In order to generate RT-GIMs, the real-time 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 RT-GIMs.

Currently, two methods are commonly used for the calculation of real-time STEC. The first method is the so-called carrier-to-code leveling (CCL) as shown in Eq. () . The geometry-free (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 phase-arc length in real-time mode, the impact of multipath and thermal noise is higher than in post-processing mode . PGF,t≡P2,t-P1,t1=αGF⋅STECt+c⋅(Dr+Ds)+ϵM+ϵT2LGF,t≡L1,t-L2,t=αGF⋅STECt+BGFP̃GF,t≡LGF,t-1k∑i=1kLGF,i-PGF,i3≈αGF⋅STECt+c⋅(Dr+Ds) Here P1,t and P2,t are the pseudorange observations of epoch t at first and second frequencies, respectively. αGF can be approximated as 40.3(1f22-1f12). f1 and f2 are the first and second frequencies of observation. STECt is the STEC of epoch t. r is receiver and s is satellite. c is the speed of light in vacuum. Dr and Ds are the receiver differential code biases (DCBs) and satellite DCB. ϵM and ϵT are the code multipath error and thermal noise error. L1,t and L2,t are the carrier phase observations including the priori corrections (such as wind-up term) of epoch t at first and second frequencies. BGF equals B1-B2, while B1 and B2 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 P̃GF,t represents the smoothed PGF of epoch t, which is significantly affected by the pseudorange multipath in real-time mode than in post-processing.

The second method is the GF combination of phase-only observations, and the BGF is estimated together with the real-time TEC model (for example, described in terms of tomographic voxel-based basis functions) in Eq. () . Although the STEC from the second method is accurate and free of code multipath and thermal noise in post-processing, the convergence time can affect the accuracy of the STEC, most likely in the isolated receivers. In addition, the computation methods of RT-GIMs from different IGS real-time ionosphere centers were compared in detail at the next subsection and summarized in Table . Some ionosphere centers (CAS, CNES, WHU) directly estimate and disseminate spherical harmonic coefficients in a sun-fixed reference frame as Eq. () , while UPC generates the RT-GIM in IONEX format and transforms RT-GIM into spherical harmonic coefficients for the dissemination. 4Mz=1-sin⁡2z/(1+Hion/RE)2-12VTECt=STECt/MzVTECt=∑n=0NSH∑m=0min⁡(n,MSH)Pn,m(sin⁡φI)⋅(Cn,mcos⁡(mλS,t)+Sn,msin⁡(mλS,t))λS,t=(λI+(t-t0)×π/43200) modulo 2π Here z is the satellite zenith angle, and Mz is the mapping function between STECt and VTECt. Hion is the height of the ionospheric single-layer assumption, and RE is the radius of the earth. VTECt is the VTEC of epoch t. NSH is the max degree of spherical harmonic expansion, and MSH is the max order of spherical harmonic expansion. n and m are corresponding indices. Pn,m is the normalized associated Legendre functions. Cn,m and Sn,m are sine and cosine spherical harmonic coefficients. φI and λI are the geocentric latitude and longitude of ionospheric pierce point (IPP). λS,t is the mean sun fixed and phase-shifted longitude of IPP of epoch t (typically shifted by 2 h to approximate TEC maximum at 14:00 LT). t is the current epoch. t0 is a common reference of shifted hours, taken as 0 h in the present broadcasting of RT-GIM for WHU and 2 h for CAS, CNES and UPC.

The strategies for generating RT-GIMs differ between IGS real-time ionospheric analysis centers (ACs). In this subsection, a brief introduction on the generation of RT-GIMs from individual ACs and the strategy comparison between different ACs are given.

Thanks to the contribution of the initial IGS real-time ionosphere centers (CAS, CNES and UPC) and globally distributed real-time GNSS stations, the first experimental IRTG was generated by means of the real-time dSTEC (RT-dSTEC) weighting technique (normalized inverse of the squared rms of RT-dSTEC error) in October 2018 . Recently, WHU published the first WHU RT-GIM, and UPC upgraded the real-time VTEC interpolation technique. A new version of IRTG has been developed and broadcasted since 4 January 2021. The IGS combined RT-GIM is based on the weighted mean value of VTEC from different IGS centers as Eq. (). 7VTECIRTG,t=∑g=1NAC(wg,t⋅VTECg,t)wg,t=Ig,t/∑g=1NAC(Ig,t)Ig,t=1/RMSδ,g,t2RMSδ,g,t=∑i=1Nt(δg,i)2/Nt Here VTECIRTG,t is the VTEC of IGS combined RT-GIM at epoch t, and VTECg,t is VTEC of RT-GIM g from the IGS center at epoch t. NAC is the number of IGS centers. wg,t is the weight of corresponding RT-GIM g at epoch t (the sum of wg,t at epoch t is 1). RMSδ,g,t is the root mean square of RT-dSTEC error at epoch t. Ig,t is the inverse of the mean square of RT-dSTEC error at epoch t. Nt is the number of RT-dSTEC observations from the beginning epoch to the current epoch t. δg,i is the RT-dSTEC error of RT-GIM g in the RT-dSTEC assessment.

In addition, the RT-dSTEC assessment is based on root mean square (rms) of the dSTEC error calculated by Eq. (). In order to adapt to the real-time processing mode, the ambiguous reference STEC measurement LGF,tref is set to be the first elevation angle higher than 10∘ within a continuous phase arc to enable the RT-dSTEC calculation in the elevation-ascending arc. δg,t=1αGF((LGF,t-LGF,tref)8-(Mz⋅VTECg,t-Mzref⋅VTECg,tref)), where δg,t is the dSTEC error of GIM g at epoch t. tref is the epoch when reference elevation angle is stored. Mz and Mzref are the mapping functions of zenith angle of epoch t and zenith angle of reference epoch tref, respectively.

Due to the limited number of real-time stations, 25 common real-time stations that have been used by all the IGS real-time ionosphere centers are selected for allowing a fair RT-dSTEC assessment. The distribution can be seen as Fig. . Therefore, the RT-dSTEC is the measurement of “internal” post-fit residuals of RT-GIMs and still sensitive to the accuracy of assessed GIMs. Every 20 min, the RT-dSTEC assessment is performed and used for the combination of different IGS RT-GIMs. The steps for the generation of IRTG can be seen as Fig. . The RTCM-SSR has been the standard message for real-time corrections, and the IGS State Space Representation (SSR) format version 1.00 was published on 5 October 2020 . The content of IGS-SSR is compatible with RTCM-SSR contents. And the IGS-SSR format can support more extensions such as satellite attitude, phase center offsets, and variations in the near future. At present, both RTCM-SSR and IGS-SSR formats are used for the dissemination of RT-GIMs. In addition, IGS defines different references for antenna correction: average phase center (APC) and center of mass (CoM). The current status of RT-GIMs from different ionosphere centers can be seen in Table . It should be noted that “SSRA” means the SSR with the APC reference, and “SSRC” means the SSR with the CoM reference.

The VTEC from the Jason-3 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 Jason-3 VTEC measurement error is around 1 TECU. Although the electron content above the Jason-3 altimeter (about 1300 km) is not available and the altimeter bias is around a few TECU, the standard deviation of the difference between GIM-VTEC and Jason-3 VTEC is adopted to avoid the Jason-3 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. Jason-3 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 . In this context, the daily standard deviation of the difference between Jason-3 VTEC and GIM-VTEC was suitable as the statistic for GIM assessment in Eq. (). 9Biasg=∑i=1NJ(VTECJason-3,i-VTECg,i)/NJSTDg=∑i=1NJ(VTECJason-3,i-VTECg,i-Biasg)2/(NJ-1), where VTECJason,i and VTECGIM,i are VTEC extracted from Jason-3 and GIM observation i, respectively. NJ is the number of involved observations.

The recent 3-month data (1 December 2020 to 1 March 2021), containing the two significant events (new contributing RT-GIM (WHU) from 3 January 2021 and the introduction of the new atomic decomposition UPC-GIM (UADG) on 4 January 2021), have been selected to study the consistency and performance of the IGS RT-GIMs.

As can be seen in Fig. , the standard deviation of UPC RT-GIM (upc1) VTEC versus measured Jason-3 VTEC is worse than other RT-GIMs before the transition from USRG to UADG on 4 January 2021. It should be noted that the upc1 in RTCM-SSR 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 RT-GIMs saved in a local repository during the interrupted period. The standard deviation of upc1 VTEC versus measured Jason-3 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 RT-GIM (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 post-processed GIMs and even better than some rapid GIMs. The accuracy of CAS RT-GIM (crtg) and CNES RT-GIM (cnes) is close to the post-processed GIMs, while WHU RT-GIM (whu0) is slightly worse than the other GIMs. As shown and explained in Eq. (), the whu0 is shifted by 0 h. To see the influence of phase-shifted λS,t, the whu0 is manually shifted by 2 h (i.e., take t0 as 2 h for whu0 in Eq. ) in post-processing mode. And the accuracy of the 2 h shifted WHU RT-GIM (whu1) is slightly better than whu0 as can be seen in Fig. .

In order to investigate the influence of temporal resolution on RT-GIMs over oceans, different RT-GIMs with full temporal resolution were involved. The summary of Jason-3 VTEC assessment can be seen in Table . The overall standard deviation of GIM-VTEC minus Jason-3 VTEC is computed in separate time periods to focus on the influence of the transition from USRG to UADG. As shown in Table , the overall standard deviation of GIM-VTEC versus Jason-3 VTEC is consistent with Fig. , and the quality of 20 min and full temporal resolution of RT-GIMs are similar over oceans. And the accuracy of 2 h shifted whu1 in Jason-3 VTEC assessment is higher than whu0 in Table . In particular, the overall standard deviation of upc1 VTEC versus measured Jason-3 VTEC drops from 4.3 to 2.7 TECU, and, in agreement with that, the standard deviation of irtg VTEC versus measured Jason-3 VTEC decreases from 3.3 to 2.8 TECU.

In addition, dSTEC-GPS assessment in post-processing mode was involved as a complementary tool with high accuracy (better than 0.1 TECU) over continental regions on a global scale. In the dSTEC-GPS assessment, the maximum elevation angle within a continuous arc was regarded as the reference angle in Eq. (). 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. ), containing different geometries and mapping function error are direct measurements for evaluating GIM-STEC, 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 GIM-VTEC by the commonly agreed mapping function. The dSTEC-GPS assessment was performed by globally distributed GNSS stations as shown in Fig.  on 3 January (before the transition of UPC RT-GIM from USRG to UADG) and 5 January (after the transition) in 2021, with a focus on the transition of UPC RT-GIM. The rms error and relative error were used for the assessment as Eq. (). 10RMSδ,g=∑i=1NS(δg,i)2/NSOΔSGPS,t,i=(LGF,t-LGF,tref)/αGFRMSΔSGPS=∑i=1NS(OΔSGPS,t,i)2/NSRelative errorg=100⋅RMSδ,g/RMSΔSGPS Here RMSδ,g is the rms error of GIM g. And δg,i is the dSTEC error of GIM g similar to Eq. (), while the reference angle of Eq. () is replaced by the maximum elevation angle within a continuous arc. NS is the number of involved observations. OΔSGPS,t,i is the dSTEC-GPS observation. RMSΔSGPS is the rms of the observed dSTEC-GPS. Relative errorg is the relative error of GIM g.

As shown in Table , the rms error of most post-processed GIMs reaches around 2 or 3 TECU, while the rms error ranges from 2.8 to 5.54 TECU for RT-GIMs. The transition of UPC RT-GIM (upf1) from USRG to UADG is apparent in the dSTEC-GPS assessment, and the rms error of IGS RT-GIM (irtg) decreased from 4.11 to 3.37 TECU due to the improvement of UPC RT-GIM. After the transition of UPC RT-GIM, the performance of upf1 and irtg is comparable with most post-processed GIMs. Similar to the performance in the Jason-3 VTEC assessment, the accuracy of the remaining RT-GIMs is close to post-processed 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 λS,t in Eq. (). It should be pointed out that the performance of RT-GIMs with the full temporal resolution is slightly worse than 20 min RT-GIMs. Furthermore, the full temporal resolution RT-GIM is even worse than the GIM obtained by linear interpolation of the 20 min RT-GIM in a sun-fixed reference frame. This is coincident with a smaller number of ionospheric observations at shorter timescales. In Fig. , the performance of IGS RT-GIMs after the upgrade of the UPC interpolation method in the dSTEC-GPS assessment is represented. The higher values of rms errors occur around the Equator and Southern Hemisphere for all the RT-GIMs. And the higher values might be caused by the high-electron-density gradients at the Equator and the sparse distribution of real-time stations in the Southern Hemisphere.

RT-dSTEC assessment of RT-GIMs was automatically running in real-time mode and used for real-time weighting in the combination of IGS RT-GIMs. In order to compare with the dSTEC-GPS assessment, the RT-dSTEC assessment with real-time stations in Fig.  was also performed on 3 and 5 January 2021. As can be seen in Table , the rank of RT-GIMs in the RT-dSTEC assessment is similar to the dSTEC-GPS 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 RT-dSTEC assessment.

The real-time weights of RT-GIMs can be defined as the normalized inverse of the squared rms of RT-dSTEC errors and represent the accuracy of RT-GIMs in the RT-dSTEC assessment. For each RT-GIM, the number of daily winning epochs is computed by counting the number of epochs within the day when the one RT-GIM is better than the other RT-GIMs. The evolution of daily winning epochs of RT-GIMs shown in the bottom figure of Fig.  is consistent with the Jason-3 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. . The significant improvement of the transition of upc1 from USRG to UADG shown in dSTEC-GPS and the Jason-3 VTEC assessment is also obvious in the top panel of Fig. . In addition, the daily winning epoch's evolution and the transition in Fig.  are consistent with the accuracy of RT-GIMs, providing a combined RT-GIM which is one of the best RT-GIMs, as shown in the altimeter-based and dSTEC-based 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 RT-GIMs, 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 RT-GIMs.

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 . With the purpose of further checking the consistency of IGS RT-GIMs, the GEC of RT-GIMs 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 , and the GEC evolution can be seen in Fig. . The GEC of CNES RT-GIM (cnfs) is slightly different from other RT-GIMs, and seems to be caused by the bias in CNES RT-GIM. There are some jumps in the GEC evolution of CAS RT-GIM (crfg) and WHU RT-GIM (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. . 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 post-processed IGS final combined GIM (igsg).