A Comparison of a GNSS‐GIM and the IRI‐2020 Model Over China Under Different Ionospheric Conditions

The ionosphere is a crucial factor affecting Global Navigation Satellite System positioning. The Global Ionosphere Map (GIM) or the International Reference Ionosphere (IRI) model can be used for regional ionospheric correction. Since southern China is located near the electron density equatorial anomaly, this study evaluates the performance of the Wuhan University GIM (WHU‐GIM) and the IRI‐2020 from 2008 to 2020 over the China region. The comparison indicates that the Total Electron Content (TEC) from IRI‐2020 is lower than that from WHU‐GIM overall, the discrepancy is more obvious in high solar conditions and low‐latitude regions. The differential Slant TEC (dSTEC) during a phase‐arc with about 0.1 TECU accuracy derived from Global Positioning System (GPS) observations is used for model validation, the results show that the accuracies of WHU‐GIM and IRI‐2020 are 3.14 and 4.57 TECU, respectively. The dSTEC error is larger at low latitudes and decreases with increasing latitude. GPS‐derived TEC is taken for reference to evaluate the model reliability. Results show that both models can reproduce the diurnal TEC variations, but IRI‐2020 is more influenced by geomagnetic activities. The TEC correction percentage for IRI‐2020 is about 60%–80% under different ionospheric conditions, while for WHU‐GIM is 80%–90%. The Single‐Frequency Precise Point Positioning is performed with the ionosphere delay corrected by the two models, respectively. The positioning errors show that using IRI‐2020 has a lower accuracy, and the TEC discrepancy of the IRI‐2020 can cause a large bias in the up direction, especially at low‐latitude regions.

Determination in Europe (CODE), the European Space Agency/European Space Operation Centers (ESA/ ESOC), the Jet Propulsion Laboratory, the Natural Resources Canada, the Universitat Politècnica de Catalunya (UPC) and Wuhan University (WHU) (Roma-Dollase et al., 2018).WHU has been generating the GIM (WHUG) using a spherical harmonics expansion model with an inequality-constrained least squares method since 2016.The precision of GIM produced by WHU presents a comparable accuracy with other IAACs (Zhang & Zhao, 2018).
The IRI model is the official standard empirical model for Earth's ionosphere.It assimilates data from globally distributed ground and space observations of the ionosphere.The monthly average values of electron density and temperature, ion temperature, and ion composition globally at altitudes from 60 to 20,000 km above the ground can be obtained from the IRI model.It has been updated and improved with the new accurate data participated and two-decade old data utilization (Bilitza et al., 2017(Bilitza et al., , 2022)).The latest version of the IRI model, IRI-2020, was released and includes the equatorial ion drift, the occurrence probability of the spread-F layer and the F1 layer, auroral boundaries, and the electron content from the bottom of the ionosphere to a specified altitude (Bilitza et al., 2022).
To mitigate the inaccurate VTECs in GIMs caused by the inhomogeneous distribution of ground stations, some researchers have tried to combine GIMs and the IRI model to obtain higher accuracy (Hernandez-Pajares et al., 2002;Jin et al., 2022).From the perspective of data assimilation and model refinement, it is necessary to analyze the TEC deviation between the IRI model and a GIM.Several studies have compared the TEC from the IRI model and Global Positioning System (GPS) observations, such as, over the Brazilian equatorial area (Batista & Abdu, 2004;Santos et al., 2023), over India (Bhuyan & Borah, 2007;Chauhan & Singh, 2010;Panda et al., 2015;Reddybattula et al., 2019), or the equatorial area (De Dieu Nibigira et al., 2021).However, these researches have mainly focused on the equatorial areas, regions that are close to equatorial regions still have many possibilities for investigation.Additionally, the length of the study period should be longer, such as encompassing a solar cycle, since the ionosphere is closely related to solar activity.Shi et al. (2019) compared the IGS GIM (IGSG) and IRI-2016 models globally between 2000 and 2017, and the results showed that IRI-2016 underestimates the VTEC values over the Pacific Ocean.Chen et al. (2020) assessed the IGSG and IRI-2016 between 2002 and 2018 and found that the maximum bias between the two models was larger than 30 TECU over the equatorial anomaly regions.These assessments with study periods over a solar cycle are presented on a global scale, and there are few studies located in the region of China.Luo et al. (2014) evaluated the IRI-2012 and GIM TEC at low-latitude and mid-latitude regions of China using 1-year data with medium solar activity.Wan et al. (2017) studied a comparison of a GPS-derived TEC and the IRI-2012 model at low latitudes in China in 2006 by calculating the deviation between the two models.These works simply compare the difference between two models in China which lack a reliable reference to validate the models.Besides, previous GIM assessments found that the VTEC error of the GIM changes in a compatible way with the solar activity (Hernández-Pajares et al., 2017).In this sense, an assessment with 1 year of data can be insufficient, and hard to get a reliable result.This research aims to evaluate both models focusing on the regions that are close to equatorial regions during a solar cycle.
The IRI model can provide a reliable TEC background field for modeling regional TEC maps in China and adjacent areas (Aa et al., 2015;Qiao et al., 2021) as well as a real-time regional ionospheric model (Galkin et al., 2021).Due to the lack of ionospheric data in China since the establishment of the IRI model (Wan et al., 2017), it is necessary to assess the performance of the GIMs and IRI model in this region during different ionospheric conditions.This paper presents the assessment of the WHU-GIM and IRI-2020 over China during the time from 2008 to 2020.The description of the data sources is presented in Section 2, then the evaluation methods are introduced in Section 3. The results of the experiment and the analyses are presented in Section 4. Finally, the discussions and the conclusions are presented in Sections 5 and 6, respectively.

Data Sources
Solar and geomagnetic activity are the two elements that affect the ionosphere.The solar radio flux at 10.7 cm (hereinafter F10.7) can indicate solar activity.Figure 1  and declining phase (from 2015 to 2019).Figure 1 indicates that the GMEC coincides with the F10.7 well since the solar extreme ultraviolet irradiance is the main source of ionization (Emmert et al., 2017).The GMEC is about 10 TECU at low solar activity and up to about 40 TECU at high solar activity.
To study the performance of WHU-GIM and the IRI-2020 during geomagnetic quiet and perturbed conditions under different solar activities, geomagnetic storms in 2015 and 2018 were selected: the period from 13 to 21 March 2015 and 20 to 28 August 2018, corresponding to days of the year (DOY) 072-080 and 232-240, respectively.The Kp index and Dst index are two indicators that demonstrate geomagnetic activity conditions.The Kp and Dst index series during the selected days can be downloaded from https://wdc.kugi.kyoto-u.ac.jp/ dstae/index.html,respectively.Figure 2 depicts the variation in F10.7, Kp, and Dst indexes of the geomagnetic storms during the selected periods.The top and bottom panels show the magnetic storms in 2015 and 2018, respectively.
During the storm event on 17 March 2015 with high solar activity, the F10.7 is between 107.9 and 121.6 sfu.As shown in Figure 2, each index remains stable before the storm: the Kp index on most days does not reach 3.0, and the Dst index fluctuates slightly around 0. When the storm occurs on DOY 76, the Kp index increases significantly to 8, and the Dst index decreases sharply and reaches the peak minimum value of −223 nT.During the event on 26 August 2018, with lower solar activity, the F10.7 index remained stable at approximately 70 sfu, and the indexes stayed steady before the storm.Then, the Kp index shows a noticeable enhancement, and the Dst index decreases to approximately −174 nT and stays negative on DOY 238 when the magnetic storm occurs.These two geomagnetic storms under different solar activities are selected in this research to assess the performance of WHU-GIM and the IRI-2020 model during different ionospheric conditions.We take advantage of the IGS, which provides high-quality, stable GNSS observation data sets that are evenly distributed globally.The selected stations in China are depicted in Figure 3. Observations of these stations are used for applying differential Slant TEC (dSTEC) assessment, comparison with the GPS-derived TEC, and the Single-Frequency Precise Point Positioning (SF-PPP) experiments to evaluate the accuracy of the two models.

Method Descriptions
This paper evaluates the performance of the WHU-GIM and IRI-2020 over China between 2008 and 2020 using different methods.First, the differences between the two ionospheric models are calculated.Second, take the precise dSTEC from dual-frequency observations as a reference and calculate the error between the observed dSTEC and the model value.Then, the WHU-GIM and IRI-2020 are compared directly with the GPS-derived TEC under different geomagnetic conditions for both high and low solar activities.Finally, the performance of the SF-PPP is presented by applying the two ionospheric models.

Comparison of the WHU-GIM and the IRI-2020 Model
The WHU-GIM obtained from the inequality-constraints least squares adjustment algorithm implemented in the GNSS Ionosphere Monitoring and Analysis Software (GIMAS) has been released since 2016.WHU provides GIM products containing rapid and final GIMs (labeled WHRG and WHUG) in IONsphere map EXchange (IONEX) format.The GIM contains 13 groups of VTEC maps, and each map contains the VTEC values of grid points with latitudes ranging from −87.5° to 87.5° and longitudes ranging from −180° to 180°.The increments of latitude and longitude are 2.5° and 5°, respectively.The WHUG performs comparably to the other IAACs (Zhang & Zhao, 2018) and is chosen for assessment in this research.For a given location, time, and maximum altitude, the IRI-2020 model provides the electron density of the ionosphere within a given height range.The TEC can be calculated by integrating the electron density on the signal propagation path.In this study, the NeQuick option is chosen for modeling the topside electron density, and the URSI and AMTB models are used to calculate the F2-peak plasma frequency and the F2-peak height, respectively (Bilitza et al., 2022).The VTEC value at each grid point is obtained by integrating the electron density profile derived from the IRI-2020 model.The IRI-2020 model presents the global VTEC in IONEX format named IRIG in this research.
The WHUG and IRIG are compared by calculating the daily bias and Standard Deviation (STD) of the differences at each grid point within China and adjacent regions.The latitude range of the study area is from 0°N to 60°N, and the longitude range is from 70°E to 140°E.The daily bias and STD of the difference are demonstrated in Equations 1 and 2, where  VTEC  whug and  VTEC  irig are the VTEC from the WHUG and the IRIG, respectively, and 〈•〉 refers to calculating the average of the sequence.(1)

dSTEC Method for Assessment
GNSS carrier phase observations are less affected by noise, and the multipath effect compared with the code observations.Previous studies suggested an accurate method called dSTEC for testing ionospheric models using dual-frequency carrier phase observations (Hernández-Pajares et al., 2017).The Slant TEC (STEC) obtained from the difference between two frequency phase observations at a maximum elevation angle over a phase-continuous arc of a satellite-receiver pair can be a reference with high precision with less effect on the ionospheric mapping function.The dSTEC refers to the STEC observation at each given epoch minus the STEC at the highest elevation, and its accuracy can be better than 0.1 TECU (Feltens et al., 2011;Hernández-Pajares et al., 2017).Therefore, it is reasonable to adopt the dSTEC method to assess the accuracy of different ionospheric models.The dSTEC can be calculated as follows: where  observations at two epochs for the same continuous arc can remove the phase integer ambiguities and the hardware delays of the satellite and receiver because they are supposed to be constant for a short time.
Taking the dSTEC with high precision from dual-frequency observations as a reference, the TEC from the ionospheric models can be assessed.The cutoff elevation is set to 25°, and phase arcs longer than 20 min are considered for calculating dSTEC in this research.
The bias and Root Mean Square (RMS) of the dSTEC error can be defined as: where dSTEC obs is the dSTEC calculated from the GPS observations, and dSTEC model is the dSTEC calculated from the WHUG or IRIG.

TEC Extraction From GPS Observations
Both code and carrier phases can be used to derive ionospheric information from GNSS dual-frequency observations.While the code observation was seriously affected by noise and the carrier phase was affected by unknown ambiguities, which may introduce a high complexity for utilization, a method gathering the advantages of both the code and carrier phase called "carrier-to-code leveling" (CCL) was proposed (Mannucci et al., 1993).It removes the ambiguities of the carrier phases using code observations and reduces the influence of the noise in the code observations.The extraction of STEC with the CCL method can be explained as follows (Zhang andZhao, 2018, 2019): HE ET AL.

10.1029/2023SW003646
6 of 16 where  STEC   is the STEC along the signal tracing path between satellite k and receiver i; f 1 and f 2 refer to the frequencies of the L 1 and L 2 phase observations, respectively; the details of the leveled carrier phase  L  will be discussed later; c denotes the speed of light; DCB i and DCB k represent the Differential Code Bias (DCB) of the receiver and satellite, respectively.This method does not consider the high-order ionospheric items, and for simplicity, the noise and multipath effect are not included here.For the abovementioned leveled carrier phase  L  , it can be expressed as (Zhang & Zhao, 2018): where     and     are the difference between observations on two frequencies for the phase and code, respectively.〈•〉 arc indicates the mean value in a continuous satellite-receiver arc.The VTEC can be determined by using the ionospheric mapping function (Schaer, 1999;Zhang & Zhao, 2018): where z is the satellite zenith at the station.R is the Earth's radius, which equals 6,371 km.h is the altitude for calculating the value of the modified mapping function only, which is different from the ionospheric effective height commonly used in a single-layer mapping function.α is a coefficient set to 0.9782.

SF-PPP Performance
Ionospheric delay is one of the main error sources during GNSS positioning, especially for single-frequency users.The STEC should be calculated accurately from the ionospheric model to obtain a more reliable positioning result (Jerez et al., 2023;Rovira-Garcia, 2020).On the other hand, the positioning performance can reflect the precision of ionospheric models.Hence, SF-PPP is an appropriate method to assess ionospheric models from the positioning domain.
The SF-PPP analysis was carried out using the open-source GNSS Analysis software for Multi-constellation and multi-frequency Precise positioning (GAMP) (Zhou et al., 2018), which can be obtained from the GPS Toolbox official website.The detailed SF-PPP configuration adopted is listed in Table 1.

Differences Between the WHU-GIM and the IRI-2020 Model
Figure 4 shows the spatial distribution of the VTEC difference between the WHUG and IRIG under different solar activity days.It can be seen that the WHUG and IRIG deviation on high solar condition days is more evident than on low solar condition days.The difference is mainly within −10.0 to 10.0 TECU overall.However, there is an obvious positive value at the 0°N-20°N latitude band at 6:00 UTC and 12:00 UTC on DOY 072 in 2015.This indicates that the IRIG has a lower TEC with respect to the WHUG in this area.On low solar activity days, the TEC of the two models is comparable, except there is a slightly negative value at the 20°N-30°N latitude band at 6:00 UTC, which indicates that the IRIG has a higher TEC.This area is close to the equatorial ionization anomaly (EIA) (Appleton, 1946) region, which occurs due to the fountain effect on both sides of the equator.The result

Assessment With the dSTEC Method
The distribution of the stations for presenting the dSTEC test to assess the performance of the WHUG and IRIG is depicted in Figure 3. Daily mean bias and RMS sequences of the error between the observed and modeled dSTEC are denoted in Figure 7.It is demonstrated that the WHUG is better than the IRIG in both low and high solar activity conditions.The daily mean values of the WHUG are steadier than that of the IRIG.The performance of the WHUG and IRIG remains at the same level in the years with low solar activity, but during the high solar activity years, the bias of the WHUG is worse than that of the IRIG.The daily bias of the WHUG mainly ranges from −1.0 to 1.0 TECU during the study period.In comparison, the IRIG fluctuates in a more extensive range and peaks at 3 TECU, with a trough near −3 TECU during the high solar years.The RMS series presents a prominent periodic characteristic that may be relevant to the solar condition and annual ionospheric variation (Chen et al., 2020).The RMS values for the WHUG are smaller than those for the IRIG over the entire period.The RMS of the WHUG varies from 1 to 10 TECU, and for the IRIG, it changes between 2 and 16 TECU.
To compare the dSTEC assessment results under different solar activities, the mean bias and RMS sequences of 2014 and 2018 are plotted in Figure 8.The plot shows that the difference between the WHUG and IRIG under low solar activity is more significant than that under high solar activity.In 2014, the mean bias and RMS of the IRIG changed more than those of the WHUG.The mean bias of the IRIG presents a negative deviation with an average of −0.94 TEC.The average RMS of the IRIG is 2.3 TECU larger than that of the WHUG.In 2018, the time series were more stable than in 2014: the mean values of the two models mainly range between −1 and 1 TECU, and the average RMS of the IRIG is 1.1 TECU higher than that of the WHUG.The variations in the dSTEC error of the two models, along with the latitude in 2014 and 2018, are demonstrated in Figure 9.The dSTEC error is more significant at low latitudes and decreases with increasing latitude, this characteristic is more obvious in high solar activity years.This can be expected because the ionosphere in the low-latitude regions is more active and disturbed, and the accuracy of the model in these regions will be reduced.
During high solar conditions, the dSTEC errors of the WHUG and IRIG in lower latitude areas (latitudes approximately from 20°N to 25°N) are 8.39 and 12.19 TECU, respectively.While in low solar activity year, the value decreases to 3 and 4.25 TECU, respectively.At stations with higher latitudes (latitudes approximately from 40°N to 45°N), the discrepancy in the dSTEC errors of the WHUG and IRIG is insignificant in both high and low solar activity years: the difference was 0.84 TECU in 2014 and 0.56 TECU in 2018.

Comparison With the GPS TEC Over China Under Storm Conditions
To assess the performance of the WHUG and IRIG under different geomagnetic conditions, a comparison between the observed and the modeled TEC during two magnetic storms that occurred in high ( 2015) and low (2018) solar activity is presented.The TEC obtained from GNSS observations using the CCL method is taken as the reference, and the DCB is deducted according to the WHUG header information.Only observations with elevations larger than 25° and phase arcs longer than 20 min are used during the calculation.
Figure 10 depicts the TEC calculated from observations and models at the BJFS and TWTF stations.The BJFS station is located at a mid-geographic latitude with a geomagnetic latitude of 30.10°, and the TWTF station is at a lower geographic latitude with a geomagnetic latitude of 15.65° which is close to the EIA (Appleton, 1946;Xu et al., 2012).For clarity, the TEC from DOY 75 to 77 in 2015 and DOY 237 to 239 in 2018 are used to study the capability of the two models under different magnetic conditions.From the diurnal variation in the hourly TEC calculated using the CCL method depicted in Figure 10, the TEC sequence exhibits a typical diurnal characteristic: it reaches a peak at 12:00 to 16:00 Local Time (LT, LT = UT + 8 hr), diminishes after sunset, decreases to a minimum at pre-dawn around 04:00 LT (20:00 UT) (Tariku, 2015;Xu et al., 2012).It is demonstrated that the TEC value during the high solar activity period is much larger than during the low solar activity period: the peak TEC value at BJFS in 2015 was about 40 TECU, while the peak decreased to about 15 TECU in 2018 during the geomagnetic quiet days.This is mainly related to the strength of ionization in the ionosphere, which is conducted by the solar intensity: when solar activity becomes more intense, ionization enhancement is expected, and the TEC gradually increases (Asmare Tariku, 2019;A. Liu et al., 2019;Z. Liu et al., 2019).The TEC at the TWTF station, at a lower geographic latitude and closer to the magnetic equator location, is larger than the TEC at BJFS during both high and low solar activities.
As shown in the top panel of Figure 10, the GPS-derived TEC presents fluctuations during the storm time, while the modeled TEC does not present much fluctuation in these 3 days despite the occurrence of the storm.The TEC at the BJFS station calculated from the IRI-2020 model on DOY 75 in 2015 shows good agreement with the GPS-derived TEC.When the storm occurs, the TEC from the CCL method decreases slightly on DOY 76 after 08:00 UT with a deviation of about 10 TECU.On DOY 77, the CCL TEC decreases significantly, and so does the WHUG, but the IRIG cannot realize this change.Even though its peak was lower, it overestimates the TEC by about 20 TECU compared to the observed TEC.For the 2018 storm, the GPS-derived TEC and WHUG TEC show a noticeable enhancement on DOY 238, while the IRIG cannot capture this change.The difference between the WHUG and CCL TEC remains within −5 and 5 TECU under both geomagnetic quiet and disturbed days, while the difference between the IRIG and CCL TEC is greatly affected by the storm, decreasing to almost −20 TECU on DOY 238.
Previous studies reported a pre-storm enhancement in TEC near the EIA region over the Asian-Australian sector from 12:00 to 24:00 UT on DOY 75 in 2015.A salient increase during the daytime and a decrease at nighttime were observed on DOY 76, and there was an intense negative storm in the EIA on DOY 77 (Kuai et al., 2016;   To study the correlation and difference between the observation and model TECs, the Pearson correlation coefficients between the GPS-derived TEC versus the WHUG and IRIG are calculated, as well as the RMS of the difference between the GPS-derived TEC versus the WHUG and IRIG (Jenan et al., 2022;Panda et al., 2015;Rao et al., 2023).Figure 11 presents the correlation coefficient between the GPS-derived TEC versus the WHUG and IRIG TEC during the selected periods of the 2015 and 2018 storms.The plot demonstrates an excellent correlation greater than 0.85 for the WHUG and IRIG versus the GPS-derived TEC under different ionospheric conditions.Almost all the correlation coefficients between the WHUG and CCL TEC are above 0.95 in 2015 and 2018 during the selected periods, showing a very high correlation, which can be expected because the GIM is modeled from the ground GNSS observations according to some mathematical functions or described in a few layers or voxels (Roma-Dollase et al., 2018;Zhang & Zhao, 2018).The correlation between the IRIG and CCL TEC is slightly lower than that of the WHUG and affected by ionospheric conditions: it drops when geomagnetic storms occur.The RMS values of the deviation present a more salient storm-affected characteristic: they increase by about 3-5 TECU.
During the selected periods in 2015 and 2018, the first three days were magnetic quiet days, and these days were taken as the reference.The changes in the RMS and relative error of the TEC differences between model TEC and GPS-derived TEC when the geomagnetic storms occurred are listed in Table 2.The RMS values for WHUG are 2.73 (1.4) and 4.87 (1.38) TECU during a geomagnetic quiet and disturbed period under in high (low) solar activity year, respectively.Whereas the corresponding values for IRIG are 7.11 (3.39) and 10.45 (4.70) TECU.The IRIG correction percentage of the TEC with respect to the GPS-TEC is 62.85%-80.51%under different geomagnetic conditions, while the corresponding values of WHUG are 83.2%-91.95%.The result means that the IRI-2020 model is more influenced by geomagnetic activities.

TEC Assessment in Positioning Domain
The daily mean RMS of positioning error for the SF-PPP performance of different ionospheric model corrections is shown in Figure 12.In 2015, the horizontal positioning accuracy for both models fluctuated around 0.5 m, and the vertical accuracy of IRIG was worse than that of WHUG.In 2018 with lower solar activity, the horizontal positioning accuracy is within 0.3 m and the vertical accuracy is within 0.5 m for both models.The average  3D positioning error for applying WHUG is 0.75 m, while the value for the IRIG is 1.79 m.The positioning error in 2018 was lower than that in 2015; the mean positioning errors for the WHUG and IRIG were 0.39 and 0.58 m, respectively.It can be seen that the positioning accuracy in the quiet solar activity year is much better than that in the high solar activity year, and the ionospheric error correction accuracy of WHUG is better than that of IRIG.This might be caused by the limitation of data availability from the China region in the development of the IRI-2020 model.
The mean difference between the WHUG and IRIG during the selected period is plotted in Figure 13.The difference value is mainly above 0 TECU which indicates that the IRI-2020 has a lower TEC over China region.The maximum difference reaches 12 TECU occurs at the 0°N-15°N latitude band in 2015.According to the SF-PPP results, the mean bias positioning error of each station during the same period is plotted in Figure 14.The horizontal axis of the figure indicates the stations, arranged in the descending order of latitude.The positioning error bias of the up direction of low-latitude stations using IRIG is nearly 1 m larger than that of using WHUG since the ionospheric pierce point distribution of those stations is close to the equatorial region, which is the abovementioned region with the large TEC deviation of IRIG.This indicates that the low TEC estimation of the IRI-2020 may cause a large bias in up direction in positioning, especially at low-latitude regions in China.

Discussions
During the comparison between the WHUG and IRIG, it was found that the TEC from the IRI-2020 is lower than that from WHUG overall.This can be expected since the IRI model does not consider the TEC contribution from the plasmasphere (Kumar, 2016;Pignalberi et al., 2018;Tariku, 2020), while the GPS observations contain the whole height up to 20,200 km.As Klimenko et al. (2015) suggested, the TEC contribution from the plasmasphere can potentially be up to 20% during the day and up to 50% at night, which may cause a mismatch and degrade the accuracy of the TEC estimation.
The discrepancy between the WHUG and IRIG in high solar activity years is larger than that in low solar activity years, and the discrepancy is more obvious in low-latitude areas, which are close to the EIA regions.Many studies have reported that the inaccurate representation of the topside ionosphere may be caused by the inadequate estimation of the F2-peak plasma frequency (foF2) and the F2-peak height (hmF2).2020) compared the IRI model with digisonde and occultation data over China and indicated that using the URSI and AMTB models to calculate foF2 and hmF2 may cause large deviations, especially for EIA regions.Thus, the insufficient digisonde data in   the equatorial and low-latitude regions used for foF2 and hmF2 estimation may limit the performance of the IRI model (Tariku, 2020).
As an ionospheric empirical climatological model, the IRI model cannot predict all ionospheric variations, specifically under disturbed magnetic conditions (Amarante et al., 2007).The IRI model includes a new option for simulating the ionospheric response to a geomagnetic storm according to Bilitza et al. (2022), but it cannot represent ionospheric variations well in low-latitude regions.Above all, efforts need to be made to improve the IRI model under different geomagnetic activities for the China region.

Conclusions
This study assessed the accuracy of two commonly used ionospheric models: the two-dimensional global ionosphere map WHU-GIM and the IRI-2020 three-dimensional ionospheric model with multi-instrument data assimilated during solar cycle 24 over China and adjacent areas.
The difference between the two models demonstrates that the TEC from IRIG is lower than that from WHUG by 2.26 TECU on average from 2008 to 2020, and they are in good agreement during low solar conditions and differ greatly during high solar years.Regarding the dSTEC assessment result, the performance of the WHUG is better than that of the IRIG.The RMS of the dSTEC error is 3.14 and 4.57 TECU for WHUG and IRIG, respectively.The variations in the dSTEC error for the two models along with the latitude show that the dSTEC error is more prominent at low latitudes and decreases with increasing latitude; this characteristic is more obvious during high solar activity years.Compared with the GPS-derived TEC, both the IRIG and WHUG can reproduce a typical TEC diurnal variation.The IRIG correction percentages of the TEC are 62.85% and 80.51% in geomagnetic disturbed and quiet periods, respectively, while the corresponding values of WHUG are 83.2% and 91.95%.It demonstrates that the IRI-2020 model is more influenced by geomagnetic activities.The SF-PPP performance shows that the positioning accuracy of using IRIG is worse than using the WHUG over China, and the up-direction positioning error bias of using IRIG is about 1 m larger than that of using WHUG, especially for the low-latitude stations.
This study shows that the IRIG can provide a reliable TEC during periods with low solar activity and geomagnetic quiet conditions over China.However, according to the assessment, it offers a weakened performance during high solar activity or geomagnetically disturbed days compared to the WHUG product and the GPS-derived TEC.Despite the empirical IRI-2020 model utilizing solar activity and geomagnetic conditions as input parameters, the IRI-2020 for storms or other events will be less accurate due to the relatively small experimental database.
presents the F10.7 and the Global Mean Electron HE ) time series from 2008 to 2020.The GMEC is derived from the WHUG.The study period encompasses the inclining phase (from 2008 to 2013) of the solar cycle 24, as well as the solar maximum (in 2014)

Figure 2 .
Figure 2. Variations in the F10.7,Kp, and Dst indexes from (a) days of the year (DOY) 72 to 80 in 2015 and (b) DOY 230 to 240 in 2018.

Figure 3 .
Figure 3. Locations of the International GNSS Service stations selected for presenting differential Slant Total Electron Content (TEC) assessment, comparison with the GPS-derived TEC, and the Single-Frequency Precise Point Positioning experiments in this study.

Figure 4 .
Figure 4. Vertical Total Electron Content Difference between WHUG and IRIG on high solar activity day (days of the year (DOY) 072, 2015) and low solar activity day (DOY 232, 2018) over China.

Figure 5
Figure5depicts the time series of solar flux F10.7, daily bias, and STD of the VTEC difference between the WHUG and IRIG from 2008 to 2020.As shown in Figure5, the deviation sequence of the two models is closely related to the F10.7.The deviation between the WHUG and IRIG varies from −5.0 to 15.0 TECU, with a mean of 2.26 TECU during the tested period.This demonstrates that the IRI-2020 has a lower VTEC with respect to the WHUG.The IRIG biases relative to the WHUG fluctuated slightly from −5.0 to 5.0 TECU in low solar activity years.They varied acutely during high solar activity, peaking at 17.52 TECU.The STD sequence ranges from 2.0 to 4.0 TECU under low solar conditions.However, it changes from 2.0 to 10.0 TECU during the high solar activity years.To discuss the consistency of the two models under different solar activity levels, the average and STD sequences for high (2014) and low (2018) solar activity are presented in Figure6.The biases in 2018 varied approximately 0 with an average of 0.76 TECU, indicating that there is no significant difference in the low solar activity years.In 2014, the bias sequence changed over a wide range, with a mean value of 5.59 TECU.The STDs show a similar tendency as the bias during 2014 and 2018, with averages of 6.63 and 2.85 TECU, respectively.The results demonstrate that the WHUG and IRIG agree well in low solar conditions and differ significantly in high solar years.The VTEC in the WHUG is derived from the observed GNSS data.Meanwhile, the VTEC in IRIG is calculated according to an empirical model.It can be inferred that the IRI-2020 model predicts the VTEC with lower precision under high solar activity conditions than under low solar activity conditions.

Figure 5 .
Figure 5.Time series of the F10.7, daily bias, and Standard Deviation of the Vertical Total Electron Content difference between the WHUG and IRIG during 2008-2020.

Figure 6 .
Figure 6.Daily bias and Standard Deviation of the Vertical Total Electron Content difference between the WHUG and IRIG in high (2014) and low (2018) solar activity years.The number in the subplot's upper right corner represents the corresponding sequence's average value.

Figure 7 .
Figure 7. Time series of the daily mean and Root Mean Square values for the two ionospheric models relative to the differential Slant Total Electron Content from dual-frequency observations during 2008-2020.

Figure 8 .
Figure 8. Daily mean bias and Root Mean Square sequences of the differential Slant Total Electron Content error for the WHUG and IRIG in (a) high (2014) and (b) low (2018) solar activity years.The number in the middle of each subfigure represents the average value of the corresponding sequence.

Figure 9 .
Figure 9.The variations in the differential Slant Total Electron Content error for the two models along with the latitude in the high solar activity year (2014) and low solar activity year (2018).

Figure 10 .
Figure 10.Diurnal hourly Total Electron Content (TEC) variation and difference from GPS-derived TEC, the WHUG, and the IRIG in the 2015 storm (top two panels) and 2018 storm (bottom two panels), respectively, at (a) BJFS and (b) TWTF stations.
., 2019).The trend of the GPS-derived TEC from DOY 75 to 77 in 2015 at the TWTF station coincides with the above results and the TEC from the WHUG.Meanwhile, the TEC modeled from the IRI-2020 model did not present any noticeable change during the storm.The deviation of the IRIG TEC and CCL TEC decreases to about −70 TECU on DOY 76 because of the low TEC estimation from the IRI-2020 model, and the value increases to nearly 40 TECU on DOY 77 on account of model overestimation.During the 2018 storm, the observed and WHUG TECs presented an enhancement of about 10 TECU on DOY 238, while the IRIG did not capture this increase.The deviation between the IRIG and CCL TEC is slightly than that during the 2015 storm.

Figure 11 .
Figure 11.The hourly correlation coefficient and Root Mean Square (RMS) between the WHUG/IRIG and the carrier-to-code leveling (CCL) Total Electron Content (TEC).The histogram depicts the Pearson correlation coefficient between the CCL TEC versus the WHUG TEC and IRIG TEC.The point plot shows the RMS of the difference between the CCL TEC versus the WHUG TEC and IRIG TEC.
foF2 and hmF2 are the two important parameters used to obtain the electron density profile in the IRI model.The official recommended URSI and AMTB models are chosen to calculate foF2 and hmF2 in this research.The AMTB model is based on data from 26 digisonde stations distributed globally from 1998 to 2006, including three digisonde stations in the region of China. A. Liu et al. (2019), Z. Liu et al. (2019), and Sun et al. (

Figure 12 .
Figure 12.Daily mean Root Mean Square of positioning error for different ionospheric models corrected in the Single-Frequency Precise Point Positioning solution during (a) days of the year (DOY) 072-080 in 2015 and (b) DOY 230-240 in 2018.

Figure 14 .
Figure 14.Mean bias of positioning error for different ionospheric models corrected in the Single-Frequency Precise Point Positioning solution during (a) days of the year (DOY) 072-080 in 2015 and (b) DOY 230-240 in 2018.