Performance of BDS Navigation Ionospheric Model During the Main Phase of Different Classified Geomagnetic Storms in China Region

Geomagnetic storms can have a great impact on the Earth's upper atmosphere, that is, the ionosphere. The activity of the ionosphere could be more pronounced during geomagnetic storms, which can make key ionospheric parameters, like total electron content (TEC), very hard to be modeled. The use of a Global Navigation Satellite System (GNSS) navigation ionospheric model is a conventional option for users to correct the ionospheric delay, which could suffer from the effects of storms. In this study, the performance of Beidou Navigation Satellite System (BDS) navigation ionospheric model in the China region during the main phase of different classes of geomagnetic storms is investigated for the first time. The analysis of the results revealed that the accuracy of the BDS navigation ionospheric model was impacted to different degrees during the storms. The effects during strong storms were the greatest, followed by moderate and weak storms. The impact on the accuracy of the model was characterized by latitude and local time. Furthermore, the accuracy of the model during the same class of storms was not always at the same level. The finding in this study could benefit the prediction of GNSS navigation ionospheric models' performance during geomagnetic storms.


Introduction
Geomagnetic storms are magnetospheric disturbances which are characterized by increased particle fluxes in the ring current. The enhanced fluxes can be measured as a reduction in the horizontal component of the geomagnetic field (Echer et al., 2008). Geomagnetic storms are primarily motivated by intense, long duration and southward interplanetary magnetic fields (IMFs). The southward IMFs interconnect with the geomagnetic field and transport the solar wind energy into the Earth's magnetosphere (Gonzalez et al., 1999). A geomagnetic storm can be subdivided into three phases: initial, main, and recovery. The main phase is the most influential part of a geomagnetic storm (Gonzalez et al., 1994;Loewe & Prölss, 1997).
Geomagnetic storms can induce the largest global atmospheric effects (Lastovicka, 1996). The ionosphere responds to geomagnetic storms with signs like depletion or enhancement of electron content. The response might be quite different during the storms, which depends on the location and local time of the geomagnetic storm onset (Danilov & Lastovicka, 2001). The ionosphere can be disturbed by geomagnetic storms from high latitudes (D'Angelo et al., 2018), middle latitudes (Amabayo et al., 2012;Heelis et al., 2009), to low latitudes (Chakraborty et al., 2015;Sreeja et al., 2009). The key parameters for the ionosphere, such as total electron content (TEC), height of F2 (hmF2), and frequency of F2 (foF2) could be affected to various grades (Blagoveshchenskii, 2013;D'ujanga et al., 2013;Ngwira et al., 2012) during storms.
Radio signals can be reflected, refracted, and diffracted when propagating in the ionosphere. During geomagnetic storms the ionospheric activity could be more complicated, which can impact radio propagation dependent applications. It is conventional to apply ionospheric models to correct the background effect of the ionosphere under quiet, nominal conditions. Ionospheric models can be generally divided into the following groups: theoretical models, empirical models, Global Navigation Satellite System (GNSS) data driven models, and broadcast models (Orús et al., 2002). The theoretical models, such as coupled thermosphere-ionosphere model (CTIM) (Fuller-Rowell & Rees, 1980), thermosphere-ionosphere-electrodynamic general circulation model (TIEGCM) (Richmond et al., 1992), thermosphere-ionosphere nested grid (TING) (Wang et al., 1999), and global ionosphere-thermosphere  (Ridley et al., 2006), could provide the physical theoretical prediction of ionospheric environment. The empirical models, such as IRI (Bilitza, 2001;Bilitza et al., 1990) and Nequick model (Di Giovanni & Radicella, 1990;Nava et al., 2008), could define the empirical ionospheric processes. The GNSS data driven models, such as the global ionospheric model (GIM) produced by ionospheric associated analysis centers Energy, Mines and Resources (EMR) (Gao et al., 1994), Jet Propulsion Laboratory (JPL) (Ho et al., 1996), Universitat Politècnica de Catalunya (UPC) (Juan et al., 1997), Center for Orbit Determination in Europe (CODE) (Schaer, 1999), European Space Agency (ESA) (Feltens, 2007), and Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG, CAS) (Li et al., 2015), could provide the numerical prediction of ionospheric TECs. The broadcast model or navigation ionospheric model is the easiest way for the single frequency users to correct the ionospheric delay, owing to its balance between the computation form and model accuracy. Various navigation ionospheric models were developed for individual GNSS systems, such as GPS Klobuchar model (Klobuchar, 1987) and Galileo Nequick-G model (Bidaine & Warnant, 2011). GNSS systems routinely distribute the model coefficients with signals. The end users receive the coefficients and compute the corrections with specific algorithms.
The validation of navigation ionospheric models has been performed with the development of GNSS systems. The overall percentage reduction in RMS error could be approximately 50% for GPS Klobuchar model. But the reduction was generally greater than 60% under adverse ionospheric conditions (Feess & Stephens, 1987). The Beidou Navigation Satellite System (BDS) navigation ionospheric model could contribute higher precision of correction in middle latitudes but lower precision in lower latitudes. The positioning accuracy was improved by 7.8-35.3% comparing with Klobuchar model in northern hemisphere. But the accuracy was degraded dramatically in the southern hemisphere (Wu et al., 2013). Galileo Nequick-G model could mitigate the ionospheric delay by 72.4% in continents and 68.6% in global oceans (Wang et al., 2017). For single frequency positioning, the RMS of horizontal component was around 6 m, and vertical component was about 10 m for 95% percentile (Perez et al., 2018).
Although the previous studies have focused on the validation of various navigation ionospheric models, few papers have studied the performance of BDS navigation ionospheric model during geomagnetic storms, especially during different types of storms. In this study, the effects of different classes of geomagnetic storms on the performance of the BDS navigation ionospheric model are investigated comprehensively. The differences in effects among distinctive storms are studied as well.

Data and Methodology
Geomagnetic storms could be classified based on the disturbance storm time (Dst) index (Loewe & Prölss, 1997). In this study, Dst data were extracted from combined files in the OMNIweb database (https:// omniweb.gsfc.nasa.gov). Geomagnetic storms in solar cycle 24 were analyzed by classifying them into three types, namely, strong, moderate, and weak. The threshold values applied in the classification are shown in Table 1 (see Gonzalez et al., 1994).
Large number of geomagnetic storms have occurred during the chosen period. Moreover, different kinds of storms were intertwined in the time domain. Therefore, it is necessary to design a strategy to distinguish them. The basic strategy for the selection of storms is that the Dst should be as minimum as possible and the duration of each storm should be more than 12 hr. To identify the start epoch of the main phase, a reverse searching algorithm on the Dst time series was designed. The maximum duration for the searching was empirically set to 24 hr. The maximum Dst within this time span was searched, and the epoch of this maximum Dst was identified as the start epoch. To ensure that each storm was independent and not influenced by another storm, a condition was applied that the Dst index for 10 days before and after the main phase day must be greater than the minimum value for each individual class of storms. Eventually, five prominent cases were selected for each class of storms from 2015 to 2018. The main property of a geomagnetic storm is its main phase (Loewe & Prölss, 1997), which contributes largely to the observed effects (Astafyeva et al., 2014). The main phase, the related minimum Dst, and duration of all storms taken into account in this study are shown in Table 2. MJD is the modified Julian date. The suffix 0 to each date refers to the start epoch while 1 represents the end epoch. Duration is the whole period of the main phase.
The basic form of the BDS navigation ionospheric model is similar to that of GPS. The only difference is the method to compute the amplitude and phase term of the model (Wu et al., 2013). The primary formula is  illustrated as follows: wherein I ′ z (t) is the ionospheric vertical time delay on B1 band, t is the local time, A 2 is the amplitude term, and A 4 is the period term, all in seconds. The amplitude and period term can be computed by eight broadcasted coefficients given in the navigation files. Combined with a mapping function (Wu et al., 2013), the vertical time delay can be transferred to the signal path. Hence, the slant delay could be derived from the vertical time delay and the speed of light.
The slant delay may be further converted to the slant total electron content (STEC) along the signal path with B1I frequency by where STEC is the slant TEC in TECu. D Ion is the slant delay in meters. f B1I is the B1I frequency in GHz.
In order to evaluate the performance of the BDS navigation ionospheric model during the main phase of different classes of storms, the real-measured STECs derived from GPS observations were used as reference.
In order to achieve high precision STECs in each signal path, the data processing was performed as follows. The geometry-free combination of dual-frequency (L1/L2) GPS observations was utilized to compute the initial values of STECs for the ionospheric pierce points (IPPs). The phase smoothing code method was applied in this procedure. The instrumental biases including satellite and receiver differential codes biases (DCBs) were subtracted from the initial values accordingly. The DCBs were calculated by a post-processing   method (see Montenbruck et al., 2014). Moreover, to reduce possible multipath and mapping function errors, the elevation mask angle was set to 20 • .
The observations were collected from 18 evenly distributed GPS stations in the Crustal Movement Observation Network of China (CMONOC). The sampling interval for the observations was 30 s. Figure 1 shows the distribution of those stations. The dotted line represents the geomagnetic equator, which was derived from the World Magnetic Model (WMM). The stations are located mostly in the middle and low geomagnetic latitudes. The GPS orbits were computed by the IGS SP3 precise ephemeris. The final global ionospheric model (GIM) from IGS was used to compute the instrumental biases. The coefficients of the navigation ionospheric model were extracted from IGS Navigation files (format in RINEX 2.x and RINEX 3.x).
The STECs computed by the navigation ionospheric model were compared with the corresponding real-measured STECs in the same path. The related statistics were performed for the main phase period in the latitude, local time, and whole region domains, respectively. For the latitude domain, the range of differences involved in the statistics was set to 10-50 • with a step of 2 • . The individual statistics were made for each latitudinal zone. For the local time domain, the whole day was set from 0 to 24 LT with an interval of 2 hr. The statistics were calculated for each time interval. For the whole region domain, all differences were utilized in the statistics. The statistics were implemented for the China region.
The indices such as minimum (MIN), maximum (MAX), BIAS, root mean square error (RMSE), and relative error (REL) were applied in this study. The formulas are illustrated as follows.
wherein <> is the average of the variable, TEC ref ,i is the real-measured STEC, TEC mdl,i is the model STEC, and n is the total number of samples.

Results and Discussions
Prior to presenting and discussing the results, the consistency analysis of GPS real-measured STECs with GIM-derived STECs was performed. Figure 2 presents the histogram of the differences between GPS real-measured and GIM-derived TECs during the main phase period of different classes of storms. MIN and MAX of the differences between real-measured TECs and GIM-derived ones for different classes of storms are shown in the figure as well. As seen in the figure, the differences within eight TECu accounted for more than 95% of the cases. In general, the data spread of differences for strong storms was the largest, and the MAX was also largest. The scattering for moderate and weak storms seemed similar, while the MAX of moderate storms was larger than that of weak storms. The related statistical indices, namely, BIAS and RMSE, are shown in Table 3. From the table, there are no obvious systematic offset between real-measured and GIM-derived TECs for three storm classes. The BIAS for strong storms was the largest, while that for weak storms was the smallest. The RMSE for those three storms were 5.01 TECu, 3.74 TECu, and 2.70 TECu, respectively. Therefore, the real-measured TECs were quite consistent with the GIM-derived ones. However, there were large discrepancies between them as shown in the MIN and MAX indices. It must be said that  the observations for local region (especially China region) were not fully utilized in the ionospheric modeling in the IGS analysis centers (ACs). The mismodeling error for most of the ionospheric models in ACs was another factor. On the other hand, the large discrepancy could be the reflection of GIM accuracy during geomagnetic storms. Ionospheric activity might be more complicated during the storms, making it even harder for the ionospheric model to represent the real TECs. The reason for that might be related to the equatorial ionospheric anomaly (EIA), a phenomenon characterized by the double peaked latitudinal distribution of electron density. The trough lies at the magnetic equator while the crest is at ±15 ∼20 dip latitude. In this region the ionospheric activity is the most complicated. During geomagnetic storms, the ionospheric activity could be enhanced or inhibited (Sreeja et al., 2009). Besides, the indices (BIAS, RMSE, and REL) for the latitudes above 45 • are shown to be a little higher than those for the adjacent latitudes. That could be caused by the different negative or positive storm effect over mid-low latitudes for different cases. The negative ionospheric storm effects are primarily attributed to thermospheric composition changes (Fuller-Rowell et al., 1994). The mechanism of the positive storms remains complicated, which could be collectively triggered by the storm time equatorward thermospheric winds, prompt penetration electric fields (PPEF), disturbance dynamo electric fields (DDEF), traveling atmospheric disturbances (TADs), enhanced meridional wind, or a combination of them (Balan et al., 2010). This could be further studied in the next step. It is noticed that the indices for strong storm on MJD 57098 was the most distinctive. That suggests this storm event had a widespread influence on the China region. Specifically, the minimum of MIN was up to −42 TECu for strong storms, −40 TECu for moderate storms, and −40 TECu for weak storms. The maximum of MAX was nearly 147 TECu for strong storms, 89 TECu for moderate storms, and 44 TECu for weak storms. The range of BIAS was in −12 to 28 TECu for strong storms, −21 to 11 TECu for moderate storms, and −14 to 2 TECu for weak storms. The maximum of RMSE for strong storms was up to 38 TECu, while that was nearly 25 TECu for moderate storms and 16 TECu for weak storms. For REL, the maxima were 140%, 179%, and 109% for strong, moderate, and weak storms, respectively. The mean and median of RMSE and REL for all latitude zones during each type of storm are illustrated in Table 4. The mean and median of RMSE for strong storms  were 11.19 and 7.48 TECu, while those for moderate storms were 7.78 and 6.72 TECu, and for weak storms were 6.34 and 5.85 TECu. The mean and median of REL were 35.48% and 30.46% for strong storms, while those for moderate storms were 37.65% and 30.65%, and for weak storms were 33.39% and 28.84%. Overall, the performance of the navigation ionospheric model during the main phase period of strong storms was the most unstable, followed by moderate and weak ones. In addition, the model accuracy was not comparable during the individual storms. That suggests the same class of storms may not have a consistent effect on the accuracy of navigation ionospheric model. The same feature could also be found in the other two aspects of the statistics (local time and the whole region domain).
The statistics for the performance of the BDS navigation ionospheric model in the local time domain are demonstrated in Figure 4. Generally, the statistical indices were characterized to some extent by the diurnal changes. The changes in the indices were strongest around 14 LT. That suggests the accuracy of the model worsens when the ionospheric activity is more pronounced during the main phase of storms. From the individual indices in the figure, the minimum of MIN for strong storms was up to −42 TECu, while that was −47 TECu and −49 TECu for moderate and weak storms, respectively. The maxima of MAX were approximately 147, 89, and 44 TECu for strong, moderate, and weak storms, respectively. The range of BIAS for strong storms was −5 to 34 TECu, while for moderate ones it was −7 to 15 TECu and −12 to 8 TECu for weak ones. The maximum of RMSE was up to 38 TECu for strong storms, 15 TECu for moderate ones, and 12 TECu for weak ones. The maximum of REL was up to 83%, 110%, and 119% for strong, moderate, and weak storms individually. The mean and median of all RMSEs and RELs for different types of storms are shown in Table 5. The mean and median of RMSE for strong storms were 9.33 and 6.33 TECu while those for moderate storms were 6.34 and 5.70 TECu and for weak storms were 5.37 and 5.12 TECu, respectively. For REL, the mean and median were 34.03% and 30.87% for strong storms, 34.59% and 30.92% for moderate ones, and 34.24% and 27.83% for weak ones. Therefore, the accuracy of the model suffered the largest influence during strong storms, followed by moderate and weak ones. It should be noticed that the indices, especially REL at nighttime, varied much more than those at adjacent epochs. This could be attributed to the nighttime constant assumption of the navigation ionospheric model (see constant offset term 5 ns in equation (1)). Ionospheric activity might become more complicated during geomagnetic storms; therefore, it is not reasonable to set the nighttime term as constant over this period.
The statistics were also performed for the whole China region in this study. The related results for different types of storms are illustrated in Tables 6-8   The BIAS was in range of −2.44 to 1.29 TECu, respectively. The RMSE was up to 6.19 TECu, and REL reached 34.48%. The mean and median of RMSE were 5.52 and 5.49 TECu, respectively.

Conclusions
In this study, the performance of the BDS navigation ionospheric model was analyzed comprehensively during the main phase of different classes of geomagnetic storms in the China region. From the statistical results, the performance of the model was affected to different degrees during the storms. Some conclusions can be reached specifically. First, the influence on the accuracy of the model during strong storms is greatest, followed by moderate and weak storms. Second, the impact on the accuracy of the model is clearly characterized by the latitude and local time. Third, the accuracy of the model is not always comparable even for the same class of storms, thus suggesting that the same class of storm does not have a consistent impact on the accuracy of the model.
This study could benefit the prediction of the navigation ionospheric model performance during geomagnetic storms. Especially, it could contribute to the improvement of the model in latitudinal and nighttime aspects during the storm time. Moreover, the impact of geomagnetic storms could be similar on other navigation systems such as GPS and Galileo. Thus, these findings could provide a reference for future studies involving those systems. Nevertheless, the study period was in the downward phase of the solar cycle 24, when the solar activity was not strong, therefore the related effects on the accuracy of the navigation ionospheric model might not be quite noticeable. With the forthcoming solar cycle 25, the study could be performed more comprehensively.