated by means of the realtime dSTEC (RTdSTEC) weighting technique (normalized inverse of the squared rms of RTdSTEC error) in October 2018 (RomaDollase et al., 2018a; Li et al., 2020). Recently, WHU published the first WHU RTGIM, and UPC upgraded the realtime VTEC interpolation technique. A new version of IRTG has been developed and broadcasted since 4 January 2021. The IGS combined RTGIM is based on the weighted mean value of VTEC from different IGS centers as Eq. (7).
Here VTEC_{IRTG,t} is the VTEC of IGS combined RTGIM at epoch t, and VTEC_{g,t} is VTEC of RTGIM g from the IGS center at epoch t. N_{AC} is the number of IGS centers. w_{g,t} is the weight of corresponding RTGIM g at epoch t (the sum of w_{g,t} at epoch t is 1). ${\text{RMS}}_{\mathit{\delta},g,t}$ is the root mean square of RTdSTEC error at epoch t. I_{g,t} is the inverse of the mean square of RTdSTEC error at epoch t. N_{t} is the number of RTdSTEC observations from the beginning epoch to the current epoch t. δ_{g,i} is the RTdSTEC error of RTGIM g in the RTdSTEC assessment.
In addition, the RTdSTEC assessment is based on root mean square (rms) of the dSTEC error calculated by Eq. (8). In order to adapt to the realtime processing mode, the ambiguous reference STEC measurement ${L}_{\text{GF},{t}_{\text{ref}}}$ is set to be the first elevation angle higher than 10^{∘} within a continuous phase arc to enable the RTdSTEC calculation in the elevationascending arc.
where δ_{g,t} is the dSTEC error of GIM g at epoch t. t_{ref} is the epoch when reference elevation angle is stored. M_{z} and ${M}_{{z}_{\text{ref}}}$ are the mapping functions of zenith angle of epoch t and zenith angle of reference epoch t_{ref}, respectively.
Due to the limited number of realtime stations, 25 common realtime stations that have been used by all the IGS realtime ionosphere centers are selected for allowing a fair RTdSTEC assessment. The distribution can be seen as Fig. 1. Therefore, the RTdSTEC is the measurement of “internal” postfit residuals of RTGIMs and still sensitive to the accuracy of assessed GIMs. Every 20 min, the RTdSTEC assessment is performed and used for the combination of different IGS RTGIMs. The steps for the generation of IRTG can be seen as Fig. 2. The RTCMSSR has been the standard message for realtime corrections, and the IGS State Space Representation (SSR) format version 1.00 was published on 5 October 2020 (IGS, 2020). The content of IGSSSR is compatible with RTCMSSR contents. And the IGSSSR format can support more extensions such as satellite attitude, phase center offsets, and variations in the near future. At present, both RTCMSSR and IGSSSR formats are used for the dissemination of RTGIMs. In addition, IGS defines different references for antenna correction: average phase center (APC) and center of mass (CoM). The current status of RTGIMs from different ionosphere centers can be seen in Table 2. It should be noted that “SSRA” means the SSR with the APC reference, and “SSRC” means the SSR with the CoM reference.
In this section, the performance of IGS RTGIMs was analyzed and compared with rapid IGS GIMs as well as IGS combined final GIM. It should be noted that the RTGIMs were gathered with BKG Ntrip Client (BNC) software (Weber et al., 2016) and generated by received spherical harmonic coefficients from different centers as in Table 2. And there were two kinds of temporal resolution for received RTGIMs: the common temporal resolution of 20 min and the full (original) temporal resolution. Since the IRTG is combined every 20 min, we will focus on such a common time resolution to compare the performance. The detail of compared RTGIMs can be seen in Table 3. The influence of temporal resolution on RTGIMs was also shown in this section.
Before detailing the Jason3 VTEC and GPSdSTEC assessment, it should be taken into account that the GIM error versus Jason VTEC measurements have a high correlation with the GIM error versus dSTECGPS measurements, although the Jason VTEC measurements are vertical and the dSTECGPS measurements are slanted. As demonstrated in HernándezPajares et al. (2017), the Jason3 VTEC assessment and dSTECGPS assessment are independent and consistent for GIM evaluation. In other words, the slant ray path geometry changes do not affect the capability of dSTEC reference data to rank the GIM, and the electron content between the Jason3 altimeter and the GNSS satellites does not significantly affect the assessment of GIMs based on Jason3 VTEC data.
3.1 Jason3 VTEC assessment
The VTEC from the Jason3 altimeter was gathered as an external reference over the oceans. After applying a sliding window of 16 s to smooth the altimeter measurements, the typical standard deviation of Jason3 VTEC measurement error is around 1 TECU. Although the electron content above the Jason3 altimeter (about 1300 km) is not available and the altimeter bias is around a few TECU, the standard deviation of the difference between GIMVTEC and Jason3 VTEC is adopted to avoid the Jason3 altimeter bias and the constant bias component of the plasmaspheric electron content in the assessment. The plasmaspheric electron content variation is up to a few TECU and is a relatively small part when compared with the GIM errors over the oceans. Jason3 VTEC has been proven to be a reliable reference of VTEC over the oceans. The oceans are the most challenging regions for GIMs where permanent GNSS receivers are typically far away (RomaDollase et al., 2018b; HernándezPajares et al., 2017). In this context, the daily standard deviation of the difference between Jason3 VTEC and GIMVTEC was suitable as the statistic for GIM assessment in Eq. (9).
where VTEC_{Jason,i} and VTEC_{GIM,i} are VTEC extracted from Jason3 and GIM observation i, respectively. N_{J} is the number of involved observations.
The recent 3month data (1 December 2020 to 1 March 2021), containing the two significant events (new contributing RTGIM (WHU) from 3 January 2021 and the introduction of the new atomic decomposition UPCGIM (UADG) on 4 January 2021), have been selected to study the consistency and performance of the IGS RTGIMs.
As can be seen in Fig. 3, the standard deviation of UPC RTGIM (upc1) VTEC versus measured Jason3 VTEC is worse than other RTGIMs before the transition from USRG to UADG on 4 January 2021. It should be noted that the upc1 in RTCMSSR format was stopped from 15 December 2020 to 2 January 2021, due to the change of broadcasting format and some technical issues. The assessment of upc1 was based on the UPC RTGIMs saved in a local repository during the interrupted period. The standard deviation of upc1 VTEC versus measured Jason3 VTEC reached around 7 TECU on 6 December 2020 due to the interruption of the downloading module. And the upc1 achieved a significant improvement after the transition on 4 January 2021. In addition, the accuracy of IGS experimental combined RTGIM (irtg) also increased due to the better performance of upc1. Compared with IGS rapid GIMs (corg, ehrg, emrg, esrg, igrg, jprg, uhrg, uprg, uqrg, whrg) and IGS final combined GIM (igsg), the upc1 and irtg are equivalent to the postprocessed GIMs and even better than some rapid GIMs. The accuracy of CAS RTGIM (crtg) and CNES RTGIM (cnes) is close to the postprocessed GIMs, while WHU RTGIM (whu0) is slightly worse than the other GIMs. As shown and explained in Eq. (4), the whu0 is shifted by 0 h. To see the influence of phaseshifted λ_{S,t}, the whu0 is manually shifted by 2 h (i.e., take t_{0} as 2 h for whu0 in Eq. 4) in postprocessing mode. And the accuracy of the 2 h shifted WHU RTGIM (whu1) is slightly better than whu0 as can be seen in Fig. 3.
The value in bold font means the corresponding RTGIM has the best performance among the remaining RTGIMs in each column, and values of irtg are italic for comparison.
In order to investigate the influence of temporal resolution on RTGIMs over oceans, different RTGIMs with full temporal resolution were involved. The summary of Jason3 VTEC assessment can be seen in Table 4. The overall standard deviation of GIMVTEC minus Jason3 VTEC is computed in separate time periods to focus on the influence of the transition from USRG to UADG. As shown in Table 4, the overall standard deviation of GIMVTEC versus Jason3 VTEC is consistent with Fig. 3, and the quality of 20 min and full temporal resolution of RTGIMs are similar over oceans. And the accuracy of 2 h shifted whu1 in Jason3 VTEC assessment is higher than whu0 in Table 4. In particular, the overall standard deviation of upc1 VTEC versus measured Jason3 VTEC drops from 4.3 to 2.7 TECU, and, in agreement with that, the standard deviation of irtg VTEC versus measured Jason3 VTEC decreases from 3.3 to 2.8 TECU.
3.2 dSTECGPS assessment
In addition, dSTECGPS assessment in postprocessing mode was involved as a complementary tool with high accuracy (better than 0.1 TECU) over continental regions on a global scale. In the dSTECGPS assessment, the maximum elevation angle within a continuous arc was regarded as the reference angle in Eq. (8). The dSTEC observations provide the direct measurements of the difference of STEC within a continuous phase arc involving different geometries. As has been introduced before, the STEC is proportional to VTEC by means of the ionospheric mapping function. Therefore, the dSTEC error observations (see Eq. 8), containing different geometries and mapping function error are direct measurements for evaluating GIMSTEC, which is commonly used by GNSS users to calculate ionospheric correction. In addition, the common agreed ionospheric thin layer model is set to be 450 km in height in the generation of GIM to provide VTEC in a consistent way for different ionospheric analysis centers. And in this way the GNSS users are able to consistently recover the STEC from GIMVTEC by the commonly agreed mapping function. The dSTECGPS assessment was performed by globally distributed GNSS stations as shown in Fig. 1 on 3 January (before the transition of UPC RTGIM from USRG to UADG) and 5 January (after the transition) in 2021, with a focus on the transition of UPC RTGIM. The rms error and relative error were used for the assessment as Eq. (10).
Here RMS_{δ,g} is the rms error of GIM g. And δ_{g,i} is the dSTEC error of GIM g similar to Eq. (8), while the reference angle of Eq. (8) is replaced by the maximum elevation angle within a continuous arc. N_{S} is the number of involved observations. ${O}_{{\mathrm{\Delta}}_{{S}_{\text{GPS},t,i}}}$ is the dSTECGPS observation. ${\text{RMS}}_{\mathrm{\Delta}{S}_{\text{GPS}}}$ is the rms of the observed dSTECGPS. Relative error_{g} is the relative error of GIM g.
As shown in Table 4, the rms error of most postprocessed GIMs reaches around 2 or 3 TECU, while the rms error ranges from 2.8 to 5.54 TECU for RTGIMs. The transition of UPC RTGIM (upf1) from USRG to UADG is apparent in the dSTECGPS assessment, and the rms error of IGS RTGIM (irtg) decreased from 4.11 to 3.37 TECU due to the improvement of UPC RTGIM. After the transition of UPC RTGIM, the performance of upf1 and irtg is comparable with most postprocessed GIMs. Similar to the performance in the Jason3 VTEC assessment, the accuracy of the remaining RTGIMs is close to postprocessed GIMs. And the rms error of 2 h shifted whu1 is around 4.4 TECU, which is better than the whu0. Therefore, the 2 h shift is recommended for λ_{S,t} in Eq. (4). It should be pointed out that the performance of RTGIMs with the full temporal resolution is slightly worse than 20 min RTGIMs. Furthermore, the full temporal resolution RTGIM is even worse than the GIM obtained by linear interpolation of the 20 min RTGIM in a sunfixed reference frame. This is coincident with a smaller number of ionospheric observations at shorter timescales. In Fig. 4, the performance of IGS RTGIMs after the upgrade of the UPC interpolation method in the dSTECGPS assessment is represented. The higher values of rms errors occur around the Equator and Southern Hemisphere for all the RTGIMs. And the higher values might be caused by the highelectrondensity gradients at the Equator and the sparse distribution of realtime stations in the Southern Hemisphere.
3.3 The sensibility of realtime weighting technique
RTdSTEC assessment of RTGIMs was automatically running in realtime mode and used for realtime weighting in the combination of IGS RTGIMs. In order to compare with the dSTECGPS assessment, the RTdSTEC assessment with realtime stations in Fig. 1 was also performed on 3 and 5 January 2021. As can be seen in Table 5, the rank of RTGIMs in the RTdSTEC assessment is similar to the dSTECGPS assessment, but the rms error values are larger. And the larger rms error coincides with the much lower elevation angle of the observation reference in the RTdSTEC assessment.
The value in bold font means the corresponding RTGIM has the best performance among the remaining RTGIMs in each column.
The realtime weights of RTGIMs can be defined as the normalized inverse of the squared rms of RTdSTEC errors and represent the accuracy of RTGIMs in the RTdSTEC assessment. For each RTGIM, the number of daily winning epochs is computed by counting the number of epochs within the day when the one RTGIM is better than the other RTGIMs. The evolution of daily winning epochs of RTGIMs shown in the bottom figure of Fig. 5 is consistent with the Jason3 VTEC assessment. The upc1 was not involved in the combination from 15 December 2020 to 2 January 2021 when the dissemination of upc1 was stopped, as can be seen in the bottom figure of Fig. 5. The significant improvement of the transition of upc1 from USRG to UADG shown in dSTECGPS and the Jason3 VTEC assessment is also obvious in the top panel of Fig. 5. In addition, the daily winning epoch's evolution and the transition in Fig. 5 are consistent with the accuracy of RTGIMs, providing a combined RTGIM which is one of the best RTGIMs, as shown in the altimeterbased and dSTECbased assessments. The good performance of the combination algorithm can be mainly explained from the point of view of the weights, i.e., the sensitivity of the dSTEC error to the quality of the RTGIMs, but also from the point of view of the linear combination that can play a positive role under any potential negative correlation between the performance of pairs of involved RTGIMs.
3.4 The response of RTGIMs to recent minor geomagnetic storms
The global electron content (GEC) is defined as the total number of free electrons in the ionosphere. Hence the GEC can be estimated from the summation of the product of the VTEC value and the area of the corresponding GIM cell. In addition, GEC has been used as an ionospheric index (Afraimovich et al., 2006; HernándezPajares et al., 2009). With the purpose of further checking the consistency of IGS RTGIMs, the GEC of RTGIMs was calculated and compared from 24 to 29 January 2021. It should be noted that the solar activity is low in January 2021. During the selected period, several weak geomagnetic storms and one moderate geomagnetic storm occurred according to the classification of geomagnetic indices (Loewe and Prölss, 1997; Gonzalez et al., 1999), and the GEC evolution can be seen in Fig. 6. The GEC of CNES RTGIM (cnfs) is slightly different from other RTGIMs, and seems to be caused by the bias in CNES RTGIM. There are some jumps in the GEC evolution of CAS RTGIM (crfg) and WHU RTGIM (whf0), and the jumps might be related to the handling of day boundary or unreal predicted GIM in certain cases. Compared with IGS final combined GIM (igsg), the good performance of global VTEC representation with upf1 and irfg can be seen in Fig. 6. In addition, the response of upf1 and irfg to the recent minor geomagnetic storms (detected by 3 h ap and 1 h Dst indices) is apparent and also similar to the postprocessed IGS final combined GIM (igsg).
The IGS realtime combined GIMs during the testing period are available from Zenodo at https://doi.org/10.5281/zenodo.5042622 (Liu et al., 2021b) in IONEX format (Schaer et al., 1998). In addition, more archived IGS combined RTGIMs can be found at http://chapman.upc.es/irtg/archive/ (Liu and HernándezPajares, 2021a), and the latest IGS combined RTGIMs are available in realtime mode at http://chapman.upc.es/irtg/last_results/ (Liu and HernándezPajares, 2021b).
In this paper, we have summarized the computation methods of RTGIMs from four individual IGS ionosphere centers and introduced the new version of IGS combined RTGIM. According to the results of Jason3 VTEC and dSTECGPS assessment, it could be concluded as follows.

The realtime weighting technique for the generation of IGS combined RTGIM performs well when it is compared with Jason3 VTEC and dSTECGPS assessment.

The transition of UPC RTGIM from USRG to UADG is obvious in all involved assessments and also demonstrates the sensibility of the realtime weighting technique to RTGIMs when the accuracy of RTGIMs is increased.

The quality of most IGS RTGIMs is close to postprocessed GIMs.

The difference among RTGIMs with 20 min and full temporal resolution can be neglected over oceans in the Jason3 VTEC assessment (see Fig. 3 and Table 4), while the difference is visible in some RTGIMs over continental regions in the dSTECGPS assessment (see Table 4). The lower accuracy of GIMs with full temporal resolution (2 or 5 min) might be related to the uneven distribution of ionospheric observations, the weight between predicted GIMs and realtime observations. Combined with the previous study (Liu et al., 2021a), it is suggested to find a more suitable temporal resolution for the generation of RTGIM in a sunfixed reference frame.
In addition, the GEC evolution of UPC RTGIM and IGS combined RTGIM is close to the GEC evolution of IGS final combined GIM in postprocessing mode and has an obvious response to the geomagnetic storm during the lowsolaractivity period. Future improvements might include the following.

Broadcast realtime rms maps that can be useful for the positioning users.

Increase the accuracy of hightemporalresolution RTGIMs. In addition, higher maximum spherical harmonic degrees might be adopted to increase the accuracy and spatial resolution of RTGIMs.

Coinciding with a much larger number of RTGNSS receivers in the future, the dSTEC weighting might be improved by replacing the “internal” with the “external” receivers, i.e., not used by any realtime analysis centers. In this way the weighting would be sensitive as well to the interpolation–extrapolation error of the different realtime ionospheric GIMs to be combined. And the resulting combination might behave better.

Increase the number of worldwide GNSS receivers used for the RTdSTEC up to more than 100. In this way we will be able to study the potential upgrade of the present global weighting to a regional weighting among other potential improvements in the combination strategy.
QL wrote the manuscript. QL developed the updated combination software with contributions from DRD, HY and MHP. QL and MHP designed the research, with contributions from HY, EMM, DRD and AGR. QL, HY, EMM, MHP, ZL, NW, DL, AB, Q. Zhao and Q. Zhang provided the realtime GIMs of the corresponding IGS centers. AH, MS, GW and AS contributed in creating the framework of the realtime IGS service, the ionospheric message format and BNC open software updates. LA suggested the initial idea of this work. AK, StS, JF, AK, RGF and AGR contributed in the generation of rapid and final IGS GIMs used as additional references in the manuscript.
The contact author has declared that neither they nor their coauthors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors are thankful to the collaborative and friendly framework of the International GNSS Service, an organization providing firstclass open data and open products (Johnston et al., 2017). The VTEC data from the Jason3 altimeter were gathered from the NASA EOSDIS Physical Oceanography Distributed Active Archive Center (PO.DAAC) at the Jet Propulsion Laboratory, Pasadena, CA (https://doi.org/10.5067/GHGMR4FJ01), and the National Oceanic and Atmospheric Administration (NOAA). We are also thankful to GeoForschungsZentrum (GFZ) and to World Data Center (WDC) for Geomagnetism, Kyoto, for providing the ap and Dst indices.
This research has been supported by the China Scholarship Council (CSC). The contribution from UPCIonSAT authors was partially supported by the European Unionfunded project PITHIANRF (grant no. 101007599) and by the ESSP/ICAOfunded project TEC4SpaW. The work of Andrzej Krankowski is supported by the National Centre for Research and Development, Poland, through grant ARTEMIS (grant nos. DWM/PLCHN/97/2019 and WPC1/ARTEMIS/2019).
This paper was edited by Christian Voigt and reviewed by two anonymous referees.
Afraimovich, E., Astafyeva, E., Oinats, A., Yasukevich, Y. V., and Zhivetiev, I.: Global electron content and solar activity: comparison with IRI modeling results, in: poster presentation at IGS Workshop, Darmdstadt, Germany, 8–11 May 2006. a
Caissy, M., Agrotis, L., Weber, G., HernandezPajares, M., and Hugentobler, U.: Innovation: Coming SoonThe International GNSS RealTime Service, available at: https://www.gpsworld.com/gnsssystemaugmentationassistanceinnovationcomingsoon13044/ (last access: 21 March 2021), 2012. a
Chen, J., Ren, X., Zhang, X., Zhang, J., and Huang, L.: Assessment and Validation of Three Ionospheric Models (IRI2016, NeQuick2, and IGSGIM) From 2002 to 2018, Space Weather, 18, e2019SW002422, https://doi.org/10.1029/2019SW002422, 2020. a
Ciraolo, L., Azpilicueta, F., Brunini, C., Meza, A., and Radicella, S.: Calibration errors on experimental slant total electron content (TEC) determined with GPS, J. Geodesy, 81, 111–120, https://doi.org/10.1007/s0019000600931, 2007. a
Elsobeiey, M. and AlHarbi, S.: Performance of realtime Precise Point Positioning using IGS realtime service, GPS Solut., 20, 565–571, https://doi.org/10.1007/s102910150467z, 2016. a
Feltens, J.: Development of a new threedimensional mathematical ionosphere model at European Space Agency/European Space Operations Centre, Space Weather, 5, S12002, https://doi.org/10.1029/2006SW000294, 2007. a
Feltens, J. and Schaer, S.: IGS Products for the Ionosphere, in: Proceedings of the 1998 IGS Analysis Center Workshop Darmstadt, Germany, 9–11 February 1998, pp. 3–5, 1998. a
Fernandes, M. J., Lázaro, C., Nunes, A. L., and Scharroo, R.: Atmospheric corrections for altimetry studies over inland water, Remote Sens.Basel, 6, 4952–4997, https://doi.org/10.3390/rs6064952, 2014. a
Froń, A., Galkin, I., Krankowski, A., Bilitza, D., HernándezPajares, M., Reinisch, B., Li, Z., Kotulak, K., Zakharenkova, I., Cherniak, I., Roma Dollase, D., Wang, N., Flisek, P., and GarcíaRigo, A.: Towards Cooperative Global Mapping of the Ionosphere: Fusion Feasibility for IGS and IRI with Global Climate VTEC Maps, Remote Sens.Basel, 12, 3531, https://doi.org/10.3390/rs12213531, 2020. a
GarcíaRigo, A., Monte, E., HernándezPajares, M., Juan, J., Sanz, J., AragónAngel, A., and Salazar, D.: Global prediction of the vertical total electron content of the ionosphere based on GPS data, Radio Sci., 46, RS0D25, https://doi.org/10.1029/2010RS004643, 2011. a
García Rigo, A., Roma Dollase, D., Hernández Pajares, M., Li, Z., Terkildsen, M., Ghoddousi Fard, R., Dettmering, D., Erdogan, E., Haralambous, H., Beniguel, Y., Berdermann, J., Kriegel, M., KrypiakGregorczyk, A., Gulyaeva, T., Komjathy, A., Vergados, P., Feltens, J., Zandbergen, R., Olivares, G., FullerRowell, T., Altadill, D., Blanch, E., Bergeot, N., Krankowski, A., Agrotis, L., Galkin, I., OrusPerez, R., and Prol, F. S.: St. Patrick's day 2015 geomagnetic storm analysis based on real time ionosphere monitoring, in: EGU 2017: European Geosciences Union General Assembly, Vienna, Austria, 23–28 April 2017, proceedings book, 2017. a
GhoddousiFard, R.: GPS ionospheric mapping at Natural Resources Canada, in: IGS workshop, Pasadena, 23–27 June 2014. a
Gonzalez, W. D., Tsurutani, B. T., and De Gonzalez, A. L. C.: Interplanetary origin of geomagnetic storms, Space Sci. Rev., 88, 529–562, https://doi.org/10.1023/A:1005160129098, 1999. a
Gulyaeva, T. L. and Stanislawska, I.: Derivation of a planetary ionospheric storm index, Ann. Geophys., 26, 2645–2648, https://doi.org/10.5194/angeo2626452008, 2008. a
Gulyaeva, T. L., Arikan, F., HernandezPajares, M., and Stanislawska, I.: GIMTEC adaptive ionospheric weather assessment and forecast system, J. Atmos. Sol.Terr. Phy., 102, 329–340, https://doi.org/10.1016/j.jastp.2013.06.011, 2013. a
HernándezPajares, M., Juan, J., and Sanz, J.: Neural network modeling of the ionospheric electron content at global scale using GPS data, Radio Sci., 32, 1081–1089, https://doi.org/10.1029/97RS00431, 1997. a
HernándezPajares, M., Juan, J., Sanz, J., and Solé, J.: Global observation of the ionospheric electronic response to solar events using ground and LEO GPS data, J. Geophys. Res.Space, 103, 20789–20796, https://doi.org/10.1029/98JA01272, 1998. a, b
HernándezPajares, M., Juan, J., and Sanz, J.: New approaches in global ionospheric determination using ground GPS data, J. Atmos. Sol.Terr. Phy., 61, 1237–1247, https://doi.org/10.1016/S13646826(99)000541, 1999. a, b, c
HernándezPajares, M., Juan, J., Sanz, J., Orus, R., GarcíaRigo, A., Feltens, J., Komjathy, A., Schaer, S., and Krankowski, A.: The IGS VTEC maps: a reliable source of ionospheric information since 1998, J. Geodesy, 83, 263–275, https://doi.org/10.1007/s0019000802661, 2009. a, b, c
HernándezPajares, M., RomaDollase, D., Krankowski, A., GarcíaRigo, A., and OrúsPérez, R.: Methodology and consistency of slant and vertical assessments for ionospheric electron content models, J. Geodesy, 91, 1405–1414, https://doi.org/10.1007/s001900171032z, 2017. a, b
HernándezPajares, M., Lyu, H., AragónÀngel, À., MonteMoreno, E., Liu, J., An, J., and Jiang, H.: Polar Electron Content From GPS DataBased Global Ionospheric Maps: Assessment, Case Studies, and Climatology, J. Geophys. Res.Space, 125, e2019JA027677, https://doi.org/10.1029/2019JA027677, 2020. a
Hoque, M. M., Jakowski, N., and OrúsPérez, R.: Fast ionospheric correction using Galileo Az coefficients and the NTCM model, GPS Solut., 23, 41, https://doi.org/10.1007/s1029101908333, 2019. a
IGS: IGS State Space Representation (SSR) Format Version 1.00, available at: https://files.igs.org/pub/data/format/igs_ssr_v1.pdf (last access: 21 March 2021), 2020. a, b
Jakowski, N., Hoque, M., and Mayer, C.: A new global TEC model for estimating transionospheric radio wave propagation errors, J. Geodesy, 85, 965–974, https://doi.org/10.1007/s0019001104551, 2011. a
Jiang, H., Liu, J., Wang, Z., An, J., Ou, J., Liu, S., and Wang, N.: Assessment of spatial and temporal TEC variations derived from ionospheric models over the polar regions, J. Geodesy, 93, 455–471, https://doi.org/10.1007/s0019001811756, 2019. a
Johnston, G., Riddell, A., and Hausler, G.: The International GNSS Service, in: Springer Handbook of Global Navigation Satellite Systems, 1st edn., edited by: Teunissen, P. J. and Montenbruck, O., Springer International Publishing, Cham, Switzerland, 967–982, https://doi.org/10.1007/9783319429281, 2017. a
Komjathy, A. and Born, G. H.: GPSbased ionospheric corrections for single frequency radar altimetry, J. Atmos. Sol.Terr. Phy., 61, 1197–1203, https://doi.org/10.1016/S13646826(99)000516, 1999. a
Komjathy, A., Galvan, D., Stephens, P., Butala, M., Akopian, V., Wilson, B., Verkhoglyadova, O., Mannucci, A., and Hickey, M.: Detecting ionospheric TEC perturbations caused by natural hazards using a global network of GPS receivers: The Tohoku case study, Earth Planets Space, 64, 1287–1294, https://doi.org/10.5047/eps.2012.08.003, 2012. a
Laurichesse, D. and Blot, A.: New CNES real time products including BeiDou, available at: https://lists.igs.org/pipermail/igsmail/2015/001017.html (last access: 21 March 2021), 2015. a, b
Le, A. Q. and Tiberius, C.: Singlefrequency precise point positioning with optimal filtering, GPS Solut., 11, 61–69, https://doi.org/10.1007/s1029100600339, 2007. a
Li, M., Yuan, Y., Wang, N., Li, Z., and Huo, X.: Performance of various predicted GNSS global ionospheric maps relative to GPS and JASON TEC data, GPS Solut., 22, 55, https://doi.org/10.1007/s1029101807212, 2018. a
Li, X., Ge, M., Zhang, H., and Wickert, J.: A method for improving uncalibrated phase delay estimation and ambiguityfixing in realtime precise point positioning, J. Geodesy, 87, 405–416, https://doi.org/10.1007/s001900130611x, 2013. a
Li, Z., Yuan, Y., Wang, N., HernandezPajares, M., and Huo, X.: SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions, J. Geodesy, 89, 331–345, https://doi.org/10.1007/s0019001407789, 2015. a, b
Li, Z., Wang, N., Hernández Pajares, M., Yuan, Y., Krankowski, A., Liu, A., Zha, J., García Rigo, A., RomaDollase, D., Yang, H., Laurichesse, D., and Blot, A.: IGS realtime service for global ionospheric total electron content modeling, J. Geodesy, 94, 32, https://doi.org/10.1007/s00190020013600, 2020. a, b, c, d, e, f
Liu, J.Y., Chen, Y., Chuo, Y., and Chen, C.S.: A statistical investigation of preearthquake ionospheric anomaly, J. Geophys. Res.Space, 111, A05304, https://doi.org/10.1029/2005JA011333, 2006. a
Liu, L., Wan, W., Ning, B., and Zhang, M.L.: Climatology of the mean total electron content derived from GPS global ionospheric maps, J. Geophys. Res.Space, 114, A06308, https://doi.org/10.1029/2009JA014244, 2009. a
Liu, Q. and HernándezPajares, M.: The archive of IGS combined realtime GIM [data set], available at: http://chapman.upc.es/irtg/archive, last access: 10 September 2021a. a
Liu, Q. and HernándezPajares, M.: The latest results of IGS combined realtime GIM [data set], available at: http://chapman.upc.es/irtg/last_results, last access: 10 September 2021b. a
Liu, Q., HernándezPajares, M., Lyu, H., and Goss, A.: Influence of temporal resolution on the performance of global ionospheric maps, J. Geodesy, 95, 34, https://doi.org/10.1007/s0019002101483y, 2021a. a
Liu, Q., HernándezPajares, M., Yang, H., MonteMoreno, E., Roma, D., García Rigo, A., Li, Z., Wang, N., Laurichesse, D., Blot, A., Zhao, Q., and Zhang, Q.: Global Ionosphere Maps of vertical electron content combined in realtime from the RTGIMs of CAS, CNES, UPCIonSAT, and WHU International GNSS Service (IGS) centers (from Dec 1, 2020, to March 1, 2021), Zenodo [data set], https://doi.org/10.5281/zenodo.5042622, 2021b. a, b
Loewe, C. and Prölss, G.: Classification and mean behavior of magnetic storms, J. Geophys. Res.Space, 102, 14209–14213, https://doi.org/10.1029/96JA04020, 1997. a
Lou, Y., Zheng, F., Gu, S., Wang, C., Guo, H., and Feng, Y.: MultiGNSS precise point positioning with raw singlefrequency and dualfrequency measurement models, GPS Solut., 20, 849–862, https://doi.org/10.1007/s1029101504958, 2016. a
Mannucci, A., Wilson, B., Yuan, D., Ho, C., Lindqwister, U., and Runge, T.: A global mapping technique for GPSderived ionospheric total electron content measurements, Radio Sci., 33, 565–582, https://doi.org/10.1029/97RS02707, 1998. a
Orús, R., HernándezPajares, M., Juan, J., and Sanz, J.: Improvement of global ionospheric VTEC maps by using kriging interpolation technique, J. Atmos. Sol.Terr. Phy., 67, 1598–1609, https://doi.org/10.1016/j.jastp.2005.07.017, 2005. a
Ren, X., Chen, J., Li, X., Zhang, X., and Freeshah, M.: Performance evaluation of realtime global ionospheric maps provided by different IGS analysis centers, GPS Solut., 23, 113, https://doi.org/10.1007/s1029101909045, 2019. a
RomaDollase, D., Gómez Cama, J. M., Hernández Pajares, M., and GarcíaRigo, A.: Realtime Global Ionospheric modelling from GNSS data with RTTOMION model, in: 5th International Colloquium Scientific and Fundamental Aspects of the Galileo Programme, Braunschweig, Germany, 27–29 October 2015. a
RomaDollase, D., HernándezPajares, M., García Rigo, A., Krankowski, A., Fron, A., Laurichesse, D., Blot, A., OrúsPérez, R., Yuan, Y., Li, Z., Wang, N., Schmidt, M., and Erdogan, E.: Looking for optimal ways to combine global ionospheric maps in realtime, in: IGS workshop 2018, Wuhan, 29 October–2 November, 2018a. a, b
RomaDollase, D., HernándezPajares, M., Krankowski, A., Kotulak, K., GhoddousiFard, R., Yuan, Y., Li, Z., Zhang, H., Shi, C., Wang, C., Feltens, J., Vergados, P., Komjathy, A., Schaer, S., GarcíaRigo, A., and GómezCama, J. M.: Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle, J. Geodesy, 92, 691–706, https://doi.org/10.1007/s0019001710889, 2018b. a
RTCMSC: Proposal of new RTCM SSR messages, SSR Stage 2: Vertical TEC (VTEC) for RTCM Standard 10403.2 Differential GNSS (global navigation satellite system) Services – Version 3, RTCM Special Committee, 104, 2014. a, b
Schaer, S., Beutler, G., Rothacher, M., and Springer, T. A.: Daily global ionosphere maps based on GPS carrier phase data routinely produced by the CODE Analysis Center, in: Proceedings of the IGS AC Workshop, Silver Spring, MD, USA, 19–21 March, 1996. a
Schaer, S., Gurtner, W., and Feltens, J.: IONEX: The ionosphere map exchange format version 1, in: Proceedings of the IGS AC workshop, Darmstadt, Germany, 9–11 February 1998, vol. 9, 1998. a, b
Sezen, U., Arikan, F., Arikan, O., Ugurlu, O., and Sadeghimorad, A.: Online, automatic, nearreal time estimation of GPSTEC: IONOLABTEC, Space Weather, 11, 297–305, https://doi.org/10.1002/swe.20054, 2013. a
SotomayorBeltran, C., Sobey, C., Hessels, J., De Bruyn, G. et al.: Calibrating highprecision Faraday rotation measurements for LOFAR and the next generation of lowfrequency radio telescopes, Astron. Astrophys., 552, A58, https://doi.org/10.1051/00046361/201220728, 2013. a
Tange, O.: Gnu parallelthe commandline power tool, The USENIX Magazine, 36, 42–47, https://doi.org/10.5281/zenodo.16303, 2011. a
Tomaszewski, D., Wielgosz, P., Rapiński, J., KrypiakGregorczyk, A., Kaźmierczak, R., HernándezPajares, M., Yang, H., and OrúsPérez, R.: Assessment of Centre National d'Etudes Spatiales RealTime Ionosphere Maps in Instantaneous Precise RealTime Kinematic Positioning over Medium and Long Baselines, Sensors, 20, 2293, https://doi.org/10.3390/s20082293, 2020. a
Wang, N., Li, Z., Duan, B., Hugentobler, U., and Wang, L.: GPS and GLONASS observablespecific code bias estimation: comparison of solutions from the IGS and MGEX networks, J. Geodesy, 94, 74, https://doi.org/10.1007/s00190020014045, 2020. a
Weber, G., Mervart, L., Lukes, Z., Rocken, C., and Dousa, J.: Realtime clock and orbit corrections for improved point positioning via NTRIP, in: Proceedings of the 20th international technical meeting of the satellite division of the institute of navigation (ION GNSS 2007), Fort Worth, USA, 25–28 September 2007, pp. 1992–1998, 2007. a
Weber, G., Mervart, L., Stürze, A., Rülke, A., and Stöcker, D.: BKG Ntrip Client, Version 2.12, vol. 49 of Mitteilungen des Bundesamtes für Kartographie und Geodäsie, Verlag des Bundesamtes für Kartographie und Geodäsie, Frankfurt am Main, 2016. a
Wright, J., Yang, A. Y., Ganesh, A., Sastry, S. S., and Ma, Y.: Robust face recognition via sparse representation, IEEE T. Pattern Anal., 31, 210–227, https://doi.org/10.1109/TPAMI.2008.79, 2008. a
Wright, J., Ma, Y., Mairal, J., Sapiro, G., Huang, T. S., and Yan, S.: Sparse representation for computer vision and pattern recognition, P. IEEE, 98, 1031–1044, https://doi.org/10.1109/JPROC.2010.2044470, 2010. a
Yang, H., MonteMoreno, E., HernándezPajares, M., and RomaDollase, D.: Realtime interpolation of global ionospheric maps by means of sparse representation, J. Geodesy, 95, 71, https://doi.org/10.1007/s00190021015255, 2021. a
Zhang, B., Teunissen, P. J., Yuan, Y., Zhang, X., and Li, M.: A modified carriertocode leveling method for retrieving ionospheric observables and detecting shortterm temporal variability of receiver differential code biases, J. Geodesy, 93, 19–28, https://doi.org/10.1007/s0019001811351, 2019. a
Zhang, H., Gao, Z., Ge, M., Niu, X., Huang, L., Tu, R., and Li, X.: On the convergence of ionospheric constrained precise point positioning (ICPPP) based on undifferential uncombined raw GNSS observations, Sensors, 13, 15708–15725, https://doi.org/10.3390/s131115708, 2013a. a
Zhang, H., Xu, P., Han, W., Ge, M., and Shi, C.: Eliminating negative VTEC in global ionosphere maps using inequalityconstrained least squares, Adv. Space Res., 51, 988–1000, https://doi.org/10.1016/j.asr.2012.06.026, 2013b. a
Zhang, Q. and Zhao, Q.: Global ionosphere mapping and differential code bias estimation during low and high solar activity periods with GIMAS software, Remote Sens.Basel, 10, 705, https://doi.org/10.3390/rs10050705, 2018. a
Zhang, Q. and Zhao, Q.: Analysis of the data processing strategies of spherical harmonic expansion model on global ionosphere mapping for moderate solar activity, Adv. Space Res., 63, 1214–1226, https://doi.org/10.1016/j.asr.2018.10.031, 2019. a
Zhao, B., Wan, W., Liu, L., Mao, T., Ren, Z., Wang, M., and Christensen, A. B.: Features of annual and semiannual variations derived from the global ionospheric maps of total electron content, Ann. Geophys., 25, 2513–2527, https://doi.org/10.5194/angeo2525132007, 2007. a